滚珠丝杠传动非线性刚度动态特性的数值仿真

数控工作台是一个复杂的非线性动力学系统.其滚珠丝杠副刚度的非线性变化规律分别呈软弹簧和硬弹簧特性,其动态特性分别遵循软、硬特性的Duffing方程.用MATLAB/SIMULINK仿真平台,分别对软、硬特性Duffing方程的动态特性进行仿真,得到不同工况下的特征相图.仿真结果表明其几何特征丰富多彩;存在周期运动、准周期运动和混沌运动等多种运动状态;存在由倍周期分岔向混沌运动的演变过程;软特性比硬特性运动状态复杂、出现混沌的机会更多.提出了为提高精加工过程中的质量,应把工件装夹在工作台中间,使加工过程中滚珠丝杠副运行在弱非线性区;精选走刀方向,使刚度非线性呈硬特性,以减少出现混沌的机会.

NUMERICAL SIMULATION ON DYNAMIC CHARACTERISTICS CAUSED BY NONLINERAR STIFFNESS OF BALL SCREW DRIVING MECHANISM

NC（Numerical Control） table is a complex nonlinear dynamic system.The change rules of the nonlinear stiffness of its ball screw driving mechanism show soft spring property or hard spring property.Their responses obey soft or hard property Duffing equation.Numerical simulations on soft and hard property Duffing equations are carried out separately based on MATLAB/SIMULINK simulation platform and the characteristic phase diagrams under different conditions are obtained.The simulation results show that the geometric features are in various ways.Many motion states such as periodic motion,quasi periodic motion and chaotic motion etc.are existed.The evolution processes from period doubling bifurcation to chaotic motion are existed.Compared with hard spring property,the soft spring property has more complex motion states and more chances to produce chaotic motion.The conclusions are drawn that in order to enhance the machining quality,the work piece must be clamped right in the middle of the machine table to make the ball screw driving mechanism work in the weakly nonlinear zone,and the cutting direction must be carefully chosen in order to make the nonlinear stiffness of the ball screw driving mechanism show hard spring property to reduce the chances of chaotic motion.