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Recent Patents on Engineering

Author(s): Ye Dai*, Binbin Qiao, Xinda Chen and Gaofeng Pan

DOI: 10.2174/0118722121271162231128045700

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A Review on High-speed Electric Spindle Dynamics Modeling and Vibration Response Research

Article ID: e041223224186 Pages: 27

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Abstract

Background: One of the main directions of modern technology in the field of precision machining is high-speed operation. The spindle system is commonly utilized in this kind of operation, and the electric spindle is the main preference among high-speed machine tool spindles.

Objective: High-speed electric spindle vibration characteristics affect the machining accuracy of the machine tool and the quality of the workpiece, so the research on high-speed electric spindle vibration characteristics has important engineering practical significance.

Methods: The research status of high-speed electrospindle at home and abroad has been summarized in this paper. Combined with the patents related to the dynamics modelling of electrospindle, the research on the dynamics modelling of high-speed electrospindle is analyzed. On this basis, the computational and analytical methods for the vibration modelling of the electrospindle, including the transfer matrix method and the finite element method, are investigated, the theoretical foundations of these methods are discussed in depth, and the advantages and disadvantages of the methods are evaluated. The applicability and limitations of the two methods are also compared.

Results: The analysis has shown that the current research on the vibration characteristics of highspeed electrospindle is mainly based on mechanical modal analysis and electromagnetic analysis. At present, the dynamic modeling of the electrospindle mainly includes bearing modeling, shaft bearing modeling, spindle-case modeling, electrospindle electromechanical coupling modeling, electrospindle thermal coupling modeling, etc. The correctness of the modelling theory is verified through experimental and simulation results. Although these models tend to be perfected, they are still insufficient in the case of multiple influencing factors coupling and need further development.

Conclusion: Finally, through the analysis of the patent and dynamic characteristics related to the high-speed electric spindle, thermal deformation, magnetic tension, material, and other factors should be considered comprehensively, and these factors should be coupled to establish an overall dynamics model for the vibration characteristics analysis. The dynamic modelling, vibration modelling method, and vibration characteristics of the high-speed electric spindle have been summarized in this study, and the outlook is presented.

Keywords: Electric spindle, vibration characteristics, dynamic model, finite element method, transfer matrix method, vibration response.

