Thermal Analysis of Vented and Normal Disc Brake Rotorsdoc
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Thermal Analysis of Vented and Normal Disc Brake Rotorsdoc...
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THERMAL AND STRUCTURAL ANALYSIS OF VENTED AND NORMAL DISC BRAKE ROTORS A PROJECT REPORT SUBMITTED IN PARTIAL FULLFILMENT FOR THE AWARD OF DEGREE OF “BACHELOR OF TECHNOLOGY” IN MECHANICAL ENGINEERING BY CH. KRISHNA CHAITANYA VARMA (07241A0309) PADMANABH DAS (07241A0313) PUNEET KUMAR. J (07241A0315)
DEPARMENT OF MECHANICAL ENGINEERING GOKARAJU RANGARAJU INSTITUTE OF ENGINEERING AND TECHNOLOGY (AFFLIATED TO JAWAHARLAL N EHRU TECHNOLOGICAL UNIVERSITY) HYDERABAD 2007‐2011
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DEPARTMENT OF MECHANICAL ENGINEERING JNTUCOLLEGE OF ENGINEERING
CERTIFICATE
Certificate This is to certify that the project entitled THERMAL AND STRUCTURAL ANALYSIS OF VENTED
AND NORMAL DISC BRAKE ROTORS being submitted by Mr. ch c h Krishna chaitanya varma, Mr. puneet kumar.j, Padmanabh das, in partial fulfillment fulfillment for the award of degree of bachelor of technology in mechanical engineering to the jawaharlal Nehru technological university is a record
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of bonafide work carried out under my guidance and supervision The results embodied in this project have not been submitted to any other university or institute for the award of degree
external guide
internal guide
Mr. pradeep reddy.
Mr. v. ratna kiran.
Proprietor.
asst. professor.
orange technologies.
griet.
Ameerpet,
bachupally,
Hyderabad.
Hyderabad.
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DEPARTMENT OF MECHANICAL ENGINEERING JNTUCOLLEGE OF ENGINEERING
CERTIFICATE
Certificate This is to certify that the project entitled THERMAL AND STRUCTURAL ANALYSIS OF VENTED
AND NORMAL DISC BRAKE ROTORS being submitted by Mr. ch c h Krishna chaitanya varma, Mr. puneet kumar.j, Padmanabh das, in partial fulfillment fulfillment for the award of degree of bachelor of technology in mechanical engineering to the jawaharlal Nehru technological university is a record
.
of bonafide work carried out under my guidance and supervision The results embodied in this project have not been submitted to any other university or institute for the award of degree
external guide
internal guide
Mr. pradeep reddy.
Mr. v. ratna kiran.
Proprietor.
asst. professor.
orange technologies.
griet.
Ameerpet,
bachupally,
Hyderabad.
Hyderabad.
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ACKNOWLEDGEMENT I express my gratitude to chairman, project Review Committee, JNTU College of Engineering, for their valuable recommendations and for accepting this project work. I express my deep sense of gratitude towards my able and acknowledge guide, Mr. Ratna kiran, Asst. Professor, Mechanical Engineering , GRIET, Hyderabad, to whom I owe the credit of being the moving spirit behind this project, whose guidance and constant inspiration led me towards its completion. I convey my sincere thanks to Mr.K.G.K MURTHY, Head of the Mechanical Engineering Department & Mr.P.S.V.KURMA RAO Professor, GOKARAJU RANGARAJU INSTITUE OF ENGINEERING AND TECNOLOGY, HYDERABAD for his kind cooperation in the completion of the project. At this juncture, I feel that, I am grateful to Mr.PRADEEP, ORANGE TECHNOLOGIES, AMEERPET, HYDERABAD, for assistance assistance in completion of project work. work. Finally, I extend my sense of gratitude to all my friends, teaching and non teaching staff, who directly or indirectly help me in this endeavor.
CH, Krishana chaitanya varma (07241A0309) Padmanabh Das (07241A0313) ( 07241A0313) Puneet kumar. J (07241A0315)
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ABSTRACT
Safety aspect in automotive engineering has been considered as a number one priority in development of new vehicle. Each single system has been studied and developed in order to meet safety requirement. Instead of having air bag, good suspension systems, good handling and safe cornering, there is one most critical system in the vehicle which is brake systems. Without brake system in the vehicle will put a passenger in un safe position. Therefore, it is a must for all vehicles to have proper brake system. Due to critical system in the vehicle, many of researchers have conducted a study on brake system and its entire component. In this project, the author has conducted a study on ventilated and normal disc brake rotor of normal passenger vehicle with full load of capacity. The study is more likely concern of heat and temperature distribution on disc brake rotor. Steady state and transient response has been conducted through the heat transfer analysis where to predict the worse case scenario and temperature behaviors of disc brake rotor. In this study, finite element analysis approached has been conducted in order to identify the temperature distributions and behaviors of disc brake rotor in steady state and transient responses. Ansysis has been used as finite elements software to perform the thermal analysis on both responses. Both results have been compared for better justification. Thus, both results provide better understanding on the thermal characteristic of disc brake rotor and assist the automotive industry in developing optimum and effective disc brake rotor.
