zheng han - comparison study of two disk brake systems used in motorcyles

COMPARISON STUDY OF TWO DISK BRAKE SYSTEMS USED IN

MOTORCYCLES

SUBMITTED BY

ZHENG HAN

DEPARTMENT OF MECHANICAL ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

SESSION 2005/2006

Summary

SUMMARY

The objective of this final year project was to study and compare the mechanical

performances of a conventional brake-disk system and a newly designed Perimetral

brake-disk system using the finite element method (FEM).

Finite element (FE) models of the brake-disks were created using Pro-E and

simulated using ANSYS which is based on the finite element method (FEM). The

brake-disks were simulated under three different loading conditions: two static tests

(torsional and lateral strength simulation) and one thermal analysis (residual stress

simulation). Particular attention was given to the residual stress simulation for the

Perimetral brake-disk where a potential problem may arise due to its design.

Three-dimensional modelling and meshing using the simulation program ANSYS

were successfully implemented in this project, allowing for greater flexibility and

accuracy in the results achieved.

For the two static tests, the maximum stresses (weak points) were found to be at the

mounting holes for Perimetral brake-disk. Overall, the Perimetral brake-disk showed

good performance under the static tests, with stress values close to or lower than

those of the conventional brake-disk.

i

Summary

For the residual stress simulation, the maximum stresses concentrated at the piercing

holes for both brake-disks. For the Perimetral brake-disk, maximum stress values

were significantly higher than those found in the conventional brake-disk. These

maximum stresses occurred at its inner piercing holes (weak points). At these weak

points, there is the danger of yielding or crack initiation under repeat residual stresses.

Compared to the conventional brake-disk, the numbers of areas with localized stress

concentration were much higher in the Perimetral brake-disk. This indicated that the

number of potential points for crack initiation is higher for the Perimetral brake-disk

resulting in a higher risk of failure. It was also observed that high stress

concentrations occur at the piercing holes in-between the mounting holes, whereas

the piercing holes located directly below the mounting holes experienced much lower

stresses.

To counter the potential problem of failure under residual stress, several

countermeasures were proposed, modelled and analysed. Among them,

countermeasures 1, 3 and 5 were recommended to improve on the original design of

the Perimetral brake-disk.

In order to achieve more accurate results and better understanding of the Perimetral

brake-disk’s performance, the entire Perimetral brake system (including the rim and

tyres) should be incorporated for simulation.

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Acknowledgement

ACKNOWLEDGEMENT

I would like thank my parents, for without them, all these would not have been

possible. I would also like to thank Jaslyn for all her support and encouragement

during the course of this project.

I would like to express my sincere appreciation to all who helped in any way in the

preparation and completion of this final year project, especially the R&D engineers

from Sunstar Logistic Singapore Pte Ltd and his supervisor Associate Professor G. R.

Liu.

Special thanks must also be extended to Dr. Cai Chao from IHPC for his help and

guidance in the course of the project.

iii

Table of Contents

TABLE OF CONTENTS

SUMMARY……………………………………………………………………….. i

ACKNOWLEDGEMENT……………………………………………………….. iii

TABLE OF CONTENTS……………………………………………………….... iv

LIST OF FIGURES………………………………………………………………. vii

LIST OF TABLES………………………………………………………………... ix

LIST OF SYMBOLS……………………………………………………………... x

Chapter 1 Introduction……………………………………………………………1

1.1 Purpose……………………………………………………………………... 1

1.2 The Problem………………………………………………………………... 1

1.3 Scope……………………………………………………………………….. 4

1.4 Literature Survey…………………………………………………………....6

Chapter 2 Theory………………………………………………………………..... 10

2.1 Three-Dimensional Meshing………………………………………………..10

2.2 Techniques of 3D Meshing………………………………………………… 12

2.3 Stress Analysis Methods…………………………………………………… 13

Chapter 3 Experimental Procedures…………………………………………... 16

3.1 Pro-E Modelling…………………………………………………………….16

3.2 Simulation by ANSYS……………………………………………………... 17

3.3 Simulation Procedures……………………………………………………... 18

iv

Table of Contents

(a) Static Test – Torsional Strength Simulation……………………………. 18

Purpose of Test…………………………………………………….. 18

Assumptions………………………………………………………... 19

(b) Static Test – Lateral Strength Simulation……………………………… 20

Purpose of Test…………………………………………………….. 20

Assumptions………………………………………………………... 20

(c) Thermal Analysis – Residual Stress Simulation……………………….. 21

Purpose of Test…………………………………………………….. 21

Assumptions………………………………………………………... 22

Chapter 4 Experimental Results………………………………………………….24

4.1 Mesh Results……………………………………………………………….. 24

4.2 Simulation Results in ANSYS……………………………………………... 26

(a) Static Test – Torsional Strength Simulation…………………………… 26



Chapter 5 Discussion……………………………………………………………... 30

(a) Static Test – Torsional Strength Simulation…………………………… 30



Chapter 6 Final Analysis……………………………………………………….... 37

6.1 Proposed Countermeasure Designs…………………………………………38

(a) Changing the Width of the Brake-Disk: Countermeasures 1 and 2……. 38

(b) Changing the Shape of the Piercing Holes: Countermeasures 3 and 4.... 39

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Table of Contents

(c) Joining the Piercing Holes: Countermeasures 5 and 6…………………. 40

6.2 Results of Countermeasures………………………………………………... 40

6.3 Interpretation of Results……………………………………………………. 42

Chapter 7 Conclusion………………………………...………………………….. 43

Chapter 8 Recommendations…………………………………………………….. 46

List of References…………………………………………………………………. 47

APPENDICES…………………………………………………………………….. 48

Appendix 1: Details of Design of Perimetral Brake-Disk System and its

Material Properties…………………………………………… 48

Appendix 2: Comparison of Braking Force………………………………... 50

Appendix 3: ANSYS Meshing Procedure…………………………………. 53

Appendix 4: Calculation of Maximum Torsional Force Experienced

During Hard Braking………………………………………….55

Appendix 5: ANSYS Procedure for Torsional Strength Simulation………. 58

Appendix 6: ANSYS Procedure for Lateral Strength Simulation…………. 59

Appendix 7: Calculation of Maximum Temperature in Brake-Disk………. 60

Appendix 8: Temperature Distribution Profiles and Source Codes………... 62

Appendix 9: ANSYS Procedure for Residual Stress Simulation…………... 66

Appendix 10: Details of Simulation Results ………………………………. 68

Appendix 11: Stress Concentrations in Circular and Elliptical Holes……... 86

Appendix 12: Results for Residual Stress Simulation for Countermeasures. 87

vi

List of Figures

LIST OF FIGURES

Figure 1: Conventional Brake System

Figure 2: Perimetral Brake System

Figure 3: Pro-E Drawing of Perimetral Brake-Disk

Figure 4: Pro-E Drawing of Entire Perimetral Brake System

Figure 5: Pro-E drawing of Chosen Conventional Brake-Disk

Figure 6: Pro-E Drawing of Rotor of Chosen Conventional Brake-Disk

Figure 7: Model of Entire Meshed Perimetral Brake-Disk

Figure 8: Close-Up of Meshing of Perimetral Brake-Disk

Figure 9: Model of Entire Meshed Conventional Brake-Disk

Figure 10: Close-Up of Meshing at Outer Diameter of Conventional Brake-Disk

Figures 11 (a) and (b): First Principal Stress – Close-Up on Area of Maximum Stress

