The document analyzes brake biasing using a balance bar on a Baja vehicle. It discusses the concept and need for brake biasing. An actual balance bar method is described, including how it works using mechanical leverage. An analysis is then presented using a case study of a Baja vehicle to determine the balance bar diameter and pitch, optimum braking forces, maximum deceleration, system efficiency, and deceleration achieved at different speeds. Graphs are included showing results. The conclusions state that the rear wheels must not lock before the front, balance bar system effectiveness increases with pitch, and only one brake force distribution is possible given the vehicle parameters.

1. Analysis of Brake Biasing (Balance Bar)
on BajaVehicle
Presented by:
Deshpande Aditya Naresh
VISHWAKARMA INSTITUTE OF TECHNOLOGY,
PUNE
10th December 2015
Aditya Deshpande (deshadi805@gmail.com)

2. CONTENTS
1. Concept of brake biasing, need, various methods
2. Actual balance bar method: construction and working
3. Analysis using a case study: Determination of
a) Balance Bar Diameter, Pitch
b) Optimum Braking Force through Adhesion Graph
c) Maximum possible achievable deceleration at static condition for all
wheels lockup
d) System Efficiency
e) Deceleration achieved vs speed
4. Conclusion and Comments
Aditya Deshpande (deshadi805@gmail.com)

3. Concept of Brake Biasing:
Applying variable force for both front and rear axles for better performance.
Need: To bring braking efficiencies closer to unity for variety of conditions
Non
biasing
Low
Deceleration
Front Axle
Lock
Rear Axle
Lock
Less Brake
Force
Generation
Aditya Deshpande (deshadi805@gmail.com)

4. Balance Bar: Construction and Working
 Use of mechanical leverage principle
 Varying length from fulcrum, vary the
force
 So adjustable force mechanism
 Types of configuration
𝑅𝑓 =
𝑡𝑜𝑡𝑎𝑙 𝑝𝑢𝑠ℎ 𝑟𝑜𝑑 𝑙𝑜𝑎𝑑 𝑥 𝑋
𝐿
Rr= 𝑡𝑜𝑡𝑎𝑙 𝑝𝑢𝑠ℎ 𝑟𝑜𝑑 𝑙𝑜𝑎𝑑 − 𝑅𝑓
Aditya Deshpande (deshadi805@gmail.com)

5. System Components:
1.Balance bar
2.Spherical bearing or Trunnion
3.Yoke, brass rod
4.Master cylinder, brake pedal
Working:

6. Analysis of System : Mass 230 Kg
Wheel Base 1.35 m
C.G Height 0.47 m
Acceleration G 9.81
Road Friction Coeff. 0.75
Pad Friction Coeff. 0.8
M.C Bore Dia 0.01905 m
Calliper Bore Diameter 0.03105 m
Pedal Ratio 5
Tire Radius 0.3175 m
Pad Clearance 2 mm
Disc Effective Radius 0.075 m
Pedal Length 250 Mm
Sample BajaVehicle Specifications
 Analysis done by using a Case Study
of Baja vehicle
 To consider some basic parameters
 Formulae used:
Front reaction=
𝑤𝑒𝑖𝑔ℎ𝑡 𝑥 𝐶.𝐺. 𝑓𝑟𝑜𝑚 𝑟𝑒𝑎𝑟 𝑎𝑥𝑙𝑒
𝑤ℎ𝑒𝑒𝑙 𝑏𝑎𝑠𝑒
Rear reaction = weight – front reaction
Deceleration = μroad x acceleration (9.81 m/sec2)
Weight shift=
𝑚𝑎𝑠𝑠 𝑥 𝑑𝑒𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑥 𝐶.𝐺. ℎ𝑒𝑖𝑔ℎ𝑡
𝑤ℎ𝑒𝑒𝑙 𝑏𝑎𝑠𝑒
Aditya Deshpande (deshadi805@gmail.com)

