Stability and Bifurcation Analysis of Precision Motion Stage with Nonlinear Friction Isolator

Abstract

The application of servo-controlled mechanical-bearing-based precision motion stages (MBMS) is well-established in advanced manufacturing, semiconductor industries, and metrological applications. Nevertheless, the performance of the motion stage is plagued by self-excited friction-induced vibrations. Recently, a passive mechanical friction isolator (FI) has been introduced to reduce the adverse impact of friction in MBMS, and accordingly, the dynamics of MBMS with FI were analyzed in the previous works. However, in the previous works, the nonlinear dynamics components of FI were not considered for the dynamical analysis of MBMS. This work presents a comprehensive, thorough analysis of an MBMS with a nonlinear FI. A servo-controlled MBMS with a nonlinear FI is modeled as a two DOF spring-mass-damper lumped parameter system. The linear stability analysis in the parametric space of reference velocity signal and differential gain reveals that including nonlinearity in FI significantly increases local stability of the system's steady-states. This further allows the implementation of larger differential gains in the servo-controlled motion stage. Furthermore, we perform a nonlinear analysis of the system and observe the existence of sub and supercritical Hopf bifurcation with or without any nonlinearity in the friction isolator. However, the region of Sub and Supercritical Hopf bifurcation on stability curves depends on the nonlinearity in FI. These observations are further verified by a detailed numerical bifurcation which reveals the existence of nonlinear attractors in the system.