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Analysis and design of automotive brake systems
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ENGINEERING DESIGN
HANDBOOK
DARCOM PAMPHLET DARCOM-P 706-358
ANALYSIS AND DESIGN OF
AUTOMOTIVE BRAKE SYSTEMS
HQ,us ARMY MATERIEL DEVELOPMENT &READINESS COMMAND DECEMBER 1976
DARCOM·P 706-358
LISTOFILLUSTRATIONS
Fig. No.
I-I
1-2
1-3
2-1
2-2
2-3
2-4
2-5
2-6
2-7
2-8
2-9
2-10
2-11
2-12
2-13
2-14
2-15
2-16
2-17
2-18
2-19
2-20
2-21
2-22
2-23
2-24
2-25
3-1
3-2
3-3
3-4
3-5
3-6
3-7
3-8
3-9
3-10
4-1
4-2
4-3
4-4
5-1
viii
Title Page
Idealized Deceleration Diagram I-I
Mean Deceleration as a Function of Initial Velocity
for a Maximum Deceleration ofO.8lg and Different
Time Delays 1-2
Dynamic Axle Load of a 3-Axle Tractor-Semitrailer 1-3
Basic Drum Brakes 2-2
Disc Brake :..................... 2-3
Basic Disc Brakes 2-3
Brake Shoe Geometry 2-4
Disc Brake Clearance Adjustment 2-5
Self-Energizing in a Drum Brake 2-6
Leading Shoe Analysis 2-7
Measured Pressure Distribution Over Lining Angle a
for Different Linings 2-8
Computed Pressure Distribution as a Function of Wear
After Successive Brake Applications 2-9
Pressure Distribution on a Disc Brake 2-9
Leading Shoe With Pivot 2-11
Brake Factor Curves for Different Lengths of Distance a' 2-11
Leading Shoe With Parallel Sliding Abutment 2-12
Leading Shoe With Inclined Abutment 2-12
Duo-Servo Brake With Sliding Abutment 2-13
Duo-Servo Brake With Pivot 2-14
Brake Shoes of Different Stiffness 2-14
Brake Torque vs Temperature for Different Brake
Line Pressures (215, 430, 645 psi) 2-15
General Design of External Band Brake 2-15
Single Application External Band Brake 2-16
Opposing Application External Band Brake 2-16
Inline Application External Band Brake 2-16
Self-Energizing of Caliper Disc Brake 2-17
Schematic ofSelf-Energizing Full Covered Disc Brake 2-17
Comparison of Measured Braking Performance of Disc
and Drum Brakes for a Truck 2-18
Heat Distribution for Continued Braking 3-4
Physical System Representing Brake Rotor 3-5
Ventilated Disc 3-10
Radiative Heat Transfer Coefficient as Function of Temperature 3-11
Thermal Model for Finite Difference Computation (Drum Brake Shown) 3-12
Brake Lining Temperature Attained in Fade Test 3-14
Brake Lining Temperature Attained in Brake Rating Test 3-14
Thermally Loaded Surface Element Resulting in Surface Rupture 3-17
Flat Plate Representation ofBrake Rotor 3-18
Thermal Stresses at the Surface Attained in Stops from 60 and 80 mph 3-19
Integrated Foundation Brake/Retarder Control System . . . . . 4-3
Hydrodynamic Retarder Performance Characteristics 4-4
Distribution ofBraking Energy Between Retarder and Foundation
Brakes for 60 and 40 mph Stops for Optimum Lining Life Design 4-5
Distribution of Braking Energy Between Retarder and Foundation
Brakes for a 60 mph Stop for Minimum Stopping Distance Design 4-5
Hydraulic Brake System 5-2
DARCOM·P 706-358
LIST OF ILLUSTRATIONS (Continued)
Fig. No.
5-2
5-3
5-4
5-5
5-6
5-7
5-8
5-9
5-10
5-11
5-12
5-13
5-14
6-1
6-2
6-3
6-4
6-5
7-1
7-2
7-3
7-4
7-5
8-1
8-2
8-3
8-4
8-5
8-6
8-7
8-8
8-9
8-10
8-11
8-12
8-13
8-14
8-15
8-16
8-17
8-18
8-19
Title
Hydrovac in On Position ..
Mastervac in Applied Position .
Mastervac Characteristics .
Vacuum Booster Design Chart .
Schematic of Pump Power Hydraulic Brake System .
