Structural Analysis of Car Disk Brake

1

CHAPTER I

INTRODUCTION

1.1 GENERAL INTRODUCTION:

When a brake is working, the transformation of kinetic energy of moving masses into

thermal energy takes place. Brake elements are heated, which leads to the deterioration of

work conditions of a brake pad, increasing its, wear and decreasing the coefficient of friction.

Therefore, the limitation of brake heating is one of the important problems in the calculation

and construction brake blocks, and in certain cases the thermal calculation defines the choice

of a brake.

When the construction of brake systems is being designed, it is necessary to know the

temperature and the thermal distortion of the interface in the frictional contact region. The

analytical definition of heating parameters must take into account the condition under which

the mechanism must work. Thus, in intensive momentary braking the radiation of heat into

the surroundings may be neglected. Then since the brake pads are made of materials with

low thermal conductivity, almost all the heat generated in friction is directed inside the disk.

In view of the short duration of the braking process, the heat generated has no time to heat all

the disk and, hence, the temperature of the disk working surface is considerably higher than

the mean value of the volume temperature.

A. Yevtushenko [1] have studied the determination of heat and thermal distortion in

braking system and have shown that the change is magnitude of a contact area due to a

thermal distortion of a originally plane disk surface may be neglected.

D.M. Rowson [2] Has rederived the equations for the surface temperature rise at the

interface between a friction material and a brake disk to show how they are interrelated by

making suitable assumptions. He has also calculated for actual contact area to how the heat

generated during braking enters the disk brake, using an asbestos based friction material

rubbing on a cast iron disk brake.

Thomas Valvano [3] has developed an analytical method to predict thermal distortion

of a brake rotor. His technique involves utilizing a PC based computer program to calculate

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the necessary thermal parameters and apply the result as input to a finite element based

thermal stress analysis.

Ji-Hoon Choi [4] has preformed transient analysis for thermoelastic contact problem

of disk brake with frictional heat generation using Finite Element Method. He has

investigated the thermoelastic instability (TEI) phenomenon i.e. The unstable growth of

contact pressure and temperature and the influence of the material properties on the

thermoelastic behavior.

G.H. Gao [5] has shown that using a two dimensional model for thermal analysis

implies that the contact conditions and frictional heat flux transfer are independent of ,

which may lead to false thermal elastic distortions and unrealistic contact conditions. Hence

he has presented an analytical model for the determination of the contact temperature

distribution on the working surface of a brake.

R.El Abdi & H Samrout [6] have presented an Anisothermal elasto viscoplastic three

dimensional model used to predict the response of disk brakes mounted on the French TGV

(High speed trains). They have studied the cyclic viscoplastic behaviours under in phase

changes of temperature and strain is analyzed by using this elaborate anisothermal model

with its material constants determined from isothermal experiments.

In the present work an attempt has been made for the transient heat conduction

analysis of disk brakes with frictional heat generation is performed using FEM. At the

present work the experimental data of A. Yevtushenko & Ivanyk [1] have been employed for

comparison. Further the variation of temperatures & thermal stress induced in the disk brake

is reported for various flange widths & various materials. Finally conclusion has been drawn

for the proper material for disk brake and it is shown that the Ansys results are consistent

with the experimental data for the same time of braking.

1.2 STATEMENT OF THE PROBLEM:

The statement of the problem is ―Transient thermal analysis as a disc brake rotor

using F.E.A (Finite Element Analysis)‖.

3

1.3 OBJECTIVES OF THE PROJECT:

The present investigation is aimed to study.

The given disc brake rotor for its stability and rigidity (for this Thermal analysis and

coupled structural analysis is carried out on a given disc brake rotor).

Best combination of parameters of disc brake rotor like Flange width, wall thickness

and material there by a best combination is suggested. (for this three different

combinations in each case is analyzed)

The correlation between Ansys results and experimental results.

1.4 FUTURE SCOPE OF THE PROJECT:

In the present investigation of Thermal analysis of disc brake, a simplified model of

the disc brake without any vents with only ambient air cooling is analyzed by FEM package

ANSYS.

As a future work, a complicated model of Ventilated disc brake can be taken and there

by forced convection is to be considered in the analysis.

The benefit of utilizing analytical methods in the development of components is that

multiple design iterations can be evaluated of minimal costs. With the successful correlation

of test and analytical data, it is felt confident that this method can be utilized to evaluate

multiple design proposals with respect to rotor distortion and recommended optimum

component design parameters to meet the design specifications.

The determination of thermal fatigue life is another development to be investigated.

Thermal fatigue evaluation would require long heat cycles to ensure that temperature and

resultant stresses attain steady state operating conditions. Also, the finite element is close to

the friction surface may need to be further refined to accurately predict thermal stresses and

thus computer file sizes and running time need to be addressed.

Considering variable thermal conductivity, variable specific heat and non uniform

deceleration of the vehicle still complicates the analysis. This can be considered for the

future work.

4

CHAPTER-2

LITERATURE REVIEW

2.1 INTRODUCTION:

A brake is a device by means of which artificial frictional resistance

is applied to moving machine member, in order to stop the motion of a machine.

In the process of performing this function, the brakes absorb either kinetic energy of

the moving member or the potential energy given up by objects being lowered by hoists,

elevators etc., the energy absorbed by brakes is dissipated in the form of heat. This heat is

dissipated in the surrounding atmosphere.

2.2 BRAKING REQUIREMENTS:

The brakes must be strong enough to stop the vehicle with in a minimum distance in

an emergency.

The driver must have proper control over the vehicle during braking and vehicle must

not skid.

The brakes must have well anti fade characteristics i.e, their effectiveness should not

decrease with constant prolonged application.

The brakes should have well anti wear properties.

2.3 CLASSIFICATION OF BRAKES:

Hydraulic brakes.

Electric brakes.

Mechanical brakes.

The mechanical brakes according to the direction of acting force may be sub divided

into the following two groups:

1. Radial brakes.

2. Axial brakes.

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2.3.1 RADIAL BRAKES:

In these brakes the force acting on the brake drum is in radial direction. The radial

brake may be sub divided into external brakes and internal brakes.

2.3.2 AXIAL BRAKES:

In these brakes the force acting on the brake drum is only in the axial direction e.g.

Disc brakes, Cone brakes.

Fig 2.1 Disc Brake

2.4 DISC BRAKES:

A disc brake consists of a cast iron disc bolted to the wheel hub and a stationary housing

called caliper. The caliper is connected to some stationary part of the vehicle like the axle

casing or the stub axle as is cast in two parts each part containing a piston. In between each

piston and the disc there is a friction pad held in position by retaining pins, spring plates etc.

passages are drilled in the caliper for the fluid to enter or leave each housing. The passages

are also connected to another one for bleeding. Each cylinder contains rubber-sealing ring

between the cylinder and piston. A schematic diagram is shown in the figure.

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2.4.1 PRINCIPLE:

The principle used is the applied force (pressure) acts on the brake pads,

which comes in to contact with the moving disc. At this point of time due to friction the

relative motion is constrained.

A moving car has a certain amount of Kinetic energy and the brakes have to remove

this energy from the car in order to stop it. Each time the car is stopped, the brakes convert

Kinetic energy to heat generated by the friction between the pads and the disc slows the disc

down.

Fig 2.2 Working of Disc brake

2.4.2 WORKING:

When the brakes are applied, hydraulically actuated pistons move the

friction pads in to contact with the disc , applying equal and opposite forces on the later. On

releasing the brakes the rubber-sealing ring acts as return spring and retract the pistons and

the friction pads away from the disc (see fig 2.2)

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2.5 LOCATION OF DISC BRAKE:

Fig 2.3 Location of Disc Brakes

The main components of the disc brake are:

The Brake pads

The caliper which contains the piston

The Rotor , which is mounted to the hub

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2.6 VENTED DISC BRAKES:

Most car disc brakes are vented as shown in the below figure:

Fig 2.4 Vents provided on Disc Brakes

Vented disc brakes have a set of vanes, between the two sides of the disc that pumps

air through the disc to provide cooling.

