project 1.pdf

Coupled Field Finite Element Analysis of Car Disc Brake Rotors

Dept. of Mechanical Engineering SDMCET, Dharwad 1

TABLE OF CONTENTS

Chapters Page No.

ACKNOWLEDGEMENT

ABSTRACT

CHAPTER 1: INTRODUCTION 06

1.1 Fundamentals of Braking System

1.1.1 Principle of braking. 07

1.1.2 Coefficient of friction 08

1.2 Braking systems.

1.2.1 Brake types in cars.

1.2.1.1 Drum Brake. 08

1.2.1.2 Disc Brake. 08

1.2.1.3 Antilock Braking System (ABS) 08

1.2.2 Air brakes. 09

1.2.3 Exhaust brakes. 09

1.2.4 Electric brakes. 09

1.2.5 Parking brakes. 10

1.3 Braking system components.

1.3.1 Brake pedal. 10

1.3.2 Brake lines. 10



1.3.3 Brakes fluid. 10

1.3.4 Master cylinder. 11

1.3.5 Divided systems. 11

1.3.6 Tandem master cylinder. 12

1.3.7 Power booster or brake unit. 12

1.3.8 Hydraulic brake booster. 12

1.3.9 Electrohydraulic braking (EHB). 12

1.4 Disc brake systems.

1.4.1 Disc brake operation. 13

1.4.2 The rotor. 15

1.4.2.1 Brake fade 16

1.4.2.2 Rotor Metallurgy 16

1.4.2.3 Rotor Surface finish 17

1.4.3 Disc brake pads. 17

1.4.4 Disc brake calipers. 18

CHAPTER 2: LITERATURE REVIEW 19

CHAPTER 3: MATERIAL PROPERTIES OF DISC BRAKE

ROTORS 25

3.1 Materials used 25



3.2 Cast Iron 25

3.3 Specifications of car and Material Properties of Gray cast iron

3.3.1 Solid disc brake rotor

3.3.1.1 The specifications of car 26

3.3.1.2 The materials properties 26

3.3.2 Ventilated disc brake rotor

3.3.2.1 The specifications of car 27

3.3.2.2 The materials properties 27

CHAPTER 4: THEORY AND CALCULATIONS

4.1 Assumptions. 29

4.2 Stopping distance. 29

4.3 Weight transfer. 30

4.4 Braking efficiency. 31

4.5 Kinetic energy and Heat flux.

4.5.1 Approaches 32

4.5.2 Macroscopic model approach 32

4.6 Calculations

4.6.1 Calculations for heat flux application time 33

4.6.2 Calculations for kinetic energy heat flux time

4.6.2.1 Solid disc brake rotor 33



4.6.2.2 Ventilated disc brake rotor 35

CHAPTER 5: GEOMETRIC MODELING

5.1 Pro e Wildfire 4. 37

5.2 Module 2 - Part Modeling. 37

5.3 Module 5 - Drawing. 38

5.4 Modeled and drafted components. 38

CHAPTER 6: FINITE ELEMENT MODELING 41

6.1 Meshed components 42

6.2 SOLID90 43

6.2.1 SOLID90 Element Description 43

6.2.2 SOLID90 Input Data 44

6.2.3 SOLID90 Input Summary 44

6.2.4 SOLID90 Output Data 45

6.2.5 SOLID90 Assumptions and Restrictions 45

CHAPTER 7: FINITE ELEMENT ANALYSIS

7.1 Introduction. 47

7.2 Steps in FEA.

7.2.1 General Steps. 47

7.2.2 Steps in ANSYS. 47



7.3 Coupled field analysis. 48

7.3.1 Thermal Structural Analysis 49

7.3.2 Thermal and Structural Boundary Conditions 49

7.4 Modal analysis. 50

7.5 Procedure adopted for thermal analysis

of disc brake rotors. 50

7.6 Procedure adopted for structural analysis


7.7 Procedure adopted for modal analysis


CHAPTER 8: RESULTS

8.1 Inputs and results of ANSYS 11 52

8.2 Plots of Results

8.2.1 Solid disc brake rotor 53

8.2.2 Ventilated disc brake rotor 61

CHAPTER 9: CONCLUSION 69

CHAPTER 10: FUTURE SCOPE 70

REFERENCES



CHAPTER 1

INTRODUCTION

At the end of the 19th century the development of a brake system for the newly

invented automobile vehicles was needed. From that moment on, brake system which

makes use of several components (the brake disc among them), was developed. It was

after the beginning of the Second World War, in 1938, that the brake system

technological advance got great impulse due to the aeronautics industry necessity. Around

1886, in Germany, Gotlieb Daimler and Carl Benz would change the history of the world

forever, because they created, independently, the first prototypes of internal combustion

automobiles. This invention gave rise to the development of several automobile

components, and among them was the brake system. In the United States, in 1890,

according to Hughes, the American Elmer Ambrose Sperry invented a brake similar to the

present disc brake. An automotive brake disc brake rotor is a device for slowing or

stopping the motion of a wheel while it runs at a certain speed. In this project work the

complete study of brake systems used in cars is studied and the actual dimensions of the

solid and ventilated disc brake rotors of TATA indica cars are taken which are used to 3D

modeling of rotors in Pro e Wildfire 4. The model is then converted to iges format and

imported to Altair Hypermesh 7 for meshing. After meshing it is imported to ANSYS 11

with element for meshing defining as SOLID 90. Here coupled field finite element

analysis and modal analysis is carried using general purpose finite element analysis. Then

the results are compared for both solid and ventilated disc brake rotors and alternate

materials are also suggested.

The goals of our project are as follows:

i. Complete study of braking system in car.

ii. Conceptualization of working of the disc rotor.

iii. To carry out coupled-field analysis i.e., thermal to static structural analysis which

gives thermal stresses and their corresponding displacements in the disc brake

rotor due to the application of temperature.



iv. To predict natural frequencies and associated mode shapes by considering density

of the disc material.

v. Comparison of solid and ventilated rotor based on the above results.

vi. Suggesting the suitable material for disc brake rotor and checking whether the

design is safe or not based on the above results.

1.1 Fundamentals of Braking system

1.1.1 Principle of braking:

A basic braking system of a car has:

Brake pedal.

Master cylinder to provide hydraulic pressure.

Brake lines and hoses to connect the master cylinder to the brake assemblies.

Fluid to transmit force from the master cylinder to the wheel cylinders of the

brake assemblies, and

Brake assemblies drum or disc that stop the wheels.

The driver pushes the brake pedal; it applies mechanical force to the piston in the

master cylinder. The piston applies hydraulic pressure to the fluid in the cylinder, the

lines transfer the pressure which is undiminished in all directions within the brake lines

to the wheel cylinders, and the wheel cylinders at the wheel assemblies apply the brakes.

Force is transmitted through the fluid. For cylinders of the same size, the force

transmitted from one is the same value as the force applied to the other. By using

cylinders of different sizes, forces can be increased or reduced. In an actual braking

system, the master cylinder is smaller than the wheel cylinders, so the force at all of the

wheel cylinders is increased. When brakes are applied to a moving vehicle, they absorb

the vehicles kinetic energy. Friction between the braking surfaces converts this energy

into heat. In drum brakes, the wheel cylinders force brake linings against the inside of the

brake drum. In disc brakes, pads are forced against a brake disc. In both systems, heat

spreads into other parts and the atmosphere, so brake linings and drums, pads and discs

must withstand high temperatures and high pressures.



1.1.2 Coefficient of friction

Friction is a force that resists the movement of one surface over another. It can be

desirable but often is not. It's caused by surface rough spots that lock together. These

spots can be microscopically small, which is why even surfaces that seem to be smooth

can experience friction. Friction can be reduced but never eliminated. Friction is always

measured for pairs of surfaces, using what is called a coefficient of friction. A low

coefficient of friction for a pair of surfaces means they can move easily over each other.

