A review on spindle thermal error compensation in machine tools

International Journal of Machine Tools and Manufacture

Volumn 95, Issue , 2015, Pages 20-38

  Li, Yang ^a   Zhao, Wanhua ^a   Lan, Shuhuai ^b   Ni, Jun ^b   Wu, Wenwu ^a   Lu, Bingheng ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Review; Spindle thermal error; Temperatures and thermal errors measurements; Thermal error compensation; Thermal error modeling; Thermal key points

Indexed keywords

MACHINE TOOLS; REVIEWS;

KEYPOINTS; SPINDLE THERMAL ERRORS; THERMAL ERROR; THERMAL ERROR COMPENSATION; THERMAL ERROR MODELING;

ERROR COMPENSATION;

EID: 84929616667     PISSN: 08906955     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijmachtools.2015.04.008     Document Type: Review

References (148)

1. R. Ramesh, M. Mannan, and A. Poo Error compensation in machine tools - a review: Part I: geometric, cutting-force induced and fixture-dependent errors Int. J. Mach. Tools Manuf. 40 9 2000 1235 1256
2. D. Bachrathy, T. Insperger, and G. Stepan Surface properties of the machined workpiece for helical mills Mach. Sci. Technol. 13 2 2009 227 245
3. I. Mancisidor, M. Zatarain, J. Munoa, and Z. Dombovari Fixed boundaries receptance coupling substructure analysis for tool point dynamics prediction Adv. Mater. Res. 223 2011 622 631
4. R. Ramesh, M. Mannan, and A. Poo Error compensation in machine tools - a review: Part II: thermal errors Int. J. Mach. Tools Manuf. 40 9 2000 1257 1284
5. J. Bryan International status of thermal error research (1990) CIRP Ann. - Manuf. Technol. 39 2 1990 645 656
6. S. Postlethwaite, J. Allen, and D. Ford Machine tool thermal error reduction - an appraisal Proc. Inst. Mech. Eng. Part B: J. Eng. Manuf. 213 1 1999 1 9
7. Z. Haitao, Y. Jianguo, and S. Jinhua Simulation of thermal behavior of a CNC machine tool spindle Int. J. Mach. Tools Manuf. 47 6 2007 1003 1010
8. Y. Li, W. Zhao, Axial thermal error compensation method for the spindle of a precision horizontal machining center, in: Proceedings of the 2012 IEEE International Conference on Mechatronics and Automation (ICMA), 2012, pp. 2319-2323.
9. J. Mayr, J. Jedrzejewski, E. Uhlmann, M. Alkan Donmez, W. Knapp, F. Härtig, K. Wendt, T. Moriwaki, P. Shore, and R. Schmitt Thermal issues in machine tools CIRP Ann. - Manuf. Technol. 61 2 2012 771 791
10. T. Moriwaki, K. Yokoyama, C. Zhao, Improving machining accuracy in turning with use of tool holder made of super-invar, in: Proceedings of the MECH'91: Australia; Engineering for a Competitive World; International Mechanical Engineering Congress and Exhibition; Conference 3; Competitive Manufacturing; Preprints of Papers, Institution of Engineers, Australia,1991, p. 88.
11. J. Jedrzejewski Effect of the thermal contact resistance on thermal behaviour of the spindle radial bearings Int. J. Mach. Tools Manuf. 28 4 1988 409 416
12. M. Weck, P. McKeown, R. Bonse, and U. Herbst Reduction and compensation of thermal errors in machine tools CIRP Ann. - Manuf. Technol. 44 2 1995 589 598
13. Y. Hatamura, T. Nagao, M. Mitsuishi, K. Kato, S. Taguchi, T. Okumura, G. Nakagawa, and H. Sugishita Development of an intelligent machining center incorporating active compensation for thermal distortion CIRP Ann. - Manuf. Technol. 42 1 1993 549 552
14. Aguirre G. PdNA, H. Urreta, Thermal error compensation for large heavy duty milling-boring machines, in: Proceedings of the 29th Annual Meeting of the American Society for Precision Engineering, 2014, pp. 57-62.