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NOMENCLATURE c Specific heat (J/kg K) C Capacity matrix D Elasticity matrix E Young.s modulus (N/mm²)
h Heat convection coefficient (W/m² K) k Thermal conductivity (W/m K) K Stiffness matrix
K Conductivity matrix P Normal pressure (N/mm²) P Force vector
Ph Hydraulic pressure (N/mm²) q Heat flux (W/m²)
r, è, z Cylindrical coordinates R Heat source vector T Temperature (K) T∞ Ambient temperature (K) U Displacement vector normal component of displacements á Thermal expansion coefficient ( /°C) å Strain vector µ Coefficient of friction í Poisson.s ratio 5
ñ Density (Kg/m³) ó Stress vector
ù Angular velocity (rad/s)
Subscripts
f Body force i,j Sub regions i and j, respectively n Normal direction surface traction
Δt Temperature rise (K)
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1. Contents 1. Introduction 1.1 Introduction
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2. Statement of problem
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3. objective of scope
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4. research methodology
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5. thesis outline
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6. literature review
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6.1 introduction
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7. brake system review
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8. vehicle brake system
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9. parts of disc brake
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9.1 disc calipers
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9.2 disc pad
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9.3 brake disc rotor
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9.3.1
disc brake rotor description
9.4 brake pads
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10. modeling software
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11. catia v5
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11.1
introduction
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11.2
part modeling
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11.3
general modeling for each part
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11.4
fundamental
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12. finite element analysis
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12.1
introduction
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12.2
procedure for ansys analysis
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12.3
built the model
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12.4
material properties
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12.5
solution
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13. finite element generation
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13.1
boundary conditions and loading
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13.2
model display
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13.3
material defection
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13.4
solution
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13.5
post processor
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14. finite element formulation for heat conduction
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15. thermal analysis
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15.1
types of thermal analysis
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15.2
planning the analysis
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16. structural analysis 16.1
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types of structural analysis
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17. structural and static analysis
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18. modeling analysis
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19. definition of problem domain
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20. modeling and analysis
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21. creating a finite element mesh
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21.1
solid90 element description
22. applying the boundary conditions 22.1
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thermal boundary conditions 8
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22.2
result
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23. structural analysis of normal disc brake rotor
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23.1
structural analysis of boundary conditions
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23.2
results
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24. creating a finite element mesh for ventilated disc brake rotor
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25. applying the boundary conditions
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26. structural analysis of ventilated disc brake rotor
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26.1
structural boundary conditions
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26.2
result
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27. conclusion
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28. references
6768
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1. INTRODUCTION 1.1. Introduction Brakes are most important safety parts in the vehicles. Generally all of the vehicles have their own safety devices to stop their car. Brakes function to slow and stop the rotation of the wheel. To stop the wheel, braking pads are forced mechanically against the rotorldisc on both surfaces. They are c ompulsory for all of the modern vehicles and the safe operation of vehicles. In short, brakes transform the kinetic energy of the c ar into heat energy, thus slowing its speed. Brakes have been retuned and improved ever since their invention. The increases in travelling speeds as well as the growing weights of cars have made these improvements essential. The faster a car goes and the heavier it is, the harder it is to stop. An effective braking system is needed to accomplish this task with challenging term where material need to be lighter than before and performance of the brakes must be improved. Today's cars often use a combination of disc brakes and drum brakes. For normal sedan car, normally disc brakes are located on the front two wheels and drum brakes on the back two wheels. Clearly shows that, together with the steering components and tyres represent the most important accident avoidance systems present on a motor vehicle which must reliably operate under various conditions. However, the effectiveness of braking system depends on the design itself and also the right selection of material. systems than follow with some improvements. In order to und erstand the behaviors of braking system, there are three functions that must be complied for all the time (Smith, 2002); a) The braking system must be decelerate a vehicle in a controlled and repeatable fashion and when appropriate cause the vehicle to stop. b) The braking should permit the vehicle to maintain a constant speed when traveling downhill. c) The braking system must hold the vehicle stationary when on the flat or on a gradient. Nowadays, there are lot of software has been developed in order to cater the modeling and the finite element analysis on the vehicle component such as (Automatic Dynamic of Mechanical Systems), CATIA, ANSYS. There is an advantage of using that powerful computational analysis software where by using those would make it easier, less cost better accuracy and less computing time. Most of the software is used in the wide range of industries such as automotive, oil and gas, aerospace, marine, heavy duty engineering ,construction, electromechanical and gen eral mechanical industries. In this project, design package CATIA and finite element package will be used to generate model and run analysis on the chosen component. 10
2. STATEMENT OF PROBLEM If looking on the overall automotive parts, besides engines, there are more crucial parts that engineers need to look into consideration. Suspension, brake, electrical, hydraulic and gear are all the crucial systems in the automotive areas. Each of all system has their own functionality which brings life to the automation industries. Brakes is such a crucial system in stopping the vehicle on all moving stages including braking during high speed, sharp cornering, traffic jam and downhill. All of those braking moments give a different value of temperature distribution and thermal stress. Good performance of disc brake rotor comes from good material with better mechanical and thermal properties. Good designs of disc brake rotor are varying across the range of the vehicles. There are different design and performance of disc brake rotor if compared between passenger, commercial and heavy duty vehicle. There are also other constraints such as cost, weight, manufacturing capability, robustness and reliability, packaging, maintenance and servicing. For example, heavy duty vehicle need large size of disc brake rotor if compared to passenger vehicle. Due to that, it will increased total weight of vehicle as well as fuel consumption and reduces performances of the vehicle. Moreover, high weight of vehicle induces to high temperature increased during braking where the higher value of temperature during braking could lead to braking failure and cracking of disc brake rotor. This project concerns of the temperature distribution and constraint of the disc brake rotor. Most of the passenger cars today have disc brake rotors that are made of grey cast iron (Mackin, 2002). Grey cast iron is chosen for its relatively high thermal conductivity, high thermal diffusivity and low cost (Mackin, 2002). In this project, the author will investigate on the thermal issues of normal passenger vehicle disc brake rotor, where the investigation are to determine the temperature behaviour of the disc brake rotor due to severe braking of the disc brake rotor by using Finite Element Analysis (FEA). According to (Valvano and Lee, 2000), braking performance of a vehicle can be significantly affected by the temperature rise in the b rake components. High temperature during braking will caused to: Brake fade, Premature wear, Brake fluid vaporization, Bearing failure, Thermal cracks, Thermallyexcited vibration. Therefore, it is important to study and predict the temperature rise of a given brake component and assess its thermal performance in the early design stage. Finite element analysis (FEA) has been preferred and chosen method to investigate some of the above 11
concerns such as disc brake rotor temperature rise and thermal cracks (Valvano and Lee,
3. OBJECTIVE AND SCOPE The aim at the end of this project is to predict the temperature rise and the temperature behaviour of ventilated disc brake rotor with full passenger in the vehicle. In achieving this aim, project objectives are set as below: To understand the working principles, components, standards and theories through a literature study. To understand the working principle of FEA Software (ANSYS) To understand the fundamental of heat transfer through thermal analysis of disc brake rotor. To clearly justifL the result and conclusion. The knowledge gained from this project is to be able to understand the steps needed in thermal analysis of disc brake rotor by using FEA method. The methods used in this project can later be used in future as reference for similar research and development. There is the wide range of study on the disc brake rotor. The disc brake rotor could be studied on the various areas such as material improvement on the disc brake rotor, vibration on the disc brake, noise and squeal of the disc brake and thermal stress analysis on the disc brake rotor. However, on this project, the author will intend to emphasize details on the thermal analysis on the disc brake rotor of normal passenger vehicle with full capacity of passenger. The scopes of the projects are: Literature review on the working principles, compon ents, standards and theories. Construction of 2D and 3D model of disc brake rotor. FE model (Meshing of Geometry model) Finite element analysis on steady state and transient analysis which shows the temperature distribution of disc brake rotor. Final justification and conclusion.