A high coefficient of friction for a pair of surfaces means they cannot move easily over

each other.

1.2 Braking Systems

1.2.1 Brake types in cars

1.2.1.1 Drum Brake

Drum brakes have a drum attached to the wheel hub, and braking occurs by means

of brake shoes, expanding against the inside of the drum. A drum brake is a brake in

which the friction is caused by a set of shoes or pads that press against the inner surface

of a rotating drum. The drum is connected to a rotating wheel.

1.2.1.2 Disc Brake

With disc brakes, a disc attached to the wheel hub maybe clamped between 2

brake pads. On light vehicles, both of these systems are hydraulically operated. The brake

pedal operates a master cylinder. Disc brakes require greater forces to operate them. A

brake booster assists the driver by increasing the force applied to the master cylinder,

when the brake is operated.

1.2.1.3 Antilock Braking System (ABS)

An anti-lock braking system (commonly known as ABS, from the German name

"Antiblockiersystem" given to it by its inventors at Bosch) is a system on motor vehicles

which prevents the wheels from locking while braking. The purpose of this is to allow the



driver to maintain steering control and to shorten braking distances. It is composed of a

central electronic unit, four speed sensors (one for each wheel) and two or more hydraulic

valves on the brake circuit.

1.2.2 Air Brakes

Air-operated braking systems are used on heavy vehicles. Compressed air,

operating on large-diameter diaphragms, provides the large forces at the brake assembly

that are needed. An air compressor pumps air to storage tanks. Driver-controlled valves

then direct the compressed air to different wheel units, to operate the friction brakes.

1.2.3 Exhaust Brakes

Heavy goods vehicles can often require increased braking, in situations where

friction brakes could overheat and fail. This is achieved by using an exhaust brake. An

exhaust brake works by restricting the flow of exhaust gases through the engine. It

achieves this by closing a butterfly valve located in the exhaust manifold. This maintains

high pressure in the exhaust manifold and the engine cylinders, which in turn acts as a

brake against the engine rotating. This then slows the road wheels through the

transmission, or power train. Other heavy goods vehicles use an engine brake that

operates by altering valve timing, and stopping fuel being injected into the engine.

1.2.4 Electric Brakes

An electric braking system is commonly used to activate the drum-type friction

brakes on the trailer. Braking effect can be increased or reduced by the driver, adjusting a

control unit to suit the load on the trailer. When the brakes in the towing vehicle are

applied, the brake-light circuit sends the signal to the control unit. The control unit then

sends an appropriate current to the trailer brake actuators, to operate the trailer brakes, at

the level selected.



1.2.5 Parking Brakes

All vehicles must be fitted with a foot brake and a park brake. Most light vehicles

use a foot brake that operates through a hydraulic system on all wheels, and a hand-

operated brake that acts mechanically on the rear wheels only. The hand brake system

holds the vehicle when it is parked. Some vehicles incorporate a drum brake for the hand

brake, in the center of the rear disc brake. Others use a mechanical linkage to operate the

disc brake from the hand brake system, or separate hand brake calipers with their own

pads. Some vehicles have the hand brake operating on the front wheels. Some vehicles

use a single drum brake on the rear of the gearbox as a hand brake. That's sometimes

called a transmission brake.

1.3. Braking system components

1.3.1 Brake Pedal

The brake pedal uses leverage to transfer the effort from the drivers foot to the

master cylinder. Different lever designs can alter the effort the driver needs to make, by

using different levels of mechanical advantage.

1.3.2 Brake lines

Brake lines carry brake fluid from the master cylinder to the brakes.

They are basically the same on all brake systems. For most of their length they are steel,

coated to reduce the possibility of corrosion, and attached to the body with clips or

brackets to prevent damage from vibration. In some vehicles, the brake lines are inside

the vehicle to protect them better from corrosion.

1.3.3 Brake fluid

Brake fluid is hydraulic fluid that has specific properties. The fluid is used to

transfer force while under pressure through hydraulic lines to the wheel braking system.

The properties of different types of brake fluids are tested for many different



characteristics such as ph value, viscosity, resistance to oxidation and graded against

compliance standards set by United States Department of Transportation (DOT).

Brake fluid DOT specifications:

DOT 2 is castor oil based

DOT 3 is composed of various glycol esters and ethers.

o Boiling point: 284 F (140 C)

DOT 4 is also composed of glycol esters and ethers.


DOT 5 is silicone-based. It is NOT recommended for any vehicle equipped with

antilock brakes (ABS). It gives better protection against corrosion, and is more

suitable for use in wet driving conditions.


DOT 5.1 is a high-boiling point fluid that is suitable for ABS-equipped vehicles. It

contains polyalkylene glycol ether, but is more expensive than other brake fluids.

o Boiling point: 375 F (190.6 C)

Even if they have similar base composition, fluids with different DOT ratings must not be

mixed.

1.3.4 Master cylinder

The master cylinder is connected to the brake pedal via a pushrod. This is a single

master cylinder for a drum brake system. Its one piston has a primary and a secondary

cup. These are also known as seals, because, when force is applied to the brake pedal, the

primary cup seals the pressure in the cylinder. The secondary cup prevents loss of fluid

past the end of the piston. An outlet port links the cylinder to the brake lines.

1.3.5 Divided systems

Modern cars use tandem master cylinders to suit divided or dual line braking

systems. A divided system is safer in the event of partial failure. Fluid loss in one half of



the system still leaves the other half able to stop the vehicle, although with an increase in

stopping distance.

1.3.6 Tandem master cylinder

With a basic master cylinder in the braking system, any loss of fluid, say because

a component fails, could mean the whole braking system fails. To reduce this risk,

modern vehicles must have at least two separate hydraulic systems. Thats why the

tandem master cylinder was introduced.

1.3.7 Power booster or Brake unit

A power booster or power brake unit uses a vacuum to multiply the drivers pedal

effort and apply that to the master cylinder. This increases the pressures available from

the master cylinder. Units on petrol/gasoline engines use the vacuum produced in the

intake manifold. Vehicles with diesel engines cannot use manifold vacuum so they are

fitted with an engine-driven vacuum pump. The most common booster operates between

the brake and master cylinder.

1.3.8 Hydraulic brake booster

Although not as common as a conventional brake system fitted with a vacuum

booster, many vehicles are now equipped with hydraulically assisted boosters for the

brakes. The system uses hydraulic pressure generated by the power steering pump rather

than engine vacuum to provide the power assistance required in a conventional system.

This application is particularly suitable to vehicles with diesel engines as a separate

vacuum source does not have to be provided for the system to operate.

1.3.9 Electrohydraulic braking (EHB)

Electrohydraulic Braking (EHB) gets rid of the vacuum booster and replaces the

current modulator with one that includes a high pressure accumulator. Like the Hydro

boost system it uses an accumulator to provide the required pressure to activate the master

cylinder, however, it uses electrical power to effectively charge the accumulator and



build sufficient pressure for efficient brake operation. This system means that less power

is taken away from the engine during operation as battery power is used.

1.4 Disc brake system

The primary components of disc brakes are: the rotor, caliper and brake pads.

Fig 1.1 Disk brake system

1.4.1 Disc brake operation

Disc brakes can be used on all four wheels of a vehicle, or combined with disc

brakes on the front wheels and drum brakes on the rear. When the brake pedal is

depressed, a push rod transfers the force through a brake booster to a hydraulic master

cylinder. The master cylinder converts the force into hydraulic pressure, which is then



transmitted via connecting pipes and hoses to one or more pistons at each brake caliper.

