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cosin/mbsMulti-Body Systems & Vehicle Dynamics Simulation

Documentation and User’s Guide

Contents

1 General Remarks 1

1.1 Aims and Scope ofcosin/mbs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Modeling Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.3 Data File Formats and Notation Used in Data Tables Below . . . . . . . . . . . . . . . . . . . . 2

2 Simulation Workbench 3

2.1 Selection of Simulation and Model Data Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Simulation Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.1 Simulation Data forcosin/mbs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.2 External Input Signals (Sources) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Model Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Program Execution and Analysis of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3 Modeling and Model Data Files 14

3.1 Model Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1.1 Group Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1.2 Element Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Element Catalogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4 Interfacing to Models for Road and Wind Velocity 22

4.1 cosin/road . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2 cosin/wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2.1 Typecalm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2.2 Typeconstant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.2.3 Typefile_v_of_t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.2.4 Typefile_v_of_x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.2.5 Typetable_v_of_t_and_x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.2.6 Typetable_v_of_x_and_y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.2.7 Typefunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

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5 ECU Interfacing 24

5.1 Standard ABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.2 Advanced ABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.3 ESP (Electronic Stability Program) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.4 Automatic Four-Wheel Drive Select . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

5.5 ATTS (Automatic Torque Transfer System) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.6 LSD (Limited Slip Differential) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5.7 Active LSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5.8 CLD (Controlled Partially Locking Differentials) . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.9 Four-Wheel Steering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.10 EPS (Electronic Power Steering) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.11 Advanced EPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.12 General Force Actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

6 Interfacing to User-Supplied Driver-Models 33

7 Command Line Invocation 35

8 Coupling to Matlab/Simulink 37

9 Element Catalogue 40

9.1 AC General Actuator with User-Written Control Code . . . . . . . . . . . . . . . . . . . . . . . . 40

9.2 AD Aerodynamic Forces and Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

9.3 AS Acceleration Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

9.4 BE General Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

9.5 BJ Ball Joint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

9.6 BF Ball Joint Friction Subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

9.6.1 Simple Ball Joint Friction Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

9.6.2 Detailed Ball Joint Friction Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

9.6.3 cosin/cb Stand-Alone Simulation Workbench . . . . . . . . . . . . . . . . . . . . . . . . 59

9.7 BO Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

9.8 BR Brake System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

9.9 CJ Cardan (Hooke) Joint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

9.10 CS Conceptual Suspension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

9.11 DI Distance Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

9.12 DS Damper Strut Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

9.13 DT Drive Torques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

9.14 EF External Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

9.15 ET External Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

9.16 FB Flexible Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

9.17 HM Hydro-Mount Subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

9.18 IFInternal Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

9.19 KC Kinematics&Compliance Output Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

9.20 MH Measuring Hub . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

9.21 PS Propulsion System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

9.22 PT Pushrod-Activated Torsion Bar Springs and Dampers . . . . . . . . . . . . . . . . . . . . . . 90

9.23 RB Rigid Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

9.24 RJ Revolute Joint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

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9.25 RO Rod and Straight Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

9.26 SC Steering Assembly for Conceptual Suspension . . . . . . . . . . . . . . . . . . . . . . . . . . 103

9.27 SD General Spring/Damper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

9.28 SJ Spherical-Spherical Joint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

9.29 SR Steering Assembly, Rack-and-Pinion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

9.30 ST Semi-Automatic Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

9.31 TI Tire Model Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

9.32 TJ Translational Joint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

9.33 TS Torsion-Bar Stabilizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

9.34 WL Watt Linkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

Index 132

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1 General Remarks

This documentation describes the multi-body and vehicle dynamics simulation packagecosin/mbs. All product or

brand names in mentioned here are trademarks or registered trademarks of their respective holders.

1.1 Aims and Scope ofcosin/mbs

cosin/mbs is designed to be a fast and easy-to-use simulation tool for general multi-body mechanisms, especially

suspensions and vehicle models for both ride comfort and vehicle handling maneuvers. It is equipped with a general

road and tire interface, allowing the combination with several existing tire models likeFTire,FETire,HTire(Magic

Formula in several variants), and others. These tire models can be made available upon request.

By using the comfortable data file formatcosin/io,cosin/mbs is easily parameterized, and combined with other

computation software, like Matlab or Excel, to provide these parameters.

cosin/mbs comes with several sample data files, defining the most important suspension types both for front and

rear axles. If you are licensed to, these will include

• five-link suspensions

• double wishbone suspensions

• several types of McPherson suspensions

• race-car suspensions

• customer-specific axles

• a ‘generic suspension model’ using a general nonlinear force element, situated between wheel and car-body

• the ‘conceptual suspension’ approach, importing files (‘.scf-files’) that describe the full elasto-kinematic

properties of a given suspension, from other vehicle dynamics simulation software.

Likewise,cosin/mbs also enables the user to definecompletely new suspension types in terms of a list ofcos-

in/mbs elements.

cosin/mbs is available for several Linux dialects, as well as for Mac OS X and Windows (XP, Vista, 7, 8; 32 and

64 bit). Even with a detailed rendered 3D on-line animation, it runs considerably faster than real-time.

1.2 Modeling Approach

cosin/mbs is a specializedmulti-body system software, especially focussing on those multi-body elements needed

in vehicle suspension models, including

• flexible bodies

• specialized ‘elasto-kinematic’ elements

• steering assembly models

• drive-train subsystems of different complexity

• brake system element

• aerodynamics

• various road and tire model interfaces.

Document Revision:2018-2-r173421

cosin/mbs uses a tailored implicit integration routine, where only stiff subsystems are integrated implicitly. Even

though implemented in lean and efficient, ‘number-crunching’ ANSI Fortran 90, it consequently observes an

object-oriented approach.

cosin/mbs provides a mechanism to get allpre-load values of all bearings, springs, and so on, in reference position.

To this end,cosin/mbs puts out all pre-load values at the end of a simulation into an output file, and appends the

original input data file. By this, a new, compatible input file is created that carries not only all original vehicle

data, but also all pre-load values to be used in subsequent simulations.

This documentation comprises the following chapters:

• chapter9 introduces and documents the working with thecosin/mbs simulation environment

• chapter3 gives a detailed documentation ofcosin/mbs models and elements

• chapter4 describes the program interfaces to user-provided ECU software

• chapter5 describes the program interfaces to user-provided ECU software

• chapter6 documents the command-line invocation ofcosin/mbs

• chapter7 gives details about usingcosin/mbs within Matlab/Simulink models.

1.3 Data File Formats and Notation Used in Data Tables Below

All data files ofcosin/mbs (apart from imported data files like .csf-files, .tdx-files, and .fem-files) use thecosin/io

syntax that is described in the separate documentationcosin/io User’s Guide. Additional relevant documentation

sheets arecosin/ip User’s Guide (description of several plotting utilities, not yet available),cosin/road User’s Guide

(description of road models), andFTire User’s Guide (documentation of thecosin/mbs compatible tire model

FTire).

In the following chapters, several tables describing input data are included. Most of these tables comprise 4

columns: thedata names, thephysical units, thetypes, and a brief description of theirmeaning. Thereby, the

following data types are distinguished:


i a single integer variablein a vector of integer variables withncomponentsf a single floating point variablefn a vector of floating point variables withn componentssig the name of acosin/ss signal, to be used as input or output signal of an elementst a text string of arbitrary length

Remark: a text string must not contain any blank spaces between the first and the lastnon-blank character

stn a text string of exact lengthnm a marker. Markers either can be defined directly by three numbers (that is, by f3 type data), or

by referring to an entry in the$markers data-block of the .cm-file, specifying the name of therespective marker in this block (cf. chapter4)

sd a spline data-block name. Spline data to be used are to be specified in a spline data- blockwith this name. All splines used incosin/mbs are 2D-splines with natural boundary conditions.That means, they approximate functionsf(x) wheref ′′(x) = 0 for the smallest andlargestx-value that appears in the data table

mo a subsystem or element data-block name. This data type specifies the data-block name of asubsystem or an element of appropriate type

t1 a 1D look-up tablet2 a 2D look-up tablefi a file name, observing the respective operating system’s naming conventionsflag boolean value only, which is true, if the data name appears in the data-block

Table 1: Data types

Mandatory data are marked with (m). If not stated otherwise, all numerical data that are neither mandatory nor

explicitly specified get the default value(s) 0.

2 Simulation Workbench

A Tcl/Tk-based graphical user interface (GUI) is part of thecosin/mbs package. This ‘simulation workbench’

allows a convenient operation ofcosin/mbs and other relatedcosin tools. Appearance and functionality of the GUI

are nearly independent on the operating system. The workbench, as it looks like in all Windows-type operating

systems, is shown in figure1.

Besides using this GUI,cosin/mbs can also be launched by a simple command line invocation.

Figure 1: cosin/mbs workbench

The workbench is divided into 5 or 6 main columns:

• the leftmost column contains severalyellow control buttons for starting/stopping/resuming simulation

runs, plotting the results, etc., as well as somecheck-boxes and‘radio buttons’ that influence program

execution

• the second column lists theparameters that are found in the active simulation and model data files; all

parameters can be changed by entering a new value or expression in the respective input field, without


editing the simulation file

• the third and fourth columns show the available simulation and model data files in a respectivefile-box

(simulation and model data files are read by the simulation program after starting the simulation)

• depending on the kind of installation, an optional fifth column shows the available input files for the 3rd-party

modelIPG-Driver, which describes human vehicle control activities

• the file-box of the last column lists output files of actual and previous simulation runs

The upperblue buttons starting with column 3 are calledfunction buttons. Depending on the mouse button

used when clicking, they allow for different ways to process the displayed (‘active’) file. Below, these actions are

described in detail.

A typical simulation run is performed as follows:

• select simulation file and model data file from the respective file-box

• edit and adapt simulation and model data

• click appropriate program execution control buttons

• launch and control program execution, using the GUI’s ‘VCR’ buttons and/or functions provided by an

interactive animation window that appears when simulation starts

• analyze results, for example by using the interactive plot softwarecosin/ip

In the following, these steps are described in more detail.

2.1 Selection of Simulation and Model Data Files

Whencosin/mbs is called for the first time, the file-boxes in columns 3 and 4 of the workbench show several sample

files (cf. figure1). The number and type of these sample files depend on thecosin/mbs options available in your

installation. A specific file isselected by left-clicking the file-name. By doing so, the name of the file will appear

in the blue function button. If required, the file may then beedited by right-clicking the blue function button.

By default, the simulation and model data files are searched for in the directoriessimul andparam, respectively.

These folders themselves are located in the foldercar, a sub-folder of that directory where you installed yourcosin

products. If you keep your data or simulation files in different folders, specify these folders in thepath entry of

column 3 or 4, respectively. You can use every kind of path definition that is valid in the operating system you

are using, for example

• simul\steady_state

• ..\temp\data

• c:\own files\cosin

in Windows-type operating systems, and

• simul/steady_state

• ../temp/data

• $home/own_files/cosin

in Unix-type operating systems.

The sample files shipped withcosin/mbs may serve as a reference while creating new user specified files. In order

to leave the original files unchanged, it is recommended to generate a copy of the reference file first, which covers


the type of maneuver or vehicle needed. For example, to create a vehicle model with a double wishbone front

and rear suspension forcosin/mbs, choose filedw_dw.cm. The procedure tocopy that file is executed in two steps:

first,left-click the file to be copied in the list-box, then hit thespace-bar. Now, a filetest_dw_dw.cm will appear

in the list box. The same procedure holds for creating a user defined simulation file.

Files aredeleted by left-clicking the file name in the list-box, then hitting the‘Del’ key.

2.2 Simulation Data

To adapt the simulation data like simulation time span, number of output steps, kind of on-line animation,

manoeuver to be driven, road profile, etc., to the problem at hand, the corresponding simulation data file (sim-file

for short) is to be edited. Typically, that file consists of the data-blocks

• $simulation

• $sources

• $road_type

Above that, as in allcosin data files, an optional data-block

• $parameters

may be used to parameterize the simulation file, cf.cosin/io documentation. All parameters in this block are

automatically displayed in the second column of the user interface, for convenient access.

2.2.1 Simulation Data forcosin/mbs

Ifcosin/mbs or a user-modified solver is used, the data-block$simulation is scanned for the following data:

Element data

Table 2: Element data

simulation s f3 (m) simulation starting time, time step, final

time

plot_output s f3 starting time, time step and final time of

plot output. If not specified, plot output is

suppressed

animation s f3 starting time, time step and final time of

animation output. If not specified,

animation output is suppressed

initial_position m f3 initial position of all bodies’

points-of-reference in global coordinates.

Default: 3*0.0

initial_angular_pos deg f3 initial angular orientation of all bodies.

Default: 3*0.0

initial_velocity rads f3 initial translational velocities of all bodies’

points-of-reference in global coordinates.

Default: 3*0.0

initial_ang_velocity ms

f3 initial angular velocities of all bodies in

body-fixed coordinates.

Default: 3*0.0


initial_gear - i initial gear to be chosen in propulsion

system and semi-automatic transmission

Default: 0 (neutral)

friction - i switch for activating all friction values

incosin/mbs elements.

0 = no

1 = yes

Default: 1

play - i switch for activating all play values

incosin/mbs elements.

0 = no

1 = yes

Default: 1

KC_analysis_type - i switch to select between normal simulation

mode and certain specialized modes for

K&C (kinematics and compliance) analysis:

0: standard mode (default)

1: vertical wheel travel kinematics, friction

and play disregarded

2: steering kinematics, friction and play

disregarded

3: vertical wheel travel kinematics including

friction and play

4: steering kinematics including friction and

play

11: wheel compliance by external forces

and/or moments, friction and play

disregarded

12: wheel compliance by external forces

and/or moments, including friction and play

road_file - st file name of road data file, containing

data-block$road_type.

Default: simulation data file name (this file)

udm_file - st name of a file containing data for a

user-supplied driver-model. The format of

this file is defined by the driver model, inde-

pendently oncosin/mbs. The user-supplied

driver-model will be used to control the

vehicle operation if and only if this data file

is specified, cf. chapter6.

Default: not specified

plot_output_start_time s f time shift for plot output. For example, a

value of 1s shifts the time scale, beginning

at t = 1s.


plotfile_format - st plot-file format. At present, the following

formats are available:

• standard

• matlab

• excel

• gnuplot

• matrix

animation_zoom mm f animation zoom. If negative, animation is

paused at the beginning and must be

started by pressing the return or enter key

while the animation window is activated.

Paused mode may be convenient for

choosing an appropriate viewing angle etc.

Default: 100

image_shift - f2 relativex/y-shift of the focused point in the

image plane of the animation window.

Default: 0,0

on_line_camera_control - i switch to make camera position and

orientation user-controllable during a

running simulation. If set to 1, azimuth

angle, altitude angle, camera-to-object

distance, and viewing angle will be

controllable by sliders

camera_position m f3 camera position in the body-fixed

coordinate system of the body that carries

the camera

camera_angles deg f3 camera viewing direction angles (with ISO

8855 / DIN 70000 definition) relative to the

orientation of the body that carries the

camera

time_const_camera_shift s f variable to define ’smoothness’ of camera

position control with respect to motion of

the camera carrier.

Camera instantaneously follows carrier, if

time constant is less or equal 1010.

Camera doesn’t follow carrier at all, if time

constant is greater or equal 99


time_const_camera_rot s f variable to define ‘smoothness’ of camera

viewing direction control with respect to

orientation of the camera carrier.

Viewing direction instantaneously follows

carrier, if time constant is less or equal 1010.

Viewing direction doesn’t follow carrier at

all, if time constant is greater or equal 99

sun_position m f3 position of the light source that illuminates

the scene

visibility m f visibility. Assumed to be ‘infinite’, if

absolute value is greater than 10000. If the

value is negative,cosin/mbs will use

orthogonal projection instead of central

perspective as starting value. During a

running simulation, the kind of projection

can be toggled by hitting the F9 key

repeatedly

show_tire_forces - i switch that indicates whether tire forces

should be shown at the beginning of the

simulation or not. When simulation is

running, you can toggle the display of tire

forces by pressing the ‘f’ key while the

animation window is active

tire_forces_scaling_factor mmkN

f scaling factor for tire forces in animation

scene: length of arrow per force unit

tire_forces_arrow_sizes mm f3 geometrical properties of the tire forces

arrows: diameter of arrowshaftmaximum

diameter of arrowheadlength of arrowhead

(this properties will only be used if

animation level is greater 1)

show_road_below_tires - f type of road to be displayed below tires:

0 none

1 grid, centered in contact point

2 grid, center fixed

3 rendered, centered in contact point

4 rendered, center fixed

animation_attribute_file - st file name of animation models attribute file

Default: cosingl.ini


scope_i - st scope definition that will appear in the

animation window. The string will describe

one scope by six semicolon-separated

substrings:

• a validcosin/ip plot signal name for

the x-axis signal (time if void)

• a minimum x-axis value (autoscaled if

void)

• a maximum x-axis value (autoscaled if

void)

• a validcosin/ip plot signal name for

the y-axis signal

• a minimum y-axis value (autoscaled if

void)

• a maximum y-axis value (autoscaled if

void)

If only a substring of a signal name is

entered, the first signal which contains this

substring will be used.


log_level - i level for output log text during simulation

Default: 2

engine_wav_file - st prefix of a set of 3 audio files for engine

sound. The full names will be build by

appending 1.wav, 2.wav, and 3.wav


first_rpm_engine_sound f rpm engine speed of first engine sound file

Default: 1680rpm

second_rpm_engine_sound f rpm engine speed of second engine sound file

Default: 2560rpm

third_rpm_engine_sound f rpm engine speed of third engine sound file

Default: 4160rpm

car_body_wav_file - st audio file for speed-dependent wind noise of

car-body


tire_wav_file - st audio file for slip- and load-dependent tire

noise Default: not specified

min_audible_slip_angle f deg minimum side-slip angle that will lead to

audible tire noise

Default: 3deg

tire_squeal_max_gain f - factor to reduce maximum tire noise

Default: 1 (no rediction)


tire_squeal_ref_wheel

_load

f kN wheel load at which tire noise at 10deg slip

angle will reach its maximum

Default: 10kN

tire_squeal_pitch f - factor to increase or decrease tire noise

frequencies. Admissible range is between

0.5 (noise spectrum shifted by one octave

towards lower frequencies) and 2.0 (tire

noise spectrum is shifted one octave

towards higher frequencies)

Default: 1 (no shift)

outall1 - st first 2-character element type or element

name for which the plot level is to be set to

’all’ no matter what is defined in the model

file. The string isnot case-sensitive


outall2 - st second 2-character element type or full

element name for which the plot level is to

be set to ’all’


outall3 - st third 2-character element type or full

element name for which the plot level is to

be set to ’all’


interpolation_mode_2d - i interpolation mode used with tables of two

independent variables

1: bilinear

2: bicubic

Default: 2

extrapolation_mode - i extrapolation mode used with tables of one

or two independent variables

0: no extrapolation

1: smoothed, nearly constant

2: linear, using left- or rightmost interval

slopes

numerical_constants - f4 system inherent numerical constants. Please

do not alter; only for testing purposes

2.2.2 External Input Signals (Sources)

To define external input signals, the ‘Sources&Sinks’ functionality ofcosin/ss is used. With these input signals,

acosin/mbs vehicle model can be controlled similar to a real car. To calculate the input signals,cosin/mbs looks

for the data-block$sources in the simulation data file. All available external input signals for that data-block are

specified in the element definitions of the model data-block, see chapter4.


2.2.3 Road Profiles, Obstacles, and Wind Velocity

To specify road and wind excitation,cosin/mbs uses the packagescosin/road andcosin/wind. These packages

read the data-blocks$road_type and$wind (either in the simulation data file or, ifroad_file orwind_file,

resp. is assigned a value, in that file). Road profile description with data-block$road_type is described in

the separatecosin/road documentation; whereas wind velocity specification with data-block$wind is presented in

chapter5 below.

2.3 Model Data

To fit the model to the problem at hand, edit the corresponding model data file. The meaning and contents of

model data files are subject of chapter4.

Effects of changes in the geometrical model data can be directly observed and validated by clicking the blue

function button of column 3 with theleft mouse button. Then, the programcosin/show is launched, which

displays the model in design position. Similar to the on-line animation when a simulation is running,cosin/show

can be interactively controlled through zooming in and out, shifting, rotating, and hard-copying. For detailed

information, press theF1-button while the graphics window is active.cosin/show is left by hitting the‘Esc’ key, or

by closing the window.

Most models use 1D and 2Dlook-up tables andspline data of different interpolation and extrapolation modes. For

validation purposes asmart browser tool has been developed, which provides a graphical interactive representation

of these data. In order to launch the browser,right-click the blue function button in column 3. The browser

opens with the graphical user interface shown in figure2.

Figure 2: cosin/show workbench

With launching the browser, the active model data file is scanned for look-up table and spline data-blocks. A list

of all corresponding block names is then shown in the left file-box of the browser. The file selection is triggered

the same way as for the model and simulation data files. After pressing the function button, the corresponding

1D or 2D function characteristic is shown (fig.3).


Figure 3: 1D and 2D spline browser

For 1D data, the browser is interactively controlled by the following function keys:

0 show spline1 1 show first derivative of spline2 show second derivative of spline+ increase the interval of independent variables- decrease the interval of independent variablesm toggle extrapolation mode (constant or linear)e leave graphics window

Table 3: 1D spline browser function keys

2D data allow for different function keys:

0 show splinex show first partial x-derivative of spliney show first partial y-derivative of splines swap independent variable (x or y)+ increase the interval of independent variables- decrease the interval of independent variablesm toggle extrapolation mode (constant, smoothed constant, or linear)e leave graphics window

Table 4: 2D spline browser function keys

As for all applications that usecosin/pgraphics, clicking and holding the middle mouse button displays the mouse

coordinates in application units, that is the values of the independent and dependent variables.

Beside look-up table and spline plotting, the browser also displaysamplitude-frequency plots for thecosin/mbs

elements ‘1D friction’ and ‘hydro-mount’ (see chapter4). For that purpose, a frequency sweep ranging from 1 to

30Hz is performed. The required amplitude of excitation is interactively provided by the user. In order to change

the default value of 1.0mm, the mouse pointer has to be located within the entry. The calculation is started

by left-clicking the corresponding function button in column 2 or 3. Please note: the list-box is empty, if the

activecosin/mbs model does not contain elements of corresponding type. To leave the graphics window, type ‘e’.

It is recommended to always quit the browser after usage by clicking theyellow quit button, because the element

lists are only refreshed when starting the browser.


2.4 Program Execution and Analysis of Results

The first column of thecosin/mbs workbench shows several yellow control buttons, as well as some radio buttons

and check boxes, cf. figure4, used to control program execution.

Figure 4: cosin/mbs workbench control buttons

The button launches a dynamic analysis simulation.

Before entering the time loop, the respective solver opens and reads thecosin/mbs data file, as well as the

simulation file that appears in the blue function buttons of column 3 and 4.

Simulation can be:

paused and resumed


run in single steps

restarted (if not yet finished)

terminated

With the radio buttonsgroup fast,std., andaccurate, the simulation step size defined in data-block$simulation

can be modified:

• fast increases step size by 50%

• std. takes time step exactly as specified in .sim-file

• accurate decreases step size by the same amount

Some further solver parameters can be modified with additional buttons:

• animate toggles interactive on-line animation

• white bg will set background color of animation window to ’white’ instead of gray

• save avi automatically grabs every single frame of the on-line animation and merges them into an .avi-file.

The user will be queried for the name of this file. On-line animation is automatically activated, even if

‘animate’ is not checked

• sound toggles output of engine sound as well as tire and wind noise (provided an OpenAL-compatible sound

card is installed)

• create plot file toggles storage of plot-data. Please note: a plot file must have been created before

clicking the plot-button;

• start with last saved state organizes next simulation to starting with the model in the operating

condition at the time the preceding simulation was terminated. To make this mechanism work properly, the

‘save state’ button has to be clicked after every simulation run, the final states of which are to be taken

as initial conditions for the next run.

For analyzing the results, the plotting toolcosin/ip is provided, which interactively displays the output variables

of the last simulation run. It is launched via the ‘plot’ button. If not only the last output file is to be opened,

but also other ‘reference’ plot-files, check the ‘with reference’ box. In that case, a list will appear before

startingcosin/ip, where additional plot-files can be entered.

The corresponding plot files can be stored by the user, in order to compare different simulation experiments or

model data etc. After left-clicking the button ‘save plot file as..’, a file selection window opens, requesting

the user to specify a file name. Then, the plot file of the preceding simulation is copied to the specified file. The

list box in column 4 shows a list of all previously stored files. In order to opencosin/ip with one of these files

directly, left-click the respective file name first, then left-click the blue function button in column 4.

All available PDF-basedcosin/products documentation chapters can be browsed by left-clicking ’?’, and finally-

cosin/mbs workbench is closed by left-clicking ‘quit’.

3 Modeling and Model Data Files

Acosin/mbs model is described by acosin/mbs model file (‘.cm-file’). Syntactically, a .cm-file is built according

to the syntax rules ofcosin/io (cf. separate documentation). Normally, it consists of

• aparameter definition block


• amodel definition block, with data sub-blocks that are either

– group definition blocks or

– element definiton blocks

• amarker definition block

• several element data-blocks

Theparameter block is an optional means to parameterize allcosin/io input files, and not a special feature of

only .cm-files. It is described in thecosin/io documentation.

Themodel definition block$modelcontains a list of allcosin/mbs elements to be included to the model, together

with handles of those elements they are linked to. In addition, this data-block carries information specifying where

to find element data, what external input and output signals are provided, and so on. Elements that ‘belong

together’, like all elements that make up a vehicle‘s front suspension, can be grouped together. Having done so,

they can easily be given common properties like plotting or animation model level, coordinate systems, etc. These

groups are also defined in $model.

The optionalmarker definition block$marker contains geometrical data in terms of marker names, together

with their coordinates. These marker names may be used in subsequentcosin/mbs element data-blocks, instead of

numerical values. Marker names may be arbitrarily assigned by the user, to customize acosin/mbs data file. One

advantage of the use of markers is the ability to concentrate the complete geometry information of a mechanical

model in one single data-block.

Element data-blocks contain all data of the elements included in the$model data-block. Normally, to every

such element there belongs at most one element data-block. The contents of these data-blocks are described

below, in the respective element chapters.

The following is part of acosin/mbs model file, and illustrates the typical structure of .cm-files.

• Parameter definition block

1 $parameters !*****************************************************************

WB 2400 ! wheel base []

3 TWF 1500 ! front track width []

RSF 3000 ! front wheels static tire radius []

5 ...

• Group definition sub-blocks

1 $model ! **********************************************************************

GR:vehicle pl=1; al=5; dz=RSF

3 GR:engine pl=1; al=5; dz=RSF

GR:steering pl=1; al=5; dz=RSF

5 GR:drive pl=1; al=5; dz=RSF

GR:brakes pl=1; al=5; dz=RSF

7 GR:front pl=1; al=5; dz=RSF

GR:rear pl=1; al=5; dx=-WB; dz=RSF

9 ...

• Element definition sub-blocks


1 RB:vehicle pl=2; camera ; o1=C1.v; o6=C1.a_lat;

o8=C1.roll; o9=C1.pitch ; o10=C1.yaw ;

3 o11=C1.roll -vel; o12 =C1.pitch -vel;

o13=C1.yaw -vel ; o18=C1.track; o19=C1.curv; g=vehicle

5 AD: aerodynamics 1= vehicle ; g=vehicle

7 DT: drive_torque l1=FL.tire; l2=FR.tire; l3=RL.tire;

l4=RR.tire; i1=C1.gas_pedal ; g=drive

9 BR:brakes l1=FL.tire; l2=FR.tire; l3=RL.tire;

l4=RR.tire; i1=C1.brake_pedal ; g=brakes

11 RB:engine subt=vehicle ; g=engine

BE:eng_m1 l1=vehicle ; l2=engine ; stiff; g=engine

13 BE:eng_m2 l1=vehicle ; l2=engine ; stiff; g=engine

BE:eng_m3 l1=vehicle ; l2=engine ; stiff; g=engine

15

RB:FL.wheel subt=vehicle ; g=front

17 RB:FR.wheel subt=vehicle ; mdb =FL.wheel ; g=front

RB:RL.wheel subt=vehicle ; g=rear

19 RB:RR.wheel subt=vehicle ; mdb =RL.wheel ; g=rear

...

• Marker definition block

$markers !********************************************************************

2 vehicle_cg -0.5* WB 0.00 CGH -RSF ! []

FL.wheel_center 0.00 0.5* TWR 0.00 ! []

4 RL.wheel_center 0.00 0.5* TWR 0.00 ! []

6 engine_cg -150.00 0.00 50.00 ! []

engine_mount1 20.00 0.00 50.00 ! []

8 engine_mount2 -320.00 -200.00 50.00 ! []

engine_mount3 -320.00 200.00 50.00 ! []

10 ...

• Element data-block #1

$vehicle !RB *****************************************************************

2 mass 1200 ! [kg]

inertia_tensor 500 3000 3000 0 0 0 ! [^2]

4 cg_in_ref_position vehicle_cg ! []

6 animation_model models /car -body.str !

• Element data-block #2

$engine !RB ******************************************************************

2 mass 120 ! [kg]

inertia_tensor 10 10 10 0 0 0 ! [^2]

4 cg_in_ref_position engine_cg ! []

6 animation_model brick ; width 300 !

height 300; depth 400 !

