BRAKE FEEL: INVESTIGATION OF THE BRAKE DESIGN PARAMETERS’ INFLUENCE

In order to investigate the influence of the brake design parameters on brake feel a braking system model has been used and run with AMESim.. pedal stroke for front bore’s diameter ...53

Supervisor: J Marco

September 2006

This thesis is submitted in partial fulfilment of the requirements

for the degree of Master of Science

© Cranfield University 2006 All rights reserved No part of this publication may

be reproduced without the written permission of the copyright owner

Abstract

The development of environmental-friendly cars has led car manufacturers to explore new propulsion systems One of them is the Hybrid Electric Vehicle This particular type of vehicle is usually fitted with a regenerative braking system that captures the vehicle kinetic energy lost when braking Therefore a brake emulator has to be implemented instead of the brake pedal to isolate the driver’s brake requirement In doing so, the feedback from the braking system – the brake feel – is lost and needs to be simulated by the brake emulator

However up to now very little research has been done on this particular domain which remains relatively unknown The purpose of this thesis is to consequently understand the role each component of a braking system plays in brake feel

In order to investigate the influence of the brake design parameters on brake feel a braking system model has been used and run with AMESim Brake feel was assessed using 10 criteria extracted from the curves representing pedal stroke vs applied force and pedal stroke vs vehicle deceleration A range of 13 brake design parameters were then tested and their influence studied

The final result is two sets of maps The first one relates a given brake feel criteria to all the design parameters, and the second relates a given design parameter to all the brake feel criteria Furthermore a ratio has been calculated that gives the average influence each parameter has on brake feel and vice-versa

These results can then be used to tune a brake emulator according to the brake feel one wants to give to a car One can also predict the brake feel associated with one particular braking system

I would also like to thank Dr Marko Tirovic for having helped me at the early stage of the thesis Thank you to the Application Engineer from Imagine, Emmanuel Domingues, who has given me a lot of time and explanations

My thanks go to the entire staff of the MSc in Automotive Product Engineering who have made this year a valuable year A special thanks goes to Catriona Rolfe who has put up with me for one year and whose e-mail will long be missed

Special thanks are extended to my classmates who I had the pleasure to meet this year in

an international context It has been a very enriching experience A very warm thank you to:

Maryneidy Arocha Santiago

Marie-Line Guillermin

Ramy Karoun

Hong Chi Lee

Pierre Tipner

Finally I would like to thank my parents and my sister for all their support throughout

my academic life and especially for this year that has not always been funny

Table of contents

Abstract i

Acknowledgment iii

Table of contents v

Table of figures vii

Table of acronyms xi

1 Presentation of the thesis 1

1.1 Context 1

1.2 Subject 3

2 Literature review 4

2.1 Electro hydraulic and regenerative braking 4

2.2 Brake feel 6

2.3 Braking system model 11

2.4 Conclusions 14

3 The braking system model 16

3.1 Model requirements 16

3.2 Presentation of AMESim’s model 16

3.2.1 The global model 17

3.2.2 The vacuum booster 18

3.2.3 The master cylinder 20

3.2.4 The calliper 23

3.3 Improvement of the model 24

3.3.1 The Calliper 24

3.3.2 The master cylinder 25

3.3.3 The brake pedal 26

3.3.4 Implementing a fluid reservoir 29

3.3.5 Implementing a vehicle dynamic model 31

3.4 Validation of the model 35

3.5 Final model 37

3.6 Simulation parameters 37

3.7 Baseline results 37

4 Investigation of the parameters influencing brake feel 42

4.1 Vehicle dynamics’ parameters 42

4.1.1 Number of bores 43

4.1.2 Mean swept radius 44

4.1.3 Friction between pad and disc 46

4.1.4 Vehicle mass 47

4.1.5 Wheel radius 48

4.1.6 Discussion 49

4.2 Calliper’s parameters 50

4.2.1 Gap between pad and disc 50

4.2.2 Front bore’s diameter 52

4.2.3 Rear bore’s diameter 54

4.3 Vacuum booster’s parameters 55

4.3.1 Engine depression 55

4.3.2 Vacuum booster’s reaction disc diameter 58

4.4 Master cylinder’s parameters 59

4.4.1 Master cylinder’s diameter 60

4.4.2 Master cylinder’s volume 61

4.4.3 Primary spring 62

4.4.4 Secondary spring 64

4.4.5 Underlap 65

4.5 Pedal’s parameters 66

4.4.2 Pedal length 66

4.4.3 Pedal ratio 68

5 Results and further work 70

5.1 Presentation of the results 70

5.1.1 Relation brake feel to parameters 70

5.1.2 Relation parameter to brake feel 72

5.2 Further work 75

5.2.1 Useability of AMESim 75

5.2.2 Model enhancement 75

5.2.3 Brake feel assessment 75

5.2.4 Brake emulator development 75

6 Conclusion 76

References 79

Bibliography 81

Appendices 83

Appendix A: AMESim Final model 84

Appendix B: Summary of the brake design characteristics 86

Appendix B: Influence of mean swept radius 88

Appendix C: Influence of the coefficient of friction between the pad and the disc 89