15. Y. Li, W. Zhao, W. Wu, B. Lu, and Y. Chen Thermal error modeling of the spindle based on multiple variables for the precision machine tool Int. J. Adv. Manuf. Technol. 2014 1 13 10.1007/s00170-014-5744-4
16. T. Harris Rolling Bearing Analysis 1991 Willey New York
17. B.R. Jorgensen, and Y.C. Shin Dynamics of machine tool spindle/bearing systems under thermal growth J. Tribol. 119 4 1997 875 882
18. N.L. de Lacalle, and A.L. Mentxaka Machine Tools for High Performance Machining 2008 Springer Science & Business Media
19. B. Bossmanns, and J.F. Tu A thermal model for high speed motorized spindles Int. J. Mach. Tools Manuf. 39 9 1999 1345 1366
20. B. Bossmanns, and J.F. Tu A power flow model for high speed motorized spindles - heat generation characterization J. Manuf. Sci. Eng. 123 3 2001 494 505
21. E. Uhlmann, and J. Hu Thermal modelling of a high speed motor spindle Procedia CIRP 1 2012 313 318
22. J. Schwartz Friction-induced heating in axially loaded ball bearings J. Lubric. Technol. 92 1 1970 105 111
23. J. Takabi, and M. Khonsari Experimental testing and thermal analysis of ball bearings Tribol. Int. 60 2013 93 103
24. J.H. Lienhard A Heat Transfer Textbook 2013 Courier Dover Publications
25. A. Zahedi, and M. Movahhedy Thermo-mechanical modeling of high speed spindles Sci. Iran. 19 2 2012 282 293
26. Z. Zhen, H. Penghao, T. Yi, and W. Debao 3D analysis of temperature field and thermal deformation of spindle axis Tool Eng. 42 4 2008 66 68
27. H. Yang, and J. Ni Dynamic modeling for machine tool thermal error compensation J. Manuf. Sci. Eng. 125 2 2003 245 254
28. J. Shan, Z. Zhigang, S. Minglu, G. Jianhui, and Y. Hong Analysis on thermal dynamic characteristics of CNC machine tool spindle J. Tianjin Univ. (Sci. Technol.) 46 9 2013 846 850
29. L.X.X.L.J. Yang The research of spindle components' thermal character in NC machine Modular Mach. Tool Autom. Manuf. Tech. 12 2007 21 22
30. M. Attia, S. Fraser, and M. Osman On-line estimation of time-variant thermal load applied to machine tool structures using a s-domain inverse solution Int. J. Mach. Tools Manuf. 39 6 1999 985 1000
31. I.A. Zverev, I.-U. Eun, W.J. Chung, and C.M. Lee Thermal model of high-speed spindle units KSME Int. J. 17 5 2003 668 678
32. J. Zhang, H. Li, Thermal performance analysis for the machine tool's spindle, in: Proceedings of the 7th IEEE Conference on Industrial Electronics and Applications (ICIEA), 2012, pp. 2131-2134.
33. J. Han, L.P. Wang, and L.Q. Yu Modeling and estimating thermal error in precision machine spindles Appl. Mech. Mater. 34 2010 507 511
34. T. Holkup, H. Cao, P. Kolář, Y. Altintas, and J. Zelený Thermo-mechanical model of spindles CIRP Ann. - Manuf. Technol. 59 1 2010 365 368
35. Y. Kang, C.-W. Chang, Y. Huang, C.-L. Hsu, and I.-F. Nieh Modification of a neural network utilizing hybrid filters for the compensation of thermal deformation in machine tools Int. J. Mach. Tools Manuf. 47 2 2007 376 387
36. N.S. Mian, S. Fletcher, A.P. Longstaff, A. Myers, C. Pislaru, Novel and efficient thermal error reduction strategy for machine tool performance improvement, 2008.
37. S. Xiang, X. Zhu, and J. Yang Modeling for spindle thermal error in machine tools based on mechanism analysis and thermal basic characteristics tests Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 2014 0954406214531219
38. M.-L. Sun, Z.-Y. Yang, W.-Q Li, Q., Liu, J.-H. Guo, An improved thermal simulation model for the spindle of CNC machine tool, in: Proceedings of the IEEE 2010 International Conference on Mechanic Automation and Control Engineering (MACE), 2010, pp. 187-190.
