Journal of Jilin University(Engineering and Technology Edition) ›› 2025, Vol. 55 ›› Issue (1): 116-124.doi: 10.13229/j.cnki.jdxbgxb.20230295

Previous Articles     Next Articles

Spindle vibration reliability analysis considering bearing nonlinear restoring force

Xian-zhen HUANG1,2(),Rui YU1,Hui-zhen LIU1,Ji-wu TANG3   

  1. 1.School of Mechanical Engineering and Automation，Northeastern University，Shenyang 110819，China
    2.Key Laboratory of Vibration and Control of Aero-Propulsion Systems Ministry of Education of China，Northeastern University，Shenyang 110819，China
    3.Apllied Technology College of Dalian Ocean University，Dalian 116300，China
  • Received:2023-04-03 Online:2025-01-01 Published:2025-03-28

RICH HTML

 0   

PDF (PC)

185

Abstract:

In order to study the effect of spindle vibration on the reliability of machine tools during service life， this paper takes a certain type of spindle as the research object， uses the sum of nonlinear bearing restoring force and rotational unbalance force as the external excitation of the spindle-bearing system， establishes a 14-degree-of-freedom dynamic model of the machine tool spindle-bearing system using the lumped mass method， and solves the dynamic equation using numerical methods. An experimental platform is built to compare the results of the experiment with the results of the dynamic model to illustrate the effectiveness of the system dynamics modeling. Then， considering the randomness of bearing parameters， a spindle vibration reliability model is established with the maximum vibration displacement of the spindle shaft end as the evaluation index. Finally， the adaptive Kriging combined with Monte Carlo simulation method（AK-MCS） is used for reliability analysis of machine tool spindle vibration. The results show that the dynamic model and reliability evaluation method proposed in this paper have high accuracy.

Key words: mechanical design, shaft end vibration displacement, centralized mass method, dynamic model, adaptive Kriging method, reliability

CLC Number: 

  • TG659

Fig.1

Spindle model diagram"

Fig.2

Simplified diagram of spindle"

Fig.3

Schematic diagram of rolling bearing model"

Fig.4

Flow chart of AK-MCS reliability analysis"

Fig.5

Vibration response test bench"

Table 1

Bearing parameters"

轴承参数SKF 7003
轴承内径r/mm17
轴承外径R/mm35
轴承宽度B/mm10
滚珠数目Z12
初始接触角α15
滚珠直径D/mm4.96
初始间隙γ/μm9.5

Table 2

Quality parameters"

参数数值
m1/kg0.26
mb1/kg0.31
m2/kg2.08
mb2/kg0.63
m3/kg0.72

Table 3

Stiffness and damping parameters"

阻尼参数数值刚度参数数值
c1b1/［N·（s·m-1）］850k1b1/（N·m-1）2.134 7×109
c2b1/［N·（s·m-1）］1 350k2b1/（N·m-1）2.368 8×109
c2b2/［N·（s·m-1）］1 350k2b2/（N·m-1）4.703 6×108
c3b2/［N·（s·m-1）］1 350k3b2/（N·m-1）3.153 8×108
cb1y /［N·（s·m-1）］1 000kb1y /（N·m-1.5）3.329×108
cb1x /［N·（s·m-1）］1 000kb1x /［N（s·m-1.5）］3.329×108
cb2y /［N·（s·m-1）］1 000kb2y /［N（s·m-1.5）］3.329×108
cb2x /［N·（s·m-1）］1 000kb2x /［N（s·m-1.5）］3.329×108

Fig.6

Spindle speed response of 27 000， 37 2000， 43 500，49 800 r/min"

Table 4

Comparison of theoretical and experimental results"

转速/（r·min-1）实验峰值/μm理论峰值/μm相对误差/%实验周期/10-3 s理论周期/10-3 s相对误差/%
27 00084.7176.749.42.22.220.9
37 20079.4372.818.31.61.610.6
43 50070.4169.181.71.41.390.7
49 80065.3870.397.61.21.210.8

Table 5

Bearing clearance and contact stiffness random parameters"

随机变量分布类型均值标准差
前轴承组接触刚度kb1/（108 N·m-1.5）正态分布3.330.2
后轴承组接触刚度kb2/（108 N·m-1.5）正态分布3.330.2
前轴承组间隙γ1/μm正态分布9.52
后轴承组间隙γ2/μm正态分布9.52

Fig.7

Comparison between the calculated values of dynamic model and adaptive Kriging"

Fig.8

Absolute error between the calculated value of dynamic model and that of adaptive Kriging"

Fig.9

Maximum displacement of spindle varies with speed of rotation"

