This document discusses an anti-lock braking system (ABS). It begins with an introduction to ABS and then outlines the objectives and components of the system. The objectives are to reduce stopping distance, improve stability, and maintain steerability during braking. The key components are the master cylinder, wheel speed sensors, and hydraulic control unit. The document then presents mathematical models of vehicle dynamics, wheel dynamics, and the overall ABS system model in Simulink. Simulation results show that ABS is able to regulate wheel slip to reduce stopping distance and maintain control compared to conventional braking without ABS.

1. VTS
ANTILOCK BRAKING SYSTEM 1

2. INTRODUCTION
ANTILOCK BRAKING SYSTEM 2
• Anti-lock braking system (ABS) is an automobile safety system that allows
the wheels on a motor vehicle to maintain tractive contact with the road surface
according to driver inputs while braking, preventing the wheels from locking up
and avoiding uncontrolled skidding.
• ABS generally offers improved vehicle control and decreases stopping distances
on dry and slippery surfaces.
• ABS modulates the brake line pressure independent of the pedal force, to bring
the wheel speed back to the slip level range that is necessary for optimal
braking performance.

3. PROJECT OUTLINE
ANTILOCK BRAKING SYSTEM 3
• Objectives of ABS
• Components of ABS
• Working of ABS
• Mathematical model
• System model
• Results
• Conclusion
• References

4. OBJECTIVES OF ABS
ANTILOCK BRAKING SYSTEM 4
• To reduce stopping distance
1. The road surface type and conditions can be inferred from the vehicle's
braking pressure, wheel slip measurements, and deceleration rate
comparisons.
2. The wheel slip is regulated so that the road adhesion coefficient is
maximized. By keeping all of the wheels of a vehicle near the maximum
friction coefficient, an antilock system can attain maximum fictional
force
3. In turn, this strategy leads to the minimization of the vehicle stopping
distance.

5. ANTILOCK BRAKING SYSTEM 5
• Stability
1. A locked-up wheel generates a reduced braking force, smaller than the peak
value of the available adhesion between tires and road. A locked-up wheel
will also lose its capability to sustain any lateral force. This may result in the
loss of vehicle stability.
2. The basic purpose of a conventional ABS system is thus to prevent any
wheel from locking and to keep the longitudinal slip in an operational range
by cycling the braking pressure.

6. ANTILOCK BRAKING SYSTEM 6
• Steerability
1. Good peak frictional force control is necessary in order to achieve
satisfactory lateral forces and, therefore, satisfactory steer-ability.
2. If an obstacle appears without warning, emergency braking may not be
sufficient. When the wheels are locked, car no longer respond to the driver’s
steering intention.
3. With ABS car remains steerable even during emergency braking, and thus the
obstacle can be safely avoided.

7. ANTILOCK BRAKING SYSTEM 7
• Power booster and master cylinder assembly
1. It is activated when the driver pushes down on the brake pedal. The master
cylinder transforms the applied pedal force into hydraulic pressure which
is transmitted simultaneously to all four wheels.
2. It provides the power assistance required during braking.
• Wheel sensor unit
1. Speed sensors are comprised of a magnet wrapped in a coil and a toothed
sensor ring. An electrical field given off by the contact between the magnet
and the toothed ring creates a AC voltage.
2. The voltage frequency is directly proportional to the wheel's rotational
speed.
3. It monitors the rotational speed of the wheel and transmits this data to the
ABS control module.

8. WORKING OF ABS
ANTILOCK BRAKING SYSTEM 8
• If a wheel-speed sensor signals a lock up - the ECU sends a current to the
hydraulic unit. This energizes the solenoid valve. The action of the valve
isolates the brake circuit from the master cylinder. This stops the braking
pressure at that wheel from rising, and keeps it constant. It allows wheel
velocity to increase and slip to decrease.
• When the velocity increases, ECU re-applies the brake pressure to restrict
the wheel slip to a particular value.
• Hydraulic control unit controls the brake pressure in each wheel cylinder
based on the inputs from the system sensor. This in result controls the wheel
speed.