7. a) Determination of bar diameter:
Using bending criterion find Max. B.M.
Find bar diameter
b) Determination of bar pitch:
0
1
2
3
4
5
6
7
0 10 20 30 40 50 60 70 80
Pitchinmm
Thread size in mm
METRI
C
Graph 1 Metric and BSF Thread vs. Pitch
1. Fineness varies by thread type
2. For same diameter,
BSF lower pitch than metric.
Aditya Deshpande (deshadi805@gmail.com)

8. 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
1.45
1.55
1.65
1.75
brakingforceperunitweight
Deceleration ,times g
braking force available
at front
braking force required
at front
brake force available at
rear
braking force at rear
c) Determination of Optimum Braking Force :
Available force at front per W=
9.81 x [ front reaction+W x deceleration x C.G. height
wheel base
]
W
Available force at rear per W=
9.81 x [ rear reaction− W x deceleration x C.G. height
wheel base
]
W
Required force at front= deceleration/ Xf;
Required force at rear= deceleration/ Xr.
Graph 2 Adhesion Utilization Graph
From this we get maximum deceleration achieved.
Aditya Deshpande (deshadi805@gmail.com)

9. 0
0.2
0.4
0.6
0.8
1
1.2
1.4
0.5
0.52
0.54
0.56
0.58
0.6
0.62
0.64
0.66
0.68
0.7
0.72
0.74
0.76
0.78
0.8
decelerationachieved,g
X f
Decelerationfront
Decelerationrear
Optimum Xf
Graph 3 Deceleration vs. Xf graph
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Efficiency
Xf
front
efficiency
rear
efficiency
Graph 4 Efficiency vs. Xf graph
𝜂front =
𝑓𝑟𝑜𝑛𝑡 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛
𝑊 𝑥 [𝑋𝑓−
𝜇𝑡𝑦𝑟𝑒−𝑟𝑜𝑎𝑑 𝑥 𝐶.𝐺.ℎ𝑒𝑖𝑔ℎ𝑡
𝑤ℎ𝑒𝑒𝑙 𝑏𝑎𝑠𝑒
]
And,
𝜂rear =
𝑓𝑟𝑜𝑛𝑡 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛
𝑊 𝑥 [𝑋𝑟+
𝜇𝑡𝑦𝑟𝑒−𝑟𝑜𝑎𝑑 𝑥 𝐶.𝐺.ℎ𝑒𝑖𝑔ℎ𝑡
𝑤ℎ𝑒𝑒𝑙 𝑏𝑎𝑠𝑒
]
Decelerationfront =
𝑤ℎ𝑒𝑒𝑙 𝑏𝑎𝑠𝑒 𝑥 𝜇𝑡𝑦𝑟𝑒−𝑟𝑜𝑎𝑑 𝑥 𝑓𝑟𝑜𝑛𝑡 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛
𝑊 [ 𝑤ℎ𝑒𝑒𝑙 𝑏𝑎𝑠𝑒 𝑥 𝑋𝑓− 𝜇𝑡𝑦𝑟𝑒−𝑟𝑜𝑎𝑑 𝑥 𝐶.𝐺. ℎ𝑒𝑖𝑔ℎ𝑡]
Decelerationrear =
𝑤ℎ𝑒𝑒𝑙 𝑏𝑎𝑠𝑒 𝑥 𝜇𝑡𝑦𝑟𝑒−𝑟𝑜𝑎𝑑 𝑥 𝑟𝑒𝑎𝑟 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛
𝑊 [ 𝑤ℎ𝑒𝑒𝑙 𝑏𝑎𝑠𝑒 𝑥 𝑋𝑟+ 𝜇𝑡𝑦𝑟𝑒−𝑟𝑜𝑎𝑑 𝑥 𝐶.𝐺. ℎ𝑒𝑖𝑔ℎ𝑡]
d) Maximum possible achievable
deceleration at static condition for all
wheels lockup :
e) System Efficiency:

10. 0
2
4
6
8
10
12
14
16
18
1.962 2.4525 2.943 3.4335 3.924 4.4145 4.905 5.3955 5.886 6.3765 6.867 7.3575
StoppingDistance,m
Deceleration m/s2
15KMP
H
25KMP
H
30KMP
H
35KMP
H
40KMP
H
20KMP
H
Graph 5 Stopping Distance vs. Deceleration Graph
f) Deceleration Achieved Vs Speed :
1. Consideration of only up to
40KMPH.
2. This is by given BFD of
53:47
3. For max. deceleration,
Stopping distance@
40KMPH= 4 m
4. Variation of both μroad and
speed one by one.
Stopping distance=
𝑚𝑎𝑠𝑠𝑥 𝑠𝑝𝑒𝑒𝑑2
2
[𝑎𝑐𝑡𝑢𝑎𝑙 𝑓𝑟𝑜𝑛𝑡 𝑏𝑟𝑎𝑘𝑖𝑛𝑔 𝑓𝑜𝑟𝑐𝑒 𝑥 2+𝑎𝑐𝑡𝑢𝑎𝑙 𝑟𝑒𝑎𝑟 𝑏𝑟𝑎𝑘𝑖𝑛𝑔 𝑓𝑜𝑟𝑐𝑒 𝑥 2]
Aditya Deshpande (deshadi805@gmail.com)

11. Conclusions and Comments:
1. Rear wheels must not lock before front wheels
2. Speed weight transfer stopping distance for same deceleration
3. From graph 2, all required and actual forces of braking meet at one point
4. System effectiveness α Pitch
5. Brake efficiency≤ 1 always. If not, indicating any one wheel locking
6. Only one BFD for given configuration of parameters
7. System can also for side force biasing
Aditya Deshpande (deshadi805@gmail.com)

12. REFERENCES:
1. Rudolf Limpert; Brake Design and Safety 2nd Edition, SAE International.
2. Rudolf Limpert; MotorVehicle Accident Reconstruction and Cause Analysis,The Michie Company, 1996
3. Thomas Gillespie; Fundamentals of vehicle dynamics; SAE International.
4. Rudolf Limpert;Vehicle System Components Design and Safety; JohnWiley and Sons publications, 1989 Ed.
5. Research paper on De`sign of Formula SAE Brake Systems; by Eric Hamilton, Eric Klang, College of
Engineering North Carolina State University published in 2009 Wolfpack Motorsports
6. Christopher Boyle ET all; Paper on 2012-2013 WPI SAE Baja Vehicle, to Worcester Polytechnic Institute,
U.S.
7. Subhash Mishra & Sagar Janghu; Balance Bar Design and Motion Analysis of Pushrod; published in Global
Journal of Researches in Engineering:Automotive Engineering; 2014 Ed.
8. Megan Scheitlin; Renewable Energy Vehicle Project: Pedal Box Design for Formula SAE; 2011; University of
Western Australia
9. Nathan C. Nantais; Active Brake Proportioning And Its Effects On Safety And Performance, A Thesis
Submitted To University ofWindsor
Aditya Deshpande (deshadi805@gmail.com)

13. Biasing by Pedal
movement
Biasing by slot and sleeve [7]
Biasing by means of elongated hole
Biasing: Various Methods
Elongated hole at
master cylinder
mounting
Aditya Deshpande (deshadi805@gmail.com)

14. Vehicle behaviour with front and rear axles locked
Aditya Deshpande (deshadi805@gmail.com)

15. Balance Bar Configurations
Aditya Deshpande
(deshadi805@gmail.com)

16. vehicle axis system
Aditya Deshpande (deshadi805@gmail.com)

17. Graph of rear deceleration Vs speed Graph of rear deceleration Vs speed
Rear Wheel Drive Front Wheel Drive
The speed decreases parabolically
with increase in declaration
The speed increases after some
max. value of deceleration (0.9g)
1. This shows the effect of
deceleration achieved by rear
wheel on stopping distance.
2. As speed increases obviously
stopping distance increases.
100mph
50mph

18. Thank You
©Aditya Deshpande
Aditya Deshpande (deshadi805@gmail.com)