• More element data-blocks

...


3.1 Model Definition

The model definition data-block$model of acosin/mbs model file consists of second-level, ‘type-equipped’ data-

blocks. In contrast to most othercosin/io files, the names of these second-level data-blocks do not start with a

double$-sign, but with a 2-lettertype acronym. This type acronym, likeRB for ‘rigid body’, is separated from

the element name by a colon, for exampleRB:car_body. All the rest of such a type-equipped data-block fully

observes all syntax rules ofcosin/io data-blocks, giving users a maximum degree of flexibility in making a .cm-file

better readable.

Every typed second-level data-block in$model either defines a newgroup or asinglecosin/mbselement. There is

no need to sort them in any way. This is done automatically bycosin/mbs during pre-processing. For example, it

is allowed to refer to other elements inside an element definition, even if these other elements are defined only

later.

Besides the second-level data-blocks defining groups and elements, data-block$model may contain several default

values, which are described in the following table:

vehicle_type - i of vehicle; used to select ranges in driving simulator displays, etc.Possible values:0 (passenger car)1 (truck)2 (race car).

pl - i plot level for all groups and elements. The actual plot level defines the number ofplot signals to be saved during simulation.Possible values:0 (no output),1 (only most important plot signals)2 (maximum number of plot signals).Default value 1

al - i animation model level for all groups and elements. The actual animation modellevel defines the degree of detailization of the elements’ geometrical animationmodel.Possible values:0 (no animation model) .. 9 (most detailed animation model).Default value 4

dx mm f x-direction shift of the design position of all groups and elements.Default: 0.0

dy mm f y-direction shift of the design position of all groups and elements.Default: 0.0

dz mm f z-direction shift of the design position of all groups and elements.Default: 0.0

roll deg f rotation angle aboutx-axis of the design position of all groups and elements.Default: 0.0

pitch deg f rotation angle abouty-axis of the design position of all groups and elements.Default: 0.0

yaw deg f rotation angle aboutz-axis of the design position of all groups and elements.Default: 0.0

Table 5: Additional default value definitions in data-block $model

3.1.1 Group Definition

Agroup definition is a collection of certain attributes, equipped with a group name. The attributes are used

as default values for elements that belong to the group. The membership of an element to a certain group is

established in the respective element definition, not in the group definition itself.


For any individual element, every group attribute can be overridden by a respective entry in the element definition

block. All data definitions in the group definition block are optional. Their respective default values are listed in

the table below.

The type of a group definition block isGR. The data-block name of a group definition block, at the same time,

serves as group name. A typical group definition might look as follows:

GR:steering; pl=1; al=5; dz=300

This block introduces a new group namedsteering. The block sets the default plotting and animation levels

(pl andal, resp.) to 1 or 5, respectively, for all elements belonging to the group. Furthermore, a certain default

vertical shift (dz) is set to 300mm.

Becausesteering is a block name, there is no need to separate this string by a semicolon from the first block

data entry (pl=1). On the other hand, a semicolon was allowed there and wouldn’t make any difference. The

same holds for a semicolon at the end of the line:

GR:steering; pl=1; al=5; dz=300;

is equivalent to the group definition above. Likewise, as described incosin/io documentation, the data entries

could have been entered in separate lines, like

GR:steering

pl = 1

al = 5

dz = 300

or

GR:steering

dz 300 ! vertical shift = front wheel static tire radius

pl 1; al 5 ! plotting and animation level

Here is the complete syntax of a group definition block:

1 GR: name p l=va lue_p l ; a l=value_an ; f=da t a_ f i l e ;

dx=value_dx ; dy=value_dy ; dz=value_dz


name - s (m) group name (and data-block name at the same time). The group name is used torefer to that group in element definitions

pl - i default plot level for all group elements. The actual plot level defines the numberof plot signals to be saved during simulation.Possible values:0 (no output)1 (only most important plot signals)2 (maximum number of plot signals)

al - i default animation model level for all group elements. The actual animation modellevel defines the degree of detailization of the elements’ geometrical animationmodel.Possible values:0 (no animation model) .., 9 (most detailed animation model)

f - s default file name, where the group elements’ data-blocks are looked for.Default value: name of actual .cm-file

dx mm f defaultx-direction shift of the design position of all group elementsdy mm f defaulty-direction shift of the design position of all group elementsdz mm f defaultz-direction shift of the design position of all group elementsroll deg f default rotation angle aboutx-axis of the design position of all group elementspitch deg f default rotation angle abouty-axis of the design position of all group elementsyaw deg f default rotation angle aboutz-axis of the design position of all group elements

Table 6: Group data

3.1.2 Element Definition

Similar to a group definition, acosin/mbs element is defined by a type-equipped sub-block of the$model block.

in thecosin/mbs data file. The type, a two-character acronym, of an element definition block must be one out of

a list of valid types as described in the cosin/mbs Element Catalogue.

The data-block name of an element definition block serves as element name and, at the same time, as default

value of the element’s data-block name to read its data from.

Besides defining type and name of the element and where to find its data, the most important task of the element

definition block is to specify the ‘topology’ of thecosin/mbs model. This is done in terms of the names of the

other elements that are linked to the element, and of the specification of external input and output signals (sources

and sinks), to be managed bycosin/ss. The specific meaning of the linked elements and the input and output

signals depends on the element, and is described in the respective element’s chapter below.

A typicalelement definitionmight look as follows:

SD:spring_fl l1=car_body; l2=wheel_fl; stiff; g=front_susp

This line defines a spring-damper element namedspring_fl, linking the two bodiescar_body andwheel_fl,

belonging to groupfront_susp, and to be recognized as ‘stiff’ in implicit integration.cosin/mbs data for this

element will be searched in data-block$spring_fl. Rigid-body elements namedcar_body andwheel_flare also

to be defined, either before or after thespring_fldefinition.

All data definitions and switches in an element definition are optional. For example, there is no need to specify

the group entry. Respective default values can be found in the tables below.

The number of othercosin/mbs elements that are linked to an element varies, also the number of external input

or output signals to or from the elements. Some of the data and flags of an element definition block can be used

with all types of elements. They are described in the table below. Some other entries are element-specific, and

are described in the respective element chapter.


This is the general syntax of an element definition block, together with a description of all data and switches

common to all element types:

XX: name f=da t a_ f i l e ; db=data_block_name : mdb=mirrored_data_block

2 db2=second_data_block_name ; mdb2=mirrored_second_data_block

l 1=name_l1 ; l 2=name_l2 ; . . .

4 i 1=name_i1 ; i 2=name_i2 ; . . .

o1=name_o1 ; o2=name_o2 ; . . .

6 p l=va lue_p l ; an=value_an ; camera ; s t i f f ; m i r r o r ; g=group

dx=value_dx ; dy=value_dy ; dz=value_dz

Table 7: General data in element definition block

xx - st2 (m) type of element. Valid types areAC, AD, AS, BE, BO, BR, CS, DS,

DT, EF, ET, F1, FB, PS, RB, RJ, SC, SD, SR, ST, TI, TJ, TS,

WL

name - st (m) arbitrary name of the element. This name can be used to refer to the

element in other element definitions. In addition, the name of the element

is used to make plot labels unique. Actually, name is thename of a

type-equippedcosin/io data-block

f - st file name, where the group element’s data-blocks are looked for.

Default value: name of the actual input file, or file name specified in the

element’s group definition block, resp.

mf - sr file name, where the group element’s data-blocks are looked for, and

mirrored with respect to thexz-plane (see below).

Default value: name of the actual input file, or file name specified in the

element’s group definition block, resp.

db - st name of the element’s data-block (without$).

Default value: element name (name)

mdb - st name of a data-block (without$) to get the element’s data from, after

mirroring with respect to thexz-plane. When mirroring, ally-coordinates

and allx- andz-angles of the element change sign.cosin/mbswill first look

for the original data-block, defined through the element’s name or through

thedb entry. Only if that data-block is not found, it will search and mirror

themdb entry. Typically, the mechanism established by themdb entry is used

for vehicle suspensions. It allows for only describing the left wheel

suspensions (if independent), and get the data for the right wheels by

mirroring. The advantages are: smaller input files and considerable

reduction of redundancy

db2 - st name of the second element data-block (without$).

Default value: element name (name). Used only with theTI element

mdb2 - st name of a second data-block (without$) to get element’s data from,

aftermirroring with respect to thexz-plane. When mirroring,

ally-coordinates and allx- andz-angles of the element change sign. Used

only with theTI element


l1, l2, .. - st name of the first, second, .. element that is linked to the element to be

defined. For force elements, this is the first (second, .. ) body the force

acts on. The number and meaning of the linked elements are documented

with the individual elements below. If a linked element is not defined,

ground (with element name#gnd#) is assumed

i1, i2, .. - st name of the first, second, .. signal provided bycosin/ss to be used as

external input signal to the element. The number and meaning of the

input signals are documented with the individual elements below. If an

input signal is not assigned, its value is held zero

o1, o2, .. - st name of the first, second, .. signal to be forwarded tocosin/ss as external

output signal of the element. If an output signal is not defined, it is not

available as input to other elements

pl - i plot level. Defines the number of plot signals to be saved during

simulation.

Possible values:

0 (no output)

1 (only most important plot signals)

2 (maximum number of plot signals).

al - i model level, defining the level of detail of the elements’ geometrical

animation model.

Possible values: 0, .., 9

camera - flag if set, element serves as ‘camera support’ (that is, the camera-fixed

coordinate system is fixed to the element)

stiff - flag if set, element will be taken into account with implicit BDF integration.

Computational effort will increase, but also numerical stability. For force

elements that approximate kinematic constraints (like theTJ

andRJelement)stiffis automatically set

mirror - flag if set, data in element data-block are mirrored (cf.mdb entry explanation

above), no matter whether element data-block is defined by name, or by

thedb ormdb entry

g - st name of group the element is assigned to

dx mm f shift value for all markers connected to the element, inx-direction

dy mm f shift value for all markers connected to the element, iny-direction

dz mm f shift value for all markers connected to the element, inz-direction

roll deg f rotation angle aboutx-axis for all markers connected to the element

pitch deg f rotation angle abouty-axis for all markers connected to the element

yaw deg f rotation angle aboutz-axis for all markers connected to the element

3.2 Element Catalogue

A detailed list of all availablecosin/mbs element types, thecosin/mbs Element Catalogue, is provided in9 below.

This chapter contains a description of allelement-specific entries in the element definition block, all input and

output signals, alldata, allanimation models, and all plot signals. All mandatory input data listed there are

marked with (m). If not stated otherwise, all numerical data that are neither mandatory nor explicitly specified

get the default value 0.


4 Interfacing to Models for Road and Wind Velocity

cosin/mbs vehicle models can be coupled with models for road surface geometry and other road attributes, as

well as with models for environmental wind velocity.

4.1 cosin/road

The separate packagecosin/road (please refer to respective documentation) provides several models for determin-

istic, stochastic, or measured 2D and 3D road surface geometry and friction attributes. The package includes

models for efficient evaluation of high-resolution measured road surfaces, models for non-rigid surfaces, interfaces

to user-written road models, and more.

4.2 cosin/wind

To specify environmental wind velocity,cosin/mbs uses the subroutineevwind. During the first call to this sub-

routine in a simulation run,evwind opens, if present, the wind file (identifierIWIND), looks for data block$wind

and, if present, reads the following data out of this block that control wind velocity calculation in all subsequent

invocations:

type - s (m) a character string out of

• calm

• constant

• file_v_of_t

• file_v_of_x

• table_v_of_t_and_x

• table_v_of_x_and_y

• function

to define the type of the wind velocity description. For most types additional parametersor data blocks are looked for, as explained in the following

frame - i switch to set the co-ordinate system relative to which the wind velocities are defined:0 wind is defined in inertial (global) co-ordinates1 wind is defined in a co-ordinate system, thex-axis of which is parallel to thevehicle’s velocity vector. This allows for simple prescription of head wind and cross wind,independent on the vehicle’s orientation

Table 8: cosin/wind data-block

Depending on the type chosen for wind velocity description, more data are read from data-block$wind, according

to the following tables:

4.2.1 Typecalm

cosin/wind returns zero wind velocities. No other data are required.


4.2.2 Typeconstant

cosin/wind sets all components of wind velocities to constant values, that are read from data-block$wind:

vx ms

f constantx-component of wind velocity. Default value is 0vy m

sf constanty-component of wind velocity. Default value is 0

vz ms

f constantz-component of wind velocity. Default value is 0

Table 9: cosin/wind typeconstant

4.2.3 Typefile_v_of_t

With this type, wind velocities are described by data columns of a file, giving the dependency of wind velocity on

time.cosin/wind reads from data-block$wind:

file_name - st name of a file to read measured or calculated data from. These data describe thedependency ofvx andvy on time. The file must be in standard or Matlab format(cf.cosin/io documentation).cosin/wind expects equidistant wind velocity data ascolumns of the matrix stored in the file. Unit is [m

s]

channel_vx - i column index ofvx data (if file contains the time channel as first channel, this willtypically be 2)

channel_vy - i column index ofvy data (if file contains the time channel as first channel, this willtypically be 3)

sampling_time s f time difference between two consecutive measured wind velocities. Time valuesoutside the range of data in the file get their wind velocity by extrapolation

Table 10: cosin/wind type file_v_of_t

Note that data columns in a file also can be used with the more general typefunction (see below), in conjunction

with one of the interpolation functionspconst(),linear(), orspline().

4.2.4 Typefile_v_of_x

With this type, wind velocities are described by data columns of a file, giving the dependency of wind velocity on

travel distance.cosin/wind reads from data-block$wind:

file_name - st name of a file to read measured or calculated data from. These data describe thedependency ofvx andvy on inertial coordinatex, or travel distance, resp. The filemust be in standard or Matlab format (cf.cosin/io documentation).cosin/windexpects equidistant wind velocity data as columns of the matrix stored in the file.Unit is [m

s]

channel_vx - i column index ofvx data (if file contains the travel distance as first channel, thiswill typically be 2)

channel_vy - i column index ofvy data (if file contains the travel distance as first channel, thiswill typically be 3)

meas_distance m f distance between two consecutive measured points in longitudinal direction.Travel distances outside the range of data in the file get their wind velocity byextrapolation

Table 11: cosin/wind typefile_v_of_x


with one of the interpolation functionspconst(),linear(), orspline().


4.2.5 Typetable_v_of_t_and_x

With this type, wind velocities are described by a 2D look-up table, giving the dependency of wind veloc-

ity on time and on travel distance.cosin/wind looks for the table data in sub-data blocks$vx_of_t_and_x

and$vy_of_t_and_x. For the syntax of spline data definitions, cf.cosin/io documentation.


with one of the interpolation functionsbilin() orbicub().

4.2.6 Typetable_v_of_x_and_y

With this type, wind velocities are described by a 2D look-up table, giving the dependency of wind velocity on

inertial x/y co-ordinates, or on travel distance and lateral distance to travel path, resp.cosin/wind looks for the

table data in sub-data blocks$vx_of_x_and_y and$vy_of_x_and_y. For the syntax of table data definitions,

cf.cosin/io documentation.


with one of the interpolation functionsbilin() orbicub().

4.2.7 Typefunction

With this type, all 3 components of the wind velocity are described by general arithmetic expressions, that are

allowed to containt,x,y, andz.cosin/wind reads from data-block$wind:

vx ms

f x-component or longitudinal component, resp., of wind velocity, as function ofx,y,z,t, andoptional furthercosin/io parameters. That function may be an arbitrary arithmetic expression asdocumented incosin/io, including 1D and 2D lookup tables, random values, etc.Default value is 0

vy ms

f y-component or lateral component, resp., of wind velocity, as function ofx,y,z,t, and optionalfurthercosin/io parameters. That function may be an arbitrary arithmetic expression asdocumented incosin/io, including 1D and 2D lookup tables, random values, etc.Default value is 0

vz ms

f z-component (vertical component) of wind velocity, as function ofx,y,z,t, and optionalfurthercosin/io parameters. That function may be an arbitrary arithmetic expression asdocumented incosin/io, including 1D and 2D lookup tables, random values, etc.Default value is 0

Table 12: cosin/wind typefunction

5 ECU Interfacing

cosin/mbs vehicle models can be coupled with several ECU (Electronic Control Unit models) models. The models

can be provided by the user as C , C++, or Fortran code. This code must observe certain interfacing rules, which

are described below.

At present, the followingcosin/mbs elements can be combined with external controllers: the brake system (BR

element), the propulsion system (PS element), the rack-and-pinion steering system (SR element), and the general

force actuator (AC element). The type and input-/output characteristic of the controllers that can be chosen is

documented in the respective element description in chapter 3. The following table summarizes these controllers.

It also lists all respective input and output signals:


Figure 5: Supported ECU controller types

C-language templates for all user-written ECU code can be found incosin/mbs sub-folder c_code. Note that all

parameters must be referenced by their addresses; that is, all parameters are either of data typedouble* orint*.

In addition to the signals listed above, all templates provide

• an input parameterint*flag. Ifflag=0,cosin/mbs indicates the code is called during the initialization phase.

This first call can be used also to initialize the user-written algorithm. For this value offlag,cosin/mbs

does not yet expect that the code returns proper values of the output signals. This is done only forflag=1,

which indicates normal invocation during simulation

• an error indicatorint*ier as output (if a call to a controller was successful, this error code should have the

value 0)

Under any of the Windows operating systems, compiling user-written ECU software in C language can be done

withMicrosoftVisual C++ V5.0 or higher, using the batch command filemdll.bat. To do this, copy the C code

intocosin/products sub-foldercar/c_code (overriding the template C code of the respective ECU), then change

to sub-foldercar and enter

mdll c-code-name

wherec-code-name is one out of the list

• abs_std (standard ABS)


• abs_adv (advanced ABS)

• esp (ESP)

• fwd(4WD select)

• atts (front-wheel ATTS)

• lsd_std (conventional LSD)

• lsd_act (active LSD)

• cld(controlled partially locking differentials)

• fws (four-wheel steering 4WS)

• eps_std (simple EPS)

• eps_adv(advanced EPS)

• actuator_i (general force actuator, i =1,..,9)

If compiling and linking was successful, a DLL (Dynamic Link Library) will be generated and copied to thecos-

in/productsbin folder. During a subsequent simulation, if the respective ECU functionality is requested in the

.cm-file, this DLL will be used.

When implementing your code, it is very important to observe the following rule:

If the C-code is called from acosin/mbs element with thestiff property set, then yourcode should not use any

static variables. Such variables can act as ‘hidden’ state variables. Hidden state variables seriously disturb the

implicit integration algorithm, because they make it impossible to properly calculate the Jacobian of the system.

Instead of using static variables, if the callingcosin/mbs element is stiff, your code should ‘remember’ all necessary

values by using thestate array. At present, thestatearray is only available inactuator_i. On demand, all other

ECU interfaces can be extended accordingly.

The following sub-chapters give more details for any of the C-code functions.

5.1 Standard ABS

Prototype

extern void abs_std

(int*flag, double*bp,

double*ws_fl, double*ws_fr, double*ws_rl, double*ws_rr,

double*bp_fl, double*bp_fr, double*bp_rl, double*bp_rr,

int*ier);

Parameter


name data flow unit meaningint*flag input - indicates first or subsequent call.

Forflag=0, output need not to be provideddouble*bp input bar nominal brake pressure

double*ws_fl

double*ws_fr

double*ws_rl

double*ws_rr

input rads

wheel rotational speeds

double*bp_fl

double*bp_fr

double*bp_rl

double*bp_rr

output bar individual wheel brake pressures

int*ier output - error indicator. Should be non-zero at return fromfunction, if an error occurred

Table 13: ECU: Parameter of Standard ABS

5.2 Advanced ABS

Prototype

extern void abs_adv



double*yaw_rate, double*lat_acc, double*long_acc,


double*t_eng,

int*ier);

Parameter



double*ws_fl

double*ws_fr

double*ws_rl

double*ws_rr

input rads


double*yaw_rate input degs

vehicle yaw ratedouble*lat_acc input m

s2vehicle lateral acceleration

double*long_acc input ms2

vehicle longitudinal accelerationdouble*bp_fl

double*bp_fr

double*bp_rl

double*bp_rr

output Nm nominal engine torque, to be regulated in propulsionsystem. Will not be used, if negative


Table 14: ECU: Parameter of Advanced ABS

5.3 ESP (Electronic Stability Program)

Prototype


extern void esp




double*gp, double*swa,


double*t_eng,

int*ier);

Parameter



double*ws_fl

double*ws_fr

double*ws_rl

double*ws_rr

input rads






vehicle longitudinal accelerationdouble*gp input % gas pedal stroke (100% = full throttle)double*swa input deg steering wheel angle, positive for left turnsdouble*bp_fl

double*bp_fr

double*bp_rl

double*bp_rr

output bar individual wheel brake pressures

double*t_eng output Nm nominal engine torque, to be regulated in propulsionsystem. Will not be used, if negative


Table 15: ECU: Parameter of ESP

5.4 Automatic Four-Wheel Drive Select

Prototype

extern void fwd

(int*flag,



double*t_eng, double*swa,

int*fwd_switch,

int*ier);

Parameter



Forflag=0, output need not to be provided

double*ws_fl

double*ws_fr

double*ws_rl

double*ws_rr

input rads






vehicle longitudinal accelerationdouble*t_eng input Nm net engine torquedouble*swa input deg steering wheel angle, positive for left turnsint*fwd_switch output bar four-wheel drive select switch

0: 4WD switched off1: 4WD switched on


Table 16: ECU: Parameter of Automatic Four-Wheel Drive Select

5.5 ATTS (Automatic Torque Transfer System)

Prototype

extern void atts

(int*flag,


double*yaw_rate, double*lat_acc,

double*t_eng, double*swa,

double*t_split_factor,

int*ier);

Parameter



double*ws_fl

double*ws_fr

double*ws_rl

double*ws_rr

input rads





double*t_eng input Nm net engine torquedouble*swa input deg steering wheel angle, positive for left turnsdouble*t_split_factor output - actor between 0 and 1 (continuously) that controls

torque split between left and right front wheel0: right wheel receives full torque ideal differential,both wheels receive same torque1: left wheel receives full torque


Table 17: ECU: Parameter of ATTS


5.6 LSD (Limited Slip Differential)

Prototype

extern void lsd_std

(int*flag,


double*t_eng, double*dt_max,

int*ier)

Parameter



double*ws_fl

double*ws_fr

double*ws_rl

double*ws_rr

input rads


double*t_eng input Nm net engine torquedouble*dt_max output - maximum difference torque of the two output shaftsint*ier output - error indicator. Should be non-zero at return from

function, if an error occurred

Table 18: ECU: Parameter of LSD

5.7 Active LSD

Prototype

extern void lsd_act

(int*flag,



double*t_eng, double*swa, double*dt_max,

int*ier);

Parameter



double*ws_fl

double*ws_fr

double*ws_rl

double*ws_rr

input rads






vehicle longitudinal accelerationdouble*t_eng input Nm net engine torquedouble*swa input deg steering wheel angle, positive for left turnsdouble*dt_max output - maximum difference torque of the two output shaftsint*ier output - error indicator. Should be non-zero at return from


Table 19: ECU: Parameter of Active LSD


5.8 CLD (Controlled Partially Locking Differentials)

Prototype

extern void cld

(int*flag,

double*throttle, int*gear, double*brp, double*swa,

double*speed, double*yaw_rate,


double*lat_acc, double*long_acc,

double*dt_maxf, double*dt_maxr, double*dt_maxc,

int*ier);

Parameter



double*ws_fl

double*ws_fr

double*ws_rl

double*ws_rr

input rads






vehicle longitudinal accelerationdouble*swa input deg steering wheel angle, positive for left turnsdouble*throttle input deg throttle opening angledouble*brp input bar pressure in main brake cylinder [bardouble*speed input m

svehicle speed [m

s]

int*gear input - actually actuated geardouble*dt_maxf output - maximum difference torque of the two front wheels

output shaftsdouble*dt_maxr output - maximum difference torque of the two rear wheels

output shaftsdouble*dt_maxc output - maximum difference torque of the central differential

output shaftsint*ier output - error indicator. Should be non-zero at return from


Table 20: ECU: Parameter of CLD

5.9 Four-Wheel Steering

Prototype

extern void fws

(int*flag,


double*yaw_rate, double*lat_acc, double*swa,

double*d_rack,

int*ier);

Parameter




double*ws_fl

double*ws_fr

double*ws_rl

double*ws_rr

input rads





double*swa input deg steering wheel angle, positive for left turnsdouble*d_rack output mm rack displacement of rear axle steering assemblyint*ier output - error indicator. Should be non-zero at return from


Table 21: ECU: Parameter of Four-Wheel Steering

5.10 EPS (Electronic Power Steering)

Prototype

extern void eps_std

(int*flag,


double*swt,

double*f_rack, double*t_col,

int*ier);

Parameter

name data flow unit meaningint*flag input - indicates first or subsequent call. Forflag=0, output need

not to be provided

double*ws_fl

double*ws_fr

double*ws_rl

double*ws_rr

input rads


double*swt input Nm steering reaction torque (pinion torque)double*f-rack output N assisting force on steering rackdouble*t_col output Nm assisting torque on steering columnint*ier output - error indicator. Should be non-zero at return from function,

if an error occurred

Table 22: ECU: Parameter of EPS

5.11 Advanced EPS

Prototype

extern void eps_adv

(int*flag,


double*yaw_rate, double*lat_acc,

double*swa, double*swv, double*swt, double*swtr,


double*f_rack, double*t_col,

int*ier);

Parameter

name data flow unit meaningint*flag input - indicates first or subsequent call. Forflag=0, output

need not to be provided

double*ws_fl

double*ws_fr

double*ws_rl

double*ws_rr

input rads





double*swa input deg steering wheel angle (positive in left turns)

double*swv input rads

steering wheel angle velocitydouble*swt input Nm steering reaction torque (pinion torque)

double*swtr input Nms

steering reaction torque ratedouble*f-rack output N assisting force on steering rackdouble*t_col output Nm assisting torque on steering columnint*ier output - error indicator. Should be non-zero at return from


Table 23: ECU: Parameter of Advanced EPS

5.12 General Force Actuator

Prototype ( i = 1,..,9 )

extern void actuator_i

(int*flag, double*s, double*sd, double*dt, double*state, double*F, int*ier);

Parameter

name data flow unit meaningint*flag input - indicates first or subsequent call. Forflag=0,

output need not to be provideddouble*s input mm deflectiondouble*sd input m

sdeflection velocity

double*dt input s integration step-sizedouble*state input/output user defined state vector, may contain up to 10 componentsdouble*F output N scalar actuator forceint*ier output - error indicator. Should be non-zero at return

from function, if an error occurredTable 25: ECU: Parameter of General Force Actuator

6 Interfacing to User-Supplied Driver-Models

cosin/mbs provides an interface to user-supplied driver-models. This interface is defined and implemented in a

similar way like the ECU models. A driver-model can be provided by the user as C , C++, or Fortran code. This

code must observe certain interfacing rules, which are described below.


Usage of a user-supplied driver-model is selected only by specifying a related data-file (udm_file) in data-

block$simulation of the sim-file, cf. chapter 2.2.12.2.1.

A C-language template (udm.c) for a driver-model can be found incosin/mbs sub-folderc_code. Note that all

parameters of this C-function must be referenced by their addresses; that is, all parameters are either of data

typedouble*,int*, orchar*.

Under any of the Windows operating systems, compiling the driver-model source code in C language can be done

withMicrosoft Visual C++ V5.0 or higher, using the batch command filemdll.bat. To do this, copy the C code

intocosin/products sub-foldercar/c_code (overriding the template C code of the driver-model), then change to

sub-foldercar and enter

mdll udm

If compiling and linking was successful, a DLL (Dynamic Link Library) will be generated and copied to thecos-

in/productsbin folder. During a subsequent simulation, if the user-supplied driver-model is called, this DLL will

be used.

The driver-model is only called once per simulation step, with a fixed step-size. As a consequence, there is no

complicated step-size controlled co-simulation technique necessary. In contrast to ECU models called by elements

with the stiff attribute set (cf. chapter 55), the driver-model may use arbitrary hidden state variables without

interfering withcosin/mbs’ integrator in any way.

