15-Suspension Systems and Components v2

7/31/2019 15-Suspension Systems and Components v2

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Suspension systems and

components


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Objectives

To provide good ride and handling performance vertical compliance providing chassis isolation

ensuring that the wheels follow the road profile

very little tire load fluctuation

To ensure that steering control is maintained during maneuvering wheels to be maintained in the proper position wrt road surface

To ensure that the vehicle responds favorably to control forces produced by thetires during longitudinal braking

accelerating forces,

lateral cornering forces and

braking and accelerating torques

this requires the suspension geometry to be designed to resist squat, dive and roll of the

vehicle body To provide isolation from high frequency vibration from tire excitation

requires appropriate isolation in the suspension joints

Prevent transmission ofroadnoise to the vehicle body


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Vehicle Axis system

Un-sprung mass

Right-hand orthogonal axissystem fixed in a vehicle

x-axis is substantiallyhorizontal, points forward, and

is in the longitudinal plane ofsymmetry.

y-axis points to driver's rightand

z-axis points downward.

Rotations: A yaw rotation about z-axis.

A pitch rotation about y-axis.

A roll rotation about x-axis

SAE vehicle axes

Figure from Gillespie,1992


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Tire Terminology - basic

Camber angle angle between the wheel

plane and the vertical

taken to be positive when thewheel leans outwards from

the vehicle Swivel pin (kingpin)

inclination angle between the swivel pin

axis and the vertical

Swivel pin (kingpin) offset distance between the centreof the tire contact patch and

intersection of the swivel pinaxis and the ground plane

Figure from Smith,2002


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Tire Terminology - basic

Castor angle inclination of the swivel pin axis

projected into the foreaftplane through the wheel centre

positive in the direction shown.

provides a self-aligning torquefor non-driven wheels.

Toe-in and Toe-out difference between the front

and rear distances separatingthe centre plane of a pair ofwheels,

quoted at static ride height toe-in is when the wheel centreplanes converge towards thefront of the vehicle



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The mobility of suspension

mechanisms



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Analysis of Suspension Mechanisms

3D mechanisms

Compliant bushes create variable link lengths

2D approximations used for analysis Requirement

Guide the wheel along a vertical path

Without change in camber Suspension mechanism has various SDOF

mechanisms


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The mobility of suspension

mechanisms Guide motion of each

wheel along (unique)vertical path relative tothe vehicle body withoutsignificant change incamber.

Mobility (DOF) analysis isuseful for checking for theappropriate number of

degrees of freedom, Does not help in synthesis

to provide the desiredmotion

M = 3(n 1) jh 2jl

Two-dimensional kinematics of common

suspension mechanisms



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Suspension Types -Dependent

Motion of a wheel on one side of the vehicle

is dependent on the motion of its partner on

the other side

Rarely used in modern passenger cars

Can not give good ride

Can not control high braking and accelerating

torques

Used in commercial and off-highway vehicles


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Hotchkiss Drive

Axle is mounted onlongitudinal leaf springs,which are compliantvertically and stiffhorizontally

The springs are pin-connected to the chassisat one end and to apivoted link at the other.

This enables the changeof length of the spring tobe accommodated due toloading

Hotchkiss Drive



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Semi-dependent Suspension

the rigid connection betweenpairs of wheels is replaced bya compliant link.

a beam which can bend andflex providing both positional

control of the wheels as wellas compliance.

tend to be simple inconstruction but lack scope fordesign flexibility

Additional compliance can beprovided by rubber or hydro-elastic springs.

Wheel camber is, in this case,the same as body roll

Trailing twist axle suspension


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Suspension Types - Independent

motion of wheel pairs is

independent, so that a

disturbance at one

wheel is not directlytransmitted to its

partner

Better ride and handling

Macpherson Strut Double wishbone

Trailing arm Swing axle

Semi trailing arm Multi-link


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Kinematic Analysis -Graphical

Graphical Analysis

Objective

The suspension ratio R

(the rate of change ofvertical movement at D

as a function of spring

compression)

The bump to scrub ratefor the given position of

the mechanism.



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Kinematic Analysis -Graphical

Draw suspensionmechanism toscale, assumechassis is fixed

Construct thevelocity diagram

VB=

BArBA



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Kinematic Analysis Sample

calculation

Double wish bone

The objectives are

Determine camber angle, and suspension ratio R(as defined in theprevious example)

For suspensionmovement described by

q varying from 80 to100

Given that in the staticladen position q = 90.

Simplified

suspensionmodel

Figure from Smith,2002, Google search


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Kinematic Analysis Sample

calculation

Positions are provided

Two non-linear equations solved for positions described

interval 1


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Kinematic Analysis

f


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Kinematic Analysis

The second part of the solution begins by expressing the length of thesuspension spring in terms of the primary variable and then proceedsto determine the velocity coefficients

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Kinematic Analysis - Results


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Roll centre analysis

Two Definitions

SAE : a point in thetransverse plane throughany pair of wheels at which

a transverse force may beapplied to the sprung masswithout causing it to roll

Kinematics : the roll centreis the point about which the

body can roll without anylateral movement at eitherof the wheel contact areas


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Limitations of Roll Centre Analysis

As roll of the sprung mass takes place, the

suspension geometry changes, symmetry of

the suspension across the vehicle is lost and

the definition of roll centre becomes invalid.