Line Pressure/Pedal Force Diagram for Full Power
Hydraulic Brake System .
Schematic of Hydraulic Booster .
Accumulator Design Chart .
Air-Over-Hydraulic Brake Unit .
Air-Over-Hydraulic Brake System (Single Circuit) .
Air-Over-Hydraulic Brakes for Tandem Axle Truck .
Air-Over-Hydraulic Brake Characteristic .
Schematic of Parking Brake .
Tire Friction Versus Wheel Slip : ..
Friction-Slip Curve for Dry Concrete as Function of
Speed .
Friction-Slip Curve for Wet Concrete Road as a
Function of Speed Obtained for an Automobile Tire .
Typical Coefficient of Friction Itx Between Tire and Road
for Truck Tire .
Forces Acting on a Free-Rolling Wheel .
Brake Factor - Lining Friction Curves for Typical Drum
Brakes .
Forces Acting on a Decelerating Vehicle .
Braking Performance Diagram of a Two-Axle Truck .
Braking Efficiency of a Two-Axle Truck .
Tractor-Semitrailer Vehicle Model ..
Forces Acting on a Decelerating Vehicle .
Dynamic Braking Forces .
Normalized Dynamic Brake Forces .
Parabola of Normalized Dynamic Braking and Driving Forces .
Normalized Dynamic and Actual Brake Forces .
Tire-Road Friction Utilization .
Braking Efficiency Diagram .
Braking Efficiency Affected by Pushout Pressures .
Simplified Vehicle Model .
Rear Braking Efficiency as Function of Speed and Road
Curvature for a Tire-Road Friction Coefficient of 0.6 .
Forces Acting on a Braking and Turning Vehicle .
Braking Efficiency for Combined Braking and Turning (Fiat 124)
Vehicle Behavior With Rear and Front Wheels Locked .
Definition of Scrub Radius .
Tandem Axle Suspensions .
Forces Acting on a Tandem Axle Truck .
Dynamic Axle Loads for a Truck Equipped With Walking
Beam Suspension .
Tire-Road Friction Utilization for a Truck Equipped
With Walking Beam Suspension .
Braking Efficiency Diagram for a Truck Equipped With
Walking Beam Suspension ..
Page
5-7
5-8
5-9
5-11
5-12
5-12
5-13
5-14
5-16
5-16
5-16
5-17
5-17
6-2
6-3
6-3
6-3
6-4
7-4
7-5
7-6
7-6
7-7
8-4
8-5
8-5
8-6
8-7
8-8
8-8
8-12
8-13
8-14
8-14
8-17
8-17
8-18
8-18
8-19
8-21
8-21
8-21
ix
DARCOM.p 706-358
LIST OF ILLUSTRATIONS (Continued)
Fig. No.
8-20
8-21
8-22
8-23
8-24
8-25
8-26
8-27
8-28
8-29
8-30
8-31
8-32
8-33
8-34
8-35
8-36
8-37
8-38
8-39
8-40
8-41
8-42
8-43
8-44
8-45
9-1
9-2
9-3
9-4
9-5
9-6
9-7
x
Title Page
Dynamic Axle Loads for a Truck Equipped With Two-Elliptic Leaf
Suspension 8-22
Tire-Road Friction Utilization for a Truck Equipped
With Two-Elliptic Leaf Suspension 8-22
Dynamic Axle Loads for Improved Two-Elliptic Leaf Suspension 8-23
Tire-Road Friction Utilization for Improved Two-Elliptic
Leaf Suspension 8-23
Two-Leaf-Two-Rod Suspension 8-23
Tire-Road Friction Utilization for Truck Equipped
With Two-Leaf-Two-Rod Suspension 8-24
Tire-Road Friction Utilization for Optimum Brake
Force Distribution 8-24
Two-Leaf Suspension With Equal Dynamic Axle Loads..................... 8-24
Dynamic Axle Loads for a Two-Leaf-Equal Axle Load
Suspension 8-25
Forces Acting on a Decelerating Tractor-Semitrailer 8-26
Normalized Dynamic Braking Forces of a Tractor-Semitrailer 8-27
Dynamic Braking Forces of the Tractor of a Tractor-Semitrailer Combination 8-27
Tire-Road Friction Utilization for a Loaded Tractor-Semitrailer 8-29
Tire-Road Friction Utilization for an Empty Tractor-Semitrailer 8-29
Forces Acting on a Tractor-Semitrailer Equipped With
Two-LeafSuspension 8-32
Dynamic Axle Loads for a Tractor-Semitrailer Combination 8-33
