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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。
Taking the machine tool feeding system as the research object, the dynamic model of the machine tool is established by Lagrange’s equation. Considering the nonlinear force of elasticity, a Duffing equation with damping is established to describe the feeding system. Using MATLAB / SIMULINK to simulate the system dynamics, the influence of screw length, lead and diameter on the phase trajectory of the system was analyzed. The analysis results show that with the change of screw structural parameters, the two stable focal points on the phase plane are distributed on both sides of the center, and the phase trajectories tend to be two focal points in the form of a spiral and cross each other, eventually reaching a steady state near the focal point . The final experimental verification shows that the system has chaos characteristics. The ball screw feed system is a nonlinear system, which provides a theoretical basis for the practical engineering application.