The pistons operate on friction pads to provide a clamping force on a rotating flat disc

that is attached to the wheel hub. This clamping tries to stop the rotation of the disc, and

the wheel. On non-driving wheels, the center of the brake disc or hub contains the wheel

bearings. The hub can be part of the brake disc or a separate assembly between the wheel

and hub with nuts or bolts. On driving wheels, the disc is mounted onto the driving axle

and may be held in place by the wheel. On front wheel drive vehicles, it can be mounted

on the front hub and wheel bearing assembly. The brake caliper assembly is bolted to the

vehicle axle housing or suspension. In most cases the brake is positioned as close as

possible to the wheel, but there are exceptions. Some high-performance cars use inboard

disc brakes on its rear wheels. The makers claim improved vehicle handling for this

design because it reduces unsprung weight. Applying brakes can absorb a lot of vehicle

energy so friction between braking surfaces generates great heat. Brake parts withstand

very high temperatures. Most of the friction area of a disc is exposed to air so cooling is

far more rapid than for a drum brake. Unlike with drum brakes, brake fade is rare.

Because of their shape, discs tend to throw off water. So after being driven through water,

they operate almost immediately. Disc brakes need much higher pressures to operate than

drum brakes, so almost all disc brake systems need a power brake booster to help reduce

the pedal forces that are needed from the driver.

Fig 1.2 Schematic diagram of disc brake operation



1.4.2 The rotor

The rotor is the main rotating part of this brake system. It is hard wearing and

resists the high temperatures that occur during braking. Rotors can be of a solid

construction or slotted. The slotted rotor is referred to as a "ventilated disc". Brake rotors

provide a friction surface for the disc brake pads to rub against when the brakes are

applied. The friction created by the pads rubbing against the rotor generates heat and

brings the vehicle to a stop. The underlying scientific principle here is that friction

converts motion into lot of heat and this heat is to be dissipated. The amount of heat that

is generated depends on the speed and weight of the vehicle, and how hard the brakes are

applied.

Fig 1.3 Schematic diagram of Solid and Ventilated disc brake rotor

The rotor's job is to provide a friction surface, and to absorb and dissipate heat.

Big rotors can obviously handle more heat than small rotors. But many cars today have

downsized rotors to reduce weight. Consequently, the brakes run hotter and require better

rotor cooling to keep brake temperatures within safe limits. Uneven rotor wear often

produces variations in thickness that can be felt as pedal pulsations when the brakes are

applied. The condition usually worsens as the rotors continue to wear, eventually



requiring the rotors to be resurfaced or replaced. Rotors can also develop hard spots that

contribute to pedal pulsations and variations in thickness. Hard spots may be the result of

poor quality castings or from excessive heat that causes changes in the metallurgy of the

rotors. A sticky caliper or dragging brake may make the rotor run hot and increase the

risk of hard spots forming. Hard spots can often be seen as discolored patches on the face

of the rotor. Resurfacing the rotor is only a temporary fix because the hard spot usually

extends well below the surface and usually returns as a pedal pulsation within a few

thousand miles. Cracks can form as a result of poor metallurgy in the rotor and from

excessive heat. Some minor surface cracking is tolerable and can often be removed by

resurfacing, but large cracks or deep cracks weaken the rotor and increase the risk of

catastrophic failure

1.4.2.1 Brake fade: When brake temperatures get too high, the pads and rotors are no

longer able to absorb any more heat and lose their ability to create any additional friction.

As the driver presses harder and harder on the brake fade, he feels less and less response

from his overheated brakes. Eventually, he loses his brakes altogether. All brakes will

fade beyond a certain temperature. Semi-metallic linings can usually take more heat than

nonasbestos organic or low-met linings. Vented rotors can dissipate heat more rapidly

than nonvented solid rotors. Thus, high performance cars and heavier vehicles often have

vented rotors and semi-metallic front brake pads to handle high brake temperatures. But if

the brakes get hot enough, even the best ones will fade.

1.4.2.2 Rotor metallurgy: The metallurgical properties of a rotor determine its

strength, noise, wear and braking characteristics. The casting process must be carefully

controlled to produce a high quality rotor. The rate at which the iron cools in the mold

must be closely monitored to achieve the correct tensile strength, hardness and

microstructure. When iron cools, the carbon atoms that are mixed in with it form small

flakes of graphite which help dampen and quiet noise. If the iron cools too quickly, the

particles of graphite do not have as much time to form and are much smaller in size,

which makes for a noisy rotor. The rate of cooling also affects the hardness of a rotor. If a

rotor is too hard, it will increase pad wear and noise. Hard rotors are also more likely to

crack from thermal stress. If a rotor is too soft, it will wear too quickly and may wear



unevenly increasing the risk of pedal pulsation and runout problems. The composition of

the iron must also be closely controlled during the casting process to keep out impurities

that may form "inclusions" and hard spots.

1.4.2.3 Rotor surface finish: Smoother is always better because it affects the

coefficient of friction, noise, pad seating, pad break-in and wear. As a rule, most new

OEM (Original Equipment Manufacturer) and quality aftermarket rotors have a finish

somewhere between 30 and 60 inches RA (roughness average) with many falling in the

40 to 50 RA range. As a general rule, there should be no more than .003 inches of rotor

runout on most cars and trucks, but some cars cannot tolerate any more than .0015 inches

of runout.

1.4.3 Disc brake pads

A disc brake pad has a rigid, molded, friction material bonded to a steel backing

plate for support during brake application. It transforms the hydraulic force of the caliper

into a frictional force against the disc. Disc brake pads consist of friction material bonded

onto a steel backing plate. The backing plate has lugs that locate the pad in the correct

position in relation to the disc. Calipers are usually designed so that the condition of the

pads can be checked easily once the wheel has been removed, and to allow the pads to be

replaced with a minimum of disassembly. Some pads have a groove cut into the friction

surface. The depth of this groove is set so that when it can no longer be seen, the pad

should be replaced. Some pads have a wire in the friction material at the minimum wear

thickness. When the pad wears to this minimum thickness, the wire touches the disc as

the brakes are applied. A warning light then tells the driver the disc pads are due for

replacement. The composition of the friction material affects brake operation. Materials

which provide good braking with low pedal pressures tend to lose efficiency when they

get hot. This means the stopping distance will be increased. Materials which maintain a

stable friction co-efficient over a wide temperature range generally require higher pedal

pressures to provide efficient braking. Disc rotors with holes or slots in them dissipate

their heat faster, and also help to remove water from the surface of the pad in wet driving

conditions. They also help to prevent the surface of the pad from becoming hard and



glassy smooth from the friction and heat of use. However, this scraping action reduces the

overall life of the brake pad, so these types of discs are generally only used in high

performance or racing cars.

1.4.4 Disc brake calipers

The disc brake caliper assembly is bolted to the vehicle axle housing or suspension.

There are 2 main types:

fixed

sliding.

Fixed calipers can have 2, 3, or 4 pistons. 2-piston calipers have one piston on each

side of the disc. Each piston has its own disc pad. When the brakes are applied, hydraulic

pressure forces both pistons inwards, causing the pads to come in contact with the

rotating disc. The sliding or floating caliper has 2 pads but only 1 piston. The caliper is

mounted on pins or bushes that let it move from side to side. When the brakes are

applied, hydraulic pressure forces the piston inwards. This pushes the pad against the

disc. The caliper is free to move on slides, so there is a clamping effect between the inner

and outer pads. Equal force is then applied to both pads which clamp against the disc. In

disc brake calipers, the piston moves against a stationary square section sealing ring.

When the brakes are applied, the piston slightly deforms the seal. When the brakes are

released, the seal returns to its original shape. The action of this sealing ring retracts the

piston to provide a small running clearance between the disc and pads. It also makes the

brake self-adjusting.



CHAPTER 2

LITERATURE REVIEEW

In order to carry out the project the following literature available are studied and

understood to the extent possible to make correct decisions, assumptions and calculations

to obtain the optimum results.