Braking Performance Diagram for a Tractor-Semitrailer Combination 8-33
Forces Acting on a Tractor-Semitrailer Equipped With
Walking Beam Suspension 8-34
Forces Acting on a Tandem Axle Tractor-Tandem Axle
Semitrailer Combination 8-35
Dynamic Axle Loads for a Tandem Axle Tractor-Tandem Axle
Semitrailer Combination 8-36
Braking Performance Diagram for a Loaded Tandem Axle
Tractor-Tandem Axle Semitrailer Combination 8-36
Braking Efficiency Diagram for a Tandem Axle TractorTandem Axle Semitrailer Combination 8-36
Axle Brake Forces 8-36
Forces Acting on a Tractor-Semitrailer-Double-Trailer
Combination 8-37
Braking Performance Diagram for a Tractor-Semitrailer-DoubleTrailer Combination 8-38
Rotational Inertias of a Rear Wheel Driven Vehicle 8-38
Dynamic and Actual Bilinear Brake Forces of Two-Axle
Vehicle '" .. 9-2
Braking Efficiency for Bilinear Distribution 9-3
Dynamic and Actual Brake Line Pressures 9-5
Brake Line Pressures for a Vehicle Weight of 47421b 9-5
Braking Efficiency Diagram for a Vehicle Weight of
47421b 9-5
Pedal Force Required for Fixed and Variable Ratio
Braking 9-6
Dynamic Brake Line Pressuies for Combined Braking and
Turning 9-7
DARCOM-P 706-358
LIST OF ILLUSTRATIONS (Continued)
Fig. No.
9-8
9-9
9-10
9-11
9-12
9-13
9-14
9-15
9-16
9-17
9-18
9-19
9-20
9-21
9-22
9-23
9-24
9-25
9-26
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-10
10-11
11-1
11-2
Title
Normalized Dynamic Braking ForceDistribution .
Schematic Brake Force Distribution, Cases I and 2 .
Tire-Road Friction Utilization, Cases I and 2,
Wz = 43,000 Ib .
Schematic Brake Force Distribution, Cases 3 and 4 .
Tire-Road Friction Utilization, Cases 3 and 4.
Wz = 27,000 Ib .
Schematic Brake Force Distribution, Case 5 .
Tire-Road Friction Utilization, Case 5, Wz = 11,500Ib .
Schematic Brake Force Distribution, Case 6 .
Tire-Road Friction Utilization, Case 6, Wz = 11,500lb .
Schematic Brake Force Distribution With Proportioning
Valves on Tractor Rear and Standard Brakes on
Trailer Axle .
Tire-Road Friction Utilization, Case 7, Wz = 11,500Ib .
Schematic Brake Force Distribution, Case 8 .
Tire-Road Friction Utilization, Case 8, Wz = 43,000 Ib .
Dynamic Brake Line Pressures for the Tractor of a
Tractor-Semitrailer Combination .
Brake Line Pressure Variation as Function of Spring
Deflection on Trailer Axle .
Tire-Road Friction Utilization for 3-S2TractorSemitrailer Combination (Empty) With Standard
Brakes (No Front Brakes) .
Tire-Road Friction Utilization for 3-S2TractorSemitrailer Combination (Loaded) With Standard
Brakes (No Front Brakes) .
Tire-Road Friction Utilization for 3-S2TractorSemitrailer (Empty) With Proportioning (No Front
Brakes) .
Tire-Road Friction Utilization for 3-S2Tractor-Semitrailer (Empty) With Front Brakes and Proportioning .
Idealized Tire-Road Friction Slip Characteristics .
Brake Torque Rate - Induced by Driver .
Wheel-Antilock Control for an Air Brake System .
Independent Front, Select-Low Rear, Control Method
Wheel-Antilock Brake System .
Typical One-Stage Vacuum-Assisted Modulator .
Oscillograph Record for Stop With Antilock System
Disabled, Dry Road Surface .
Oscillograph Record for Stop With Antilock, Dry
Road Surface .
Schematic of Pump Pressurized Wheel Antilock System .
Schematic ofWheel Antilock Modulator .
Measured and Computed Performance for Pneumatic WheelAntilock System .
Comparison of Stopping Distance on Slippery Road
Surface for a Tractor-Semitrailer Combination .
