考虑非线性迟滞力的机床颤振系统稳定性研究

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Based on the orthogonal turning process, the single degree of freedom chatter model taking the nonlinear hysteretic and exciting force into consideration is established. The nonlinear dynamic equation of chatter system is solved with the method of multiple scales, and the bifurcation equations of amplitude phase and approximate second-order periodic response can be obtained. The lobe diagram is applied to analyze the linear stability so that the critical relationship between the chatter frequency and time delay can be established for the subsequent stability analysis. The chatter instability phenomenon is characterized by the limited amplitude applied to study the impact of rotating speed and hysteretic parameters. Through the above impact analysis, the time delay factor is discussed further. The three-dimensional spectrum is adopted to analyze the impact of the rotating speed and hysteretic parameters on response and explain its nonlinear dynamics. The conclusion that the hysteretic parameters influence the nonlinear stability much more obviously in the low speed condition can be derived. The methods and data results provide a theoretical reference for the cutting stability prediction and dynamic optimization design in high-speed spindle system of machine tool.从正交车削过程出发，建立含有非线性迟滞力和激振力的机床单自由度颤振模型，利用多尺度法对系统的非线性动力学方程进行求解，得到系统振幅和相位的分岔方程以及响应的二阶近似解。利用叶瓣图对系统的线性稳定性进行分析，为后续的稳定性分析建立颤振频率与时滞间的临界关系，提出用振幅极限值表征系统的颤振失稳现象，研究转速和滞回参数对颤振失稳产生的影响，并进一步讨论系统中存在的时滞因素。通过三维图谱分析转速和滞回参数对系统响应产生的影响，对其中存在的非线性动力学现象进行阐述，结果表明：滞回参数在低转速工况下对系统非线性稳定性影响较为剧烈，所采用方法和数据结果可以为机床高速主轴系统切削稳定性预测以及动态优化设计提供参考依据。