Graphical Abstract

[1]
D. Huang, "Dynamics modeling and vibration characteristics study of high-speed electric spindle", Ph.D. thesis, Zhejiang University, Zhejiang, China, 2018.
[2]
A. El-Hanbali, and A.A. Fahoum, "The development and validation of an autonomous UVC (ultraviolet - c) disinfection robot system", Int. J. Emerg. Technol. Adv. Eng., vol. 12, no. 12, 2022.
[3]
P.P. Hou, "Study on vibration characteristics of speed ball bearings and its extended characterization method", Ph.D. thesis, Harbin Institute of Technology, Harbin, China, 2021.
[4]
X.L. Qiao, and C.S. Zhu, "Active control of multi-frequency vibration in permanent magnet type electric spindles", Zhongguo Jixie Gongcheng, vol. 25, no. 2, pp. 162-168, 2014.
[5]
X.A. Chen, P. Zhang, Y. He, and J.F. Liu, "High-speed electric spindle axial vibration study", Vibration & shock, vol. 33, no. 20, pp. 70-74-90, 2014. Available From: [https://en.czjst.com/products_list/1.html?gclid=EAIaIQobChMI64Lvwo_ZgQMV5kJBAh2Y1g_7EAAYASAAEgI2xPD_BwE]
[6]
Z. Tsedan, W. Tian, C.Y. He, and J.B. Yang, "Research on vibration characteristics of electric spindles based on experimental modal analysis", J. Hai Uni., vol. 32, no. 5, pp. 13-20, 2014.
[7]
I. Mañé, V. Gagnol, B.C. Bouzgarrou, and P. Ray, "Stability-based spindle speed control during flexible work piece high-speed milling", Int. J. Mach. Tools Manuf., vol. 48, no. 2, pp. 184-194, 2008.
[http://dx.doi.org/10.1016/j.ijmachtools.2007.08.018]
[8]
J. Xu, X.H. Zheng, J.J. Zhang, and X. Liu, "Vibration characteristics of unbalance response for motorized spindle system", Procedia. Engg., vol. 174, pp. 331-340, 2017.
[9]
K.C. Panda, and J.K. Dutt, "Optimum support characteristics for rotor–shaft system with preloaded rolling element bearings", J. Sound Vibrat., vol. 260, no. 4, pp. 731-755, 2003.
[http://dx.doi.org/10.1016/S0022-460X(02)01071-4]
[10]
M.A. Alfares, and A.A. Elsharkawy, "Effects of axial preloading of angular contact ball bearings on the dynamics of a grinding machine spindle system", J. Mater. Process. Technol., vol. 136, no. 1-3, pp. 48-59, 2003.
[11]
G.H. Xu, Y.F. Cai, Y.T. Xu, J.Z. Fu, and M.J. Gu, "A dynamic loading vibration test system for electric spindle", C. N. Patent, 208, 383, 298U, 2019.
[12]
B. Jorgensen, and Y.C. Shin, "Dynamics of Spindle-bearing system at high speed including cutting load effects", J. Manuf. Sci. Eng., vol. 120, pp. 387-394, 1998.
[http://dx.doi.org/10.1115/1.2830138]
[13]
S.Y. Jiang, and S.Y. Lin, "A design method for dynamic performance of electric spindle of rolling bearing based on optimal preload", C. N. Patent, 109, 063, 384A, 2018.
[14]
B.Y. Peng, G.F. Yin, H. Jiang, T. Hu, K.Y. Zhong, and Y.L. Zheng, "Theoretical modeling and experimental study of machining center electric spindle dynamics analysis", J. Sichuan Uni., vol. 43, no. 4, pp. 249-253, 2011.
[15]
C. Zhao, H.J. Wang, H.C. Zhang, and Y.C. Xu, "Analysis of modal recognition and high-speed effects under high-speed electric spindle operation", Mach. Sci. Technol., vol. 35, no. 6, pp. 846-852, 2016.
[16]
A. Al-Fahoum, and T. Ghobon, "An applied approach for speed estimation of induction motors using sensorless flux observer system with sliding mode field oriented control", Int. J. Electric. Engg. & Tech. (IJEET), vol. 11, no. 6, pp. 109-122, 2020.
[17]
X.A. Chen, M.H. Kang, Y. He, M. Chen, Y.Y. Miao, and W.Q. Chen, "Analysis of dynamic performance of high-speed electric spindle under speed sensor vector control", Jixie Gongcheng Xuebao, vol. 46, no. 7, pp. 96-101, 2010.