It relates to the non-rolled vehicle condition and

can therefore only be used for approximations

involving small angles of roll Assumes no change in vehicle track as a result of

small angles of roll.

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Roll-centre determination

AronholdKennedy theorem ofthree centers : when three bodiesmove relative to one anotherthey have three instantaneouscenters all of which lie on thesame straight line

Iwb can be varied by angling theupper and lower wishbones todifferent positions, therebyaltering the load transferbetween inner and outer wheelsin a cornering maneuver.

This gives the suspensiondesigner some control over thehandling capabilities of a vehicle For a double wishbone


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In the case of the

MacPherson strut

suspension the upper

line defining Iwb isperpendicular to the

strut axis.

Swing axle roll center is

located above thevirtual joint of the

axle.

Macpherson strut

Swing AxleFigure from Smith,2002

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Roll centre for a four link rigid axle

suspension

Roll centre location for semi-trailing arm

suspension

Roll centre location for a Hotchkiss suspension


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Force Analysis - spring and wheel rates

Relationship between

spring deflections and

wheel displacements in

suspensions is non-linear

Desired wheel-rate

(related to suspension

natural frequency) hasto be interpreted into a

spring-rate

W and S are the wheel and

spring forces respectively

v and u are the corresponding

deflections

Notation for analyzing spring and

wheel rates in a double wishbone

suspension

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Spring and wheel rates

From principle of virtual work

Wheel rate

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Spring and wheel rates

Combined Equation is

Similarly can be derived for other suspension

geometries

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Wheel-rate for constant natural

frequency with variable payload

Simplest representation of undamped vibration

kw wheel rate

ms proportion of un-sprung mass

Change in wheel rate required for change in payload.

Static displacement

To maintain wn constant, the static deflection needs to be

constant. Combining both equations

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frequency with variable payload

Integrating the equation and substituting with initial

conditions provides the following expression

Substituting back , we obtain

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frequency with variable payloadWheel load v. wheel deflection Wheel rate v. wheel deflection

Typical wheel load and wheel rate as functions of wheel displacement


R and dR/dv are known from geometric analysis

gives ks if kw is known from the above graphs

ks can be obtained as a function of v and u so as to get constant frequency

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Forces in suspension members - Basics

Mass of the members isnegligible compared to thatof the applied loading.

Friction and compliance atthe joints assumed

negligible and the spring orwheel rate needs to beknown

Familiar with the use offree-body diagrams for

determining internal forcesin structures

Conditions for equilibriumEquilibrium of two and three force

members, (a) Requirements for equilibrium

of a two force member (b) Requirements

for equilibrium of a three-force member


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Vertical loading

Force analysis of a double wishbone suspension (a) Diagram showing applied forces (b)

FBD of wheel and triangle of forces (c) FBD of link CD and triangle of forces


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Vertical loading

Assume FW is the wheel load and FS the force

exerted by the spring on the suspension

mechanism

AB and CD are respectively two-force and

three force members

FB and FC can be determined from concurrent

forces

Similar analysis possible for other types also.

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Vertical loading- Macpherson

Force analysis of a MacPherson strut, (a) Wheel loading, (b) Forces acting

on the strutFigure from Smith,2002

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Other Loadings

Lateral Loadings due to cornering effects

Longitudinal loadings arise from

braking,

drag forces on the vehicle and

shock loading due to the wheels striking bumps

and pot-holes.

Same method as before used to analyze these

loading conditions

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F i i b


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Forces in suspension members

Dynamic factors for Shock loading

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Anti Squat / Anti-dive

During braking there is

a tendency for the

sprung mass to dive

(nose down) and During acceleration the

reverse occurs, with the

nose lifting and the rear

end squattingFree body diagram of a vehicle during braking


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Anti-squat / Anti-dive

During braking there is

a tendency for the

sprung mass to dive

(nose down) and During acceleration the

reverse occurs, with the

nose lifting and the rear

end squattingFree body diagram of a vehicle during braking


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Wheel loads during braking

Assume fixed brakingratio

k=Bf/(Bf+Br)

Add DAlembert force (-ma)

Moment about the reartyre gives

NfL-mah-mgc=0 Nf=mah/L+mgc/L

Nr=mgb/L-mah/L

Effective load increases in the front and decreases at the rear wheel

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Consider side view and

wheel pivoting at Of

Sf suspension force

Sf= Sf+ Sf(static +change)

Moments about Ofgive

Nfe-S

fe-B

ff=0

0

( )

tan

f

f

maheB f

L

B mak

f h

e kL

Condition for no dive

%age of anti dive given bytan

( ) *100tan '

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Anti-squat / Anti-dive

For rear suspension

If these conditions are met zero deflection in front / reartires

If the pivots lie below the locus less than 100% anti-divewill be obtained.

In practice anti-dive does not exceed 50% : Subjectively zero pitch braking is undesirable

There needs to be a compromise between full anti-dive and

anti-squat conditions Full anti-dive can cause large castor angle changes (because all

the braking torque is reacted through the suspension links)

resulting in heavy steering during braking.

tan(1 )

f h

e L k

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Anti-squat/ Anti-dive

Documents

15-Suspension Systems and Components v2