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4. RESEARCH METHODOLOGY Begin with a literature review, alot of paper and journal has been read up and a part of it has been considered in this project. Meanwhile, Coordinate Measuring Machine (CMM) has been used to measure the major coordinate of real disc brake rotor. CMM has been used in order to get accurate dimension of disc brake rotor. Later, the precise dimensions have been used to translate in 2D and 3D drawing by using CATIA.
In the second stage, load analysis has been done where the heat flux and convectional heat transfer coefficients has been calculated. Load analysis calculated based on full load of passenger in the normal passenger vehicle. Later, value of load analysis has been applied on finite element analysis.
Next, the fractional 3D model of disc brake rotor has been transfer to finite element software which is ANSYS. Thermal analysis has been done on steady state and transient responses. Assigning material properties, load and meshing of the model has been done in this stages. Then, completed meshing model has been submitted for analysis. Finally an expected result from the steady state and transient responses of thermal analysis has been obtained. A flow chart below shows a better understanding of overall contents of this project.
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5. THESIS OUTLINE This project consist total of seven chapters as Chapter 1 represent as an introduction to this whole project. Chapter 1 described the problem statements, objectives and scope of the project, research methodology and the overall outline of the contents in this project. This chapter also described a description of ventilated disc brake rotor and its components. A few published papers were reviewed and discussed in this chapter. Also a few theory of finite element analysis has been reviewed and introduction to finite elements sohares are presented. A few basic functions, operations and procedure of using CMM have been presented in this chapter. Meanwhile, this chapter also discussed on material justification of disc brake rotor. The material justifications described the material properties and manufacturing process of disc brake rotor. Load analysis has been done in Chapter 4. A few assumptions have been made in order to reduce the complexity of the analysis. In load analysis, heat flux and convectional heat transfer coefficient has been calculated. Then, the value of the load analysis has been applied in the finite element analysis. This chapter explained the development of 3D model and transferred process to finite elements softwares. Then, the finite element analysis are clarified step by step from assigning material properties till submitted the model for analysis .
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6. LITERATURE REVIEW 6.1 Introduction Normally, thermal stress analysis has been performed to any of material related to thermal process in order to oversee the behaviour and character of material. Any abnormality regards to thermal input will give the high values on the stress magnitude of the studied materials. The high values of stress magnitude will shows deformation on certain areas which load has been applied on it. Design and analysis of certain parts or component will took much time and it is costly. Therefore, without any analysis or design tools, it would be limitations on repeated analysis. For decades, finite element analysis (FEA) has been a preferred method to address some of the above concerns. It can be used to compare the design alternatives and hence, optimize the brake rotor design prior to production of prototype components (Valvano and Lee, 2000). A literature review was conducted to investigate the past research that has been done in many areas related to this work. In addition, description, histories, functions and theory of disc brake rotor will be discussed in this chapter. Furthermore, theory of finite element method related to thermal analysis will be presented as well in this chapter.
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7. BRAKE SYSTEM REVIEW 7.1 HISTORY OF BRAKE SYSTEM DEVELOPMENT In the early days of the automobile, drum brakes were standard. Drum brakes offered several advantages over other types of brakes. One of these was that the drum could keep out water and dust, materials that could damage disc brakes which were out in the open. Major advancement in brake technology came in 191 8 with the invention of fourwheel hydraulic brake systems by Malcolm Loughead. The hydraulic brake system replaced the mechanical brake system that was in use at this time. The mechanical system had numerous disadvantages. It made it d ifficult to brake all the wheels evenly, often causing a loss of control. In addition, it required drivers to exert tremendous amounts of force on the brake pedal to slow the car. The hydraulic brake system multiplied the force that was applied to the brake, lessening the amount of force needed to be applied to the brake pedal by the driver. This system was first used in the 1918 Duesenberg. Its advantages quickly caught on and by 1929, four wheel hydraulic braking systems were standard equipment on higher priced cars. The main problem with drum brakes is that the heat is not efficiently disbursed. The heat that is produced inside the drum does not escape easily since the drum prevents wind from drawing it away. Howeve r, disc brakes killed the issues when it allowed the heat to be carried away which increased the efficiency of the brake. However, their use was limited up until the 1950's since their efficiency was not required and they required more pedal pressure to operate. The reason for the higher pedal pressure is that disc brakes have no selfservo effect or no selfenergizing capacity that the drum brakes have. The selfservo effect is caused by the forward motion of the car. This forward motion helps pull the brake shoe into contact with the drum. This helped lower the required pedal pressure. Now that their efficiency was needed and the hydraulic brake system multiplied the force applied to the brake pedal, disc brakes seemed to be the better alternative. Chrysler was the first to widely introduce the disc brake in its cars in the early 1950's. The system did not have much success till automaker Studebaker to reintroduce the system in 1964. This time it saw much more success and in a few years, disc brakes were common on most new cars. One of the reasons that disc brakes were a success with the Studebaker and not the Chrysler was due to the development of the power braking system. Power brakes became
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common in the 195Ots, after Chrysler had developed and dropped its disc brake program. The system assisted the movement of the piston in the master cylinder which meant that the driver needed to apply less peddle pressure to get the same braking effectiveness. Therefore, since ease of braking was no longer an issue, the adoption of the more efficient disc brake became widespread
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8. VEHICLE BRAKE SYSTEM As we know, the basic functions of the brake system are to slow down a vehicle speed to the point we need. It's also help to maintain acceleration during moving downhill and keep the vehicle on static conditions. Brakes operate by converting the kinetic energy (motion) of an automobile into heat energy (Source: Halderman J.D, 1996) Driver exerts a force on brake pedal which is further amplified by power booster. The force on brake pedal pressurizes brake fluid in a master cylinder; brake fluid is designed for extreme conditions, generally a silicone based DOT5 brake fluid is recommended. The hydraulic force developed by brake fluid is transmitted to a wheel cylinder or calliper at each wheel which is used to force friction material against the drum or rotor. The friction between the friction material and rotating drum or rotor causes the rotating part to slow and eventually stop. In the passenger or commercial vehicle, there are always two main types of brakes assemblies that have been used. Those types of brakes are drum and disc brakes which have been described as below. Drum brakes have their pads located inside of a drum. Like the disc in disc brakes, drum brakes also are attached to the wheels. Usually, main components of drum brake for passenger or commercial vehicle consist of brake shoes, backing plate, parking brake cable and wheel cylinder. When the brake peda l is pressed the curved brake shoes (pads) are pushed outward so that they make contact with the rotating drum. Retracting spring is used in this type of brake (BOSCH, 1996). Just as with disc brakes, this causes friction which turns kinetic energy into heat energy, thus slowing and stopping the car to the right point. There is an advantage of using drum brakes, where there is low cost of common parts. However, there are also some disadvantages, such as the drum heats up and expands away from the lining material which increasing fading. It is also have lower efficiency in wet braking action.