Fig.10

Vibration reliability of spindle varies with speed of rotation"

1 Cao H, Zhang X, Chen X. The concept and progress of intelligent spindles[J]. International Journal of Machine Tools and Manufacture, 2017, 112: 21-52.
2 姜彦翠, 季嗣珉, 刘献礼. 基于主轴系统动力学的铣削稳定性建模与分析[J]. 工具技术, 2019, 53(5): 73-76.
Jiang Yan-cui, Ji Si-min, Liu Xian-li. Modeling and analysis of milling stability based on spindle System dynamics[J]. Tool Technology, 2019, 53(5): 73-76.
3 陈传海, 姚国祥, 金桐彤,等. 基于响应面与遗传算法的主轴系统动力学建模及参数修正[J]. 吉林大学学报:工学版, 2022, 52(10): 2278-2286.
Chen Chuan-hai, Yao Guo-xiang, Jin Tong-tong, et al. Dynamic modeling and parameter correction of spindle system based on response surface and genetic algorithm[J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(10): 2278-2286.
4 Jorgensen B R, Shin Y C. Dynamics of spindle-bearing systems at high speeds including cutting load effects[J].ManuFacturing Science and Engineering, 1998, 120: 387-394.
5 Xi S, Cao H. Dynamic modeling of machine tool spindle bearing system and model based diagnosis of bearing fault caused by collision[J]. Procedia CIRP, 2018, 77: 614-617.
6 Lu H, Ding Y, Chang Y. Dynamics modelling and simulating of ultra-precision fly-cutting machine tool[J]. International Journal of Precision Engineering and Manufacturing, 2020, 21: 189-202.
7 Jiang S, Mao H. Investigation of variable optimum preload for a machine tool spindle[J]. International Journal of Machine Tools and Manufacture, 2010, 50(1): 19-28.
8 Chen J S. Centrifugal force induced dynamics of a motorized high-speed spindle[J]. International Journal of Advanced Manufacturing Technology, 2006, 30: 10-19.
9 金城, 高通, 怀天澍, 等. 数控机床主轴系统可靠性分析[J]. 机械制造, 2021, 59(7): 11-15,24.
Jin Cheng, Gao Tong, Huai Tian-shu, et al. Reliability analysis of CNC machine tool spindle system[J]. Machinery, 2021, 59(7): 11-15,24.
10 贺鑫元. 机床主轴的可靠性及可靠性灵敏度分析[J]. 制造技术与机床, 2018(1): 44-46,59.
He Xin-yuan. Reliability and reliability sensitivity analysis of machine tool spindles[J]. Manufacturing Technology and Machine Tools, 2018(1): 44-l46,59.
11 Miao H, Li C, Wang C, et al. The vibration analysis of the CNC vertical milling machine spindle system considering nonlinear and nonsmooth bearing restoring force[J]. Mechanical Systems and Signal Processing, 2021, 161: 1884-2023.
12 Sunnersj C S. Varying compliance vibrations of rolling bearings[J]. Journal of Sound and Vibration, 1978, 58: 363-373.
13 Akturk N, Uneeb M, Gohar R. The effects of number of balls and preload on vibrations associated with ball bearings[J]. Journal of Tribology, 1997, 119: 747-753.
14 唐云冰. 航空发动机滚动轴承力学特性研究[D]. 南京: 南京航空航天大学能源与动力学院, 2005.
Tang Yun-bing. Research on the mechanical characteristics of aero-engine shaft high-speed ball bearings[D]. Nanjing:College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, 2005.
[1] Shu-kun WANG,Yu-ze FENG,Jing-ran ZHANG,Xin-ming ZHANG,Long ZHENG. Analysis on decontamination performance of lower lip structure of imitation scavenger [J]. Journal of Jilin University(Engineering and Technology Edition), 2025, 55(1): 392-400.
[2] Xian-zhen HUANG,Bin GUO,Zhi-yuan JIANG,Ji-wu TANG. Vibration characteristics and precision reliability analysis of high-speed motorized spindle system [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(9): 2432-2440.
[3] Chang-jiang ZHENG,Tong-tong TAO,Zhi-chao CHEN. Cascading failure model based on adjustable redistribution of traffic flow [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(9): 2441-2450.
[4] Chen WANG,Te LUO,Qian-qian HUI,Zhong-hao WANG,Fang-fang WANG. Design and verification of electromechanical system for docking and locking of modular flying vehicle [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(8): 2130-2140.
[5] Yang LIU. Simulation and experiment of elastic roughing for rubber shoe [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(8): 2167-2173.
[6] Xue-lian GUO,Wan-shui HAN,Tao WANG,Kai ZHOU,Xiu-shi ZHANG,Shu-ying ZHANG. Assessment method of resistant overturning stability safety factors of curved bridge under customized transport vehicles [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(8): 2229-2237.
[7] Ying AN,Shuai GAO. Design of automatic mechanical transmission system based on torsional vibration reduction [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(7): 1844-1850.
[8] Yang LIU,Tao JIANG. Interference calculation model of Hooke joint of 6-DOF platform considering installation angle [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(6): 1519-1527.
[9] Lei WANG,Dong-xia LI,Song ZHOU,Li HUI,Zhen-xin SHEN. Fatigue crack propagation behavior and life prediction of 2024-O aluminum alloy FSW joints [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(6): 1563-1569.
[10] Xiao-dan TAN,Yong-peng WANG,Robert Hall,Tian-shuang XU,Qing-xue HUANG. Haul truck dump body optimization for autonomous shovel loading [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(5): 1227-1236.
[11] Chao CHEN,Meng-chu DAI,Le ZHOU,Yun-dong LIANG. Reliability allocation of agricultural machinery based on improved integrated factors method [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(5): 1493-1500.
[12] Shi-jun WANG,Guan-wei LUO. Periodic motion transition characteristics of a vibro-impact system with multiple impact constraints [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(4): 902-916.
[13] Shao-hua WANG,Qi-rui ZHANG,De-hua SHI,Chun-fang YIN,Chun LI. Analysis of nonlinear vibration response characteristics of hybrid transmission system with dual-planetary gear sets [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(4): 890-901.
[14] Xue-ping FAN,Heng ZHOU,Yue-fei LIU. Time⁃variant reliability analysis of bridge members based on Gaussian Copula⁃Bayesian dynamic models [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(2): 485-493.
[15] Wei SUN,Jun YANG. Finite element modeling and vibration reduction analysis of cylindrical shell structures with equal⁃angle attachment of piezoelectric shunt patches [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(2): 365-374.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] Wang Feng-wu; Zhu Chuan-gao; Fang Wen-yan; Chu Dao-bao .