Appendix D: Influence of the wheel radius 90

Appendix E: Influence of gap between pad and disc 91

Appendix F: Influence of front bore’s diameter 92

Appendix G: Influence of rear bore’s diameter 93

Appendix H: Influence of engine depression 94

Appendix I: Influence of reaction disc diameter 95

Appendix J: Influence of the master cylinder’s diameter 96

Appendix K: Influence of the master cylinder’s volume 97

Appendix L: Influence of the primary spring stiffness 98

Appendix M: Influence of the secondary spring stiffness 99

Appendix N: Influence of the underlap 100

Appendix O: Influence of the pedal length 101

Appendix P: Influence of the brake pedal ratio 102

Table of figures

Figure 1: Regenerative braking configuration 2

Figure 2: Principle of data and energy flow in Brake-by-wire systems [9] 5

Figure 3: Range of boost function with controlled amplification [3] 5

Figure 4: Objective to subjective correlation [10] 7

Figure 5: Pedal effort vs pedal stroke [5] 8

Figure 6: Deceleration vs pedal stroke [5] 8

Figure 7: Coefficient of correlation between predicted and observed parameters [5] 8

Figure 8: Matrix for ‘intelligent’ brake pedal [9] 9

Figure 9: Flow-down design method [7] 10

Figure 10: Lumped parameter of a vacuum booster [12] 12

Figure 11: Tandem master cylinder model [16] 13

Figure 12: Floating calliper simple model [16] 13

Figure 13: Floating calliper with thermal model [16] 13

Figure 14: Booster disc diameter’s influence [16] 13

Figure 15: Fluid displacement in braking system [17] 14

Figure 16: Global braking system model 17

Figure 17: Vacuum booster model 18

Figure 18: Vacuum booster drawing [12] 18

Figure 19: Vacuum booster analysis 19

Figure 20: Vacuum booster schematic 19

Figure 21: Booster characteristic curve 20

Figure 22: Master cylinder model 20

Figure 23: Physical interpretation of the master cylinder’s model [22] 21

Figure 24: Global braking system characteristic 22

Figure 25: Master cylinder’s hydraulic configuration 22

Figure 26: Calliper model 23

Figure 27: Force distribution in the calliper 24

Figure 28: New brake calliper 24

Figure 29: Comparison between parallel and series spring in calliper 25

Figure 30: New hydraulic circuit configuration 25

Figure 31: Floor mounted pedals [19] 26

Figure 32: Forward swing mounted pedals [19] 26

Figure 33: Brake pedal modelling approximation [20] 27

Figure 34: Comparison linear/non-linear model 27

Figure 35: Linear and non linear mechanical lever 28

Figure 36: Brake pedal model 29

Figure 37: Compensation port open and closed [17] 29

Figure 38: Master cylinder with reservoir 30

Figure 39: Pressure comparison with and without reservoir 31

Figure 40: Schematic of car [21] 31

Figure 41: Weight transfer when decelerating 32

Figure 42: Adhesion curves 34

Figure 43: Vehicle model 34

Figure 44: AMESim final model 37

Figure 45: Force on the brake pedal 38

Figure 46: Pedal effort vs pedal stroke 38

Figure 47: Pedal effort vs pedal stroke from literature review 38

Figure 48: Brake feel criteria for pedal effort vs pedal stroke 39

Figure 49: Deceleration vs pedal stroke 39

Figure 50: Deceleration vs pedal stroke from literature review 39

Figure 51: Deceleration vs pedal stroke, averaged 40

Figure 52: Brake feel criteria for deceleration vs pedal stroke 40

Figure 53: Linearisation of stiffness 1, 2 and 3 41

Figure 54: Deceleration vs pedal stroke for number of bores 43

Figure 55: Deceleration vs pedal stroke for mean swept radius 45

Figure 56: Influence of mean swept radius on brake feel 45

Figure 57: Deceleration vs pedal stroke for friction between pad and disc 46

Figure 58: Influence of the coefficient of friction pad/disc on brake feel 46

Figure 59: Deceleration vs pedal stroke for vehicle mass 47

Figure 60: Deceleration vs pedal stroke for wheel radius 49

Figure 61: Influence of wheel radius on brake feel 49

Figure 62: Vehicle dynamics impact on brake feel 50

Figure 63: Pedal effort vs pedal stroke for gap between ad and disc 51

Figure 64: Deceleration vs pedal stroke for gap between pad and disc 51

Figure 65: Influence of gap between pad and disc 52

Figure 66: Pedal effort vs pedal stroke for front bore’s diameter 52

Figure 67: Deceleration vs pedal stroke for front bore’s diameter 53

Figure 68: Front bore’s diameter influence on brake feel 53

Figure 69: Pedal effort vs pedal stroke for rear bore’s diameter 54

Figure 70: Deceleration vs pedal stroke for rear bore’s diameter 54

Figure 71: Influence of rear bore’s diameter on brake feel 55

Figure 72: Pedal stroke vs pedal force for engine depression 56

Figure 73: Deceleration vs pedal stroke for engine depression 56

Figure 74: Pedal and pushrod travel for several engine depression 57

Figure 75: Influence of engine depression on brake feel 57

Figure 76: Pedal effort vs pedal stroke for reaction disc diameter 58

Figure 77: Deceleration vs pedal stroke for reaction disc diameter 58

Figure 78: Influence of the reaction disc diameter on brake feel 59

Figure 79: Pedal effort vs pedal stroke for master cylinder’s diameter 60

Figure 80: Deceleration vs pedal stroke for master cylinder’s diameter 60

Figure 81: Influence of master cylinder’s diameter on brake feel 61

