1Braking Dynamics.pdf (Size: 271.5 KB / Downloads: 38)
hen a vehicle decelerates due to braking forces, normal load is transferred off the rear tires, onto
the front. The differences in tire normal load create differences in peak braking force capability.
In order to design the braking system to utilize each tire in a manner suiting its braking capability,
it is necessary to analyze the dynamics of a braking vehicle.
The differences in vehicle behaviour when locking either the front or rear axle first during braking
are dramatic, and may singly determine whether a vehicle stops safely or loses control. Thus, the
main concern in braking force analysis and design has been whether the distribution of braking
loads will cause front or rear axle lockup.
In order to investigate the effects of different lockup cases, a simple bicycle model can be used.
During straight line driving and braking, tire loads theoretically exist only in the longitudinal
direction. In reality, small lateral disturbances will exist during straight line braking, due to
small steer angles, non-uniform road surfaces, and aerodynamic loads. The result is that even
straight-line driven vehicles are required to supply lateral traction at the tires in order to remain
The situation where the front tires of the vehicle lock up is represented in Figure 5.1. Subject
to a yaw disturbance, the heading of the vehicle has rotated slightly, while the resultant path of
vehicle travel is still directly forward, in the original direction. The locked up front tires only
create forces in a direction opposite the direction of motion.
Lines of Constant Friction Coefficient
From Figure 5.5 it can be seen that at extreme decelerations the weight transfer to the front
tires increases until the point where there is no load on the rear tires. At this point the braking
force on the rear axle is zero regardless of tire-road friction coefficient. Likewise, during extreme
accelerations it can be seen the front axle tractive force is zero regardless of tire-road friction
Each point on the optimal curve implies that μ
frictionF = μ
frictionR = μfront = μrear = a, and
at each zero point the force is zero for any μ. The result is that straight lines joining the zeroforce
points to any acceleration level on the optimum curve represent lines of constant friction
coefficient, with μT i = a.
Design of Variable Brake Proportioning
Specialized brake pressure valves may be implemented to limit some or all additional pressure to
the rear brakes above a certain pressure level. This allows the designer to create a bi-linear brake
proportioning curve, and achieve higher braking efficiencies overall. The bilinear curve can be
shaped to approximate the optimal braking curve.
Brake pressure limiting valve
A brake pressure limiting valve can be installed inline with the rear brake lines. At a chosen brake
pressure level (intended to correspond to a pre-designed critical deceleration) the limiting valve
allows no additional pressure to pass to the rear brakes (Figure 5.12). Generally the baseline first
segment of the proportioning curve is chosen so that it would intercept the optimal curve at a
deceleration of 0.5g .