Figures 12 (a) and (b): Von Mises Stress – Close-Up on Area of Maximum Stress





Figures 17 (a) and (b): Maximum Von Mises Stresses for Torsional Strength

Simulation

Figures 18 (a) and (b): Maximum Von Mises Stresses for Lateral Strength Simulation

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List of Figures

Figures 19 (a) and (b): Maximum First Principal Stresses for Residual Stress

Simulation

Figure 20: Areas of Localized Stress Concentrations

Figure 21: First Principal Stress Distributions on Perimetral Brake-Disk

Figure 22: Pro-E Drawing of Countermeasure 1






viii

List of Tables

LIST OF TABLES

Table 1: Summary of Results

Table 2: Summary of Residual Stress Simulation Results for Countermeasures

Table 3: Design Factors to be Considered

ix

List of Symbols

LIST OF SYMBOLS

a deceleration, m/s2

c Specific heat capacity of brake-disks, kJ/kg.k

f maximum torsional force, N

F braking force, N

g gravity, m/s2

mp weight of Perimetral brake-disk, kg

mc weight of Conventional brake-disk, kg

M maximum motorcycle weight, kg

r disk effective radius, mm

R tyre half radius, mm

W motorcycle force, N

μ friction coefficient, dimensionless

σ1,2,3 principal stresses, N/mm2

σnom nominal stress, N/mm2

σuc ultimate compressive strength, N/mm2

σut ultimate tensile strength, N/mm2

σv Von Mises Stress, N/mm2

σy Yield Stress, N/mm2

x

Chapter 1 Introduction


1.1 Purpose

This final year project is an industrial collaborative project with Sunstar Logistic

Singapore Pte Ltd. The objective of the project is to study and compare the

mechanical performances of a conventional brake-disk system and a newly designed

Perimetral brake-disk system using the finite element method (FEM). Based on the

study of their mechanical performances, further improvements will be recommended

to the design of the new Perimetral brake-disk system.

1.2 The Problem

Traditionally, the brake-disk of a motorcycle braking system is mounted on the inner

rim of the wheels as shown in Figure 1. A new Perimetral brake-disk has recently

been developed by Sunstar. As shown in Figure 2, this new Perimetral brake system

works by mounting the brake-disk onto the outer rim of the wheel. The details of the

design specifications of the Perimetral brake-disk and its material properties can be

found in Appendix 1.

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Mounting Holes Mounting Holes

Figure 1: Conventional Brake System Figure 2: Perimetral Brake System

(Pictures courtesy of Sunstar Logistic Singapore Pte Ltd)

In conventional braking systems, the brake-disk is mounted onto the inner rims of the

wheels via the mounting holes. These mounting holes are located near the inner

diameter of the brake-disk. During braking, when the brake callipers clamp onto the

brake-disk, the braking torque is transmitted from the brake-disk to wheel-hub at its

the inner diameter of where the mounting holes are located. The braking torque is

then transferred from the rigidly fixed mounting holes to the wheel-hub at its inner

diameter, through the spokes to the rim of the wheels and eventually to the tyres.

In the new Perimetral brake system, the braking torque is directly transmitted from

the brake-disk to the outer rim of the wheel and finally to the tyres. This is due to the

brake-disk being directly mounted via its outer diameter onto the outer rim of the

wheel. As such, when the same force is applied onto the brake-disks, the Perimetral

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brake system is able to produce a larger braking torque due to its larger diameter as

compared to a conventional brake-disk (refer to Appendix 2 for details).

In the Perimetral brake system, the braking torque is transferred directly to the outer

rim, thus the braking stresses are eliminated from the spokes. Therefore, the rim can

be lighter as it only needs to withstand the normal riding forces associated with the

motorcycle. With the Perimetral brake system’s unique design, it allows better

utilisation of braking force and a light weight design for the wheel; thus showing

great potential to replace the conventional braking system. However, more analysis

and studies have to be done to verify its feasibility for mass industrial production and

use on the road.

At the initial stage, the research was focused on investigating the market potential of

this new brake-disk while exploring possible problems and advantages. Looking at

Buell, an American Company, which is currently adopting a similar brake-disk

system for its motorbikes, it was found that the selling points of this brake system are

mainly due to its light weight which is important for rough roads (street riding) and

its aesthetic values. Next, together with the engineers from Sunstar, the potential

problems and advantages that the Perimetral brake-disk may face, including both

design and technical issues, were studied. This brought to focus specific problems

and areas to be further investigated during the later stage of analysis.

3


Motorcycle brake-disks are subjected to a variety of forces during the operation of a

motorcycle. These forces include: braking forces (torsional forces) that are generated

in the wheel when the brakes are applied to stop the motorcycle, lateral forces in the

form of projectiles (such as stones) or impact during usage or riding, and residual

stress build-up due to repeated heating and cooling of the brake-disk during braking.

Simulations have to be done in order to ensure that the Perimetral brake-disk can

perform well under these conditions and loadings.

In particular, special attention has to be given to residual stress analysis. Due to the

Perimetral brake-disk’s unique design, the brake-disk’s allowance for expansion is

constricted by the rim (by the mounting holes at the outer diameter of the brake-disk).

In the course of riding, the brake-disk undergoes repeated heating and cooling due to

braking. This results in repeated expansion and contraction of the brake-disk. Due to

the constraints at its outer diameter, problems of warping or stress concentrations

may occur. In contrast, there is more allowance for expansion and contraction of the

conventional brake-disk, as the brake-disk is only fixed to the rim at its inner

diameter.

1.3 Scope

In this project, the mechanical behaviour and performance of the Perimetral brake-

disk under certain loading conditions will be studied. This shall be done by

simulating the loading conditions the brake-disk is predicted to undergo and

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analysing the results. The primary focus of this project is to simulate the

performances of the brake-disk using ANSYS.

Braking systems can be divided into mono (one disk) or duo (two disks) brake-disk

systems; representing the number of brake-disks used. In this study, mono-disk

systems from a conventional brake-disk and a Perimetral brake-disk will be modelled,

tested and then analysed. As the braking power of the front brake-disk is more

important than the rear disk during hard braking and stops, only the front brake-disk

of each system would be studied.

The analysis and comparison study will be done through modelling and simulation

using the respective software; Pro-E and ANSYS. After building a finite element (FE)

model of the brake-disks in Pro-E, the models would be simulated using ANSYS.

The brake-disks will be simulated under three different loading conditions: two static

tests and one thermal analysis. The two static cases are torsional strength simulation

and lateral strength simulation. For thermal analysis, residual stress simulation will

be performed.

In order to obtain accurate and reliable results for the simulations, the meshing of the

brake-disks must be properly carried out. In ANSYS, simulation tests can be either

carried out in two or three dimensions. At Sunstar, the conventional method has

always been to use the less complex two-dimensional simulation. However, there are

limitations in using this simple method such as the difficulty in meshing large

5


complicated parts. In this project, three-dimensional simulation techniques shall be

studied and used to carry out the various tests in attempt to achieve more accurate

results. Various simulation methods, such as techniques to input load conditions and

thermal profiles will also be studied and improved. These will enable a more accurate

simulation of the “real-life” conditions that the brake-disks actually experience.

