[1]
Y.X. Zheng, "Research status of thermal error modeling of CNC machine tools in China", Mech. Engin. Auto, pp. 222-223, 2016.
[2]
W.J. Gong, L.X. Zhang, JP Li, L. Li, and J.Y. Xiao, "Summary of prediction models of spindle thermal deformation", Develop. Innov. Mach. Electric. Prod, no. 003, pp. 125-128, 2016.
[3]
Q.C. Guo, H.M. Wang, and A.J. Li, "Research progress of thermal error modeling technology for machine tools", J. Hebei Uni. Sci. Technol., vol. 32, no. 004, pp. 344-350, 2015.
[4]
E.M. Miao, and Y.S. Liu, "Method and system for determining sectional modeling point of temperature sensitive interval", Patent: CN110716500A, 2020.
[5]
X.Y. Wei, J.T. Wu, X.L. Ding, X.G. Feng, Q.S. Pan, and M.Y. Qian, "Self-adaptive selection method of temperature sensitive point of machine tool thermal error", Patent: CN114967592A, 2022.
[7]
X.L. Liu, H.W. Song, and S Wu, "Selection method of temperature sensitive points for thermal error modeling of dual-turntable five-axis CNC machine tools", Patent: CN109765846A, 2022.
[8]
J.X. Shen, "Machine tool information acquisition and separation method based on thermal characteristic mechanism analysis", Patent: CN114357660A, 2022.
[9]
W. Wu, "A Virtual Instrument for Thermal Characteristic Analysis of Machine Tools” ring of CNC machine tool spindle", Patent: CN207541454U, 2018.
[10]
W.F. Si, "Method for predicting machining accuracy of numerical control milling and boring machine based on thermal analysis", Patent: CN112475904A, 2021.
[11]
W.G. Gao, D.L. Ni, D.W. Zhang, and L.T. Weng, "Method for analyzing thermal characteristics of electric spindle based on heat generation and heat dissipation power", Patent: CN110717294A, 2019.
[12]
J.H. Wang, S.F. Xue, C.B. Yang, Y.S. Zhao, and K. Chen, "Comprehensive theoretical modeling and analysis method for thermal characteristics of spindle of numerical control machine tool", Patent: CN110705147A, 2019.
[13]
Z.Y. Cui, "Thermal deformation model acquisition method, thermal deformation estimation acquisition method, thermal deformation compensation value acquisition method and recording medium thereof", Patent: K.R.1020040050013, 2018.
[14]
Z. Huang, J.J. Li, L. Du, X.S. Chen, F.Q. Heng, K. Xu, and Z.J. Wang, "Numerical simulation method, prediction method and modeling system for thermal characteristics of heavy numerical control floor milling lathe", Patent: CN104200019A, 2018.
[15]
Z.D. Zhou, J.M. Hu, P. Lou, Q. Liu, and Z. Jiang, "BP neural network thermal error modeling method for heavy machine tools optimized by genetic algorithm", Patent: CN104597842A, 2015.
[16]
C. Ma, J.L. Liu, L.L. Yi, and S.L. Wang, "Thermal error modeling method and thermal error compensation system of shaft system based on LSTM neural network", Patent: CN111259498A, 2020.
[17]
F. Fang, S.T. Xiang, L. Liu, and Z.P. Luo, "Modeling and detection method of thermal error of NC machine tool spindle based on detection neural network", Patent: CN109739181A, 2019.
[19]
C.Y. Wu, S.T. Xiang, C.W. Lu, and C. Liu, "A Thermal Error Modeling Method of Rotating Shaft of Five-axis Machine Tool Based on Convolutional Network", Patent: CN111985149A, 2020.
[20]
G.H. Chen, H. Xiang, Y. Wang, J.H. Chen, J. Zhang, and B. Li, "A spatial error modeling method of CNC machine tools based on spatial grid compensation", Patent: CN105404237A, 2016.
[21]
L.Q. Du, H.C. Wang, Y.W. Yu, X.B. Yi, G. Chen, H. Yang, J. He, and A.Y. Hu, "A Modeling Method of Machine Tool Thermal Error Based on Deep Learning", Patent: CN110083125A, 2019.
[22]
L.Q. Du, R.J. Li, Y.W. Yu, X.B. Yi, J.Y. Zhang, G. Chen, Q. Zhang, and X.J. Lu, "A thermal error modeling method of NC machine tools based on optimized fuzzy neural network", Patent: CN110058569A, 2019.
