Anti-lock braking system (ABS)

The ABS was first introduced in 1978 in a passenger car. In case of emergency braking the ABS prevents locking of wheels.

Explanation of slip

Vd-Driving velocity of vehicle (actual velocity with which vehicle is moving)

Vc-velocity according to tyre angular speed(Vc=R*w) R-static radius of tyre, w- angular velocity of tyre

Two types of slip

    

• Driven wheel slip- (Vc-Vd)/Vc

Example- Vehicle standstill and tyres rotating ,Vd=0,Vc>0

Driven wheel slip S=1

•  Braked wheel slip-(Vd-Vc)/Vd

Example-  Locking of wheel when braked ,Vd>0,Vc=0

Braked wheel slip S=1

Value of slip lies between (0-1)

In a vehicle 3 types of wheel locking effects are possible which are as following

E-1-Effect of locking at front axle.

No steering is possible in this condition

Kamm's circle

Fx represents longitudinal force longitudinal forces.

Fy represents lateral forces.

fa is the coefficient of adhesion (friction)-maximum static friction coefficient.

fs is the coefficient of sliding.

Vw=velocity of wheel.

O<(alpha) lateral slip angle-angle between Fx and Vw.

In the graph,

Sqrt(Fy^2 + Fx^2) <= faFz

Its the equation of circle with radius faFz. This equation satisfies the kamm’s circle.

As we see in figure,

The lateral forces increase with increase in slip angle (first linearly ) and Fy decreases with increase in Fx.

At Fx(max)=fsFz ,Fy=0 ,it interprets

No lateral force that means we cannot steer the car as we need lateral force for it(static friction) that can balance the centrifugal force (m*v^2/R) generated during steering. Slip is maximum (s=1).

E-2 Locking of rear axle

If Fy=0 (lateral force) at rear axle then if small amount will be generated due to small difference in fa or fs between the wheels, the car will quickly turn which can cause side impact. The side impacts are dangerous for passengers.

E-3 Locking in general

Due to locking of tyre the sliding friction acts on the tyre which is less than the static friction hence the stopping distance increases up

fa>fs

Fx =fsFz<faFz

Less Fx means less braking force.

Control variables for wheel locking

• Slip maybe obvious. Locking means high value of slip.
• The problem is it’s not easy to measure slip.

SLIP and ANGULAR ACCELERATION for a wheel are control variables.

The first switching point of ABS (i.e. closure of input fluid valve) is determined if deceleration of wheel is higher than deceleration of vehicle,

Radius (tyre) * angular deceleration > deceleration of vehicle.

Goals of ABS

1)      Limiting the slip in order to preserve lateral force.

2)      If possible adhesive limit of friction should be reached

3)      Brake pressure from driver is to be reduced

ABS components (Hydraulic parts)

Working of hydraulic components

When the driver presses the brake pedal the fluid pressure increases. The input valve is open and the output valve is closed in normal condition so the pressure directly goes to piston (calliper) and the wheel brakes. If the brake pressure is too high that one of the wheels tries to lock the ABS automatically closes the input valve (so that pressure remains constant) and opens up the output valve decreasing the pressure by sending the fluid into the reservoir.

ABS control cycles

As you can see in the above three graphs when the driver applies the brake, the brake pressure in the brake calliper increases linearly, angular acceleration of tyre decreases up to acceleration= –a. At this point the input valve is closed hence the pressure remains constant .After that point as you see the velocity of vehicle suddenly decreases the possibility of slip increases due to large amount of wheels angular deceleration so the output valve is opened to reduce pressure by allowing fluid to flow to reservoir. Due to reduce in pressure on calliper the wheels angular acceleration increases back and the input valve is opened back. Same cycle repeats again and again but velocity keeps decreasing and finally reaches to zero without slipping.

Split mu braking

The difference in the values of coefficient of friction between the wheels of vehicle due to road surface variance is known as split mu. The hard braking over split mu can create the yaw moment (moment about vertical axis) immediately due to different friction forces (braking force) on two side of vehicle hence, yaw moment starts to act quickly and driver gets very less time to react.

 But the ABS has a safety feature that recognizes the high difference in pressures is arising, it slowly increases the pressure difference so that driver may get enough time to react on the yaw moment.

The yaw moment reaction time also depends on the car size. For small cars (red line in graph), with small moment of inertia about vertical axis and small wheel base the pressure built up is slower than the larger cars (green line), with larger moment of inertia and larger wheel base. So the larger cars have small steering correction (that's a good point) and smaller cars have larger steering correction. Now days the vehicle’s EPS (Electric Power Steering) unit works simultaneously with the stability control (ESP-electronic stability programme) and anti-lock braking system (ABS).

So, Split mu stability function is part of the integration of algorithms within the EPS (Electric Power Steering) unit that works simultaneously with the stability control and anti-lock braking system. The feature provides the following enhancements:

•  Provides a steering torque or angle to compensate for the yaw moment generated by the side-to-side imbalance of braking forces

• Enables the brake system to build maximum braking forces quicker to minimize stopping distance on split-mu surfaces (Surfaces with different grip coefficients).
• Integration of ABS and Steering controls.

Doubts are to be put in the comments