2.7 TYPES OF DISC BRAKES:

1. Swinging caliper disc brake.

2. Sliding caliper disc brake.

3. Self-adjusting disc brake.

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2.7.1 SWINGING CALIPER DISC BRAKE:

Fig 2.5 Swinging Caliper Type Disc Brake

The caliper is hinged about a fulcrum pin and one of the friction pads is fixed to the

caliper. The fluid under pressure presses the other pad against the disc to apply the brake. The

reaction on the caliper causes it to move the fixed pad inward slightly applying equal pressure

to the other side of the disc. The caliper automatically adjusts its position by swinging about

the pin. This is shown in the fig 2.5

2.7.2 SLIDING CALIPER DISC BRAKE:

Fig 2.6 Sliding Caliper Type Disc Brake

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There are two pistons between which the fluid under pressure is sent which presses on

friction pad directly on to the disc where as the other pad is passed indirectly via the caliper.

Figure (2.6) shows the Sliding Caliper Type Disc Brake System.

2.7.3 SELF-ADJUSTING BRAKES :

Fig 2.7 Self Adjusting Disc Brake

The single-piston floating-caliper disc brake is self-centering and self-

adjusting. The caliper is able to slide from side to side so it will move to the center each time

the brakes are applied. Also, since there is no spring to pull the pads away from the disc, the

pads always stay in light contact with the rotor ( the rubber piston seal and any wobble in the

rotor may actually pull the pads a small distance away from the rotor ). This is important

because the pistons in the brakes are much larger in diameter than the ones in the master

cylinder. If the brake pistons retracted into their cylinders, it might take several applications

of the brake pedal to pump enough into the brake cylinder to engage the brake pads. The

figure 2.7 shows Self –adjusting disc brake.

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2.8 SHAPE OF DISC:

Fig 2.8 A 3-D model of disc

While it is true that some discs were and still are produced according to simple, flat

and circular geometry, there shape is normally more complex and can be broken down into a

number of parts, each corresponding to the particular function performed.

The braking surface is the area on which the braking action of the friction material

takes place. Dimensions are such as to ensure that the specific power output is too high. A

value of 230 W/cm2 of braking surface is the basis for calculating size, although this value

can change considerably when the disc is very well ventilated and can reach 623 W/cm2

The second function is that of attachment provided by the central part of the disc

which has a circular aperture which serves to center the wheel axle. The central part of the

disc is surrounded by a number of holes for the hub screws and wheel bolts.

The disc is therefore required to perform two additional tasks: induce air movement

like the rotor in a centrifugal fan and, simultaneously, act as a heat exchanger like a radiator.

The circular shape of a disc makes it particularly well suited to this dual role. In fact as the

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disc rotates it sets in motion the laminar stratum of air with which it is in contact. The

external part of the disc rotates at a greater linear speed that the part near to the carrier of hat.

Here, dynamic pressure acting on the air is greater in as much as it varies with the square of

the speed.

The shape of the blades is a compromise between efficiency and the production

difficulties they create. The output of a turbine is given by the ratio between energy

transmitted to the gas and the energy required to make the turbine rotate. This output

improves when the blades are shaped and does not obstruct movement of the gas. This is

why discs receiving a considerable quantity of energy have shaped blades which, at a given

rotational speed, optimize the speed of circulation. There is, however, a limit represented by

the speed of heat transfer from within the metal towards the gas. We have to bear in mind

that same blades shape requires the production of both specific right and left discs.

2.9 BRAKE PADS STRUCTURE AND GEOMENTRY:

Fig 2.9 Section of a Pad

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Fig 2.10 Disc Brake Pad

The pad is essentially a piece of material designed to rub against the disc

surface in order to convert mechanical energy into thermal energy. In this sense it is no

different from the linings in a drum brake. Its distinguishing feature, however, is that the

friction surface is flat. We can imagine calipers where pads are nothing more than a piece of

friction material.

In reality the pad is rather more complicated as it is made up on numerous parallel

layers produced from different materials. The thickest layer is the true friction material that

comes into contact with the disc and gradually wears down. On the opposite side is the

support or plate, a flat plate of mild steel about 5 mm thick. Its main purpose is to distribute

the force exerted by the piston on a limited area would risk damaging them. The thickness of

the support is therefore calculated so that under maximum force it has an imperceptible

flexing distortion that does not cause the material to wear unevenly. The purpose of the

support is also to secure and position the pad. In particular, sections of this metal plate rest

against the caliper during braking. This is because the disc tends to drag the pad in the

direction of rotation.

The definitive form is the result of this compromise, but it is also based on

calculations. Calculations performed on finished elements not only make it possible to

determine pressure distribution but also provide useful information relative to both localized

stresses that may possible cause breakage, and heat diffusion.

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CHAPTER-3

FINITE ELEMENT METHOD

3.1 INTRODUCTION:

The finite element method is numerical analysis technique for obtaining approximate

solutions to a wide variety of engineering problems, Because of its diversity and flexibility as

an analysis tool, it is receiving much attention in engineering schools and industries. In more

and more engineering situations today, we find that it is necessary to obtain approximate

solutions to problems rather than exact closed form solution.

It is not possible to obtain analytical mathematical solutions for many engineering

problems. An analytical solutions is a mathematical expression that gives the values of the

desired unknown quantity at any location in the body, as consequence it is valid for infinite

number of location in the body. For problems involving complex material properties and

boundary conditions, the engineer resorts to numerical methods that provide approximate, but

acceptable solutions.

The finite element method has become a powerful tool for the numerical solutions of

a wide range of engineering problems. It has developed simultaneously with the increasing

use of the high-speed electronic digital computers and with the growing emphasis on

numerical methods for engineering analysis. This method started as a generalization of the

structural idea to some problems of elastic continuum problem, started in terms of different

equations or as an extrinum problem.

The fundamental areas that have to be learned for working capability of finite element

method include:

Matrix algebra.

Solid mechanics.

Variational methods.

Computer skills.

Matrix techniques are definitely most efficient and systematic way to handle algebra

of finite element method. Basically matrix algebra provides a scheme by which a large

number of equations can be stored and manipulated. Since vast majority of literature on the

finite element method treats problems in structural and continuum mechanics, including soil

and rock mechanics, the knowledge of these fields became necessary. It is useful to consider

15

the finite element procedure basically as a Variational approach. This conception has

contributed significantly to the convenience of formulating the method and to its generality.

The term ―finite element‖ distinguishes the technique from the use of infinitesimal

―differential elements‖ used in calculus, differential equations. The method is also

distinguished from finite difference equations, for which although the steps in to which space

is divided into finite elements are finite in size; there is a little freedom in the shapes that the

discrete steps can take. F.E.A is a way to deal with structures that are more complex than

dealt with analytically using the partial differential equations. F.E.A deals with complex

boundaries better than finite difference equations and gives answers to the ‗real world‘

structural problems. It has been substantially extended scope during the roughly forty years

of its use.

F.E.A makes it possible it evaluate a detail and complex structure, in a computer

during the planning of the structure. The demonstration in the computer about the adequate

strength of the structure and possibility of improving design during planning can justify the

cost of this analysis work. F.E.A has also been known to increase the rating of the structures

that were significantly over design and build many decades ago.

In the absence of finite element analysis (or other numerical analysis), development of

structures must be based on hand calculations only. For complex structures, the simplifying

assumptions are required to make any calculations possible can lead to a conservative and

heavy design. A considerable factor of ignorance can remain as to whether the structure will

be adequate for all design loads. Significant changes in design involve expensive strain

gauging to evaluate strength and deformation.

3.1.1 TERMS COMMONLY USED IN FINITE ELEMENT METHOD:

Descritization: The process of selecting only a certain number of discrete points in

the body can be termed as Descritization.

Continuum: The continuum is the physical body, structure or solid being analyzed.

Node: The finite elements, which are interconnected at joints, are called nodes or

nodal points.

Element: Small geometrical regular figures are called elements.

Displace Models: The nodal displacements, rotations and strains necessary to specify

completely deformation of finite element.

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Degree of freedom: The nodal displacements, rotations and strains necessary to

specify completely deformation of finite element.

Local coordinate system: Local coordinate system is one that is defined for a

particular element and not necessary for the entire body or structure.

