Vehicle Dynamics (ME5670)
ANTILOCK BRAKING SYSTEM
MODELING AND DEVELPOMENT
Indian Institute of Technology, Hyderabad
Siva Teja Golla (ME14MTECH11025)
Harshad Keskar (ME14MTECH11027)
Mohini Kale (ME14MTECH11029)
Nikhil Mhaske (ME14MTECH11030)
Sukanya Joshi (ME14MTECH11037)
ANTILOCK BRAKING SYSTEM
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INTRODUCTION
• 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.
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PROJECT OUTLINE
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Objectives of ABS
Components of ABS
Working of ABS
Mathematical model
System model
Results
Conclusion
References
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OBJECTIVES OF ABS
•
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.
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• 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.
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• 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.
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COMPONENTS OF ABS
The primary components of the ABS braking system are:
• Electronic control unit (ECU)
1. It receives signals from the sensors in the circuit and controls the brake
pressure at the road wheels according to the data analysed by the Unit.
2. ECU assists the vehicle operator to prevent wheel lockup by regulating the
wheel slip.
• Hydraulic control unit or modulator
1. It receives operating signals from the ECU to apply or release the brakes
under ABS conditions.
2. It executes the commands using three solenoid valves connected in series
with the master cylinder and the brake circuits- one valve for each front
wheel hydraulic circuit, and one for both of the rear wheels. Thus brakes can
be actuated by controlling hydraulic pressure.
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•
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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.
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WORKING OF ABS
• 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.
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MATHEMATICAL MODEL
• 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
𝑉𝑐𝑜𝑠𝛼 − 𝜔𝑅𝑤
𝑆=
𝑉𝑐𝑜𝑠𝛼
The side slip angle is
𝑉𝑠𝑦
−1
𝛼 = 𝑡𝑎𝑛
𝑉𝑥
Force and velocity components on tyre
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• Vehicle Dynamics
According to Newton's second law, the equation of motion of the
simplified vehicle can be expressed by,
𝑚𝑡 𝑉 = −𝐹𝑡 − 𝐹𝑎
The road friction force is given by Coulomb law
𝐹𝑡 = 𝜇𝑁
The total mass of the quarter vehicle can be written as
𝑚𝑐
𝑚𝑡 = 𝑚𝑡𝑖𝑟𝑒 +
4
Thus, the total normal load cm be expressed by
𝑁 = 𝑚𝑡 𝑔 − 𝐹𝑙
𝐹𝑙 is the longitudinal weight transfer load due to braking
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Simulink model for vehicle dynamics
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• Wheel dynamics
According to Newton's second law, the equation of motion at wheel
level for the rotational DOF is given by,
𝐽𝑤 𝜔 = −𝑇𝑏 + 𝐹𝑡 𝑅𝑤
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Simulink model for wheel dynamics
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SYSTEM MODEL
Assumption: Only a linear model was considered and does not include actual road
conditions. The system here is modelled only for straight line braking.
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INPUT PARAMETERS FOR SIMULINK MODEL
Gravitational constant
Initial velocity of vehicle
Wheel Radius
Mass of vehicle
Maximum Braking Torque
Hydraulic Lag
Moment of Inertia
𝑔 = 32.18 𝑓𝑡/𝑠 2
𝑣0 = 88 𝑓𝑡/𝑠
𝑅𝑟 = 1.25 𝑓𝑡
𝑚 = 50 lbs
𝑇𝑏𝑚𝑎𝑥 = 1500 𝑙𝑏𝑓 ∗ 𝑓𝑡
𝑇𝐵 = 0.01 𝑠
𝐽𝑤 = 5 𝑓𝑡 4
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RESULTS
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VEHICLE SPEED AND WHEEL SPEED
(WITHOUT ABS)
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VEHICLE SPEED AND WHEEL SPEED
(WITH ABS)
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SLIP (WITHOUT ABS)
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SLIP (WITH ABS)
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STOPPING DISTANCE (WITHOUT ABS)
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STOPPING DISTANCE (WITH ABS)
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CONCLUSION
•
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.
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REFERENCES
• 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.
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THANK YOU!
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