[http://dx.doi.org/10.3901/JME.2010.07.096]
[18]
L.Y. Wang, "Analysis of electromagnetic force and loss of ceramic electric spindle", M.S. Thesis, Shenyang University of Architecture, Liaoning, China, 2012.
[19]
W. Wang, H. Wang, and H.H. Shen, "Analysis of electromagnetic force and vibration characteristics for transverse flux permanent magnet motor", In 2016 Chinese Control and Decision Conference (CCDC), 2016, pp. 6929-6934 Yinchuan, China
[http://dx.doi.org/10.1109/CCDC.2016.7532247]
[20]
W. Zhang, "Harmonic analysis of air-gap potential of multi-phase induction motor", Micromotor, vol. 43, no. 2, pp. 5-8, 2010.
[21]
Wang, W.Z. He, S.Y. Du, and Z. Yuan, "Study on the unbalanced fault dynamic characteristics of eccentric motorized spindle considering the effect of magnetic Pull", Shock & Vibration, vol. 2021, no. 19, 2021.
[22]
J. Liu, T. Lai, and X. Chen, "Dynamics analysis of unbalanced motorized spindles supported on ball bearings", Shock Vib., vol. 2016, no. 2, pp. 1-10, 2016.
[http://dx.doi.org/10.1155/2016/2787524]
[23]
W. Feng, K. Zhang, Z.Y. Liu, and B.G. Liu, "Modeling and analysis of unbalanced magnetic pull in synchronous motorized spindle considering magneto-thermal coupling", Research Square, 2021.
[24]
Z.H. He, Y.K. Wang, J.B. Li, R. Fan, and M. Wei, "Nature of electromagnetic torque coefficient of power system and its calculation method", Journal of Power Systems and Automation, vol. 23, no. 1, p. 8691, 2021.
[25]
E. Abele, Y. Altintas, and C. Brecher, "Machine tool spindle units", CIRP Annals, vol. 59, no. 2, pp. 781-802, 2010.
[http://dx.doi.org/10.1016/j.cirp.2010.05.002]
[26]
S.E. Deng, and Q.Y. Jia, Rolling bearing design principle, China Standard Publishing House: Beijing, 2008.
[27]
A.B. Jones, "Ball Motion and Sliding Friction in Ball Bearings", J. Basic Eng., vol. 81, no. 1, pp. 1-12, 1959.
[http://dx.doi.org/10.1115/1.4008346]
[28]
T.A. Harris, and M.H. Mindel, "Rolling element bearing dynamics", Wear, vol. 23, no. 3, pp. 311-337, 1973.
[http://dx.doi.org/10.1016/0043-1648(73)90020-3]
[29]
Z.Z. Yu, M. Jin, Z. Liu, F. Wang, C.G. Li, J.J. Zhang, and L. Ding, "A sliding bearing modeling method based on ADAMS", C.N. Patent, 109, 583, 079A, 2019.
[30]
S.Q. Liu, Q.H. Zong, and Z.G. Bian, "A method for modeling magnetic levitation bearings under multi-parameter uncertainties", C.N. Patent, 112, 784, 452A, 2021.
[31]
C.L. Gao, "Simulation and analysis of rolling bearing dynamics", Mech. Design & Manufac., vol. 2, pp. 193-195, 2011.
[32]
H. Dong, X.Z. Zhu, and L. Chen, "Analysis of vibration characteristics of spindle-bearing of high-speed milling machine", J. Liaoning Uni. Petrol. & Chem. Tech., vol. 41, no. 01, pp. 56-60, 2021.
[33]
V. Gagnol, B.C. Bouzgarrou, P. Ray, and C. Barra, "Modelling approach for a high speed machine tool spindle-bearing system", In: IDETC-CIE, 2005, pp. 305-313.
[http://dx.doi.org/10.1115/DETC2005-84681]
[34]
Y. Cao, and Y. Altintas, "A general method for the modeling of spindle-bearing systems", J. Mech. Des., vol. 126, no. 6, pp. 1089-1104, 2004.
[http://dx.doi.org/10.1115/1.1802311]
[35]
Y. Cao, and Y. Altintas, "Modeling of spindle-bearing and machine tool systems for virtual simulation of milling operations", Int. J. Mach. Tools Manuf., vol. 47, no. 9, pp. 1342-1350, 2007.
[http://dx.doi.org/10.1016/j.ijmachtools.2006.08.006]
[36]
C.F. Zhu, "Theoretical modeling and experimental verification of spindle bearing system dynamics", Modern Vibra. & Noise, vol. 10, 2012.
[37]