Catalin Spulber and Stefan Voloaca [1]: This paper proposes a new simulation method

of a disc brake thermal stress resistance, for different temperatures, by interactive

processing of images obtained by thermography. Temperature evaluation for different

working regimes can be made by recording and processing thermograms of a disc brake

heated inside the laboratory by an external heating source. Taken pictures along the

temperature variation, from the ambient value to a value close to real one obtained on the

usual experiments, are processed using image analyse softwares. This way can be

simulated different working regimes (temperature, humidity etc.) without the need of

experimental determination on the road or on a test bench.

V.M.M.Thilak, R.Krishnaraj, Dr.M.Sakthivel, K.Kanthavel, Deepan Marudachalam

and M.G, R.Palani [2]: Transient Thermal and Structural Analysis of the Rotor Disc of

Disc Brake is aimed at evaluating the performance of disc brake rotor of a car under

severe braking conditions and there by assist in disc rotor design and analysis. An

investigation into usage of new materials is required which improve braking efficiency

and provide greater stability to vehicle. This investigation can be done using ANSYS

software. ANSYS 11.0 is a dedicated finite element package used for determining the

temperature distribution, variation of the stresses and deformation across the disc brake

profile. In the present work, an attempt has been made to investigate the suitable hybrid

composite material which is lighter than cast iron and has good Youngs modulus, Yield

strength and density properties. Aluminum base metal matrix composite and High

Strength Glass Fiber composites have a promising friction and wear behavior as a Disc

brake rotor. The transient thermo elastic analysis of Disc brakes in repeated brake

applications has been performed and the results were compared. The suitable material for



the braking operation is S2 glass fiber and all the values obtained from the analysis are

less than their allowable values. Hence the brake Disc design is safe based on the strength

and rigidity criteria. By identifying the true design features, the extended service life and

long term stability is assured.

Rajendra Pohane and R.G.Choudhari [3]: Repetitive braking of the vehicle leads to

heat generation during each braking event. The resulting rise in temperatures has very

significant role in the performance of the braking system. Passenger car disc brakes are

safety critical component whose performance depends strongly on contact conditions at

the pad to disc interface. During braking both brake pad & disc surface is worn. The

objective of the paper is to study disc brake system, to simulate disc brake assembly and

to prepare the FEM model for contact analysis. A three dimensional finite element model

of the brake pad and the disc is developed to calculate static structural analysis, and

transient state analysis. The comparison is made between the solid and ventilated disc

keeping the same material properties and constraints and using general purpose finite

element analysis. This paper discusses how general purpose finite element analysis

software can be used to analyze the equivalent (von-mises) stresses& the thermal stresses

at disc to pad interface.

H.Mazidi, S.Jalaifar and J. Chakhoo [4]: In this study the heat conduction problems of

the disc brake components (pad and rotor) are modeled mathematically and is solved

numerically using Finite Difference Method. In the discretization of time dependent

equations the implicit method is taken into account. In the derivation of the heat

equations, parameters such as the duration of braking, vehicle velocity geometries and the

dimensions of the brake components, material of the disc brake rotor and the pad and

contact pressure distribution have been taken into account. Results show that there is a

heat partition at the contact surface of two sliding components, because of thermal

resistance due to the accumulation of wear particles between contact surfaces. This

phenomenon prevents absorption of more heat by the discs and causes brake lining to be

hot. As a result, heat soaking to the brake fluid increases and may cause brake fluid to

evaporate.



M.A. Maleque, S.Dyuti and M.M. Rahman [5]: An automotive brake disc or rotor is a

device for slowing or stopping the motion of a wheel while it runs at a certain speed. The

widely used brake rotor material is cast iron which consumes much fuel due to its high

specific gravity. The aim of this paper is to develop the material selection method and

select the optimum material for the application of brake disc system emphasizing on the

substitution of this cast iron by any other lightweight material. Two methods are

introduced for the selection of materials, such as cost per unit property and digital logic

methods. Material performance requirements were analyzed and alternative solutions

were evaluated among cast iron, aluminium alloy, titanium alloy, ceramics and

composites. Mechanical properties including compressive strength, friction coefficient,

wear resistance, thermal conductivity and specific gravity as well as cost, were used as

the key parameters in the material selection stages. The analysis led to aluminium metal

matrix composite as the most appropriate material for brake disc system.

Muhammad Zahir Hassan [6]: Automotive disc brake squeal has been a major concern

in warranty issues and a challenging problem for many years. A variety of tools have

been developed which include both experimental studies and numerical modeling

technique to tackle the problem. The aim of this project is to develop a validated thermo-

mechanical finite element model considering both the mechanical structural compliance

and thermal effects in the dynamic instability of a disc brake system leading to squeal. A

key issue in the process is to investigate the structural deformation of the brake

components due to the combined effect of thermal expansion and contact loading between

pad and disc when subjected to temperature change during a typical braking cycle. A new

methodology is introduced whereby a fully coupled transient thermo-mechanical analysis

is carried out to provide the temperature and contact distributions within the brake before

executing an instability analysis using the complex eigenvalue method. A case study is

carried out based on a typical passenger car brake as it undergoes a partial simulation of

the SAE J2521 drag braking noise test. The actuation pressure, coefficient of friction and

vehicle travelling speed are all considered to derive the temperature dependent contact

pressure distributions making allowance for the "rotating heat source" effect. An

experimental investigation using a brake dynamometer is also carried out to measuring

the squealing noise and thermal deformation which leads to a validation of the results



predicted by the numerical modeling. It is demonstrated that the fully coupled thermo-

mechanical FE model enhances understanding of the time dependent non-linear contact

behavior at the friction interface. This, in turn, demonstrates the fugitive nature of brake

squeal through the system eigenvalues that appear and disappear as a function of

temperature throughout the braking period. Parametric studies on the geometrical effect

and materials of brake components determine the contribution of each of these factors to

brake squeal. The approach therefore can be use as a predictive tool to evaluate disc brake

squeal using finite element method.

Prashant Chavan [7]: Typically thermo-mechanical analysis including complexities

such as contacts and bolt preloads are carried out using three dimensional models. These

analyses require significant time and effort in FE model building, analysis setup, solution,

and results processing. It also requires special effort to ensure it is error free. In order to

get stable and accurate results element size and time step selection is very important in

transient analysis. These aspects are discussed in this paper. This paper also talks about

simplified yet almost equally accurate modeling and analysis method for thermo-

mechanical analysis using brake fade test simulation as an example. This methodology is

based on use of ABAQUS Axisymmetric analysis technique modified to represent effect

of discrete bolting, bolt preloads, and contacts within various components of the

assembly. Analysis results as well as analysis turnaround times are compared between

this new method and the conventional method. Up to 80% time can be saved with

significant improvement in the accuracy of the results.

Junichiro yamabe, Masami takagi and Toshiharu matsui [8]: A new method has been

developed to evaluate thermal fatigue by a simulating high-speed braking test using an

actual disc brake rotor. Thermal fatigue strength is confirmed to be improved with

increasing graphite number in the microstructure. It is also confirmed that the graphite

number increases in proportion to the amount of nickel added, and that the inoculation of

cerium, a rare earth element, produces an effect similar to that of adding nickel. Based on

this approach, a new, low cost material for disc brake rotors for heavy- and medium-duty

trucks is developed using both nickel and cerium.



