Nonlinear vibration analysis of a servo controlled precision motion stage with friction isolator

Abstract

Precision motion stages are used in advanced manufacturing, metrological applications, and semiconductor industries for high precision positioning with high speed. However, friction-induced vibration undermines the performance of a servo-controlled motion stage. Recently, it was found that passive isolation in the form of friction isolator is very effective to mitigate the undesirable effects of friction in precision motion stages. This work presents, for the first time, a detailed nonlinear analysis of the dynamics of motion stage with a friction isolator. We consider a lumped parameter model of the precision motion stage with PID and a friction isolator modeled as two degrees of freedom system. Linear analysis of the system in the space of integral gain and reference velocity reveals that the inclusion of friction isolator increases the local stability region of steady states. We further observe the sensitivity of the stability of steady states towards the internal resonance between the motion stage and friction isolator. The influence of friction isolator on the nonlinear response of the system is examined analytically using the method of multiple scales and harmonic balance. We observe that the inclusion of friction isolator does not change the nature of Hopf bifurcation for higher values of reference velocity, and it remains subcritical bifurcation with or without friction isolator. However, for lower values of reference velocity, the inclusion of friction isolator leads to change in bifurcation from supercritical to subcritical for the given values of parameters. This observation further implies that the inclusion of friction isolator increases the local stability of steady states, whereas the global stability of steady states depends on the interaction between friction isolator and operating parameters. Furthermore, a detailed numerical bifurcation analysis of the system reveals the existence of period-2, period-4, quasi-periodic, and chaotic solutions. Also, the stability of period-1 solutions near Hopf point is determined by Floquet theory, which further reveals the existence of period-doubling bifurcation.