Abstract Global behavior of a simplified non-smooth dynamic model for a micro-vibration molding machine in parameter-state space is explored. Solutions for the periodic motions of the impact oscillator are obtained by the semi-analytical method. Conditions for the grazing motions and sticking motions of the model are deduced. The motions distribution and transition in the fundamental periodic motion regions and the periodic inclusions areas are studied. Transition of the motions due to the singularity of the grazing bifurcation is analyzed. Polymorphic coexistence under the effect of the grazing bifurcation and the saddle-node bifurcation are revealed. Through the global analysis method in parameter-state space, the global distribution map in high frequency region can be acquired, which is rarely considered before. Under the guidance of the global motions distribution, the evolution of the polymorphic coexistence areas can be further discussed. The results can provide some references and ideas for the dynamic design and motion control of the micro-vibration molding machine.

中文翻译：

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参数状态空间中微振动成型机简化模型的全局行为

摘要 探讨了参数状态空间中微振动成型机简化非光滑动力学模型的全局行为。冲击振荡器周期运动的解是通过半解析方法获得的。推导出模型的掠动和粘滞运动条件。研究了基本周期运动区域和周期包裹体区域的运动分布和过渡。分析了由于掠分岔的奇异性引起的运动过渡。揭示了在放牧分叉和鞍结分叉作用下的多晶型共存。通过参数-状态空间中的全局分析方法，可以获得高频区域的全局分布图，这是以前很少考虑的。在全局运动分布的指导下，可以进一步讨论多态共存区域的演变。研究结果可为微振动成型机的动态设计和运动控制提供一定的参考和思路。