39. D. Chen, M. Bonis, F. Zhang, and S. Dong Thermal error of a hydrostatic spindle Precis. Eng. 35 3 2011 512 520
40. E. Creighton, A. Honegger, A. Tulsian, and D. Mukhopadhyay Analysis of thermal errors in a high-speed micro-milling spindle Int. J. Mach. Tools Manuf. 50 4 2010 386 393
41. J. Mayr, M. Ess, S. Weikert, K. Wegener, Simulation and prediction of the thermally induced deformations of machine tools caused by moving linear axis using the FDEM simulation approach, in: Proceedings of the ASPE Annual Meeting, 2008.
42. J. Mayr, M. Ess, S. Weikert, K. Wegener, Compensation of thermal effects on machine tools using a FDEM simulation approach, in: Proceedings of Lamdamap,2009, p. 9.
43. D. Huang, J. Hong, J. Zhang, D. Wu, and C. Li Thermal Resistance Network for Solving Temperature Field in Spindle System J. Xi'an Jiaotong Univ. 46 5 2012 63 66
44. C. Liu, G. Luo, W. He, and X. Hu Steady state thermal analysis of a spindle system based on thermal network China Mech. Eng. 6 2010 631 635
45. Y.-C. Wang, C.-P. Chang, and M.-C. Kao Investigation on the spindle thermal displacement and its compensation of precision cutter grinders Measurement 44 6 2011 1183 1187
46. R. Ramesh, M. Mannan, and A. Poo Thermal error measurement and modelling in machine tools: Part I. Influence of varying operating conditions Int. J. Mach. Tools Manuf. 43 4 2003 391 404
47. Y. Li, X. Sun,G. Yuan, X. Yang, Measurement of surface temperature with thermal infrared imager, in: Proceedings of the International Symposium on Instrumentation Science and Technology, International Society for Optics and Photonics, 2008, pp. 71333G-71337G.
48. A. Abuaniza, S. Fletcher, A.P. Longstaff, Thermal error modelling of a three axes vertical milling machine using finite element analysis (FEA), 2013.
49. N.S. Mian, S. Fletcher, A.P. Longstaff, A. Myers, C. Pislaru, Efficient offline thermal modelling for accurate assessment of machine tool thermal behaviour, 2009.
50. X. Ma, J. Qiu, Q.W. Liu, and J. Lin Study on spindle thermal field distribution and thermal errors of horizontal machine tool Materials Science Forum 2012 Trans Tech Publication 273 276
51. A.M. Abdulshahed, A.P. Longstaff, S. Fletcher, and A. Myers Thermal error modelling of machine tools based on ANFIS with fuzzy c-means clustering using a thermal imaging camera Appl. Math. Model. 2014
52. Y. Li, J. Yang, T. Gelvis, and Y. Li Optimization of measuring points for machine tool thermal error based on grey system theory Int. J. Adv. Manuf. Technol. 35 7-8 2008 745 750
53. J. Yan, and J. Yang Application of synthetic grey correlation theory on thermal point optimization for machine tool thermal error compensation Int. J. Adv. Manuf. Technol. 43 11-12 2009 1124 1132
54. Q. Guo, J. Yang, and H. Wu Application of ACO-BPN to thermal error modeling of NC machine tool Int. J. Adv. Manuf. Technol. 50 5-8 2010 667 675
55. D. Zhang, X. Liu, H. Shi, R.-Y. Chen, Identification of position of key thermal susceptible points for thermal error compensation of machine tool by neural network, in: Proceedings of the International Conference on Intelligent Manufacturing, International Society for Optics and Photonics, 1995, pp. 468-472.
