An impact model of mechanical backlash for control system analysis

Simple models of mechanical backlash found in the control system literature fail to account for the impact behavior that dominates motion at low amplitudes. As a result, such models exhibit certain shortcomings in characterizing the low-amplitude limit cycle oscillations that occur in closed-loop control systems. This paper presents a model of mechanical backlash which incorporates viscoelastic contact forces between the two masses. Simulations of the model show that low amplitude motions are dominated by stable impact patterns, or “contact regimes,” which differ greatly from the predictions of simple backlash models. Experimental results from a geared servosystem confirm the existence and robustness of these contact regimes. The implications of these findings on control system analysis conclude the paper