Global system: The coordinate system for the entire body is called the Global

coordinate system.

Natural coordinate system: Natural coordinate system is a local system, which

permits the specification of point with in the element by a set of dimensionless

numbers, whose magnitudes never exceeds unity.

Interpolation function: It is a function, which has unit value at one nodal point and a

zero value at all other nodal points.

Aspect ratio: The aspect ratio describes the shapes of the element in the assemblage

for two dimensional elements; this parameter is defined as the ratio of largest

dimension of the element to the smallest dimension.

Field variables: The principal unknowns of a problem are called the field variables.

17

Fig 3.1 Process of Finite Element Analysis

18

3.2 GENERAL DESCRIPTION OF F.E.M:

In the finite element method, the actual continuum of

body of matter like solid, liquid or gas is represented as an assemblage of sub divisions called

Finite elements. These elements are considered to be inter connected at specified points

known as nodes or nodal points. These nodes usually lie on the element boundaries where an

adjacent element is considered to be connected. Since the actual variation of the field

variables (like Displacement, stress, temperature, pressure and velocity) inside the continuum

are is not know, we assume that the variation of the field variable inside a finite element can

be approximated by a simple function. These approximating functions (also called

interpolation models) are defined in terms of the values at the nodes. When the field

equations (like equilibrium equations) for the whole continuum are written, the new unknown

will be the nodal values of the field variable. By solving the field equations, which are

generally in the form of the matrix equations, the nodal values of the field variables will be

known. Once these are known, the approximating function defines the field variable

throughout the assemblage of elements.

The solution of a general continuum by the finite element method always follows as orderly

step-by-step process. The step-by-step procedure for static structural problem can be stated

as follows:

STEP 1:- DESCRIPTION OF STRUCTURE (DOMAIN):

The first step in the finite element method is to divide the structure of solution region

in to sub divisions or elements.

STEP 2:- SELECTION OF PROPER INTERPOLATION MODEL:

Since the displacement (field variable) solution of a complex structure under any

specified load conditions cannot be predicted exactly, we assume some suitable solution,

within an element to approximate the unknown solution. The assumed solution must be

simple and it should satisfy certain convergence requirements.

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STEP 3:- DERIVATION OF ELEMENT STIFFNESS MATRICES

(CHARACTERISTIC MATRICES) AND LOAD VECTORS:

From the assumed displacement model the stiffness matrix [K(e)] and the load vector

P(e) of element ‗e‘ are to be derived by using either equilibrium conditions or a suitable

Variation principle.

STEP 4:- ASSEMBLAGE OF ELEMENT EQUATIONS TO OBTAIN THE

EQUILIBRIUM EQUATIONS:

Since the structure is composed of several finite elements, the individual element

stiffness matrices and load vectors are to be assembled in a suitable manner and the overall

equilibrium equation has to be formulated as

[K]φ = P

Where [K] is called assembled stiffness matrix,

Φ is called the vector of nodal displacement and

P is the vector or nodal force for the complete structure.

STEP 5:- SOLUTION OF SYSTEM EQUATION TO FIND NODAL VALUES OF

DISPLACEMENT (FIELD VARIABLE)

The overall equilibrium equations have to be modified to account for the boundary

conditions of the problem. After the incorporation of the boundary conditions, the

equilibrium equations can be expressed as,

[K]φ = P

For linear problems, the vector ‗φ‘ can be solved very easily. But for non-linear

problems, the solution has to be obtained in a sequence of steps, each step involving the

modification of the stiffness matrix [K] and ‗φ‘ or the load vector P.

STEP 6:- COMPUTATION OF ELEMENT STRAINS AND STRESSES.

From the known nodal displacements, if required, the element strains and stresses can

be computed by using the necessary equations of solid or structural mechanics.

In the above steps, the words indicated in brackets implement the general FEM step-

by-step procedure.

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3.3 ADVANTAGES OF F.E.M:

The F.E.M is based on the concept of discretization. Nevertheless as either a

variational or residual approach, the technique recognizes the multi dimensional continuity of

the body not only does the idealizations portray the body as continuous but it also requires no

separate interpolation process to extend the approximate solution to every point with in the

continuum. Despite the fact that the solution is obtained at a finite number of discrete node

points, the formation of field variable models inherently provides a solution at all other

locations in the body. In contrast to other variational and residual approaches, the F.E.M

does not require trail solutions, which must all, apply to the entire multi dimensional

continuum. The use of separate sub-regions or the finite elements for the separate trial

solutions thus permits a greater flexibility in considering continua of the shape.

Some of the most important advantages of the F.E.M derive from the techniques of

introducing boundary conditions. This is another area in which the method differs from other

variational or residual approaches. Rather than requiring every trial solution to satisfy the

boundary conditions, one prescribes the conditions after obtaining the algebraic equations for

assemblage.

No special techniques or artificial devices are necessary, such as the non-cantered

difference equations or factious external points often employed in the finite difference

method.

The F.E.M not only accommodates complex geometry and boundary conditions, but it

also has proved successful in representing various types of complicated material properties

that are difficult to incorporate in to other numerical methods. For example, formulations in

solid mechanics have been devised for anisotropy, nonlinear, hysteretic, time dependant or

temperature dependant material behavior.

One of the most difficult problems encountered in applying numerical procedures of

engineering analysis is the representation of non-homogeneous continua. Nevertheless the

F.E.M readily accounts for non-homogeneity by the simple tactic of assigning different

properties with in an element according to the pre selected polynomial pattern. For instance

it is possible to accommodate continuous or discontinuous variations of the constitutive

parameters or of the thickness of a two-dimensional body.

21

The systematic generality of the finite element procedure makes it a powerful and

versatile tool for a wide range of problems. As a result, flexible general-purpose computer

programs can be constructed. Primary examples of these programs are several structural

analysis packages which include a variety of element configurations and which can be

applied to several categories of structural problems. Among these packages are ASKA,

STRUDL, SAP and NASTRAN & SAFE. Another indicator of the generality of the method

is that programs developed for one field of engineering have been applied successfully to

problems in different field with a little or no modification.

Finally an engineer may develop a concept of the F.E.M at different levels. IT is

possible to interpret the method in physical terms. On the other hand the method may be

explained entirely in mathematical terms. The physical or intuitive nature of the procedure is

particularly useful to the engineering student and practicing engineer.

3.4 LIMITATION:

One limitation of finite element method is that a few complex phenomenon‘s are not

accommodated adequately by the method as its current state of development. Some examples

of such phenomenon form the realm of solid mechanics are cracking and fracture behaviour,

contact problems, bond failures of composite materials, and non-linear material behaviour

with work softening. Another example is transient, unconfined seepage problems. The

numerical solution of propagation or transient problem is not satisfactory in all respects.

Many of these phenomenon‘s are presently under research and refinements of the methods to

accommodate these problems better can be expected.

The finite element method has reached a high level of development as a solution

technique. How ever the method yields realistic results only if the coefficients or material

parameters, which describe the basic phenomenon, are available. Material non-linearity in

solid mechanics is a notable example of a field in which our understanding of material

behaviour has lagged behind the development of the analytical tool. In order to exploit fully

the power of the finite element method, significant effort must be direct towards the

development of constitutive laws and the evaluation of realistic coefficients and material

parameters.

22

Even the most efficient finite element computer code requires a relatively large

amount of computer memory and time. Hence use of this method is limited to those who

have access to relatively large, high-speed computers. The advent of time-sharing, remote

batch processing and computer service bureaus or utilities ahs alleviated this restriction to

some degree. In addition the method can be applied indirectly to common engineering

problems by utilizing tables, graphs and other analysis aids that have been generated by finite

element codes.

The most tedious aspects of the use of finite element methods are the basic processes

of sub-dividing the continuum and of generating error free input data for the computer.

Although these processes my be automated to a degree they have been totally accomplished

by computer because some engineer judgement may be employed in the descritization. Error

in the input data may go undetected and erroneous result obtained there form may appear

acceptable. Consequently it is essential that the engineer/programmer provide checks to

detect such errors. In addition to check internal code, an auxiliary routine that reads the input

data and generates a computer plot of the discritized continuum is desirable. This plot

permits a rapid visual check of the input data.