56. Z. Chen, and R. Di The researching status analysis about the identification of the thermal key point of the machine tool Modular Mach. Tool Autom. Manuf. Tech. 2 2004 33 34
57. S. Veldhuis, and M. Elbestawi A strategy for the compensation of errors in five-axis machining CIRP Ann. - Manuf. Technol. 44 1 1995 373 377
58. J. Vyroubal Compensation of machine tool thermal deformation in spindle axis direction based on decomposition method Precis. Eng. 36 1 2012 121 127
59. C.D. Mize, and J.C. Ziegert Neural network thermal error compensation of a machining center Precis. Eng. 24 4 2000 338 346
60. J. Yuan, and J. Ni The real-time error compensation technique for CNC machining systems Mechatronics 8 4 1998 359 380
61. C.-H. Lo, J. Yuan, and J. Ni Optimal temperature variable selection by grouping approach for thermal error modeling and compensation Int. J. Mach. Tools Manuf. 39 9 1999 1383 1396
62. J. Chen, J. Yuan, and J. Ni Thermal error modelling for real-time error compensation Int. J. Adv. Manuf. Technol. 12 4 1996 266 275
63. H. Yang, and J. Ni Adaptive model estimation of machine-tool thermal errors based on recursive dynamic modeling strategy Int. J. Mach. Tools Manuf. 45 1 2005 1 11
64. C.-H. Lo, J. Yuan, and J. Ni An application of real-time error compensation on a turning center Int. J. Mach. Tools Manuf. 35 12 1995 1669 1682
65. J. Yang, Y. Ren, G. Liu, H. Zhao, X. Dou, W. Chen, and S. He Testing, variable selecting and modeling of thermal errors on an INDEX-G200 turning center Int. J. Adv. Manuf. Technol. 26 7-8 2005 814 818
66. J.-H. Lee, and S.-H. Yang Statistical optimization and assessment of a thermal error model for CNC machine tools Int. J. Mach. Tools Manuf. 42 1 2002 147 155
67. S. Yang, J. Yuan, and J. Ni The improvement of thermal error modeling and compensation on machine tools by CMAC neural network Int. J. Mach. Tools Manuf. 36 4 1996 527 537
68. J. Han, L. Wang, H. Wang, and N. Cheng A new thermal error modeling method for CNC machine tools Int. J. Adv. Manuf. Technol. 62 1-4 2012 205 212
69. D.A. Krulewich Temperature integration model and measurement point selection for thermally induced machine tool errors Mechatronics 8 4 1998 395 412
70. D. Krulewich Error Compensation for Thermally Induced Errors on a Machine Tool 1996 Lawrence Livermore National Lab CA, United States
71. J. Yan, H. Zhang, G. Liu, and J. Yang Application of a new optimizing method for the measuring points of CNC machine thermal error based on grey synthetic degree of association J. Sichuan Univ. (Eng. Sci. Ed.) 40 2 2008 160 164
72. J. Yang, J. Yuan, and J. Ni Thermal error mode analysis and robust modeling for error compensation on a CNC turning center Int. J. Mach. Tools Manuf. 39 9 1999 1367 1381
73. J. Zhu, J. Ni, and A.J. Shih Robust machine tool thermal error modeling through thermal mode concept J. Manuf. Sci. Eng. 130 6 2008 061006
74. A. Koevoets, H. Eggink, J. Van Der Sanden, J. Dekkers, T. Ruijl, Optimal sensor configuring techniques for the compensation of thermo-elastic deformations in high-precision systems, in: IEEE THERMINIC, Thermal Investigation of ICs and Systems, 2007, pp. 208-213.
75. H. Li, and X. Yang A design method of temperature measurement points for thermal error of machine spindle Chin. J. Mech. Eng. 21 7 2010 804 808
76. H. Zhang, H. Zeng, and J. Tang Optimization for temperature measurement points of compensating thermal error on machine tools based on rough sets Mach. Tool Hydraul. 1 2010 39 40
77. R. Babu, V.P. Raja, J. Kanchana, and D.V. Krishna Identification, development and testing of thermal error compensation model for a headstock assembly of CNC turning centre Int. J. Eng. Technol. 3 2 2014 113 122
78. T. Moriwaki, and E. Shamoto Analysis of thermal deformation of an ultraprecision air spindle system CIRP Ann. - Manuf. Technol. 47 1 1998 315 319
79. H. Yang, and J. Ni Dynamic neural network modeling for nonlinear, nonstationary machine tool thermally induced error Int. J. Mach. Tools Manuf. 45 4 2005 455 465
80. ISO 230-3:2007(E): Test code for machine tools - Part 3: Determination of thermal effects, 2007.
81. H.J. Pahk, S.W. Lee, Thermal error measurement and real time compensation system for the CNC machine tools incorporating the spindle thermal error and the feed axis thermal error, in: Proceedings of the 33rd International MATADOR Conference, Springer, 2000, pp. 249-254.