• Prototype:

extern void udm

(int*job, double*din, double*dout, int*ier, char*file);

• Parameter:

Table 26: Driver-model parameter

name data flow meaning

int*job input job control flag

0: normal call, output signals to be provided

1: final call, no output signals required bycosin/mbs

At present, the driver model has to take care for loading the data

file only during the first call toudm; no special job-value for

’initialization’ is provided at that time.

double*din input

vehicle signals made available as sensor signals:

din[0] s actual simulation time

din[1] m x-position driver’s eye in global coord.

din[2] m y-position driver’s eye in global coord.

din[3] ms

x-velocity driver’s eye in global coord.

din[4] ms

y-velocity driver’s eye in global coord.

din[5] ms2 x-acceleration driver’s eye in global coord.

din[6] ms2 y-acceleration driver’s eye in global coord.

din[7] deg vehicle’s yaw angle (ISO 8855)

din[8]degs

vehicle’s yaw velocity (ISO 8855)

din[9]degs

2 vehicle’s yaw acceleration (ISO 8855)

din[10] Nm steering torque

din[11] - not used


din[12] - not used

din[13] - not used

din[14] rmp engine speed

din[15] - actual gear selection (-1: reverse gear; 0:

neutral; 1: 1st gear, etc.)

din[16] % wheel slip front left wheel

din[17] % wheel slip front right wheel

din[18] % wheel slip 1st rear axle left wheel

din[19] % wheel slip 1st rear axle right wheel

din[20] deg side-slip angle front left wheel

din[21] deg side-slip angle front right wheel

din[22] deg side-slip angle 1st rear axle left wheel

din[23] deg side-slip angle 1st rear axle right wheel

double*dout output driver’s control signals computed by the driver model:

dout[0] deg steering wheel angle (counterclockwise)

dout[1] - gas pedal operating travel

(normalized between 0 and 1)

dout[2] - brake pedal operating travel


dout[3] - clutch pedal operating travel


dout[4] - gear selection (-1: reverse gear;

0: neutral; 1: 1st gear, etc.)

dout[5] - hand-brake lever operating travel


int*ier output error flag 0: normal and successful operation of the driver model All

other values will abort thecosin/mbs simulation

char*file input name of the data file containing model data, to be opened, read,

interpreted, and used solely by the driver-model. Path separators

etc. follow the respective operating system’s rules

7 Command Line Invocation

Instead of using thecosin/mbs workbench, likewise thecosin/mbs solver can be called directly from a command

window (Windows) or command shell (Unix), respectively. For Windows, that invocation reads

<cosin-path>\bin\cosinmbs cfd-file -option1 -option2 ...

or simply

cosinmbs cfd-file -option1 -option2 ...

if you have added<cosin-path>\bin to your search-path environment variable. For Unix-type operating systems,

replace the back-slashes by slashes.

In the above commands,<cosin-path> is the path where you installedcosin/products (during installation under

Windows, you might have changed the default valuec:\cosin_products for that path).<cfd-file> is the file-

definition file (cf.cosin/io), containing a list of assignments between logical file identifiers and ‘physical’ file


names. Acosin/mbs .cfd-file might look as follows (in that example, it is assumed your actual working directory

is<cosin-path>/car):

* sample .cfd-file for cosin/mbs command line invocation *************

ISIM=simul/cornering.sim

ISRC=simul/cornering.sim

IROAD=simul/cornering.sim

IWIND=simul/cornering.sim

IPAR=param/st_fl.cm

OPAR=param/st_fl.cmp

OBIST=simul/temp.cms

OPLOT=work/temp

Note that simulation data (data-block$simulation), external input-signal data (data-block$sources), and road-

profile data (data-block$road_type) are combined to only one file (simul/cornering.sim). This is also done

when calling the solver form the workbench, but by no means obligatory.

Note also that even if called under Windows, a path in a .cfd-file may be defined by using slashes instead of

back-slashes. This facilitates interchange of files between Windows and Unix.

The following logical file identifiers can be specified:

logical fileidentifier

data flow (m:mandatory)

meaning of file

ISIM input (m) simulation file, containing data-block$simulationISCR input sources&sinks file, containing data-block$sourcesIROAD input road data file, containing data-block$road_typeIWIND input wind data file, containing data-block$windIPAR input (m) model data file (.cm-file)IBIST input model states input fileOPAR output (ASCII) copy of model data file (.cmp-file), pre-load values addedOBIST output (binary) model states output fileOPLOT output (ASCII or

binary)plot file (if file name has no extension, an extension will beappended according to the plot-file format specified inthe$simulation data-block)

Table 27: File identifiers in command line invocation

In addition to the .cfd-file, certain program options can be defined. The following is a list of all available options:

program option meaning-acc (‘accurate’): decrease simulation time step by 50%-anim show on-line animation during simulation-clean before launching simulation, delete temporary files which might be left over

from previous simulations that did not finish regularly-fast increase simulation time step by 50%-movie prepare movie generation by grabbing every single animation frame into a

.bmp file. These files will be saved to folder.\temp or./temp, resp.-plot generate a plot-file

Table 28: Program options in command line invocation


8 Coupling to Matlab/Simulink

If licensed to, you can use anycosin/mbs assembly as block in a Matlab/Simulinkmodel, see figure6.

Figure 6: cosin/mbs Simulink block

The central block in figure6, thecosin/mbs block, can be used in several instances, which will in no way interfere

with each other. The block (with those sample external connections as shown in figure6) is called cm.mdl and

can be loaded into

after changing to sub-folder Matlab of thecosin/products folder.Note that simulations withcosin/mbs un-

derSimulink can not reach the full speed experienced withcosin/mbs stand-alone. This is inevitable, and

due to a certain computational overhead in Simulink.

The block (for experts: it is implemented as time-discrete wrapped and masked C-code level-2 S-function) au-

tomatically shows all those input and output signals that are defined in the underlyingcosin/mbs model file (the

cm-file). It is up to the user to define all those input and output signals he wants to use with the Simulink block.

Allcosin/mbs sample files provide the most important ones of these signals.

Due to certain restrictions with the programming and masking of Simulink blocks, thecosin/mbs block will always


show 40 input signals and 40 output signals, even if the cm-file defines less. Surplus input signals are not used,

while surplus output signals will put out constantly zero.

To get the best compromise between flexibility in user-defined signals, and interchangeability ofcosin/mbs blocks

for different vehicles, the most commonly used signals (with pre-defined names) will always appear in the same

places of the block. These signals are labeled with upper-case letters, while all other signals are shown in lower-case

letters. If a pre-defined signal does not appear in the cm-file, its place is left blank.

At present, the following input signals are pre-defined:

steering_type - i steering type (signali1 inSR orSC element)steering_wheel_angle deg f steering wheel angle (signali2 inSR orSC element)steering_wheel_torque Nm f steering wheel torque (signali3 inSR orSC element)gas_pedal - f normalized gas pedal travel (signali1 inSR or DTelement)clutch_pedal - f normalized clutch pedal travel (signali2 inPSelement)selector_lever - i selector lever position (signali2 inST element)gear - i gear to actuate (signali3 inST element)brake_pedal - f normalized brake pedal travel (signali1 inSR orDTelement)hand_brake - f normalized hand-brake handle travel (signali2 inBR element)

Table 29: Simulink block input signals

These are the pre-defined output-signals:

v - i vehicle total speed (signalo1 in car-bodyBOelement)yaw_vel deg f vehicle yaw velocity (signalo13 in car- bodyBO element)a-long Nm f vehicle longitudinal acceleration in car- body fixed co-ordinates

(signalo5 in car- bodyBO element)a_lat - f vehicle lateral acceleration in car-body fixed co-ordinates (signalo6

in car-bodyBO element)fl.wheel_speed - f rotational wheel speed of front left wheel (signalo2 in front left

wheelTI element)fr.wheel_speed - i rotational wheel speed of front right wheel (signalo2 in front right

wheelTIelement)rl.wheel_speed - i rotational wheel speed of rear left wheel (signalo2 in rear left

wheelTI element)rr.wheel_speed - f rotational wheel speed of rear right left wheel (signalo2in rear right

wheelTIelement)

Table 30: Simulink block output signals

When double-clicking on thecosin/mbs blocks, an input mask opens like shown in figure7.


Figure 7: cosin/mbsinput mask in Simulink

Here, you can enter, in Matlab/Simulink syntax,

• file names of the .cm-file and of the road model data file to be used for the assembly

• values for initial position and velocity of the car-body

• thecosin/mbs integration, plot-output, and animation step-sizes (‘time-step’)

• the log-level which determines the details of terminal output (which will appear in the Matlab Command

Window).

If the plot-output step-size is greater than zero, during a simulation a filetemp.mtl will be generated in the

working directory. This file contains allcosin/mbs plot-output signals and can be loaded in the Matlab command

window as follows:

load –ascii temp.mtl

Equally well, temp.mtl can be browsed withcosin/ip.cosin/ip is opened by double-clicking the right magenta block

above thecosin/mbs block. Double-clicking the left one will open the cm-file with Matlab’s text editor.

Before running a simulation, you can check in the input mask whether or not to observe dry friction and backlash

(‘play’) in allcosin/mbs elements. For linearization in Matlab, it is highly recommended to switch off both dry

friction and backlash. In contrast, for non-linear time-domain simulations it is recommended to switch on both.

Using the last check-box in the input mask, you can toggle on-line animation.


9 Element Catalogue

9.1 AC General Actuator with User-Written Control Code

This element serves as interface to user-defined force actuators that are located between two bodies. Similar

to the SD element (see below), the force acts in the direction of a straight line connecting these bodies, the

endpoints of which are defined by two body-fixed markers.

User-written code should return the scalar force along that line as function of distance and rate of change of

distance of the two markers. Such user-written C code can be easily simulated together withcosin/mbs by

observing certain interfacing definitions, and providing a DLL under Windows or a shared object under any of the

Unix dialects. For details about this interfacing, see chapter 4.

I/O signals and other element-specific data in the element definition block

l1 - st name of first body (RB,FB, orBO element) actuator is attached tol2 - st name of second body (RB,FB, orBO element) actuator is attached to

id - i actuator id (optional, may be used to identify the actuator instance inside theuser-written subroutine)

i1 - sig additionalscalar force [N ]i2 - sig forcedactuator elongation [mm]

Remark: this input signal is useful for example to test the actuator software witha prescribed forced elongation, when connected to ground on either side.Typically, it will be set to zero in normal operation mode

o1 - sig x-component ofactuator force in body-fixed coordinates acting onfirst body [N ]o2 - sig y-component ofactuator force in body-fixed coordinates acting onfirst body [N ]o3 - sig z-component ofactuator forcein body-fixed coordinates acting onfirst body [N ]o4 - sig x-component ofactuator force in body-fixed coordinates acting onsecond body

[N ]o5 - sig y-component ofactuator force in body-fixed coordinates acting onsecond body

[N ]o6 - sig z-component ofactuator force in body-fixed coordinates acting onsecond body

[N ]o7 - sig actuator deflection [mm]o8 - sig actuator deflection velocity[m

s]

o9 - sig scalar actuator force [N ]

Table 31: AC I/O signals and other element-specific data

Element data

attachm_body1 mm m (m) body-fixed attachment point of the actuator at body 1attachm_body2 mm m (m) body-fixed attachment point of the actuator at body 2actuator_version - i switch to choose one out of nine different user-written

functions. Names of these functions must beactuator_i, wherei = 1,..,9 is the valueofactuator_version.For details of the program interfaces of these functions, seechapter 4

Table 32: AC element data

Animation models


cylinder

cylinder_diameter mm f diameter of actuator housing (default 50mm)cylinder_length mm f length of actuator housing (default 500mm)piston_rod_diameter mm f diameter of actuator piston rod (default 10mm)piston_rod_length mm f length of actuator piston rod (default 500mm)

Table 33: AC animation models

Plot signals

level 1deflection mm f deflection of actuator: change in distance of the two points

of attachment relative to reference position distancedeflection vel. m

sf deflection velocity of actuator

force N f actuator force, as returned from the user-written control code

Table 34: AC plot signals

9.2 AD Aerodynamic Forces and Moments

This element calculates aerodynamic forces and moments, using different modeling approaches.

The standard model (type = 1) uses two-dimensional look-up tables. These tables give all 6 components of the

formoment vector that act on a prescribed point of reference, as function of

• wind approach velocity ([ms])

• angle of approach ([deg])

Forces and moments are described in a co-ordinate system that is moving parallel to the road surface. Thez-axis

of this system coincides with the road normal, evaluated at the center point of the 4 tire foot-print centers.

Thex-axis is parallel to the connecting line of the center-point of the two rear wheel foot-print centers to that one

of the two front wheel foot-print centers. The origin of this co-ordinate system is given by the ‘point of reference’.

If, for what reason ever, the tire contact patch center points are not all given, a vehicle-fixed frame is used instead.

Origin and axis direction of this co-ordinate system will coincide with the above mentioned system, as long as the

vehicle’s pitch angle, roll angle, and vertical displacement of c.o.g. are all zero relative to the road.

Optionally, forces and torques may be dynamically delayed by first order differential equations.

Other models are customer-specific, or will be defined later. In addition to the above mentioned independent

variables, they may use

• body roll and pitch angle relative to ground ([deg])

• height of the point of reference relative to ground ([mm])

• height of two sensor points (‘front’ and ‘rear’) relative to ground ([mm])

• mean toe angle of front wheels ([deg])

The element uses the environmental wind velocity as input, which can be described by an appropriatecosin/ev

data-block.



l1 - st name of body (RB,FB, orBO element) the aerodynamic forces act onl2 - st name offront left tire element (TI element). Only used in customer- specific

aerodynamics models, if forces depend on toe angles or on car-body distance toroad

l3 - st name offront right tire element (TI element). Only used in customer- specificaerodynamics models, if forces depend on toe angles or on car-body distance toroad

l4 - st name ofrear left tire element (TI element). Only used in customer- specificaerodynamics models, if forces depend on toe angles or on car-body distance toroad

l5 - st name ofrear right tire element (TI element). Only used in customer- specificaerodynamics models, if forces depend on toe angles or on car-body distance toroad

o1 - sig body’s approach velocity, longitudinal component [ms]

o2 - sig body’s approach velocity, lateral component [ms]

o3 - sig body’s approach angle [deg]o4 - sig body’s roll angle relative to ground [deg]o5 - sig body’s pitch angle relative to ground [deg]o6 - sig distance of reference point to ground [mm]o7 - sig distance of front sensor to ground [mm]o8 - sig distance of rear sensor to ground [mm]o9 - sig mean toe angle of front wheels [deg]

Table 35: AD I/O signals and other element-specific data

Element data


meas_point_of_ref mm m (m) point of reference of aerodynamicforces/moments measurements

front_height_sensor mm m sensor point for measurement of front distanceto ground

rear_height_sensor mm m sensor point for measurement of rear distanceto ground

frontal_area m2 f (m) frontal area of body as measured perpendicularto normal velocity vector

model - i type of aerodynamics model to be used.Default:1

air_density kgm3 f air density

data for type 1 model:

drag_coeff_table_Fx - t2 (m) longitudinal aerodynamic force drag coefficientcFx, whereFx = −

1

2cFxρAv

2

drag_coeff_table_Fy - t2 lateral aerodynamic force drag coefficientcFy, whereFy = −

1

2cFyρAv

2

drag_coeff_table_Fz - t2 vertical aerodynamic force drag coefficientcFz, whereFz = −

1

2cFzρAv

2

drag_coeff_table_Mx m t2 aerodynamic rolling moment drag coefficientcTx, whereTx = − 1

2cTxρAv

2

drag_coeff_table_My m t2 aerodynamic pitching moment drag coefficientcTy, whereTy = −

1

2cTyρAv

2

drag_coeff_table_Mz m t2 aerodynamic yawing moment drag coefficientcTz , whereTz = − 1

2cTzρAv

2

path_constant_Fx m f path-domain constant used in first orderdifferential equation describing dynamic delayinFx.A time constant is calculated through dividingby approach velocity.

path_constant_Fy m f path-domain constant used in first orderdifferential equation describing dynamic delayinFy

path_constant_Fz m f path-domain constant used in first orderdifferential equation describing dynamic delayinFz

path_constant_Mx m f path-domain constant used in first orderdifferential equation describing dynamic delayinMx

path_constant_My m f path-domain constant used in first orderdifferential equation describing dynamic delayinMy

path_constant_Mz m f path-domain constant used in first orderdifferential equation describing dynamic delayinMz

data for type 2 model to be defined later

Table 36: AD element data

Animation models


arrow

an arrow represents the momentary magnitude and direction of the environmental windvelocity near the vehiclescaling_factor m/(m

s) f arrow length in m perm

swind velocity

z_shift mm f height of arrow starting node relative tovehicle’s center of gravity

Table 37: ADanimation models

Plot signals

level 1long. wind velocity m

swind velocity in motion direction of center of gravity

lat. wind velocity ms

wind velocity perpendicular to motion direction of center ofgravity

longitudinal force N body-fixedx-component of aerodynamic forcelateral force N body-fixedy-component of aerodynamic forcelift force N body-fixedz-component of aerodynamic force

level 2approach velocity m

sbody’s absolute approach velocity

approach angle deg body’s approach angleroll angle rel. to

ground

deg body’s roll angle relative to ground

pitch angle rel. to

ground

deg body’s pitch angle relative to ground

ref. point height mm distance of reference point to groundfront height mm distance of front sensor to groundrear height mm distance of rear sensor to groundfront wheels mean toe

angle

deg mean toe angle of front wheels

rolling moment Nm body-fixedx-component of aerodynamic momentpitching moment Nm body-fixedy-component of aerodynamic momentyawing moment Nm body-fixedz-component of aerodynamic momentx velocity wind m

sinertialx-component of wind velocity vector near vehicle

y velocity wind ms

inertialy-component of wind velocity vector near vehiclez velocity wind m

sinertialz-component of wind velocity vector near vehicle

Table 38: AD plot signals

9.3 AS Acceleration Sensor

This element puts out accelerations at a specified location of that body the sensor is linked to:

• the translational accelerations at the sensor’s location in the sensor-fixed coordinate system

• the inertial accelerations at the sensor’s location

• the angular accelerations, expressed in the sensor-fixed coordinate system.



l1 - st name of body (RB,FB, orBO element) sensor is attached to (‘sensor carrier’)

o1 - sig x-component of sensor position in inertial coordinates [m]o2 - sig y-component of sensor position in inertial coordinates [m]o3 - sig z-component of sensor position in inertial coordinates [m]o4 - sig x-component of sensor velocity in inertial coordinates [m

s]

o5 - sig y-component of sensor velocity in inertial coordinates [ms]

o6 - sig z-component of sensor velocity in inertial coordinates [ms]

o7 - sig x-component of translational acceleration of sensor in inertial coordinates [ms2

]o8 - sig y-component of translational acceleration of sensor in inertial coordinates [m

s2]

o9 - sig z-component of translational acceleration of sensor in inertial coordinates [ms2

]o10 - sig x-component of translational acceleration of sensor in sensor-fixed coordinates

[ms2

]o11 - sig y-component of translational acceleration of sensor in sensor-fixed coordinates

[ms2

]o12 - sig z-component of translational acceleration of sensor in sensor_fixed coordinates

[ms2

]o13 - sig side-slip angle of sensor (angle betweenx-axis and velocity vector of sensor carrier,

after projection into inertialx/y plane) [deg]

Table 39: AS I/O signals and other element-specific data

Element data

location mm m location of sensor in reference position

One of:direction_

angles_DIN_70000

deg f3 sensor orientation, expressed in anglesdefined in ISO 8855 / DIN 70000

direction_

angles_Bryant

deg f3 sensor orientation, expressed in Bryantangles

Table 40: AS element data

Animation models

arrow

an arrow represents the translational acceleration magnitude and directionscaling_factor m/(m

s2) f arrow length in m perm

s2

trajectory

a trajectory is displayed which the sensor has been following recentlyRGB_color - f3 RGB color representation of the trajectoryline_width - i line width (must be an integer value between 1

and 9).Default value: 3

Table 41: ASanimation models

Plot signals


level 1sensor-fixed

acceleration[1]

ms2

x-component of sensor acceleration in sensor- fixedcoordinates

sensor-fixed

acceleration[2]

ms2

y-component of sensor acceleration in sensor- fixedcoordinates

sensor-fixed

acceleration[3]

ms2

z-component of sensor acceleration in sensor- fixedcoordinates

level 2inertial

acceleration[1]

ms2

x-component of sensor acceleration in global coordinates

inertial

acceleration[2]

ms2

y-component of sensor acceleration in global coordinates

inertial

acceleration[3]

ms2

z-component of sensor acceleration in global coordinates

sensor-fixed ang.

accel.[1]

degs2

x-component of angular sensor acceleration in sensor-fixedcoordinates (‘roll acceleration’)

sensor-fixed ang.

accel.[2]

degs2

y-component of angular sensor acceleration in sensor-fixedcoordinates (‘pitch acceleration’)

sensor-fixed ang.

accel.[3]

degs2

z-component of angular sensor acceleration in sensor-fixedcoordinates (‘yaw acceleration’)

side-slip angle deg side-slip angle of sensor (angle betweenx-axis and velocityvector of sensor carrier, after projection into inertialx/yplane)

Table 42: AS plot signals

9.4 BE General Bearing

This element serves as general description of all kinds of elasticity and damping that can assumed to be con-

centrated in one elasticity point, joining two rigid or flexible bodies. Among others, theBE element can describe

rubber bushings, revolute joints, cylindrical joints, and hydro-mounts.

All stiffness and damping data are understood in a bearing-fixed frame, where for cylindrical joints thex-axis

typically coincides with the axis of symmetry. This bearing-fixed frame is assumed to move and rotate with the

first body, the bearing is attached to. The orientation of the bearing-fixed frame can be defined by three markers,

two of which are situated on the bearing-fixedx-axis, a third on the bearing-fixedy-axis. Note that the origin

of this frame is of no relevance, but only the orientation. For this reason, nothing changes if all of these three

markers are shifted by the same vector.

All translational and rotational stiffness and damping characteristics can either be defined by constant values, or

by nonlinear characteristics, defined through spline data. Moreover, the stiffness characteristic in the bearing-

fixedx-direction can be replaced by a one-dimensional hydro-mount model. ‘Deflection’ for the characteristics is

understood to be the respective coordinate of the attachment point on the first body minus the coordinate of the

attachment point on the second body, eventually calculated in a bearing-fixed frame.

Signs are such that forces or moments normally share it with the respective translational or angular displacement

or displacement velocity, respectively.

I/O signals and other element-specific data

Table 43: BE I/O signals and other element-specific data


l1 - st name of first body (RB,FB, orBO element) bearing is mounted on.Remark:

the bearing-fixed co-ordinate system is assumed to move and rotate with

that body

l2 st name of second body (RB,FB, orBO element) bearing is mounted on.

i1..i3 - sig x/y/z-components ofextra body-fixeddisplacement of bearing position

[mm]

i4..i6 - sig translational stiffness modification percentages inx/y/z-direction [%]

i7..i9 - sig rotational modification percentages inx/y/z-direction [%]

Element data

Table 44: BE element data

position mm m (m) point of elasticity in reference

position

One

of:

(m)

stiffness Nmm

f3 translational stiffness in

body-fixedx/y/z-direction

One

of:

stiff_x_

spline

mm,N sd translational stiffness

characteristic inx-direction

hydromount mo hydro-mount model for

elasticity inx-direction (see

separateHM element

documentation)

stiff_y_spline mm,N sd translational stiffness

characteristic iny-direction

stiff_z_spline mm,N sd translational stiffness

characteristic inz-direction

One

of:

(m)

rot_stiffn Nmdeg

f3 rotational stiffnesses

aboutx/y/z-axes

rot_stiffn_x_spline deg,Nm sd rotational stiffness

characteristic inx-axis

rot_stiffn_y_spline deg,Nm sd rotational stiffness

characteristic iny-axis

rot_stiffn_z_spline deg,Nm sd rotational stiffness

characteristic inz-axis

One

of:

(m)

damping Nsm

f3 transl. damping coefficients

inx/y/z-direction

damping_x_spline

damping_y_spline

damping_z_spline

ms,N

ms,N

ms,N

sd

sd

sd

translational damping

characteristic inx-direction


characteristic iny-direction


characteristic inz-direction

One

of:

(m)

rot_damping Nmsrad

f3 rotational damping

coefficients aboutx/y/z-axes


rot_damping_x_spline

rot_damping_y_spline

rot_damping_z_spline

rads

,Nmrads

,Nmrads

,Nm

sd

sd

sd

rotational damping

characteristic aboutx-axis

rotational damping

characteristic abouty-axis

rotational damping

characteristic aboutz-axis

friction_torque Nm f friction torque, acting

opposite to momentary axis of

relative rotation of the

connected bodies. This value

is overridden with 0,

iffriction = 0 is specified in

thesimulation data-block of

the simulation data file

preloads N ,Nm f6 preload formoment vector in

bearing-fixed frame. If

data-blockpreloads is

present, these values are

overridden with the respective

values of this data-block

x_axis_marker1 mm m first marker defining

bearing-fixedx-axis. If not

specified, the bearing-fixed

frame, in reference position,

coincides with the global

frame

x_axis_marker2 mm m second marker defining

bearing-fixedx-axis. This is

the origin of the bearing-fixed

frame. If not specified, the

point of elasticity (position)

is taken instead

y_axis_marker mm m marker defining

bearing-fixedy-axis. If not

specified, the bearing-fixed

frame, in reference position,

coincides with the global

frame

Animation models

ball_joint

ball_diameter mm f diameter of the outer ball

cylindrical_joint

cylinder_diameter mm f diameter of the outer cylindercylinder_length mm f length of the outer diameter

Table 45: BEanimation models


Plot signals

(if hydro-mount model is included, see also the hydro-mount subsystem chapter for additional plot signals):

Table 46: BEplot signals

level 1

force x

(bearing-fixed)

N bearing fixedx-component of bearing force (only

provided, if bearing has translational stiffness or

damping)

force y

(bearing-fixed)

N bearing fixedy-component of bearing force (only


damping)

force z

(bearing-fixed)

N bearing fixedz-component of bearing force (only


damping)

level 2

defl. x

(bearing-fixed)

mm bearing deflection in bearing-fixedx-direction (only


damping)

defl. y

(bearing-fixed)

mm bearing deflection in bearing-fixedy-direction (only


damping)

defl. z

(bearing-fixed)

mm bearing deflection in bearing-fixedz-direction (only


damping)

ang. defl. x

(bearing-fixed)

deg angular bearing deflection about

bearing-fixedx-direction (only provided, if bearing has

rotational stiffness or damping)

ang. defl. y

(bearing-fixed)


bearing-fixedy-direction (only provided, if bearing has


ang. defl. z

(bearing-fixed)


bearing-fixedz-direction (only provided, if bearing has


torque x

(bearing-fixed)

Nm bearing-fixedx-component of bearing torque (only

provided, if bearing has rotational stiffness or

damping)

torque y

(bearing-fixed)

Nm bearing-fixedy-component of bearing torque (only


damping)

torque z

(bearing-fixed)

Nm bearing-fixedz-component of bearing torque (only


damping)


9.5 BJ Ball Joint

This element connects two bodies with a ball joint. The degrees of freedom of the bodies are constraint in such

a way that the location of two points, each fixed to one of the bodies, always coincides.

In addition to this kinematic constraint, an optional sliding friction torque is provided, acting against the relative

rotational motion in the ball joint. Optionally, this sliding friction torque can be described by a separate ball-joint

friction model.

This element will automatically use thestiffattribute, no matter whether or not this attribute is specified in the

element or group definition.


l1 - st name of first body (RB,FB, orBO element) connected by ball jointl2 - st name of second body (RB,FB, orBO element) connected by ball joint

i1 - sig x-component of extra body-fixed displacement of ball joint position [mm]i2 - sig y-component of extra body-fixed displacement of ball joint position [mm]i3 - sig z-component of extra body-fixed displacement of ball joint position [mm]

Table 47: BJ I/O signals and other element-specific data

Element data

position mm m position of ball joint in body-fixed co-ordinatesof both bodies

Oneof:

friction_torque Nm f scalar maximum sliding-friction torque, actingagainst rotational motion in ball joint

friction_model mo ball-joint friction model (see separateBFelement documentation)

Table 48: BJ element data

Animation models

ball_joint

ball_diameter mm f diameter of the outer ball

Table 49: BJanimation models

Plot signals

Table 50: BJ plot signals

level 1

force x (body-fixed) N x-component of reaction force in body-fixed

co-ordinates of first body

force y (body-fixed) N y-component of reaction force in body-fixed


force z (body-fixed) N z-component of reaction force in body-fixed


level 2


resid. defl. x

(body-fixed)

mm x-component of residual translational joint deflection

in body-fixed co-ordinates of first body (only for

diagnosis purposes; should be extremely small)

resid. defl. y

(body-fixed)

mm y-component of residual translational joint deflection



resid. defl. z

(body-fixed)

mm z-component of residual translational joint deflection



torque x (body-fixed) Nm x-component of friction torque in body-fixed

co-ordinates of first body (replaced byBF element plot

output, if this element is used)

torque y (body-fixed) Nm y-component of friction torque in body-fixed



torque z (body-fixed) Nm z-component of friction torque in body-fixed



9.6 BF Ball Joint Friction Subsystem

The ball joint friction element calculates a ball joint’s anisotropic friction torque, provided the ball joint’s vector-

valued constraint force is known.

Withincosin/mbs, this element cannot be invoked directly, as multi-body force element, but rather serves as

optionalsubsystem of the ball joint bearing element (BJ).

The ball joint friction model has two levels of detail, calledsimple and detailed ball joint friction model. The

selection is controlled by the data itemnumber_rings. Only if specified and greater or equal to 1, the detailed

ball joint friction model will be used.

9.6.1 Simple Ball Joint Friction Model

The simple model is composed of three different friction elements for rotation about the joint-fixed longitudinal,

lateral, and vertical axis. Each single friction element can either be a simple sliding friction characteristic, or may

consist of a series connection of a dry friction characteristic and a linear spring. The selection among these two

simple model alternatives is made with data itemfriction_model.