After the various tests are carried out, the performance of the conventional and

Perimetral brake-disks will be compared and analysed. The ability of the Perimetral

brake-disk to withstand these loading conditions would be examined, and their

weaknesses and strengths will be discussed. Particular attention will be paid to

residual strength simulation for the Perimetral brake-disk where a potential problem

may arise. Recommendations will be suggested to change various aspects of its

design. These changes will be modelled and simulated to test if there are any

improvements in its performance.

1.4 Literature Survey

In this project, the design of a new Perimetral brake-disk is modelled and simulated

to evaluate its mechanical performance. The use of simulations to analyse possible

designs is a common practice in the automobile industry where there is a continuing

demand for reduction in product development time and cost to maintain profitability

and competitiveness. Therefore, different ways to make product development more

efficient have been developed. Advancements in the entire spectrum of computer-

6


aided design, manufacturing, and engineering (CAD, CAM, CAE) tools in particular

have automated many design, engineering, and analysis tasks to shorten development

cycles, mostly as labour savings to minimize overhead costs [1].

As the studies done in this project are preliminary, the ANSYS simulations are not

expected to be the most accurate. In fact, most loads, boundary conditions, material

properties, and other data are not fully defined or even known due to the lack of

actual experimental data. The main objective of using simulations in this project is to

compare the possible advantages and disadvantages the Perimetral brake-disk may

have over the conventional brake-disk. Furthermore, based on the present design of

the Perimetral brake-disk, it is hoped that possible design flaws may be discovered

and eliminated without going into actual production of the prototype.

Computational simulation techniques require solving the complex differential or

partial differential equations that govern these phenomena. There are many types of

methods being used to solve these complex partial differential equations. In this

project, the simulation software, ANSYS, uses the finite element method (FEM) to

solve these equations [2]. Other common, numerical methods are boundary element

methods, finite difference methods, finite volume methods, and spectral methods. In

these methods, the spatial domain where the partial differential governing equations

are defined is often discretized into meshes. In recent years, element-free or meshfree

methods have emerged as a developed class of numerical methods [3].

7


The FEM is a general numerical method seeking an approximated solution of the

distribution of field variables in the problem domain that is difficult to obtain

analytically. It is a member of a set of methods called Weighted Residual Methods

and can be used in many different applications. The FEM was first used to solve

problems of stress analysis and has since been applied to many other problems such

as thermal analysis, fluid flow analysis and piezoelectric analysis [4].

The modern development of the finite element method began in the 1940s. Since the

finite element equations are usually cumbersome to solve by hand, the method

became popular only with the advent of the digital computer in the early 1950s. Since

the early 1960s, a large amount of research has been devoted to the technique. FEM is

the dominating method in engineering analysis because of its generality and

numerical efficiency [5]. Although other methods retain advantages in certain niche

applications, they are difficult or impossible to apply to other types of analysis. At the

same time, FEM can be applied to almost any type of analysis, handling complex

geometry and varying boundary conditions well. Thus the versatility and efficiency of

the FEM has resulted in its dominance in the market of commercial analysis software.

For decades, finite element analysis (FEA) has been a preferred method of analysis in

the motorcycle industry to simulate problems involving rotor temperature rise and

thermal cracks. ANSYS is a general purpose finite element analysis (FEA) package

used widely in the industry for simulating the response to the loading of a wide

variety of physical problems, including static and dynamic structural analysis (both

8


linear and nonlinear), heat transfer, computational fluid dynamics, as well as acoustic

and electromagnetic problems [6]. ANSYS uses the finite element method (FEM) to

numerically solve the underlying governing equations subjected to the boundary

conditions associated to the problem. Therefore, the ANSYS package is suitable for

use in this project which requires structural and thermal analysis of the brake-disk.

9

Chapter 2 Theory

Chapter 2 Theory

2.1 Three-Dimensional Meshing

The primary focus of this project is to simulate the performances of the brake-disks

using ANSYS which is developed based on the finite element method (FEM). In

order to obtain accurate and reliable results for the simulations, the meshing of the

brake-disks must be properly carried out. Meshing is performed to discretize the

geometry created into small pieces called elements. By using a properly predefined

mesh and by applying a proper principle, complex differential or partial differential

governing equations can be approximated by a set of algebraic equations for the mesh.

Assembling sets of algebraic equations for all the meshes can form the system of

algebraic equations for the whole problem domain [7].

In Sunstar, there is an established procedure for carrying out the meshing of the

brake-disks for simulation. Sunstar has always used 2D (two-dimensional) meshing

and simulation in ANSYS for the testing of its brake-disks. However in this project,

3D (three-dimensional) modelling and meshing will be used for more comprehensive

and accurate results.

10

Chapter 2 Theory

By using 3D elements, it is more demanding on computer resources, and geometry

creation and meshing may be tedious. However, 3D meshing is the preferred choice

here as it has the following advantages:

• In 3D meshing, 3D solids can be used for structures in 3D space that has neither a

constant cross section nor an axis of symmetry [8]. It allows for more flexibility

as it enables the meshing of different types of brake-disk shapes.

• It allows easier incorporation of other system parts, such as pins and brake

callipers, in the simulations. With 3D meshing, it is even possible to incorporate

the whole wheel assembly for analysis in the future.

In 3D meshing, the two general types of solid elements to be used are tetrahedron

shaped elements and hexahedron shaped elements. In this project, the majority of the

meshing will be carried out using hexahedron shaped elements as it has a better

aspect ratio, better accuracy and is easier to control in terms of size as compared to

tetrahedron shaped elements. The eight-node hexahedral element is linear (p = 1),

with a linear strain variation displacement mode [8]. Tetrahedral elements are also

linear, but can have more discretization errors because they have a constant strain.

Meshes comprised of hexahedrons are also easier to visualize than meshes comprised

of tetrahedrons. In addition, the reaction of hexahedral elements to the application of

body loads corresponds to loads under real world conditions more precisely. The

11

Chapter 2 Theory

eight-node hexahedral elements are therefore superior to tetrahedral elements for

finite element analysis.

2.2 Techniques of 3D Meshing

Meshing can be done manually or automatically. For manual mesh, the analyst

manually defines the nodes and elements. For automatic meshing, there is free and

mapped meshing. A free mesh has no restrictions in terms of element shapes, and has

no specified pattern applied to it. It usually works with triangle elements for 2D or

tetrahedral elements for 3D. Compared to a free mesh, a mapped mesh is restricted in

terms of the element shape it contains and the pattern of the mesh. For 3D meshing, a

mapped volume mesh contains only hexahedron elements. Mapped meshing is

normally done for symmetrical and uniformly shaped bodies; it may be too restrictive

for complex geometry but usually produces good mesh quality (well-shaped elements)

when they work [5].

The main technique used in this project’s simulation is mapped meshing. This is

because the model of the brake-disk is relatively uniform and symmetrical; hence by

using mapped meshing, well-shaped elements can be obtained. Volume sweep

meshing is then used to map the entire model. Using volume sweeping, an existing

unmeshed volume is filled with elements by sweeping the mesh from a bounding area

(also referred to as the "source area") throughout the volume. Since the source area

mesh (done by meshing the area) consists of quadrilateral elements, the volume is

12

Chapter 2 Theory

filled with hexahedral elements. The swept mesh is fully associated with the volume.

Unlike other methods for extruding a meshed area into a meshed volume, volume

sweeping is intended for use in existing unmeshed volumes. Thus it is particularly

useful in these situations [8]:

• Importing a solid model that was created in another program and meshing it in

ANSYS, which is precisely the case in this project as the model is created in Pro-

E and subsequently exported to ANSYS.