82. H. Pahk, S. Lee, and H. Kwon Thermal error measurement and modelling techniques for the five-degree-of-freedom spindle drifts in computer numerically controlled machine tools Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 215 4 2001 469 485
83. Y.Q. Fu, W.G. Gao, J.Y. Yang, Q. Zhang, and D.W. Zhang Thermal error measurement, modeling and compensation for motorized spindle and the research on compensation effect validation Adv. Mater. Res. 889 2014 1003 1008
84. Y.M. Zhang, Y. Chen, and H. Li Temperature field analysis and thermal error testing for CNC machine tool's headstock Adv. Mater. Res. 889 2014 316 320
85. C.-H. Wu, and Y.-T. Kung Thermal analysis and compensation of a double-column machining centre Proc. Inst. Mech. Eng. Part B: J. Eng. Manuf. 220 2 2006 109 117
86. A.A. Sarhan Investigate the spindle errors motions from thermal change for high-precision CNC machining capability Int. J. Adv. Manuf. Technol. 70 5-8 2014 957 963
87. H. Castro A method for evaluating spindle rotation errors of machine tools using a laser interferometer Measurement 41 5 2008 526 537
88. J.-S. Chen Fast calibration and modeling of thermally-induced machine tool errors in real machining Int. J. Mach. Tools Manuf. 37 2 1997 159 169
89. S. Li, Y. Zhang, and G. Zhang A study of pre-compensation for thermal errors of NC machine tools Int. J. Mach. Tools Manuf. 37 12 1997 1715 1719
90. M. Yang, and J. Lee Measurement and prediction of thermal errors of a CNC machining center using two spherical balls J. Mater. Process. Technol. 75 1 1998 180 189
91. S.-H. Yang, K.-H. Kim, and Y.K. Park Measurement of spindle thermal errors in machine tool using hemispherical ball bar test Int. J. Mach. Tools Manuf. 44 2 2004 333 340
92. N. Srinivasa, J. Ziegert, and C. Mize Spindle thermal drift measurement using the laser ball bar Precis. Eng. 18 2 1996 118 128
93. J. Li, W. Zhang, G. Yang, S. Tu, and X. Chen Thermal-error modeling for complex physical systems: the-state-of-arts review Int. J. Adv. Manuf. Technol. 42 1-2 2009 168 179
94. L. Ruijun, Y. Wenhua, H.H. Zhang, and Y. Qifan The thermal error optimization models for CNC machine tools Int. J. Adv. Manuf. Technol. 63 9-12 2012 1167 1176
95. 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. 43 11 2003 1163 1170
96. C. Brecher, P. Hirsch, and M. Weck Compensation of thermo-elastic machine tool deformation based on control internal data CIRP Ann. - Manuf. Technol. 53 1 2004 299 304
97. I. Petráš, and D. Bednárová Total least squares approach to modeling: a Matlab toolbox Acta Montan. Slov. 15 2 2010 158
98. S.J. Miller The Method of Least Squares 2006 Mathematics Department Brown University 1 7
99. J. Yang, Y. Ren, W. Zhu, M. Huang, and Z. Pan Research on on-line modeling method of thermal error compensation model for CNC machines Chin. J. Mech. Eng. 39 3 2003 81 84
100. R.H. Myers Classical and Modern Regression With Applications vol. 2 1990 Duxbury Press Belmont, CA
101. J. Fox Applied Regression Analysis, Linear Models, and Related Methods 1997 Sage
102. J.-S. Chen A study of thermally induced machine tool errors in real cutting conditions Int. J. Mach. Tools Manuf. 36 12 1996 1401 1411
103. M. Efroymson Multiple regression analysis Math. Methods Digit. Comput. 1 1960 191 203
104. J. Han, L. Wang, N. Cheng, H. Wang, Thermal error modeling of machine tool based on fuzzy c-means cluster analysis, in: Proceedings of the IEEE International Conference on Electronic and Mechanical Engineering and Information Technology (EMEIT), 2011, pp. 2333-2336.
