During the operation of the high-speed motorized spindle, the heating of motorized spindle components can cause thermal deformations, which worsens the work performance and shortens the life expectancy of the motorized spindle. In response to the above behaviors, the thermal network model for the motorized spindle in this investigation was built in which the lubricating oil properties and contact characteristics were considered. Next, according to Kirchhoff’s energy balance principle, the theoretical equations of steady-state temperature were established, and the temperature rise of the motorized spindle was obtained by Newton–Raphson method. Lastly, the influences of speed, cooling water flow rate, airflow rate, and other variables on the temperature were analyzed and verified by the experiment. The results show that the thermal network model including lubricating oil and contact factors can predict the temperature rise of motorized spindle accurately, which provides some references and suggestions in motorized spindle design.
GramaSNMathurABadheAN. A model-based cooling strategy for motorized spindle to reduce thermal errors. Int J Mach Tool Manu2018; 132: 3–16. DOI: 10.1016/j.ijmachtools.2018.04.004.
2.
UhlmannEHuJ. Thermal Modelling of a High Speed Motor Spindle. Proced Cirp2012; 1(1): 313–318. DOI: 10.1016/j.procir.2012.04.056.
3.
BossmannsBTuJF. A thermal model for high speed motorized spindles. Int J Mach Tool Manu1999; 39(9): 1345–1366. DOI: 10.1016/s0890-6955(99)00005-x.
4.
LiuJLMaCWangSL, et al.Thermal-structure interaction characteristics of a high-speed spindle-bearing system. Int J Mach Tool Manu2019; 137: 42–57. DOI: 10.1016/j.ijmachtools.2018.10.004.
5.
MaCYangJZhaoL, et al.Simulation and experimental study on the thermally induced deformations of high-speed spindle system. Appl Therm Eng2015; 86: 251–268. DOI: 10.1016/j.applthermaleng.2015.04.064.
6.
LiuTGaoWGZhangDW, et al.Analytical modeling for thermal errors of motorized spindle unit. Int J Mach Tool Manu2017; 112: 53–70. DOI: 10.1016/j.ijmachtools.2016.09.008.
7.
PoulyFChangenetCVilleF, et al. Investigations on the power losses and thermal behaviour of rolling element bearings. P Mech Eng J J Eng Tribol2010; 224(9): 925–933. DOI: 10.1243/13506501jet695.
8.
BallKSFaroukBDixitVC. An experimental study of heat transfer in a vertical annulus with a rotating inner cylinder. Int J Heat Mass Transfer1989; 32(8): 1517–1527. DOI: 10.1016/0017-9310(89)90073-2.
9.
NakajimaK.. Thermal contact resistance between balls and rings of a bearing under axial, radial, and combined loads. J Thermophys Heat Tr1995; 9(1): 88–95. DOI: 10.2514/3.632.
YangQDWangKSMengLX, et al.Design method of automatic adjustment of bearing preload based on thermal characteristic of materials. Chin J Mech Eng-en2008; 44(9): 183–187. DOI: 10.3901/jme.2008.09.183.
12.
HuangDYZhangJHWuDL, et al. Thermal resistance network for solving temperature field in spindle system. J Xi'an Jiaotong Univ2012; 46(5): 63–66.
YanKHongJZhangJ, et al.Thermal-deformation coupling in thermal network for transient analysis of spindle-bearing system. Int J Therm Sci2016; 104: 1–12. DOI: 10.1016/j.ijthermalsci.2015.12.007.
15.
LiuYMaYXMengQY, et al.Improved thermal resistance network model of motorized spindle system considering temperature variation of cooling system. Adv Manuf2018; 6: 384–400. DOI: 10.1007/s40436-018-0239-4.
16.
PoulyFChangenetCVilleF. Power loss predictions in high-speed rolling element bearings using thermal networks. Tribol Trans2010; 53(6): 957–967. DOI: 10.1080/10402004.2010.512117.
17.
BossmannsBTuJF. A Power Flow Model for High Speed Motorized Spindles-Heat Generation Characterization. J Manuf Sci E-t Asme2001; 123(3): 494–505. DOI: 10.1115/1.1349555.
18.
HarrisTAKotzalasMN. Advanced Concepts of Bearing Technology: Rolling Bearing Analysis. Fifth Edition. Boca Raton, FL: CRC Press, 2007.
19.
DengSEJiaQYXueJX. Rolling Bearing Design Principle. Beijing, China: Standards Press of China, 2014.
20.