The overall vector-valued friction torque is computed by vector-wise summing up the products of local friction

forces and ball radius. The friction forces in turn are determined as a function of local sliding velocity, and local

normal force between ball and housing surface. The normal force consists of the respective component of the

joint’s constraint force, together with an optional preload force.

The three directional-dependent friction characteristics are shaped by specifying three data points each, denoted

with

• adhesion friction (‘stiction’)

• maximum friction


• sliding friction

see figure 1. The friction characteristics are piecewise linearly interpolated between the respective three data

points, like shown in figure8.

Figure 8: BFfriction characteristic data points and approximation

If extrapolation is necessary (that is, if sliding velocities larger thanvsliding occur),µsliding will be used as friction

coefficient.

The vector-wise summing of the friction torque components is performed in such a way that the torque vector is

exactly anti-parallel to the relative angular velocity vector, if the friction characteristics are isotropic:

Tfriction,x = −Ñx

Ñ

.rball.Fxfriction (νsliding,x, Fn,x)

Tfriction,y = −Ñy

Ñ

.rball.Fyfriction (νsliding,y , Fn,y)

Tfriction,z = −Ñz

Ñ

.rball.Fzfriction (νsliding,z , Fn,z)

(1)

where

νsliding = rball.Ñ

The effective normal force is determined to be the respective component of the integrated normal contact pressure.

Here, for simplicity, it is assumed that both the ball and the housing surfaces are geometrical ideal spheres:

Fn,x = max(

Fpreload,2

3

√

F 2constr,y + F 2

constr,z +1

6Fconstr,x

)

Fn,y = max(

Fpreload,2

3

√

F 2constr,x + F 2

constr,z +1

6Fconstr,y

)

Fn,z = max(

Fpreload,2

3

√

F 2constr,x + F 2

constr,y +1

6Fconstr,z

)

(2)

Note that all vector computations listed above are carried out in the joint-fixed coordinate system. If the dynamic

model variant is activated,F friction does not just depend on sliding velocity and normal force in a steady-state

manner. Rather, this is a dynamic dependency, modeled by using a state variable to take into account the

momentary elongation of the spring in series.

Element data (simple model)


Table 51: BF element data, simple model

ball_diameter mm f(m) ball diameter

max_friction_velocity ms

f sliding velocity at which friction coefficients

have maximum value (same for all rotation

directions).

Default value is (nearly) zero

sliding_velocity ms

f sliding velocity at which sliding friction

coefficients are measured (same for all rotation

directions). Default value is (nearly) infinity

One of (m):mu_adhesion - f adhesion friction (‘stiction’) coefficient,

effective if ball joint housing is rotated relative

to ball about the joint-fixed longitudinal axis

mu_adhesion_

about_long_

axis

- f stiction coefficient, effective if ball joint

housing is rotated relative to ball about the

joint-fixed longitudinal axis

mu_max_about_long_axis - f maximum friction coefficient, effective if ball

joint housing is rotated relative to ball about

the joint-fixed longitudinal axis. Default value

ismu_adhesion_about_long_axis

mu_sliding_about_long_axis - f maximum friction coefficient, effective if ball


the joint-fixed longitudinal axis.

Default value ismu_max_about_long_axis

mu_adhesion_about_lat_axis - f stiction coefficient, effective if ball joint


joint-fixed lateral axis.

Default value


mu_max_about_lat_axis - f maximum friction coefficient, effective if ball


the joint-fixed lateral axis.

Default value ismu_max_about_long_axis

mu_sliding_about_lat_axis - f sliding friction coefficient, effective if ball joint


joint-fixed lateral axis.

Default value

ismu_sliding_about_long_axis

mu_adhesion_about_vert_axis - f stiction coefficient, effective if ball joint


joint-fixed vertical axis.

Default value



eff_Youngs_modulus_contact GPa f(m) to control both normal and shear stiffness

between ball and housing surface. In case both

ball and housing surface consist of the same

material, and the ball housing wall thickness is

sufficiently large, this value is Young’s modulus

of the material. In case of different material

properties or a small housing wall thickness, the

value has to be determined by parameter

identification. Parameter is mandatory only

iffriction_model = 1

mu_max_about_vert_axis - f maximum friction coefficient, effective if ball


the joint-fixed vertical axis. Default value

ismu_max_about_long_axis

mu_sliding_about_vert_axis - f sliding friction coefficient, effective if ball joint


joint-fixed vertical axis.

Default value

ismu_sliding_about_long_axis

ball_surface_rel_damping s f quotient of effective surface damping to surface

stiffness between ball and housing.

Default value is 0

normal_force_preload N f lower bound for effective normal force, used in

friction force estimation.

Default value is 0

friction_model - i 0: use simplified pure sliding friction models for

all 3 directions of rotation

1: use dynamic friction models, consisting of

series connections of friction characteristics and

springs, for all 3 directions of rotation.

Default value is 0

Plot signals (simple model)


level 1

rel. ang. vel. x

(joint-fixed)

rads

x-component of angular velocity vector of ball housingrelative to ball, expressed in joint-fixed coordinate system

rel. ang. vel. y

(joint-fixed)

rads

y-component of angular velocity vector of ball housingrelative to ball, expressed in joint-fixed coordinate system

rel. ang. vel. z

(joint-fixed)

rads

z-component of angular velocity vector of ball housingrelative to ball, expressed in joint-fixed coordinate system

constraint force x

(joint-fixed)

N x-component of constraint force between ball and ballhousing, expressed in joint-fixed co-ordinate system

constraint force y

(joint-fixed)

N y-component of constraint force between ball and ballhousing, expressed in joint-fixed co-ordinate system

constraint force z

(joint-fixed)

N z-component of constraint force between ball and ballhousing, expressed in joint-fixed co-ordinate system

friction torque x

(joint-fixed)

Nm x-component of friction torque between ball and ball housing,expressed in joint-fixed co-ordinate system

friction torque y

(joint-fixed)

Nm y-component of friction torque between ball and ball housing,expressed in joint-fixed co-ordinate system

friction torque z

(joint-fixed)

Nm z-component of friction torque between ball and ball housing,expressed in joint-fixed co-ordinate system

Table 52: BFplot signals

9.6.2 Detailed Ball Joint Friction Model

The detailed model version accumulates the friction forces of a user-definable, usually large number of two-

dimensional friction elements (see figure9 for a typical discretization). These elements are distributed over the

ball surface as uniformly as possible.

Figure 9: BF friction nodes placement (here along 20 rings), ball top and bottom boundaries defined by anglesαmin

andαmax

In this model version, the normal force is estimated individually for each friction element. To this end, a fic-

tiveintrusion value between ball and housing, in the vicinity of the respective friction element, is computed. This


intrusion is a function of the housing and ball joint translational position, together with two-dimensionalradius

variation splines both for ball and housing surface. The normal force is either a linear or a non-linear function

of intrusion.

Ball and housing are subject to small elastic displacements, such that the vector-sum of all normal and friction

forces is in exactequilibrium to the constraint force. This condition, a consequence of the assumed negligible

ball mass, is solved using one up to three steps of a Newton-Raphson iteration. Each step requires the complete

update of all friction elements.

In a similar way as with the simple model, each single friction element of the detailed model in turn can either be a

simple sliding friction characteristic, or may consist of a series connection of a dry friction characteristic and a linear

spring. The selection among these two detailed model alternatives again is made with data itemfriction_model.

This model variant allows the precise specification of radius variations both for ball and/or housing surface.

This variation is defined in terms of 2D table data, describing the radius variation in micrometers as function of

azimuth and elevation angle. Using these specifications, ball friction anisotropies due towear can easily be taken

into account.

Together with the surface normal stiffness, defined by the effective Young’s modulus, anormal force preload

arises if ball radius is slightly larger than housing radius. Vice versa, there will be somefree play if ball radius is

slightly smaller than housing radius.

Element data (detailed model)

Table 53: BF element data, detailed model

number_rings - i(m) number of rings used for triangulating the ball surface.

The detailed model will be used if this parameter is

specified and greater or equal to 1

friction_model - i 0: use simplified pure sliding friction model for all

friction elements

1: use dynamic friction model, consisting of series

connections of friction characteristics and springs, for

all friction elements.

Default value is zero

number_displ_iterations - i number of Newton-Raphson iteration steps in every

time step, to compute force equilibrium.

Default value is 1

ball_diameter mm f(m) ball diameter

ball_start_angle deg f elevation angle of ball surface top boundary, measured

relative to vertical axis (see figure 2).

Default value: 0deg

ball_end_angle deg f elevation angle of ball surface bottom boundary,

measured relative to vertical axis (see figure 2).

Default value: 180deg

housing_start_angle deg f elevation angle of housing surface top boundary,


Default value: 0deg

housing_end_angle deg f elevation angle of housing surface bottom boundary,


Default value: 180deg


ball_radius_variation µm t2 optional 2D table data, defining ball radius variation

as function of azimuth (rows, ranging from 0 to

360deg) and elevation (columns, ranging from 0 to

180deg) angle.

Default: no radius variation

housing_radius_variation GPa f(m) optional 2D table data, defining housing radius

variation as function of azimuth (rows, ranging from 0

to 360deg) and elevation (columns, ranging from 0 to

180deg) angle.

Default: no radius variation

eff_Youngs_modulus_contact s f reference value to control both normal and shear

stiffness between ball and housing surface. In case

both ball and housing surface consist of the same

material, and the ball housing wall thickness is

sufficiently large, this value is Young’s modulus of the

material. In case of different material properties or a

small housing wall thickness, the value has to be

determined by parameter identification. Parameter is

mandatory only iffriction_model = 1

ball_surface_rel_damping ms

f quotient of effective surface damping to surface

stiffness between ball and housing.

Default value is 0

max_friction_velocity ms

f sliding velocity at which friction coefficient has

maximum value.

Default value is (nearly) zero

sliding_velocity - f(m) sliding velocity at which sliding friction coefficient is

measured.

Default value is (nearly) infinity

mu_adhesion - f adhesion friction (‘stiction’) coefficient

mu_max - f(m) maximum friction coefficient.

Default value ismu_adhesion

mu_sliding - f maximum friction coefficient.

Default value is mu_max

Animation model (detailed model)

In stand-alone simulations using thecosin/cb workbench, or from within Matlab/Simulink simulations, a de-

tailedanimation modelis provided, see figure10. This animation model shows the ball and housing surfaces,

completed with contour plots of one of the following variables:

• contact intrusion

• contact pressure

• x-component surface stress

• y-component surface stress

• z-component surface stress

• x-component sliding velocity


• y-component sliding velocity

• total sliding velocity.

As an alternative to these contour plots, vector-valued contact/friction forces of all surface nodes can be displayed.

Figure 10: BF ball joint friction animation model in stand-alone simulation usingcosin/cb

In addition, arrows indicating relative angular velocity and the resulting friction torque vector are shown.

The different contour plots or display modes can be toggled by repeatedly hitting the ‘c’ and/or ‘d’ key, or by

left-clicking the respective entry incosin/gl’s menu.

Plot signals (detailed model)

Table 54: BF plot signals, detailed model

level 1

rel. ang. vel. x

(joint-fixed)

rads

x-component of angular velocity vector of ball housing relative to

ball, expressed in joint-fixed coordinate system

rel. ang. vel. y

(joint-fixed)

rads

y-component of angular velocity vector of ball housing relative to


rel. ang. vel. z

(joint-fixed)

rads

z-component of angular velocity vector of ball housing relative to


constraint force x

(joint-fixed)

N x-component of constraint force between ball and ball housing,

expressed in joint-fixed co-ordinate system

constraint force y

(joint-fixed)

N y-component of constraint force between ball and ball housing,


constraint force z

(joint-fixed)

N z-component of constraint force between ball and ball housing,


friction torque x

(joint-fixed)

Nm x-component of friction torque between ball and ball housing,



friction torque y

(joint-fixed)

Nm y-component of friction torque between ball and ball housing,


friction torque z

(joint-fixed)

Nm z-component of friction torque between ball and ball housing,


level 2

Fx (iterated) N x-component of the total contact force. Only for diagnosis

purposes; should equal thex-component of the constraint force.

Increasenumber_displ_iterations, if not

Fy (iterated) N y-component of the total contact force. Only for diagnosis

purposes; should equal they-component of the constraint force.


Fz (iterated) N z-component of the total contact force. Only for diagnosis

purposes; should equal thez-component of the constraint force.


contact area % percentage of the ball surface, being in contact with the housing

surface

9.6.3 cosin/cb Stand-Alone Simulation Workbench

The ball joint friction model can be analyzed with acosin/io-based, convenient but simple stand-alone simulation

workbench. For further details, see the respective documentation.

9.7 BO Body

This element is either a rigid or a flexible body, depending on the contents of its data-block.cosin/mbs automatically

detects that. Every body, no matter whether it is rigid or flexible, can be defined with element typeBO instead

ofRB orFB.BO has exactly the same element definition asRB orFB, resp. (cf. the respective chapters below).

9.8 BR Brake System

The brake system model describes all parts of a vehicle’s braking system, using the brake pedal travel, the wheel

rotational angles, and the wheel speeds as input, and providing the non-negative maximum braking torques for

all wheels as output. The effective braking torques might differ in sign and might have smaller absolute values,

depending on the sign of the wheel speed. If a wheel is not blocked and rolling forward, maximum braking torque

and effective (‘actual’) braking torque will have the same value.

The brake pedal travel is normalized to the interval [0,1].

So far, the implemented brake model is only a place-holder for a more detailed one. The brake pedal travel is

input to a spline that calculates the brake pressure. In turn, brake pressure is multiplied by a transmission-ratio

factor to result in the sum of the braking torques of all four wheels. This braking torque is distributed to the front

and rear wheels, observing either a constant brake-balance factor or a braking torque dependent brake-balance

characteristic, resulting from the proportioning control valve (CVP) characteristic. The wheel braking torques can

be modulated by a wheel rotational angle dependent sinusoidal torque, describing the first harmonic of brake disk

thickness variations.


In addition to the main brake system, the operating travel of a hand-brake can be prescribed. This travel results

in additional braking torques, being determined by a gain factor, and by a front/rear distribution factor. The

hand-brake is especially useful in driving simulator applications.

The mechanical brake model is completed with interfaces to several ECUs:

• conventional ABS

• advanced ABS

• ESP (Electronic Stability Program), including ABS functionality

User-specific ECU controller software can be easily simulated together withcosin/mbs by observing certain inter-

facing definitions, and providing a DLL under Windows or a shared object under any of the Unix dialects. For

details about this interfacing, see chapter5.

Equally well, wheel braking torques and possibly a modification of the nominal engine torque can beexternally con-

trolled. This is done either by setting appropriatecosin/ss signals, or by coupling the Simulink variant ofcosin/mbs

with a separate Simulink subsystem. For details of the Simulink interface see chapter7.

For use as signal in ECU’s, the element puts out a signal called brake pedal stroke, which is the actual position

of the brake pedal in [%] instead of the normalized value that varies between 0 and 1.


Table 55: BR I/O signals and other element-specific data

l1 - st name of front left tire (TI element)

l2 st name of front right tire (TI element)

l3 - st name of rear left tire (TI element)

l4 - st name of rear right tire (TI element)

l5 - sig name of car-body (BO element). Only needed for ABS or ESP sub-system models

l6 - sig name of propulsion sub-system (PS element). Only needed for ESP sub-system

models

l7 - sig name of steering sub-system (SR orSC element). Only needed for ESP sub-system

models

i1 - sig normalizedbrake pedal operating travel with values between 0.0 and 1.0

i2 - sig normalizedhand brake handle operat-ing travel with values between 0.0 and 1.0

i3 - sig manually or externally controlledbrake pressure at front left wheel [bar]. This

signal will only be used ifcontroller is set toexternal

i4 - sig manually or externally controlledbrake pressure at front right wheel [bar]. This


i5 sig manually or externally controlledbrake pressure at rear left wheel [bar]. This


i6 - sig manually or externally controlledbrake pressure at rear right wheel [bar]. This


i7 - sig manually or externally controllednominal engine torque value [Nm]. This signal

will only be used in a linked PS element (vial6) ifcontroller is set toexternal

i8 - sig normalizedgas pedaloperating travel with values between 0.0 and 1.0 (only

needed for ESP sub-system models)

o1 - sig brake pedal stroke (100 timesi1) [%]

o2 - sig nominal brake pressure in brake master cylinder, without ABS modulation [bar]


Element data

Table 56: BR element data

brake_pedal_char_spline -,bar sd (m) nominal brake pressure as function of brake

pedal travel

brake_press_transm_ratio Nmbar

f (m) hydraulic/mechanic transmission-ratio:

total braking torque, divided by nomi-nal

brake pressure

One

of:

brake_balance_factor - f constant braking torque distribution factor

1.0 = only front wheels are braked

0.0 = only rear wheels are braked

Default: 0.5

brake_balance_spline Nm, - sd braking torque distribution spline as

function of total braking torque

FL_cyclic_irregularity %,deg f2 braking torque cyclic irregularity of front left

wheel, described by

1. the percentage of the amplitude with

respect to the braking torque mean

value, and

2. the wheel rotational angle where the

cyclic torque takes its maximum

FR_cyclic_irregularity %,deg f2 similar to FL_cyclic_irregularity, for front

right wheel

RL_cyclic_irregularity %,deg f2 similar to FL_cyclic_irregularity, for rear

left wheel

RR_cyclic_irregularity %,deg f2 similar to FL_cyclic_irregularity, for rear

right wheel

hand_brake_transm_ratio Nm f hand-brake transmission-ratio: total

hand-brake torque, divided by hand-brake

handle operating travel

hand_brake_balance_factor - f constant hand-brake torque distribution

factor

0.0 = only rear wheels are hand-braked

1.0 = only front wheels are hand-braked

Default: 0.0


controller - st type of brake controlling ECU: one out

ofnone, ABS, ABS_advanced, ESP,

external.

A separately compiled subsystem will be

coupled to the brake model, if name is

notnone orexternal. The ABS or ESP

controller puts out individual wheel brake

pressures as function of brake pedal stroke

and certain other signals. In the case of

ESP, this con-troller software is expected to

include the ABS functionality (see chapter4

for a complete description of the

interfacing).

If name isexternal, the brake system will

set the wheel brake pressures and the

nominal engine torque according to the

value of input signalsi3 toi7. These input

signals either can be manually set, or

controlled by a Simulink ECU model

Plot signals

Table 57: BR plot signals

level 1

brake pedal - normalized brake pedal operating travel

hand brake - normalized hand brake handle operating travel

nominal brake pressure bar nominal brake pressure in brake master cylinder, without

ABS modulation

level 2

brake torque FL Nm max. non-negative braking torque at front left wheel

brake torque FR Nm max. non-negative braking torque at front right wheel

brake torque RL Nm max. non-negative braking torque at rear left wheel

brake torque RR Nm max. non-negative braking torque at rear right wheel

9.9 CJ Cardan (Hooke) Joint

This element connects two bodies with a cardan (sometimes called universal) joint. The degrees of freedom of

the bodies are constrained respectively.

This element will automatically use the stiff attribute, no matter whether or not this attribute is specified in the



l1 - st name of first body (RB,FB, orBO element) connected by revolute jointl2 - st name of second body (RB,FB, orBO element) connected by revolute joint

Table 58: CJ I/O signals and other element-specific data


Element data

x x x xx x x xx x x xx x x x

Table 59: CJ element data

Table 60: CJ plot signals

level 1

x x x

level 2

x x x

9.10 CS Conceptual Suspension

The conceptual suspension element imports a so-called ’.scf-file’, used and documented in other vehicle dynamics

simulation software. This file describes important elasto-kinematic properties of a suspension in terms of general

functional dependencies, without specifying the underlying detailed mechanics.

A conceptual suspension is implemented as very general force element coupling car-body and left and right

wheel-carriers. The conceptual suspension takes vertical wheel travel, steering angle, and tire forces/moments to

calculate, among others, elasto-kinematic toe and camber changes. These values define nominal wheel position

values. Any difference between nominal and actual wheel position leads to stiff restoring forces. For that reason,

it is highly recommended to use attributestiff for the CS element.


Table 61: CS I/O signals and other element-specific data

l1 - st name of left wheel-carrier (RB,FB, orBO element)

l2 - st name of right wheel-carrier (RB,FB, orBO element)

l3 - st name of car-body (RB,FB, orBO element)

l4 - st (m) name of left tire (TI element)

l5 - st (m) name of right tire (TI element)

i1 - sig normalized rotationangle of the steering pinion in [rad].

Only taken as external input, if no conceptual suspension steering (SC element) is

linked to theCS element

i2 - sig angular velocity of the steering pinion in [ rads

].

Only taken as external input, if no conceptual suspension steering (SC element) is

linked to theCS element

o1 - sig reaction torque acting on steering pinion [Nm]

o2 - sig partial derivative of pinion reaction torque with respect to pinion rotation

angle [Nmrad

]

o3 - sig left wheel elasto-kin. longitudinal displacement (‘wheel-base change’) [m]

o4 - sig left wheel elasto-kin. lateral displacement (‘track width change’) [m]

Remark: this isnot track width w.r.t. road contact point, but w.r.t. wheel center


o5 - sig left wheel elasto-kin. camber angle change [rad]

o6 - sig left wheel elasto-kin. caster angle change [rad]

o7 - sig left wheel elasto-kin. toe angle change [rad]

o8 - sig right wheel elasto-kin. longitudinal displacement (‘wheel-base change’) [m]

o9 - sig right wheel elasto-kin. lateral displacement (‘track width change’).Remark: this

isnot track width w.r.t. road contact point, but w.r.t. wheel center

o10 - sig right wheel elasto-kin. camber angle change [rad]

o11 - sig right wheel elasto-kin. caster angle change [rad]

o12 - sig right wheel elasto-kin. toe angle change [rad]

Element data

Table 62: CS element data

scf_file fi name of .scf file to be used. Detailed format

and contents of the .scf file is documented

elsewhere. .scf-files are imported tocosin/mbs,

and so their format differs fromcosin/io.

.scf-files describe the position and orientation

of both wheels as function

• of the kinematic degrees of freedom,

• of forces and moments induced by the

tire.

Furthermore, they define forces introduced by

the torsion stabilizer (‘anti-roll-bar’), as well as

the kinematics of spring and damper motion

point_of_ref_left_wheel mm m point fixed to left wheel-carrier, the kinematic

motion of which is described by the .scf-file.

Default: geometrical wheel center, if defined;

wheel center of gravity else

point_of_ref_right_wheel mm m point fixed to right wheel-carrier, the kinematic

motion of which is described by the .scf-file.

Default: geometrical wheel center, if defined;

wheel center of gravity else

One of:left_spring_stiffness N

mmf left spring stiffness (spring deflection is

calculated using ‘spring motion’ information in

.scf file)

left_spring_spline mm,N sd left spring characteristics (spring deflection is


.scf file)

One of:right_spring_stiffness N

mmf right spring stiffness (spring deflection is


.scf file)


right_spring_spline mm,N sd right spring characteristics (spring deflection is


.scf file)

left_preload N f left spring preload (cf. .scf-file docu.)

right_preload N f right spring preload (cf. .scf-file docu.)

One of:left_damper_coeff Ns

mf left damper coefficient (damper deflection

velocity is calculated using ’damper motion’

information in .scf file)

left_damper_spline mm,N sd left damper characteristic (positive deflection

velocity and positive force for bump, negative

for rebound). Friction and gas force not

included .Damper deflection velocity is

calculated using ‘damper motion’ information

in .scf- file

One of:right_spring_stiffness N

mmf right damper coefficient (damper deflection

velocity is calculated using ‘damper motion’

information in .scf file)

right_spring_spline mm,N sd right damper characteristic (positive deflection



included .Damper deflection velocity is

calculated using ‘damper motion’ information

in .scf- file

left_gas_force N f left damper constant gas force

right_gas_force N f right damper constant gas force

Animation models

Table 63: CS animation models

ball_joint

ball_diameter mm f diameter of the outer ball (the two balls mark the actual position of

the kinematic point of reference, together with its elasto-kinematic

displacement)

cylindrical_joint

cylinder_diameter mm f diameter of the outer cylinder (the two cylinders mark the actual

position and orientation of the kinematic point of reference,

together with its elasto-kinematic displacement)

cylinder_length mm f length of the outer diameter

Plot signals

Table 64: CS plot signals

level 1

left wheel travel mm left wheel travel (vertical wheel center

displacement)


left kinematic camber angle deg left wheel camber angle change due to wheel

kinematics

left kinematic toe angle deg left wheel toe angle change due to wheel

kinematics

left elasto-kin. camber angle deg left wheel camber angle change due to wh.

compliance

left elasto-kin. toe angle deg left wheel toe angle change due to wheel

compliance

right wheel travel mm right wheel travel (vertical wheel center

displacement)

right kinematic camber angle deg right wheel camber angle change due to wheel

kinem.

right kinematic toe angle deg right wheel toe angle change due to wheel

kinematics

right elasto-kin. camber angle deg right wheel camber angle change due to wheel

compliance

right elasto-kin. toe angle deg right wheel toe angle change due to wheel

compliance

left suspension spring defl. mm left suspension spring deflection

left suspension damper velocity ms

left suspension damper deflection velocity

left suspension spring force N left suspension spring force

left suspension damper force N left suspension damper force, including gas

force and damper friction

left anti-roll bar force N vertical force on left wheel, induced by anti-roll

bar

right suspension spring defl. mm right suspension spring deflection

right suspension damper velocity ms

right suspension damper deflection velocity

right suspension spring force N right suspension spring force

right suspension damper force N right suspension damper force, including gas

force and damper friction

right anti-roll bar force N vertical force on right wheel, induced by

anti-roll bar

level 2

pinion rotation angle deg rotation angle of steering pinion

left kinematic base change mm left wheel base change due to wheel kinematics

left kinematic track change mm left wheel track width change w.r.t. wheel

center, due to wheel kinematics

left kinematic caster angle deg left wheel caster angle change due to wheel

kinematics

left elasto-kin. base change mm left wheel base change due to wheel compliance

left elasto-kin. track change mm left wheel track width change w.r.t. wheel

center, due to wheel compliance

left elasto-kin. caster angle deg left wheel caster angle change due to wheel

compliance


right kinematic base change mm right wheel base change due to wheel

kinematics

right kinematic track change mm right wheel track width change w.r.t. wheel

center, due to wheel kinematics

right kinematic caster angle deg right wheel caster angle change due to wheel

kinematics

right elasto-kin. base change mm right wheel base change due to wheel

compliance

right elasto-kin. track change mm right wheel track width change w.r.t. wheel

center, due to wheel compliance

right elasto-kin. caster angle deg right wheel caster angle change due to wheel

compliance

kinematics extrapolated 0 or 1 flag that indicates extrapolation (=1) of

kinematic characteristics read from .csf-file, in

actual operating point

compliance extrapolated 0 or 1 flag that indicates extrapolation (=1) of

compliance characteristics read from .csf-file, in

actual operating point

forces extrapolated 0 or 1 flag that indicates extrapolation (=1) of

anti-roll-bar (torsion stabilizer) forces read from

.csf-file, in actual operating point

9.11 DI Distance Sensor

This element computes distance and distance velocity between two markers on two different bodies. In conjunction

with the IF (Internal Force) element, it can be used to construct multiple degrees-of-freedom actively controlled

motion systems. This can be done more generally than by only using the AC (User-Written Hydraulic Actuator)

element. Note that distance velocity sign is opposite to the deflection velocity sign in SD and AC elements:

increasing deflection means decreasing distance.


l1 - st name of first body (RB,FB, orBO element) distance is to be calculated for

i1 - st name of second body (RB,FB, orBO element) distance is to be calculated fori2 - sig distance [mm]i3 - sig distance velocity [m

s]

Table 65: DI I/O signals and other element-specific data

marker1_on_body_1 mm m (m) marker on body 1 (first end point for distancecalculation)

marker2_on_body_2 mm m (m) marker on body 2 (second end point fordistance calculation)

Table 66: DI element data

Animation models


lineno additional data

Table 67: DI animation models

Plot signals

level 1distance mm actual distance of the two markersdistance vel. m

sactual distance velocity of the two markers

Table 68: DI plot signals

9.12 DS Damper Strut Assembly

The damper strut assembly model describes all those forces of a damper strut that are induced into the car-body

via the damper bearing. The calculation of these forces takes into account

• the damper characteristic

• the damper gas force and dry friction, the latter depending on the lateral or longitudinal force in the damper

bearing

• the elastic damper bearing characteristic, optionally modeled as a hydro-mount

• the damper bump-and-rebound stop characteristic

• the bending of the damper piston under lateral or longitudinal forces, where the bending stiffness depends

on the damper deflection

• the coil spring stiffness (in the case of a spring strut type suspension)

• preloads of coil spring and damper bearing.


l1 - st name of car-body (RB,FB, orBO element)l2 - st name of wheel-carrier (RB,FB, orBO element)

i1..i3 - sig x/y/z-components ofextra body-fixeddisplacement of damper topbearing position [mm]

i4 - sig additional, actively actuatedspringelongation [mm]i5 - sig additional spring preload [N ]i6 - sig spring stiffness modification percentage [%]i7 - sig damper coefficient modification percentage [%]

o1 - sig suspension spring force [N ]

Table 69: DS I/O signals and other element-specific data

Element data

Table 70: DS element data

pos_damper_bearing mm m (m) elastic center of damper top bearing


pos_damper_bottom mm m (m) position of an arbitrary point on the damper

middle axis near the bottom of the damper.