105. P. Lahiri Model Selection 2001 Institute of Mathematical Statistics
106. P.J. Huber Projection pursuit Ann. Stat. 1985 435 475
107. O.C. Lingjærde, and K. Liestøl Generalized projection pursuit regression SIAM J. Sci. Comput. 20 3 1998 844 857
108. G. Qianjian, and Y. Jianguo Application of projection pursuit regression to thermal error modeling of a CNC machine tool Int. J. Adv. Manuf. Technol. 55 5-8 2011 623 629
109. A. El Ouafi, M. Guillot, and A. Bedrouni Accuracy enhancement of multi-axis CNC machines through on-line neurocompensation J. Intell. Manuf. 11 6 2000 535 545
110. A. El Ouafi, M. Guillot, and N. Barka An integrated modeling approach for ANN-based real-time thermal error compensation on a CNC turning center Adv. Mater. Res. 664 2013 907 915
111. M.T. Hagan, H.B. Demuth, and M.H. Beale Neural Network Design 1996 PWS Publications Boston
112. Z. Du, J. Yang, Z. Yao, and B. Xue Modeling approach of regression orthogonal experiment design for the thermal error compensation of a CNC turning center J. Mater. Process. Technol. 129 1 2002 619 623
113. H. Demuth, and M. Beale Neural Network Toolbox for Use With MATLAB 1993
114. M. Hattori, H. Noguchi, S. Ito, T. Suto, and H. Inoue Estimation of thermal-deformation in machine tools using neural network technique J. Mater. Process. Technol. 56 1 1996 765 772
115. J.-S. Chen Neural network-based modelling and error compensation of thermally-induced spindle errors Int. J. Adv. Manuf. Technol. 12 4 1996 303 308
116. Z. Wang, Y. He, M. Jiang, A comparison among three neural networks for text classification, in: Proceedings of the IEEE 8th International Conference on Signal Processing, 2006.
117. W. Hao, Z. Hongtao, G. Qianjian, W. Xiushan, and Y. Jianguo Thermal error optimization modeling and real-time compensation on a CNC turning center J. Mater. Process. Technol. 207 1 2008 172 179
118. Y. Huang, J. Zhang, X. Li, and L. Tian Thermal error modeling by integrating GA and BP algorithms for the high-speed spindle Int. J. Adv. Manuf. Technol. 2014 1 7
119. L. Fausett Fundamentals of Neural Networks: Architectures, Algorithms, and Applications 1994 Prentice-Hall, Inc.
120. J.J. Hopfield Learning algorithms and probability distributions in feed-forward and feed-back networks Proc. Natl. Acad. Sci. 84 23 1987 8429 8433
121. D. Pham, and X. Liu Neural Networks for Identification, Prediction and Control 1995
122. Z. Yang, M. Sun, W. Li, and W. Liang Modified Elman network for thermal deformation compensation modeling in machine tools Int. J. Adv. Manuf. Technol. 54 5-8 2011 669 676
123. W.J. Tian, Y. Geng, J.C. Liu, L.A. Ai, A new neural network approach to machine tool thermally induced error, in: Proceedings of the IEEE International Workshop on Intelligent Systems and Applications, ISA 2009, 2009, pp. 1-5.
124. A. Srivastava, S. Veldhuis, and M. Elbestawit Modelling geometric and thermal errors in a five-axis CNC machine tool Int. J. Mach. Tools Manuf. 35 9 1995 1321 1337
125. Y. Zhang, J. Yang, and H. Jiang Machine tool thermal error modeling and prediction by grey neural network Int. J. Adv. Manuf. Technol. 59 9-12 2012 1065 1072
126. S. Liu, Y. Lin, and J.Y.L. Forrest Grey Systems: Theory and Applications vol. 68 2010 Springer
127. L. Sifeng, J. Forrest, Y. Yingjie, A brief introduction to grey systems theory, in: Proceedings of the 2011 IEEE International Conference on Grey Systems and Intelligent Services (GSIS), 2011, pp. 1-9.
128. Y. Li, J. Yang, H. Zhang, and H. Tong Application of grey system model to thermal error modeling on machine tools Knowledge Enterprise: Intelligent Strategies in Product Design, Manufacturing, and Management 2006 Springer 511 518
129. K.-C. Wang, Thermal error modeling of a machining center using grey system theory and HGA-trained neural network, in: Proceedings of the 2006 IEEE Conference on Cybernetics and Intelligent Systems, 2006, pp. 1-7.