When the brake pedal is pushed, the pads (often called brake shoes) push up against the wheel disc. The wheel that attached with the rotor will affected by force from pads and makes the wheel stop rotate. Those for both of disc and drum brakes are refer to mechanical, hydraulic and power brake systems in order to make the brake systems function smoothly. According to many researche rs, disc brake system has many advantages over drum brakes. The major part of rotor is exposed to air; therefore there is sufficient air flow over brakes to dissipate the heat ge nerated resulting in cooling down of 18
rotor temperature easily. The rotor expands in the direction of the friction material in disc brakes as opposed to drum brakes. The pressure applied on the rotor is more uniform resulting in even braking action as compared with drum brakes. It is also possible on wet stopping when water slide off the rotor surface. WHEEL
)
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9. Parts of disc brake 9.1 DISC CALLIPERS There are two types of disc callipers where further classified as floating and fixed calliper. shows a type of floating calliper. This type of brake uses only a single piston to squeeze the brake pad against the rotor (BOSCH, 1996). The reactive force shifts the calliper housing and presses opposite side of b raking pad against rotor. Referring to Figure the brake fluid pushes the piston when the brake is applied to the left of the piston and immediately pushes the inner pads and presses it against the rotorldisc, the sliding calliper housing reacts by shifting towards right pushing the left pad against the disc. Floating Calliper Design (Source: BOSCH Automobile Handbook, 1996) Other type of disc callipers is a fixed calliper. shows a type of fixed calliper. In these types of brakes, the caliper body is fixed and uses two or more pistons on each side of the rotor. The pistons are located in each half section of the fixed calliper. Hydraulic pressure is applied during braking to each of the piston. Each of the pistons has a function to press against the brake pads of the brake disc. Shaped piston seals will retract the piston when the brakes are released. Referring t, the brake fluid pushes the both piston when the brake is applied to the left and the right of the piston and immediately pushes the both inner pads and presses it against the rotorldisc. Normally, these types of brake calliper are used in high performance and heavy duty vehicle due to high physical strength.
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9.2BRAKE PADS As shown in Figure brake pads consist of steel carrier which the pad are bonded to the steel carrier. According to (Gerschler, 1980), organically bonded pads consist of metallic, ceramic or organic friction materials in a bonded mass such as rubber or synthetic resin. The bonded friction materials can withstand temperatures up to 750°c, with short term peaksup to 950'~ whe re the friction coefficient is between 0.25 and 0.5. There is an advantage of brake pads, where most of them are poor to thermal conductivity which protects the hydraulic actuating elements from overheating. It is also ease to manufacture and low cost. However, the pads needs to inspect frequently due to rapid wear as result from higher temperatures and contact pressures associated with the operation of abrake disc.
9.3 BRAKE DISC / DISC BRAKE ROTOR The heat generated on the surfaces of disc brake rotor when brake applied. Materials of disc brake rotor usually are made from cast iron, spheroidalgraphite cast iron or cast steel. It is chosen as a rotor material due to low cost of material and performs high thermal resistance. This type of material normally suit to normal passenger vehicle but not for high performance car. Once brake pads contacts to rotating rotor, there will be huge amount of heat generated to stop or slow down the vehicle. The rotor temperature can exceed 350'~ for normal cars and 1500'~ for race cars (Halderman, 1996). Disc brake rotor is a crucial part in the brake system where the main role of the rotor is to reduce the heat generated by dissipates all of the heat. In that case, ventilated disc brake rotor is much better than solid rotor where more airflow from the surrounding area to dissipate produced heat. Figure 2.9, shows the internal vanes allow air to circulate between two friction surfaces of the rotors
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9.3.1. DISC BRAKE ROTOR DESCRIPTION Overall idea on vehicle brake system and disc brake theories has been described as above. As similar to the type disc brake described above, the author used the disc brake rotor from normal passenger vehicle. The disc brake rotor was taken from normal passenger vehicle which having type of ventilated disc (Figure 2.1 0). Basically, disc brake rotor consists of rotating circular plate and cylinder disc (hat) attached and rotated to wheel hub. The rotating circular plate which also call annular disc has two flat surfaces separated by 32 internal vanes. Figure 2.1 1 shows the cross sectional view of ventilated disc brake rotor with outer diameter measured as 250 mm, 4.5 mm thickness of plate and having mass approximately 4 kg
9.4. BRAKE PADS As shown in Figure 2.7, brake pads consist of steel carrier which the pad are bonded to the steel carrier. According to (Gerschler, 1980), organically bonded pads consist of metallic, ceramic or organic friction materials in a bonded mass such as rubber or synthetic resin. The bonded friction materials can withstand temperatures up to 750°c, with short term peaksup to 950'~ whe re the friction coefficient is between 0.25 and 0.5.
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There is an advantage of brake pads, where most of them are poor to thermal conductivity which protects the hydraulic actuating elements from overheating. It is also ease to manufacture and low cost. However, the pads needs to inspect frequently due to rapid wear as result from higher temperatures and contact pressures associated with the operation of a brake disc.
A Sample of Brake Pads
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10. MODELLING SOFTWARE There are different softwares available for modeling some of them are: 1. Solid works 2. ProE 3. Ideas 4. Inventor 5. Mechanical desktop 6. Unigraphics 7. Catia v5
CATIA V5 (computer aided thre dimensional interactive application)a multi platform CAD/CAM/CAE is used as the modeling tool in this project
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11.CATIA V5 11.1 INTRODUCTION CATIA V5 provides the power of parametric design. With parametric, we define the modal according to the size and positional relationship of its parts.