This marker serves only to calculate the

damper axis in reference position

pos_spring_bottom mm m (m) geometric center of the lowest coil of the spring

(if present). Together with the body-fixed

damper-bearing position, this hub-carrier-fixed

marker serves to determine the actual length of

the coil spring and the direction of the spring

force

One

of:

spring_stiffn Nmm

f coil spring stiffness

spring_spline mm,N sd coil spring characteristic (positive deflection

values mean compression; deflection and force

normally have the same sign)

spring_preload N f static preload force of coil spring in reference

position. If data-blockpreloads is present, this

value is overridden with the respective value of

this data-block

rad_bearing_stiffn_

spline

mm,N sd characteristic of the damper top bearing in

directions perpendicular to the damper axis

One

of:

(m)

ax_bearing_

stiffn_spline

mm,N sd characteristic of the damper top bearing in

damper axis direction

ax_hydromount mo hydro-mount model of the damper top bearing

elasticity in damper axis direction

ax_bearing_damping Nsm

f damping coefficient of the damper top bearing

in damper axis direction

rad_bearing_damping Nsm

f damping coefficient of the damper top bearing

in direction perpendicular to damper axis

bearing_preloads N f3 static bearing preload forces in bearing-

fixedx/y/z direction. If data-blockpreloads is

present, these values are overridden with the

respective values of this data-block

damper_spline ms,N sd (m) damper characteristic (positive deflection



included

gas_force N f constant damper gas force

min_friction_force N f damper friction force for zero lateral and

longitudinal force

sliding_friction_

coeff

− f describes damper friction force due to lateral or

longitudinal force in terms of a constant

friction coefficient

piston_rod_length mm f overall length of the damper piston rod (needed

to calculate the piston bending stiffness)


cylinder_length mm f overall length of the damper housing (needed to

calculate the overall damper bending stiffness)

piston_immersion_

length

mm f length of piston between the two sealings, in

reference position

piston_rod_diameter mm f piston rod diameter, needed to calculate piston

rod bending stiffness

piston_rod_wall

_thickness

mm f piston rod wall thickness (if hollow; else half

diameter), needed to calculate piston rod

bending stiffness

cylinder_inner

_diameter

mm f damper housing inner diameter, needed to

calculate piston bending stiffness. In the case

of a double-tube damper, this is the inner

diameter of the inner tube

cylinder_wall

_thickness

mm f damper housing wall thickness, needed to

calculate piston bending stiffness. In the case

of a double-tube damper, this is the wall

thickness of the inner tube

outer_tube_inner

_diameter

mm f if this (or the next) parameter is defined, the

damper is modeled as a double-tube damper.

In that case, the parameter gives the inner

diameter of the outer tube

outer_tube_wall

_thickness

mm f if this (or the preceding) parameter is defined,

the damper is modeled as a double-tube

damper. In that case, the parameter gives the

wall thickness of the outer tube

bump_rebound_stop

_spline

mm,N sd damper bump-and-rebound stop characteristic;

calculates forces due to bump-and-rebound

stop as function of damper deflection relative

to reference position. Any further share of the

damper force, that is dependent on damper

deflection only, should be included in this spline

Animation models

(standard: the damper or spring strut is displayed by a damper and a coil spring, resp., withthe appropriate position, orientation, and deflection)wire_diameter mm f diameter of coil spring wire. Coil spring is only shown if

spring stiffness is not negligible (default 10mm)coil_diameter mm f Diameter of one coil (default 100mm)number_of_coils − i number of coils (default 10)cylinder_length mm f damper housing length to be drawn (default 500mm)piston_rod length mm f max. damper piston rod length to be drawn (default 500mm)cylinder_diameter mm f cylinder outer diameter to be drawnpiston_rod_diameter mm f piston rod diameter to be drawn

Table 71: DS animation models

Plot signals

(if hydro-mount model is included, see also hydro-mount subsystem chapter for additional plot signals)


level 1spring deflection mm spring deflection (signal is only provided if strut is

equipped with a coil spring)spring force N spring force (signal is only provided if strut is

equipped with a coil spring)damper deflection vel. m

sdamper deflection velocity

damper force N damper force in axial directionaxial bearing deflection mm axial damper strut bearing deflectionaxial bearing force N axial damper strut bearing force

level 2long. bearing deflection mm longitudinal damper strut bearing deflectionlat. bearing deflection mm lateral damper strut bearing deflectionlong. bearing force N drive torque at rear left wheellat. bearing force N drive torque at rear right wheeldamper friction force N damper friction force in damper deflection directiondamper friction torque Nm friction torque about damper axisbump & rebound stop force N bump & rebound stop force

Table 72: DS plot signals

9.13 DT Drive Torques

The drive torques element is a simple replacement of the more detailed propulsion system element, providing the

drive torques for all wheels, as output, as a function of the gas pedal travel as input.

The gas pedal travel is normalized to the interval [0,1].

The gas pedal travel is multiplied by a constant factor, resulting in the sum of the drive torques of all four wheels.

This drive torque is distributed to the front and rear wheels, observing a constant propulsion power fraction factor.


l1 - st name of front left tire (TIelement)l2 - st name of front right tire (TI element)l3 - st name of rear left tire (TI element)l4 - st name of rear right tire (TI element)

i1 - sig normalizedgas pedal operating travel, with values between0.0and1.0

o1 - sig drive torque front left wheel[Nm]o2 - sig drive torque front right wheel[Nm]o3 - sig drive torque rear left wheel[Nm]o4 - sig drive torque rear right wheel[Nm]

Table 73: DT I/O signals and other element-specific data

Element data

gas_pedal_transm_ratio Nm m (m) transmission ratio of normalized gas pedaltravel to total driving torque

propulsion_power_fraction − m (m) constant driving torque distribution factor.1.0 = front wheel drive0.5 = all wheel drive with equal torque distr.0.0 = rear wheel driveDefault: 1.0

Table 74: DT element data


Plot signals

level 1gas pedal - normalized gas pedal operating travel

level 2drive torque FL Nm drive torque at front left wheeldrive torque FR Nm drive torque at front right wheeldrive torque RL Nm drive torque at rear left wheeldrive torque RR Nm drive torque at rear right wheel

Table 75: DT plot signals

9.14 EF External Force

This element allows defining arbitrary, time and/or event-dependent external forces that act on a prescribed

rigid or flexible body. The input signals are the three components of the external force, described in body-fixed

coordinates. This vector-valued force acts on the body in a prescribed, body-fixed point of attack. This point

can be optionally shifted in body-fixed coordinates, using three more input signals.


l1 - st name of body (RB,FB, orBO element) external force acts on

i1 - sig x-component ofexternal forcein body-fixed coordinatesi2 - sig y-component ofexternal forcein body-fixed coordinatesi3 - sig z-component ofexternal forcein body-fixed coordinatesi4 sig x-component of additionalshift of point of attack in body-fixed

coordinatesi5 sig y-component of additionalshift of point of attack in body-fixed

coordinatesi6 sig z-component of additionalshift of point of attack in body-fixed

coordinates

Table 76: EF I/O signals and other element-specific data

Element data

point_of_attack mm m body-fixed point of attack

Table 77: EF element data

Plot signals

level 1body-fixed force [1] N x-component of applied force in body-fixed coordinatesbody-fixed force [2] N y-component of applied force in body-fixed coordinatesbody-fixed force [3] N z-component of applied force in body-fixed coordinatesbody-fixed point of attack

[1]

mm x-component of point of attack in body-fixed coordinates

body-fixed point of attack

[2]

mm y-component of point of attack in body-fixed coordinates

body-fixed point of attack

[3]

mm z-component of point of attack in body-fixed coordinates

Table 78: EF plot signals


9.15 ET External Torque

This element allows to define arbitrary, time and/or event-dependent external torques that act on a prescribed

rigid or flexible body. The input signals are the three components of the external torque, described in body-fixed

coordinates. This element doesn’t need any further element data.


l1 - st name of body (RB,FB, orBO element) external torque acts on

i1 - sig x-component ofexternal momentin body-fixed coordinatesi2 - sig y-component ofexternal momentin body-fixed coordinatesi3 - sig z-component ofexternal momentin body-fixed coordinates

Table 79: ET I/O signals and other element-specific data

Plot signals

level 1body-fixed torque[1] Nm x-component of applied torque in body-fixed coordinatesbody-fixed torque[2] Nm y-component of applied torque in body-fixed coordinatesbody-fixed torque[3] Nm z-component of applied torque in body-fixed coordinates

Table 80: ET plot signals

9.16 FB Flexible Body

This element can be used instead of a rigid body. Its internal flexibility is defined by astiffness matrix. This

matrix is normally imported as result of a preceding FE (Finite Element) static condensation analysis. After

having read and pre-processed the stiffness matrix,cosin/mbs splits the flexible body into several sub-bodies, each

having one of the recognized FE node as center of gravity. The nodes themselves need not to be entered, but are

automatically reconstructed bycosin/mbs, using the ‘rigid-body condition’ of the stiffness matrix. That condition

is the consequence of the assumed kind of FE modelization:cosin/mbs considers the FE model to be free, which

means not connected by any element whatsoever to ground.

cosin/mbs will put out an error message, if either

• the stiffness matrix isnot symmetric (a certain tolerance is allowed), or

• the stiffness matrix isindefinite (again, a certain tolerance is allowed), or

• the system matrix apparently does not observe the‘rigid-body’ condition, or

• the body cannot be split into sub-bodies with allpositive definite inertia tensors.

The stiffness matrix is internally taken into account by defining appropriate force elements between each pair of

sub-bodies. These force elements are integrated stiffly, if the flexible body itself is given the attribute ‘stiff’.

For anycosin/mbs element that is linked to a flexible body,cosin/mbs will link that element to a certain sub-body

of the flexible body. To this end, that sub-body is chosen, the center of gravity of which lies closest to the linked

element.

cosin/mbs considers any rigid body to be nothing but a special case of a flexible body. Instead ofFB orRB, resp.,

the element typeBO can be used for both.cosin/mbs recognizes the actual type of a body by inspecting the contents

of its data-block. The data-block of a flexible body is a super-set of a rigid-body data-block. Rigid-body data


are used to get the mass geometry of the flexible body, which is to be split into the sub-bodies’ mass geometries.

For the meaning of that rigid-body data, see the rigid-body chapter. Here, only the additional data are described,

that can be entered to define stiffness and damping properties of the flexible body.

I/O signals and other element-specific data in the element definition block in addition to rigid-body

data: None.

Element data in addition to rigid-body data

FEM_file st (m) name of file that contains the stiffness matrix.The format is automatically recognized. At themoment,cosin/mbsonly recognizes NASTRAN‘punch files’

Oneof:(m)

fem_node_i

(i=1,..,99)

i coordinates (incosin/mbs units) ofone of theFE nodes (number 1or 2or 3 ..). Thisinformation is used to locate all flexible bodynodes relative to the body-fixed frame.

shift_geom_ct_

to_point_of_ref

flag if that flag is set, all nodes are shifted suchthat the geometrical center of the flexible bodycoincides with its center of gravity

coord_system_FEM_data i coordinate system of FE data:0 axis direction as incosin/mbs (ISO 8855)1x-axis rearward,y-axis to the right,y-axisupward (SAE)

length_unit_FEM_data i length unit of FE data: 0 = m, 1 =mmcorr_factor_FEM_stiffn_matrix f a factor the stiffness matrix is to be multiplied

with. That factor can be used to convenientlystudy the principle influence of flexibility,without providing several stiffness matrices

factor_FEM_damping_matrix f a factor the stiffness matrix is to be multipliedwith, to result in the damping matrix. Notethat in the presentcosin/mbs version thedamping matrix is always a certain multiple ofthe stiffness matrix (or zero)

Table 81: FB element data

Animation models other than that of rigid bodies

auto

for every sub-body, a brick is generated, the size and orientation of which resembles the mass and theinertia tensor of the sub-body, if density is constant. Furthermore, all sub-bodies are connected withstraight lines

Table 82: FBanimation models

Plot signals in addition to rigid bodies

(all signals are provided for all sub-bodies of the flexible body. The sub-body number appears as label prefix of

the respective plot signal)


level 1defl. x mm x-component of the sub-body’s displacement relative to the flexible-body

reference frame.defl. y mm y-component of the sub-body’s displacement relative to the flexible-body

reference frame.defl. z mm z-component of the sub-body’s displacement relative to the flexible-body

reference frame.

level 2ang. defl. x deg x-component of the sub-body’s angular displacement relative to the flexible-body

reference frameang. defl. y deg y-component of the sub-body’s angular displacement relative to the flexible-body

reference frameang. defl. z deg z-component of the sub-body’s angular displacement relative to the flexible-body

reference frame

Table 83: FBplot signals

9.17 HM Hydro-Mount Subsystem

This element cannot be directly invoked as multi-body force element, but rather serves as optionalsubsystem of

the general bearing element (BE), the damper strut element (DS), and the general spring-damper element (SD).

The hydro-mount model comprises a structurally simple, but highly nonlinear physically oriented model approach

of a hydro-mount. It is valid in frequency domain up to about 30Hz.

Figure 11: HMhydro-mount model

The model consists of

• a resilient fluid volume, the elasticity of which is described by spring stiffnessesk1 andk2 (the fluid itself is

considered to be incompressible)

• a fluid massm, moving with velocityw = A1/A2 · u − v, whereA1 andA2 are the cross-sectional areas of

fluid chamber and fluid channel, respectively,

• springsk3 andk4, describing the rubber elasticity of upper and lower part of the hydro-mount,

• a damperd , approximately describing the energy dissipation caused by fluid viscosity, producing a force

dependent on the flow rate in the fluid channel. The flow rate equals the velocity of the fluid mass, which

in turn is proportional tou−v. For this reason, the damper can be thought of to be located as shown in

figure11.

The inertia forces of rubber and fluid when moving inx1−x2 direction are neglected. The equations of motion

inx1−x2 direction then read


mw = A1∆p

A1∆p+ k1 · (u− x1) + d · (u− v) = 0

A1∆p+ k2 · (x2 − v) + d · (u− v) = 0.

Combining the last two equations, one gets

(k1 + k2)·A1∆p+ k1k2 · (u− v + x2 − x1) + (k1 + k2) · d · (u−v) = 0,

that is, using the abbreviationsz = u− v and∆x = x1 − x2,

m

(

A1

A2

)2

z =k1k2

k1 + k2· (∆x− z)− dz (3)

The reaction forces in the two linkage nodes are

F2 =k1k2

k1 + k2· (∆x− z) +

k3k4k3 + k4

∆x, F1 = −F2 (4)

Equation(3) can be interpreted as equation of motion of a series connection of a spring with stiffnessk = k1k2

k1+k2

(‘coupling spring’), a massm = m(

A1

A2

)2

(‘virtual mass’), and damperd, the latter being linked to ground:

Figure 12: HM representation of hydro-mount model as single-mass oscillator

The overall hydro-mount reaction forceFh(∆x, z) then is given by the sum of the ‘coupling spring force’k ·(∆x−z)

and the ‘support spring force’ks∆x, whereks = k3k4

k3+k4. The support spring is placed parallel to the single-mass

oscillator.

For sake of simplicity, the above equations are given only in the case of linear spring and damper characteristics.

Analogously, they also hold in the nonlinear case. Thecosin/mbs hydro-mount model optionally allows for general

table data, describing the characteristics of coupling spring, damper, and support spring.

To identify the parameters and characteristics of the hydro-mount model,cosin/idprovides a special fitting proce-

dure on the basis of measured dynamic stiffness characteristics, cf. separate documentation.

Element data


One of:(m)

stiffn_

support_

spring

Nmm

f stiffness of the support spring

support_

spring_

spline

mm,N sd stiffness characteristic of the supportspring

One of:(m)

stiffn_

coupl_

spring

Nmm

f stiffness of the coupling spring

coupl_

spring_

spline

mm,N sd stiffness characteristic of the couplingspring

One of:(m)

damper Ns,m f damper coefficient of the damper that isin-line with the coupling spring and thevirtual mass

damper_

spline

ms,N sd damper characteristic of the damper

that is in-line with the coupling springand the virtual mass

virtual_coupl_mass kg f (m) virtual mass (this virtual mass carries noweight)

play mm f play of the coupling spring = max.spring deflection with zero spring force

Table 84: HMelement data

Plot signals

level 1hydromount defl. mm change in distance between upper and lower point of

attachmenthydromount force at lower attach. N scalar hydro-mount force at lower point of attachment

Remark: due to inertia forces inside the hydro-mount,this force might dynamically differ from the negativeforce at the upper attachment point

hydromount force at upper attach. N scalar hydro-mount force at upper point of attachment

level 2hydromount couple-spring defl. mm deflection of the coupling springhydromount damper defl. vel. m

sdeflection velocity of damperd

hydromount support-spring force N scalar force in support springRemark: the support spring deflection coincides withthe total hydro-mount deflection, cf. above

hydromount couple-spring force N scalar force in coupling springhydromount damper force N scalar force in damper

Table 85: HMplot signals

9.18 IFInternal Force

This element allows to defining an arbitrary, time and/or event-dependent internal force that acts along a connec-

tion line between two prescribed rigid or flexible bodies. The sole input signal is this scalar internal force.

The internal force element can be used in conjunction with the distance sensor and the user-defined active

suspension control algorithm, to build active suspension models that simultaneously consider all four (or even

more) wheels.



l1 - st name of first body (RB,FB, orBOelement) force is acting onl2 - st name of second body (RB,FB, orBOelement) force is acting on

i1 - sig scalar force [N ]

o1 - sig x-component of internal force in body-fixed coordinates acting onfirst body [N ]o2 - sig y-component of internal force in body-fixed coordinates acting onfirstbody [N ]o3 - sig z-component of internal force in body-fixed coordinates acting onfirstbody [N ]o4 - sig x-component of internal force in body-fixed coordinates acting onsecond body [N ]o5 - sig y-component of internal force in body-fixed coordinates acting onsecondbody [N ]o6 - sig z-component of internal force in body-fixed coordinates acting onsecondbody [N ]

Table 86: IFI/O signals and other element-specific data

Element data

point_of_attack_body1 mm m (m) body-fixed point of attack of the internal force atbody 1

point_of_attack_body2 mm m (m) body-fixed point of attack of the internal force atbody 2

Table 87: IFelement data

Animation models

cylinder

cylinder_diameter mm f diameter of actuator housing (default 50mm)cylinder_length mm f length of actuator housing (default 500mm)piston_rod_diameter mm f diameter of actuator piston rod (default 10mm)piston_rod_length mm f length of actuator piston rod (default 500mm)

Table 88: IFanimation models

Plot signals

level 1force N scalar internal force

Table 89: IFplot signals

9.19 KC Kinematics&Compliance Output Signals

If activated, this element puts out important K&C-related signals for the left and right wheel of one axle.

The element is activated if theK&C analysis type (as defined in the data block $simulation of the sim-file;

documentation is repeated below for your convenience) is set to a non-zero value. The element will compute and

put out those signals that are meaningful with the respective analysis type.

Relevant data

in the$simulation data block of the sim-file


KC_analysis_type - i switch to select between normal simulation mode and certain specializedmodes for K&C (kinematics and compliance) analysis:0: standard mode, no K&C analysis (default)1: vertical wheel travel kinematics, friction and play disregarded2: steering kinematics, friction and play disregarded3: vertical wheel travel kinematics including friction and play4: steering kinematics including friction and play11: wheel compliance by external forces and/or moments, friction and playdisregarded12: wheel compliance by external forces and/or moments, includingfriction and play

Table 90: KCdata in$simulation data block of sim-file



l1 - st name of axle’s left tire element (TIelement)l2 - st name of axle’s right tire element (TI element)l3 - st name of axle’s rack&pinion steering element (SR, if any)l4 - st name of axle’s rack&pinion steering element (SR, if any)l5 - st name of axle’s right suspension spring element (SD orDS, if any)l6 - st name of axle’s left shock absorber element (SD orDS, if any)l7 - st name of axle’s right shock absorber element (SD orDS, if any)l8 - st name of car-body (RB,FB, orBO element)

o1 - sig wheel travel left wheel [mm]o2 - sig wheel travel right wheel [mm]o3 - sig steering rack displacement [mm]o4 - sig track width [mm]o5 - sig anti-dive left wheel [%]o6 - sig anti-dive right wheel [%]o7 - sig anti-lift left wheel [%]o8 - sig anti-lift right wheel [%]o9 - sig roll center height [mm]o10 - sig roll center lateral displacement [mm]o11 - sig camber angle left wheel [deg]o12 - sig camber angle right wheel [deg]o13 - sig toe-in angle left wheel [deg]o14 - sig toe-in angle right wheel [deg]o15 - sig toe difference angle [deg]o16 - sig Ackermann angle error [deg]o17 - sig caster angle left wheel [mm]o18 - sig caster angle right wheel [mm]o19 - sig kingpin inclination angle left wheel [mm]o20 - sig kingpin inclination angle right wheel [mm]o21 - sig caster offset left wheel [mm]o22 - sig caster offset right wheel [mm]o23 - sig scrub radius left wheel [mm]o24 - sig scrub radius right wheel [mm]o25 - sig caster offset at wheel center (longitudinal), left wheel [mm]o26 - sig caster offset at wheel center (longitudinal), right wheel [mm]o27 - sig caster offset at wheel center (lateral), left wheel [mm]o28 - sig caster offset at wheel center (lateral), right wheel [mm]o29 - sig caster offset at wheel center (total), left wheel [mm]o30 - sig caster offset at wheel center (total), right wheel [mm]o31 - sig spring suspension ratio left [mm]o32 - sig spring suspension ratio right [mm]o33 - sig damper suspension ratio left [mm]o34 - sig damper suspension ratio right [mm]

Table 91: KCI/O signals and other element-specific data

Element data

axis_location - i 0: front axle1: rear axle.Default value is 0

KC_wheel_base mm f assumed wheel-base, needed to compute certain wheel-basedependent output signals. Default value is 2500mm

KC_cg mm m assumed location of total vehicle’s center of gravity, needed tocompute cg-dependent output signals. Point of reference by default

Table 92: KCelement data


Plot signals

Table 93: KC plot signals

level 1

wheel travel left mm wheel travel left wheel

wheel travel right mm wheel travel right wheel

steering rack displacement mm steering rack displacement

track width mm track width

camber angle left deg camber angle left wheel

camber angle right deg camber angle right wheel

toe-in angle left deg toe-in angle left wheel

toe-in angle right deg toe-in angle right wheel

the following level 1 signals are only available,

if K&C analysis type is ‘vertical wheel travel’ (type 1 or 3)

anti-dive left % anti-dive left wheel

anti-dive right % anti-dive right wheel

anti-lift left % anti-lift left wheel

anti-lift right % anti-lift right wheel

roll center height mm roll center height

roll center lateral displ. m roll center lateral displacement

spring suspension ratio

left

- spring suspension ratio left wheel

spring suspension ratio

right

- spring suspension ratio right wheel

damper suspension ratio

left

- damper suspension ratio left wheel

damper suspension ratio

right

- damper suspension ratio right wheel

the following level 1 signals are only available,

if K&C analysis type is ‘steering’ (type 2 or 4)

toe difference angle deg toe difference angle

Ackermann angle error deg Ackermann angle error

caster angle left deg caster angle left wheel

caster angle right deg caster angle right wheel

kingpin inclination angle

left

mm kingpin inclination angle left wheel

kingpin inclination angle

right

mm kingpin inclination angle right wheel

caster offset left mm caster offset left wheel

caster offset right mm caster offset right wheel

scrub radius left mm scrub radius left wheel

scrub radius right mm scrub radius right wheel

caster offset at wh. cen.

(long.) left

mm longitudinal caster offset at wheel center,

left wheel


(long.) right

mm longitudinal caster offset at wheel center,

right wheel



(lat.) left

mm lateral caster offset at wheel center, left

wheel


(lat.) right

mm lateral caster offset at wheel center,

right wheel


(tot.) left

mm total caster offset at wheel center, left

wheel


(tot.) right

mm total caster offset at wheel center, right

wheel

level 2 None

9.20 MH Measuring Hub

This element calculates the forces and moments that will be sensored by a 6-channel measuring hub, measuringFx,Fy,Fz,Tx,Ty,Tz.

It is assumed that the force and moment transducers are applied in such a way that they separate the rotating

parts of the unsprung mass into two, the outer one being referred to in the sequel as ‘measuring wheel’. Mass

and moments of inertia of the tire are to be included in the measuring wheel.

The forces slightly differ from the tire forces that are put out by theTI element, because the inertia and gyroscopic

forces and moments of the measuring wheel are taken into account.

Forces and moments are put out in the wheel-carrier fixed co-ordinate system.


l1 - st name of body (RB,FB, orBO element) external force acts onl2 - st name of tire interface (TIelement)

o1 - sig longitudinal force as sensored by the hub [N ]o2 - sig side force as sensored by the hub [N ]o3 - sig wheel load as sensored by the hub [N ]o4 - sig overturning moment as sensored by the hub [Nm]o5 - sig torque about wheel spin axis, as sensored by the hub [Nm]o6 - sig aligning torque as sensored by the hub [Nm]

Table 94: MH I/O signals and other element-specific data

Element data

sensor_location mm m geometrical center of the formoment transducerremaining data exactly like RB element, defining the mass properties of the measuring wheel(that is, of all parts that are located outside the force transducers). Mass and moments ofinertia of the tire are to be included.

Table 95: MH element data

Plot signals


level 1meas. hub force signals [1] N longitudinal force as sensored by the hubmeas. hub force signals [2] N side force as sensored by the hubmeas. hub force signals [3] N wheel load as sensored by the hubmeas. hub moment signals [1] mm overturning moment as sensored by the hubmeas. hub moment signals [2] mm torque about wheel spin axis, as sensored by the hubmeas. hub moment signals [3] mm aligning torque as sensored by the hub

Table 96: MH plot signals

9.21 PS Propulsion System

This subsystem element describes several different types of a vehicle’s 2WD or 4WD propulsion system. It replaces

the trivial elementDT. The element covers all mechanical parts of the drive-train:

• engine torque as function of engine revs and throttle opening angle

• dry clutch

• transmission with up to 30 different transmission reductions for forward and reverse gears

• completely or partially lockable central differential (for 4WD assemblies)

• front and rear axle cardan shafts with elasticity and damping

• completely or partially lockable front axle differential

• completely or partially lockable rear axle differential

• torsional stiffness and damping properties of drive shafts (whereas drive-shaft kinematics and exact force &

moment transfer is taken into account in theTI element).

The transmission of the propulsion system element is being shifted manually, by actuating simultaneously throttle

opening angle, clutch pedal, and transmission lever. This can be done by a respective human driver model, or

alternatively by using theST (semi-automatic transmission) element. This element receives a nominal gear as

input, and, if necessary, shifts by appropriately actuating the above-mentioned controls.

The mechanical drive-train model is completed with interfaces to several ECUs:

• automatic 4WD select

• ATTS control (Automatic Torque Transfer System) for driven front wheels

• conventional LSD (Limited Slip Differential)

• Active LSD

• controlled 4WD locking differentials (CLD).



details about this interfacing, see chapter 4.

Equally well, the propulsion system can beexternally controlled. This is done either by setting appropriatecosin/ss

signals, or by coupling the Simulink variant ofcosin/mbs with separate Simulink subsystems. For details of the

Simulink interface see chapter 6.

Finally, if respective data are provided, this element will estimate the remaining fuel by integrating thefuel

consumptionrate, being a function of throttle opening and engine revs. Consumed fuel mass will be subtracted


from vehicle mass, oberserving location and change of center of gravity. If maximum and initial fuel levels are

specified, the vehicle’s total mass geometry is assumed to be specified withfullfuel tank. The mass difference to

initial fuel level will be automatically subtracted from the car-body’s initial mass geometry.


Table 97: PS I/O signals and other element-specific data

l1 - st name of front left tire (TIelement)

l2 - st name of front right tire (TIelement)

l3 - st name of rear left tire (TIelement)

l4 - st name of rear right tire (TIelement)

l5 - st name of car-body (BO element)

l6 - st name of engine/transmission assembly (BO element)

l7 - st name of steering sub-system (SR orSC element). Only needed for 4WD, ATTS,

or LSD sub-system models

l8 - st name of brake sub-system (BR element). Only needed for CLD sub-system model

i1 - sig throttle opening angle [deg]

i2 - sig normalizedclutch pedaloperating travel [0..1]

(0: clutch is completely released,

1: clutch is completely open)

i3 - sig selectedgear. Value will be correctly rounded to an integer value. Negative values stand

for reverse gears

i4 - sig ‘ignition on’and‘starter running’ flag

(0: ignition off,

1: ignition on, starter not running,

2: ignition on, starter running)

i5 - sig manually or externally controlled4WD select switch.

(0: 4WD switched off,

1: 4WD switched on).

This signal will only be used ifFWD_controlleris set toexternal_4WD

i6 - sig manually or externally controlledfront axle differential locking switch.

(0: differential not locked,

1: differential locked).

This signal will not be used, if differential is controlled by an LSD ECU

i7 - sig manually or externally controlledrear axle differential lockingswitch.



This signal will not be used, if differential is controlled by an LSD controller ECU

i8 - sig manually or externally controlledcentral differential locking switch.



