基于改进迁移矩阵法的滚珠丝杠横扭耦合振动研究

兰州理工大学学报 ›› 2023, Vol. 49 ›› Issue (5): 42-49.

基于改进迁移矩阵法的滚珠丝杠横扭耦合振动研究

吴沁^*, 罗殿立, 杨冉冉

兰州理工大学机电工程学院, 甘肃兰州 730050

收稿日期:2022-08-25 出版日期:2023-10-28 发布日期:2023-11-07
通讯作者: 吴沁(1973-),女,安徽颍上人,副教授. Email:1261099906@qq.com
基金资助:
国家自然科学基金(51765039)

Research on transverse torsional coupling vibration of ball screw based on improved transfer matrix method

WU Qin, LUO Dian-li, YANG Ran-ran

School of Mechanical and Electrical Engineering, Lanzhou Univ. of Tech., Lanzhou 730050, China

Received:2022-08-25 Online:2023-10-28 Published:2023-11-07

摘要/Abstract

摘要： 传统2~4阶迁移矩阵法只能用于研究梁类系统的单自由度振动问题,若将其直接应用于研究含有耦合振动的梁类系统时,系统固有频率计算结果将会出现很大误差.对此,以机床滚珠丝杠进给系统为研究对象,对其进行简化并将滚珠丝杠视为柔性梁,在考虑梁转动惯量和横向剪切变形的基础上,采用Timoshenko梁理论将传统2~4阶迁移矩阵法改进到6阶,建立系统的力学和理论模型,获得包含横向振动和扭转振动的系统状态迁移矩阵方程.通过对比系统前两阶固有频率的仿真结果与实验结果,验证了改进迁移矩阵法的合理性和精确性.另外,通过数值仿真研究负载对系统前两阶固有频率和滚珠丝杠横扭耦合振型的影响,探究滚珠丝杠的横扭耦合振动特性.

关键词: 滚珠丝杠, Timoshenko梁理论, 改进迁移矩阵法, 固有频率, 耦合振动特性

Abstract: The traditional 2~4-order transfer matrix method can only be used to study the single degree of freedom vibration of beam systems. If it is directly applied to the study of beam systems with coupled vibration,a large error will exist in the calculation results of the natural frequencies of the system. In order to solve this problem, the ball screw feed system of the machine tool is taken as the research object in this paper, which is simplified and regarded the ball screw as a flexible beam. Based on considering the moment of inertia and transverse shear deformation of the beam, the traditional 2~4-order transfer matrix method is improved to 6-order by using Timoshenko beam theory. The mechanical and theoretical model of the system is established, and the system state transfer matrix equation including transverse vibration and torsional vibration is obtained. By comparing the simulation results and experimental results of the first two natural frequencies of the system, the accuracy and rationality of the improved transfer matrix method are verified. In addition, the influence of load on the first two natural frequencies of the system and the transverse torsional coupling vibration modes of the ball screw are studied through numerical simulation, and the transverse torsional coupling vibration characteristics of the ball screw are explored.

Key words: ball screw, Timoshenko beam theory, improved transfer matrix method, natural frequency, coupled vibration characteristics

中图分类号:

TH113.1

吴沁, 罗殿立, 杨冉冉. 基于改进迁移矩阵法的滚珠丝杠横扭耦合振动研究[J]. 兰州理工大学学报, 2023, 49(5): 42-49.

WU Qin, LUO Dian-li, YANG Ran-ran. Research on transverse torsional coupling vibration of ball screw based on improved transfer matrix method[J]. Journal of Lanzhou University of Technology, 2023, 49(5): 42-49.

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