Modeling Rack Force for Steering Maneuvers in a Stationary Vehicle 2021-01-1287

A steering system converts circular motion of the steering wheel into yaw motion of the road-wheels. In absence of a steering assist mechanism, the driver torque overcomes the tire-road friction forces, which is transmitted to the steering rack through tie rods attached to the road-wheels. The net force acting on the rack is then transmitted to the steering wheel through mechanical linkages which results in a natural haptic feedback, commonly referred to as the steering feel. In an electric/hydraulic power steering, an electro-mechanical actuator applies assist force, which reduces the torque required by the driver. In order to maintain stability of the power steering system while generating a desired steering feel, it is therefore crucial to accurately model steering rack force. We present a model for the rack force, which is generated while performing steering maneuvers in a stationary vehicle. In contrast to the well-known LuGre tire friction model, our rack force model is simpler as it has no internal states, however, it captures nonlinear tire friction characteristics such as the stick-slip motion, Stribeck effect, and rate dependent hysteretic phenomenon. To identify the model parameters, we employ standard gradient based optimization using sensor data from a test vehicle. The accuracy of our model is established by close fit of the predicted rack force to that measured in experiments. The rack force model presented in this paper includes well known tire friction characteristics and therefore, can be easily adapted to model desired braking torque, for instance in Anti-lock Braking Systems (ABS).