Impact-Based Modeling of Backlash in Gear Driven Systems

Backlash in gears creates nonlinear dynamics in mechanical systems and has been analyzed using a variety of methods and models. In this paper, we present a nonlinear, piecewise model for backlash dynamics that incorporates a coefficient of restitution to account for impact behavior during limit cycling. We analyze the energy absorbed by the collisions and derive a constraint for feedback controllers. We conclude with simulation results using this modeling approach.