H. Li, and Y.C. Shin, "Integrated dynamic thermo-mechanical modeling of high speed spindles, part 1: model development", J. Manuf. Sci. Eng., vol. 126, no. 1, pp. 148-158, 2004.
[http://dx.doi.org/10.1115/1.1644545]
[38]
H. Li, and Y.C. Shin, "Integrated dynamic thermo-mechanical modeling of high speed spindles, part 2: solution procedure and validations", J. Manuf. Sci. Eng., vol. 126, no. 1, pp. 159-168, 2004.
[http://dx.doi.org/10.1115/1.1644546]
[39]
H. Li, and Y.C. Shin, "Analysis of bearing configuration effects on high speed spindles using an integrated dynamic thermo mechanical spindle model", Int. J. Mach. Tools Manuf., vol. 44, no. 4, pp. 347-364, 2004.
[http://dx.doi.org/10.1016/j.ijmachtools.2003.10.011]
[40]
B.W. Huang, and H.K. Kung, "Variations of instability in a rotating spindle system with various bearings", Int. J. Mech. Sci., vol. 45, no. 1, pp. 57-72, 2003.
[http://dx.doi.org/10.1016/S0020-7403(03)00039-0]
[41]
Y.H. Lin, and S.C. Lin, "Optimal weight design of rotor systems with oil-film bearings subjected to frequency constraints", FiniteElem. Anal. Des., vol. 37, no. 10, pp. 777-798, 2001.
[http://dx.doi.org/10.1016/S0168-874X(00)00072-X]
[42]
Y.H. Lin, and H.C. Yu, "Active modal control of a flexible rotor", Mech. Syst. Signal Process., vol. 18, no. 5, pp. 1117-1131, 2004.
[http://dx.doi.org/10.1016/j.ymssp.2003.10.004]
[43]
C.W. Lin, J.F. Tu, and J. Kamman, "An integrated thermomechanical-dynamic model to characterize motorized machine tool spindles during very high speed rotation", Int. J. Mach. Tools Manuf., vol. 43, no. 10, pp. 1035-1050, 2003.
[http://dx.doi.org/10.1016/S0890-6955(03)00091-9]
[44]
J.S. Chen, and K-W. Chen, "Bearing load analysis and control of a motorized high speed spindle", Int. J. Mach. Tools Manuf., vol. 45, no. 12-13, pp. 1487-1493, 2005.
[http://dx.doi.org/10.1016/j.ijmachtools.2005.01.024]
[45]
C. Chen, "Research on dynamic loading reliability test of high-speed electric spindle and its fault diagnosis", Ph.D. Thesis, Jilin University, Jilin, China, 2016.
[46]
G.X. Li, and Y. Yang, "Research on vibration characteristics of hobbing spindle of CNC hobbing machine", Jixie Gongcheng Xuebao, vol. 53, no. 1, pp. 130-139, 2017.
[http://dx.doi.org/10.3901/JME.2017.01.130]
[47]
Y. Amirat, M. Benbouzid, B. Bensaker, and R. Wamkeue, "Condition Monitoring and ault Diagnosis in Wind Energy Conversion Systems: A Review", In 2007 IEEE International Electric Machines and Drives Conference, 2007pp. 1434-1439 Antalya, Turkey.
[http://dx.doi.org/10.1109/IEMDC.2007.383639]
[48]
C.Y. Liu, F. Zheng, and L.P. Wang, "Spindle-case vibration transmission mechanics model in high-speed electric spindles", J. Tsinghua Uni., vol. 58, no. 07, pp. 671-676, 2018.
[49]
F. Gao, M. Cheng, and Y. Li, "Analysis of coupled vibration characteristics of PMS grinding motorized spindle", J. Mech. Sci. Technol., vol. 34, no. 9, pp. 3497-3515, 2020.
[http://dx.doi.org/10.1007/s12206-020-0802-3]
[50]
L. Lv, "Research on the design method of high-speed grinding electric spindle system based on electromechanical coupling dynamics", Ph.D. Thesis, Hunan University, Hunan, China, 2010.
[51]
M.H. Kang, H.Q. Li, J. Meng, D.S. Liu, C.H. Deng, Z.J. Zhou, and B.J. Hu, "Modeling and simulation study of electromechanical coupling of high-speed electric spindle", J. Hunan Uni. Sci. & Tech., vol. 27, no. 04, pp. 18-22, 2012.
[52]
C. Brecher, G. Spachtholz, and F. Paepenmüller, "Developments for high performance machine tool spindles", CIRP Ann., vol. 56, no. 1, pp. 395-399, 2007.