Figure 82: Pedal effort vs pedal stroke for master cylinder’s volume 62

Figure 83: Deceleration vs pedal stroke for master cylinder’s volume 62

Figure 84: Pedal effort vs pedal stroke for primary spring 63

Figure 85: Deceleration vs pedal stroke for primary spring 63

Figure 86: Pedal effort vs pedal stroke for secondary spring 64

Figure 87: Deceleration vs pedal stroke for secondary spring 64

Figure 88: Pedal effort vs pedal stroke for underlap 65

Figure 89: Deceleration vs pedal stroke for underlap 65

Figure 90: Influence of the underlap on brake feel 66

Figure 91: Pedal effort vs pedal stroke for pedal length 67

Figure 92: Deceleration vs pedal stroke for pedal length 67

Figure 93: Influence of pedal length on brake feel 68

Figure 94: Pedal effort vs pedal stroke for pedal ratio 68

Figure 95: Deceleration vs pedal stroke for pedal ratio 69

Figure 96: Influence of the brake pedal ratio on brake feel 69

Figure 97: Stiffness 1 70

Figure 98: Stiffness 2 70

Figure 99: Stiffness 3 70

Figure 100: Hysteresis 70

Figure 101: Threshold 71

Figure 102: Slope 1 71

Figure 103: Slope 2 71

Figure 104: Dead stroke 71

Figure 105: Pedal stroke 71

Figure 106: Maximum deceleration 71

Figure 107: Gap between pad and disc 72

Figure 108: Front bore’s diameter 72

Figure 109: Rear bore’s diameter 72

Figure 110: Engine depression 72

Figure 111: Reaction disc diameter 73

Figure 112: Master cylinder’s diameter 73

Figure 113: Underlap 73

Figure 114: Pedal length 73

Figure 115: Pedal ratio 73

Figure 116: Linear parameters 73

Figure 117: Inversely linear parameters 74

Table of acronyms

ABS: Antilock Braking System

ACC: Adaptative Cruise Control

ASR: Anti Slip Regulation

BBW: Brake By Wire

ECB: Electronically Controlled Brake system

ECU: Electronic Control Unit

EHB: Electro Hydraulic Brake actuation system

ESP: Electronic Stability Program

HEV: Hybrid Electric Vehicle

ICE: Internal Combustion Engine

TMC: Tandem Master Cylinder

VDC: Vehicle Dynamic Control

VDM: Vehicle Dynamic Management

1 Presentation of the thesis

The first area of concern of this thesis is the Hybrid Electric Vehicle (HEV) From a hybrid vehicle viewpoint the main issue is relative to the storage of its electric energy in batteries If the vehicle is to be run in an all electric mode or if one wants to make the most of its electric capability then a problem arises which is the autonomy of the vehicle (under 100 km [1]) Indeed, high quantity of electricity is used and in order

to have a sufficient autonomy very big batteries are required thus limiting the occupant volume in the car and in the boot Consequently a compromise has to be found between the volume given to the occupant and the volume occupied by the battery

A solution to this problem exists and consists in recharging the battery while driving This can be done by capturing the vehicle’s kinetic energy lost when braking ; no stops

at the ‘petrol station’ are required anymore and the size of the battery can be lowered With friction brakes (disc or drum brakes) a great part of the kinetic energy is transformed into heat which is not usable Whereas with the electric motor used as an engine brake a substantial braking torque can be provided and the kinetic energy captured and used to recharge the battery This solution is called regenerative braking and the most common braking system of that sort is an Electro-Hydraulic Brake Actuation System (EHB)

The implication of such a system is that the physical link between the brake pedal and the friction system has to be ‘disconnected’: the driver’s brake requirement has to be isolated from the actual braking force That is to say that a control strategy has to be implemented in the vehicle in order to decide whether the car should be braked by friction or by regenerative braking ; the decision will mainly depend on the way the driver applies the brakes and the vehicle motion parameters Consequently if the ECU (Electronic Control Unit) decides to provide the braking only in a regenerative manner then the friction brakes should not be applied even if the driver is actually pressing the brake pedal As a matter of fact, if the connection between the pedal and the brakes does not exist as such anymore, the brake feel associated – i.e the force feedback on the brake pedal due to all the hydro mechanical parts of the braking system – will also disappear as shown in Figure 1

Brake feel is understood as all the braking sensations associated with the braking process It goes from the relationship between the pedal displacement, the required force and the vehicle deceleration, but also the strengthening of the pedal when its travel becomes important etc

Figure 1: Regenerative braking configuration

The brake feel is something highly subjective because it depends on the driver’s sensations Every driver’s braking process is dependant on this brake feel ; everyone knows that the first centimetres of pedal travel provides a light braking whereas the ratio between force applied on the brakes and pedal travel becomes bigger as the pedal is pressed further This brake feel comes from all the mechanical and hydraulic devices that are between the pedal and the brakes but also from the surrounding environment