• If the source area is unmeshed prior to volume sweeping, ANSYS meshes it

automatically when the volume sweeper is invoked. The other extrusion methods

require the area to be meshed manually before invoking them.

2.3 Stress Analysis Methods

Failure analysis in brake-disks can be divided into two parts; ductile failure and

brittle failure. It is useful to adopt the view point that facture and yielding are separate

events and that either one may occur first depending on the combination of material

or stress states involve.

Ductile failure would predict the yielding or deformation of the brake-disk. For

ductile failure, the Von Mises Stress (Octahedral Shear Stress Yield) criterion is used.

Finite element analysis results are typically presented as Von Mises stresses. It is

13

http://en.wikipedia.org/wiki/Finite_element_analysis

Chapter 2 Theory

calculated by combining stresses in two or three dimensions, with the result

compared to the tensile strength of the material loaded in one dimension. Stress is in

general a symmetric 3×3 matrix. Von Mises stress reduces this to a single number (a

scalar) for the purposes of calculating yield criteria.

The Von Mises Stress in three dimensions is given by,

where σ1, σ2, σ3 are the principal stresses [9].

It should be noted that both Tresca (Maximum Shear Stress Yield) Criterion and Von

Mises Criterion are widely used in metals. The maximum difference between them is

15% which is relatively small compared to safety factors commonly used and to

various uncertainties usually involved in mechanical design [9]. Thus, the choice

between the two is not a matter of major importance. Von Mises Criterion is used

here as it is readily available in the software used. If more conservatism is desired,

Tresca Criterion could be chosen.

To predict cracking and locate weak points that may lead to crack formation, the

Maximum Normal Stress Criterion is used. The Maximum Normal Stress Criterion

states that failure occurs in a multiaxial state of stress when either a principal tensile

stress reaches the uniaxial tensile strength σut or a principal compressive stress

reaches the uniaxial compressive strength σuc. Since σuc is usually considerably

14

http://en.wikipedia.org/wiki/Stress_%28physics%29

http://en.wikipedia.org/wiki/Tensile_strength

http://en.wikipedia.org/wiki/Stress_%28physics%29#Principal_stresses

Chapter 2 Theory

greater than σut, σut is used. For a more conservative analysis in this project, the yield

stress is used as a comparison instead of ultimate tensile strength.

σut = MAX | σ1 , σ1 , σ1 |

where σ1, σ2, σ3 are the principal stresses [9].

Both Von Mises and Maximum Normal Stress Criterion are used in this project as a

relative gauge to predict the performances of the brake-disk in ductile and brittle

failure respectively.

15

http://en.wikipedia.org/wiki/Stress_%28physics%29#Principal_stresses

Chapter 3 Experimental Procedures


3.1 Pro-E Modelling

Before any simulations or tests can be carried out, it is important to first draw an

accurate model of the brake-disks. The Pro-E model of the Perimetral brake-disk is

shown below:

Figure 3: Pro-E Drawing of Perimetral

Brake-Disk Figure 4: Pro-E Drawing of Entire

Perimetral Brake System

(Pictures courtesy of Sunstar Logistic Singapore Pte Ltd)

A few models of motorcycles which the Perimetral brake system is suitable for use

were narrowed down by Sunstar. The Perimetral brake system is supposed to be able

to replace these conventional brake systems to operate efficiently in these

motorcycles. The most suitable brake-disk for comparison was then chosen and

modelled as shown in Figure 5.

16


Figure 5: Pro-E Drawing of Chosen

Conventional Brake-Disk

Figure 6: Pro-E Drawing of Rotor of

Chosen Conventional Brake-Disk

3.2 Simulation by ANSYS

After modelling the brake-disks in Pro-E, the models are then exported to ANSYS in

the form of IGES files. In ANSYS, the models are allocated their material properties

and then meshed (refer to Appendix 3 for ANSYS meshing procedure). The material

properties for both brake-disks are the same, as both are made from SUS410DB

Stainless Steel. By applying appropriate loading conditions, simulations are then

carried out using ANSYS to study the performance of the different designs.

For conventional brake-disk simulations, it is only necessary to carry out the

simulation on the rotor (outer-most portion) of the brake-disk. The pins and hub of

the brake-disk can be excluded as they are rarely prone to failure. The rotor is the area

which comes into contact with the brake-pads, and is subjected to the highest

17


temperatures and loadings. For these reasons, failure often occurs first at the rotor

rather than at the hub or pins. Thus, by only simulating the rotor, it allows the model

to be less complicated and the reduction of computation time.

There are three important simulations carried out to investigate the performance of

the brake-disks and their mechanical behaviour. They are static tests: torsional and

lateral strength simulation. For thermal analysis, residual stress simulation is carried

out. It is important to note that as much of the final design and specifications of the

Perimetral brake system are not yet finalized, some assumptions have had to be made

about the design in order to carry out the tests.

3.3 Simulation Procedures

(a) Static Test - Torsional Strength Simulation

Purpose of Test

In this simulation, a torsional force is exerted on the brake-disk, simulating the

torsional force that a brake-disk experiences during hard braking. This is similar to

actual braking conditions, when the rider comes to an emergency stop while

travelling at high speed. It is important to ensure that the brake-disk is able to

withstand the high torsional stress generated due to the brake-pads clamping down on

the spinning brake-disk. In this test, it is important to check for any distortions,

18


especially near holes (mounting or piercing holes), where there might be stress

concentrations during braking.

Assumptions

1) The maximum torque is concentrated on a single brake pad that is in contact with

the brake-disk.

2) The maximum weight of the motorcycle is the same for the Perimetral brake-disk

and the conventional brake-disk: which is equal to the total weight of the

motorcycle, the rider and luggage.

3) Maximum friction coefficient between the wheels and the ground is assumed to

be 0.8.

A torsional force is simulated on the surface of the brake-disks. The nodes within a

rectangular shape on the surface of the brake-disk are chosen, simulating the

dimensions of a brake pad. In this way, the torsional force is simulated to be applied

from the brake pad onto the disk. A torisonal force of 5365N and 7283N is applied on

the Perimetral and conventional brake-disk (onto the chosen nodes) respectively. This

value of torsional force is calculated based on the maximum deceleration that the

motorcycle would experience during hard braking (refer to Appendix 4 for details).

The mountings holes are then constrained to give zero displacement and the solution

is then obtained (refer to Appendix 5 for exact ANSYS procedures).

19


(b) Static Test - Lateral Strength Simulation

Purpose of Test

In this simulation, a lateral force is exerted on the disk to check for any distortions or

warping in the disk. This test studies the behaviour of the brake-disk when it

encounters lateral loading during usage, for example a person kicking the disk, stones

or other similar materials coming into contact with the brake-disk during riding. If it

is distorted, the contact area between the brake pad and brake-disk will become

uneven, which may result in vibrations that affect the performance of the brake-disk.

Assumptions

1. The lateral load is exerted onto the brake-disk through the brake pad.

2. A force of 1000N/mm2 is enough to test the behaviour of the brake-disk under

lateral loading. (The same value is used in industry standard tests.)

3. The force is purely transmitted in the lateral direction.

A lateral force is simulated on the surface of the brake-disks. The nodes within a

rectangular shape on the surface of the brake-disk are chosen, simulating the

dimensions of a brake pad. In this way, the lateral force is simulated to be applied

from the brake pad onto the brake-disk. A total force of 1000N is applied in the z-

direction on the nodes. The mountings holes are then constrained to give zero

20


displacement and the solution is then obtained (refer to Appendix 6 for exact ANSYS

procedures).

