Modeling and friction estimation for automotive steering torque at very low speeds

The torque developed in the steering system of an automobile is a result of multiple interactions between a tyre and the roadway surface. Models are well established for high-speed ground vehicle operation where the tyre is rolling rapidly and the dominant source of tire tread stress is deformation due to lateral force on the tyre. In contrast, for situations where the vehicle is operating at low speeds or even steering when stationary, the torque required to turn the wheels is predominantly a function of the steering rate. However, the torque still can be predicted using models of the deformation of the tyre rubber. This paper introduces such a model of the tyre dynamics that considers the low-speed tyre deformation behaviour considering the interacting effects of steering while the tyre is slowly rolling, allowing for the prediction of steering torques during low speed manoeuvring. The physics-based model is validated with steering torque data from an instrumented steer-by-wire vehicle. The validated model also allows for opportunistic friction estimation in certain steady conditions by inversion of the model with the steering rate, steering torque, and vehicle speed as input data.