机床进给系统滚珠丝杠轴向非线性振动分析

将机床进给系统滚珠丝杠简化为Timoshenko梁,对滚珠丝杠进行受力分析,建立滚珠丝杠的运动微分方程。采用假设模态法,对运动微分方程进行化简,得到丝杠轴向振动方程,轴向振动方程满足Duffing方程形式,轴向振动具有非线性特征。利用MATLAB对Duffing方程进行数值仿真,研究丝杠长度、激振力和阻尼系数对振动的影响,得到轴向振动的相轨迹图和截面,分析轴向振动的稳定性和周期性。相图极限环封闭,轴向振动具有两个中心型奇点分布在原点两侧,奇点对振动具有吸引作用,使系统轴向振动在奇点附近达到稳定状态,Poincare截面显示轴向振动出现混沌运动、拟周期运动或周期运动,奇点位置随振动系统参数变化,但分布情况不变化。周期性随着激振频率和阻尼系数的增大而增强。试验验证了机床滚珠丝杠进给系统轴向振动存在混沌运动。为滚珠丝杠进给系统的动态特性分析和结构参数优化提供了一定的理论基础。

Analysis of Axial Nonlinear Vibration about Machine Feed System Ball-screw

The ball-screw of machine tool feed system is simplified as Timoshenko beam. The forced state of the ball-screw is analyzed and the differential equation of motion for the ball-screw is built. To obtain the ball-Screw axial vibration equation, the differential equation of motion was simplified by using the assumed mode method. Axial vibration equation was satisfied of the form of duffing equation with the characteristics of nonlinearity. The numerical simulation of Duffing equation was proceeded by MATLAB. The effect of screw length, exciting force and damping coefficient on vibration were researched, and the axial vibration phase track diagram and Poincare section were obtained. The stability and periodic of the axial vibration were analyzed. The limit cycle of phase track diagram was enclosed. Axial vibration had two type-center singularity distributions on both sides of the origin. The singularity was attracted of vibration so as to reach a stable state, and Poincare section was shown that axial vibration appeared chaotic motion, quasi periodic motion or periodic motion. Singularity position was changed with the vibration system parameters, but not changed in distribution. The Periodic of the vibration was enhanced with increasing of exciting frequency and damping coefficient. Test of the feed system ball-screw axial vibration exists chaos movement, which provides a certain theoretical basis for the dynamic characteristic analysis of machine feed system ball-screw and optimization of structural parameters.