This signal will not be used, if differential is controlled by an LSD controller ECU,

or if drive type is not any 4WD variant


i9 - sig manually or externally controlledfront wheels’ torque split factor (varies continuously

between 0 and 1.

0: full torque goes to right wheel,

1: full torque goes to left wheel).

This signal will only be used ifATTS_controlleris set toexternal_atts

i10 - sig manually or externally controlledlimited-slip maximum difference torque

(= locking torque)of front axle differential [Nm]. This signal will only be used if

LSD_controller is set toexternal_lsd

i11 - sig manually or externally controlled limited-slip maximum difference torque

(= locking torque)of rear axle differential[Nm]. This signal will only be used

ifLSD_controller is set toexternal_lsd

i12 - sig manually or externally controlledlimited-slip maximum difference torque

(= locking torque)of central differential [Nm]. This signal will only be used

ifLSD_controller is set toexternal_lsd

i13 - sig engine torque reduction percentage, typically controlled by a traction control system

o1 - sig throttle opening angle [deg]

o2 - sig engine revs [rpm]

o3 - sig engine torque [Nm]

o4 - sig drive torque front left wheel [Nm]

o5 - sig drive torque front right wheel [Nm]

o6 - sig drive torque rear left wheel[Nm]

o7 - sig drive torque rear right wheel [Nm]

o8 - sig fuel level[%]

Element data

Table 98: PS element data

engine_moment_of_inertia kgm2 f (m) mean moment of inertia of all running engine

parts, with respect to crankshaft rotation

engine_graph deg,rpm,Nmt2 (m) net engine torque as function of throttle opening

angle and engine revs

max_fuel_level ltr f fuel tank volume

initial_fuel_level ltr f initial fuel volume

fuel_cg_at_full_tank mm m center of gravity of fuel when tank is full

fuel_cg_at_nearly_empty_

tank

mm m center of gravity of fuel when tank is nearly empty

fuel_consumption_table deg,rpm,m,mlst2 fuel consumption rate in ml/s, depending on

throttle opening angle and engine revs

clutch_pedal_char_spline -,Nm sd (m) maximum friction torque in clutch as function of

normalized clutch pedal operating travel


autom_engine_speed_sync - i switch to choose whether automatic engine speed

control during de- clutching is to be performed. If

this switch is on ( = 1), engine speed will

automatically be controlled in such a way that

clutch slip is as close to zero as possible during a

gear change.

Default value is 0 ( = off)

clutch_pedal_at_sync_start - f normalized clutch pedal travel when automatic

engine speed synchronization begins (or ends,

respectively).

Default value is 0.05

transm_reductions - i1 (m)

.. i30

1 to 30 transmission reduction values. Reverse

gears have negative transmission reduction. At

present, at mostone reverse gear is possible

transm_moments_of_inertia kgm2 f2 (m) moments of inertia of transmission input- and

output shafts, including all respective gear wheels

that are fixed to the shaft.

Remark: by taking the actually engaged gear’s

transmission ratio, these two values are used to

estimate the total moment of inertia with respect

to input shaft rotation

gear_sync_time s f time span during which the transmission reduction

is continuously changed when gear changes.

Remark: this parameter approximates the

synchronization effect. It should be set to the

average time a driver needs to move gear-lever

from one position to the next

drive_type - i type of drive train:

0: front drive

1: rear drive

2: permanent 4WD

3: front drive, non-permanent 4WD

4: rear drive, non-permanent 4WD

(default 0 = front drive)

central_diff_transm_ratio - f transmission ratio of central differential. This

value ismandatory for any 4WD variant

central_diff_torque_split % f torque split modification percentage of central

differential (front axle torque share). This value is

optional and 50% by default

front_cardan_shaft_tors_

stiffn

Nmdeg

f torsional stiffness of front axle cardan shaft,

located between transmission (or central

differential) and front axle differential. This value

ismandatory, if front wheels are driven

front_cardan_shaft_tors_

damp

Nmsdeg

f torsional damping of front axle cardan shaft


front_axle_diff_transm_

ratio

- f transmission ratio of front axle differential. This

value ismandatory, if front wheels are driven

front_axle_diff_mom_of_

inertia

kgm2 f moment of inertia of rotating parts of front axle

differential, with respect to rotation of input shaft.

This value ismandatory, if front wheels are driven

front_drive_shafts_tors_

stiffn

Nmdeg

f torsional stiffness of front axle drive shafts, located

between differential and wheels. This value

ismandatory, if front wheels are driven

front_drive_shafts_tors_

damp

Nmsdeg

f torsional damping of front axle drive shafts,

located between differential and wheels

rear_cardan_shaft_tors_

stiffn

Nmdeg

f torsional stiffness of rear axle cardan shaft, located

between transmission (or central differential) and

rear axle differential. This value is mandatory, if

rear wheels are driven

rear_cardan_shaft_tors_

damp

Nmsdeg

f torsional damping of rear axle cardan shaft

rear_axle_diff_transm_

ratio

- f transmission ratio of rear axle differential. This

value ismandatory, if rear wheels are driven

rear_axle_diff_mom_of_

inertia

kgm2 f moment of inertia of rotating parts of rear axle

differential, with respect to rotation of input shaft.

This value is mandatory, if rear wheels are driven

rear_drive_shafts_tors_

stiffn

Nmdeg

f torsional stiffness of rear axle drive shafts, located

between differential and wheels. This value

ismandatory, if rear wheels are driven

rear_drive_shafts_tors_

damp

Nmsdeg

f torsional damping of rear axle drive shafts, located

between differential and wheels

starter_torque Nm f torque applied to crankshaft when starter is

running

FWD_controller - st type of 4WD controller ECU:none, or4WD,

orexternal_4WD. A separately compiled

subsystem will be coupled to the drive train model,

if name is4WD. The 4WD controller selects

activation of four-wheel drive. This is done on

basis of several sensor signals (see chapter 4 for a

complete description of the interfacing).

If name isexternal_4WD, the propulsion

subsystem will select four-wheel-drive according to

the value of input signali5. This input signal can

be used for manually selecting four-wheel-drive, or

for coupling to a Simulink ECU model


ATTS_controller - st type of ATTS (Active Torque Transfer System)

controller ECU:none, orATTS, orexternal_ATTS.

A separately compiled subsystem will be coupled to

the drive train model, if name isATTS. The ATTS

controller modifies the front axle torque split

between left and right wheel, if the differential is

not locked. This is done actively, on basis of

several sensor signals (see chapter 4 for a complete

description of the interfacing).

If name isexternal_ATTS, the propulsion

subsystem will set the front wheels’ torque-split

factor according to the value of input signal i9.

This input signal can be used for manually

choosing a torque-split factor, or for coupling to a

Simulink ECU model

LSD_controller - st type of LSD (Limited Slip Differential) controller

ECU: one out

ofnone,LSD,LSD_active,external_LSD,CLD. A

separately compiled subsystem will be coupled to

the drive train model, if name isLSD,LSD_active,

orCLD. An LSD ECU controls a partially lockable

differential in such a way that the difference in

output torque in the two output shafts is kept

under a certain maximum value. This is done

actively, on basis of several sensor signals (see

chapter 4 for a complete description of the

interfacing).

If name isexternal_LSD, the propulsion subsystem

will set the maximum torque difference according

to the value of input signali10. This input signal

can be used for manually choosing that torque, or

for coupling to a Simulink ECU model

local_time_steps - i number of local time steps to be used for

integration of drive-train (to improve numerical

stability and accuracy).

Default value is 100

Plot signals

Table 99: PS plot signals

level 1

throttle opening angle deg throttle opening angle

clutch pedal - normalized operating travel of clutch pedal

engaged gear - actually engaged gear (integer number, negative for reverse,

0 if no gear is engaged)

engine revs rpm engine revs: rotational speed of crankshaft


engine torque Nm net engine torque, resulting from combustion, after

subtracting all losses (cylinder friction, generator torque,

etc.) from engine and auxiliaries. Mean value during one

complete revolution

level 2

ignition on - ‘ignition on’ and ‘starter running’ indicator. Meaning exactly

as that of input signali4

fuel level ltr remaining fuel volume

clutch slip % clutch slip, non-negative if engine is driving

clutch torque Nm torque transmitted through clutch

transm. input shaft speed rpm rotational speed of transmission input shaft

transm. output shaft speed rpm rotational speed of transmission output

centr. diff. inp. shaft

speed

rpm rotational speed of transmission input shaft

central diff. max. torque

diff.

Nm max. possible difference in front and rear axle total drive

torque, as seen in the output shafts of the central differential

(if present)

central diff. act. torque

diff.

Nm actual difference in front and rear axle total drive torque, as

seen in the output shafts of the central differential (if

present)

automatic 4WD activation - automatic 4WD selection status (output signal of 4WD ECU)

front cardan shaft torque Nm torque transmitted through front axle cardan shaft (if

present)

front diff. inp. shaft

speed

rpm rotational speed of front axle differential input shaft (if

present)

front axle ATTS split

factor

- torque split factor of driven front wheels (output signal of

ATTS ECU). If no ATTS ECU is used, this factor is 0.5

front diff. max. torque

diff.

Nm max. possible difference in left and right front wheel drive

torque, as seen in the output shafts of the front axle

differential (if present)

front diff. act. torque

diff.

Nm actual difference in left and right front wheel drive torque, as

seen in the output shafts of the front axle differential (if

present)

drive torque FL Nm drive torque of front left wheel (if driven)

drive torque FR Nm drive torque of front right wheel (if driven)

rear cardan shaft torque Nm torque transmitted through rear axle cardan shaft (if present)

rear diff. inp. shaft

speed

rpm rotational speed of rear axle differential input shaft (if

present)

rear diff. max. torque

diff.

Nm max. possible difference in left and right rear wheel drive

torque, as seen in the output shafts of the rear axle

differential (if present)

rear diff. act. torque

diff.

Nm actual difference in left and right rear wheel drive torque, as

seen in the output shafts of the rear axle differential (if

present)

drive torque RL Nm drive torque of rear left wheel (if driven)


drive torque RR Nm drive torque of rear right wheel (if driven)

engine torque reduction % externally controlled engine torque reduction percentage

9.22 PT Pushrod-Activated Torsion Bar Springs and Dampers

This element describes the forces that are produced by a typical race-car suspension springing assembly. This type

of springing consists of two pushrods, connecting the lower wishbones with two rockers. These rockers, in turn,

are attached to two torsion bars on each side of the vehicle, as well as to two dampers and to the cantilevers of

an anti-roll bar (ARB). This complex element works as a ‘three-body force element’: it connects the car-body

and the two lower wishbones of an axle, or the two hub-carriers, resp. The forces and moments that arise are a

respective function of the rigid-body states of all three bodies, and, on the other hand, affect all three bodies.

The model comprises

• two pushrods, situated between the rockers and the respective lower wishbones or hub-carriers

• two mass-less rockers that can rotate about a general, car-body-fixed axis

• two linear or non-linear torsion bars with pre-load, replacing the coil springs of conventional suspensions

• two non-linear dampers, with integrated non-linear bump-and-rebound stop and a constant gas force

• a linear or non-linear anti-roll bar, activated by two linkages that are attached to the rockers. The linkages

twist the anti-roll bar by pushing or pulling two stiff levers on either side of the bar.

Optionally, a third damper (‘heave damper’) can be specified which is either located between the two rockers

(‘type 1’), or between car-body and a beam connected to the two rockers by two additional drop links (‘type 2’).

Like the other two dampers, this damper is equipped with an integrated non-linear bump-and-rebound stop, and

a constant gas force. An additional coil spring parallel to the heave damper can also be taken into account, by

an appropriate modification of the bump-and-rebound stop spline.

For simplicity, it is assumed that left and right side of the whole assembly are symmetric, both with respect to

geometry and to stiffness/damping values. Only exception: the torsion bars may have different static preload

values.


l1 - st name of body (RB,FB, or BO element) the assembly is linked to on left vehicle side(lower wishbone, hub-carrier, etc.)

l2 - st name of body (RB,FB, or BO element) the assembly is linked to on right vehicle side(lower wishbone, hub-carrier, etc.)

l3 - st name of body (RB,FB, or BO element)Table 101: PT I/O signals and other element-specific data

Table 102: PT element data

attachm_pushrod_at_

wishb

mm m (m) position of the outer left pushrod attachment

point (typically on wishbone)

attachm_pushrod_at_

rocker

mm m (m) geometrical center of the left torsion bar

(where the rocker rotation axis passes through)


attachm_damper_at_

rocker

mm m (m) position of the left damper attachment point

on the rocker

attachm_damper_at_body mm m (m) position of the left damper attachment point

on the car-body

attachm_ARB_link_at_

lever

mm m (m) position of the left anti-roll bar linkage on the

left ARB cantilever

attachm_ARB_at_body mm m (m) position of the left anti-roll bar bearing on the

car-body (or of any other point on the anti-roll

bar rotation axis)

rot_axis_rocker - f3 direction vector of left rocker rotation axis.

Default: car-body-fixedx-axis

One of

(m):

torsion_bar_stiffness Nmdeg

f torsion bar torsion stiffness

torsion_bar_stiffn_

spline

deg,Nm sd torsion bar stiffness characteristic (typically

with non-negative slope)

preload_left_torsion_bar Nm f static preload torque of left torsion bar in

reference position. If data-blockpreloads is

present, this value is overridden with the

respective value of this data-block

preload_right_torsion_bar Nm f static preload torque of right torsion bar in

reference position. If data-blockpreloads is

present, this value is overridden with the

respective value of this data-block

damper_spline ms,N sd (m) damper characteristic (typically with

non-negative slope). Might contain dry friction.

In that case, thePT element should be marked

‘stiff’


bump_rebound_stop_spline mm,N sd bump-and-rebound stop spline. The

bump-and-rebound stop is assumed to be

integrated into the damper


One

of:

spring_stiffn Nmm

f stiffness of additional coil spring, sharing center

axis with the damper

spring_spline mm,N sd spline of additional coil spring, sharing center

axis with the damper

bump_rebound_stop_

spline

mm,N sd bump-and-rebound stop spline. The

bump-and-rebound stop is assumed to be

integrated into the damper

One of

(m):

ARB_tors_stiffness Nmdeg

f ARB torsion stiffness

ARB_tors_stiffn_spline deg,Nm sd ARB torsion characteristic (typically with

non-negative slope), using difference in left and

right ARB lever rotation angles as independent

variable

ARB_tors_stiffn_

spline

or

ARB_left_tors_stiffn_

table

deg,

deg,

Nm

t2 ARB torsion characteristic 2D look-up table for

left side, using left and right ARB lever rotation

angles independently as input variables

ARB_right_tors_stiffn_

table

deg,

deg,

Nm

t2 ARB torsion characteristic 2D look-up table for

right side. Optional; default is the look-up

table of the left side

ARB_stiffn_table_

interp_mode

- i 1: piecewise bilinear interpolation

2: piecewise bicubic interpolation Optional;

default value is given by global 2D interpolation

mode

heave_damper_type - i 0: no heave damper

1: heave damper located between, and

actuated by, rockers

2: heave damper located between car-body and

extra beam, which is moved by two drop links

located between beam and rockers

attachm_heave_da_at_

rocker

mm m (m) position of the left heave damper bearing on

the left rocker. Only mandatory if

heave_damper_type=1

attachm_drop_link_at_

rocker

mm m (m) position of the left drop link bearing on the left

rocker. Only mandatory

ifheave_damper_type=2

attachm_drop_link_at_

beam

mm m (m) position of the left drop link bearing on the

additional beam. Only mandatory


direction_heave_da - f3 (m) direction vector of the heave damper axis.

Motion of the beam along thatdirection

increases the damper length. Due to the

assumption of symmetry, a non-zero second

component will be neglected. Only mandatory



heave_da_spline ms,N sd (m) heave damper characteristic (typically with

non-negative slope. Might contain dry friction.

In that case, thePTelement should be marked

stiff. Only mandatory ifheave_damper_type=1

or2

heave_da_gas_force N f constant heave damper gas force

heave_da_bump_reb_

stop_spline

mm,N sd bump-and-rebound stop spline of heave

damper. The bump-and-rebound stop is

assumed to be integrated into the damper

Animation models

(standard: the element is displayed by using standard objects: rods and hydraulic cylinders)rod_diameter mm f diameter of the rods representing pushrods, ARB linkages

and ARB (default 10mm)piston_rod_

diameter

mm f diameter of damper piston rod (default 10mm)

piston_rod_length mm f length of damper piston rod (default 300mm)

Table 103: PT animation models

Plot signals

Table 104: PTplot signals

level 1

left torsion bar torque Nm left torsion-bar torque

right torsion bar torque Nm right torsion-bar torque

left damper force N left damper force

right damper force N right damper force

left bump & rebound stop force N left bump-and-rebound stop force

right bump & rebound stop force N right bump-and-rebound stop force

left pushrod force N left pushrod force

right pushrod force N right pushrod force

antiroll bar torque Nm ARB torque

heave damper force N heave damper force (only if such a damper is

provided)

heave damper force N heave damper bump-and-rebound stop force

(only if such a damper is provided)

level 2

left torsion bar tors. angle deg left torsion bar torsion angle

right torsion bar tors. angle deg right torsion bar torsion angle

left damper deflection vel. ms

left damper deflection velocity

right damper deflection vel. ms

right damper deflection velocity

antiroll bar torsion angle deg antiroll bar torsion angle

left damper deflection mm left damper deflection

right damper deflection mm right damper deflection


heave damper deflection vel. ms

heave damper deflection velocity (only if such a

damper is provided)

heave damper deflection mm heave damper deflection (only if such a damper

is provided)

9.23 RB Rigid Body

This element is the most important one incosin/mbs. It describes the dynamic properties of a rigid body under

the influence of arbitrary vector-valued external forces and moments. The element is fully nonlinear, reflecting

nearly exactly (besides minor unavoidable numerical errors) all gyroscopic effects of a rigid body even for extremely

large rotational velocities. Theoretical basis of the element are the equations of motion of Newton and Euler.

Among other specialties, theRB element internally uses quaternions as over-determined state-space description of

the angular position of the body. Depending on the stiffness of the coupling of the rigid bodies of acosin/mbs

model, the equations of motion of these bodies are integrated simultaneously and implicitly.

There are several ways to define the so-called mass geometry of the rigid body, consisting of

• the mass

• the center of gravity (cg) in reference position

• the 3x3 inertia tensor (which is always symmetric).

Either the full, body-fixedinertia tensor can be prescribed, consisting of the three diagonal elementsIx ,Iy ,Iz,

and the three different off-diagonal elementsIxy = Iyx ,Ixz = Izx ,Iyz = Izy , or the body-fixedprinciple axes,

together with theprinciple moments of inertia have to be specified. Again, two different ways of defining the

directions of these principle axes can be chosen: either by describing the respective transformation matrix on basis

of elementary rotations about thez-,y-, andx-axes (this sequence of rotations is defined in international vehicle

dynamics standardISO 8855 as well as in German vehicle dynamics standardDIN 70000), or with elementary

rotations about thex-,y-, andz-axes, instead. This latter sequence of rotations is known asBryant’s angles

(orcardan angles).

To conveniently define the position of the center of gravity, and optionally the geometrical center, a local body-

fixed reference frame may be introduced. With the aid of this frame, the center of gravity and the geometrical

center need not to be recalculated if the position or orientation of the body changes for different assemblies using

the same body.

Please note: in the table above, the term ‘body-fixed’ means ‘co-ordinates that are fixed relative to the respective

rigid body’, butnot ‘fixed relative to the reference body’ (which typically is chosen to be the car-body in vehicle

dynamics applications).


Table 105: RBI/O signals and other element-specific data

i1 - sig mass and moment-of-inertia modification percentage [%]

i4..i13 - sig x/y/z-components ofextra body-fixeddisplacements [mm] offirst

three points used in respective animation model (as described below).

Useful to visualize interactive geometry changes during K&C

simulations


o1 - sig absolute velocity of cg:

v =√

v2x + v2y + v2z ≥ 0[ms]

o2 - sig x-component of velocity of cg in body-fixed coordinates [ms]

o3 - sig y-component of velocity of cg in body-fixed coordinates [ms]

o4 - sig z-component of velocity of cg in body-fixed coordinates [ms]

o5 - sig x-component of translational acceleration of cg in body-fixed

coordinates [ms2]

o6 - sig y-component of translational acceleration of cg in body-fixed

coordinates [ms2]

o7 - sig z-component of translational acceleration of cg in body-fixed

coordinates [ms2]

o8 - sig ISO 8855 / DIN 70000 rotation angle about x-axis (‘roll angle’) [deg]

o9 - sig ISO 8855 / DIN 70000 rotation angle about x-axis (‘pitch angle’)

[deg]

o10 - sig ISO 8855 / DIN 70000 rotation angle about x-axis (‘yaw angle’) [deg]

o11 - sig ISO 8855 / DIN 70000roll velocity [degs

]

o12 - sig ISO 8855 / DIN 70000pitch velocity [degs

]

o13 - sig ISO 8855 / DIN 70000yaw velocity [degs

]

o14 - sig ISO 8855 / DIN 70000roll acceleration [degs

2]

o15 - sig ISO 8855 / DIN 70000pitch acceleration [degs

2]

o16 - sig ISO 8855 / DIN 70000yaw acceleration [degs

2]

o17 - sig angle between body-fixedx-axis and velocity vector (‘side-slip angle’)

[deg]

o18 - sig distance of a body-fixed sensor pointto the nominal track, as defined

by cosin/ev [m]. In vehicle dynamics, signalo18can be used as input to

driver models that keep the vehicle on or near-by the nominal track.

o19 - sig curvature radius of nominal track (notthat one of the vehicle

itself!), evaluated in that point which is nearest to the vehicle’s sensor

point [m] (the vehicle’s trajectory curvature radius is given by output

signal 27, see below)

o20 - sig x-component of cgposition in global frame [m]

o21 - sig y-component of cgposition in global frame [m]

o22 - sig z-component of cgposition in global frame [m]

o23 - sig travel distance of cg since start of simulation [m]

o24 - sig ISO 8855 / DIN 70000longitudinal acceleration [ms2]

o25 - sig ISO 8855 / DIN 70000lateral acceleration [ms2]

o26 - sig ISO 8855 / DIN 70000vertical acceleration [ms2]

o27 - sig actualcurvature radius of cg trajectory [m]

o28 - sig yaw angle relative to nominal track [deg]

o29 - sig travel path along nominal track [m]

o30 - sig nominal velocity, as determined from nominal track curvature or from

extra velocity signal in track file, respectively [m/s]


add - st element name, to which mass and inertia tensor of the body has to be

added. That element must be a body itself, that is it must have one of

the types BO,FB, orRB. add combines the two body into one rigid body.

It is especially useful to build complex animation models out of ‘body

primitives’ likebrick,rod, etc.

Bodies that use theadd option donot lead to any new degree of

freedom. If output level of log output is greater or equal to 4, the

resulting mass properties of the body that was modified will be put out

on screen.

subt - st element name, from which mass and inertia tensor of the body has to

be subtracted. That element must be a body itself, that is it must have

one of the typesBO,FB, orRB.

subt is especially useful in vehicle dynamics, where mass properties of

the car-body are calculated from that of the full vehicle, ‘minus’ that of

wheels, engine, steering assembly, etc.

If output level of log output is greater or equal to 4, the resulting mass

properties of the body that was modified will be put out on screen.

reference - flag if set, several plot signals of all other rigid bodies are calculated relative

to that body (i.e., they are displayed in a body-fixed reference

coordinate system).

By default, the reference coordinate system coincides with the

body-fixed coordinate system

dx_ref - mm shift value of the origin of the reference coordinate system relative to

the body-fixed coordinate system, inx-direction

dy_ref - mm shift value of the origin of the reference coordinate system relative to

the body-fixed coordinate system, iny-direction

dz_ref - mm shift value of the origin of the reference coordinate system relative to

the body-fixed coordinate system, inz-direction

roll_ref - deg rotation angle of the reference coordinate system aboutx-axis of the


pitch_ref - deg rotation angle of the reference coordinate system abouty-axis of the


yaw_ref - deg rotation angle of the reference coordinate system aboutz-axis of the


Element data

Table 106: RB element data

mass kgm2 f (m) mass

One

of:

(m)

inertia_tensor kgm2 f6 elements of the inertia tensor in the following

sequence:Ix,Iy,Iz ,Ixy,Ixz ,Iyz,

whereI =

Ix Ixy Ixz

Ixy Iy Iyz

Ixz Iyz Iz

princ_moments_

of_inertia

deg f3 principle moments of inertia with respect to the

bodies’ principle axes, in the sequenceIa,Ib,Ic


One of:DIN_70000_

angles_

princ_axes

deg f3 angles defining the direction of the principle

axesa,b,c. Sequence of elementary rotations:z,y,x

Bryant_

angles_

princ_axes

deg f3 angles defining the direction of the principle

axesa,b,c. Sequence of elementary rotations:x,y,z

estimate_inertia_

tensor

flag if this flag is set, the inertia tensor is estimated on

basis of the other mass geometry properties.

Normally, this only makes sense for flexible

bodies.

For a rigid body, the estimation of principal

moments of inertia will lead to very large values

cg_in_ref_position mm m center of gravity in reference position:

• in global frame,

ifpoint_of_refandangular_ref_pos_xx is

not defined

• in local body-fixed reference frame, else

geom_center_in_ref_

position

mm m geometrical center in reference position:

• in global frame, ifpoint_of_ref

andangular_ref_pos_xx is not defined

• in local body-fixed reference frame, else

Used for example in the tire interface (TI) to

specify the geometrical wheel center

point_of_ref mm m defines the origin of a local body-fixed reference

frame. If specified, cg and geometrical center is

understood to be defined in this frame

One

of:

angular_ref_

pos_DIN_70000

deg f3 defines the orientation of a local body-fixed

reference frame. If specified, cg and geometrical

center is understood to be defined in this frame.

Orientation is defined by ISO 8855 / DIN 70000

angles, cf. above

angular_ref_

pos_Bryant

deg f3 defines the orientation of a local body-fixed

reference frame. If specified, cg and geometrical

center is understood to be defined in this frame.

