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

The application of servocontrolled 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 servocontrolled 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 the local stability of the system's fixed-points. This further allows the implementation of larger differential gains in the servocontrolled 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.

Automated summary

This study presents a comprehensive analysis of an MBMS with a nonlinear FI. The inclusion of nonlinearity in the friction isolator significantly increases the local stability of the system's fixed-points, allowing for larger differential gains in the servocontrolled motion stage. The system exhibits sub and supercritical Hopf bifurcation, and the region of bifurcation depends on the nonlinearity in the FI.