Measured Steady-State and Transient Brake-Line
Pressure/Pedal Force Response .
Schematic of Pressure Rise in Air Brake System .
Page
9-8
9-9
9-9
9-10
9-10
9-11
9-11
9-12
9-12
9-13
9-13
9-14
9-14
9-15
9-16
9-17
9-17
9-18
9-18
10-3
10-3
10-5
10-6
10-7
10-9
10-9
10-10
10-11
10-13
10-.15
11-2
11-4
xi
DARCOM.p 706-358
LIST OF ILLUSTRATIONS (Continued)
Fig. No.
11-3
11-4
12-1
12-2
12-3
12-4
12-5
12-6
12-7
12-8
12-9
12-10
\2-\1
12-12
14-1
14-2
14-3
14-4
14-5
14-6
14-7
14-8
14-9
14-10
14-11
14-12
14-13
14-14
14-15
14-16
14-17
14-18
14-19
14-20
14-21
14-22
14-23
15-1
15-2
15-3
15-4
15-5
xii
Title Page
Air Brake System Schematic............................................... 11-4
Brake Response Times for Tractor-Semitrailer Combination 11-5
Different Dual-Circuit Brake Systems 12-6
Tandem Master Cylinder 12-8
Calculated Deceleration in g-Units for Partial
Failure................................................................. 12-10
Maximum Pedal Travel Ratios Required for Partial Failure
Stops, System 1 12-11
Normal Pedal Travel Ratios Required for Partial Failure
Stops, System 1 12-12
Pedal Travel Ratio as a Function of Piston Travel
Utilization 12-12
Stepped Bore Tandem Master Cylinder 12-13
Comparison of System Complexity 12-14
Dual Systems, Front Brake Failure Due to Brake Fluid
Vaporization........................................................... 12-15
Braking Performance Diagram for a Vacuum Assisted Brake
System 12-16
Fade EffectivenessDiagram 12-17
Steering Schematic 12-18
Brake Factor Characteristic ofa Duo-Servo Brake.......................... 14-6
Brake Sensitivity 14-6
Emergency Brake Performance, VehicleNo.1.............................. 14-8
Emergency Brake Performance, VehicleNo.3.............................. 14-8
Emergency Brake Performance, VehicleNo.4.............................. 14-8
Emergency Brake Performance, VehicleNo.6.............................. 14-8
Road Gradient on Which VehicleNo.3 Can Be Held
Stationary 14-9
Downhill Emergency Braking Capability of VehicleNo.6................... 14-9
Normalized Dynamic and Actual Brake Forces, Vehicle No.1.............. 14-10
Normalized Dynamic and Actual Brake Forces, Vehicle No.3.............. 14-11
Normalized Dynamic and Actual Brake Forces, VehicleNo.4"............... 14-11
Normalized Dynamic and Actual Brake Forces, VehicleNo.6............... 14-11
Braking Efficiency,VehicleNo.1.......................................... 14-12
Braking Efficiency,VehicleNo.3.......................................... 14-12
Braking Efficiencyof Loaded Vehicle I as Function of
Brake Force Distribution rP for a Tire-Road Friction
Coefficient of 0.8 14-12
Braking Efficiency,VehiclesNo.4 and 6 14-12
Braking Performance Diagram, VehicleNo.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-13
Braking Performance Diagram, VehicleNo.6.............................. 14-13
Normalized Dynamic and Actual Brake Forces............................. 14-14
Braking Efficiencyfor Fixed Ratio Braking, rP = 0.52 14-15
Normalized Dynamic and Actual Forces for Variable Ratio Braking......... 14-16
Braking Efficiencyfor Variable Ratio Braking 14-16
Dynamic and Actual Brake Line Pressures 14-16
Hydraulic Brake System................................................... 15-1
Master Cylinder 15-2
Residual-Pressure Check ValveOperation ,......................... 15-3
Primary Seal Operation 15-3
Stepped Master Cylinder 15-4
DARCOM.p 706-358
LIST OF ILLUSTRATIONS (Continued)
Fig. No.
15-6
15-7
15-8
15-9
15-10
15-11
15-12
15-13
15-14
15-15
15-16
15-17
15-18
Title
Single Acting Wheel Cylinder .
Double Acting Wheel Cylinder .
"S" Cam and Wedge Brake .
Brake Shoe Adjustment .