In regenerative braking one has to find a way to recreate this brake feel because the pedal is free to move since no permanent link with the braking system exists anymore and it is impossible to brake accurately if the driver has no feedback That is why a brake emulator has to be introduced to give the driver the expected feedback The brake emulator should be made of tuneable elements to provide the right pedal feel in accordance with the kind of car it is fitted into (different brake feels are expected for different cars) The tuning step requires some track testing and trial and error processes

to find the right adjustment This tuning method is not cost efficient since it requires the employment of test drivers, to fill the car with measuring devices, to rent a track and to spend time finding the right adjustment for the car A better solution in the first stage of development of regenerative braking – when a car with a ‘normal’ braking system already exists – would be to use the existing data on the ‘normal’ braking system in order to predict the associated brake feel which will in turn give the set of parameters to implement in the brake emulator

The ultimate goal of the brake emulator is to completely avoid the phase of tuning and

to generate the right brake feel first time In order to avoid any experimentation, it is necessary to clearly understand how brake feel is generated by the braking system and which parameters have a greater influence on it In order to achieve this goal, a model of

a braking system has to be implemented in a simulation software and validated with experiments Once it has been validated, the model can be used to assess the brake feel given by any braking system and then can be used the other way round by giving the braking system parameters for a required brake feel

1.2 Subject

As a consequence of what has been previously discussed this thesis is aiming at providing information regarding the influence of a braking system’s parameters on brake feel

The thesis is therefore entitled: investigation of the brake design parameters’ influence

on brake feel

The following objectives will have to be fulfilled:

• Understand how to assess brake feel

• Find all the design parameters of a braking system

• Model the braking system

• Validate the model

• Investigate the influence of the design parameters on brake feel

The modelling and simulation software used is AMESim

2 Literature review

This part aims at summarising the state of the art at the moment with regards to Electro-Hydraulic Brake Actuation Systems, brake feel and brake system models with a critical perspective The information provided here were taken from scientific publications but their scope may be limited to one particular area of the problem or some assumptions may have been made Consequently it is important not to take these information for granted, to keep a critical state of mind and to cross check with other articles It is also worth noticing that this domain of vehicle design is not quite well understood and undergoes a lot of research, therefore a single explanation on which everybody agrees has not yet been found

As it has been said, the study of the specific problem of brake feel comes from the development of regenerative braking through EHB

Today, regenerative braking is receiving increasing attention because of:

• The development of Hybrid Electric Vehicle dictated by environmental, political and socioeconomic issues HEV nowadays seems to be a credible alternative to Internal Combustion Engines (ICE) and fully electric vehicles HEV represents a first step towards a fully electric vehicle [2]

• Fuel economy in HEV By using regenerative braking it is assumed that fuel economy can be enhanced by up to 15% [2]

However, this technology is undergoing some extensive research in order to find the right control strategy that should be used in order to meet fuel economy, emission targets and battery state of charge requirements as well as safety and of course braking requirements [2], [3], [4], [5] For instance the combination of diesel engines – instead

of gasoline engines – with an electric motor seems to be a better solution since diesel engines have a better thermal efficiency But ‘proper matching of the diesel engine, the motor, and the battery pack, and proper modulation between the motor and the engine power flows is crucial to minimising emissions level, while simultaneously increasing overall vehicle fuel efficiency and performance’ [2] The increasing complexity of regenerative braking has forced the companies to use software tools such as ADVISOR

to quantify and optimise the potential benefits of regenerative braking [2]

The first brake-by-wire system called ECB for Electronically Controlled Brake system was implemented on the Toyota Estima Hybrid On top of regenerative braking this car used a Vehicle Dynamic Management system that took braking and driving functions of the hybrid system into account The ECB system was able to:

• Linearly control the hydraulic brake force over the normal operating range,

• Generate the required brake force without the driver feeling the coordination functions of the regenerative and friction brakes,

• Independently control the brake force at each wheel for preventive safety

In order to satisfy these requirements, the ECB system has two subsystems, one that detects the pedal operation of the driver and the other one that controls the hydraulic pressure A failsafe syste m also had to be implemented in order to compensate for any failure of the ECB [3] The system is similar to the one presented in Figure 2

Figure 2: Principle of data and energy flow in Brake-by-wire systems [10]

Regenerative braking is an interesting tool when it comes to fuel economy and emissions and the way to implement regenerative braking in a vehicle is through EHB However EHB in itself can have a much wider use as it has been shown with the Toyota Estima Other functionalities may be [4]:

• Vehicle Dynamic Management • Anti-lock Braking System

• Anti Slip Regulation • Adaptative Cruise Control

• Collision avoidance • Hill-holder systems

It is worth noticing that current technology for passenger cars has not evolved much and still consists of hydraulic actuated friction brakes with some add-on like vacuum booster and ABS The development of this new technology that is EHB, the cost of electronic control getting cheaper, the rising ability to incorporate complicated strategies, the development of electronically controlled pneumatic boosts and vacuum pumps instead of engine driven pumps should make the reader wonder if it is not better

to reconsider the whole brake system design The integration, amplification, modulation and energy generation should be reconsidered and lead towards the next step that is fully electric braking (no more hydraulic system) [4], as it has already been shown with Figure 2 and Figure 3 The brake emulator is a first step in that direction