Finally as for any approximate numerical method the results of the finite element

analysis must be interpreted with care. We must be aware of the assumptions employed in

the formulation, the possibility of the numerical difficulties and the limitations in the material

characterizations used. A large volume of solution information is generated by a finite

element routine but this data is worthwhile only when its generation and interpretation are

tempered by proper engineering judgement.

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CHAPTER 4

F.E.A SOFTWARE – ANSYS

4.1 INTRODUCTION TO ANSYS PROGRAM:

ANSYS Stands for Analysis System Product.

Dr. John Swanson founded ANSYS. Inc in 1970 with a vision to commercialize the

concept of computer simulated engineering, establishing himself as one of the pioneers of

Finite Element Analysis (FEA). ANSYS inc. supports the ongoing development of

innovative technology and delivers flexible, enterprise wide engineering systems that enable

companies to solve the full range of analysis problem, maximizing their existing investments

in software and hardware. ANSYS Inc. continues its role as a technical innovator. It also

supports a process-centric approach to design and manufacturing, allowing the users to avoid

expensive and time-consuming ―built and break‖ cycles. ANSYS analysis and simulation

tools give customers ease-of-use, data compatibility, multi platform support and coupled field

multi-physics capabilities.

4.2 EVOLUTION OF ANSYS PROGRAM:

ANSYS has evolved into multipurpose design analysis software program, recognized

around the world for its many capabilities. Today the program is extremely powerful and

easy to use. Each release hosts new and enhanced capabilities that make the program more

flexible, more usable and faster. In this way ANSYS helps engineers meet the pressures and

demands modern product development environment.

4.3 OVERVIEW OF THE PROGRAM:

The ANSYS program is flexible, robust design analysis and optimization package.

The software operates on major computers and operating systems, from PCs to workstations

and to super computers. ANSYS features file compatibility throughout the family of

24

products and across all platforms. ANSYS design data access enables user to import

computer aided design models in to ANSYS, eliminating repeated work. This ensures

enterprise wide, flexible engineering solution for all ANSYS user.

USER INTERFACE:

Although the ANSYS program has extensive and complex capabilities, its

organization and user-friendly graphical user interface makes it easy to learn and use.

There are four graphical methods to instruct the ANSYS program:

1. Menus.

2. Dialog Boxes

3. Tool bar.

4. Direct input of commands.

MENUS:

Menus are groupings of related functions or operating the analysis program located in

individual windows. These include:

Utility menu

Main menu

Input window

Graphics window

Tool bar

Dialog box

DIALOG BOXES:

Windows that present the users with choices for completing operations or specifying

settings. These boxes prompt the user to input data or make decisions for a particular

function.

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TOOL BAR:

The tool bar represents a very efficient means for executing commands for the

ANSYS program because of its wide range of configurability. Regardless of how they are

specified, commands are ultimately used to supply all the data and control all program

functions.

OUTPUT WINDOW:

Records the ANSYS response to commands and functions.

GRAPHICS WINDOW:

Represents the area for graphic displays such as model or graphically represented

results of an analysis. The user can adjust the size of the graphics window, reducing or

enlarging it to fit to personal preferences.

INPUT WINDOW:

Provides an input area for typing ANSYS commands and displays program prompt

messages.

MAIN MENU:

Comprise the primary ANSYS functions, which are organized in pop-up side menus,

based on the progression of the program.

UTILITY MENU:

Contains ANSYS utility functions that are mapped here for access at any time during

an ANSYS session. These functions are executed through smooth, cascading pull down

menus that lead directly to an action or dialog box.

PROCESSORS:

ANSYS functions are organized into two groups called processors. The ANSYS

program has one pre-processor, one solution processor; two post processors and several

auxiliary processors such as the design optimizer. The ANSYS pre-processor allows the user

to create a finite element model to specify options needed for a subsequent solution. The

solution processor is used to apply the loads and the boundary conditions and then determine

26

the response of the model to them. With the ANSYS post processors, the user retrieves and

examines the solutions results to evaluate how the model responded and to perform additional

calculations of interest.

DATABASE:

The ANSYS program uses a single, centralized database for all model data and

solution results. Model data (including solid model and finite element model geometry,

materials etc) are written to the database using the processor. Loads and solution results data

are written using the solutions processor. Post processing results data are written using the

post processors. Data written to the database while using one processor are therefore

available as necessary in the other processors.

FILE FORMAT:

Files are used, when necessary, to pass the data from part of the program to another,

to store the program to the database, and to store the program output. These files include

database files, the results file, and the graphics file and so on.

4.4 REDUCING THE DESIGN AND MANUFACTURING COSTS

USING ANSYS (F.E.A):

The ANSYS program allows engineers to construct computer models or transfer CAD

models of structures, products, components, or systems, apply loads or other design

performance conditions and study physical responses such as stress levels, temperature

distribution or the impact of lector magnetic fields.

In some environments, prototype testing is undesirable or impossible. The ANSYS

program has been used in several cases of this type including biomechanical applications

such as hi replacement intraocular lenses. Other representative applications range from

heavy equipment components, to an integrated circuit chip, to the bit-holding system of a

continuous coal-mining machine.

ANSYS design optimization enables the engineers to reduce the number of costly

prototypes, tailor rigidity and flexibility to meet objectives and find the proper balancing

geometric modifications.

27

Competitive companies loom for ways to produce the highest quality product at the

lowest cost. ANSYS (FEA) can help significantly by reducing the design and manufacturing

costs and by giving engineers added confidence in the products they design. FEA is most

effective when used at the conceptual design stage. It is also useful when used later in

manufacturing process to verify the final design before prototyping.

PROGRAM AVAILABILITY:

The ANSYS program operates on 486 and Pentium based PCs running on Wndows95

or WindowsNT and workstations and super computers primarily running on UNIX operating

system. ANSYS Inc. continually works with new hardware platforms and operating systems.

ANALYSIS TYPES AVAILABLE:

1. Structural static analysis.

2. Structural dynamic analysis.

3. Structural buckling analysis.

Linear buckling

Non linear buckling

4. Structural non linearities

5. Static and dynamic kinematics analysis.

6. Thermal analysis.

7. Electromagnetic field analysis.

8. Electric field analysis

9. Fluid flow analysis

Computational fluid dynamics

Pipe flow

10. Coupled-field analysis

11. Piezoelectric analysis.

4.5 PROCEDURE FOR ANSYS ANALYSIS:

Static analysis is used to determine the displacements, stresses, strains and forces in

structures or components due to loads that do not induce significant inertia and damping

effects. Steady loading in response conditions are assumed. The kinds of loading that can be

applied in a static analysis include externally applied forces and pressures, steady state

28

inertial forces such as gravity or rotational velocity imposed (non-zero) displacements,

temperatures (for thermal strain).

A static analysis can be either linear or non linear. In our present work we consider

linear static analysis.

The procedure for static analysis consists of these main steps:

1. Building the model.

2. Obtaining the solution.

3. Reviewing the results.

4.5.1 BUILD THE MODEL:

In this step we specify the job name and analysis title use PREP7 to define the

element types, element real constants, material properties and model geometry element types

both linear and non-linear structural elements are allowed. The ANSYS element library

contains over 80 different element types. A unique number and prefix identify each element

type.

E.g. PLANE 42, PLANE 77

29

MATERIAL PROPERTIES:

Young‘s modulus(EX) must be defined for a static analysis .If we plan to apply inertia

loads(such as gravity) we define mass properties such as density(DENS).Similarly if we plan

to apply thermal loads (temperatures) we define coefficient of thermal expansion(ALPX).

4.5.2 OBTAIN THE SOLUTION:

In this step we define the analysis type and options, apply loads and initiate the finite

element solution. This involves three phases:

Pre – processor phase

Solution phase

Post-processor phase

The following table shows the brief description of steps followed in each phase:

Table 4.1 Description of steps in FEA

PREPROCESSOR

PHASE

SOLUTION PHASE POST-PROCESSOR

PHASE

GEOMETRY

DEFINITIONS

ELEMENT MATRIX

FORMULATION

POST SOLUTION

OPERATIONS

MESH GENERATION OVERALL MATRIX

TRIANGULARIZATION

POST DATA PRINT

OUTS(FOR REPORTS)

MATERIAL (WAVE FRONT) POST DATA

DEFINITIONS SCANNING POST DATA

DISPLAYS

CONSTRAINT

DEFINITIONS

DISPLACEMENT.