11.2 PART MODELLING Many techinacal designs consists of complex assemblies made from angular shaped parts. This type of design work can be made asier by part and assembly modeling capabilities that are well integrated. The CATIA V5 is a 3D parametric solid modeler with both part and assembly modeling capabilities. You can see the CATIA V5 to model piece parts and then combine them into more complex assemblies. With CATIA V5 a part is designed by sketching its components shapes and defining their size shape and inter relationships. By succesfuly creating these features you counstruct the part in a building block fashion. Since CATIA V5 has parametric features, you can change one feature and all related features are automatically updated to reflectthe change and its effects throughout the part. It can be used to create angular shaped part, to which 3D surface can be applied to create hybrid parts consisting of mixture of angular and curved shapes. This provides the ability to create model designs with shapes of varying types.
11.3 GENERAL MODELING PROCESS FOR EACH PART
® Plan the part ® Create the base feature ® Create the remaining features ®Analyze the part ®Modify the features as necessary 25
®Assembly modeling
Assemblies can be created from parts, either combined individually or grouped in subassemblies. The CATIA V5 builds these individualparts and subassemblies into an assembly in a hierachica manner according to relationships defined cy constrains. As in part modeling , the parametric relationship allows you to quickly update an entire assembly based on a change in one of its parts. The general process for assemblies and subassemblies is similar to that of building parts: ®Lay out the assembly ®Create the base part ®Create and attach the remaining parts ®Analyze the assembly ® Modify the assembly as necessary
11.4 FUNDAMENTALS CATIA V5 employs two operating modes for part modeling, model made for modeling 3Dparametric parts and drawing mode for c reating 2D drawings of them. These modes operate independently but share the same design data. Part modeling requires beginning the design work in model mode where a model of the part is immediately built. Then the drawing mode can be used at any point to document the design. In traditional CUMPUTER AIDED DESIGN, a 2D drawing is created at the beginning and then 3D model is built to analyze, and verify the initial concept. 26
12. FINITE ELEMENT ANALYSIS 12.1 INTRODUCTION The finite element method is numerical analysis technique for obtaining approximate solutions to a wide variety of engineering problems. Because of its diversity and flexibility as an analysis tool, it is receiving much attention in almost every industry. In more and more engineering situations today, we find that it is necessary to obtain approximate solutions to problem rather than exact closed form solution. It is not possible to obtain analytical mathematical solutions for many engineering problems. An analytical solutions is a mathematical expression that gives the values of the desired unknown quantity at any location in the body, as consequence it is valid for infinite number of location in the body. For problems involving complex material properties and boundary conditions, the engineer resorts to numerical methods that provide approximate, but acceptable solutions. The finite element method has become a powerful tool for the numerical solutions of a wide range of engineering problems. It has been developed simultaneously with the increasing use of the high speed electronic digital computers and with the growing emphasis on numerical methods for engineering a nalysis. This method started as a generalization of the structural idea to some problems of elastic continuum problem, started in terms of different equations
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.
12.2 PROCEDURE FOR ANSYS ANALYSIS Static analysis is used to determine the displacements stresses, stains and forces in structures or components due to loads that do not induce significant inertia and damping effects. Steady loading in response conditions are assumed. The kinds of loading that can be applied in a static analysis include externally applied forces and pressures, steady state inertial forces such as gravity or rotational velocity imposed (nonzero) displacements, temperatures (for thermal strain). A static analysis can be either linear or non linear. In our present work we consider linear static analysis. The procedure for static analysis consists of these main steps Building the model Obtaining the solution Reviewing the results.
12.3 BUILD THE MODEL In this step we specify the job name and analysis title use PREP7 to define the element types, element real constants, material properties and model geometry element type both linear and non linear structural elements are allowed. The ANSYS elements library contains over 80 different element types. A unique number and prefix identify each element type. E.g. BEAM 94, PLAN 71, SOLID 96 and PIPE 16E
12.4 MATERIAL PROPERTIES Young.s modulus (EX) must be defined for a static analysis. If we plan to apply inertia loads (such as gravity) we define mass properties such as density (DENS). Similarly if we plan to apply thermal loads (temperatures) we define coefficient of thermal expansion
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12.5 SOLUTION In this step we define the analysis type and options, apply loads and initiate the finite element solution. This involves three phases:
Preprocessor phase Solution phase Postprocessor phase Preprocessor: Pre processor has been developed so that the same program is available on micro, mini, supermini and mainframe computer system. This slows easy transfer of models one system to other. The following Table 3.1 shows the brief description of steps followed in each phase:
TABLE .1
PRE PROCESSOR PHASE
SOLUTION PHASE
POST PROCESSOR
GEOMETRY DEFINITION
ELEMENT MATRIX FORMATION
POST SOLUTION OPERATION
MESH GENERATION
OVERALL MATRIX TRIANGULARIZATION
POST DATA PRINT OUT FOR REPORTS
MATERIAL
WAVE FRONT
DEFINITIONS
POST DATA SCANING POST DATA DISPLAY
CONSTRAIN DEFINITIONS
DISPLACEMENT, STRESS,ET.,
LOAD DEFINITIONS
CALCULATION
MODEL DISPLAY
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13. FINITE ELEMENT GENERATION: The maximum amount of time in a finite element analysis is spent on generating elements and nodal data. Pre processor allows the user to generate nodes and elements automatically at the same time allowing control over size and number of elements. There are various types of elements that can be mapped or generated on various geometric entities. The elements developed by various automatic element generation capabilities of pre processor can be checked element characteristics that may need to be verified before the finite element analysis for connectivity, distortionindex etc. Generally, automatic mesh generating capabilities of pre processor are used rather than defining the nodes individually. If required nodes can be defined easily by defining the allocations or by translating the existing node s. Also on one can plot, delete, or search nodes.
13.1 BOUNDARY CONDITIONS AND LOADING : After completion of the finite element model it has to constrain and load has to be applied to the model. User can define constraints and loads in various ways. All constraints and loads are assigned set ID. This helps the user to keep track of load cases.
13.2 MODEL DISPLAY : During the construction and verification stages of the model it may be necessary to view it from different angles. It is useful to rotate the model with respect to the global system and view it from different angles. Pre processor offers this capabilities. By windowing feature pre processor allows the user to enlarge a specific area of the model for clarity and details. Pre processor also provides features like smoothness, scaling, regions, active set, etc for efficient model viewing and editing.
13.3 MATERIAL DEFECTIONS: All elements are defined by nodes, which have only their location defined. In the case of plate and shell elements there is no indication of thickness. This thickness can be given as element property. Property tables for a particular property set 1D have to be input. Different types of elements have different properties for e.g. Beams: Cross sectional area, moment of inertia etc 30
Shell: Thickness Springs: Stiffness Solids: None The user also needs to define material properties of the elements. For linear static analysis, modules of elasticity and Poisson.s ratio need to be provided. For heat transfer, coefficient of thermal expansion, densities etc. are required. They can be given to the elements by the material property set to 1D.