If one wants to isolate the driver’s brake requirement from the braking force, one has to be able to disconnect the pedal from the actuating mechanism This leads to the fact that the pedal cannot provide any feedback to the driver any more and presents a major problem

Even without EHB the problem of brake feel existed for one good reason which is customers satisfaction [7] Indeed, brake engineers are able to provide braking systems that comply with all the regulations and give a reasonable amount of braking torque but

it is not sufficient to satisfy the customer Customers often judge the braking capacity of

a vehicle by the feel they get from it (soft/hard, long/short travel etc.) These feelings are often expressed in subjective terms and are difficult to interpret in physical terms That is why a process that converts customer’s preference into design parameters would

be of a great help to brake engineers

Several approaches are given in the literature One can either use track tests of several braking systems (from different cars or from different braking system configuration on the same car) and asking people their view about it [6], [7] Or one can use models and simulation in order to produce curves which can then be interpreted with regards to brake feel [8]

An old paper [9] deals with driver’s behaviour during braking Even if it does not concern brake feel directly it is mentioned and the results provided can help understand the complexity of assessing brake feel Indeed experiments were made in order to know

if drivers were able to judge the brake pedal effort, deceleration, speed and distance when braking It turned out that the driver’s judgment was depending on the driving conditions and especially on the surrounding environment It is highly possible that such

an inconsistent judgment also applies to the assessment of brake feel Consequently great care should be taken when dealing with brake feel evaluation

The concept of the tests is to use a brake emulator where physical – objective – parameters can be modified and ask some testers for their impressions on the brake feel under several driving conditions If the number of people doing the test is sufficient then

a relatively good correlation between a subjective feeling and an objective parameter

may be found From the plot of the subjective opinion against objective measure, Figure

4, one can extract two important measures that are:

• The degree of correlation,

• The sensitivity (slope of the best fit line) of one parameter to the other

Figure 4: Objective to subjective correlation [11]

Flat slopes with good correlation indicate that customer do not perceive any difference

in brake feel for that parameter, whereas a steeper slope means that they are sensitive to

a change in the given parameter The method is well explained in [7] but does not provide any real example

The actual use of a similar method to predict brake feel is used in [6] It is considered that the braking law is the combination of two curves:

• The relationship between brake pedal force and brake pedal travel, called the brake pedal characteristic,

• The relationship between the driver’s request and the deceleration of the vehicle, called the command law

For each curve some characteristic features are extracted It turns out that 11 parameters were considered to be sufficient to completely define the braking law They are presented in Figure 5 and Figure 6

Figure 5: Pedal effort vs pedal stroke [6] Figure 6: Deceleration vs pedal stroke [6]

In the same way brake feel was said to be characterised by only 7 attributes:

• Deceleration perceived, • Graduality of the braking,

• Ease of balance (or ease of

modulation)

In this study the degree of correlation was going from 0.98 for pedal travel to 0.56 for

graduality of braking 5 of the 7 attributes had a correlation factor superior to 0.7 which

was considered to be the lowest permitted value for a reliable qualitative indication of

brake feel, Figure 7 Also emergency braking was not tested Two models have then

been created, one that gives the expected brake feel from technical parameters and

another one that predicts the technical parameters from an expected brake feel

Figure 7: Coefficient of correlation between predicted and observed parameters [6]

The same method is also applied in paper [10] The authors explain that brake feel is a combination of brake pedal characteristic, feel of deceleration and driver’s judgement They give a list of variables influencing brake pedal feel in more details:

• Pedal damping and hysteresis, • Vehicle deceleration,

• Environment

Figure 8: Matrix for ‘intelligent’ brake pedal [10]

Then the influence of jump-in and idle travel was assessed for several driving conditions It turned out that different brake feels were expected for different driving conditions as Figure 8 shows This conclusion is very important and confirms what was said previously about being careful when assessing brake feel

This type of reasoning is theoretically correct but it can have some limitations When the degree of correlation is high this method is really useful because conclusions can be drawn But if the degree of correlation is below a given value, say 0.7, then it means that one cannot really assume that the objective parameter has an impact on the subjective sensation Consequently, no conclusions can be drawn and time and money have been lost Furthermore no mistake is allowed for the testing because it occurs only once It means that if someone has forgotten to ask one question or if another parameter has been found later in the research its impact cannot be evaluated unless another experiment is run That is why a computer based model is maybe a safer solution since many different parameters can be measured at any moment in time and almost all design parameters can also be tuned Therefore the scope of a computer based model is much wider but maybe less accurate compared with real on-road tests

The second method for predicting brake feel is by deriving the braking system equations and by giving them a physical interpretation [8] In this paper the authors have created a method for computing brake system design parameters directly from specific requirements such as stopping distance, pedal travel, braking efficiency or thermal requirements However no mention was made of customer’s requirements, but it is not a

problem since this model can provide the braking law from which brake feel can be predicted as it has just been proven In this paper it was said that 8 parameters were sufficient to characterise a typical disc brake system Again, the braking system was divided in two subsystems For each subsystem 4 physical component parameters were defined For each set of parameters, independent constrains were used to define them One should note that brake specific torque is made-up of the piston area, rotor effective radius and friction coefficient