G. Cueva, A. Sinatora, W.L. Guesser and A.P. Tschiptschin [9]: The wear resistance

of three different types of gray cast iron (gray iron grade 250, high-carbon gray iron and

titanium alloyed gray iron), used in brake disc rotors, was studied and compared with the

results obtained with a compact graphite iron (CGI). The wear tests were carried out in a

pin-on-disc wear-testing machine, the pin being manufactured from friction material

usually used in light truck brake pads. The rotating discs (500 rpm) were subjected to

cyclical pressures of 0.7, 2 and 4MPa and forced cooled. The wear was measured by

weighing discs and pads before and after the test. The operating temperatures and friction

forces were also monitored during each test. The results showed that compact graphite

iron reached higher maximum temperatures and friction forces as well as greater mass

losses than the three gray irons at any pressure applied. However, when compact graphite

iron was tested with lower applied pressures and same friction forces sustained by the

gray iron rotors, CGI presented the same performance, as did the gray cast iron.

Tretsiak, Dzmitry, Kliauzovich and Siarhei [10]: The current tendencies in automotive

industry need intensive investigation in problems of interaction of active safety systems

with brake system equipment. At the same time, the opportunity to decrease the power

take-off of single components, for example such as brake system, is investigated. Authors

propose a modification of disc brake structure with self-boosting characteristic for

commercial vehicles. This brake gear due to original construction will allow decrease

force required for its drive under the condition that brake gear will generate such brake

torque as conventional disc brake. The compilation and investigation on proposed brake

gear model in AMESim software is supposed. The obtained results can find application

during designing of new types of brake systems especially for heavy vehicles and buses.

Omar Maluf, Maurcio Angeloni, Marcelo Tadeu Milan, Dirceu Spinelli and Waldek

Wladimir Bose Filho [11]: At the end of the 19th century the development of a brake

system for the newly invented automobile vehicles was needed. From that moment on,

this equipment, which makes use of several components (the brake disc among them),

was developed. It was after the beginning of the Second World War, in 1938, that the



brake system technological advance got great impulse due to the aeronautics industry

necessity. Historically, the first material used to make brake discs was the gray cast iron,

which is a material that fits the requirements it is intended for, such as: good thermal

conductivity, good corrosion strength, low noise, low weight, long durability, steady

friction, low wear rate, and a good price/benefit ratio. Therefore, for more than one

hundred years, a great number of materials were developed with this intention, but the

most used until today is the cheap and easily produced gray cast iron. Nowadays, a lot of

emphasis has been given to the study of fatigue strength of gray cast iron alloys through

modeling to improve the service life of the component. Although this kind of analysis

presents meaningful results, experimental works are necessary to validate them, i.e., the

component must be studied under real rather than only virtual conditions.

Centric White Paper [12]: This paper gives various equations related to the physics of

braking system such as conversion of kinetic energy, brake pedal force, pressure on

master cylinder piston and caliper pistons, force on brake pad, rotor and tire and equation

for weight distribution.

Ali.Belhocine and Mostefa.Bouchetara [13]: The main purpose of this study is to

analysis the thermomechanical behavior of the dry contact between the brake disc and

pads during the braking phase. The simulation strategy is based on the calculation code

ANSYS11. The modeling of transient temperature in the disk is actually used to identify

the factor of geometric design of the disk to install the ventilation system in vehicles. The

thermal-structural analysis is then used coupling to determine the deformation established

and the Von Mises stresses in the disk, the contact pressure distribution in pads. The

results are satisfactory compared to those found in the literature.

M. Siroux, S. Harmand and B. Desmet [14]: This paper presents an experimental

technique which allows reaching the local convective heat transfer coefficient on a

rotating TGV brake disc model in the actual environment and submitted to an air flow

parallel to the disc surface. The heat transfer measurement technique is based on the

combination of infrared thermography and of a numerical computation code.

Experimental set-up, infrared temperature determination and results are detailed.



CHAPTER 3

MATERIAL PROPERTIES OF DISC BRAKE

ROTORS

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. SAE specifications dictate the correct range of

hardness, chemical composition, tensile strength, and other properties necessary for the

intended use. It is investigated the temperature distribution, the thermal deformation, and

the thermal stress of automotive brake disks have quite close relations with car safety [2].

3.1 Materials used

Materials which can be used for manufacturing of the car disk brake rotors and which can

perform intended functions are [2] and [5]:

Gray cast iron (GCI).

Aluminium Metal Matrix Composite (AMC) 20% SiC reinforced Al-composite

(AMC 1), 20% SiC reinforced Al-Cu alloy (AMC 2).

E Glass Fiber.

S2 Glass Fiber.

Titanium alloy (Ti-6Al-4V).

75 WT% WC and 7.5 wt% TiC reinforced Ti-composite (TMC).

3.2 Cast Iron

Disc brake discs are commonly manufactured out of a material called cast iron.

Cast iron usually refers to gray cast iron, but identifies a large group of ferrous alloys,

which solidify with a eutectic. Iron accounts for more than 95%, while the main alloying



elements are carbon and silicon. The amount of carbon in cast iron is the range 2.1-4%, as

ferrous alloys with less are denoted carbon steel by definition. Cast irons contain

appreciable amounts of silicon, normally 1-3%, and consequently these alloys should be

considered ternary Fe-C-Si alloys. Here graphite is present in the form of flakes. [2]. The

SAE maintains a specification for the manufacture of gray iron for various applications.

For normal car and light truck applications, the SAE specification is J431 G3000

(superseded to G10) [2] and [5].

3.3 Specifications of car and Material Properties of Gray cast

iron

The disc brake rotors selected are of TATA indica cars. And the material selected is gray

cast iron Gray cast iron [2] and [5].

3.3.1 Solid disc brake rotor

3.3.1.1The specifications of car

Make: Tata

Model: Indica

Year: 1999

0 to 100km/h (0 to 62mph):

Drive train: Front

Country of origin: India

Weight: 936 kg (2053,18 pounds)

Total length: 3670 mm (143,78 inches)

Total width: 1630 mm (63,88 inches)

Total height: 1490 mm (58,41 inches)

Wheelbase: 2410 mm (94,43 inches)

Brakes type (front): Discs

Brakes type (rear): Drums



3.3.1.2 The material properties

Material Gray Cast iron

Thermal conductivity, K = 57.0 W/mK

Density, = 7272 kg/m3

Specific heat, c = 450 J/kgK

Thermal diffusivity, = 17.03 X 10-6

Thermal expansion coefficient in meters of expansion per meter of material per

Kelvin, 10.8 X 10-6

m/mK

Poissons ratio, = .2 to .3

Youngs modulus, E = 83 to 170 GPa

Shear modulus, G = 32 to 69 GPa

Coefficient of friction, = .4 (dry) and, = .2 (wet).

3.3.2 Ventilated disc brake rotor

3.3.2.1The specifications of car

Make: Tata

Model: Indica LX

Year: 2006

0 to 100km/h (0 to 62mph):

Drive train: Front

Country of origin: India

Weight: 1600 kg (3509,76 pounds)

Total length: 4410 mm (172,73 inches)

Total width: 1630 mm (63,88 inches)

Total height: 1780 mm (69,75 inches)

Brakes type (front): Discs

Brakes type (rear): Drums

3.3.2.2 The material properties:

Material Material Gray Cast iron



Thermal conductivity, K = 57.0 W/mK

Density, = 7272 kg/m3

Specific heat, c = 450 J/kgK

Thermal diffusivity, = 17.03 X 10-6

Thermal expansion coefficient in meters of expansion per meter of material per

Kelvin, 10.8 X 10-6

m/mK

Poissons ratio, = .2 to .3

Youngs modulus, E = 83 to 170 GPa

Shear modulus, G = 32 to 69 GPa

Coefficient of friction, = .4 (dry) and, = .2 (wet).

TABLE 3.1 Material Properties

TABLE 3.2 Youngs Modulus and Melting Temperature of gray cast iron

Grade Youngs Modulus MPa

Melting Temperature

K

Poisons ratio

G10 126 x 103

1448 0.25

Disc material Density * 10-9

3mmkg

Specific Heat PC

KkgJ

Conductivity

k *10-3

mmKW

Coefficient Of

Thermal

Expansion

*-6 K-1

Gray cast

iron

7272 450 57 10.8



CHAPTER 4

THEORY AND CALCULATIONS

4.1 Assumptions

The following assumptions are made in the finite element analysis of the four wheelers

disc brake rotors [1] to [14].