9. MATHEMATICAL MODEL
ANTILOCK BRAKING SYSTEM 9
• Wheel slip:
When the braking action is initiated, a slippage between the tire and the
contacted road surface will occur, which make the speed of the vehicle to be
different from that of the tire.
• The longitudinal slip is defined as
𝑆 =
𝑉𝑐𝑜𝑠𝛼 − 𝜔𝑅𝑤
𝑉𝑐𝑜𝑠𝛼
The side slip angle is
𝛼 = 𝑡𝑎𝑛−1 𝑉𝑠𝑦
𝑉𝑥
Force and velocity components on tyre

10. ANTILOCK BRAKING SYSTEM 10
• Vehicle Dynamics
According to Newton's second law, the equation of motion of the
simplified vehicle can be expressed by,
𝑚𝑡𝑉 = −𝐹𝑡 − 𝐹𝑎
The road friction force is given by Coulomb law
𝐹𝑡 = 𝜇𝑁
The total mass of the quarter vehicle can be written as
𝑚𝑡 = 𝑚𝑡𝑖𝑟𝑒 +
𝑚𝑐
4
Thus, the total normal load cm be expressed by
𝑁 = 𝑚𝑡𝑔 − 𝐹𝑙
𝐹𝑙 is the longitudinal weight transfer load due to braking

11. ANTILOCK BRAKING SYSTEM 11
Simulink model for vehicle dynamics

12. ANTILOCK BRAKING SYSTEM 12
• Wheel dynamics
According to Newton's second law, the equation of motion at wheel
level for the rotational DOF is given by,
𝐽𝑤𝜔 = −𝑇𝑏 + 𝐹𝑡𝑅𝑤

13. ANTILOCK BRAKING SYSTEM 13
Simulink model for wheel dynamics

14. SYSTEM MODEL
ANTILOCK BRAKING SYSTEM 14
Assumption: Only a linear model was considered and does not include actual road
conditions. The system here is modelled only for straight line braking.

15. INPUT PARAMETERS FOR SIMULINK MODEL
ANTILOCK BRAKING SYSTEM 15
Gravitational constant 𝑔 = 32.18 𝑓𝑡/𝑠2
Initial velocity of vehicle 𝑣0 = 88 𝑓𝑡/𝑠
Wheel Radius 𝑅𝑟 = 1.25 𝑓𝑡
Mass of vehicle 𝑚 = 50 lbs
Maximum Braking Torque 𝑇𝑏𝑚𝑎𝑥
= 1500 𝑙𝑏𝑓 ∗ 𝑓𝑡
Hydraulic Lag 𝑇𝐵 = 0.01 𝑠
Moment of Inertia 𝐽𝑤 = 5 𝑓𝑡4

16. RESULTS
ANTILOCK BRAKING SYSTEM 16

17. VEHICLE SPEED AND WHEEL SPEED
(WITHOUT ABS)
ANTILOCK BRAKING SYSTEM 17

18. ANTILOCK BRAKING SYSTEM 18
VEHICLE SPEED AND WHEEL SPEED
(WITH ABS)

19. SLIP (WITH ABS)
ANTILOCK BRAKING SYSTEM 19

20. STOPPING DISTANCE (WITHOUT ABS)
ANTILOCK BRAKING SYSTEM 20

21. STOPPING DISTANCE (WITH ABS)
ANTILOCK BRAKING SYSTEM 21

22. CONCLUSION
ANTILOCK BRAKING SYSTEM 22
• It is inferred that ABS improves the braking performance.
• The stopping distance after using ABS system has considerably reduced.
• The error in slip and desired slip is used to manipulate brake pressure in brake
cylinder.

23. REFERENCES
ANTILOCK BRAKING SYSTEM 23
• Tianku Fu,“Modelling and performance analysis of ABS system with non-linear control”,
2000.
• Tobias Eriksson,“Co-simulation of full vehicle model in Adams and anti-lock brake system
model in Simulink”, 2014.

24. ANTILOCK BRAKING SYSTEM 24
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