Proportioning valve knee pressure

Maximum deceleration rate/braking efficiency Proportioning valve slope Deceleration rate at proportioning

valve knee pressure Front brake specific

torque

Braking efficiency at proportioning valve knee pressure

force/deceleration rate Booster reaction ratio Booster runout pedal force/

deceleration rate Apply system

Booster area Packaging, available hardware

By relating each component parameter to a

more subjective set of requirements the

brake engineer can select the right

component design with regards to the

wanted requirements by solving the set of

coupled equations as Figure 9 shows This

method has the advantage of providing a

design solution where all the specific

requirements should be met It also allows

the engineer understanding the relationship

between the various components that must

be maintained to satisfy the requirements

However in order to solve the equations the

number of requirements has to be equal to

the number of design parameters That is to

say that one has to rank the design

parameters in a preferential order since

generally there are more than 8

requirements to design a brake system

Figure 9: Flow-down design method [8]

In [11] the author says that there are 9 features affecting brake feel:

• Initial pedal travel • Initial effort

• Intermediate pedal travel • Intermediate effort

• High deceleration pedal travel • High deceleration effort

• Path motion

It is interesting to see that for the four last examples the set of characteristics defining brake feel are not the same In the first, second and last case the parameters are the consequences of the brake design parameters because the selection of those parameters

is based on the final braking law In the third case the parameters are the physical dimensions of the braking system The latter seems to be more logical because it is really what creates the shape of the braking law Furthermore in the other papers brake feel was influenced by varying the brake parameters which in turn had an impact on the braking law Even if it is better to deal with the problem at its source by taking the braking parameters as input one has to be aware of the fact that there are not only 8 design parameters, consequently the problem has been simplified The type of braking fluid used, the length of the pipes, the material of the braking discs also have their importance That is why the solution that only considers the braking law is maybe better because it shows the final results, which is what matters

It has been proven in [12] that the lining properties of a brake system had no influence

on brake feel

Other researchers have looked at ways to recreate brake feel In [16] the authors have tested two different brake emulators The first one uses a gas filled metal bellows in conjunction with a coil spring, whereas the second one uses variable rate rubber spring Those two solutions were simply used to replace the vacuum booster, the master cylinder remained in use for safety reasons

A normal braking system works as follows When the driver presses the brake pedal the force that is applied is multiplied by the pedal ratio which is then increased thanks to the vacuum booster The pushrod coming from the vacuum booster is linked

to the piston of the tandem master cylinder where hydraulic pressure is built and split in two hydraulic circuits (generally one for the front and one for the rear) A proportioning valve is used to prevent the pressure from being too important in the rear brakes so that the rear wheels are not locked before the front wheels (for stability reasons mainly) The hydraulic pipes are then linked to the piston of the calliper which compresses the disc between the two pads thus decelerating the vehicle

The phenomena that occur in a braking system are really complex and highly non linear because of the fact that fluids are compressible, non-wanted friction occurs in all components (pipes, hoses etc.) and wanted friction between the discs and the pads is

so far not well understood either Consequently many models have been developed to

have a better understanding of such a vital system The models either consist of analytical ones where the solution of the equations are found thanks to mathematical software such as Matlab/Simulink [13] [14] [15], or the models can also be implemented in simulation software such as AMESim [16] [17] In both cases it is the validation of the model that is the most important part of the work

The model given in [13] is an analytical dynamic model of a brake apply system including brake pedal, vacuum booster, master cylinder and proportioning valves The interactions with the wheel brake system, which comprises the front and rear foundation brakes, are included by modelling their compliances The model described is quite complex and realistic

Figure 10: Lumped parameter of a vacuum booster [13]

The vacuum booster was modelled by two chambers on either side of the power piston

as shown on Figure 10 The check valves were considered to be relief valves that allow air flow in one direction only to provide vacuum in the booster The master cylinder was modelled using the position of the by-pass holes and the area of the pistons A lot

of care was given to the proportioning valve model and two different sorts were tested Eventually the front and rear brakes were modelled as capacitance based on the assumption that a given line pressure results in a certain displacement of the piston Validation experiments have shown that the vacuum supplied by the engine was not constant and was varying by up to 30% and this vacuum transient was not taken into account in the model The most interesting result was that the discharge coefficient and the friction constants of the proportioning valve piston and check valve poppet were greatly affecting the dynamic response of the apply system However the predictions were pretty close to the experiments

Another model using AMESim was described in [17] and is given in Figure 11, Figure

12 and Figure 13 A passive braking model was developed paying great attention to the vacuum booster in both semi-stationary and dynamic conditions Then the callipers, roll-back and thermal phenomena were modelled Eventually ABS and VDC were added to the model It was possible to see the typical zone of idle travel, boost effect, booster saturation, jump-in and hysteresis Some design modifications were tested in

order to see their influence on brake feel (booster reaction disc diameter as shown in Figure 14, vacuum level)

Figure 11: Tandem master cylinder model [17] Figure 12: Floating calliper simple model [17]