STRESS,ETC

LOAD DEFINITION CALCULATION

MODEL DISPLAYS

30

4.6 PRE – PROCESSOR:

Pre processor has been developed so that the same program is available on micro,

mini, super-mini and mainframe computer system. This slows easy transfer of models one

system to other.

Pre processor is an interactive model builder to prepare the FE (finite element) model

and input data. The solution phase utilizes the input data developed by the pre processor, and

prepares the solution according to the problem definition. It creates input files to the

temperature etc., on the screen in the form of contours.

4.6.1 GEOMETRICAL DEFINITIONS:

There are four different geometric entities in pre processor namely key points, lines,

areas and volumes. These entities can be used to obtain the geometric representation of the

structure. All the entities are independent of other and have unique identification labels.

MODEL GENERATIONS:

Two different methods are used to generate a model:

Direct generation.

Solid modeling

With solid modeling we can describe we can describe the geometric boundaries of the

model, establish controls over the size and desired shape of the elements and then instruct

ANSYS program to generate all the nodes and elements automatically. By contrast, with the

direct generation method, we determine the location of every node and size, shape and

connectivity of every element prior to defining these entities in the ANSYS model.

Although, some automatic data generation is possible (by using commands such as FILL,

NGEN, EGEN etc) the direct generation method essentially a hands on numerical method

that requires us to keep track of all the node numbers as we develop the finite element mesh.

This detailed book keeping can become difficult for large models, giving scope for modeling

errors. Solid modeling is usually more powerful and versatile than direct generation and is

commonly preferred method of generating a model.

31

MESH GENERATION:

In the finite element analysis the basic concept is to analyze the structure, which is an

assemblage of discrete pieces called elements, which are connected, together at a finite

number of points called Nodes. Loading boundary conditions are then applied to these

elements and nodes. A network of these elements is known as Mesh.

FINITE ELEMENT GENERATION:

The maximum amount of time in a finite element analysis is spent on generating

elements and nodal data. Pre processor allows the user to generate nodes and elements

automatically at the same time allowing control over size and number of elements. There are

various types of elements that can be mapped or generated on various geometric entities.

The elements developed by various automatic element generation capabilities of pre

processor can be checked element characteristics that may need to be verified before the

finite element analysis for connectivity, distortion-index, etc.

Generally, automatic mesh generating capabilities of pre processor are used rather

than defining the nodes individually. If required, nodes can be defined easily by defining the

allocations or by translating the existing nodes. Also one can plot, delete, or search nodes.

BOUNDARY CONDITIONS AND LOADING:

After completion of the finite element model it has to constrain and load has to be

applied to the model. User can define constraints and loads in various ways. All constraints

and loads are assigned set 1-D. This helps the user to keep track of load cases.

MODEL DISPLAY:

During the construction and verification stages of the model it may be necessary to

view it from different angles. It is useful to rotate the model with respect to the global system

and view it from different angles. Pre processor offers this capability. By windowing feature

pre processor allows the user to enlarge a specific area of the model for clarity and details.

Pre processor also provides features like smoothness, scaling, regions, active set, etc for

efficient model viewing and editing.

32

4.6.2 MATERIAL DEFINITIONS:

All elements are defined by nodes, which have only their location defined. In the case

of plate and shell elements there is no indication of thickness. This thickness can be given as

element property. Property tables for a particular property set 1-D have to be input.

Different types of elements have different properties for e.g.

Beams: Cross sectional area, moment of inertia etc

Shells: Thickness

Springs: Stiffness

Solids: None

The user also needs to define material properties of the elements. For linear static

analysis, modules of elasticity and poisson‘s ratio need to be provided. For heat transfer,

coefficient of thermal expansion, densities etc are required. They can be given to the

elements by the material property set to 1-D.

4.7 SOLUTION:

The solution phase deals with the solution of the problem according to the problem

definitions. All the tedious work of formulating and assembling of matrices are done by the

computer and finally displacements are stress values are given as output. Some of the

capabilities of the ANSYS are linear static analysis, non-linear static analysis, transient

dynamic analysis, etc.

4.8 POST – PROCESSOR :

It is a powerful user-friendly post-processing program using interactive colour

graphics. It has extensive plotting features for displaying the results obtained from the finite

element analysis. One picture of the analysis results (i.e. the results in a visual form) can

often reveal in seconds what would take an engineer hour to asses from a numerical output,

say in tabular form. The engineer may also see the important aspects of the results that could

be easily missed in a stack of numerical data.

33

Employing state of art image enhancement techniques, facilities viewing of:

Contours of stresses, displacements, temperatures, etc.

Deform geometric plots

Animated deformed shapes

Time-history plots

Solid sectioning

Hidden line plot

Light source shaded plot

Boundary line plot etc.

The entire range of post processing options of different types of analysis can be

accessed through the command / menu mode there by giving the user added flexibility and

convenience.

34

CHAPTER 5

CALCULATIONS OF DISC BRAKE

5.1. THE TEMPERATURE FIELD:

The circumstances noted above permit us to determine the heating temperature of the

brake disk surface by the solution of a transient boundary-value problem of thermal

conductivity for a half-space 0z , in a circular region Rr 0 of the surface on which

heat sources with a density of distribution are acting.

)()()(),( rRHrptfVtrq (5.1)

where the sliding speed V changes according to the law

s

s

ttt

tVtV

01)( 0 (5.2)

and the contact pressure p(r) is given by Hertz formula [5]

20

2

02

31)(

R

Pp

R

rprp

(5.3)

It is obvious that by the symmetry of the problem the maximum value of the

temperature on the surface of the half-space will be reached at the point r=0. At an arbitrary

moment of time t > 0 the temperature at the circular region centre r=0 of the surface of the

half-space due to the heat flux influence (5.1)-(5.3) is represented in the form [6]

ddss

R

s

tt

e

kkc

qtT

R

s

St

v

2

0

2/3

0

0 11)(2

)(

2

(5.4)

where

000 pfVq (5.5)

)(4

22

tk

sS (5.6)

Changing the order of integration in (5.4), which is valid because the conditions of the

theorem about integration under the integral sign hold, we obtain.

35

dstsPt

tsPt

t

R

ss

kkc

qtT

ss

R

v

),(

1),(11

2)( 10

2

0

0

(5.7)

Hence Pm denotes

)1,0()(

),(0

2/3

2

mdt

esP

t

m

S

m

(5.8)

Using the substitution of variable (5.6) to calculated the integral (5.8), if m=0, we

obtain

kts

S

kt

serfc

s

kdse

s

ktsP

2/

02

24),(

2 (5.9)

where erferfc 1

In that way, using also the rule of differentiation under the integral sign, we calculate

P1(s,T). After some transformations we have

ktSetkt

serfc

kstsP 4/

1

2

22

),(

(5.10)

Taking (5.9) and (5.10) into account, the temperature (5.7) at the centre of the disk

brake surface takes a form

dsek

t

t

s

kt

serfc

kt

s

t

t

R

s

K

qtT

R

ktS

sss

0

4/22

02

2211)(

(5.11)

In long braking (ts) it follows from (5.11) that

dskt

serfc

R

s

K

qtT

R

0

2

0

21)( (5.12)

If in addition we take t then from (5.12) it follows that

K

RqT

4

0

Or including the definition (5.5)

KR

PfVT

8

3 0 (5.13)

Formula (5.13) determines the maximum temperature of the disk brake surface in a

steady state of heat generation in long braking [4].

36

It follows from (5.13) that, at a constant power of heat generation (f VoP), the

temperature at the friction surface can be lowed by increasing the contact area or the thermal

conductivity coefficient of the disk material.