ZhengDXChenWFLiMM. An optimized thermal network model to estimate thermal performances on a pair of angular contact ball bearings under oil-air lubrication. Appl Therm Eng2018; 131: 328–339.
21.
TruongDSKimBSRoSK. An analysis of a thermally affected high-speed spindle with angular contact ball bearings. Tribol Int2021; 157: 106881. DOI: 10.1016/j.triboint.2021.106881.
22.
JorgensenBRShinYC. Dynamics of Machine Tool Spindle/Bearing Systems Under Thermal Growth. J Tribol-t Asme1997; 119(4): 875–882. DOI: 10.1115/1.2833899.
23.
BergmanTLIncroperaFPLavineAS, et al.Introduction to Heat Transfer. Hoboken, NJ: John Wiley & Sons, 2011.
BergmanTLIncroperaFPDeWittDP, et al.Fundamentals of Heat and Mass Transfer. New York: John Wiley & Sons, 2011.
26.
QiXY. Study on the Static-Dynamic-Thermal Characteristics of Spindle of Machine Tool and its Effects on Deformation. Tianjin, China: Tianjin Univ, 2013.
27.
MuzychkaYYovanovitchM. Thermal resistance of model for non circular moving heat sources on a half space. J Heat Trans-t Asme2001; 123(4): 624–632. DOI: 10.1115/1.1370516.
28.
GaoWJLiuZXZhuPF, et al.Steady Thermal Analysis of Main Shaft Roller Bearing for Aero-Engine Based on Multi-Nodes Thermal Network Methods. J Propul Technol(chinese)2019; 40(02): 382–388.
29.
HamrockBJDowsonD. Isothermal Elastohydrodynamic Lubrication of Point Contacts. Part III– Fully Flooded Results. J Tribol-t Asme1977; 99(2): 264–275. DOI: 10.1115/1.3453074.
30.
ZivkovicAZeljkovicMMladjenovicC, et al.A study of thermal behavior of the machine tool spindle. Therm Sci2019; 23: 2117–2130. DOI: 10.2298/tsci180129118z.
31.
KolondzowskZ. Thermal and Mechanical Analysis of High-Speed Permanent-Magnet Electrical Machines. Helsinki, Finland: Aalto Univ, 2010.
32.
KayeJElgarEC. Modes of adiabatic and diabatic fluid flow in an annulus with an inner rotating cylinder. J Trans ASME1958; 80: 753–765.
33.
GazleyC. Heat transfer characteristics of rotational and axial flow between concentric cylinders. J Trans ASME1958; 1: 79–90.
34.
TachibanaFFukuiSMitsumuraH. Heat Transfer in an Annulus with an Inner Rotating Cylinder. J Bull JSME1960; 3(9): 119–123. DOI: 10.1299/jsme1958.3.119.
35.
BjorklundISKaysWM. Heat Transfer Between Concentric Rotating Cylinders. J Heat Trans-t Asme1959; 81(3): 175–183. DOI: 10.1115/1.4008173.
36.
TachibanaFFukuiS. Convective heat transfer of the rotational and axial flow between two concentric cylinders. J Bull JSME1964; 7(26): 385–391. DOI: 10.1299/jsme1958.7.385.
37.
TaylorGI. Distribution of velocity and temperature between concentric rotating cylinders. J P Roy Soc Lond A Mat1935; 151(874): 494–512.
38.
CaoJCLiWLChengSK, et al.Temperature Field Calculation and Associated Factor Analysis of Induction Motor With Compound Cage Rotor. Proc CSEE(Chinese)2008; 28(30): 96–103.
39.
BossmannsB. Thermomechanical Modeling of Motorized Spindle Systems for High-Speed Milling. West Lafayette, IN: Purdue Univ, 1997.
40.
LiBCaoHYangX, et al.Thermal energy balance control model of motorized spindle system enabling high-speed dry hobbing process. J Manuf Process2018; 35: 29–39. DOI: 10.1016/j.jmapro.2018.07.010.
41.
FengTQinYDongG, et al.An optimal convective heat transfer coefficient calculation method in thermal analysis of spindle system. Int J Adv Manuf Tech2017; 91(5): 2549–2560.
42.
KylanderG.. Thermal Modelling of Small Cage Induction Motors. Gothenburg, Sweden: Chalmers Univ Tech, 1995.
43.
YuJLiSYuanW, et al.Dynamic property of spindle bearing considering the effect of thermal deformation. J Aerosp Power (Chinese)2018; 33(2): 477–486.