The kinetic energy produced by the vehicle is converted into heat by

neglecting the losses.

Heat flux is constant throughout the disc rotor.

Material of the disc is isotropic.

60% of the weight is being distributed on the front axle.

The time difference between the stopping time and heat flux application time

as one second.

4.2 Stopping Distance:

The distance in which a car is brought to rest from any speed depends upon [12]:

Nature of the road

Braking efficiency

The condition and inflation pressure of the tires

Let a vehicle be brought to rest by the braking action from a steady speed of V m/s.

As we know, the acceleration of a vehicle can be found out from the force acting on it,

viz.,

ag

WamF (4.1)



Here, F = force acting on the vehicle (N)

W = weight of the vehicle

g = acceleration due to gravity

a = acceleration of the vehicle (m/s2)

The application of brakes causes deceleration or negative acceleration and the

decelerating force is

W=F ... (4.2)

Here = coefficient of friction between tire tread and dry concrete road

But a*g

W=F g=a

Time taken to bring a vehicle traveling at a steady speed of V m/s to rest, rate of

deceleration being g is

g

V=t . (4.3)

With constant deceleration mean velocity is half initial velocity i.e. V/2. Hence

stopping distance = mean velocity time

Stopping distance = g2

V=

g

V

2

V 2

. (4.4)

Thus we can say that stopping distance increase with vehicle speed because

coefficient of friction and g are constants.

4.3 Weight Transfer:

When at rest, the weight of the vehicle is divided on its axles. This division of

weight does not remain the same during braking action. A retarding force acts on the

point of road contact towards the rear, and the inertia force at the center of gravity



towards the front. Both these forces being opposite and equal form a couple pressing the

front portion of the vehicle, the result being transfer of weight from rear to the front.

Let F= retarding force

= Coefficient friction

W = weight of the vehicle

h= height of CG of vehicle from road

W=F (Inertia force) and couple = hW

Let w be the weight transferred from the rear to the front and = wheelbase.

The balancing couple = ( w )

Whw ....... (4.5)

hWw ... (4.6)

4.4 Braking Efficiency:

The rate at which the braking system will bring the vehicle to a stationary position

from a given speed is known as braking efficiency. It is a ratio of its rate of deceleration

to the acceleration due to gravity.

Braking efficiency = %100g

F. (4.7)

The efficiency being 100% when F = g

Highly efficient brakes give a large value of deceleration subjecting the passengers to

heavy jolts. The minimum braking efficiency is 30% and the highest should be 80%.



4.5 Kinetic Energy and Heat Flux

4.5.1 Approaches

In contact area of brake components; the pads and the disc; heat is generated due to

friction. For calculation of heat generation at the interface of these two sliding bodies two

approaches are suggested [4].

Macroscopic model approach: On the basis of law of generation of energy the

kinetic energy of the vehicle during motion is equal to the dissipated heat after

vehicle stop.

Microscopic model approach: By knowing the friction coefficient, pressure

distribution at the contact area, geometric characteristics of the pad and the disc,

relative sliding velocity and duration of braking action one can calculate the heat

generated due to friction.

In this project we are considering macroscopic model approach.

4.5.2 Macroscopic model approach

Brakes are essentially a mechanism to change the energy types. When a car is

moving with speed, it has kinetic energy. Applying the brakes, the pads or shoes that

press against the brake drum or rotor converts this energy into thermal energy. The

cooling of the brakes dissipates the heat and the vehicle slows down. This is all to do with

the first law of thermodynamics, sometimes known as the law of conservation of energy

that states that energy cannot be created nor destroyed; it can only be converted from one

to another form. In the case of brakes, it is converted from kinetic energy to thermal

energy.

Kinetic Energy = M*2

1 V2 . (4.8)

Where, M is the total mass of the vehicle and V is the initial speed of the vehicle. To

obtain amount of heat dissipated by each of the front brake discs, we should know the



weight distribution of the vehicle. So, the amount of heat dissipated by each of the discs

will be:

Heat generated, Q = .5 * M*2

1 V2 = .25 mV

2... (4.9)

Heat flux = A

Q ... (4.10)

where, m is the weight distribution on the front axle and A is the area of the disc and pad

contact surfaces.

4.6 Calculations

4.6.1 Calculations for heat flux application time

From equation 4.3, we have

g

V=t

Taking initial speed of the vehicle V = 50kmph = 13.88 m/s and coefficient of friction as

0.4, we have

9.81 x .4

13.88=t = 3.5 s

Therefore, time for which the heat flux is applied on the disc can be taken as 3.5 s.

4.6.2 Calculations for kinetic energy heat flux time

4.6.2.1 Solid disc brake rotor

Let,

Initial Velocity, 1v = 50 kmph.

= 13.88 m/sec.

Final Velocity, 2v = 0 kmph.



Mass of the vehicle, 1m = 936 kg.

Mass of the driver, 2m = 70 kg

Total mass, M = 1m + 2m

= 936 + 70

= 1006 kg.

Mass on the front axle, m = 60 % of M

= .6 x 1006

= 603.6 kg

We know from equation 4.9 that,

Kinetic Energy Q = .25 mV2

= .25 x 603.6 x 13.882

Q = 29, 071.54 J

Heat, Q = 29, 071.54 J.


Heat Flux, A

Q=

Let,

Outside diameter of the disc 1d = 241 mm.

Inside diameter of the disc, 2d = 147 mm.

Effective area on which heat flux is applied, A = ( ) 2d-d4 2

2

2

1

= 2147-2414

22



A = 57,290.08 2mm .

Heat flux, A

Q=

= 08.57290

29071.54

Heat flux = .507 J/mm2

4.6.2.2 Ventilated disc brake rotor

Let,

Initial Velocity, 1v = 50 kmph.

= 13.88 m/sec.

Final Velocity, 2v = 0 kmph.

Mass of the vehicle, 1m = 1600 kg.

Mass of the driver, 2m = 70 kg

Total mass, M = 1m + 2m

= 1600 + 70

= 1670 kg.

Mass on the front axle, m = 60 % of M

= .6 x 1670

= 1002 kg


Kinetic Energy Q = .25 mV2

= .25 x 1002 x 13.882



Q = 48259.92 J

Heat, Q = 48259.92 J.


Heat Flux, A

Q=

Let,

Outside diameter of the disc 1d = 228.4 mm.

Inside diameter of the disc, 2d = 150.32 mm.

Effective area on which heat flux is applied, A = ( ) 2d-d4 2

2

2

1

= 2150.32-4.2284

22

A = 46, 449.16 2mm .

Heat flux, A

Q=

= 16.46449

48259.92

Heat flux = 1.04 J/mm2



CHAPTER 5

GEOMETRIC MODELLING

For geometric 3D modeling and 2D drafting of the selected solid disc brake rotors

we used higher end CAD package Pro-e Wildfire 4 as a software tool.

5.1 Pro e Wildfire 4: It is one of the higher end CAD software which has the

following modules:

Module 1: Sketcher

Module 2: Part modeling

Module 3: Assembly

Module 4: Manufacturing

Module 5: Drawing

Module 6: Format

Module 7: Report

Module 8: Diagram

Module 9: Layout

Module 10: Markup

Out of these 10 modules, we are making use of Module 2 i.e. Part modeling and Module 5

i.e. drawing for our project.

