Abstract
Drivers control their steering wheel using both angle and torque. Method of controlling steering wheel by steering angle is called position control and controlling by steering torque is called force control. Vehicle dynamics under position control has been studied and developed, however that under force control has been hardly studied. The objective of this study is to understand and improve vehicle behaviour under force control. Sakashita formulated the vehicle stability condition under force control and pointed out those vehicles, having a lower natural frequency of their steering system than the natural frequency of their vehicles, are unstable above a certain forward velocity. However all passenger cars seem to be stable at any velocity. Therefore it is not stability but response that should be improved. To increase natural frequencies of vehicle–steering systems under force control, in this study, the natural frequencies have been formulated. In the beginning of the formulating, the natural frequencies for neutral steer vehicles have been exactly formulated. Based on these formulas, the natural frequencies for under steer vehicles have been approximately formulated. Furthermore the accuracy and applicable range of the approximated formulas have been investigated by comparison with the natural frequencies from numerical simulations. The formulas of the natural frequencies will be used to predict vehicle behaviour under force control. The formulas of the natural frequencies consist of front cornering stiffness Cf and rear cornering stiffness Cr, non-dimensional inertia of yaw moment kN2, momentum of steering system inertia Ih, ratio of normal load distribution of front axle p, vehicle mass m, wheelbase l, length of trail ξ. The magnitude of coupling between steering system and vehicle is dominated by a non-dimensional number Ih / kN2pmlξ. The main finding is that vehicle behaviour under force control can be improved by larger Cf and Cr and smaller Ih/kN2pml. This finding will contribute to improve vehicle manoeuvrability. The formulas of the natural frequency are only valid for vehicles that are stable at any forward velocity. This stability condition is described as Cf /( Cf + Cr)>2 Ih/kN2pml. Formulating the natural frequencies under force control is new. Moreover, improving vehicle dynamic behaviour under force control is also new. The natural frequencies under force control have been expressed as formulas. By utilizing there formulas, vehicle behaviour under force control can be improved.
KEYWORDS –vehicle dynamics, force control, natural frequency, damping ratio, free control