13.4 SOLUTION: The solution phase deals with the solution of the problem according to the problem definitions. All the tedious work of formulating and assembling of matrices are do ne by the computer and finally displacements are stress values are given as output. Some of the capabilities of the ANSYS are linear static analysis, non linear static analysis, transient dynamic analysis, etc.
13.5 POST PROCESSOR: It is a powerful user friendly post processing program using interactive colour graphics. It has extensive plotting features for displaying the results obtained from the finite element analysis. One picture of the analysis results (i.e. the results in a visual form) can often reveal in seconds what would take an engineer hour to assess from a numerical output, say in tabular form. The engineer may also see the important aspects of the results that could be easily missed in a stack of numerical data. Employing state of art image enhancement techniques, facilities viewing of:
Contours of stresses, displacements, temperatures etc. Deform geometric plots Animated deformed shapes Timehistory plots Solid sectioning Hidden line plot Light source shaded plot Boundary line plot etc. The entire range of post processing options of different types of analysis can be accessed through the command/menu mode there by giving the user added flexibility and convenience.
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14. FINITE ELEMENT FORMULATION FOR HEAT CONDUCTIOIN The unsteady heat conduction equation of each body for an axisSymmetric problem described in the cylindrical coordinate system is given as follows: 1 rz
TTT crkk trrrzz
ρ ∂∂⎛∂⎞∂⎛∂⎞=⎜⎟+⎜⎟∂∂⎝∂⎠∂⎝∂⎠ (3.1) With the boundary conditions and initial condition * 0
T = T o n Γ (3.2)
1
(  ) n q h T T o n ∞ = Γ (3.3)
*
q = q o n Γ (3.4) 0 T = T a t t i m e = 0 (3.5) nn2
Whereρ , c , r k and z k are the density, specific heat ant thermal conductivities in r and z direction of the material, respectively. Also , T * is the prescribed temperature, h the heat transfer coefficient, *
q the heat flux at each contact interface due to friction, T ∞ the ambient temperature, 0 T the initial temperature and 0 Γ , 1 Γ and 2 Γ are the boundaries on which temperature, convection and heat flux are imposed, respectively. Using Galerkin.s approach, a finite element for mulation of unsteady heat Eq. (3.1) can be written in the following matrix form as n
C T T + K H T T = R (3.6) Where T C is the capacity matrix, T KH is the conductivity matrix. T and R and are the nodal temperature and heat source vector, respectively. The most commonly used method for solving Eq. (3.6) is the direct integration method based on the assumption that temperature t T at time t and temperature t t T + Δ at time t + Δt have the following relation:
() ttt
..
1 ttT +ΔT β T β T +Δt
= + ⎡ − + ⎤ Δ ⎢⎣ ⎥⎦ 32
(3.7)
Eq.(3.7) can be used to reduce the ordinary differential Eq.(3.6) to the following implicit algebraic equation:
()()
T1 T t t T 2T t 2 t1t t
C b K H T C b K H T b R b R +Δ+Δ+ = − + +
(3.8) Where the variable 1 b and 2 b are given by
b=βΔt,( (3.9) 1
)
2
b=1−βΔt
For different values of
β , the wellknown numerical integration scheme
can be obtained [23].in this study, 0.5 ≤ β ≤1.0 was used, which is an unconditionally stable scheme.
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15 THERMAL ANALYSIS A thermal analysis calculates the temperature distribution and related thermal quantities in brake disk. Typical thermal quantities are: 1. The temperature distribution 2. The amount of heat lost or gained 3. Thermal fluxes
15.1 Types of thermal analysis: 1. A steady state thermal analysis determines the temperature distribution and other thermal quantities under steady state loading conditions. A steady state loading condition is a situation where heat storage effects varying over a period of time can be ignored. 2. A transient thermal analysis determines the temperature distribution and other thermal quantities under conditions that varying over a period of time.
15.2 PLANNING THE ANALYSIS: In this step a compromise between the computer time and accuracy of the analysis is made. The various parameters set in analysis are given below: Thermal modeling Analysis type . thermal hmethod. Steady state or Transient? Transient Thermal or Structural? Thermal Properties of the material? Isotropic Objective of analysis to find out the temperature distribution in the brake disk when the process of braking is done. Units SI
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16. STRUCTURAL ANALYSIS Structural analysis is the most common application of the finite element analysis. The term structural implies civil engineering structure such as bridge and building, but also naval, aeronautical and mechanical structure such as ship hulls, aircraft bodies and machine housing as well as mechanical components such as piston, machine parts and tools. 16.1 Types of structural analysis:
The seven types of structural analyses in ANSYS. One can perform the following types of structural analysis. Each of these analysis types are discussed as follows: Static analysis Modal analysis Harmonic analysis Transient dynamic analysis Spectrum analysis Buckling analysis Explicit dynamic analysis
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17. STRUCTURAL STATIC ANALYSIS: A static analysis calculates the effects of steady loading conditions on a structure, while ignoring inertia and damping effects such as those caused by time varying loads. A static analysis can, however include steady inertia loads (such as gravity and rotational velocity), and time varying loads that can be approximated as static equivalent loads (such as static equivalent wind and seismic loads).
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18. MODELING AND ANALYSIS It is very difficult to exactly model the brake disk, in which there are still researches are going on to find out transient thermo elastic behavior of disk brake during braking applications. There is always a need of some assumptions to model any complex geometry. These assumptions are made, keeping in mind the difficulties involved in the theoretical calculation and the importance of the parameters that are taken and those which are ignored. In modeling we always ignore the things that are of less importance and have little impact on the analysis. The assumptions are always made depending upon the details and accuracy required in modeling. The assumptions which are made while modeling the process are given below:1. The disk material is considered as homogeneous and isotropic. 2. The domain is considered as axissymmetric. 3. Inertia and body force effects are negligible during the analysis. 4. The disk is stress free before the application of brake. 5. Brakes are applied on the entire four wheels. 6. The analysis is based on pure thermal loading and vibration and thus only stress level due to the above said is done. The analysis does not determine the life of the disk brake. 7. Only ambient aircooling is taken into account and no forced Convection is taken. 8. The kinetic energy of the vehicle is lost through the brake disks i.e. no heat loss between the tyre and the road surface and deceleration is uniform. 9. The disk brake model used is of solid type and not ventilated one. 10. The thermal conductivity of the material used for the analysis is uniform throughout. 11. The specific heat of the material used is constant throughout and does not change with temperature.
