速度型切削颤振的非线性分析

Nonlinear Analysis of Speed-Type Machine Tool Chatter

本文应用微分方程稳定性理论与极限环理论分析受非线性因素影响的速度型切削颤振问题,着重研究动态切削力中的非线性阻尼与机床结构特性中的非线性刚度对切削过程稳定性与颤振振幅稳定性的影响。结果表明,切削过程的稳定性取决于切削阻尼与机床结构阻尼,而与机床结构的刚度特性(线性或非线性)无关;非稳态的切削过程是否存在极限环,亦与机床结构的刚度特性无关,只取决于切削过程的阻尼特性,也就是说,满足一定条件的切削过程的非线性阻尼,亦是导致切削颤振振幅稳定性的原因。

The theories of stability and limit cycles of differential equations are used to analyse the speed-type chatter of machine tool during the cutting process which is affected by nonlinear factors. The interest is focused on investigating the effects of nonlinear damping of cutting process and nonlinear stiffness of machine tool structure on the stability of the cutting process and stabilization of chatter amplitudes. The results show that the stability of the cutting process and the stabilization of chatter amplitudes are dependent on the damping of uctting process and machine tool structure, but independent of the characteristic of the stiffness of machine tool structure. Under certain conditions, the nonlinear damping of the cutting process may lead to the stabilization of chatter amplitudes.