Influence of Tire Parameters on ABS Performance
The antilock braking system (ABS) is an active control system, which prevents the wheels from locking-up during severe braking. The ABS control cycle rapidly modulates braking pressure at each wheel mainly based on tire peripheral acceleration. Significant wheel speed oscillations and consequent fast variations of tire longitudinal slip are a consequence, which, in turn, produce a corresponding variation of tire longitudinal force according to the ABS control cycle. Clearly, tire characteristics, namely, tire peak friction (regulating maximum vehicle deceleration), longitudinal stiffness, optimal slip ratio, curvature factor (regulating the position of the peak of μ-slip curve and the subsequent drop), and relaxation length (accounting for tire dynamic response) may significantly influence ABS performance. The aim of the present paper is to evaluate the effect of the main tire parameters on ABS performance. This task is, however, very challenging, since tire characteristics are intrinsically related, and the analysis involves interaction between tires, vehicle, and ABS control logic. A methodology based on the hardware-in-the-loop (HiL) technique is used. This approach was selected to overcome limitations of numerical simulations or difficulties related to the execution of on-road experimental tests (repeatability, costs, etc.). The developed HiL test bench includes all the physical elements of the braking system of a vehicle (comprising the ABS control unit) and a 14 degrees of freedom (dofs) vehicle model, which are synchronized by a real-time board. With the developed HiL test bench, a sensitivity analysis was carried out to assess the influence of tire peak friction, longitudinal stiffness, and relaxation length on ABS performance, evaluated in terms of braking distance, mean longitudinal acceleration, and energy distribution.ABSTRACT
Bosch wheel-acceleration–based ABS control algorithm.
Block diagram of the implemented HiL test bench focusing on hardware and software components.
HiL test bench: (1) pump, (2) sensor cluster, (3) servo-valve, (4) emulators of wheel speed sensors, (5) hydraulic actuator, (6) ESP/ABS ECU, (7) pressure sensors, (8) brake calipers.
14 dofs vehicle model.
Contact mass transient tire model.
Longitudinal force vs slip. Dynamic response of the tire model.
ABS braking maneuver, initial speed 115 km/h, high adherence. Comparison between front tires on-road (left) and HiL (right) slip ratio data.
ABS braking maneuver, initial speed 115 km/h, high adherence. Comparison between rear tires on-road (left) and HiL (right) slip ratio data.
ABS braking distance percentage variation vs tire model parameter variation: mean value and data dispersion. Mean baseline braking distance: 44.74 m.
Longitudinal deceleration percentage variation vs tire model parameter variation: mean value and data dispersion. Mean baseline longitudinal acceleration: 1.16 m/s2.
Friction coefficient vs slip ratio and vehicle speed. (a) Baseline; (b) μ , +5%; (c) μ , −5%; (d) Kx, −30%; (e) Lx, −15%. The red dots represent the trace of the curve in the μx–ɛx plane. The yellow area represents the slip range in which the 12.5% up to the 87.5% of the normalized energy is cumulated.
Effect of parameters variation during acceleration build-up and ABS-controlled braking.
Evolution of stopping distance percentage variation with respect to baseline vs vehicle speed.
ABS braking distance percentage variation vs longitudinal stiffness.
Friction coefficient vs slip ratio and vehicle speed. (a) Kx, −65%; (b) Kx, +130%.
Force vs slip curve, indicating the meaning of some of the coefficients of the MF–Tire model.
Contributor Notes