考虑径向间隙的非理想双圆弧滚道滚珠丝杠副接触角建模和分析

PDF(1689 KB)

振动与冲击 ›› 2019, Vol. 38 ›› Issue (20) : 181-187.

论文

姜洪奎 1，宋现春 1，许向荣 1，李彦凤 1，王乐源 1，刘涛 1,杜伟 2,荣伯松 2

作者信息 +

Modeling the elastic contact angle of preloaded ball screw pair with non-ideal double-arc raceway considering radial clearance

JIANG Hongkui 1 SONG Xianchun 1 XU Xiangrong 1 LI Yanfeng 1 WANG Leyuan 1 DU Wei 2 RONG Bo-song 2

Author information +

文章历史 +

摘要

双圆弧（哥特式）滚道可以使滚珠丝杠副的承载能力、刚度和传动精度更加稳定，在精密型滚珠丝杠副结构中广泛采用，但是双圆弧滚道的制造和测量都比较困难，往往得到非理想滚道。由于滚道误差、径向间隙与滚珠丝杠副的主要性能指标-弹性变形接触角之间存在非线性关系，导致精密滚珠丝杠副装配后的性能不易控制。为了优化滚珠丝杠副的装配质量，本文考虑初始游隙和接触角变化等因素，基于赫兹弹性接触理论和变形协调原理建立了非理想滚道截形的滚珠丝杠副弹性变形接触角的计算模型，并通过对比双半内圈球轴承初始接触角的计算公式，验证了本文提出的计算模型的通用性和正确性。以精密滚珠丝杠副3210为例，分析了内外滚道误差、径向间隙及滚珠大小对弹性接触角的影响规律。研究结果可为滚珠丝杠副的装配方法和优化设计等提供理论参考和依据。

Abstract

Double-arc raceway (Gothic raceway) is widely adopted in precision ball screw mechanism because it can made the ball screw’s mechanical properties such as bearing capacity, stiffness and transmission accuracy more stable.However, it is more difficult to manufacture and measure the double-arc raceway, and non-ideal raceway are often obtained in practical production.The geometric errors of raceway and radial clearance seriously affect the overall performance of the precision ball screw.In order to improve the assembling quality of ball screw pair, a mathematical model of elastic contact angle of double nut ball screw mechanism with non-ideal profile under pretention load was established based on the Hertz elastic contact theory and the deformation compatibility principle, considering initial radial clearance.The proposed model was verified by applying the model into the calculation of contact angle of split inner-ring ball bearing.Taking the example of double nut ball screw mechanism 3210, the influences of tolerance of raceway and ball diameter on elastic contact angle were analyzed.This method can provide a theoretical reference for optimization design of ball screw, and the intelligent optimization of assembly.

导出引用

姜洪奎 1，宋现春 1，许向荣 1，李彦凤 1，王乐源 1，刘涛 1,杜伟 2,荣伯松 2. 考虑径向间隙的非理想双圆弧滚道滚珠丝杠副接触角建模和分析[J]. 振动与冲击, 2019, 38(20): 181-187

JIANG Hongkui 1 SONG Xianchun 1 XU Xiangrong 1 LI Yanfeng 1 WANG Leyuan 1 DU Wei 2 RONG Bo-song 2 . Modeling the elastic contact angle of preloaded ball screw pair with non-ideal double-arc raceway considering radial clearance[J]. Journal of Vibration and Shock, 2019, 38(20): 181-187