The experimental data for the temperature of the frictional surface of a disc brake in an

automobile weighing 1 ton when its velocity changes from V0 =96.6kmph to a complete halt

are presented in [2]. It has been found by dynamometric measurements that the load P carried

by the disc is on average 680 N. At a breaking moment the initial surface temperature of the

disc measured with a thermocouple was 175 oC and the maximum during braking was

215 oC, i.e. the temperature flash was 40

oC. The breaking time was ts = 4.8 s, the disc

material was cast iron for which k=1.286x10-4

m2 s

-1, K = 50 W m

-1 oC

-1 . The area of the

lateral disc surface was Aa = 329x10-4

m2 (the nominal contact area), and the

coefficient of friction was f = 0.25. Then on the basis (5.5) the density of the heat

flow directed into the disc is qo = 750000 W / m2

5.2 DISC BRAKE CALCULATIONS:

Given Data:

Velocity of the vehicle = 96.6 k.m.p.h = 26.833 m/s

Time for stopping the vehicle = 4.8 seconds

Mass of the vehicle = 1000 kg.

STEP-1:

Kinetic Energy (K.E) = ½ * m * v2

= ½ * 1000 * 26.8332

= 360 KJ

The above said is the Total Kinetic Energy induced while the vehicle is under motion.

STEP-2:

The total kinetic energy = The heat generated but the heat generated in one of the

wheel of the car is 1/3rd

the total kinetic energy.[2]

i.e. this 28.6 K. Cal/ft2 – hr.

1 Cal = 1/252 Btu [10]

& 1 Btu = 1.05504 KJ [10]

37

:. 05504.1252

10006.28

Q

= 120 KJ

which is 1/3rd

the total kinetic energy.

STEP-3:

The area of the rubbing faces

A =

A = )(2

1

2

2 rr

= (0.145622 – 0.1036

2)

A = 329x10-4

m2

STEP-4:

The density of heat flow (Heat Flux) directed in to the disc.

Heat Flux = ngtimefacexBrakiractingsurAreaofcont

generatedHeat

= 8.410329

1204 xx

q = 750000 w/m2

38

5.3 ASSUMPTIONS:

The analysis is done taking the disc brake efficiency as 30% (since the distribution

of the braking torque between the front and rear axle is 70:30)

Brakes are applied on all the four wheels.

The analysis is based on pure thermal loading and vibrations and thus only stress

levels due to the above is done. The analysis does not determine the life of the disc

brake.

Only ambient air-cooling is taken in to account and no forced convection is taken.

The kinetic energy of the vehicle is lost through the brake discs i.e. no heat loss

between the tyres and the road surface and the deceleration is uniform.

The disc brake model used is of solid type and not the ventilated one.

The thermal conductivity of the material used for the analysis is uniform throughout.

The specific heat of the material used is constant throughout and does not change

with the temperature.

39

CHAPTER 6

THERMAL ANALYSIS

6.1 INTRODUCTION:

A Thermal analysis calculates the temperature distribution and related thermal

quantities in a system or component. Typical thermal quantities are:

1. The temperature distributions

2. The amount of heat lost or gained

3. Thermal fluxes

TYPES OF THERMAL ANALYSIS:

1. A Steady State Thermal Analysis determines the temperature distribution and other

thermal quantities under steady state loading conditions. A steady state loading

condition is a situation where heat storage effects varying over a period of time can be

ignored.

2. A Transient thermal analysis determines the temperature distribution and other

thermal quantities under conditions that vary over a period of time

6.2 DEFINITION OF PROBLEM:

Due to the application of brakes on the car disc brake rotor, heat generation takes

place due to friction and this temperature so generated has to be conducted and dispersed

across the disc rotor cross section. The condition of braking is very much severe and thus the

thermal analysis has to be carried out.

The thermal loading as well as structure is axis-symmetric. Hence axis-symmetric

analysis is performed which is an exact representation for this thermal analysis.

40

Linear thermal analysis is performed to obtain the temperature field since

conductivity and specific heat of the material considered here are independent of temperature.

The analysis performed here is transient thermal analysis as temperature distribution varies

with time. (The time for thermal analysis is taken as 4.8 seconds of braking)

An Ansys thermal model was developed to predict temperatures through the brake

corner. The model includes the brake disc, pads, caliper, wheel, spindle and axle in order to

accurately predict brake system temperatures during long braking and heat soaking

conditions. In addition, the model can be used to predict the brake fluid temperature rise.

Various aspects of the brake thermal analysis process are schematically summarized in fig 6.1

below.

Fig 6.1 Brake Thermal Analysis Process for a Vehicle Under a Given Braking Schedule

6.3 ELEMENT CONSIDERED FOR THERMAL ANALYSIS:

According to the given specifications the element type chosen is PLANE 77

(Dimensions: 2-D; shape or characteristics: Quadrilateral, eight nodes; Degrees of freedom:

Temperature at each node; usage notes: Useful for modeling curved boundaries). The

following Figure shows the schematic diagram of the 8-noded thermal solid element.

41

Fig 6.2 Schematic Diagram of 8 – Noded Thermal Sold Element

PLANE 77 is a higher order version of the two dimensional, four node thermal

element. The element has one degree of freedom, temperature at each node. The 8-node

elements have compatible temperature shapes and are well suited to model curved

boundaries.

The 8-node thermal element is applicable to a two dimensional, steady state or

transient thermal analysis. If the model containing this element is also to be analyzed

structurally, the element should be replaced by an equivalent structural element, a similar

axis-symmetric thermal element which accepts non axis symmetric loading.

6.4 MATERIAL PROPERTIES GIVEN AS FOLLOWS:

Table 6.1 Thermal Material Properties of CI, Al & Steel

CAST IRON ALUMINIUM STEEL

Thermal Co-efficient of

expansion ( xx) / 0

C

10.4e-6 22.2e-6 13e-6

Thermal Conductivity (K)

W/mk

55 250 43

Specific Heat (Cp)

J/Kg 0

C

460 870 486

Density(kg/m3) 6800 2712 7850

Poisson‘s ratio 0.22 0.334 0.303

Young‘s Modulus 120e9 70e9 200e9

Heat Flux (q) =750000 W/m2

42

6.5 MESH GENERATION:

Before building the model, it is important to think about whether a free mesh or a

mapped mesh is appropriate for the analysis. A free mesh has no restrictions in terms of

element shapes and has no specified pattern applied to it.

Compared to the free mesh, a mapped mesh is restricted in terms of the element shape

it contains and pattern of the mesh. A mapped mesh contains either only quadrilateral or only

triangular element, while a mapped volume mesh contains only hexahedral elements. In

addition, a mapped mesh typically has a regular pattern, with obvious rows of elements.

For mapped mesh, we must build the geometry as a series of fairly regular volumes

and / or areas that can accept a mapped mesh.

The type of mesh generation considered here is a free mesh since the 2D figure is not a

regular shape. Axis-symmetric element 77 is used to model in ANSYS by considering axis-

symmetric geometry. After convergence check the final mesh is shown in the figure 6.5.

6.6. BOUNDARY CONDITIONS:

a). GEOMETRY BOUNDARY CONDITIONS:

The temperature 250 C is fixed at the hub bore grinds as the boundary conditions. The

standard convection law is used.

b). THERMAL BOUNDARY CONDITIONS:

i) A convection boundary condition is applied on all sides of the axis symmetric

model except in the region of tread and the hub. The heat transfer coefficient

of 50 W/m2k is considered.

ii) The thermal load is applied axis symmetrically on the tread of the wheel is a

heat flux (q) of value 75e4 W/m2 and is analyzed for 4.8 seconds of braking

i.e. the heat generate is going to be distributed along the profile after the

application of the brakes .