Synthesis of nanocrystalline Ni /TiO2 modified electrode and
its electrochemical behavior

[J]. 吉林大学学报(工学版), 2006, 36(06): 861 -0865 .
[2] Hu Xing-jun;Zhang Ying-chao;Li Sheng;Lin You-zhi;Wang Jia-xue;Yang Yong-bai . Numerical simulation of vehicle aerodynamic characteristics based on DRSM[J]. 吉林大学学报(工学版), 2008, 38(03): 504 -0507 .
[3] Sun Hua-dong,Su Fu-lin,Gao Jian-jun,Zhang Ye . Parameter estimation of SAR moving target
based on DPCAFrFT algorithm[J]. 吉林大学学报(工学版), 2008, 38(02): 476 -0482 .
[4] Zhan Jun. Setup of vehicle longitudinal dynamic model for adaptive cruise control[J]. 吉林大学学报(工学版), 2006, 36(02): 157 -0160 .
[5] Dong Wen,Wang Hai-dong,Li Guang-yu,Tan Jian-jun . Surface microstructure of Cr film by Nd:YAG pulsed laser oxidation[J]. 吉林大学学报(工学版), 2007, 37(01): 17 -21 .
[6] Zhang Fei-jun,Wang Yun-peng,Shi Shu-ming,Li Shi-wu,Sun Fu-shen, Wang Bin-bin . Simulation of road alignment design safety evaluation[J]. 吉林大学学报(工学版), 2007, 37(03): 528 -0532 .
[7] Hu Feng-ye;Wang Shu-xun;Guo Gang . Performance analysis of adaptive interleaving for MIMO-OFDM systems[J]. 吉林大学学报(工学版), 2008, 38(03): 704 -0708 .
[8] He Hong-wen, Yu Xiao-jiang . Performance evaluation of electric vehicle power battery
[J]. 吉林大学学报(工学版), 2006, 36(05): 659 -0663 .
[9] . [J]. 吉林大学学报(工学版), 2007, 37(06): 1380 -1385 .
[10] Zhang Han-zhuo, Jiang Zhong-hao, Lian Jian-she, Li Guang-yu . Influence of current density on synthesized technique and microstructure
of nanocrystalline Cu deposition
[J]. 吉林大学学报(工学版), 2007, 37(05): 1074 -1077 .
Copyright © Journal of Jilin University(Engineering and Technology Edition), All Rights Reserved.
Tel: +86-431-85095297　Fax: +86-431-85094074　E-mail: xbgxb@jlu.edu.cn
Powered by Beijing Magtech Co. Ltd