(c) Thermal Analysis - Residual Stress Simulation

Purpose of Test

The main challenge of this project is to study the behaviour of the Perimetral brake-

disk under residual stress, and compare it to the conventional brake-disk. Special

attention has to be given to this test as the Perimetral brake-disk is constrained by the

rim (by the mounting holes at the outer diameter of the brake-disk). Hence during the

expansion and contraction of the brake-disk, there may be problems of warping or

stress concentrations due to constraints at its outer diameter. In conventional brake-

disk systems, there is more allowance for expansion and contraction of the brake-disk,

as the brake-disk is only fixed to the rim at its inner diameter. The severe thermal

distortion of a brake-disk can affect important brake system characteristics such as

system response and brake judder propensity [6].

A temperature profile of the brake-disk during hard braking is simulated. By

subjecting the brake-disk to cool to room temperature from this temperature profile,

residual stress can be simulated in the brake-disks. In order to perform residual stress

analysis on the brake-disk, a reasonable approximation of the temperature distribution

on the brake-disk is necessary. The maximum temperature reached will be

21


approximated using basic conservation of energy principals [10] (refer to Appendix 7

for calculation of the maximum temperature in the brake-disks during braking).

Assumptions

1) All heat generated by the contact of the brake pad and the brake-disk goes to the

rotor.

2) All the kinetic energy at maximum velocity is converted to heat energy.

3) The maximum weight of the motorcycle is the same for the Perimetral brake-disk

and the conventional brake-disk: which is equal to the total weight of the

motorcycle, the rider and luggage.

A thermal profile of the brake-disk during hard braking is assumed: with a maximum

temperature of about 550°C to a minimum temperature of about 300°C (refer to

Appendix 8 for details of temperature profile). One additional advantage of using 3D

meshing is that the brake-disks can be meshed such that the nodes can be positioned

in the middle of the brake-disk (in z-direction). Thus, the nodes of the brake-disk will

be basically divided into three layers; the top surface, the bottom surface, and the

middle section. This allows the surface of the middle section to be given a

temperature of 30°C lower then the two outer surfaces to simulate the temperature

difference within the brake-disk.

22


Zero degree of freedom constraints are then given to the mounting holes. The brake-

disk is then simulated to cool from its temperature during hard braking to about room

temperature of 20°C. Effects of warping or stress concentrations which may cause

cracking are observed and possible weak points are identified. The thickness of the

brake-disk is given a slight displacement at the inner diameter to simulate

manufacturing defects and to help study the effects of warping (refer to Appendix 9

for exact ANSYS procedures).

23

Chapter 4 Experimental Results


4.1 Mesh Results

Figures 7 to 10 show the models of the Perimetral and conventional brake-disk

meshed using ANSYS. For the Perimetral brake-disk, the element used is solid brick

8 node 185 hexahedron. There is a two element thickness in the z-direction: this

ensures that there are enough elements to represent model stiffness and captures more

complex stress patterns.

Figure 7: Model of Entire Meshed

Perimetral Brake-Disk

Figure 8: Close-Up of Meshing of

Perimetral Brake-Disk

For the conventional brake-disk, there is a minor groove at the outer diameter of the

brake-disk. This groove allows for a greater surface area to release heat during

braking. However, this renders hexahedral elements unsuitable for meshing at the

outer diameter as the area is too irregular. Hence, tetrahedral elements are used to

24


mesh the outer diameter as shown. The remaining parts are meshed with solid brick 8

node 185 elements which are hexahedral in shape.

Figure 9: Model of Entire Meshed

Conventional Brake-Disk

Figure 10: Close-Up of Meshing at Outer

Diameter of Conventional Brake-Disk

25


4.2 Simulation Results in ANSYS

(Refer to Appendix 10 for details of results)



(a) Conventional Brake-Disk (b) Perimetral Brake-Disk


(a) Conventional Brake-Disk (b) Perimetral Brake-Disk

26



Figures 13 (a) and (b): First Principal Stress – Close-up on Area of Maximum Stress

(a) Conventional Brake-Disk

(b) Perimetral Brake-Disk

Figure 14 (a) and (b): Von Mises Stress – Close-Up on Area of Maximum Stress



27






Figures 16 (a) and (b) Von Mises Stress – Close-Up on Area of Maximum Stress



28


Table 1: Summary of Results First Principal Stresses Von Mises Stress

Conventional Disk Perimetral Disk Conventional Disk Perimetral Disk

Maximum Stress

(N/mm2)

Location of Maximum Stresses

Maximum Stress

(N/mm2)


Maximum Stress

(N/mm2)


Maximum Stress

(N/mm2)


Torsional Strength

Simulation

235 Piercing holes near

applied force

178 Mounting holes near

applied force

249 Piercing holes near

applied force


applied force

Lateral Strength

Simulation

651 Pin-connections near applied

force


applied force

880 Pin-connections near applied

force


applied force

Residual Strength

Simulation

1015 Piercing holes

1108 Piercing holes at inner

diameter

977 Piercing holes

1049 Piercing holes at inner

diameter

29

Chapter 5 Discussion


It is important to remember that the interpretation of displacement and stress results

for finite element analysis (FEA) is more of a qualitative rather than a quantitative

one. It is neither sufficient nor accurate to judge whether the brake-disk will yield or

crack by purely looking at the value of the stresses generated. In this study, the

purpose of including the modelling and simulation of the conventional brake-disk is

to act as a control for the analysis of the new Perimetral brake-disk. As the

conventional brake-disk selected for this project has been trialled and tested to be safe

for actual use, it can act as a reference for the value of stresses obtained. If the stress

values of the Perimetral brake-disk are close to or lower than those of the

conventional brake-disk, it would be reasonable to assume that failure would not

occur.


In the conventional brake-disk, the stresses concentrate near the piercing holes where

the torsional load is applied. For the Perimetral brake-disk, the stresses concentrate

around the area where the torsional load is applied; especially on the adjacent

mounting holes as shown in Figure 17(b). For the Perimetral brake-disk, maximum

values of the First Principal Stress and Von Mises Stress are significantly lower than

30


those in the conventional brake-disk, 32% and 22% lower respectively. This can be

attributed to the lower torsional force experienced by the Perimetral brake-disk due to

its larger effective radius as shown by the calculations done previously in Appendix 4.

Figures 17(a) and (b): Maximum Von Mises Stresses for Torsional Strength

Simulation


Maximum stresses at mounting holes

Maximum stresses at piercing holes

Applied load

Applied load


For both brake-disks, the maximum stresses are much lower than the yield stress

(981N/mm2) of the material, indicating that yielding is unlikely to occur during hard

braking of the motorcycle. Thus, it is safe to conclude that the Perimetral brake-disk

which experiences lower stresses than the conventional brake-disk, is unlikely to

experience yielding or distortion under torisonal loading during hard braking,

31



When a lateral load is applied on a conventional brake-disk, the stresses concentrate

at the pin-connection nearest the applied lateral load. For the Perimetral brake-disk,

the stresses concentrate on the adjacent mounting holes where the lateral load is

applied. The maximum values of the First Principal Stress are almost the same (less

than 1% difference). The maximum value of Von Mises Stress is about 20% lower in

the Perimetral brake-disk. Again, the maximum stresses are much lower than the

yield stress (981N/mm2) of the material, indicating that bending or yielding is

unlikely to occur in the Perimetral brake-disk during lateral loading.

