基于Ritz级数法滚珠丝杠的混合模型研究  

Hybrid modeling of ball screw based on Ritz series method

作　　者：王娜[1] 姜宝华[1] 宗成国[2] WANG Na;JIANG Bao-hua;ZONG Cheng-guo(Department of intelligent manufacturing,Qingdao Huanghai University,Qingdao 266427,China;College of Mechanical and Electronic Engineering,Shandong University of Scienceand Technology,Qingdao 266590,China)

机构地区：[1]青岛黄海学院智能制造学院,山东青岛266427 [2]山东科技大学机械电子工程学院,山东青岛266590

出　　处：《机电工程》2020年第10期1179-1185,共7页Journal of Mechanical & Electrical Engineering

基　　金：山东省重点研发计划项目(2019GGX105001);山东省博士后创新项目专项资金项目(201702038)。

摘　　要：为研究高速滚珠丝杠进给系统的混合模型与振动特性,提出了一种混合模型方法。使用功率平衡公式和Ritz级数法,建立了承受移动载荷作用下的丝杠轴扭耦合振动模型,并采用Timoshenko梁理论,建立了承受移动载荷作用下的丝杠弯曲振动模型;针对滚珠丝杠常用的3种支撑方式,提出了适用于对应不同支撑方式的基函数表达式,并得到了通用的质量、刚度和阻尼矩阵表达式;通过实验和数值仿真验证了该模型的正确性,并研究了工作台位置、质量及导程等对振动的影响。研究结果表明:轴向振动受工作台位置和质量因素影响较大,扭转振动所受影响较小;随着工作台重量增加,工作台的振动频率对于丝杠导程的变化更为敏感,这为后续相关研究奠定理论基础。In order to study the hybrid modeling and vibration characteristics of high-speed ball screw feed system,a hybrid modeling method was proposed.The power balance formula and the Ritz series method were used to establish the shaft-torsional coupled vibration model of the ball screw under the action of moving load.And the Timoshenko beam theory was used to establish the bending vibration model of the ball screw under the action of moving load.According to the three support methods commonly used in ball screws,the basis function expressions corresponding to different support modes were proposed,and the general mass,stiffness and damping matrix expressions were obtained.The correctness of the model was verified by experiments and numerical simulations.The influence of the position,mass and lead of the table on the vibration was studied.The research results indicate that the axial vibration is greatly affected by the position and quality of the table,and the torsional vibration is less affected.As the weight of the table increases,the vibration frequency of the table is more sensitive to changes in the lead of the screw,which lays a theoretical foundation for the subsequent related research.

关 键 词：滚珠丝杠 振动特性 仿真分析 混合模型 

分 类 号：TH113[机械工程—机械设计及理论] TG502[金属学及工艺—金属切削加工及机床]