Orientation is defined by Bryant angles, cf. above

Animation models

Table 107: RBanimation models

brick

height mm f height (default 100mm)

lenght mm f length (alongx-axis, default 100mm)


width mm f width (alongy-axis, default 100mm)

RGB_color - f3 RGB color representation of the brick

rod

rod_diameter mm f rod diameter (default 10mm)

marker1 mm f first end-point

marker2 mm f second end-point

RGB_color - f3 RGB color representation of the rod

plate(extruded polygon)

thickness mm f plate thickness (default 10mm)

number_codes - i number of polygon nodes. Polygon will be closed automatically, by

connecting last node with first node. A maximum of 10 nodes can

be specified

marker1..

marker10

mm m polygon nodes (do not need to be complanar). The actual number

to be specified depends onnumber_nodes

RGB_color - f3 RGB color representation of the plate

A-arm

rod-diameter mm f diameter of rods forming A-arm (def. 10mm)

marker1 mm m position of first inner bearing

marker2 mm m position of second inner bearing

marker3 mm m position of outer bearing

RGB_color - f3 RGB color representation of the A-arm

auto

a parallelepiped (’brick’) is generated, the size and orientation of which resembles the mass and

the inertia tensor of the body, where constant density is assumed

blow_up_

factor

- f factor to blow-up (>1) or shrink (<1) the size of the parallelepiped

standard: the animation model is read from file. Any name of the animation model other

thanbrick,rod,A_arm, or auto is interpreted as file name

RGB_color - f3 RGB color representation of the animation model

Plot signals

Table 108: RBplot signals

level 1

the following level 1 signals are only available, if no reference body is defined or body itself is taken for

reference:

x position cg m globalx coordinate of center of gravity position. The body’s cg is

determined after performing all subtraction commands of any other parts

y position cg m globaly coordinate of center of gravity position. The body’s cg is


z position cg m globalz coordinate of center of gravity position. The body’s cg is


rel. x

displacement cg

mm x coordinate of displacement of center of gravity in body-fixed reference

coordinates of reference body


rel. y

displacement cg

mm y coordinate of displacement of center of gravity in body-fixed reference


rel. z

displacement cg

mm z coordinate of displacement of center of gravity in body-fixed reference


the following level 1 signals are only available, if at least one output signal

is specified in the respective RB element definition block:

abs. velocity

cg

ms

absolute velocity of cg:

v =√

v2x + v2y + v2z ≥ 0[ms]


is specified in the respective RB element definition block, and a reference

body is defined which is not the body itself:

rel. roll angle deg ISO 8855 / DIN 70000 rotation angle aboutx-axis of reference coordinate

system of reference body

rel. pitch

angle

deg ISO 8855 / DIN 70000 rotation angle abouty-axis of reference coordinate


rel. yaw angle deg ISO 8855 / DIN 70000 rotation angle aboutz-axis of reference coordinate



is specified in the respective RB element definition block, and if no

reference body is defined or body itself is taken for reference:

travel distance

cg

m travel distance of cg since start of simulation

roll angle deg ISO 8855 / DIN 70000 rotation angle aboutx-axis (more precisely: the

angle between the body-fixedy-axis and a plane, which includes the

body-fixedx-axis, and which is perpendicular to another, vertical, plane,

which includes the body-fixedx-axis)

pitch angle deg ISO 8855 / DIN 70000 rotation angle abouty-axis (more precisely: the

angle between the body-fixed x-axis and the globalxy-plane)

yaw angle deg ISO 8855 / DIN 70000 rotation angle aboutz-axis (more precisely: the

angle between globalx-axis and the projection of the body-fixedx-axis onto

the globalxy-plane)

long. velocity ms

ISO 8855 / DIN 70000 longitudinal velocity (more precisely:x-component

of velocity vector in intermediate coordinate system). The velocity is

measured in a body-fixed point that coincides with the body’s cg, before

subtracting any other rigid-body parts

lat. velocity ms

ISO 8855 / DIN 70000 lateral velocity (more precisely:y-component of

velocity vector in intermediate coordinate system). The velocity is



vert. velocity ms

ISO 8855 / DIN 70000 vertical velocity (more precisely:z-component of

velocity vector in intermediate coordinate system). The velocity is



roll velocity degs

ISO 8855 / DIN 70000 roll velocity (more precisely:x-component of

angular velocity vector in intermediate coordinate system)


pitch velocity degs

ISO 8855 / DIN 70000 pitch velocity (more precisely:y-component of


yaw velocity degs

ISO 8855 / DIN 70000 yaw velocity (more precisely:z-component of


long.

acceleration

ms2 ISO 8855 / DIN 70000 longitudinal acceleration (more

precisely:x-component of acceleration vector in intermediate coordinate

system). The acceleration is measured in a body-fixed point that coincides

with the body’s cg, before subtracting any other rigid-body parts

lat.

acceleration


precisely:y-component of acceleration vector in intermediate coordinate



vert.

acceleration


precisely:z-component of acceleration vector in intermediate coordinate



roll

acceleration

degs

2 ISO 8855 / DIN 70000 roll acceleration (more precisely:x-component of

angular acceleration vector in intermediate coordinate system)

pitch

acceleration

degs

2 ISO 8855 / DIN 70000 roll acceleration (more precisely:y-component of


yaw acceleration degs

2 ISO 8855 / DIN 70000 roll acceleration (more precisely:z-component of


level 2

body-fixed x

ang. vel.

degs

2 angular velocity about body-fixedx-axis

body-fixed y

ang. vel.

degs

2 angular velocity about body-fixedy-axis

body-fixed z

ang. vel.

degs

2 angular velocity about body-fixedz-axis

body-fixed x

ang. accel.

degs

2 angular acceleration about body-fixedx-axis

body-fixed y

ang. accel.

degs

2 angular acceleration about body-fixedy-axis

body-fixed z

ang. accel.

degs

2 angular acceleration about body-fixedz-axis


is specified in the respective RB element definition block:

body-fixed x

velocity cg

ms

body-fixedx-component of the cg velocity

body-fixed y

velocity cg

ms

body-fixedy-component of the cg velocity

body-fixed z

velocity cg

ms

body-fixedz-component of the cg velocity

body-fixed x

accel.

ms2 body-fixedx-component of the cg acceleration


body-fixed y

accel.

ms2 body-fixedy-component of the cg acceleration

body-fixed z

accel.

ms2 body-fixedz-component of the cg acceleration

side-slip angle deg angle from thex-axis of the intermediate axis system to the projection of

the cg velocity vector onto thexy-plane, about they-axis of the

intermediate axis system. Here, the intermediate axis system is obtained by

rotating the earth-fixed axis system about thez-axis by the body yaw angle

total energy J body’s total kinetic energy

cg trajectory

curv. radius

m curvature radius of the cg’s trajectory inxy-plane

9.24 RJ Revolute Joint

This element connects two bodies with a revolute joint, or one that is related to such a joint. The degrees of

freedom of the bodies are constraint in such a way that they can only rotate about a body-fixed axis relative to

each other, and that any point on that axis, fixed to either one of the bodies,

• is fixed to both bodies (revolute joint), or

• can only move along the axis (cylindrical joint), or

• can move only in a fixed plane perpendicular to the axis (in-plane joint), or

• is completely free (rotational joint).




l1 - st name of first body (RB,FB, orBO element) connected by revolutejoint

l2 - st name of second body (RB,FB, orBO element) connected by revolutejoint

i1 - sig x-component of extra body-fixed displacement of revolute jointposition [mm]

i2 - sig y-component of extra body-fixed displacement of revolute jointposition [mm]

i3 - sig z-component of extra body-fixed displacement of revolute jointposition [mm]

i4 - sig forced rotation switch (rotation is forced using signali5, ifi4 signalvalue is greater 0.5)

i5 - sig forced rotation value (only used ifi4signal value is greater 0.5) [deg]

Table 109: RJ I/O signals and other element-specific data

Element data


direction mm f3 (m) direction vector of rotation axis in body-fixedcoordinates of both bodies

position mm m position of an arbitrary point of the rotation axis inbody-fixed coordinates of both bodies

cylindrical_joint - flag if set, the joint can be used to describe a cylindricaljoint: any marker on the second body, located on theaxis is forced to stay on the axis if it is considered fixrelative to the first body.

inplane_joint - flag if set, the joint can be used to describe a so-calledin-plane joint: a marker on the second body is forcedto stay in a plane fixed relative to the first body. Thisplane is perpendicular to the axis of rotation.The flagscylindrical_jointandinplane_jointmay be combined to remove anytranslational constraint from the joint. In contrast, ifneither of the flags is set, the joint behaves like arevolute joint.

Table 110: RJ element data

Plot signals

level 1rotation angle deg rotation angle of second body relative to first body,

about rotation axis

level 2displacement along

axis

mm displacement of first body relative to second body,measured in a point on body 1 on the axis, indirection of the axis

torque x

(body-A-fixed)

Nm x-component of constraint torque in body-fixedco-ordinates of first body

torque y

(body-A-fixed)

Nm y-component of constraint torque in body-fixedco-ordinates of first body

torque z

(body-A-fixed)

Nm z-component of constraint torque in body-fixedco-ordinates of first body

Table 111: RJ plot signals

9.25 RO Rod and Straight Pipe

This element is just another way of defining an ordinary rigid body. It provides the simplified definition of a

rigid body’s data, in terms of geometry and density data of a rod or straight pipe. Center of gravity, mass, and

moments of inertia are automatically computed on basis of the data specified. For more about rigid bodies, please

refer to the9.23 element description.


see9.23 element description.

Element data


marker1 mm m (m) position of first end point of rod or pipe inreference configuration

marker2 mm m (m) position of second end point of rod or pipe inreference configuration

diameter mm f (m) outer rod or pipe diameterinner_diameter mm f inner diameter in case of a hollow cylinder (pipe).

Default: 0 (solid cylinder)

One of:mass_per

_length_

unit

kgm

f mass per length unit

density kgm3 f density (default: steel)

Table 112: RO element data

Animation models

assigned automatically

Plot signals

see9.23 element description.

9.26 SC Steering Assembly for Conceptual Suspension

This subsystem element describes the mechanical part of a conceptual suspension steering model. The input to

the steering system model is either the steering wheel angle or the steering wheel torque that is applied by the

driver. During a simulation, you may switch between steering wheel angle input and steering wheel torque input.

A power-steering model is not yet implemented in the current version ofcosin/mbs, but will be added in a future

release.

The steering model comprises

• a steering wheel with moment of inertia and eccentric center of gravity

• a steering column with

– two cardan joints, defined by prescribed buckling angles and respective reference angles that describe

the angular position of maximum transmission ratio

– a flexible joint between the cardan joints, including damping

– dry friction torque

• a torsion bar stiffness, the torsion angle of which can later serve as input to a power-steering model.

Both flexible joint stiffness and torsion bar stiffness can optionally be described nonlinearly, using spline data.


Table 113: SC I/O signals and other element-specific data

l1 - st name of conceptual suspension (CSelement) steering model is linked to

i1 - sig type of steering:

1: input is steering-wheel angle [deg]

2: input is steering-wheel torque [Nm]

Default value of steering type, if that signal is not provided: 1


i2 - sig steering-wheel angle [deg]

Remark: this signal is only used if steering type is 1 (steering-wheel angle

input)

i3 - sig steering-wheel torque [Nm]

Remark: this signal is only used if steering type is 2 (steering-wheel torque

input)

o1 - sig steering-wheel angle[deg]

o2 - sig steering-wheel angle rate [degs

]

o3 - sig steering-wheel reaction torque [Nm]

o4 - sig steering-wheel reaction torque rate [Nms

]

Element data

Table 114: SC element data

steering_wheel_

inertia

kgm f (m) moment of inertia of the steering wheel

steering_wheel_ecc_

torque

Nm f maximum steering wheel torque due to

eccentric center of gravity

angle_at_max_ecc_

torque

deg f steering wheel angle at which maximum

steering wheel eccentric torque appears. The

steering angle is positive in left turns;

a positive eccentric torque tends to turn the

steering wheel counter-clockwise

buckl_angle_cardan_

joint_1

deg f buckling angle of the first cardan joint

ref_angle_cardan_

joint_1

deg f steering wheel angle at which the transmission

ration of the first cardan joint reaches its

maximum

buckl_angle_cardan_

joint_2

deg f buckling angle of the second cardan joint

ref_angle_cardan_

joint_2

deg f steering wheel angle at which the transmission

ration of the second cardan joint reaches its

maximum

One

of:

(m)

flexible_joint_

stiffness

Nmdeg

f flexible joint torsional stiffness

flex_joint_

stiffn_spline

deg,Nm sd flexible joint torsional stiffness characteristic

flexible_joint_

damping

Nmsrad

f (m) flexible joint torsional damping

One

of:

(m)

torsion_bar_

stiffness

Nmdeg

f torsion bar torsional stiffness

torsion_bar_

stiffn_spline

deg,Nm sd torsion bar torsional stiffness characteristic,

including stiff-elastic stop characteristic

st_column_friction_

torque

Nm f steering column constant friction torque


rack_friction_force N f dry static friction force between steering box

and steering rack

max_rack_displacement mm f maximum lateral displacement of steering rack

rack_displ_stop_

stiffness

Nmm

f stiffness of mechanical steering rack

displacement stop

rack_direction - f3 direction vector of translational rack motion,

expressed in body-fixed coordinates of steering

box

Plot signals

level 1steering wheel angle deg steering wheel turning angle. Positive for left

turnssteering wheel torque Nm external torque, applied to the steering wheel

by the driver. For steering wheel angle input,this is the torque that was necessary to turnthe steering wheel as requested. Normallypositive in steady-state left cornering

level 2pinion rotation angle deg pinion rotation angle1. cardan joint output angle deg 1. cardan joint rotation angle on lower side2. cardan joint input angle deg 2. cardan joint rotation angle on upper side2. cardan joint output angle deg 2. cardan joint rotation angle on lower sideflex. joint torsion angle deg 2. cardan joint rotation angle on lower sideflex. joint torque deg flexible joint transmitted torquetorsion bar torsion angle deg torsion bar torsion angletorsion bar torque deg torsion bar transmitted torque

Table 115: SCplot signals

9.27 SD General Spring/Damper

This element serves as general description of all kinds of elasticity and damping that act in the direction of a

straight line connecting two bodies, the endpoints of which are defined by two body-fixed markers. Among others,

theSD element can describe coil springs, dampers with rubber or hydro-mount bearing, tie-rods (including friction

torque in their bearings), and so on.

The spring stiffness, the damper coefficient, and the damper bearing stiffness can be either defined by constant

values, or by nonlinear characteristics, given by spline data. The damper characteristic’s spline data will be

evaluated as inverse spline (that is, deflection velocity vs. force), if the damper is placed in series with an elastic

bearing.

Furthermore, the stiffness of the damper bearing can be replaced by a one-dimensional hydro-mount model. If no

damper bearing stiffness is specified, the damper is considered to have no elasticity in the bearings. The damper

friction force is to be included in the damper characteristic.

At both ends of the spring-damper element, a dry friction torque value can optionally be prescribed. This is

to take into account friction in the spring-damper bearing that produces a moment in the opposite direction of

rotation of the spring-damper unit relative to the attached body.



Table 116: SD I/O signals and other element-specific data

l1 - st name of first body (RB,FB, orBO element) spring/damper is attached to

l2 - st name of second body (RB,FB, orBO element) spring/damper is attached to

i1..i3 - sig x/y/z-components ofextra body-fixed displacement of attachment atfirst body

[mm]

i4..i6 - sig x/y/z-components ofextra body-fixed displacement of attachment atsecond

body [mm]

i7 - sig additional spring elongation [m]

Remark: this input signal is useful for example to couplecosin/mbs models with

simplified hydraulics models. Here, the stiff spring is used to describe a hydraulics

cylinder with a certain residual elasticity, whereas the cylinder displacement is

given byi7. Signali7, together witho7, are coupled to the hydraulics model

viacosin/ss [mm]

i8 - sig additional spring preload [N ]

i9 - sig spring stiffness modification percentage [%]

i10 - sig damper coefficient modificationpercentage [%]

i11 - sig damper compression/rebound proportion modification percentage [%]

o1 - sig x-component ofspring/damper force in body-fixed coordinates acting on first

body [N ]

o2 - sig y-component ofspring/damper force in body-fixed coordinates acting on first

body [N ]

o3 - sig z-component ofspring/damper force in body-fixed coordinates acting on first

body [N ]

o4 - sig x-component ofspring/damper force in body-fixed coordinates acting on

second body [N ]

o5 - sig y-component ofspring/damper force in body-fixed coordinates acting on

second body [N ]

o6 - sig z-component ofspring/damper force in body-fixed coordinates acting on

second body [N ]

o7 - sig scalar spring/damper force[N ]

Element data

Table 117: SDelement data

attachm_body1 mm m(m) body-fixed attachment point of the spring-damper

element at body 1

attachm_body2 mm m (m) body-fixed attachment point of the spring-damper

element at body 2

One

of:

spring_stiffn Nmm

f spring stiffness

spring_spline mm,N sd spring characteristic (positive deflection values

mean compression; deflection and force normally

have the same sign)

One

of:

damper_coeff Nsm

f damper coefficient


damper_spline ms,N sd damper characteristic (positive deflection velocity

mean compression; deflection velocity and force

normally have the same sign). Note that the

damper spline will be evaluated as inverse

characteristic (i.e., deflection velocity vs. force), if

the damper is placed in series with an elastic

bearing

One

of:

damper_bearing_

stiffn

Nmm

f damper bearing stiffness

damper_bearing_

spline

mm,N sd damper bearing characteristic (positive deflection

values mean compression; deflection and force

normally have the same sign)

damper_hydromount mo data-block name of hydro-mount model (HM) of

damper bearing

damper_bearing_damping Nsm

f damper bearing damping coefficient


preload N f static preload force of spring in reference position.

If data-blockpreloads is present, this value is

overridden with the respective value of this

data-block

hard_stop_defl_perc % f spring deflection percentage at which an additional

hard stop stiffness comes into effect (default 90%)

hard_stop_stiffn Nmm

f additional hard stop stiffness (default 0). Should

by one or more orders of magnitude larger than

spring stiffness if hard-stop is used

force_unilateral flag selects whether the spring-damper force is always

to be nonnegative (‘unilateral’), and by this is a

contact force (default ‘false’)

friction_torque_at_body1 Nm f dry friction torque in spring-damper bearing at

body 1. This value is overridden with 0,

iffriction = 0 is specified in the$simulation

data-block of the sim.data file

friction_torque_at_body2 Nm f dry friction torque in spring-damper bearing at

body 2. This value is overridden with 0,

iffriction = 0 is specified in the$simulation

data-block of the sim.data file

Animation models

Table 118: SDanimation models

rod


coil_spring

wire_diameter mm f diameter of coil spring wire (default 5mm)

coil_diameter mm f diameter of one coil (default 50mm)

number_of_coils − i number of coils (default 10)


dist_attachm_cap_top mm f distance of upper spring cap to upper bearing

dist_attachm_cap_bottom mm f distance of upper spring cap to lower bearing

cylinder

cylinder_diameter mm f diameter of damper housing (default 50mm)

cylinder_length mm f length of damper housing (default 500mm)

piston_rod_diameter mm f diameter of damper piston rod (default 10mm)


coil_spring_cylinder

wire_diameter mm f diameter of coil spring wire (default 5mm)

coil_diameter mm f diameter of one coil (default 50mm)

number_of_coils − i number of coils (default 10)

dist_attachm_cap_top mm f distance of upper spring cap to upper bearing

dist_attachm_cap_bottom mm f distance of lower spring cap to lower bearing

cylinder_diameter mm f diameter of damper housing (default 50mm)

cylinder_length mm f length of damper housing (default 500mm)

piston_rod_diameter mm f diameter of damper piston rod (default 10mm)


Plot signals

(if hydro-mount model is included, see also the hydro-mount subsystem chapter for additional plot signals)

Table 119: SD plot signals

level 1

deflection mm deflection of spring/damper element: change in

distance of the two points of attachment relative to

reference position distance. Only provided, if spring

stiffness is nonzero

damper piston displ. vel. ms

displacement velocity of damper piston. Only

provided, if damper coefficient is nonzero

total force N total scalar spring/damper force. Only provided, if

both spring stiffness and damper coefficient are

nonzero

force N scalar spring or damper force, respectively. Only

provided, if either spring stiffness or damper

coefficient is zero.

Remark: the distinction betweentotal force

andforce is only for ‘cosmetic’ reasons. Internally,

both signals are the same

level 2

spring force N scalar spring force. Only provided, if spring stiffness is

nonzero

damper force N scalar damper force. Only provided, if damper

coefficient is nonzero


damper bearing defl. mm axial deflection of damper bearing. Only provided, if

both damper coefficient and damper bearing

compliance are nonzero

9.28 SJ Spherical-Spherical Joint

This element connects two bodies with a spherical-spherical joint. The degrees of freedom of the bodies are

constraint in such a way that two points, one on either one of the two bodies, have constant distance.




l1 - st name of first body (RB,FB, orBO element) connected by revolute jointl2 - st name of second body (RB,FB, orBO element) connected by revolute jointl3 - sig additional distance change [mm]

Table 120: SJI/O signals and other element-specific data

Element data

attachm_body1 mm m (m) body-fixed attachment point of the spherical-spherical jointat body 1

attachm_body2 mm m (m) body-fixed attachment point of the spherical-spherical jointat body 2

Table 121: SJelement data

Animation models

rod


Table 122: SJanimation models

Plot signals

level 1constraint force N scalar joint constraint force along joint axis

level 2residual deflection mm residual distance error. Only for diagnosis purposes;

should be extremely small

Table 123: SJplot signals

9.29 SR Steering Assembly, Rack-and-Pinion

This subsystem element describes the mechanical part of a rack-and-pinion steering assembly. The input to the

steering system model is either the steering wheel angle, the steering wheel torque that is applied by the driver,

or directly the displacement of the steering rack. The latter is especially useful for four-wheel steering systems, if


the rack displacement of the rear steering-box is controlled by wire. During a simulation, you may switch between

the different input types.

At present, no dynamic hydraulic power-steering model is implemented yet, but only a steady-state torque/force

amplification characteristic. A more detailed hydraulic power-steering model will be added in a future release

ofcosin/mbs.

The steering model comprises

• a steering wheel with moment of inertia and eccentric center of gravity

• a steering column with

– two cardan joints, defined by prescribed buckling angles and respective reference angles that describe

the angular position of maximum transmission ratio

– a flexible joint between the cardan joints, including damping

– dry friction torque

• a torsion bar stiffness and damping, the torque of which serves as input to the power-steering characteristic

• a rack-and-pinion contact stiffness, damping, and play

• a steering gear-box with

– constant or variable transmission ratio

– stiff-elastic steering-rack stop

• a steering damper, located between rack and steering gear-box

• a dry friction element, located between rack and steering gear-box

• an optional quasi-static hydraulic power steering model

• an optional dynamic electric power steering (EPS) model.

Both flexible joint stiffness and torsion bar stiffness can optionally be described nonlinearly, using spline data.

The steering model can be viewed to be a (very sophisticated) force element, acting between the steering box

(which might be fixed to car-body, or modeled as a free mass), and the steering rack. This general force consists

of a constraint force that is defining a translational joint between steering box and steering rack, a friction force,

a highly nonlinear spring force describing a mechanical stop, and the contact force between rack and pinion. The

latter itself is a result of the steering column model, outlined above.

It is recommended to use thestiffattribute for this element, due to the constraint forces that are modeled as

extremely stiff elasticities.

Typically, the steering model will be completed by two rigid bodies: steering box and steering rack. The latter

will typically be connected to the front or rear wheel-carriers by two very stiff spring-damper elements, describing

the tie-rods.

The mechanical steering model is completed with interfaces to several ECU’s:

• four-wheel steering (4WS) ECU, controlling the rack displacement of a rear axle steering

• standard EPS (Electronic Power Steering), providing an additional torque acting on the steering column, as

well as an additional force acting on the steering rack

• advanced EPS, using several additional input signals as compared to standard EPS.




details about this interfacing, see chapter 4.

Equally well, rack displacement (in case of four-wheel steering) or assisting fortorque (in case of electronically

controlled hydraulic or electric power steering) can be externally controlled. This is done either by setting

appropriatecosin/ss signals, or by coupling the Simulink variant ofcosin/mbs with a separate Simulink subsystem.

For details of the Simulink interface see chapter 6.


Table 124: SRI/O signals and other element-specific data

l1 - st name of steering box body (RB,FB, orBO element) steering model is linked to

Remark: though formally not required, steering box should be arigidbody

l2 - st name of steering rack body (RB,FB, orBO element) steering model is linked to

Remark: though formally not required, steering rack should be arigid body

l3 - st name of front left tire (TI element). Only needed for 4WS or EPS sub-system models

l4 - st name of front right tire (TI element). Only needed for 4WS or EPS sub-system models

l5 - st name of rear left tire (TIelement). Only needed for 4WS or EPS sub-system models

l6 - st name of rear right tire (TI element). Only needed for 4WS or EPS sub-system models

l7 - st name of car-body (BOelement). Only needed for 4WS or EPS sub-system models

l8 - st name of opposite front axle steering (SR element). Only needed for 4WS sub-system

models

i1 - sig type of steering:

1: input is steering-wheel angle [deg]

2: input is steering-wheel torque [Nm]

3: input is rack displacement [mm] Default value of steering type, if that signal is not

provided: 1

i2 - sig steering-wheel angle [deg]

Remark: this signal is only used if steering type is 1 (steering-wheel angle input)

i3 - sig steering-wheel torque [Nm]

Remark: this signal is only used if steering type is 2 (steering-wheel torque input)

i4 - sig steering-rack displacement [mm]

Remark: this signal is only used if steering type is 3 (rack displacement input)

i5 - sig power-steering on/off switch [0,1]

i6 - sig active additional force, applied to rack [N ]

i7 - sig active additional torque, applied to steering column [Nm]

i8 - sig motor voltage for detailed EPS model[V ]

i9 - sig additional external force on steering rack in rack direction (meant to connect the

steering model with simplified user-defined vehicle models) [N ]

o1 - sig steering-wheel angle [deg]

o2 - sig steering-wheel angle rate [degs

]

o3 - sig steering-wheel reaction torque [Nm]

o4 - sig steering-wheel reaction torque rate [Nms

]

o5 - sig steering rack displacement [mm]

Element data


Table 125: SR element data

steering_wheel_mom_of_

inertia

kgm2 f (m) moment of inertia of the steering wheel

steering_wheel_ecc_

torque

Nm f maximum steering wheel torque due to eccentric

center of gravity

Default value 0

angle_at_max_ecc_torque deg f steering wheel angle at which maximum steering

wheel eccentric torque appears. The steering angle is

positive in left turns;

a positive eccentric torque tends to turn the steering

wheel counter-clockwise

buckl_angle_cardan_

joint_1

deg f buckling angle of the first cardan joint

Default value 0

ref_angle_cardan_

joint_1

deg f steering wheel angle at which the transmission ration

of the first cardan joint reaches its maximum

buckl_angle_cardan_

joint_2

deg f buckling angle of the second cardan joint

Default value 0

ref_angle_cardan_

joint_2

deg f steering wheel angle at which the transmission ration

of the second cardan joint reaches its maximum

One

of:

(m)

steering_

ratio

mmdeg

f constant steering ratio (rack displacement, divided by

pinion rotation angle)

steering_

ratio_spline

deg,mm sd steering ratio characteristic

One

of:

(m)

flexible_joint_

stiffness

Nmdeg

f flexible joint torsional stiffness

flex_joint_

stiffn_spline

deg,Nm sd flexible joint torsional stiffness characteristic

flexible_joint_damping Nmsrad

f (m) flexible joint torsional damping

Default value (nearly) 0

One

of:

(m)

torsion_bar_

stiffness

Nmdeg

f torsion bar torsional stiffness

torsion_bar_

stiffn_spline

deg,Nm sd torsion bar torsional stiffness characteristic, including

stiff-elastic stop characteristic

torsion_bar_damping Nmsrad

f torsion bar torsional damping.

Default value 0

st_column_friction_

torque

Nm f steering column constant friction torque.

Default value 0

One

of:

(m)

steer_damper Nsm

f steer damper coefficient.

Default value 0

steer_damper_

spline

ms,N sd steer damper characteristic

rack_friction_force N f rack displacement constant friction force.

Default value 0


num_rack_friction_

slope

Nsm

f numerical slope of rack friction characteristic at zero

rack displacement velocity.

Default value 10.000Nsm

rack_pinion_

contact_stiffn

Nmdeg

f rack-and-pinion contact stiffness.

Default value (nearly) infinity

rack_pinion_

contact_damping

Nmsrad

f rack-and-pinion contact damping.

Default value 0

rack_pinion_contact_

play

deg f rack-and-pinion contact play.

Default value 0

max_rack_

displacement

Nmm

f rack displacement where stop is reached

rack_displ_

stop_stiffn

Nmm

f stiffness of rack displacement stop

One

of:

power_

steering_

spline

Nm,N sd steady-state power-steering characteristic: assisting

hydraulic force on steering rack asfunction of torque

in torsion bar.

Remark:y-values (forces) must be either ascending or

descending

power_

steering_force_

spline

deg,N sd steady-state power-steering characteristic: assisting

hydraulic force on steering rack asfunction of torsion

bar torsion angle.

Remark:y-values (forces) must be either ascending or

descending

power_steering_

time_constant

s f time-constant of first-order delay between torsion bar

torsion angle and power-steering assisting force

signals.

Default value 0

EPS_motor_mom_of_

inertia

kgm2 f moment of inertia of EPS motor’s rotor. This value

also activates the EPS subsystem. EPS is assumed

ifEPS_motor_mom_of_inertia > 0. All following

EPS data are only used in this case

EPS_input_gain Vdeg

f EPS torsion bar torsion to motor voltage gain

EPS_max_voltage_

supply

V maximum motor voltage supply (typically 12V )

EPS_current_to_

torque_gain

NmA

f EPS motor current to torque amplification factor

EPS_motor_damping Nmsrad

f EPS motor inner damping

EPS_motor_inductance mH f EPS motor inductance

EPS_motor_resistance Ohm f EPS motor resistance

EPS_motor_indu_volt_

coeff

V srad

f EPS inductive voltage coefficient

EPS_motor_transm_

ratio

mmdeg

f transmission ratio EPS motor rotation to rack

displacement


controller - st type of steering controlling ECU: one out

ofnone,4WS,EPS_std,EPS_advanced,external_4WS,external_EPS,

orexternal_EPS_voltage

A separately compiled subsystem will be coupled to

the steering model, if name

is4WS,EPS_std,EPS_advanced. The 4WS puts out a

nominal value of the steering rack displacement

(normally for the rear axle steering. Only effective if

input signal ‘steering type’i1 has value 3).

EPS results in the output of an additional torque in

the steering column, as well as an additional force

applied to the rack. 4WS and EPS are mutually

exclusive (see chapter 4 for a complete description of

the interfacing).

If name isexternal_4WS orexternal_EPS, the rack

displacement or the steering assisting forces/torques,

resp., will be set to the values of input signalsi4 ori6

andi7, resp.. These input signals either can be

manually set, or controlled by a Simulink ECU model.

If name isexternal_EPS_voltage, and if using a

detailed EPS model, the EPS motor voltage will be

set to the values of input signalsi8. This input signal

either can be manually set, or controlled by a Simulink

ECU model

Plot signals


level 1steering wheel angle deg steering wheel turning angle. Positive when

turning to the leftsteering wheel reaction torque Nm reaction torque acting on the steering wheel as

a result of steering column torsion. Insteady-state condition, this torque is inequilibrium with the driver’s torque applied tothe steering wheel. Normally positive duringsteady-state left cornering

steering rack displacement mm steering rack displacement

level 2

steering wheel angle vel. degs

steering wheel turning angle velocity. Positivewhen steering to the left

1. cardan joint output angle deg 1. cardan joint rotation angle on lower side2. cardan joint input angle deg 2. cardan joint rotation angle on upper side2. cardan joint output angle deg 2. cardan joint rotation angle on lower sidepinion input angle deg pinion rotation angleflex. joint torsion angle deg flexible joint (Hardy disk) torsion angleflex. joint torque Nm flexible joint transmitted torquesteering rack displ. vel. m

ssteering-rack displacement velocity

steer-damper force N actual steer-damper forcesteering rack friction force N actual steering rack friction forcesteering rack stop force N steering rack stop force (zero, if stop is not

active)rack-pinion contact force N contact force between rack and pinionpower-steering assisting force deg power-steering assisting force on racktorsion bar torsion angle Nm torsion bar torsion angletorsion bar torque mm torsion bar transmitted torquevertical rack displacement mm vertical rack displacement, relative to steering

boxlong. rack displacement deg longitudinal rack displacement, relative to

steering boxang. rack displacement x deg angular rack displacement, relative to steering

box, aboutx-axisang. rack displacement y deg angular rack displacement, relative to steering

box, abouty-axisang. rack displacement z deg angular rack displacement relative to steering

box, aboutz-axisadditionally, if EPS is active:EPS motor voltage V EPS motor voltageEPS motor rotation angle deg EPS motor rotation angle

EPS motor rotation velocity rads

EPS motor rotation velocityEPS motor current A EPS motor currentEPS motor torque Nm EPS motor torqueEPS assisting force N EPS net assisting force

Table 126: SRplot signals

9.30 ST Semi-Automatic Transmission

This element can serve either as a replacement, in parts, of a human driver model, or as a true semi-automatic

transmission model. It operates (or modulates) the drive-train controls: clutch pedal, gear, and throttle opening

angle.

