New models for backlash and gear play

Backlash is the most important non-linearity that limits the performance of speed control in industrial drives and is an important impediment to position control as well. A new simple model based on phase plane analysis is derived for an elastic shaft with internal damping connected to a backlash The model is extended to include the case of a so-called flexible coupling, where some of the backlash gap is filled with rubber. Extensive measurements on an industrial drive with a flexible coupling are compared with simulations and fit very well. With internal damping the classical dead-zone model gives an unphysical behaviour of the dynamics. However, the new model converges to the classical dead-zone model when the damping tends to zero.