Geared PM coreless motor modelling for driver's force feedback in steer-by-wire systems

Gearboxes allow for changes in the motor's torque and speed ranges, thus allowing the motor to function at its best operation ranges. As a consequence, smaller and low cost motors can be used in comparison with direct drive motors. Nevertheless, gearboxes introduce nonlinearities to the system such as friction, backlash and flexibility. When geared motors are employed, a controller using a torque sensor or a torque observer is normally required to compensate for the drawbacks associated with the gearbox and the servo-amplifier. The design of such a controller requires the comprehensive knowledge of the system's dynamics. In this paper, a general approach to model accurately amplifier-motor-gearbox assemblies has been developed. This approach that takes into account backlash, flexibility, friction for stiction and sliding, identification procedures, is applicable to a wide range of amplifier-motor-gearbox assemblies. It is explained by applying it to a particular case: an amplifier-motor-gearbox assembly for a driver's force feedback system. In the design of driver's force feedback systems for steer-by-wire systems or for high fidelity Human in the Loop (HiL) driving simulators, either direct drive motors or geared motors are used, independently of the motor type. The assembly considered here is composed of a two stage planetary gearbox, a coreless PMDC motor and a linear four quadrant servo-amplifier. It is installed in an X-by-wire (XBW) vehicle prototype, Both the amplifier and the mechanical components were built in the model. The four quadrant operating modes of the amplifier were taken into account. Friction within both the motor and the gearbox are modelled using a modification of the LuGre friction model that allows friction to be considered as load-dependent. Backlash and flexibility in the gearbox are considered together using a fifth order polynomial for each rotational direction. The identification procedures necessary to calculate the parameters of the model are presented. Because all the parameters of the model have a direct physical significance, these identification procedures are easy to realize. Comparisons between simulations realized with Simulink and the experimental data for three typical driving situations show that the model is highly accurate at representing real system dynamics.