Figures 18 (a) and (b): Maximum Von Mises Stresses for Lateral Strength Simulation

Maximum stresses at mounting holes Applied load

Applied load Maximum stress at

pin-connection

(b) Perimetral Brake-Disk (a) Conventional Brake-Disk

Overall, the Perimetral brake-disk shows good performance under the static tests,

with stress values close or lower than those of the conventional brake-disk. Since the

conventional brake-disk is already proven to be safe for use, it is thus reasonable to

32


conclude that the Perimetral brake-disk would perform likewise. It is also evident that

the weak points of the Perimetral brake-disk under static tests lies on its mounting

holes, thus it is important to ensure that the mounting holes are properly

manufactured. It is also recommended that the Perimetral brake-disk is properly heat-

treated for strengthening purposes.


For residual stress simulation, it is important to look out for weak points in the brake-

disks that may cause cracking. Cracking is often the cause of failure in brake-disks

after being subjected to repeated heating and cooling during braking.

For both types of brake-disks, the stresses concentrate at their piercing holes. For the

Perimetral brake-disk, maximum values of the First Principal Stress and Von Mises

Stress are higher than those in the conventional brake-disk, 8% and 7% higher

respectively. This is probably due to the design of the conventional brake-disk (fixed

at its inner diameter) which gives it more allowance during expansion and contraction.

33


Figures 19 (a) and (b): Maximum First Principal Stresses for Residual Stress

Simulation



Maximum stresses at piercing holes

Maximum stresses at inner piercing holes

For the conventional brake-disk, the maximum stresses concentrate on the piercing

holes at areas near the middle of the disk as shown in Figure 19(a). As these areas at

the piercing holes are subjected to the highest temperature, they experience the

highest stresses during expansion and contraction. For the Perimetral brake-disk, it is

observed that maximum stresses occur at the piercing holes (weak points), especially

at the inner piercing holes, i.e. the piercing holes on the inner diameter of the brake-

disk as shown in Figure 19(b). This is due to the design of the brake-disk which

concentrates the stresses on its inner diameter during expansion and contraction.

Therefore, there is the danger of yielding or crack formation under repeated residual

stresses, especially at these weak points (the inner piercing holes). For the Perimetral

brake-disk, it is noted that the maximum stresses of 1108 N/mm2 (First Principal

Stress) and 1049 N/mm2 (Von Mises Stress) exceeds the given yield stress of the

material.

34


In the Perimetral brake-disk, many

localized stress concentrations (both

First Principal and Von Mises) are

also found in-between the piercing

holes which are adjacent to each other

as shown in Figure 20.

Localized stress concentrations in-between adjacent piercing holes

Figure 20: Areas of Localized Stress Concentrations

Compared to the conventional brake-disk, the number of areas with localized stress

concentration is much higher. This indicates that the number of potential points for

crack initiation is higher for the Perimetral brake-disk, thus it may result in a higher

risk of failure.

It is useful to note that the highest stresses occur on the inner piercing holes in-

between the mounting holes of the brake-disk as shown in Figure 21, whereas the

piercing holes which are directly below the mounting holes have much lower stresses.

As the mounting holes are fixed, this means the areas in-between them are subjected

to more stress as they undergo more expansion and contraction. The highest stress

concentrations can be found at the piercing holes directly in-between two adjacent

mounting holes. This knowledge allows for designers to predict potential crack

initiation points more accurately.

35


High stress concentrations in-between adjacent mounting holes

Low stress regions directly below the mounting holes

Figure 21: First Principal Stress Distributions on Perimetral Brake-Disk

36

Chapter 6 Further Analysis


After comparing the performances of the two brake-disks, further analysis is then

carried out to investigate if improvements can be made to the Perimetral brake-disk.

For the static tests, the maximum stresses (weak points) in the Perimetral brake-disk

are at the mounting holes. Due to the design of the brake-disk, the mounting holes are

subjected to the most stresses under lateral and torsional loads. Even though the

stresses are much lower than the yield strength of material, failure may result after

repeated loadings (fatigue failure). As the mounting holes act as stress raisers, one

possible improvement is to remove the mounting holes, thus eliminating stress

concentration points. Instead of mounting holes, the brake-disk can be fixed to the

rim using a metal plate fixed by two bolts.

A more important problem faced by the Perimetral brake-disk is the high stresses that

concentrate at the inner piercing holes under residual stress simulation. As discussed

previously, these high stresses may lead to crack formation or yielding. Theoretically

the ideal design would be to remove all the piercing holes, as this would eliminate

stress raisers. However, the piercing holes are necessary for removing of dirt and

other particles from the brake pads, to increase flexibility and for prevention of

37


thermal warping. Hence, other alternatives must be explored. A number of

countermeasures will be proposed, modelled and tested.

6.1 Proposed Countermeasures Designs

To improve the performance of the Perimetral brake-disk, there are three main areas

that can be targeted for change.

(a) Changing the Width of the Brake-Disk: Countermeasures 1 and 2

Figure 22: Pro-E Drawing of

Countermeasure 1


Countermeasure 2

As the brake-disk is fixed at its outer diameter, there is less allowance for expansion

or contraction and the stresses tend to concentrate on the inner diameter of the brake-

disk. By adjusting the width of the brake-disk, the stress concentrations can be shifted

away from the inner piercing holes, hence lowering the maximum stresses. In

countermeasure 1, the inner diameter of the brake-disk is reduced by 50%, that is, the

width of the brake-disk is increased by 50%. The position of the piercing holes

38


remains the same on the outer diameter. In countermeasure 2, the inner diameter of

the brake-disk is reduced by 50%, similar to countermeasure 1. The piercing holes are

shifted accordingly to the middle of the brake-disk.

(b) Changing the Shape of the Piercing Holes: Countermeasures 3 and 4


Countermeasure 3


Countermeasure 4

The piercing holes act as stress raisers which lead to localised high stresses. By

changing its shape, it is possible to reduce the maximum stress value. The holes in the

brake-disk can be assumed to behave like elliptical cracks in a structure. Elliptical

cracks under tensile loading would raise the value of yield stress to σy = S (1 + 2

(c/d)) [11] (refer to Appendix 11 for details.) This simply means that different

orientations of an ellipse hole can increase or decrease the stress concentration

depending on the direction of loading. As the Perimetral brake-disk is subjected to

residual stress, the force it experiences is probably bilateral in direction with the

stresses being unequal in different directions as observed. Hence, by changing the

piercing hole into an ellipse, it is possible to reduce the maximum stress if oriented in

39


40

the right direction. In countermeasure 3, the inner piercing holes are replaced by

elliptical holes with its larger radius in the radial direction. In countermeasure 4,

elliptical holes are used to replace all circular holes, with the smaller radius in the

radial direction.

(c) Joining the Piercing Holes: Countermeasures 5 and 6

In the following table, the results for residual stress analysis for the countermeasures

discussed above are shown (refer to Appendix 12 for details of results).

6.2 Results for Countermeasures

As discussed previously, there are a high number of localized stress concentrations

forming in-between adjacent piercing holes. By joining them together, these stress

concentrations can be eliminated. In countermeasure 5, the piercing holes are joined

vertically. In countermeasure 6, the piercing holes are joined diagonally.


