Modeling and Reliability Global Sensitivity Analysis of Motorized Spindles Considering Thermal Errors

doi:10.12068/j.issn.1005-3026.2024.05.009

Abstract

Abstract:

Taking the motorized spindle of computer numerical control machine tools as the research object， the influence of its axial thermal elongation on the reliability of the motorized spindle is explored. The Svenska Kullager?Fabriken （SKF） friction torque model is used to analyze the heat generation of the bearing. The convective heat transfer coefficient is set as the boundary heat dissipation condition. The finite element coupling model of thermal analysis is established to solve the temperature and axial thermal elongation distribution of the spindle. The finite element model is compared with the experimental results to verify the accuracy of the established finite element model. Considering the influence of random factors， the reliability analysis model of spindle thermal deformation is established， and the reliability is solved by the Kriging model. Finally， the global sensitivity analysis of the thermal error reliability of the motorized spindle is carried out. The results show that the rotational speed and cooling water flow have a great influence on the reliability， and the axial force and radial force have little influence on the reliability.

Key words: motorized spindle, thermal characteristics, finite element analysis, Kriging model, reliability, global sensitivity

CLC Number:

TG 659

Xian-zhen HUANG, Rui YU, Zhi-yuan JIANG, Zhi-ming RONG. Modeling and Reliability Global Sensitivity Analysis of Motorized Spindles Considering Thermal Errors[J]. Journal of Northeastern University(Natural Science), 2024, 45(5): 675-682.

Figures/Tables 13

Fig.1 Model of the motorized spindle

Fig.2 Convective heat transfer position of the motorized spindle

Fig.3 Finite element modeling and analysis process

Table 1 Cooling medium parameters

介质名称	密度/（kg·m^-3）	运动黏度×10^-6/（m²·s^-1）	普朗特数	导热系数/(W·（m·K）^-1)
20°冷却水	998.5	1.006	7.020	0.599
22°干空气	1.205	16.06	0.703	0.026
ISO VG32	—	21	—	—

Table 2 Material parameters of the motorized spindle

部件	材料名称		密度×10³		导热系数		弹性模量×10⁵	泊松比		线膨胀系数×10^-5
部件	材料名称		kg·m^-3		W·（m·K）^-1		MPa	泊松比		℃^-1
外壳	HT300	7.35		50		2.1		0.32	1.22
轴承内、外圈	GCr15	7.83		42		2.09		0.32	1.28
滚珠	Si₃N₄	3.25		29.5		3.2		0.27	0.322
定子、转子	硅钢	7.70		12.9		2.0		0.26	1.28
转轴	20CrMo	7.84		50		2.1		0.28	1.35
轴环、挡圈	1045	7.81		48.15		2.1		0.30	1.18

Fig.4 Temperature and thermal deformation distribution of the motorized spindle

Fig.5 Experimental measurement device

Fig.6 Comparison of the temperature test results and simulation results

Fig.7 Comparison of the thermal deformation test results and simulation results

Table 3 Random parameter distribution

随机变量	转速	冷却水流量	轴向力	径向力
随机变量	r·min^-1	kg·s^-1	N	N
均值	60 000	0.167	350	300
变异系数	0.002	0.02	0.05	0.05

Fig.8 Comparison between the calculated values of the hot deformation finite element model and the Kriging calculation values

Fig.9 Relative error between the calculated values of the hot deformation finite element model and the Kriging calculation values