The standard convection law used is

Q = h (t-t) ...(6.1)

43

The main conduction equation in heat transfer analysis is

γ

T.Cpδq

z

TK

y

TK

x

TK

2

2

zz2

2

yy2

2

xx

..(6.2)

where Kxw, Kyy, Kzz are thermal conductivities in x, y, z direction w/mK

Q - Heat generation/unit volume

- Time

T = Tn

Where Tn = boundary temperature defined over a surface S1

If the heat gained or lost boundary S2 is due to convection the boundary is

0)TT(hz

TKI

y

TKI

x

TK zzyyyxxx

...(6.3)

where h - heat transfer coefficient w/m2 K

T - Fluid temperature

As 2-D solid element is consider there

.0z

T2

2

0Qy

TK

x

TK

2

2

yy2

2

xx

...(6.4)

Most of the heat transfer takes place in X-direction

we assume 0y

T2

2

...(6.5)

Then final equation is

γ

TCpδq

x

TK

2

2

x

...(6.6)

The functional formulation of equation and its boundary conditions is

=

v 2S

2

1Sv2

2

zz2

2

yy2

2

xx dsTqdsTTh2

1dvTqdv

z

TK

y

TK

x

TK

2

1

+ Cp

2T

1T γ

T

=

V v 1S

2T

1T

2

2

2

xxγ

TCpδdsTTh

2

1dvTqdv

x

TK

2

1 ...(6.7)

44

e)e()e(

TNT ...(6.8)

minimize equation (6.7) with respect to set of nodal value T

Temperature gradient matrix (represented by column matrix g

z

T

y

T

x

Tg ...(6.9)

and D =

zz

YY

xx

K

K

K

00

00

00

...(6.10)

The first integral term on RHS of equation (6.7) can be written as

dvz

TK

y

TK

x

TK

2

1I

v2

2

zz2

2

yy2

2

xx1

=

T

v

zz

yy

xx

z

T

y

T

x

T

K

K

K

z

T

y

T

x

T

00

00

00

2

1 ...(6.11)

Substituting equation (6.9) (6.10) in equation 6.11 we get

v 3S

22T1 dsTq

2

1ds)TTT2T(h

2

1dvTQdvgDg

2

1I ...(6.12)

Function is not continuous over the region but in equation (6.12) element )e(

T separated into

integral over individual element yielding.

=

N

e v

e

S

eeeeeTe dtT

CpdsTTTThdvTQdvgDg1

2 ..22

1

2

1

2

...(6.13

This is for one element

If where N number and element than

=

N

1e

)e()N()3()2()1(

ππ....πππ ...(6.14)

When )e(

π is contribution of a single element of

The set of integral can written in condensed form

eeee

fTKT

...(6.15)

minimize with respect to T

45

0T

π

Then the final equation obtained is

0fTKeeN

1e

e

FTKee

....(6.16)

Where [F] = element force vector

[K] = element conduction matrix

=

A

T

v

ee

AdNNhdvBDB

46

6.7 GIVEN DIMENSIONS OF DISC BRAKE:

Fig 6.3 Geometric Model of a Disc Brake

(All Dimensions are in mm)

291.24

47

Fig 6.4 3-D Model of Disc Brake

Fig 6.5 Meshed Model

48

Fig 6.6 Front view of Meshed Model

Fig 6.7 Top view of Meshed Model

49

Fig 6.8 All applied boundary conditions

The figure 6.4, 6.5, 6.6, 6.7, 6.8 respectively shows the 3-D disc brake model finite

element model of the 3-D disc brake with the applied boundary conditions.

Finally the boundary conditions are verified before going for a solution. At the hub

surface the heat transfer is taken as zero i.e. Q= 0

Thermal load of q= 750000 W/m2

is applied as a boundary conditions and is

analyzed for 4.8 seconds of braking.

6.8 DISC MATERIAL:

The two main functions of a brake disc or drum are the transmission of a considerable

mechanical force and dissipation of the heat produced, that implies functioning at medium or

high temperatures. From a theoretical standpoint numerous materials would be able to fulfill

these functions. In reality, for reasons of performances stability, cost of raw materials and

ease of production, cast iron is the material universally used. However, other materials are

used for specific braking applications. For example, composite carbon matrix materials are

50

employed in the production of brake discs for competition cars and airplanes, although their

particular performance level and cost make them inappropriate for use on standard vehicles.

Also aluminum alloys containing silicon carbide can be considered as they afford a

significant reduction in weight, although their inability to support high temperatures means

that brakes have to be oversized, a factor which partly cancels out the weight advantage. Cast

iron is one of its numerous forms therefore remains the preferred material.

6.9 RESULTS AND DISCUSSIONS:

TABLE 6.2 Results of maximum Temperatures attained

Flange width

In mm

CAST IRON

In oC

ALUMINIUM

In oC

STEEL

In oC

8 131.328 123.754 126.783

10 124.328 108.139 123.166

12 121.252 98.247 121.965

14 119.971 91.619 121.601

The above table 6.2 indicates the maximum temperature attained for different flange

widths and for different materials.

For Cast Iron Disc, the maximum temperature is attained for a flange width of 10mm,

which is 124.328 C. This temperature value is nearest to the experimental value of 124 C

[2]. The temperature variation for different flange width is as shown in the Graph (6.3).

For Aluminium Disc, the maximum temperature is attained for a flange width of

8mm, which is 131.328C. The temperature variation for different flange width is as shown

in the Graph (6.4).

For Steel Disc, the maximum temperature is attained for a flange width of 8mm,

which is 126.783C. The temperature variation for different flange width is as shown in the

Graph (6.5)

From the above results we can conclude that the Cast Iron Disc of flange width 10mm

nears to the experimental value, hence this is recommended.

51

Moreover the temperature distribution on the contacting surface along X direction and

Y direction is as shown in the Graphs (6.1 & 6.2).

Fig 6.9 Temperature distribution for Cast Iron 8mm flange width

52



53


Temperature distribution for Aluminium8mm flange width

54



55


Temperature distribution for Steel 8mm flange width

56



57


Graph 6.1.Temperature Vs Distance along the contacting surface of 10mm flange width

of Cast Iron in X-direction.

58

Graph 6.2 Temperature Vs Distance along the contacting surface of 10mm flange width

of Cast Iron in Y-direction.

Graph 6.3 Flange width Vs Temperature for CAST IRON

59

Graph 6.4 Max Temperature Vs Flange width for ALUMINIUM

Graph 6.5 Max Temperature Vs Flange width for STEEL

60

CHAPTER 7

STRUCTURAL ANALYSIS

7.1 INTRODUCTION:

Structural analysis is the most common application of the finite element method. The

term structural (or structure) implies civil engineering structures such as bridges and

buildings, but also naval, aeronautical and mechanical structures such as ship hulls, aircraft

bodies and machines housings as well as mechanical components such as pistons, machine

parts and tools.

STRUCTURAL STATIC ANALYSIS:

A static analysis calculates the effects of steady loading condition on a structure,

while ignoring inertia and damping effects such as those caused by time varying loads. A

static analysis can, however include steady inertia loads (such as gravity and rotational

velocity), and time varying loads that can be approximated as static equivalent loads (such as

the static equivalent wind and seismic loads commonly defined in many building codes.)

7.2 DEFINITION OF THE PROBLEM:

Due to the application of brakes on the car disc brake rotor heat generation takes place

due to friction and this temperature so generated has to be conducted away and dispersed

across the disc brake cross section. The condition of braking is very severe and thus thermal

analysis is carried out and with the above load structural analysis is also performed for

analyzing the stability of the structure.

From the virtual work energy principle i.e. δ we = δ ue ….. (7.1)

The basic analysis equation is

[ K ] [ Q ] = F ….. (7.2)

Where K = global stiffness matrix.

F = Load vector.

Q = Displacement vector

61

7.3 THERMAL DISC DISTORTION:

Fig 7.1 Disc Distortion Due to Heat

Distribution of heat flows depends on the physical- chemical properties of the two

materials; it remains relatively constant as far as cast irons are concerned whereas it tends to

vary somewhat in the case of friction materials. It can be seen, however, that in more than

80% of cases the heat generated ends up in the disc but above all from air movement induced

by the vehicle itself. Depending on the maximum quantity of heat to be eliminated, various

methods are used that in turn make the shape of the disc more or less complex. For instance

the heat exchange surface can be increased, as in the case of ventilated discs. Air flow can

also be increased and performance improved by shaping the blades. Entry of air through the

side to which the wheel is attached is generally less efficient since the disc‘s environment is

more confined and create a circulation of hotter air. An excessive temperature increase in the

pads cause their material to deteriorate and increase the temperature of the piston and, as a

consequence, the brake fluid. Moreover, excessive temperature increases in the disc have

numerous consequences.