参考文献

[1] 冯虎田. 滚珠丝杠副动力学与设计基础[M]. 北京：机械工业出版社, 2015.
[2] WEI C C, LIN J F. Kinematic analysis of the ball screw mechanism considering variable contact angles and elastic deformations[J]. Journal of Mechanical Design, 2003, (04):717-733.
[3] Xu N, Tang W, Chen Y, et al. Modeling analysis and experimental study for the friction of a ball screw[J]. Mechanism & Machine Theory, 2015, 87:57-69.
[4] 陈勇将, 汤文成, 王洁璐. 滚珠丝杠副刚度影响因素及试验研究[J]. 振动与冲击, 2013, 32(11):70-74.
CHEN Yong-jiang, TANG Wen-cheng, WANG Jie-lu. Influence factors on stiffness of a ball screw[J]. Journal of vibration and shock, 2013, 32(11): 70-74.
[5] Tao L, Wang Y, He Y, et al. A numerical method for evaluating effects of installation errors of grinding wheel on rotor profile in screw rotor grinding[J]. Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture, 2016, 230(8).
[6] 张学宁, 韩勤锴, 褚福磊. 基于简化Jones-Harris方法的球轴承接触角研究[J]. 振动与冲击, 2013, 32(13):170-175.
ZHANG X, HAN Q, CHU F. Research on contact angle of ball bearings based on simplified Jones-Harris method[J]. Journal of Vibration and Shock, 2013, 32(13):170-175.
[7] Chen J S, Huang Y K, Cheng C C. Mechanical model and contouring analysis of high-speed ball-screw drive systems with compliance effect[J]. International Journal of Advanced Manufacturing Technology, 2004, 24(3-4):241-250.
[8] 王燕霜, 袁倩倩, 曹佳伟, 李璞, 李燕. 特大型双排四点接触球轴承承载能力的研究[J]. 机械工程学报, 2014, 09：65-70.
WANG Yan-shuang, YUAN Qian-qian, CAO Jia-wei, LI Pu, LI Yan. Research on Static Load--carrying Capacity of Large Size Double Row Four-point Contact Ball Bearings[J]. Chinese Journal of Mechanical Engineering, 2014, 50(09):65-70.
[9] 胡建忠, 王民, 高相胜, 等. 双螺母定位预紧滚珠丝杠副轴向接触刚度分析[J]. 机械工程学报, 2014, 50(7)：106-113.
HU Jian-zhong, WANG Min, GAO Xiang-sheng, et al. Axial contact stiffness analysis of position preloaded ball screw mechanism[J]. Chinese Journal of Mechanical Engineering, 2014, 50(7):106-113.
[10] Wang Q, Lin M. Electromechanical coupling measurement of a new giant magnetostrictive structure for double-nut ball screw pre-tightening[J]. Measurement Science & Technology, 2016, 27(12):125906.
[11]赵国平,范元勋,张立柱,等.高负荷滚珠丝杠副弹塑性变形与失效的理论与试验研究[J].南京理工大学学报(自然科学版),2016,40(01):89
Zhao Guoping,Fan Yuanxun,Zhang Lizhu,et al.Theoretical and experimental research of plastoelastic deformationand failure of ball screw under high load condition[J].Journal of Nanjing University of Science and Technology,2016,40(01):89.
[12] 赵训贵, 平舜娣. 滚珠丝杠螺纹滚道参数误差对接触角和变位导程及摩擦力矩的影响及其相互关系[J]. 磨床与磨削,1995(3)：6-15.
[13] 李梦奇, 庾辉, 李冬英,等. 面向结构参数的滚珠丝杠副动态接触角建模[J]. 农业工程学报, 2016(4):98-104.
Li Meng-qi, Yu Hui, Li Dong-ying, Wang Bin, Zhang Gen-bao. Modeling for dynamic contact angle of ball screw mechanism aimed to structural parameters[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2016, 32(4): 98-104.
[14] 王永强, 张承瑞. 滚珠丝杠进给系统仿真建模[J]. 振动与冲击, 2013, 32(3):46-49.
WANG Yong-qiang, ZHANG Cheng-rui. Simulation modeling of a ball screw feed drive system[J]. Journal of Vibration and Shock, 2013, 32(3):46-49.
[15] 黄俊, 袁军堂, 汪振华. 双驱动进给系统动态建模及变化规律研究[J]. 振动与冲击, 2017, 36(18):148-153.
HUANG Jun, YUAN Juntang ,WANG Zhenhua. Dynamic modeling of a dual-drive system and its dynamic characteristics[J]. Journal of Vibration and Shock, 2017, 36(18):148-153.
[16] 杨勇, 张为民, 仇炜谏, 陈盛. 基于模态综合法与动态凝聚的滚珠丝杠进给系统状态空间建模与实验验证[J]. 振动与冲击, 2017, 36(13):53-59.
YANG Yong, ZHANG Weimin, QIU Weijian, et al. State space modeling and test verification for a ball screw feed system based on modal synthesis and dynamic condensation[J]. Journal of Vibration and Shock. 2017, 36(13):53-59.
[17] HARRIS T A, Rolling bearing analysis[M]. NewYork: John Wiley and Sons Inc, 2006.
[18] 姜洪奎;李彦凤;马建春，等. 非等适应比滚道的滚珠丝杠副弹性变形接触角的确定方法[P]. 中国CN201510512754.X，20151209.