Fig.10 Global sensitivity analysis results

References 24

1	Aalilija A， Gandin CA， Hachem E.A simple and efficient numerical model for thermal contact resistance based on diffuse interface immersed boundary method［J］.International Journal of Thermal Sciences，2021，166：106817.
2	Mayr J， Jedrzejewski J， Uhlmann E，et al.Thermal issues in machine tools［J］.CIRP Annals-Manufacturing Technology，2012，61（2）：771-791.
3	Cao H R， Zhang X W， Chen X F.The concept and progress of intelligent spindles：a review［J］.International Journal of Machine Tools and Manufacture，2017，112：21-52.
4	Zhang L L， Xuan J P， Shi T L，et al.Robust，fractal theory，and FEM‑based temperature field analysis for machine tool spindle［J］.The International Journal of Advanced Manufacturing Technology，2020，111（5/6）：1571-1586.
5	Fang B， Cheng M N， Gu T Q，et al.An improved thermal performance modeling for high‑speed spindle of machine tool based on thermal contact resistance analysis［J］.The International Journal of Advanced Manufacturing Technology，2022，120（7）：5259-5268.
6	Ma C， Yang J， Zhao L，et al.Simulation and experimental study on the thermally induced deformations of high‑speed spindle system［J］.Applied Thermal Engineering，2015，86：251-268.
7	Yao X P， Hu T， Yin G F，et al.Thermal error modeling and prediction analysis based on OM algorithm for machine tool’s spindle［J］. The International Journal of Advanced Manufacturing Technology，2020，106（7）：3345–3356.
8	Liu K， Li T， Li T J，et al.Thermal behavior analysis of horizontal CNC lathe spindle and compensation for radial thermal drift error［J］.The International Journal of Advanced Manufacturing Technology，2018，95（1）：1293-1301.
9	Zhang L X， Gong W J， Zhang K，et al.Thermal deformation prediction of high‑speed motorized spindle based on biogeography optimization algorithm［J］.The International Journal of Advanced Manufacturing Technology，2018，97（5）：3141-3151.
10	Lee J， Kim D H， Lee C M.A study on the thermal characteristics and experiments of high‑speed spindle for machine tools［J］.International Journal of Precision Engineering and Manufacturing，2015，16（2）：293-299.
11	Harris T A， Kotzalas M N.Essential Concepts of Bearing Technology［M］，5th ed.New York：CRC Press，2007.
12	Liu J L， Ma C， Wang S L，et al.Thermal‑structure interaction characteristics of a high‑speed spindle‑bearing system［J］.International Journal of Machine Tools and Manufacture，2019，137：42-57.
13	Kullager‑Fabriken Svenska.Rolling bearings catalogue［EB/OL］.（2018-10-12）［2022-03-24］..
14	张雪亮.新型高速电主轴轴承-轴芯热场分布规律与实验研究［D］.哈尔滨：哈尔滨理工大学，2019.
	Zhang Xue‑liang.Distribution law and experimental study of heat field new high‑speed motorized spindle bearing‑spindle core ［D］.Harbin：Harbin University of Science and Technology，2019.
15	Jiang Z Y， Huang X Z， Chang M X，et al.Thermal error prediction and reliability sensitivity analysis of motorized spindle based on Kriging model［J］.Engineering Failure Analysis，2021，127：105558.
16	Yan B， Yan K， Luo T，et al.Thermal coefficients modification of high speed ball bearing by multi‑object optimization method［J］.International Journal of Thermal Sciences，2019，137：313-324.
17	崔向昆.高速电主轴温度分布及其热位移研究［D］.沈阳：沈阳建筑大学，2018.
	Cui Xiang‑kun.Research on temperature distribution and thermal displacement of high speed spindle［D］.Shenyang：Shenyang Jianzhu University，2018.
18	Chien C H， Jang J Y.3‑D numerical and experimental analysis of a built‑in motorized high‑speed spindle with helical water cooling channel［J］.Applied Thermal Engineering，2008，28（17/18）：2327-2336.
19	黄贤振，曹辉，张义民.基于蒙特卡罗方法的直角切削切削力概率特性分析［J］.东北大学学报（自然科学版），2015，36（2）：254-258.
	Huang Xian‑zhen， Cao Hui， Zhang Yi‑min.Probabilistic analysis of cutting force in orthogonal cutting based on using Monte‑Carlo method［J］.Journal of Northeastern University （Natural Science），2015，36（2）：254-258.
20	Ding P F， Huang X Z， Li Y X，et al.Reliability optimization of cutting parameters considering the diameter error of slender shaft［J］.Journal of Mechanical Science and Technology，2021，35（10）：4673-4683.
21	Liu H Z， Huang X Z， Yan M，et al.Dynamic response and time-variant reliability analysis of an eight‑rod shock isolator［J］.Proceedings of the Institution of Mechanical Engineers，Part C：Journal of Mechanical Engineering Science，2022，236（13）：7041-7054.
22	吕震宙，宋述芳，李璐祎，等.结构/机构可靠性设计基础［M］，西安：西北工业大学出版社，2019.
	Zhen‑zhou Lyu， Song Shu‑fang， Li Lu‑yi，et al.Reliability sensitivity analysis of angular contact ball bearing skidding［M］，Xi 'an：Northwestern Polytechnical University Press，2019.
23	Cui L J， Lu Z Z， Zhao X P.Moment‑independent importance measure of basic random variable and its probability density evolution solution［J］.Science China Technological Sciences，2010，53（4）：1138-1145.
24	黄贤振，朱会彬，姜智元等.角接触球轴承打滑可靠性灵敏度分析［J］.东北大学学报（自然科学版），2021，42（12）：1731-1738.
	Huang Xian‑zhen， Zhu Hui‑bin， Jiang Zhi‑yuan，et al.Fundamental of structure and mechanism reliability design［J］.Journal of Northeastern University（Natural Science），2021，42（12）：1731-1738.

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