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19. DEFINITION OF PROBLEM DOMAIN Due to the application of brakes on the car disk brake rotor, heat generation takes place due to friction and this thermal flux has to be conducted and dispersed across the disk rotor cross section. The condition of braking is very much severe and thus the thermal analysis has to be carried out. The thermal loading as well as structure is axissymmetric. Hence axissymmetric analysis can be performed, but in this study we performed 3D analysis, which is an exact representation for this thermal analysis. Thermal analysis is carried out and with the above load structural analysis is also performed for analyzing the stability of the structure
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20. MODELING AND ANALYSIS
It is very difficult to exactly model the brake disk, in which there are still researches are going on to find out transient thermo elastic behavior of disk brake during braking applications. There is always a need of some assumptions to model any complex geometry. These assumptions are made, keeping in mind the difficulties involved in the theoretical calculation and the importance of the parameters that are taken and those which are ignored. In modeling we always ignore the things that are of less importance and have little impact on the analysis. The assumptions are always made depending upon the details and accuracy required in modeling. The assumptions which are made while modeling the process are given below:1. The disk material is considered as homogeneous and isotropic. 2. The domain is considered as axissymmetric. 3. Inertia and body force effects are negligible during the analysis. 4. The disk is stress free before the application of brake. 5. Brakes are applied on the entire four wheels. 6. The analysis is based on pure thermal loading and thus only stress level due to the above said is done the analysis does not determine the life of the disk brake. 7. Only ambient aircooling is taken into account and no forced Convection is taken. 8. The kinetic energy of the vehicle is lost through the brake disks i.e. no heat loss between the tyre and the road surface and deceleration is uniform. 9. The disk brake model used is of solid type and ventilated one. 10. The thermal conductivity of the material used for the analysis is uniform throughout. 11. The specific heat of the material used is constant throughout and does not change with temperature. DEFINITION OF PROBLEM DOMAIN Due to the application of brakes on the car disk brake rotor, heat generation takes place due to friction and this thermal flux has to be conducted and dispersed across the disk rotor cross section. The condition of braking is very much severe and thus the thermal analysis has to be carried out. The thermal loading as well as structure is axissymmetric. Hence axissymmetric analysis can be performed, but in this study we performed 3D analysis, which is an exact representation for this thermal analysis. 39
Thermal analysis is carried out and with the above load structural analysis is also performed for analyzing the stability of the structure. The 3d model of the solid type brake is done in CATIA and converted into parasolid file.
Fig. solid type disk brake 3D model isometric view
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Fig. solid type disk brake 3D model front view
Fig. solid type disk brake 3D model wireframe 21. CREATING A FINITE ELEMENT MESH
According to given specifications the element type chosen is solid 90.Solid 90 is higher order version of the 3D eight node thermal element (Solid 70). The element has 20 nodes with single degree of freedom, temperature, at each node. The 20node elements have compatible temperature shape and are well suited to model curved boundaries. The 20node thermal element is applicable to a 3D, 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 (Solid 95). The parasolid file is imported into ansys and is meshed with 20 node thermal solid 90 element type. The structure, number of nodes and input summary of the element is given below. 21.1 SOLID90 Element Description
SOLID90 is a higher order version of the 3D eight node thermal element (SOLID70). The element has 20 nodes with a single degree of freedom, temperature, at each node. The 20node elements have compatible temperature shapes and are well suited to model curved boundaries. The 20node thermal element is applicable to a 3D, steadystate or transient thermal analysis
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The geometry, node locations, and the coordinate system for this element are shown in Figure "SOLID90 Geometry". The element is defined by 20 node points and the material properties. A prismshaped element may be formed by defining duplicate K, L, and S; A and B; and O, P, and W node numbers.
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 Material Properties KXX, KYY, KZZ, DENS, C, ENTH Surface Loads Convection or Heat Flux (but not both) and Radiation (using Lab = RDSF) ‐‐ 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 Loads Heat Generations ‐‐ 42
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)
Fig. solid type disk brake mesh model
Fig. solid type disk brake mesh model isometric view Total number of elements = 39800 Total number of nodes = 98104
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22. APPLYING THE BOUNDARY CONDITIONS
In thermal and structural analysis of disk brake, we have to apply thermal and boundary conditions on 3D disk model of disk brake. 22.1 THERMAL BOUNDARY CONDITIONS
As shown in Fig. a model presents a three dimensional solid disk squeezed by two finitewidth friction material called pads. The entire surface, S, of the disk has three different regions including S1 and S2. On S1 heat flux is specified due to the frictional heating between the pads and disk, and S2 is defined for the convection boundary. The rest of the region, except S1 U S2, is either temperature specified or assumed to be insulated: the inner and outer rim area of disk.
Fig. Thermal model of Disk brake
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Fig. Temperature boundary condition of 77degrees C applied on solid type Disk brake
Fig. Convection boundary condition applied on solid type Disk brake
Material Properties on Pad and Disk Thermal conductivity, K (w/m k) 
ρ
Density, (kg/m3) Specific heat, c (J/Kg k) Poisson’s ratio, v Thermal expansion, á (10 6 / k ) Elastic modulus, E (GPa) Coefficient of friction, µ

1800 1.88 0.3 0.3 50.2 0.2
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22.2 Results
Fig. Temperature distribution on solid type Disk brake on the front side
Fig. Temperature distribution on solid type Disk brake on the rear side
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Fig. Temperature distribution on solid type Disk brake along the thickness
Fig. Graphical representation of Temperature distribution on solid type Disk brake along the thickness
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23. STRUCTURAL ANALYSIS NORMAL DISC BRAKE ROTOR 23.1STRUCTURAL BOUNDARY CONDITIONS
Since the axissymmetric model is considered all the nodes on the hub radius are fixed. So the nodal displacements in the hub become zero i.e. in radial, axial and angular directions
Fig. Structural boundary condition applied on solid type Disk brake
Fig. Temperature distribution is applied as Thermal loads on solid type Disk brake from the thermal analysis
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23.2 RESULTS
Fig. Total deflection of solid type Disk brake
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Fig. Deflection in Xdir of solid type Disk brake
Fig. Deflection in Ydir of solid type Disk brake
50
Fig. Deflection in Zdir of solid type Disk brake
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Fig. VonMises stress on solid type Disk brake
Fig. Xdir stress on solid type Disk brake
Fig. Ydir stress on solid type Disk brake 52
Fig. Zdir stress on solid type Disk brake
To optimize the above disk brake a complicated model of ventilated disk brake is taken and there by forced convection is considered in the analysis.