Figure 13: Floating calliper with thermal model

in order to make the model work in a proper way

The model developed in [14] first finds the variation of hydraulic pressure with the pedal force, from which the friction and braking forces are calculated They are then introduced into the vehicle’s equations of motion which take into account the slip between tyre and ground, rolling resistance and aerodynamic drag This set of equations

is then solved using Newmark Integration Method Then a thermal analysis of disc and drum brakes was done looking at heat transfer by convection, radiation and conduction The authors say that the model is in very good agreement with tests, to such an extent that it can replace road tests This model has been used in particular to optimise the hydraulic pressure in the rear brakes A higher pressure was used without locking the rear wheels hence achieving better braking capability However the authors do not explain how they managed to find the hydraulic pressure in the braking system ; it is therefore difficult to completely follow their reasoning

An insight into air-over-hydraulic brake system model is given in [15] This model deals in details with the pipings that are known to have a great effect on the response characteristic and hence on brake feel as Figure 15 shows It has been modelled from fundamental principles by considering that fluid is compressible and given the dimensions of a brake line, turbulent flow was assumed Here again it is said that heat release (which was not modelled) has a great influence on the pressure curves and explain the difference between simulations and experiments

Figure 15: Fluid displacement in braking system [18]

Paper [18] deals with the tandem master cylinder According to the authors three functions are to be performed:

• Ensuring that there is no pressure in the wheel brake when the pedal is not actuated That is why the chambers are connected to t he reservoir via the compensation ports,

• Separating the connection between pressure chamber and the reservoir so that pressure can be built up,

• Fluid compensation in the brake circuit due to wear For this, brake fluid must

be fed into the chambers from the reservoir

The main problem that all researchers came up with was the modelling of non linear phenomena, e.g loss by friction, seals, rubber, fluid compressibility The other problem was the one related to the dynamic behaviour of the system

It has been shown that the investigation of brake feel was of most importance because it represents a necessary step towards EHB and brake-by-wire systems

The investigation of the parameters influencing brake feel suggests that several concepts are to be understood First, brake feel has to be defined Then the parameters that can potentially influence it have to be listed A model has to be developed based on those parameters Afterwards, the most important step consists in validating the model Finally the influence of the brake design parameters on brake feel can be assessed

One has to agree that brake feel is something subjective But this feeling mainly comes from the design of the brake system even if the driver and the environment also play a role Given that no survey can be made with people for cost and time constrains, the definition of brake feel will only be based on empirical curves and key parameters ;

it is assumed that brake feel is only defined by the braking law The parameters influencing brake feel will be the design parameters of the braking system and their influence on brake feel will be assessed by studying the variation of the braking law curves, which will be similar to the one given in Figure 5 and Figure 6 Then, the simulation conditions have to be chosen They are:

- Vehicle speed: 30 m/s,

- Braking force reaching 200 N (see section 3.6 for more details)

The model that will be developed to study brake feel will take into account as many design parameters as possible in order to be the most accurate However, in the first place the global parameters given in the literature will be implemented and in a second time a more detailed model will be created ; the model will be limited to the basic braking system, that is to say that additional systems like ABS etc will not be modelled

3 The braking system model

Based on the literature review the model should provide enough information to allow plotting pedal force, pedal stroke and vehicle deceleration In order to investigate the influence of the design parameters the model should also be made tuneable, that is

to say that each component of the braking system should be clearly identified, its model should be representative of the real component and its characteristics physically understandable

Nowadays the trend is to fit most vehicles with disc brakes for both the front and the rear Depending on the vehicle’s weight either an X or II split path configuration is used For practical reasons it seems better to choose the II configuration for the model That way the model is symmetrical and one can clearly separate the front and the rear of the vehicle and study their impact separately

The components to be modelled in order to give a relatively accurate representation of the braking system are:

• The brake pedal

• The vacuum booster

• The master cylinder

All the electronic devices such as ABS and ESP are not be modelled as well for time and complexity reasons Furthermore it is in agreement with the previous argument: if the study only focuses on small decelerations on normal roads then ABS should not be used nor ESP or any kind of electronic control device

AMESim is already provided with a brake system model It is made of a vacuum booster, a master cylinder and the callipers This paragraph briefly describes the model and summarises the comments that were made about it in the help menu Furthermore, potential problems and differences with the required model will be put forward

3.2.1 The global model

The global model is shown in Figure 16

Figure 16: Global braking system model

Some comments can be made on this global design:

• the configuration is an X-split path That is to say that each chamber of the tandem master cylinder is linked to one wheel at the front and another wheel on the opposite side at the rear,

• the four brakes are disc brakes,

• the brake lines are of different length and their length suggest that the master cylinder is situated at the rear of the vehicle since the pipes to reach the front callipers are longer than that to reach the rear It is quite an unusual configuration,

• there is no proportioning valve for the rear brakes,

• the brake pedal has not been modelled,

• there is no vehicle model

The elements presented on this figure are supercomponents That is to say that it is a component which is made of other components Consequently one can go in more details in the model

3.2.2 The vacuum booster

The vacuum booster is modelled as shown in Figure 17

Figure 17: Vacuum booster model

This model is based on the vacuum booster shown in Figure 18, which corresponds to the one described earlier in the literature review [13]

Figure 18: Vacuum booster drawing [13]