[http://dx.doi.org/10.1016/j.cirp.2007.05.092]
[53]
B.R. Jorgensen, and Y.C. Shin, "Dynamics of machine tool spindle/bearing systems under thermal growth", J. Tribol., vol. 119, no. 4, pp. 875-882, 1997.
[http://dx.doi.org/10.1115/1.2833899]
[54]
X.A. Chen, P. Zhang, J.F. Liu, and Y. He, "Multi-field coupling dynamics of high-speed electric spindle", J. Vibration Engg., vol. 26, no. 3, pp. 303-310, 2013.
[55]
X.A. Chen, P. Zhang, Y. He, and J.F. Liu, "High-speed electric spindle power flow model and thermal state characteristics study", Mashin/Ha-Yi Kishavarzi, vol. 44, no. 9, pp. 251-254, 2013.
[56]
J. Meng, X.A. Chen, and Y. He, "Electromechanical coupling dynamics modeling of high-speed electric spindle motor-spindle system", Jixie Gongcheng Xuebao, no. 12, pp. 160-165, 2007.
[http://dx.doi.org/10.3901/JME.2007.12.160]
[57]
K. Yamazaki, and H. Ishigami, "Rotor-shape optimization of interior-permanent-magnet motors to reduce harmonic iron losses", IEEE Trans. Ind. Electron., vol. 57, no. 1, pp. 61-69, 2010.
[http://dx.doi.org/10.1109/TIE.2009.2025285]
[58]
F. Ishibashi, M. Matsushita, and S. Noda, "Harmonic electromagnetic forces in induction motors", IEEJ Transactions on Industry App., vol. 129, no. 4, pp. 375-381, 2009.
[http://dx.doi.org/10.1541/ieejias.129.375]
[59]
D. Verdyck, R. Belmans, and W. Geysen, "An acoustic model for a permanent magnet machine: Modal shapes and magnetic forces", IEEE Transactions on Industry Applications, vol. 30,, 1994, no. 6, pp. 1625-1631, .
[60]
B. Bossmanns, and J.F. Tu, "A thermal model for high speed motorized spindles", Int. J. Mach. Tools Manuf., vol. 39, no. 9, pp. 1345-1366, 1999.
[http://dx.doi.org/10.1016/S0890-6955(99)00005-X]
[61]
B. Bossmanns, and J.F. Tu, "A power flow model for high speed motorized spindles—Heat generation characterization", J. Manuf. Sci. Eng., vol. 123, no. 3, pp. 494-505, 2001.
[http://dx.doi.org/10.1115/1.1349555]
[62]
J.S. Chen, and W.Y. Hsu, "Characterizations and models for the thermal growth of a motorized high speed spindle", Int. J. Mach. Tools Manuf., vol. 43, no. 11, pp. 1163-1170, 2003.
[http://dx.doi.org/10.1016/S0890-6955(03)00103-2]
[63]
X. Chen, "Thermal properties of high speed motorized spindle and their effects", Jixie Gongcheng Xuebao, vol. 49, no. 11, p. 135, 2013.
[http://dx.doi.org/10.3901/JME.2013.11.135]
[64]
X. Min, J. Shuyun, and C. Ying, "An improved thermal model for machine tool bearings", Int. J. Mach. Tools Manuf., vol. 47, no. 1, pp. 53-62, 2007.
[http://dx.doi.org/10.1016/j.ijmachtools.2006.02.018]
[65]
C. Ma, X. Mei, J. Yang, L. Zhao, and H. Shi, "Thermal characteristics analysis and experimental study on the high-speed spindle system", Int. J. Adv. Manuf. Technol., vol. 79, no. 1-4, pp. 469-489, 2015.
[http://dx.doi.org/10.1007/s00170-015-6821-z]
[66]
Y. Cui, H. Li, T. Li, and L. Chen, "An accurate thermal performance modeling and simulation method for motorized spindle of machine tool based on thermal contact resistance analysis", Int. J. Adv. Manuf. Technol., vol. 96, no. 5-8, pp. 2525-2537, 2018.
[http://dx.doi.org/10.1007/s00170-018-1593-x]
[67]
E. Uhlmann, and J. Hu, "Thermal modelling of a high speed motor spindle", Procedia CIRP, vol. 1, no. 1, pp. 313-318, 2012.
[http://dx.doi.org/10.1016/j.procir.2012.04.056]
[68]
L. Zhang, C. Li, Y. Wu, K. Zhang, and H. Shi, "Hybrid prediction model of the temperature field of a motorized spindle", Appl. Sci. (Basel), vol. 7, no. 10, p. 1091, 2017.
[http://dx.doi.org/10.3390/app7101091]
[69]