130. K.-C. Wang, Thermal error modeling of a machining center using grey system theory and adaptive network-based fuzzy inference system, in: Proceedings of the 2006 IEEE Conference on Cybernetics and Intelligent Systems, 2006, pp. 1-6.
131. Y. Wang, G. Zhang, K.S. Moon, and J.W. Sutherland Compensation for the thermal error of a multi-axis machining center J. Mater. Process. Technol. 75 1 1998 45 53
132. D. Meyer, Support Vector Machines. The Interface to libsvm in package e1071 e1071, Vignette, 2012.
133. Y.-Y. Gong, E.-M. Miao, H.-D. Chen, and T.-J. Cheng Application of support vector regression machine to thermal error modelling of machine tools Opt. Precis. Eng. 4 2013 023
134. R. Ramesh, M. Mannan, and A. Poo Support vector machines model for classification of thermal error in machine tools Int. J. Adv. Manuf. Technol. 20 2 2002 114 120
135. E.-M. Miao, Y.-Y. Gong, P.-C. Niu, C.-Z. Ji, and H.-D. Chen Robustness of thermal error compensation modeling models of CNC machine tools Int. J. Adv. Manuf. Technol. 69 9-12 2013 2593 2603
136. L. Weiqing, F. Jianzhong, Support vector machine and neural network united system for NC machine tool thermal error modeling, in: Proceedings of the 2010 Sixth International Conference on Natural Computation (ICNC), 10-12 August 2010, pp. 4305-4309, doi: 10.1109/ICNC.2010.5583620.
137. R. Ramesh, M. Mannan, A. Poo, and S. Keerthi Thermal error measurement and modelling in machine tools. Part II. Hybrid Bayesian network - support vector machine model Int. J. Mach. Tools Manuf. 43 4 2003 405 419
138. J. Ni CNC machine accuracy enhancement through real-time error compensation J. Manuf. Sci. Eng. 119 4B 1997 717 725
139. L. Cui, W. Gao, D. Zhang, H. Zhang, and L. Han Thermal error compensation for telescopic spindle of CNC machine tool based on SIEMENS 840D system Trans. Tianjin Univ. 17 2011 340 343
140. J. Shen, Y. Li, Z. Lu, Z. Chen, and J. Yang A real·time compensation method for the geometric and thermal error on CNC turning machine J. Sichuan Univ. (Eng. Sci. Ed.) 40 1 2008 163 166
141. J. Yang, H. Zhang, H. Tong, H. Cao, and Y. Ren The application of real-time thermal error compensation on NC machine tools J. Shanghai Jiaotong Univ. 39 9 2006 1389 1392
142. J. Chen, and G. Chiou Quick testing and modeling of thermally-induced errors of CNC machine tools Int. J. Mach. Tools Manuf. 35 7 1995 1063 1074
143. D. Lee, J. Choi, and D.-H. Choi ICA based thermal source extraction and thermal distortion compensation method for a machine tool Int. J. Mach. Tools Manuf. 43 6 2003 589 597
144. T. Moriwaki Thermal deformation and its on-line compensation of hydrostatically supported precision spindle CIRP Ann. - Manuf. Technol. 37 1 1988 393 396
145. M. Donmez, K. Lee, C. Liu, M.M. Barash, A real-time error compensation system for a computerized numerical control turning center, in: Proceedings of the 1986 IEEE International Conference on Robotics and Automation, 1986, pp. 172-176.
146. K. Kim, M. Kim, and S. Chung Real-time compensatory control of thermal errors for high-speed machine tools Proc. Inst. Mech. Eng. Part B: J. Eng. Manuf. 218 8 2004 913 924
147. J.-S. Chen Computer-aided accuracy enhancement for multi-axis CNC machine tool Int. J. Mach. Tools Manuf. 35 4 1995 593 605
148. J. Liang, H. Li, J. Yuan, and J. Ni A comprehensive error compensation system for correcting geometric, thermal, and cutting force-induced errors Int. J. Adv. Manuf. Technol. 13 10 1997 708 712