5.2 Module 2: Part Modeling

In Part modeling we can create a part from a conceptual sketch through solid

feature-based modeling, as well as build and modify parts through direct and intuitive

graphical manipulation. The Part Modeling requires knowing the terminology, basic

design concepts, and procedures that we must know before we start building a part. Part

Modeling shows how to draft a 2D conceptual layout, create precise geometry using basic

geometric entities, and dimension and constrain the geometry. We can build a 3D



parametric part from a 2D sketch by combining basic and advanced features, such as

extrusions, sweeps, cuts, holes, slots, and rounds. Finally, Part Modeling provides

procedures for modifying part features and resolving failures.

5.3 Module 5: Drawing

A detailed drawing lets us create and manipulate detailed engineering drawings

that use our 3D model as a geometry source. With Detailed Drawings, we can pass

dimensions, notes, and other elements of design between the model and its views on the

plotted sheet. It helps in creating drawings directly from the solid model, customizing the

drawings with sketched geometry, and making cosmetic changes to the drawings. This

also helps us to manipulate items in a drawing, annotate our drawings, and add different

kinds of textual and symbolic information. It helps to create views and custom formats

and to use logic statements to control the look of the drawing.

5.4 Modeled and Drafted Components

The dimensions are of the actual disc are taken by screw gauge and calipers and

modeled using Pro-e Wildfire 4: In FEA it is not necessary to discritize the entire body or

structure. For this we are considering the symmetry of structure based on the geometry.

The symmetry which we have considered is axial symmetry.

Fig 5.1 3D model and axial symmetry model of solid disc brake rotor which is

modeled in Pro-e Wildfire 4.



Fig 5.2 3D model and axial symmetry model of ventilated disc brake rotor

which is modeled in Pro-e Wildfire 4.

Fig 5.3 2D Drafting of solid disc brake rotor using Pro-e Wildfire 4.



Fig 5.4 2D Drafting of ventilated disc brake rotor using Pro-e Wildfire 4.

The 3D symmetric models of both solid and ventilated disc rotors are then

imported to Altair HyperMesh 7 in iges format for meshing purpose.



CHAPTER 6

FINITE ELEMENT MODELING

The imported symmetric models of solid and ventilated rotors are then meshed in

Altair HyperMesh 7. HyperMesh is a Computer Aided Engineering (CAE) tool as

described in the figure 6.1. HyperMesh is a high performance finite element pre and post

processor that allows building finite element and finite difference models, viewing their

results and performing data analysis. In addition, we can use Altairs OptiStruct linear

solver to quickly validate component level and improve product design.

Fig 6.1 Schematic arrangement of HyperMesh usage



6.1 Meshed components

The meshed models are shown below:

Fig 6.2 Meshed symmetric model of solid disc brake rotor

Fig 6.3 Meshed symmetric model of ventilated disc brake rotor

TABLE 6.1 FEA Model Details of Rotors

Type of

rotors

D.O.F at each

node

Element

type

No. of

Elements.

No. Of Nodes.

Solid Three SOLID90 2077 3526

Ventilated Three SOLID90 5974 11097



6.2 SOLID90

While importing the meshed model to the ANSYS the element used for meshing

is specified as SOLID90. There are lots of elements available for meshing, but based on

the type of analysis, model and properties of elements available the suitable element is

selected. For our project the SOLID 90 element is selected which has the following

nature.

6.2.1 SOLID90 Element Description

SOLID90 is a higher order version of the 3-D eight node thermal element. The

element has 20 nodes with a single degree of freedom, temperature, at each node. The 20-

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

boundaries. The 20-node thermal element is applicable to a 3-D, steady-state or transient

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

the element should be replaced by the equivalent structural element such as SOLID95 or

SOLID185.

Fig 6.4 SOLID90 Element Geometry



6.2.2 SOLID90 Input Data

The geometry, node locations, and the coordinate system for this element are

shown in Fig 6.3. The element is defined by 20 node points and the material properties. A

prism-shaped element may be formed by defining duplicate K, L, and S; A and B; and O,

P, and W node numbers. A tetrahedral-shaped element and a pyramid-shaped element

may also be formed as shown in Fig 6.4. Orthotropic material directions correspond to the

element coordinate directions. The element coordinate system orientation is as described

in Coordinate Systems. Specific heat and density are ignored for steady-state solutions.

Properties not input default as described in Linear Material Properties. Element loads are

described in Node and Element Loads. Convection or heat flux (but not both) and

radiation may be input as surface loads at the element faces as shown by the circled

numbers on Fig 6.3. Heat generation rates may be input as element body loads at the

nodes. If the node I heat generation rate HG (I) is input, and all others are unspecified,

they default to HG (I). If all corner node heat generation rates are specified, each midside

node heat generation rate defaults to the average heat generation rate of its adjacent

corner nodes.

6.2.3 SOLID90 Input Summary

Nodes: I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A, B

Degrees of Freedom: TEMP

Real Constants: None

Material Properties: KXX, KYY, KZZ, DENS, C, ENTH

Surface Loads: Convection or Heat Flux (but not both) and Radiation

face 1 (J-I-L-K), face 2 (I-J-N-M), face 3 (J-K-O-N),

face 4 (K-L-P-O), face 5 (L-I-M-P), face 6 (M-N-O-P)

Body Load: Heat Generations

HG(I), HG(J), HG(K), HG(L), HG(M), HG(N), HG(O), HG(P), HG(Q), HG(R),

HG(S), HG(T), HG(U), HG(V), HG(W), HG(X), HG(Y), HG(Z), HG(A), HG(B)



6.2.4 SOLID90 Output Data

The solution output associated with the element is in two forms:

Nodal temperatures included in the overall nodal solution.

Additional element output.

Convection heat flux is positive out of the element; applied heat flux is positive into

the element. The element output directions are parallel to the element coordinate system.

6.2.5 SOLID90 Assumptions and Restrictions

The element must not have a zero volume. This occurs most frequently when the

element is not numbered properly.

Elements may be numbered either as shown in Fig 6.3 or may have the planes

IJKL and MNOP interchanged.

The condensed face of a prism-shaped element should not be defined as a

convection face.

The specific heat and enthalpy are evaluated at each integration point to allow for

abrupt changes (such as melting) within a coarse grid of elements.

If the thermal element is to be replaced by a SOLID95 or SOLID 185 structural

element with surface stresses requested, the thermal element should be oriented

such that face IJNM and/or face KLPO is a free surface.

A free surface of the element (i.e., not adjacent to another element and not

subjected to a boundary constraint) is assumed to be adiabatic.

Thermal transients having a fine integration time step and a severe thermal

gradient at the surface will also require a fine mesh at the surface.



An edge with a removed midside node implies that the temperature varies linearly,

rather than parabolically, along that edge.

The element sizes, when degenerated, should be small in order to minimize the

field gradients.



CHAPTER 7

FINITE ELEMENT ANALYSIS

7.1 Introduction

Finite Element Analysis (FEA) is computer oriented numerical analysis technique

used to find solution to the complex problems whose behavior could be explained by

means of equation of calculus.

7.2 Steps in FEA

7.2.1 General Steps

1. Discretization of problem region (physical problem).

2. Selection of displacement model or function.

3. Derivation of element stiffness matrix.

4. Assembly of element stiffness matrices.

5. Applying the boundary conditions.

6. Solution of unknown displacement, stress and strains.

7.2.2 Steps in ANSYS

ANSYS is a general purpose finite element modeling package for numerically

solving a wide variety of mechanical problems. These problems include: static/dynamic

structural analysis (both linear and non-linear), heat transfer and fluid problems, as well

as acoustic and electro-magnetic problems. Here Finite Element Analysis may be broken

into the following three stages. This is a general guideline that can be used for setting up

any finite element analysis.



1. Preprocessing: It involves defining the problem. The major steps in preprocessing are

given below:

Define key points/lines/areas/volumes

Define element type and material/geometric properties

Mesh lines/areas/volumes as required

The amount of detail required will depend on the dimensionality of the analysis (i.e. 1D,

2D, axisymmetric, 3D).