J.F. Liu, X.A. Chen, M.H. Kang, P. Zhang, and Y. He, "Analysis of thermal performance of grease lubricated ball bearings", Mach. Sci. Technol., vol. 33, no. 6, pp. 845-848, 2014.
[70]
X.A. Chen, J.F. Liu, Y. He, P. Zhang, and W.Y. Shan, "High-speed electric spindle thermal performance and its influence", Jixie Gongcheng Xuebao, vol. 49, no. 11, pp. 135-142, 2013.
[http://dx.doi.org/10.3901/JME.2013.11.135]
[71]
Z. Liu, M. Pan, A. Zhang, Y. Zhao, Y. Yang, and C. Ma, "Thermal characteristic analysis of high-speed motorized spindle system based on thermal contact resistance and thermal-conduction resistance", Int. J. Adv. Manuf. Technol., vol. 76, no. 9-12, pp. 1913-1926, 2015.
[http://dx.doi.org/10.1007/s00170-014-6350-1]
[72]
K. Yan, J. Hong, J. Zhang, W. Mi, and W. Wu, "Thermaldeformation coupling in thermal network for transient analysis of spindle-bearing system", Int. J. Therm. Sci., vol. 104, pp. 1-12, 2016.
[http://dx.doi.org/10.1016/j.ijthermalsci.2015.12.007]
[73]
Y. Liu, Y.X. Ma, Q.Y. Meng, X.C. Xin, and S-S. Ming, "Improved thermal resistance network model of motorized spindle system considering temperature variation of cooling system", Advances in Manufact., vol. 6, no. 4, pp. 384-400, 2018.
[http://dx.doi.org/10.1007/s40436-018-0239-4]
[74]
S.M. Kim, and S.K. Lee, "Prediction of thermo-elastic behavior in a spindle–bearing system considering bearing surroundings", Int. J. Mach. Tools Manuf., vol. 41, no. 6, pp. 809-831, 2001.
[http://dx.doi.org/10.1016/S0890-6955(00)00103-6]
[75]
J. Lee, D.H. Kim, and C.M. Lee, "A study on the thermal characteristics and experiments of High-Speed spindle for machine tools", Int. J. Precis. Eng. Manuf., vol. 16, no. 2, pp. 293-299, 2015.
[http://dx.doi.org/10.1007/s12541-015-0039-8]
[76]
A. Zivkovic, M. Zeljkovic, S. Tabakovic, and Z. Milojevic, "Mathematical modeling and experimental testing of high-speed spindle behavior", Int. J. Adv. Manuf. Technol., vol. 77, no. 5-8, pp. 1071-1086, 2015.
[http://dx.doi.org/10.1007/s00170-014-6519-7]
[77]
J. Liu, and P. Zhang, "Thermo-mechanical behavior analysis of motorized spindle based on a coupled model", Adv. Mech. Eng., vol. 10, no. 1, 2018.
[http://dx.doi.org/10.1177/1687814017747144]
[78]
B. Wang, X. Mei, Z. Wu, and F. Zhu, "Dynamic modeling for thermal error in motorized spindles", Int. J. Adv. Manuf. Technol., vol. 78, no. 5-8, pp. 1141-1146, 2015.
[http://dx.doi.org/10.1007/s00170-014-6716-4]
[79]
J. Liu, and X. Chen, "Dynamic design for motorized spindles based on an integrated model", Int. J. Adv. Manuf. Technol., vol. 71, no. 9-12, pp. 1961-1974, 2014.
[http://dx.doi.org/10.1007/s00170-014-5640-y]
[80]
Z.W. Yang, G.F. Yin, X. Shang, H. Jiang, and K.Y. Zhong, "Coupled analysis model of thermal and dynamic characteristics of highspeed electric spindle", J. Jilin Uni., vol. 41, no. 1, pp. 100-105, 2011.
[81]
X.S. Han, and H.H. Li, "Thermal weak coupling analysis of electric spindle based on thermal effect", Mech. Engg. & Autom., no. 4, pp. 3-5, 2018.
[82]
S.T. Wang, F.J. Chen, T. Liu, and W.D. Gou, "Modeling of force thermal coupling characteristics of high-speed electric spindles", J. Huazhong Uni. Sci. & Tech., vol. 43, no. 10, pp. 1-5, 2015.
[83]
J.B. Chen, Research on thermal coupling modeling and optimization design method for high-speed electric spindle M.S. Thesis, Xi'an University of Technology, Xi'an, China, 2021.
[84]
X.D. Wang, H.L. Wang, and J.X. Su, "Modeling and experimental analysis of electric spindle based on transfer matrix method", Mach. Tools & Hydraul., vol. 50, no. 04, pp. 13-18, 2022.