Hydrovac Brake System .
Dual Circuit Mastervac Brake System .
Air-Over-Hydraulic Brake Operation .
Tractor-Semitrailer Air Brake System .
Brake Application Valve .
Quick-Release Valve .
Relay Quick-Release Valve .
Air Brake Chamber .
Brake Chamber With Spring Brake .
Page
15-5
15-5
15-5
15-6
15-7
15-7
15-8
15-9
15-10
15-11
15-12
15-13
15-13
xiii
DARCOM.p 706-358
xiv
Table No.
2-1
3-1
3-2
3-3
6-1
8-1
8-2
9-1
10-1
10-2
10-3
10-4
14-1
14-2
14-3
14-4
14-5
14-6
14-7
14-8
14-9
LIST OF TABLES
Title
Disc and Drum Brake Comparison .
Roots of Transcendental Equation .
Brake Design Values .
Energy Absorption Capacity of Various Fluids .
Tire Rolling Resistance Coefficients .
Tandem AxleTruck Data .
VehicleData for Tractor-Semitrailer Calculations .
Tractor-Semitrailer Data .
Evaluation of Vacuum Powered Wheel-Antilock Brake .
Passenger Car Wheel-Antilock Brake SystemTest Data .
PassengerCar Test Speed. mph .
Tire-Road Friction Coefficients .
BFj VSilL •••••••••••••••••••••••••••••.•••••.••••••.••••••••••••••••••••••
Fd2/ Fax vsilL •••••••••••••••.••••.•..••.••..•..•••••. , .••••••••••••••••••••
Fax / Fa VS ilL •.••••••••••••••••••.•••••••••••••••.•••........... \••••••.••••
BEl VS ilL ••••••••••••••••••••••••••••.••••.•.....•.•.••••••••••••••••.••••
BFvSIlL .
So VSIlL ••'•••••••••••••••••••••••••••••.•.••......••••..••..••••••••••••••
Loading and Geometrical Data .
Brake System Design and Performance Data .
Geometrical and Loading Data .
Page
2-10
3-6
3-7
3-15
6-4
8-20
8-30
9-17
10-10
10-14
10-14
10-14
14-4
14-5
14-5
14-5
14-5
14-6
14-7
14-7
14-14
DARCOM·P 706-358
PREFACE
The Engineering Design Handbook Series of the US Army Materiel Development and Readiness Command is a coordinated series of handbooks containing basic information and fundamental data useful in
the analysis, design, and development of Army materiel and systems.
This handbook treats the braking of motor vehicles such as passenger cars, trucks, and trailers. No
attempt has been made to address fully the braking of specialty vehicles. However, the engineering
relationships presented can be applied to the analysis of any automotive braking system, including those of
tanks and special carriers.
The text is structured so that it can be used by junior engineers with a minimum of supervision provided
by a senior engineer. Chapters 2,3,4,5, and 6 present the analysis of brake system components and should
provide sufficient detail for the computations required for the analysis of entire brake systems. Chapter 7
and those that follow address the analysis and design of the brake system of motor vehicles including the
computation of partial braking performance with the brake system in a failed condition. The examples in
Chapter 14 are presented in considerable detail to provide the engineer with insight into the methodology
used in solving brake problems. A brief description of brake system hardware is provided in Chapter IS for
the engineer not fully familiar with the functioning of various brake system components.
This Handbook was written by Dr. Rudolf Limpert, Salt Lake City, Utah, for the Engineering Handbook Office, Research Triangle Institute, prime contractor to the US Army Materiel Development and
Readiness Command. The handbook is based on lecture material and practical experience gained in industry and university research.
The Engineering Design Handbooks fall into two basic categories, those approved for release and sale,
and those classified for security reasons. The US Army Materiel Development and Readiness Command
policy is to release these Engineering Design Handbooks in accordance with current DOD Directive
7230.7, dated 18 September 1973.All unclassified Handbooks can be obtained from the National Technical
Information Service (NTIS). Procedures for acquiring these Handbooks follow:
a. All Department of Army activities having need for the Handbooks must submit their request on an official requisition form (DA Form 17, date Jan 70) directly to:
Commander
Letterkenny Army Depot
ATTN: DRXLE-ATD
Chambersburg, PA 17201
(Requests for classified documents must be submitted, with appropriate "Need to Know" justification, to
Letterkenny Army Depot.) DA activities will not requisition Handbooks for further free distribution.
b. All other requestors, DOD, Navy, Air Force, Marine Corps, nonmilitary Government agencies, contractors, private industry, individuals, universities, and others must purchase these Handbooks from:
National Technical Information Service
Department of Commerce
Springfield, VA 22151
Classified documents may be released on a "Need to Know" basis verified by an official Department of
Army representative and processed from Defense Documentation Center (DDC), ATTN: DDC-TSR,
Cameron Station, Alexandria, VA 22314.
