中文摘要：

以机床进给系统为研究对象,运用拉格朗日方程建立其动力学模型。考虑到弹性力的非线性化因素,建立了含有阻尼的Duffing方程来描述进给系统。利用MATLAB/SIMULINK对系统进行动力学仿真,分析丝杠长度、导程以及直径等因素对系统相轨迹的影响。分析结果表明,随着丝杠结构参数的变化,相平面上两个稳定焦点分布于中心两侧,相轨迹呈螺旋线的形式趋于两焦点并发生相互交叉现象,最终在焦点附近达到稳定状态。最后实验验证表明,系统存在混沌特征,滚珠丝杠进给系统是一个非线性系统,为实际工程中的应用提供了理论依据。

英文摘要：

By taking machine feed system as the research subject, a dynamics model is established using the Lagrange equation. Nonlinear form expresses the elastic force, and a Duffing equation with damping is established to describe the feed system. Using MATLAB/SIMULINK to simulate the system dynamics, the influence of the length, the lead and the diameter of the screw on the system is analyzed. On phase plane, there are two stable focuses distributing on both sides of the center, phase trajectory tends to be the two focuses in the form of a spiral line and crosses each other, and finally phase trajectory is stable near the focus. Experiment shows that the system has chaotic characteristics from the time domain waveform and power spectrum, and proves that the ball screw feed system is a nonlinear dynamic system, and provides a theoretical basis for the practical engineering application.