[85]
S. Jiang, and S. Lin, "A technical note: an ultra-high-speed motorized spindle for internal grinding of small-deep hole", Int. J. Adv. Manuf. Technol., vol. 97, no. 1-4, pp. 1457-1463, 2018.
[http://dx.doi.org/10.1007/s00170-018-1984-z]
[86]
C.H. Li, Y.L. Hou, C. Du, and Y.C. Ding, "An analysis of the electric spindle’s dynamic characteristics of high-speed grinder", J. Adv. Manuf. Syst., vol. 10, no. 1, pp. 159-166, 2011.
[http://dx.doi.org/10.1142/S0219686711002107]
[87]
S.Y. Lin, S.W. Zhang, and K.K. Geng, "Dynamic analysis of a high speed motorized spindle for internal grinding of slender holes", In 10th International Conference on Mechatronics and Manufacturing, 2019, p. 012013 Bangkok, Thailand
[http://dx.doi.org/10.1088/1757-899X/635/1/012013]
[88]
H.H. Feng, and S.Y. Jiang, "Dynamics of a motorized spindle supported on water-lubricated bearings", J. Mech. Engg. Sci., vol. 231, no. 3, pp. 1989-1996, 2015.
[89]
K. Zhang, L.Q. Zhang, Z. Wang, and L.W. Gao, "Nonlinear dynamic characteristics of full-ceramic motorized spindle considering axial transfer of unbalanced magnetic pull", Mech. Engg. Sci., vol. 0, no. 0, 2022.
[90]
D. Fedorynenko, R. Kirigaya, and Y. Nakao, "Dynamic characteristics of spindle with water-lubricated hydrostatic bearings for ultraprecision machine tools", Precis. Eng., vol. 63, no. 4, pp. 187-196, 2020.
[http://dx.doi.org/10.1016/j.precisioneng.2020.02.003]
[91]
W. Luo, B. Lu, F. Chen, and Y. Song, "FRF prediction modeling and joint parameter identification of motorized spindle-tool handle", J. Braz. Soc. Mech. Sci. Eng., vol. 44, no. 7, p. 303, 2022.
[http://dx.doi.org/10.1007/s40430-022-03552-5]
[92]
J. Liu, and E.D. Hu, "Analysis of dynamic characteristics of CNC lathe spindle unit", Ningxia Engg. Tech., no. 01, pp. 43-44, 2003.
[93]
J.W. Chen, S.J. Hu, and W. Chen, "High-speed electric spindle finite element modeling and static and dynamic characteristics analysis,", vol. 35, no. 07, pp. 27-35,2017.
[94]
Y. Cao, and Q. Li, "Finite element analysis of dynamic characteristics of high-speed electric spindles", Baosteel Technology, vol. 39, no. 03, pp. 53-55, 2013.
[95]
L. Cai, S.M. Ma, Y.S. Zhao, Z.F. Liu, and W.T. Yang, "Finite element modeling and modal analysis of heavy-duty mechanical spindle under multiple constraints", Jixie Gongcheng Xuebao, vol. 48, no. 3, pp. 165-173, 2012.
[http://dx.doi.org/10.3901/JME.2012.03.165]
[96]
X.Z. Huang, B. Guo, and Z.Y. Jiang, "Vibration characteristics and accuracy reliability analysis of high-speed motorized spindle system", J. Jilin Uni., vol. 2023, pp. 1-9, 2023.
[97]
Y.D. Lian, "Simulation analysis of static and dynamic characteristics of electric spindle based on ANSYS", Mach. Build. & Automa., vol. 50, no. 04, pp. 76-100, 2021.
[98]
X.J. Bai, "Vibration analysis and research of high-speed motorized spindle in cutting process", J. Qinghai University, vol. 36, no. 01, pp. 69-74, 2018.
[99]
C.W. Lin, and J.F. Tu, "Model-based design of motorized spindle systems to improve dynamic performance at high speeds", J. Manuf. Process., vol. 9, no. 2, pp. 94-108, 2007.
[http://dx.doi.org/10.1016/S1526-6125(07)70111-1]
[100]
X.L. Q, "Review of dynamic analysis and vibration control technology of magnetic levitation electric spindle system", J. Hebei Uni. Sci. & Tech., vol. 37, no. 05, pp. 25-31, 2016.
[101]
W.L. Xiong, F.F. Li, Z.H. Ji, and L. Lv, "A review of the dynamics of rolling bearing electric spindle systems", Manufact. Tech. & Mach. Tools, no. 03, pp. 25-31, 2010.