Countermeasure 5


Countermeasure 6


41

Table 2: Summary of Residual Stress Simulation Results for Countermeasures

First Principal Stresses Von Mises Stress Counter- measure

Maximum Stress

(N/mm2)


Maximum Stress (N/mm2)


Comments

1

1016

Piercing hole at middle diameter.

1023

Piercing hole at outer diameter

Acceptable

2

1084

In between adjacent piercing holes.

1025


Worse than 1. Rejected

3

1057


1041


Acceptable

4

1361

Edge of ellipse piercing hole near inner diameter.

1084

Edge of ellipse piercing hole near inner diameter.

Worse than original. Rejected

5

1144

Edge of joined hole near inner diameter.

1034

Edge of joined hole near inner diameter.

Acceptable

6

1278

Edge of joined hole near outer diameter.

1117

Edge of joined hole near outer diameter.

Worse than original. Rejected


6.3 Interpretation of Results

As seen from Table 2, the maximum stresses experienced by countermeasures 1 and 3

during residual stress simulation are lower than that of the original Perimetral brake-

disk. Among all the designs, countermeasure 1 gives the greatest reduction in First

principal Stress (8% reduction). In countermeasure 5, although the maximum stresses

are similar to the original, the high stress concentrations previously found between

the adjacent piercing holes are eliminated. It is observed that the number of local

stress concentrations is reduced with this design.

Other than the stress level, it is also important to consider other factors like the

weight, processing cost, die-set tooling cost. The table below shows the effect of the

countermeasures and other costs or factors to be considered. The final design choice

can only be made after weighing the importance of these factors against each other.

Table 3: Design Factors to be Considered

Factors to be Considered Counter-measure

Maximum Stress level

Number of stress

concentration points

Weight

Processing / Tooling cost

1

Reduced (better than 2)

Almost the Same About 50% increase

More raw materials needed

3 Reduced Almost the Same Almost the Same

New Ellipse piercing hole die-set needed

5 Almost the same

Greatly reduced Almost the Same

New die-set needed

42

Chapter 7 Conclusion


In this final year project, three-dimensional modelling and meshing using the

simulation program ANSYS were successfully implemented. The two-dimensional

technique previously used by Sunstar has been successfully modified and improved

to using three-dimensional techniques for modelling and simulation. This has allowed

for greater flexibility and accuracy in the results achieved.

The mechanical performances of a conventional brake-disk system and the Perimetral

brake-disk system under three different simulation environments were studied and

compared.

Under torsional strength simulation, the Perimetral brake-disk performs better with its

maximum values of First Principal Stress and Von Mises Stress being significantly

lower than those in the conventional brake-disk, 32% and 22% lower respectively.

This can be attributed to the lower torsional force experienced by the Perimetral disk

due to its larger effective radius.

Under lateral strength simulation, the Perimetral brake-disk yielded almost similar

results to that of the conventional brake-disk, with its maximum First Principal Stress

43


being almost the same (less than 1% difference) and maximum Von Mises Stress

being about 20% lower.

For both the static tests mentioned, the maximum stresses (weak points) in the

Perimetral brake-disk occur at the mounting holes. Hence, it is important to ensure

that the mounting holes are properly manufactured. It is also recommended to be

properly heat-treated for overall strengthening purposes. On the whole, the Perimetral

brake-disk shows good performance under the static tests, with stress values lower or

close to those of the conventional brake-disk. Since the conventional brake-disk is

already proven to be safe for use, it is reasonable to conclude that the Perimetral

brake-disk would perform likewise.

For the most important test: the residual stress simulation, the maximum stresses

concentrate at the piercing holes for both brake-disks. For the Perimetral brake-disk,

maximum values of the First Principal Stress and Von Mises Stress are higher than

those in the conventional brake-disk (8% and 7% higher respectively). These

maximum stresses occur at the piercing holes (weak points), especially at the inner

piercing holes. This is due to the design of the brake-disk which concentrates the

stress on the inner diameter during expansion and contraction. At these weak points

(the inner piercing holes), there is the danger of yielding or crack initiation under

repeated residual stresses.

44


Many localized stress concentrations (for both First Principal and Von Mises Stresses)

are also found in-between adjacent piercing holes. Compared to the conventional

brake-disk, the numbers of areas with localized stress concentration are much higher.

This indicates that the number of potential points for crack initiation is higher for the

Perimetral brake-disk, thus it may result in a higher risk of failure. These high stress

areas occur on the piercing holes directly in-between the mounting holes, whereas the

piercing holes directly below the mounting holes have much lower stresses.

Designers can use this knowledge to help them predict potential crack initiation

points more accurately.

To counter the potential problem of cracking under residual stress, several

countermeasures have been proposed, modelled and analysed. Among them,

countermeasures 1, 3 and 5 have shown improvements in their performance under

residual stress simulations. These countermeasures are recommended to improve on

the original design of the Perimetral brake-disk.

In making a final design choice, not only should the performance of the brake-disks

be of importance, the considerations of their production costs (as shown in Table 3) is

just as pertinent in the decision making process.

45

Chapter 8 Recommendations

Chapter 8 Recommendations In order to achieve a higher accuracy of results and a better understanding of the

performance of the Perimetral brake-disk, the whole Perimetral brake system

(including the rim and tyres) should be incorporated for simulation. This task will be

facilitated by the three-dimensional modelling and simulation techniques already

implemented in this project.

For a more accurate understanding of the ductile and brittle failure behaviour of the

brake-disk, the prototype of the brake-disk should be manufactured and tested. It is

only through actual experiments and testing that the yielding and cracking behaviour

of the brake-disk be better understood.

46

List of References

List of References

1. Roth, G., “Analysis in Action: The Value of Early Analysis,” SAS IP, Inc., USA, 1999.

2. Zienkiewiez, O. C., and Taylor, R. L., “The Finite Element Method,”

Butterworth Heinemann, 5th edition, 2000, pp. 1-27. 3. Liu, G.R., “Mesh Free Methods, Moving Beyond the Finite Element Method,”

CRC Press, 2002, pp. 1-25. 4. Liu, G.R. and Quek, S.S., “The Finite Element Method: A Practical Course,”

Butterworth Heinemann, 2003, pp. 199-232, 246-280. 5. Kurowski, P. M., “Finite Element Analysis for Design Engineers,” SAE

International, Warrendale, 2004, pp. 1-147. 6. Valvano, T. and Lee, K., “An Analytical Method to Predict Thermal

Distortion of a Brake Rotor,” Society of Automotive Engineers, Inc, 2000. 7. Tan, H.N., “2-D Heat Transfer Analysis Using Meshfree Methods,”

Department of Mechanical Engineering, NUS, 2002/2003, pp. 1-7. 8. ANSYS Modelling and Meshing Guide, ANSYS Release 5.6, SAS IP, Inc.,

4th edition, 1999, Chapter 7. 9. Pilkey, Walter D., “Peterson’s Stress Concentration Factors,” John Wiley and

Sons, Inc., 2nd edition, 1997, pp. 1-59. 10. Yevtushenko, A. and Ivanyk, E., “Determination of Heat and Thermal

Distortion in Braking Systems,” Wear 185, Elsevier, 1995, pp. 159-165. 11. Dowling, N. E., “Mechanical Behaviour of Materials: Engineering Methods

for Deformation, Fracture and Fatigue,” Prentice Hall, 2nd edition, 2000.