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Fig. Ventilated type disk brake 3D model isometric view
Fig. Ventilated type disk brake 3D model isometric view on the rear side
Fig. Ventilated type disk brake 3D model front view
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Fig. Ventilated type disk brake 3D model in wireframe
24. CREATING A FINITE ELEMENT MESH FOE VENTED ROTOR According to given specifications the element e lement type chosen is solid 90.Solid 90 is higher order version of the 3D eight node thermal element (Solid 70). The element has 20 nodes with single degree of freedom, temperature, at each node. The 20node elements have compatible temperature shape and are well suited to model curved boundaries. The 20node thermal element is applicable to a 3D, 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 (Solid 95). The parasolid file is imported into ansys and is meshed with 20 node thermal solid 90 element type. The structure, number of nodes and input summary of the element is given below.
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Fig. Ventilated type disk brake mesh model in isometric view
Fig. Ventilated type disk brake 3D model in showing the vents
25. APPLYING THE BOUNDARY CONDITIONS In thermal and structural analysis of disk brake, we have to apply thermal and boundary conditions on 3D disk model of disk brake.
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Fig. Temperature boundary condition of 77degrees C applied on Vent type Disk brake
Fig. Convection boundary condition applied on Vent type Disk brake Results
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Fig. Temperature distribution on Vent type Disk brake on the front side
Fig. Temperature distribution on Vent type Disk brake on the rear side
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Fig. Temperature distribution on Vent type Disk b rake along the thickness
Fig. Graphical representation of Temperature distribution on vent type Disk brake along the thickness
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26. STRUCTURAL ANALYSIS FOR VENTED DISC BRAKE ROTOR 26.1STRUCTURAL BOUNDARY CONDITIONS
Since the axissymmetric model is considered all the nodes on the hub radius are fixed. So the nodal displacements in the hub become zero i.e. in radial, axial and angular directions
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Fig. Structural boundary condition applied on Vent type Disk brake
Fig. Temperature distribution is applied as Thermal loads on Vent type Disk brake from the thermal analysis 26.2 Results
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Fig. Total Deflection on Vent type Disk brake
Fig. Deflection in Xdir of Vent type Disk brake
Fig. Deflection in Ydir of Vent type Disk brake 62
Fig. Deflection in Zdir of Vent type Disk brake
Fig. VonMises stress on Vent type Disk brake
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Fig. Xdir stress on Vent type Disk brake
Fig. Ydir stress on Vent type Disk brake
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Fig. Zdir stress on Vent type Disk brake
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27. CONCLUSIONS
The present study can provide a useful design tool and improve the brake performance of disk brake system. From the below Table we can say that all the values obtained from the analysis are less than their allowable values. Hence the brake disk design is safe based on the strength and rigidity criteria. Comparing the different results obtained from analysis. It is concluded that ventilated type disk brake is the best possible for the present application.
Solid Type Total Deflection in (mm) Vonmises Stress
Ventilated Type 2.351
0.248
2.26E+12
2.17E+06
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28. REFRENCES 1. KENNEDY, F. E., COLIN, F. FLOQUET, A. AND GLOVSKY, R. Improved Techniques for Finite Element Analysis of Sliding Surface Temperatures. Westbury House page 138150, (1984). 2. LIN , J. Y. AND CHEN, H. T. Radial Axis symmetric Transient Heat Conduction in Composite Hollow Cylinders with Variable Thermal Conductivity, vol. 10, page 2 33, (1992). 3. BRILLA, J. Laplace Transform and New Mathematical Theory of Visco elasticity, vol. 32, page 187 195, (1997). 4. TSINOPOULOS, S. V, AGNANTIARIS, J. P. AND POLYZOS, D. An Advanced Boundary Element/Fast Fourier Transform Axis symmetric Formulation for Acoustic Radiation and Wave Scattering Problems, J.ACOUST. SOC. AMER., vol 105, page 15171526, (1999). 5. WANG, H. C. AND BANERJEE, P. K.. Generalized Axis symmetric Elastodynamic Analysis by Boundary Element Method, vol. 30, page 115131, (1990). 6. FLOQUET, A. AND DUBOURG, M.C. Non axis symmetric effects for three dimensional Analyses of a Brake, ASME J. Tribology, vol. 116, page 401407, (1994). 7. BURTON, R. A. Thermal Deformation in Frictionally Heated Contact, Wear, vol. 59, page 1 20, (1980). 8. ANDERSON, A. E. AND KNAPP, R. A. Hot Spotting in Automotive Friction System Wear, vol. 135, page 319337, (1990). 9. COMNINOU, M. AND DUNDURS, J. On the Barber Boundary Conditions for Thermo elastic Contact, ASME J, vol. 46, page 849853, (1979). 10. BARBER, J. R. Contact Problems Involving a Cooled Punch, J. Elasticity, vol. 8, page 409 423, (1978). 11. BARBER, J. R. Stability of Thermo elastic Contact, Proc. International Conference on Tribology, p Institute of Mechanical Engineers, page. 981986, (1987). 12. DOW, T. A. AND BURTON, R. A. Thermo elastic Instability of Sliding Contact in the absence of Wear, Wear, vol. 19, page 315328, (1972). 13. LEE, K. AND BARBER, J.R. FrictionallyExcited Thermo elastic Instability in Automotive Disk Brakes, ASME J. Tribology, vol. 115, page 607614, (1993). 14. LEE, K. AND BARBER, J. R. An Experimental Investigation of Frictionallyexcited Thermo elastic Instability in Automotive Disk Brakes under a Drag Brake Application, ASME J. Tribology, vol. 116,page 409414, (1994). 15. LEE, K. AND BARBER, J. R. Effect of Intermittent Contact on the Stability of Thermo elastic Contact, ASME J. Tribology, vol. 198, page 27 32, (1995). 16. ZAGRODZKE, S, BARBER, J. R. AND HULBERT, G.M. Finite Element Analysis of Frictionally Excited Thermo elastic Instability, J. Thermal Stresses, vol. 20, page 185201, (1997). 17. LEROY, J. M., FLOQUET, A. AND VILLECHAISE, B. Thermomechanical Behavior of Multilayered Media: Theory, ASME J. Tribology, vol. 111, page 530544, (1989). 67
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