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

Abstract

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

CLC Number:

TH113.1

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.

References

[1] WANG C R,LIU D S,HUANG C H,et al.Numerical investigation into dynamic behavior of adjustable preload double-nut ball screw [J].Journal of Mechanical Science and Technology,2016,30(10):4489-4496.
[2] 吴福光,蔡承武,徐兆.振动理论 [M].北京:高等教育出版社,1987.
[3] 金斯伯格 J H.机械与结构振动—理论与应用 [M].白化同,李俊宝,译.北京:中国宇航出版社,2005.
[4] 付振彪,王太勇,张雷.滚珠丝杠进给系统动力学建模与动态特性分析 [J].振动与冲击,2019,38(16):56-63.
[5] 钱荣荣,骆敏舟,赵江海,等.基于Ritz级数的滚珠丝杠驱动系统建模与振动研究 [J].系统仿真学报,2017,29(10): 2268-2275.
[6] ZHANG L,WANG T Y,WANG G F,et al.Hybrid dynamic modeling and analysis of a ball-screw-drive spindle system [J].Journal of Mechanical Science and Technology, 2017,31(10):4611-4618.
[7] WU Q,GU F S,ANDREW B,et al.Hybrid model for the analysis of the modal properties of a ball screw vibration system [J].Journal of Mechanical Science and Technology, 2021,35(12):461-470.
[8] 肖勇刚,李龙.基于传递矩阵法的变截面梁自振特性分析 [J].公路与汽运,2022(4):129-133.
[9] 程胜杰,李娟,焦邵华.传递矩阵法验证发电机轴系扭振特性 [J].电气技术,2019,20(10):19-24.
[10] LEE J W,LEE J Y,LEE D M.Free vibration analysis of axially moving beams using the transfer matrix method [J].Journal of Mechanical Science and Technology,2021,35(4):1369-1376.
[11] FEYZOLLAHZADEH M,BAMDAD M.A modified transfer matrix method to reduce the calculation time: A case study on beam vibration [J].Applied Mathematics and Computation, 2020,378:125238.
[12] LEE J W.Free vibration analysis of tapered Rayleigh beams using the transfer matrix method [J].Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2020,42(11):1-19.
[13] VICENTE D A,HECKER R L,VILLEGAS F J,et al. Modeling and vibration mode analysis of a ball screw drive [J].International Journal of Advanced Manufacturing Technology,2012,58(1/2/3/4):257-265.
[14] HENKE B,SAWODNY O,NEUMANN R.Distributed parameter modeling of flexible ball screw drives using Ritz series discretization [J].IEEE/ASME Transactions on Mechatronics,2015,20(3):1226-1235.
[15] ZHANG J,ZHANG H J,DU C,et al.Research on the dynamics of ball screw feed system with high acceleration [J].International Journal of Machine Tools and Manufacture, 2016,111:9-16.
[16] ZHANG C,ZHANG J R.Bending vibration analysis of tensioned ball screw under nonuniform stress during the cutting process [J].Shock and Vibration, 2019,2019:1-10.