47

Appendices

APPENDICES

Appendix 1: Details of Design of Perimetral Brake-Disk System and its

Material Properties

Mounting hole

Piercing hole

Figure 1.1: Pro-E Drawing of Perimetral Brake-Disk

Removed due to Confidential Reasons

48

Appendices

Figure 1.2: Pro-E Drawing of Perimetral Rim

(Courtesy of Sunstar Logistic Pte Ltd)

Figure 1.3: Pro-E Drawing of Perimetral Brake-disk System


49

Appendices

Appendix 2: Comparison of Braking Force Conventional Braking System


- ωwheel: wheel’s angular velocity

- TB: braking torque applied on the

brake-disk through the brake

callipers

- F: force applied by the road on

the tyre

In the conventional braking system the

braking torque is transmitted by the

brake-disk to the wheel-hub, and from it

to the rim, through the spokes.

Perimetral Braking System


- ωwheel: wheel’s angular velocity

- TB: braking torque applied on the

brake-disk through the brake

callipers

- F: force applied by the road on

the tyre

In the Perimetral braking system the

braking torque is directly transmitted

from the disk to the rim. In this way

the spokes do not undergo torsional

stress and the wheel-hub and rim can

be designed to be lighter.

Comparing the Two Systems

50

Appendices

Conventional System

Perimetral System

(Pictures Courtesy of Sunstar Logistic Pte Ltd)

- R1: Perimetral disk Radius

- BF1: Perimetral disk braking force

- R2: Conventional disk Radius

- BF2: Conventional disk Braking force

- Rw: Wheel Radius

- Fstreet: Force exercised on the tyre by the road

When applying the brakes on the motorcycle, a torque equal to the product of Fstreet

and Rw must be applied.

Thus: BF1• R1= Fstreet • Rw

51

Appendices

BF2• R2= Fstreet • Rw

So: BF1• R1= BF2• R2

Since R1is greater than R2,

BF1< BF2

Conclusion:

For the same braking power needed, the Perimetral brake system requires a lower

force to be applied, giving the same braking power with a lower force on the brake-

disk.

52

Appendices

Appendix 3: ANSYS Meshing Procedure For Perimetral Brake-Disk


53

Appendices

For Conventional Brake-Disk


54

Appendices

Appendix 4: Calculation of Maximum Torsional Force Experienced During Hard Braking

Removed due to

Confidential Reasons

55

Appendices

Removed due to


56

Appendices

Appendix 5: ANSYS Procedure for Torsional Strength Simulation


57

Appendices

Appendix 6: ANSYS Procedure for Lateral Strength Simulation

Removed due to


58

Appendices

Appendix 7: Calculation of Maximum Temperature in Brake-Disk

Removed due to


59

Appendices

Removed due to


60

Appendices

Appendix 8: Temperature Distribution Profiles and Source Codes

Temperature Profile for Perimetral Brake-disk during Hard Braking

Figure 8.1: Simulated Temperature Profile

during Hard Braking

Figure 8.2: Close-Up of Temperature

Profile

Temperature Profile for Conventional Brake-Disk during Hard Braking

Figure 8.3: Simulated Temperature Profile

during Hard Braking

Figure 8.4: Close-Up of Temperature

Profile

61

Appendices

ANSYS Source Codes for Temperatures Distributions on Nodes For Surface Temperature Distribution of Perimetral Brake-Disk

Removed due to


62

Appendices

Removed due to


63

Appendices

Removed due to


64

Appendices

Appendix 9: ANSYS Procedure for Residual Stress Simulation

Removed due to


65

Appendices

For Conventional Brake-Disk

Removed due to


66

Appendices

Appendix 10: Details of Simulation Results A) Results of Torsional Strength Simulations For Conventional Brake-Disk

Figure 10.1: First Principal Stress Distribution on Entire Disk

Figure 10.2: First Principal Stress Concentrations near Applied Torsional Load

67

Appendices

Figure 10.3: Maximum First Principal Stress at Piercing Hole

Figure 10.4: Von Mises Stress Distribution on Entire Disk

68

Appendices

Figure 10.5: Von Mises Stress Concentrations near Applied Torsional Load

Figure 10.6: Maximum Von Mises Stress at Piercing Hole

69

Appendices

For Perimetral Brake-Disk


Figure 10.8: First Principal Stress Concentrations near Applied Torsional Load

70

Appendices

Figure 10.9: Maximum First Principal Stress at Mounting Hole


71

Appendices

Figure 10.11: Von Mises Stress Concentrations near Applied Torsional Load

Figure 10.12: Maximum Von Mises Stress at Mounting Hole

72

Appendices

B) Results of Lateral Strength Simulations For Conventional Brake-Disk


Figure 10.14: First Principal Stress Concentrations near Applied Lateral Load

73

Appendices

Figure 10.15: Maximum First Principal Stress at Pin Connection


74

Appendices

Figure 10.17: Von Mises Stress Concentrations near Applied Lateral Load

Figure 10.18: Maximum Von Mises Stress at Pin Connection

75

Appendices



Figure 10.20: First Principal Stress Concentrations near Applied Lateral Load

76

Appendices

Figure 10.21: Maximum First Principal Stress at Mounting Hole


77

Appendices

Figure 10.23: Von Mises Stress Concentrations near Applied Lateral Load

Figure 10.24: Maximum Von Mises Stress at Mounting Hole

78

Appendices

C) Results of Residual Strength Simulations For Conventional Brake-Disk


Figure 10.26: Close-up of First Principal Stress Concentrations

79

Appendices

Figure 10.27: Maximum First Principal Stress at Piercing Hole


80

Appendices

Figure 10.29: Close-up of Von Mises Stress Concentrations

Figure 10.30: Maximum Von Mises Stress at Piercing Hole

81

Appendices



Figure 10.32: Close-up - First Principal Stress Concentrations

82

Appendices

Figure 10.33: Maximum First Principal Stress at Inner Piercing Hole


83

Appendices

Figure 10.35: Close up - Von Mises Stress Concentrations

Figure 10.36: Maximum Von Mises Stress at Inner Piercing Hole

84

Appendices

Appendix 11: Stress Concentrations in Circular and Elliptical Holes

Figure 11.1: Stress at an elliptical hole [3]

Stress at cracks can be given by,

σy = kt . σnom

where kt is the stress concentration factor

For elliptical cracks: σy = S (1 + 2 (c/d))

Hence,

For a circle, a = b, kt = 3

For an ellipse of b/a = 4, kt = 7

For an ellipse of a/b=3, kt =1.67

It is important to remember that stress amplification not only occurs on a microscopic

level (e.g. small flaws or cracks,) but it can also occur on the macroscopic level in the

case of sharp corners, holes, fillets, and notches. Hence, this basic theory can be

applied to the piercing holes in the brake-disk.

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Appendices

Appendix 12: Results for Residual Stress Simulation for Countermeasures

Countermeasure 1


Figure 12.2: Close-Up at Region with Maximum First Principal Stress


Figure 12.4: Close-Up at Region with Maximum Von Mises Stress

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Appendices

Countermeasure 2





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Appendices

Countermeasure 3





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Appendices

Countermeasure 4





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Appendices

Countermeasure 5


Figure 12.18: Close-Up at region with Maximum First Principal Stress

Figure 12.19: Von Mises Stress Distribution on Entire disk

Figure 12.20: Close-up at Region with Maximum Von Mises Stress

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Appendices

Countermeasure 6





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zheng han - comparison study of two disk brake systems used in motorcyles

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