A Semi-Physical Model of a Hydraulic Power Steering System for Vehicle Dynamics Simulations

Abstract

A semi-physical model of an hydraulic power steering system is presented in this paper. The proposed model allows to evaluate the wheels dynamic response to steering inputs and to calculate the corresponding reaction torque on the steering-wheel (steering torque). The analyzed steering system increases its stiffness (so that the steering assist level is decreases) with the rise of the vehicle speed. Thus, vehicle maneuverability is improved during parking maneuvers, while at high vehicle speeds, stability and driver perceived steering feel are ensured. A two d.o.f. (steering-wheel and rack-pinion rotations) model has been implemented during this study. The model parameters have been identified through the standard laboratory tests carried out to characterize a steering system, minimizing the difference between the experimental data and the model numerical results. During laboratory tests the hydraulic power system has been characterized first, measuring its stiffness variation as a function of the relative rotation between the steering-wheel and the rack-pinion, and the steering torque as a function of the difference between the delivery and the reversal pressure of the double-acting ram. The complete steering system has been then characterized, suspending the vehicle and placing the wheels on appropriate low-friction plates which permit them to turn; sine and frequency sweep steering input have been applied by a robot and the corresponding reaction torque on the steering-wheel has been measured. Simulations results are in good agreement with the experimental ones for all the performed tests. The steering system model has been integrated into a 14 d.o.f. vehicle model developed by the Mechanical Department of the Politecnico di Milano in order to access its reliability during handling maneuvers. Several simulations have been performed both in open (step-steer, steering pad, etc.) and in closed loop (lane change, double lane change, slalom, etc). Simulation results have shown a reduction of the toe angle due to the deformability of the steering system and a time delay of the wheel angle respect to the cinematic condition introduced by the steering system dynamics. The reaction torque on the steering-wheel has also been calculated during the simulations to access the driver perceived steering feel during the maneuvers.