If one looks closer at the model, one can see 4 distinct parts as shown in Figure 19 and the way it works is explained on the simplified schematic in Figure 20 The plunger is the rod that is connected to the brake pedal and receives the braking force Its action can

be split in two Firstly it is directly (there is still a small gap, 0.8mm in the model for instance) linked to the reaction disc Therefore the force is transmitted with a ratio of 1,

there is no assistance, it can be seen as a safety design in case the assistance does not work Its second role is to move the sliding mechanism which is going to isolate the two chambers and then open the atmospheric pressure valve to create the assistance That is why there is a position transducer on the sliding mechanism model Depending on its position either there is a vacuum in the two chambers (one can see that the engine depression is linked to the two chambers of the piston) or atmospheric pressure comes

in and the engine depression fills only one port of the piston The force created is then added to the direct force from the plunger and gives the final assistance

Figure 19: Vacuum booster analysis

Figure 20: Vacuum booster schematic

The major problem of such an element is the consideration of internal movements of the rubber part noted and called the reaction disc (or elastic disc) This part is inserted in the

"exit" rod The static behaviour and so the pneumatic amplification of the booster

derives from the quality of the model of this rubber part In this model the stiffness of the rubber reaction disc is considered linear As a result the jump in phenomenon which usually appears at the end of the dead zone is not represented, see Figure 21

Figure 21: Booster characteristic curve

It has already been said in the literature review that the most complex part to model was the vacuum booster This model confirms that statement and that is why no changes will

be made since the non linearity are much too complex to model and go beyond the scope of this study

The model of the master cylinder is the one presented in Figure 22

Figure 22: Master cylinder model

If one looks at Figure 23 one can understand the role of each of the model’s components The force coming from the vacuum booster through the rod is the input of the model This force is acting on the primary piston (1) which compresses the fluid in the primary chamber (5) and builds up pressure that go to the front brakes This pressure

is also used to push the secondary piston (2), the mechanical link via the spring is also modelled (4) The secondary piston and its spring are modelled by block (3) and pressure is built up in chamber (6) Block (7) is here to represent the case when the primary piston has travelled the whole way until it touches the secondary piston, at this point there is a contact between the two pistons

Figure 23: Physical interpretation of the master cylinder’s model [23]

For the master cylinder, the main function modelled is the piston effect within its two chambers One can notice that the brake fluid reservoir has not been modelled, therefore

a back pressure remains in the circuit after the brake pedal has been released It implies

a non zero force acting on the brakes even when there is no force acting on the brake pedal, as Figure 24 shows The master cylinder model only takes into account the restrictions on the output of the front chamber, the rear chamber has restrictions but with a big hole diameter The proportioning valve has not been modelled but it is not a problem as it has been justified in the model requirements The friction force as a function of the pressure is also not taken into account

Figure 24: Global braking system characteristic

There is also a problem in the titles of the labels which do not correspond to the X-split path that is suggested by the global model Indeed, when one explores the supercomponent one can see the labels of the ports

Figure 25: Master cylinder’s hydraulic configuration

According to the master cylinder model port 1 and 4 are meant to be linked to the front left and right calliper and correspond to the two first port on the submodel icon But the two ports of the submodel icon are linked to the front right and rear left callipers as Figure 16 and Figure 25 show The same thing can be applied to the rear brakes

The calliper has been modelled as shown in Figure 26

Figure 26: Calliper model

The callipers are modelled with their mechanical equivalent stiffness mainly due to the hydraulic stiffness of the brake hoses The pressure that has been built up by the whole system comes in at the pressure port Then it makes the piston move towards the left side and compresses the disc brake which has only been modelled as a gap and a contact force In fact when the program is run, one just looks at the force applied at the pads’ ports The gap between the pad and the disc is modelled by the bottom mechanical block (it is set at 3mm) The brake pad was modelled by a zero displacement block on the left and a moving part on the right, consequently it can be said that the model represents a fixed calliper

The rollback effect due to the piston seal which leads to retraction of the piston is not taken into account in the model Nor is the dynamic of the vehicle since the disc is not rotating and has no inertia, it is therefore impossible to know the vehicle deceleration whereas it is an important feature to assess brake feel as it has already been proven by the literature review

When one looks closer at the calliper model one can see that the braking force is computed on the left pad where the gap and the spring are connected Figure 27 shows how the force is distributed in the calliper when 400N are applied on the vacuum booster It can be seen that a force is already applied to the brake pads even if the clearance between the pads and the disc is not null This force corresponds exactly to the force acting in the spring in parallel When the clearance eventually becomes zero (and then turns negative because there is some penetration to model the compliances of the pad) then the contact force is build and added to the spring force already existing

Figure 27: Force distribution in the calliper

Consequently this model, even if it is working correctly, does not give the right physical interpretation of what is really occurring in the calliper Only the contact force when the gap is zero should be taken into account

A problem occurred with the calliper that was related to the role of the spring in parallel with the gap As it was said before, it is probably to model some compliances but by doing so the physics of the system is lost As the seal was not modelled it has been assumed that it would be used to model the rubber seal between the piston and the housing Indeed, this seal is used to prevent any leak of the oil onto the pads, but it is also used as a return spring so that the pad and the disc do not touch any more when the brake pressure is released In that case the spring should be mounted in series with the gap Consequently the new brake calliper model should look like the one in Figure 28

Figure 28: New brake calliper