Comments and suggestions on this Handbook are welcome and should be addressed to:
Commander
US Army Materiel Development and Readiness Command
Alexandria, VA 22333
(DA Forms 2028, Recommended Changes to Publications, which are available through normal
publications supply channels, may be used for comments/suggestions.)
xv
DARCOM·P 706-358
DEPARTMENT OF THE ARMY
HEADQUARTERS US ARMY MATERIEL DEVELOPMENT AND READINESS COMMAND
5001 Eisenhower Ave, Alexandria, VA 22333
DARCOM PAMPHLET
No. 706-358
1 December 1976
ENGINEERING DESIGN HANDBOOK
ANALYSIS AND DESIGN OF AUTOMOTIVE BRAKE SYSTEMS
TABLE OF CONTENTS
Paragraph Page
LIST OF ILLUSTRAnONS viii
LIST OF TABLES xiv
PREFACE xv
1-0
I-I
1-2
1-3
1-4
2-0
2-1
2-2
2-3
2-4
2-4.1
2-4.2
2-4.3
2-4.4
2-4.5
2-4.6
2-4.7
2-4.8
2-4.9
2-4.10
2-4.11
2-4.12
CHAPTER I. INTRODUCTION
List of Symbols .
Factors Influencing Stopping Distance .
Braking Dynamics .
Methods to Improve Braking Capability .
Overviewof Brake System Design .
CHAPTER 2. MECHANICAL
ANALYSIS OF FRICTION BRAKES
List of Symbols .
Different Brake Designs .
Brake Shoe Displacement and Application .
Brake Shoe Adjustment .
Torque Analysis of Friction Brakes .
Self-Energizingand Self-Locking .
Leading and Trailing Shoe .
Pressure Distribution Along Brake Lining .
Lining Wear and Pressure Distribution .
Brake Factor and Brake Sensitivity .
Brake Factor of a Caliper Disc Brake .
Brake Factor of a Leading-Trailing Shoe Brake With
Pivot on Each Shoe .
Brake Factor of a Two-Leading Shoe Brake With Pivot
on Each Shoe .
Brake Factor of a Leading-Trailing Shoe Brake With
Parallel Sliding Abutment .
Brake Factor of a Two-Leading Shoe Brake With
Parallel Sliding Abutment .
Brake Factor ofa Leading-Trailing Shoe Brake With
Inclined Sliding Abutment .
Brake Factor of a Two-Leading Shoe Brake With
Inclined Sliding Abutment .
I-I
I-I
1-2
1-3
1-3
2-1
2-2
2-2
2-3
2-4
2-4
2-6
.2-7
2-8
2-9
2-10
2-1\
2-11
2-\2
2-12
2-12
2-13
DARCOM-P 706-358
TABLE OF CONTENTS (Continued)
ii
Paragraph
2-4.13
2-4.14
2-5
2-6
2-7
2-8
3-0
3-1
3-1.\
3-1.2
3-1.3
3-1.4
3-1.5
3-1.6
3-1.7
3-1.8
3-2
3-2.1
3-2.2
3-2.3
4-0
4-1
4-2
4-3
4-4
5-0
5-1
5-2
5-3
5-4
5-5
5-6
5-7
5-8
5-9
Brake Factor of a Duo-Servo Brake With Sliding
Abutment .
Brake Factor of a Duo-Servo Brake With Pivot
Support .
Effect of Shoe and Drum Stiffness on Brake Torque .
Analysis of External Band Brakes .
Analysis of Self-Energizing Disc Brakes .
Comparison of Brakes .
References .
CHAPTER 3. THERMAL ANALYSIS
OF FRICTION BRAKES
List of Symbols .
Temperature Analysis .
The Friction Brake as a Heat Exchanger .
Fundamentals Associated With Brake Temperature Analysis .
Prediction of Brake Temperature During Continued Braking .
Prediction of Brake Temperature During a Single Stop .