2. Processing or Solution: It involves assigning loads, constraints and solving.

3. Postprocessing: It involves further processing and viewing of the results. In this stage

one can have:

Lists of nodal displacements.

Element forces and moments.

Deflection plots.

Stress contour diagrams etc.

7.3 Coupled Field Analysis

Coupled-field analysis is a combination of analyses from different engineering

disciplines (physics fields) that interact to solve a global engineering problem; hence, we

often refer to a coupled-field analysis as a multiphysics analysis. When the input of one

field analysis depends on the results from another analysis, the analyses are coupled.

Some analyses can have one-way coupling. For example, in a thermal stress

problem, the temperature field introduces thermal strains in the structural field, but the

structural strains generally do not affect the temperature distribution. Thus, there is no

need to iterate between the two field solutions. More complicated cases involve two-way

coupling. A piezoelectric analysis, for example, handles the interaction between the

structural and electric fields: it solves for the voltage distribution due to applied



displacements, or vice versa. In a fluid-structure interaction problem, the fluid pressure

causes the structure to deform, which in turn causes the fluid solution to change. This

problem requires iterations between the two physics fields for convergence. The coupling

between the fields can be accomplished by either direct or load transfer coupling.

Coupling across fields can be complicated because different fields may be solving for

different types of analyses during a simulation. For example, in an induction heating

problem, a harmonic electromagnetic analysis calculates Joule heating, which is used in a

transient thermal analysis to predict a time-dependent temperature solution. The induction

heating problem is complicated further by the fact that the material properties in both

physics simulations depend highly on temperature.

Some of the applications in which coupled-field analysis may be required are

pressure vessels (thermal-stress analysis), fluid flow constrictions (fluid-structure

analysis), induction heating (magnetic-thermal analysis), ultrasonic transducers

(piezoelectric analysis), magnetic forming (magneto-structural analysis), and micro-

electromechanical systems (MEMS). In our project we are using Thermal Structural

Analysis.

7.3.1 Thermal Structural Analysis

In thermal structural analysis, we have first carried out the thermal analysis by

giving material properties and thermal boundary conditions and load as heat flux, the

results obtained is in the form of temperature distribution. Then the structural analysis is

carried out by giving material properties, structural boundary conditions and load is given

interms of the temperature obtained in thermal analysis.

7.3.2 Thermal and Structural Boundary Conditions

Thermal boundary conditions are given by applying heat flux on the brake to pad

contact surfaces and convection on remaining surfaces. The structural boundary condition

is given by fixing the bolt hole and disc to wheel hub contact surface. The load in

structural load is in the form of temperature obtained in thermal analysis.



7.4 Modal Analysis

Any physical system can vibrate. The frequencies at which vibration naturally

occurs, and the modal shapes which the vibrating system assumes are properties of the

system, and can be determined analytically using Modal Analysis.

Analysis of vibration modes is a critical component of a design, but is often

overlooked. Inherent vibration modes in mechanical components can shorten equipment

life, and cause premature or completely unanticipated failure, often resulting in hazardous

situations. Detailed fatigue analysis is often required to assess the potential for failure or

damage resulting from the rapid stress cycles of vibration. Detailed modal analysis

determines the fundamental vibration mode shapes and corresponding frequencies. This

can be relatively simple for basic components of a simple system, and extremely

complicated when qualifying a complex mechanical device or a complicated structure

exposed to periodic wind loading. These systems require accurate determination of

natural frequencies and mode shapes using techniques such as Finite Element Analysis.

7.5 Procedure Adopted For Thermal Analysis Of Disc Brake

Rotor in ANSYS 11:

Initially Thermal analysis is selected as the preference for analyzing.

The suitable element is selected while importing from Altair HyperMesh 7 for

Thermal analysis.

Specify the material properties such as Thermal conductivity (K), Specific

heat (Cp) and density (DENS) must be defined for transient analysis.

Select different sections in the geometry for applying heat flux and

convection.

Solution method of transient analysis is selected.

Give minimum time for selected vehicle come to rest from 50 kmph to 0

kmph.

Plot the temperature distributions from the post processors.



7.6 Procedure Adopted For Structural Analysis Of Disc Brake

Rotor in ANSYS 11:

After completion of thermal analysis select structural analysis as the

preference for analysing.

The suitable element is selected automatically for structural analysis by

switching from thermal to structural analysis.

Specify the material properties such as Youngs modulus and Poisons ratio.

Apply temperature on all the elements as obtained in thermal analysis.

Apply boundary conditions to the disc rotor by fixing all degrees of freedom at

the holes provided for bolts and the surface touching the wheel hub.

Solution method of transient is selected.

Then solve for thermal stresses and deformations developed in the disc rotor

due to the applied temperature.

7.7 Procedure Adopted For Modal Analysis Of Disc Brake

Rotor:

Initially Structural analysis is selected as the preference for analyzing.

The suitable element is selected automatically for modal analysis by switching

from thermal to structural analysis.

Specify the material properties such as Young's modulus (EX) and density

(DENS) must be defined for modal analysis.

Apply boundary conditions to the disc rotor by fixing all degrees of freedom at

the holes provided for bolts and the surface touching the wheel hub.

Solution method of modal analysis is selected.

Here subspace method is used for the extraction of mode shapes. And specify

the number of modes to extract. The subspace method uses the subspace

iteration technique.

After specifying the number of modes to extract the software gives the

required frequencies and the mode shapes.



CHAPTER 8

RESULTS

8.1 Inputs and results of ANSYS 11

Initial temperature of the disc rotors = 298 K and convection heat transfer coefficient h =

50 W/m2K [13] and [14].

Table 8.1 Inputs & Results for Transient Thermal Analysis

Vehicle name Time required to

come rest from 50

kmph-0 kmph (sec)

Heat flux applied

(J/ 2mm )

Max. Temperature

of the disc brake

rotor (K)

Solid 3.5 0.57 838.022

Ventilated 3.5 0.72 414.029

Table 8.2 Results Obtained From Thermal to Transient Structural Analysis

Type of rotors Maximum Stress (N/ 2mm ) Maximum deformation (mm)

Solid 1869 0.893

Ventilated 756 0.479

Table 8.3 Results Obtained From Modal Analysis

Type of rotors Frequency in Hz

f1 f2 f3 f4 f5

Solid 42.939 43.406 44.656 53.141 61.759

Ventilated 67.07 67.09 75.738 76.799 77.429



8.2 Plots of Results

8.2.1 Solid Disc Brake Rotor

Fig 8.1 Temperature distribution in auxiliary view

Fig 8.2 Temperature distribution in top view



Fig 8.3 Auxiliary view of the fixed model




Fig 8.5 Auxiliary view of deformed shape of the model with undeformed edges

Fig 8.6 Side view of deformed shape of the model with undeformed edges



Fig 8.7 Auxiliary view of displacement distribution

Fig 8.8 Top view of displacement distribution



Fig 8.9 1st Principal Stress Distributions

Fig 8.10 2nd

Principal Stress Distributions



Fig 8.11 3rd

Principal Stress Distributions

Fig 8.12 1st or fundamental frequency Distribution



Fig 8.13 2nd

Frequency Distribution

Fig 8.14 3rd




Fig 8.15 4th


Fig 8.16 5th




8.2.2 Ventilated Disc Brake Rotor

Fig 8.17 Temperature distribution in auxiliary view

Fig 8.18 Temperature distribution in top view



Fig 8.21 Deformed shape in the auxiliary view

Fig 8.22 Displacement distribution in auxiliary view



Fig 8.23 Displacement distribution in top view

Fig 8.24 1st Principal Stress Distribution

Coupled Field Finite Element Analysis of C

Documents

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