The cast iron can undergo a transformation that leads to the bluing of the surface or a

permanent distortion of the disc itself. By the conduction, heat transferred towards the carrier.

In this case the disc surface curves, the disc becomes conical and does not return to its

62

original shape on cooling. Lastly the carrier is in contact with the wheel and, as a

consequence heats the tyre.

The only way to make improvements to a physical system is first to fully understand

how it functions. This is why technicians commence by taking a large number of

measurements in order to form an idea of systems reaction to various stresses. This widely

applied approach is costly and only partly effective since it is rather difficult, or often

impossible, to obtain precise measurements of moving parts affected by a transitory

phenomena. Low cost, powerful computers have made it possible to expand such studies by

modeling, also in the brake disc field. The principal is to breakdown the component, in a

virtual sense, into small parts which are assigned certain pertinent basic characteristic:

geometry, weight, mechanical and thermal properties. Following this they are reduced to the

form of simplified linear equations that describe all the possible relationships that can exists

between the various elements : for example between heat conduction and elastic properties.

Of course, data representing the initial situations must be provided (for instance, the

temperature map) and indications are given to the external stresses to which the elements

under consideration is exposed. All of these data are then processed by what is known as

―Finite element‖ Software that provides new maps of the stresses and flows. After a small

time increment, it is then possible to calculate the new state of the various disc elements

being studied before progressing to the examination of braking itself.

7.4 MATERIAL PROPERTIES:

Table 7.1 Structural material properties of Ci, Al & Steel

Properties Material Cast iron Aluminium Steel

1. YOUNG’S MODULUS (E) Gpa 120e9 70e9 200e9

2. POISSON’S RATIO (V) 0.22 0.334 0.303

3. COEFFICIENT OF THERMAL

EXPANSION () /oC

10.4e-6 22.2e-6 13e-6

Table 6.1 Thermal Material Properties of CI, Al & Steel

63

7.5 BOUNDARY CONDITIONS:

Geometric Boundary conditions:

Since the axis-symmetric model is considered all the nodes in the hub radius are

fixed. So the nodal displacements in the hub become Zero i.e. both in radial and axial

direction.

7.6 RESULTS AND DISCUSSIONS:

The table 7.2 indicates the variation of stress for different materials having different flange

widths.

For Disc made of Cast Iron, maximum Vonmises stress is observed for 8mm flange

width which is 174Mpa and minimum Vonmises stress is observed for 14mm flange width

which is 128 MPa.

For Disc made of Aluminium, maximum Vonmises stress is observed for 14mm

flange width which is 205 MPa and minimum Vonmises stress is observed for 8mm flange

width which is 258 MPa.

For Disc made of Steel, maximum Vonmises stress is observed for 14mm flange

width which is 276 MPa and minimum Vonmises stress is observed for 8mm flange width

which is 325 MPa.

Hence it is seen that the Vonmises stress decreases with increase in flange width for

Cast Iron Disc (refer Graph 7.1) and increases with increase in flange width for Steel and

Aluminium Discs (refer Graphs 7.2 & 7.3)

Viewing the above results and the discussion made in this chapter regarding the

material of the Disc Brake we can conclude that the Cast Iron Disc of 10mm flange width can

be preferred.

64

Vonmises stress for Aluminium 8mm flange width


65


Vonmises stress for Cast Iron 8mm flange width

66



67


Vonmises stress for Steel 8mm flange width

68



69


Graph 7.1 Vonmises stress Vs Flange width for Cast Iron

VONMISES STRESS Vs FLANGE WIDTH (CAST

IRON)

0

50

100

150

200

250

8 10 12 14

FLANGE WIDTH (mm)

VO

NM

ISE

S S

TR

ES

S

(MP

a)

Series1

70

Graph 7.2 Vonmises stress Vs Flange width for Aluminium

Graph 7.3 Vonmises stress Vs Flange width for Steel

VONMISES STRESS Vs FLANGE WIDTH (ALUMINIUM)

0

10

20

30

40

50

60

70

80

90

8 10 12 14

FLANGE WIDTH (mm)

VO

NM

ISE

S S

TR

ES

S (

MP

a)

Series1

VONMISES STRESS Vs FLANGE WIDTH (STEEL)

0

50

100

150

200

8 10 12 14

FLANGE WIDTH (mm)

VO

NM

ISE

S S

TR

ES

S

(MP

a)

Series1

71

TABLE 7.2 RESULTS OF VARIOUS STRESSES OBTAINED FOR CI, AL & STEEL.

Sl

No. Matirial

Flange

width in mm

Stress in

X–Direction

mpa

Stress in

Y-direction

mpa

1st principal

stress mpa

2nd

principal

stress mpa

Vonmi

sses

stress

mpa

1. CAST IRON

8 mm 40.4 59.7 62.6 26.5 230

10 mm 80.1 69.8 81.0 68.8 222

12 mm 70.6 73.2 85.8 48.5 206

14 mm 62.2 21.1 62.2 20.8 179

2. ALUMINIUM

8 mm 24.8 7.73 24.8 5.23 48.6

10 mm 31.3 7.55 31.3 7.12 63.7

12 mm 35.2 9.41 35.2 9.04 75.7

14 mm 36.6 11.9 36.6 11.7 84.2

3. STEEL

8 mm 52.0 13.3 52.0 10.6 106

10 mm 62.6 14.7 62.6 13.8 137

12 mm 66.0 17.4 66.0 16.7 157

14 mm 63.3 21.0 63.3 20.7 169

72

8. CONCLUSIONS

The following conclusions are drawn from the present work.

An axis-symmetric analysis of disc brake has been carried out using plane

77 and plane 42 through ANSYS R 10.0 (F.E.A) software.

A transient thermal analysis is carried out using the direct time integration

technique for the application of braking force due to friction for time

duration of 4.8 seconds.

The maximum temperature obtained in the brake disc is at the contact

surface and is observed to be 124.328°C for cast iron disc of 10mm flange

width, which varies only by 0.16% from the experimental value.

Static structural analysis is carried out by coupling the thermal solution to

the structural analysis and the maximum Vonmises stress is observed to be

174 MPa for Cast Iron Disc of 8mm flange width.

The brake disc design is safe based on the strength and rigidity criteria.

Comparing the different results obtained from the analysis, it is concluded

that disc brake with 10 mm flange width, 6.5 mm wall thickness and of

material cast iron is the best possible combination for the present

application.

73

9.REFERENCES

[1] A. Yevtushenko and E. Ivanyk,‖ Determination of heat & thermal

distortion in braking systems,‖ WEAR, Vol.185, pp. 159—165, 1995.

[2] D. M. Rowson, ― The Interfacial Surface Temperature Of A Disc Brake,‖

WEAR, Vol. 47, pp 323—328, 1978.

[3] Ji-Hoon Choi and In Lee,‖ Finite element analysis of transient

thermoelastic behaviours in Disc Brakes,‖ WEAR, Vol.257, pp. 47—58,

2004.

[4] Thomas Valvano and Kwangjin Lee,‖ An Analytical Method to Predict

Thermal Distortion of a Brake Rotor,‖ SAE, 2000-01-0445, 2000.

[5] C. H. Gao and X. Z. Lin,‖ Transient temperature field analysis of a Break

in a non-axisymetrical three dimensional model,‖ Journal Of

Materials Processing Technology, Vol.129, pp. 513—517, 2002.

[6] El Abdi and H. Samrout,‖ Anisothermal modelling applied to brake discs,‖

International Journal of Nonlinear Mechanics, Vol.34, pp. 795—805, 1999.

[7] ― The Brake Disc Manual,‖ www. Brembodiscbrakes.com.

[8] www. howstuffworks.com.

[9] User Guide for ANSYS version 10.0

[10] D. Q. Kern, ―Process heat transfer,‖ Tata McGraw Hill, 9th edition, 2003.

[11] J. P. Holman, ―Heat Transfer,‖ Tata McGraw Hill, 8th edition, 2002.

[12] Chandraputla, ―Introduction to Finite Element Analysis,‖

[13] Dr. P. Ravinder Reddy, ―Finite Element Analysis & ANSYS‖,

Documents

Structural Analysis of Car Disk Brake