Prediction of Brake Temperature During Repeated Braking .
Prediction of Convective Heat Transfer Coefficient .
Computer Equations for Predicting Brake Temperature .
Analysis of Sealed Brakes ..
Thermal Stress Analysis ..
Fundamentals Associated With Thermal Cracks .
Thermal Stresses in Solid-Rotor Disc Brakes .
Thermal Stresses in Brake Drum .
References .
CHAPTER 4. ANALYSIS
OF AUXILIARY BRAKES
List of Symbols .
Exhaust Brakes .
Hydrodynamic Retarders .
Electric Retarders .
Analysis of Integrated Retarder/Foundation Brake Systems .
References .
CHAPTER S. BRAKE FORCE PRODUCTION
List of Symbols .
Introduction .
Nonpowered Hydraulic Brake System .
Vacuum-Assisted Hydraulic Brake System .
Full-Power Hydraulic Brake System .
Air Brake System .
Compressed Air-Over-Hydraulic Brake System .
Mechanical Brake System .
Surge Brakes .
Electric Brakes .
References .
Page
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2-18
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7-1.1
7-1.2
7-1.3
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7-1.5
7-2
7-3
7-3.1
7-3.2
7-3.3
7-4
7-4.1
7-4.2
7-4.3
7-4.4
7-4.5
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8-1
8-1.1
8-1.2
8-1.3
8-1.4
8-1.5
8-1.6
8-1.7
8-1.8
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8-2.2
8-2.3
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8-3.1
8-3.2
CHAPTER 6. TIRE-ROAD FRICTION
List of Symbols .
Tire-Road Interface .
Road Friction Measurement .
Tire Friction Characteristics .
Tire Rolling Resistance .
Tire Design and Composition .
References .
CHAPTER 7. VEHICLE BRAKING PERFORMANCE
List of Symbols .
Braking Performance Measures .
Effectiveness .
Efficiency .
Response Time .
Controllability .
Thermal Effectiveness .
Brake Force Modulation .
Braking Performance Prediction and Analysis .
Braking Performance Calculation Program .
Dynamic Braking Program .
Tractor-Trailer Braking and Handling Program .
VehicleDrags .
Rolling Resistance .
Aerodynamic Drag .
Viscous Damping Drag .
Drag Due to Turning .
Engine Drag .
References .
CHAPTER 8. BRAKING OF VEHICLES EQUIPPED WITH
FIXED RATIO BRAKING SYSTEM
List of Symbols .
Braking of Two-Axle Vehicle .
Dynamic Brake Force .
Actual Brake Force Distribution .
Tire-Road Friction Utilization .
Braking Efficiency .
Optimum Brake Force Distribution for Straight-Line Braking .
Straight-Line Versus Curved Path Braking Performance .
General Braking Efficiency .
VehicleStability Considerations .
Braking of Tandem Axle Truck .
Walking Beam Suspension .
Two-Elliptic Leaf Spring Suspension .
Air Suspension .
Braking of Tractor-Semitrailer Combination Without Tandem Axles .
Dynamic and Actual Brake Forces .
Optimum Brake Force Distribution .
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7-8
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10-0
Straight-Line Versus Curved Path Braking Performance .
Vehicle Stability Considerations .
Braking ofTractor-Semitrailer Combination Equipped
With Tandem Axles .
Two-Axle Tractor Coupled to a Trailer Equipped With
a Two-Elliptic LeafSpring Suspension .
Two-Axle Tractor Coupled to a Trailer Equipped With a
Walking Beam Suspension .
Three-Axle Tractor Equipped With a Walking Beam
Suspension Coupled to a Trailer Equipped With a
Two-Elliptic LeafSpring Suspension .
Braking of a Two-Axle Tractor Coupled to a Single-Axle
Semitrailer and a Double Axle Trailer .
Braking ofCombat Vehicles .
Effects ofRotational Energies .
Track Rolling Resistance .
Braking of Half-Track Vehicle .
Braking of Full-Track Vehicle and Special Carriers .
Concluding Remarks on Vehicles Equipped With Fixed
Ratio Braking Systems .
References .
CHAPTER 9. BRAKING OF VEHICLES
EQUIPPED WITH VARIABLE RATIO BRAKING SYSTEMS
List of Symbols .
Two-Axle Vehicles .
Dynamic and Actual Brake Forces .
Optimum Variable Ratio Braking Distribution .
