滚珠丝杠进给系统刚柔耦合动力学建模与时变动态特性分析

Dynamic Modeling and Time-Varying Dynamic Characteristics Analysis of Rigid-Flexible Coupling for Ball Screw Feed System

数控机床运行过程中,多轴滚珠丝杠进给系统的刚度和惯量会随着各轴位姿的变化而变化,致使其动态特性呈时变的特点。多轴滚珠丝杠进给系统时变动态特性的高保真建模与分析已成为数控机床轮廓误差精准预测的瓶颈难题之一。针对这一难题,提出基于拉格朗日方程与Ritz级数法的滚珠丝杠进给系统刚柔耦合动力学建模与分析方法。以某型号五轴加工中心的两轴滚珠丝杠进给系统为具体对象,重点考虑丝杠本体轴扭方向的连续弹性体变形影响,采用拉格朗日方程建立滚珠丝杠进给系统的刚柔耦合动力学模型,并采用Ritz级数法对方程求解,得到动力学模型的数值解。利用所建立的动力学模型分析进给轴位姿对两轴进给系统固有频率和模态振型的影响,发现各阶固有频率和模态振型随进给轴位姿的变化规律与对应阶次的主导轴有关。随着主导轴进给台由固定端移动至支撑端,对应阶次的固有频率逐渐减小,对应阶次的振型中丝杠本体的弹性振动幅值逐渐增大。此外,两轴进给系统的低阶模态振型主要由承载轴主导,高阶模态振型主要由附属于承载轴的子轴主导。最后,通过模态实验对所提方法进行应用验证,证明所建立动力学模型的准确性。研究结果对数控机床轮廓误差的精准预测具有重要参考价值。

During the operation of CNC machine tools,the stiffness and inertia of the multi-axis ball screw feed system will change with the change of the poses of the feeding shafts,resulting in the time-varying characteristics of its dynamic characteristics.The high-fidelity modeling and analysis of the time-varying dynamic characteristics of the multi-axis ball screw feed system has become one of the bottlenecks in the accurate prediction of the contour error of CNC machine tools.Aiming at this problem,a rigid-flexible coupling dynamic modeling and analysis method of ball screw feed system based on Lagrange equation and Ritz series method was proposed.Taking the two-axis ball screw feed system of a five-axis machining center as the specific object,the rigid-flexible coupling dynamic model of the ball screw feed system was established by using the Lagrange equation,and the Ritz series method was used to solve the equation,and the numerical solution of the dynamic model was obtained.The influence of the poses of the feeding shaft on the natural frequency and modal shape of the two-axis feed system was analyzed by using the established dynamic model.It is found that the variation of the natural frequency and modal shape of each order with the poses of the feeding shaft is related to the dominant axis of the corresponding order.As the feed table of the main shaft moves from the fixed end to the support end,the natural frequency of the corresponding order gradually decreases,and the elastic vibration amplitude of the screw body in the corresponding modal mode gradually increases.In addition,the low-order modal shapes of the two-axis feed system are mainly dominated by the bearing shaft,and the high-order modal shapes are mainly dominated by the sub-shafts attached to the bearing shaft.Finally,the application of the proposed method is verified by modal experiments to prove the accuracy of the established dynamic model.The research results have important reference value for the accurate prediction of contour error of CNC machine tools.