轴车削过程的时变边界动力学分析

Analysis on Shaft-lathe Coupled Vibration by Dynamics of Systems with Variable Boundaries

在对轴车削过程进行几何描述的基础上,利用微分变分原理建立了轴与车床耦合振动的动力学模型,并利用谱截断的方法,降阶为4自由度的模型.通过数值计算,讨论了车削过程中动力学特性.研究表明,由于轴边界的时变,轴的振动不存在固有的模态,其自振频率和主振型为时变的;由于轴-车床耦合附加刚度的作用,轴的自振频率不是随时间单调减小,并且在车刀处于轴中央截面的时刻轴的振动位移未达到其最大值.在材料的几何方程和物理方程都是线性的条件下,轴边界和车刀位置的时变导致轴-车床耦合振动微分方程的非线性,轴振动位移的最大值与车削工艺参量成非线性关系.

On the basis of geometric description about the turning procedure of a shaft, a dynamic model of shaftlathe coupled vibration is established by differential-variation-principle, and a reduced model with 4 degrees of freedom is developed by using truncated spectra method. The dynamic characteristics of the system are discussed by numerical calculations. The results show that the natural frequencies and modes of the shaft-lathe coupled vibration are variable because of the variable boundaries of the shaft and of the variable location of the lathe tool. So there is no intrinsic mode in the vibration system. The natural frequencies do not decrease monotonously with time due to the additional stiffness caused by the coupling between the shaft and lathe; the maximum of the vibration amplitude of the shaft does happen at the exact moment when the lathe tool is on the middle cross-section of the shaft; it is because of the variable boundary of the shaft and the variable location of the lathe tool that the differential equation of the shaft-lathe coupled vibration is nonlinear even though both the geometric equation and the constitute equation are linear, and so the maximum of the vibration displacement of the shaft is not proportion to the technical parameters.