Dynamic Brake Line Pressures .
Pedal Force Requirements .
Pressure Regulating Valves .
Straight-Line Versus Curved Line Braking Performance .
Vehicle Stability Considerations .
Braking ofTractor-Semitrailer Vehicle .
Dynamic and Actual Brake Forces .
Dynamic Brake Line Pressures .
Pressure Variation as Function ofSuspension
Deflection .
Two-Axle Tractor Coupled to a Trailer Equipped
With Two-Elliptic Leaf Spring Suspension .
Three-Axle Tractor Equipped With Walking Beam
Suspension Coupled to a Trailer Equipped With
Two-Elliptic LeafSpring Suspension .
Concluding Remarks on Vehicle Equipped With
Variable Ratio Braking Systems .
References .
CHAPTER 10. WHEEL-ANTI LOCK BRAKE SYSTEMS
List of Symbols .
Page
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Fundamentals Associated With Antilock Brake System
Analysis .
Hydraulic Vacuum Powered Systems .
Wheel-Antilock Control Systems .
Analysis of Vacuum-Powered Systems .
Hydraulic Pump Pressurized Systems .
Pneumatic Systems .
Straight-Line Versus Curved Path Performance , ..
Theoretical and Experimental Results .
Different Antiskid System Designs .
References .
CHAPTER 11. DYNAMIC ANALYSIS OF BRAKE SYSTEMS
List of Symbols .
Fundamentals of Response Time Analysis •.................................
Hydraulic Brake Systems .
Pneumatic Brake Systems .
References .
CHAPTER 12. BRAKE SYSTEM FAILURE
List of Symbols .
BasicConsiderations .
Development ofBrake Failure .
Development of Drum and Rotor Failure .
Brake Failure Analysis ; .
Brake Line Failure .
Vehicle Deceleration .
Pedal Force .
Braking Efficiency .
Pedal Travel .
Performance Calculation .
Improved Dual Brake System Design .
Comparison of Dual Brake Systems .
Vacuum Assist Failure .
Failure of Full Power Hydraulic Brake Systems .
Failure of Pneumatic Brake Systems .
Brake Fade .
Brake Assembly Failure Due to ExcessiveTemperature .
Consequences ofBrake Failure .
Brake System Component Deterioration .
Vehicle Stability and Controllability .
Human Factors Considerations .
Effect of Maintenance on Brake Failure .
Minimizing Brake Failure Through Proper Design .
References .
CHAPTER 13. TESTING OF VEHICLE BRAKE SYSTEMS
List of Symbols .
Basic Testing Requirements .
General Outline ofa Brake Test Standard .
Page
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14-6.1
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15-1.3
Measurement of Braking Performance .
Effectiveness .
Efficiency .
Response Time .
Controllability .
Thermal Effectiveness .
Brake Usage and Maintenance .
Brake System Inspection and Diagnosis .
Brake System Testing .
Roller Dynamometer .
Platform Tester .
Brake Road Testing .
Brake Test Procedures for Military Vehicles .
Road Test Procedures for Wheeled Vehicles .
Road Test Procedures for Tracked Vehicles .
Component Testing .
References .
CHAFfER 14. DESIGN APPLICATIONS
List of Symbols .
Basic Considerations .
Specific Design Measures .
Design of Related Components Such as Suppression, Tires, and Rims .
Brake System Design Check .
Brake Factor Calculation .
Design of Light Truck Brake System .
Emergency Brake Analysis .
Dynamic Brake Forces .
Braking Efficiency .
Braking Performance Diagram .
Brake Fluid Volume Analysis .
Specific Design Measures .
Design of Truck Proportional Brake System .
Fixed Ratio Braking - Drum Brakes .
Fixed Ratio Braking - Disc Brakes .
Variable Ratio Braking - Drum Brakes .
Variable Ratio Braking - Disc Brakes .
Design of Tank Disc Brakes .
Mechanical Analysis .
Thermal Analysis .
Temperature Analysis of Drum Brake System .
Design of Fun Power Hydraulic Brake System for Heavy Truck .
Determination ofWheel Cylinder Areas .
Determination of Booster and Accumulator Size .
CHAFfER 15. BRAKE SYSTEMS AND THEIR COMPONENTS
Pedal Force Transmission - Hydraulic Brakes .
Basic Principles of Hydraulic Brakes .
Single Circuit Brake System .
Dual Circuit Brake System .
Page
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