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.

精密运动平台用于先进制造，计量应用和半导体行业，以实现高速高精度定位。但是，摩擦引起的振动会破坏伺服控制运动平台的性能。最近，发现以摩擦隔离器形式的被动隔离对于减轻精密运动阶段的摩擦的不良影响非常有效。这项工作首次展示了带有摩擦隔离器的运动平台动力学的详细非线性分析。我们考虑带有PID的精密运动平台的集总参数模型和建模为两个自由度系统的摩擦隔离器。在积分增益和参考速度空间内对系统进行线性分析表明，包含摩擦隔离器会增加稳态的局部稳定性区域。我们进一步观察到稳态对运动级与摩擦隔离器之间的内部共振的敏感性。采用多尺度和谐波平衡的方法，分析了摩擦隔离器对系统非线性响应的影响。我们观察到，对于较高的参考速度值，包含摩擦隔离器不会改变Hopf分叉的性质，并且在有或没有摩擦隔离器的情况下，它仍然是亚临界分叉。但是，对于较低的参考速度值，对于给定的参数值，包含摩擦隔离器会导致分叉从超临界变为亚临界。该观察结果进一步暗示，包括摩擦隔离器会增加稳态的局部稳定性，而稳态的整体稳定性取决于摩擦隔离器和工作参数之间的相互作用。此外，对该系统进行的详细数值分叉分析揭示了周期2，周期4，准周期和混沌解的存在。另外，通过Floquet理论确定了Hopf点附近的1期解的稳定性，这进一步揭示了倍增分岔的存在。而稳态的整体稳定性取决于摩擦隔离器和工作参数之间的相互作用。此外，对该系统进行的详细数字分叉分析揭示了周期2，周期4，准周期和混沌解的存在。另外，通过Floquet理论确定了Hopf点附近的周期1解的稳定性，这进一步揭示了周期加倍分支的存在。而稳态的整体稳定性取决于摩擦隔离器和工作参数之间的相互作用。此外，对该系统进行的详细数字分叉分析揭示了周期2，周期4，准周期和混沌解的存在。另外，通过Floquet理论确定了Hopf点附近的1期解的稳定性，这进一步揭示了倍增分岔的存在。