[23]
Q.J. Guo, R.F. Xu, and L. He, "A Modeling Method of Machine Tool Thermal Error Based on Ant Colony Neural Network", Patent: CN105094053A, 2015.
[24]
J.H. Zhang, Y.F. Zhang, Q. Yin, T.M. Huang, J. Ming, and C. Li, "Grey neural network modeling method for thermal error compensation of numerical control machine tools", Patent: CN103984287A, 2014.
[25]
K. Liu, and Y.Q. Wang, "Calculation method based on deep neural network and Monte Carlo Carlo method, reliability of thermal error model of machine tool", Patent: WO2020168584A1, 2019.
[26]
X.D. Yao, J.G. Yang, and G.F. Hou, "Modeling method of real-time compensation for thermal error of CNC machine tools based on time series algorithm", Patent: CN102736558A, 2011.
[27]
B. Li, W.C. Su, X. Wei, M.H. Lan, L. Chen, Z.D. Jiang, and J.F. Bai, "Grey theory piecewise weighted thermal error modeling method with lag data processing", Patent: CN110262393A, 2019.
[28]
J.H. Chen, Y. Chen, Y.Y. He, and P.C. Hu, "Modeling method and system for Z-axis thermal error of vertical machine tool under environmental influence", Patent: CN114488945A, 2022.
[29]
Z. Huang, Z.J. Wang, J.Y. Li, K. Xu, L. Chen, L.P. Wang, and L. Du, "Modeling method of thermal drift of NC machine tool spindle based on FA-LSSVM", Patent: CN105607575A, 2016.
[30]
Z. Huang, Z.J. Jia, T. Deng, L. Du, and L.P. Wang, "Modeling method of thermal error of NC machine tool spindle based on FS+WPSVM", Patent: CN107391888A, 2017.
[31]
Z. Huang, Y.C. Liu, and T. Zhou, "Comprehensive modeling method of thermal error of five-axis CNC machine tools based on LSO-LSSVM", Patent: CN112433507A, 2021.
[32]
Q.J. Guo, X.N. Qi, and X.H. Yang, "Modeling method of machine tool thermal error based on multivariate projection pursuit clustering", Patent: CN105204435A, 2014.
[33]
S.B. Wang, B.R. Tang, S.L. Sun, Q. Huang, Z.Y. Zhao, and Z.H. Wang, "Method for creating thermal error model and solving method based on cutting force", Patent: CN113779726A, 2021.
[34]
C. Ma, J.L. Liu, L.L. Yi, and S.L. Wang, "Thermal characteristic analysis method, thermal error modeling method and thermal error compensation system of shaft system based on analytical method", Patent: CN111310373A, 2022.
[35]
C. Ma, J.L. Liu, H.Q. Gui, and S.L. Wang, "Thermal error modeling method and compensation system of linear servo system based on energy balance", Patent: CN113093545A, 2021.
[36]
C. Ma, J.L. Liu, L.L. Yi, and S.L. Wang, "Thermal error modeling method, total error modeling method and thermal error compensation system of shaft system with two axial constraints", Patent: CN111190390A, 2020.
[37]
H.T. Yue, C.G. Guo, Q. Li, L.J. Zhao, and G.S. Ding, "Modeling and Compensation Method of Thermo-mechanical Coupling Error of CNC Machine Tools Considering Processing Parameters", Patent: CN110196572A, 2019.
[38]
H. Shi, Y. Xiao, and T. Tao, "Measuring device and modeling method for thermal error of spindle of numerical control lathe", Patent: CN114296396A, 2021.
[39]
J.Z. Fu, X.H. Yao, W.Q. Lin, and Z.C. Chen, "Modeling method of thermal error least squares support vector machine for NC machine tools", Patent: CN101446994A, 2008.
[41]
G.H. Chen, D.Q. Liu, L. Zhang, H. Xiang, D.Z. Zhao, G.Q. Tong, B. Li, and Y.X. Chen, "Method for modeling thermal error of whole machine tool", Patent: CN111666659A, 2020.
[42]
J. Yuan, J. Lu, Z.X. Qiu, Y.F. Shen, and J.X. Shao, "Machine tool thermal error modeling method and testing system based on golden section and cumulative regression", Patent: CN104090526A, 2017.