There are two modes provided: one with an integrated automatic gear selection algorithm, and another one


without such a control. The first will decide automatically, if a gear shift is necessary, the second will receive the

respective decision from outside, in terms of acosin/ss signal.

The semi-automatic transmission uses two input signals: the gas pedal operating travel (without any modification

that is necessary during a gear shift), and the nominal gear (or selector lever position, respectively).

If automatic gear selection algorithm is activated (by a switch which is part of the element data), selector lever

position and other signals are used to determine the nominal gear. In the present version, this is done in the

following way: gear-dependent values of engine revs and longitudinal accelerations are read from the element’s data

block. When running a simulation, gear will be shifted up if engine revs exceed a certain bound and longitudinal

acceleration is less than another positive bound at the same time. Vice versa, gear will be shifted down if engine

revs fall below another engine revs bound and longitudinal acceleration is larger than another negative bound.

In either mode, if nominal gear is not equal to actual gear, a gear shift is initiated after a certain delay time. The

shift takes place in a certain period of time. During that period, clutch is smoothly opened and closed again,

and simultaneously throttle is closed and opened again. When clutch is completely open and throttle completely

closed, the gear is shifted. This is done in a way such that no discontinuities or other numerical problems can

occur.

In addition to the semi-automatic shift, the element automatically declutches if engine revs falls below 600rpm.

This is especially useful in driving simulator applications.

For use as signal in ECU’s, the element puts out a signal called gas pedal stroke, which is the actual position

of the gas-pedal, including all modifications during gear shift, in [%] instead of a normalized value that varies

between 0 and 1.


l1 - st name of propulsion system (PS element) which is to be controlledl2 - st name of car-body (BOelement). This body needs to have the reference attribute

set, in order to provide all signals needed for automatic gear selection

i1 - sig gas pedal operating travel[-]i2 - sig nominal gear or selector lever, resp. [-1,0,1,2,3,..]

o1 - sig actually engaged gear [-1,0,1,2,3,..]o2 - sig throttle opening angle [deg]o3 - sig normalizedclutch pedal travel [0..1]o4 - sig actual gas pedal stroke, including modification during gear shift [%]

Table 127: ST I/O signals and other element-specific data

Element data


gas_ped_to_throttle_

spline

-,deg sd gas pedal kinematics, describing dependency betweennormalized gas pedal operating travel, and throttleopening angle

shift_delay_time s f time to wait for a gear shift after nominal gear beginsto differ from actual one.Default value 0.1 s

shift_time s f time during which clutch and throttle is operatedduring a gear shift.Default value 0.1 s

automatic_gear_

selection

- i switch which determines whether (1) or not (0)automatic gear selection is to be performed.Default value is 0

shift_up_rpm_accel rpm,ms2

t2 engine revs and acceleration bounds forshift-up-decision. The table has n-1 rows, if thetransmission has n forward gears. Rows refer to 1st,2nd, 3rd, .. second last gear

shift_down_rpm_accel rpm,ms2

t2 engine revs and acceleration bounds forshift-up-decision. The table has n-1 rows, if thetransmission hasn forward gears. Rows refer to 2nd,3rd, .. last gear

Table 128: ST element data

Plot signals

level 1engaged gear - actually engaged gearclutch pedal - normalized clutch pedal operating travel

level 2throttle opening angle deg throttle opening angle, including modulation due to

gear shift

Table 129: ST plot signals

9.31 TI Tire Model Interface

This element serves as interface to severalcosin/mbs compatible tire models, such asHTire (the driver function

for several versions of Magic Formula),FTire,FETire, andRTire.

The tire model to be used, and the data to be read in, is automatically recognized bycosin/mbs, by inspecting

the contents of the tire data-block or tire data file, resp. The name of this data-block or data file, resp., is to be

entered in the tire element definition line of thecosin/mbs data-block$model. Of course, any tire of acosin/mbs

suspension or full vehicle model can be simulated by an individual tire model, using individual data.

This element also takes into account the vector-valued drive reaction torque (and force), which acts on the

differential. Due to the specific kinematics of the drive shafts, this torque is more than just a scalar torque

iny-direction. It is assumed that the drive-shaft carries constant velocity joints, where length compensation is

realized at the drive-shaft side of one of the joints.

The description of the tire model parameters and their meaning is subject to the documentation of the respective

tire model. The user does not have to provide any further data besides those of the tire model itself.



Table 130: TII/O signals and other element-specific data

l1 - st name of wheel-carrier (RB,FB, orBO element) wheel and tire is mounted on

l2 - st name of body (RB,FB, orBO element) the drive reaction torque is to be applied to (e.g.

axle differential)

l3 - st name of body (RB,FB, orBO element) to be used in road surface calculation for those

road types that are related to a body’s motion (e.g. car-body)

l4 - st name ofTI element which tire is linked to as dual or twin tire

l5 - st name of body (RB,FB, orBO element), the point of reference of which defines the rim

center

utmf - st name of tire data file to be used with user-defined tire model

Remark: this data item is an alternative to, and mutually exclusive with, an entryf =

data-file-name

id - i tire id (needed for severalcosin/ev road profiles). Tires on left-hand side of vehicle

should have an odd id, tires on right-hand side an even one

cam deg f extra inclination angle of wheel relative to wheel carrier (for both vehicle sides negative

if wheel tops point towards vehicle mid-plane)

toe deg f extra toe angle of wheel relative to wheel carrier (for both vehicle sides negative if wheel

fronts point towards vehicle mid-plane)

et mm f lateral wheel offset (lateral shift of wheel center relative to point of reference; for both

vehicle sides positive if rim is shifted towards vehicle mid-plane) = ’ET’ = ’Einpresstiefe’

shift mm m additional offset vector, containing an extra shift from tire point of reference to tire

center (for example,containing rim offset (ET) as second component)

i1 - sig actual inflation pressure [bar]

Remark: not all tire models use that information

i2 - sig actual tread depth [mm]

Remark: not all tire models use that information

i3 - sig drive torque[Nm]

Remark: if a drive torques(DT) or propulsion system (PS) element is connected to the

respective wheel,i3 will be overridden

i4 - sig maximum braking torque [Nm]

Remark: if a brake system model (BR) is connected to the respective wheel,i4 will be

overridden

i5 - sig ambient temperature [degC]

Remark: at present, onlyFTire uses that information

i6 - sig road surface temperature [degC]

Remark: at present, onlyFTire uses that information

i7 - sig tire model level [-]

Remark: for the exact meaning refer to the respective tire model documentation. At

present, onlyFTire uses that information

o1 - sig rim rotation angle [deg]

o2 - sig wheel speed (= rim angular velocity relative to wheel carrier) [ rads

]

o3 - sig actual braking torque [Nm]

o4 - sig longitudinal slip [%]

o5 - sig side-slip angle [deg]

o6 - sig tirecamber angle [deg]


o7 - sig x-component oftire force in Tydex C-axis system [N ]

o8 - sig y-component oftire force in Tydex C-axis system [N ]

o9 - sig z-component oftire force in Tydex C-axis system [N ]

o10 - sig x-component oftire force in Tydex C-axis system [Nm]

o11 - sig y-component oftire force in Tydex C-axis system [Nm]

o12 - sig z-component oftire force in Tydex C-axis system [Nm]

Element data

(see the respective tire model documentation for tire model specific element data. Here, only some important

data are listed for convenience)

Table 131: TIelement data

tire model HTire (general driver for simple handling models)

dimension - i3 (m) tire size, like 195 65 15

rolling_circumference mm f1 tire rolling circumference. If not specified, a value is

estimated from tire size

load_index - i load index, following ETRTO. Default value LI 90

rim_inertia kgm2 f (m) moment of inertia of all rotating parts, besides tire,

about wheel spin axis

deflection mm f2 (m) two tire deflection values for which wheel loads are

measured

load_at_deflection N f2 (m) wheel loads at specified tire deflections

vertical_damping Nsm

f (m) tire damping coefficient in vertical direction

rolling_resistance - f (m) Fx/Fzfor free rolling tire

longitudinal_stiffness Nmm

f tire longitudinal stiffness (long. force, divided by long.

displacement of a standing tire, which is blocked and

not sliding)

lateral_stiffness Nmm

f tire lateral stiffness (lat. force, divided by lat.

displacement of a standing tire, which is blocked and

not sliding)

step_size_contact_

plane_calc

mm f step-size used in numerical differentiation to get

contact-plane inclination.

Default value 30mm

relaxation_length_Fx m f rolling distance needed to build up 63% of stationary

longitudinal force.

Default value 0.5 m

max_time_constant_Fx s f upper bound for resulting time constant of first order

differential equation for longitudinal force lag.

Default value 0.01 s

relaxation_length_

reduction_Fx

m f reduction of relaxation length, when longitudinal force

is decreasing rather than increasing. Default value 0.7

relaxation_length_Fy m f rolling distance needed to build up 63% of stationary

side for.

Default value 0.5 m


max_time_constant_Fy s f upper bound for resulting time constant of first order

differential equation for side force lag.


relaxation_length_

reduction_Fx

- f reduction of relaxation length, when longitudinal force

is decreasing rather than increasing.

Default value 0.7

relaxation_length_Fy m f rolling distance needed to build up 63% of stationary

side for.

Default value 0.5 m

max_time_constant_Fy s f upper bound for resulting time constant of first order

differential equation for side force lag.


relaxation_length_

reduction_Fy

- f reduction of relaxation length, when side force is

decreasing rather than increasing.

Default value 0.7

relaxation_length_Mz m f rolling distance needed to build up 63% of stationary

aligning torque.

Default value 0.5 m

max_time_constant_Mz s f upper bound for resulting time constant of first order

differential equation for aligning torque lag. Default

value 0.01 s

relaxation_length_

reduction_Mz

- f reduction of relaxation length, when aligning torque is

decreasing rather than increasing. Default value 0.7

Element data in second data block

(specified bydb2 ormdb2; alternatively, these data may also be specified directly in element definition block)

Table 132: TI element data in second data block

toe deg f toe angle relative to wheel-carrier.

Default value: 0.0

camber deg f camber angle relative to wheel-carrier.

Default value: 0.0

shift_wheel_center mm f additional shift vector from wheel point of reference to

geometrical wheel center.

Default value [0,0,0]

rim_inertia kgm2 f default value of rim moment of inertia about wheel spin axis.

To be used, if tire model does not provide another value

inner_joint mm m position of inner constant velocity joint

dist_outer_joint_

wheel_center

mm f distance of outer constant velocity joint to geometrical wheel

center


frame - i co-ordinate system to be used for output of tire forces and

moments (not supported by all tire models):

0: TYDEX C-axis system = ISO 8855 wheel system

1: rotated wheel frame, x-axis backward

2: TYDEX W-axis system = ISO 8855 contact frame

3: rotated contact frame, x-axis backward

4: TYDEX H-axis system

Animation models

see tire model

Plot signals

(see also the respective tire model documentation for additional, tire model specific plot signals)

Table 133: TIplot signals

level 1

wheel speed rads

wheel speed (wheel rotational velocity)

fore-aft force (tire/road) N longitudinal tire force (as defined in Tydex STI

standard).

Following this standard, tire forces and moments are

expressed in the ISO 8855 and DIN 70000

W-frame:x-axis is given by the intersection of the

central plane of the wheel with the track surface,y-axis

is given by the projection of the spin axis onto ground,

andz-axis is normal to the ground and points upwards

side force (tire/road) N lateral tire force, as defined in Tydex STI standard,

see above

wheel load (tire/road) N vertical tire force, as defined in Tydex STI standard,

see above

aligning torque (tire/road) Nm self-aligning torque, as defined in Tydex STI standard,

see above

slip angle deg tire slip angle

long. slip % longitudinal tire slip:

κ=100rdynωwheel−νwheel

max

(

rdynωwheel , νwheel

)%

tire camber angle deg tire camber angle following Tydex STI standard

road height m mean road height in contact patch

camber angle rel. to

car-body

deg wheel camber angle relative to car-body

toe-in angle deg wheel toe-in angle relative to car-body

road friction factor - modification factor of tire/road friction coefficients

near mean contact point, as provided by the road

interface.

Default value is 1

level 2

wheel rotation angle deg wheel rotation angle about wheel spin axis


overturning torque

(tire/road)

Nm overturning tire moment (moment about longitudinal

axis, as defined in Tydex STI standard, see above)

roll. res. torque

(tire/road)

Nm rolling resistance moment (tire moment about lateral

axis, as defined in Tydex STI standard, see above)

foot print x m x-component of contact patch center in global

coordinates

foot print y m y-component of contact patch center in global

coordinates

long. slip (altern. def.) % longitudinal slip (alternative definition, not available

for all tire models):

κ=100rdynωwheel−νwheel

rdynωwheel

%

long. force drive shaft to

hub

N additional longitudinal force, acting on wheel carrier,

due to drive torque and drive shaft kinematics,

expressed in wheel-carrier-fixed co-ordinate system

vert. force drive shaft to

hub

N additional vertical force, acting on wheel carrier, due

to drive torque and drive shaft kinematics, expressed

in wheel-carrier-fixed coordinate system

long. force drive shaft to

diff.

N additional longitudinal force, acting on differential,

due to drive torque and drive shaft kinematics,

expressed in differential-fixed coordinate system

vert. force drive shaft to

diff.

N additional vertical force, acting on differential, due to

drive torque and drive shaft kinematics, expressed in

differential-fixed coordinate system

9.32 TJ Translational Joint

This element connects two bodies with a translational joint. The degrees of freedom of the bodies are constraint

in such a way that they can only move along a specified direction vector relative to each other. The angular

orientation of the bodies always coincides.

In addition to the kinematic constraint, an optional sliding friction force is provided in the direction of the relative

translational motion of the bodies. Moreover, an optional stopping stiffness comes in effect when the relative

displacement of the bodies exceeds a maximum value.

This element will automatically use thestiff attribute, no matter whether or not this attribute is specified in the



l1 - st name of first body (RB,FB, orBO element) connected by translational jointl2 - st name of second body (RB,FB, orBO element) connected by translational joint

i1 - sig forced motion switch (translational motion is forced using signali2, ifi1 signal value isgreater 0.5)

i2 - sig forced displacement value (only used ifi1 is greater 0.5) [mm]

Table 134: TJ I/O signals and other element-specific data

Element data


direction mm f3 (m) direction vector of translational degree offreedom in body-fixed coordinates of bothbodies

position mm m position of joint (only needed for animationmodel if available) in body-fixed coordinates ofboth bodies

friction_force N f scalar maximum sliding-friction force, acting indirection of translational joint

max_displacement mm f maximum displacement of the bodies relativeto each other, in direction of translational joint

displ_stop_stiffness N f displacement-stop stiffness that comes in effectwhen actual displacement is greater thanmaximum displacement

Table 135: TJ element data

Plot signals

level 1axial defl. mm axial deflection of translational jointfriction force N actual scalar friction force, acting in direction of

translational joint, including signstop force N actual scalar force induced from stop stiffness, acting

in direction of translational joint

level 2residual radial defl. y mm residual radial deflection of joint in

joint-fixedy-direction (only for diagnosis purposes;should be extremely small)

residual radial defl. z mm residual radial deflection of joint injoint-fixedz-direction (only for diagnosis purposes;should be extremely small)

residual ang. defl. x deg residual angular deflection of joint alongbody-fixedx-axis (only for diagnosis purposes; shouldbe extremely small)

residual ang. defl. y deg residual angular deflection of joint alongbody-fixedy-axis (only for diagnosis purposes; shouldbe extremely small)

residual ang. defl. z deg residual angular deflection of joint alongbody-fixedz-axis (only for diagnosis purposes; shouldbe extremely small)

Table 136: TJ plot signals

9.33 TS Torsion-Bar Stabilizer

This element describes the forces that are produced by the torsion-bar stabilizer, due to different wheel travel

values for the wheels of one axle. The stabilizer works as a ‘three-body force element’: it connects the car-body

and the two lower links of an axle, or the two hub-carriers, resp. The forces and moments that arise are a function

of the rigid-body states of all three bodies, and, on the other hand, affect all three bodies.

The model comprises

• two connection rods, situated between the stabilizer cantilevers, and the respective lower links or hub-carriers

• non-stiff cantilevers


• torsional stiffness of the torsion-bar

• two elastic bearings that connect the stabilizer to the car-body

• series connections of friction torque and torsional stiffness of the bearings.


l1 - st name of body (RB,FB, orBO element) the stabilizer is linked to on left wheel (lower link,hub-carrier, etc.)

l2 - st name of body (RB,FB, orBO element) the stabilizer is linked to on right wheel (lower link,hub-carrier, etc.)

l3 - st name of car-body (RB,FB, orBO element)

i1 - sig torsion-bar torsion stiffness modification percentage [%]

Table 137: TS I/O signals and other element-specific data

Element data

pos_left_conn_rod_bottom mm m (m) position of the bottom of the left connectingrod

pos_right_conn_rod_bottom mm m position of the bottom of the right connectingrod. If this marker is not specified, therespective marker of the left side is mirroredwith respect to the vehiclexz-mid-plane

pos_left_conn_rod_top mm m (m) position of the top of the left connecting rodpos_right_conn_rod_top mm m position of the top of the right connecting rod.

If this marker is not specified, the respectivemarker of the left side is mirrored with respectto the vehiclexz-mid-plane

pos_left_car_body_bearing mm m (m) position of the left bearing that links thestabilizer to the car-body

pos_right_car_body_bearing mm m position of the right bearing that links thestabilizer to the car-body. If this marker is notspecified, the respective marker of the left sideis mirrored with respect to thevehiclexz-mid-plane

torsion_bar_stiffness Nmdeg

f (m) torsion-bar torsional stiffness, without effect ofthe cantilevers

cantilever_stiffness Nmdeg

f cantilever stiffness, described by a torsionalstiffness in series to the torsion-bar stiffness

bearing_stiffness Nmm

f radial stiffness of the stabilizer bearings

bearing_torsional_stiffn Nmdeg

f torsional stiffness of the stabilizer bearings

bearing_friction_torque Nm f friction torque of the stabilizer bearings,situated in-line with the torsional stiffness

Table 138: TS element data

Animation models

(standard: the element is displayed by a ‘wire’ automatically following the geometry and the elasticdeformation of the stabilizer)wire_diameter mm f diameter of the wire (default value reflecting actual torsion-bar

torsion stiffness)

Table 139: TS Animation models


Plot signals

level 1torsion-bar torsion angle deg torsion-bar torsion angletorque left-hand side Nm torque acting on left cantilever

Remark: due to friction in bearings, this torque mightdiffer slightly from right cantilever torque

torque right-hand side Nm torque acting on right cantilever

level 2bearing friction torque

left-hand side

Nm actual friction torque in left bearing

bearing friction torque

right-hand side

Nm actual friction torque in right bearing

force left-hand side [1] N x-component of body-fixed stabilizer force acting onleft lower link (or hub-carrier, resp.)

force left-hand side [2] N y-component of body-fixed stabilizer force acting onleft lower link (or hub-carrier, resp.)

force left-hand side [3] N z-component of body-fixed stabilizer force acting onleft lower link (or hub-carrier, resp.)

force right-hand side [1] N x-component of body-fixed stabilizer force acting onright lower link (or hub-carrier, resp.)

force right-hand side [2] N y-component of body-fixed stabilizer force acting onright lower link (or hub-carrier, resp.)

force right-hand side [3] N z-component of body-fixed stabilizer force acting onright lower link (or hub-carrier, resp.)

Table 140: TS plot signals

9.34 WL Watt Linkage

Watt linkage couples three bodies in the following way: one body (the ‘central one’) carries an ‘equalizer lever’

with two bearings, that can rotate freely about a body-fixed axis. On the bearings, two rods are mounted, each

connecting one of the other two bodies (the ‘left’ and the ‘right’ one) with the equalizer lever. Thus, in the case

of ideally stiff bearings and rods, one degree of freedom of the set of three bodies is removed.

Incosin/mbs, for the sake of accuracy, the rods and bearings can be chosen non-stiff as well. In that case, the

Watt linkage behaves as a three-body force element rather than a kinematic constraint.

I/O signals and other element-specific data in the definition block

l1 - st name of left body (RB,FB, orBO element) the left rod is mounted tol2 - st name of right body (RB,FB, orBO element) the right rod is mounted tol3 - st name of central body (RB,FB, orBO element) the equalizer lever is mounted on

Table 141: WL I/O signals and other element-specific data

Element data


attachm_left_rod_body mm m (m) body-fixed attachment point of left rod at leftbody

attachm_left_rod_equal_lever mm m (m) body-fixed attachment point of left rod atequalizer lever

attachm_right_rod_body mm m (m) body-fixed attachment point of right rod atright body

attachm_right_rod_equal_lever mm m (m) body-fixed attachment point of right rod atequalizer lever

equalizer_lever_bearing mm m (m) body-fixed position of equalizer bearing atcentral body

rot_axis_equal_lever mm f3 (m) direction vector of equalizer lever rotation axis

spring_stiffn_left_rod Nmm

f (m) spring stiffness of left rodpreload_left_rod N f static preload force of left rod in reference

position. If data-blockpreloads is present, thisvalue is overridden with the respective value ofthis data-block

damper_coeff_left_rod Nsm

f damper coefficient of left rod

spring_stiffn_right_rod Nmm

f (m) spring stiffness of right rodpreload_right_rod N f static preload force of right rod in reference

position. If data-blockpreloads is present, thisvalue is overridden with the respective value ofthis data-block

damper_coeff_right_rod Nsm

f damper coefficient of right rod

Table 142: WL element data

Animation models

rod


Table 143: WL animation models

Plot signals

Table 144: WL plot signals

level 1

deflection left rod mm deflection of left rod

deflection right rod mm deflection of right rod

deflection vel. left rod ms

deflection velocity of left rod

deflection vel. right rod ms

deflection velocity of right rod

total force left rod N total force along left rod: spring + damper

total force right rod N total force along right rod: spring + damper

equal. lever rot. angle deg equalizer lever rotation angle

level 2

spring force left rod N spring force along left rod

spring force right rod N spring force along right rod

damper force left rod N damper force along left rod

damper force right rod N damper force along right rod

equal. lever ang. velocity rads

equalizer lever angular velocity


List of Figures

1 cosin/mbs workbench . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 cosin/show workbench . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 1D and 2D spline browser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 cosin/mbs workbench control buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5 Supported ECU controller types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

6 cosin/mbs Simulink block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

7 cosin/mbsinput mask in Simulink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

8 BFfriction characteristic data points and approximation . . . . . . . . . . . . . . . . . . . . . . . 52

9 BF friction nodes placement (here along 20 rings), ball top and bottom boundaries defined by

anglesαmin andαmax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

10 BF ball joint friction animation model in stand-alone simulation usingcosin/cb . . . . . . . . . . . 58

11 HMhydro-mount model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

12 HM representation of hydro-mount model as single-mass oscillator . . . . . . . . . . . . . . . . . . 76


List of Tables

1 Data types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 1D spline browser function keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 2D spline browser function keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5 Additional default value definitions in data-block $model . . . . . . . . . . . . . . . . . . . . . . 17

6 Group data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

7 General data in element definition block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

8 cosin/wind data-block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

9 cosin/wind typeconstant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

10 cosin/wind type file_v_of_t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

11 cosin/wind typefile_v_of_x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

12 cosin/wind typefunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

13 ECU: Parameter of Standard ABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

14 ECU: Parameter of Advanced ABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

15 ECU: Parameter of ESP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

16 ECU: Parameter of Automatic Four-Wheel Drive Select . . . . . . . . . . . . . . . . . . . . . . . 29

17 ECU: Parameter of ATTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

18 ECU: Parameter of LSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

19 ECU: Parameter of Active LSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

20 ECU: Parameter of CLD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

21 ECU: Parameter of Four-Wheel Steering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

22 ECU: Parameter of EPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

23 ECU: Parameter of Advanced EPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

25 ECU: Parameter of General Force Actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

26 Driver-model parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

27 File identifiers in command line invocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

28 Program options in command line invocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

29 Simulink block input signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

30 Simulink block output signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

31 AC I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

32 AC element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

33 AC animation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

34 AC plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

35 AD I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

36 AD element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

37 ADanimation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

38 AD plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

39 AS I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

40 AS element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

41 ASanimation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

42 AS plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

43 BE I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

44 BE element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

45 BEanimation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

46 BEplot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49


47 BJ I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

48 BJ element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

49 BJanimation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

50 BJ plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

51 BF element data, simple model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

52 BFplot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

53 BF element data, detailed model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

54 BF plot signals, detailed model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

55 BR I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

56 BR element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

57 BR plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

58 CJ I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

59 CJ element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

60 CJ plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

61 CS I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

62 CS element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

63 CS animation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

64 CS plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

65 DI I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

66 DI element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

67 DI animation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

68 DI plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

69 DS I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

70 DS element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

71 DS animation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

72 DS plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

73 DT I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

74 DT element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

75 DT plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

76 EF I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

77 EF element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

78 EF plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

79 ET I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

80 ET plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

81 FB element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

82 FBanimation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

83 FBplot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

84 HMelement data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

85 HMplot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

86 IFI/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

87 IFelement data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

88 IFanimation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

89 IFplot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

90 KCdata in$simulation data block of sim-file . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

91 KCI/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

92 KCelement data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

93 KC plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81


94 MH I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

95 MH element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

96 MH plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

97 PS I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

98 PS element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

99 PS plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

101 PT I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

102 PT element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

103 PT animation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

104 PTplot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

105 RBI/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

106 RB element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

107 RBanimation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

108 RBplot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

109 RJ I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

110 RJ element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

111 RJ plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

112 RO element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

113 SC I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

114 SC element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

115 SCplot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

116 SD I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

117 SDelement data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

118 SDanimation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

119 SD plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

120 SJI/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

121 SJelement data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

122 SJanimation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

123 SJplot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

124 SRI/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

125 SR element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

126 SRplot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

127 ST I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

128 ST element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

129 ST plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

130 TII/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

131 TIelement data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

132 TI element data in second data block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

133 TIplot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

134 TJ I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

135 TJ element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

136 TJ plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

137 TS I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

138 TS element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

139 TS Animation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

140 TS plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

141 WL I/O signals and other element-specific data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125


142 WL element data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

143 WL animation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

144 WL plot signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126


Index

AC General Actuator with User-Written Control Code,

40

AD Aerodynamic Forces and Moments, 41

AS Acceleration Sensor, 44

BE General Bearing, 46

BF Ball Joint Friction Subsystem, 51

BJ Ball Joint, 50

BO Body, 59

BR Brake System, 59

CJ Cardan (Hooke) Joint, 62

CS Conceptual Suspension, 63

data types, 3

DI Distance Sensor, 67

DS Damper Strut Assembly, 68

DT Drive Torques, 71

ECU:Active LSD (Limited Slip Differential), 30

ECU:Advanced ABS, 27

ECU:Advanced EPS, 32

ECU:ATTS (Automatic Torque Transfer System), 29

ECU:Automatic Four-Wheel Drive Select, 28

ECU:CLD (Controlled Partially Locking Differentials),

31

ECU:EPS (Electronic Power Steering), 32

ECU:ESP (Electronic Stability Program), 27

ECU:Four-Wheel Steering, 31

ECU:General Force Actuator, 33

ECU:LSD (Limited Slip Differential), 30

ECU:Standard ABS, 26

EF External Force, 72

element data, 5

ET External Torque, 73

FB Flexible Body, 73

HM Hydro-Mount Subsystem, 75

IFInternal Force, 77

KC Kinematics&Compliance Output Signals, 78

MH Measuring Hub, 82

multi-body system, 1

PS Propulsion System, 83

PT Pushrod-Activated Torsion Bar Springs and Dampers,

90

RB Rigid Body, 94

RJ Revolute Joint, 101

RO Rod and Straight Pipe, 102

SC Steering Assembly for Conceptual Suspension, 103

SD General Spring/Damper, 105

simulation workbench, 3

SJ Spherical-Spherical Joint, 109

SR Steering Assembly, Rack-and-Pinion, 109

ST Semi-Automatic Transmission, 115

TI Tire Model Interface, 117

TJ Translational Joint, 122

TS Torsion-Bar Stabilizer, 123, 125

132