[43]
Z.F. Liu, M.H. Pan, A.P. Zhang, B. Luo, J.Y. Zhang, and L.G. Cai, "A Thermal Error Modeling Method Based on Grey Linear Regression", Patent: CN103268082A, 2013.
[44]
Y. Dai, H. Qu, S.Q. Zhan, Y.H. Gao, and Z.C. Zhou, "Thermal error modeling method of high-speed motorized spindle based on bond graph", Patent: CN113110295A, 2021.
[45]
F.X. Du, X.Y. Feng, and H. Li, "Two-step-based thermal error modeling method for CNC machine tools", Patent: CN109240204A, 2019.
[46]
F. Fang, S.T. Xiang, J.B. Li, and Y.G. Cui, "Deep learning-based thermal error modeling method for CNC machine tool spindle", Patent: CN108363870A, 2021.
[47]
C.X. Zhang, F.H. Kong, and M. Cui, "A nonlinear autoregressive neural network thermal error modeling method for machine tools with external input", Patent: CN110705180A, 2019.
[48]
S.B. Wang, and B.R. Tang, "A modeling method of cutting force model considering spindle thermal error and tool runout", Patent: CN114036671A, 2021.
[49]
Z.L. Zhang, S. Feng, Y. Yuan, C. Yue, and X.D. Lu, "Method for modeling thermal error of spindle of numerical control machine tool and reliability analysis of machining accuracy", Patent: CN114329837A, 2021.
[50]
M. Yin, J. Peng, and L. Cao, "Physical modeling method of axial thermal error of NC machine tool spindle", Patent: CN113126566A, 2021.
[52]
H. Dong, "A new modeling method of thermal error least squares support vector machine for CNC machine tools", Patent: CN102479261A, 2010.
[53]
B. Li, B. Tan, and X.Y. Mao, "Analytical modeling method for environmental temperature of heavy machine tools", Patent: CN103543637A, 2016.
[54]
C. Ma, J.L. Liu, H.Q. Gui, and S.L. Wang, "Main shaft thermal error modeling method, error prediction system, error control system, error control method and cloud computing system", Patent: CN113051832A, 2021.
[55]
J.H. Chen, Y. Chen, and Y.Y. He, "Modeling method, forecasting method and modeling system for spindle thermal error", Patent: CN114019909A, 2021.
[56]
J. Zang, W.H. Zhao, and B. Li, "Modeling method of positioning error of ball screw feed system of semi-closed loop control CNC machine tool", Patent: CN104483900A, 2018.
[57]
C. Ma, J.L. Liu, H.Q. Gui, and S.L. Wang, "Modeling method of self-learning prediction model of machine tool thermal error and control method of machine tool thermal error based on digital twinning", Patent: CN113051831A, 2022.
[58]
J.N. Gu, Y.X. Wang, S.L. Wang, Y.F. Zhang, Y.J. Ling, Q. Yin, P.L. Zhou, and Y.Q. Liu, "Selection and optimization method of temperature measuring point combination for numerical control machine tool thermal error compensation modeling", Patent: CN103926874A, 2014.
[59]
N.M. Miao, Y. Liu, S.X. Yang, and H. Liu, "Method and system for predicting thermal error of numerical control machine tool based on unbiased estimation split model", Patent: CN105759719A, 2016.
[60]
B. Li, B. Tan, X.Y. Mao, K.M. Mao, and G.Y. Ren, "A prediction method of thermal error of heavy machine tool considering ambient temperature", Patent: CN103823991A, 2014.
[61]
L. Yin, F. Zhang, W.C. Lin, P. Wu, and C. Chen, "Method, device and storage medium for predicting thermal error of machine tool feed shaft", Patent: CN114310485A, 2022.
[63]
G.Q. Fu, Y.J. Rao, Y.P. Xie, C. Tao, H.W. Gong, C.J. Lu, H.L. Gao, and L. Guo, "Combination selection method of weighted integrated temperature sensitive points for spindle thermal error modeling", Patent: CN111414977A, 2020.
[64]
G.Q. Fu, C. Tao, Y.P. Xie, H.W. Gong, Y.J. Rao, C.H. Lu, H.L. Gao, and L. Gao, "Selection method of temperature sensitive point combination in machine tool thermal error modeling by region", Patent: CN111459094A, 2021.
[65]
S.B. Wang, R.B. Tang, S.L. Sun, H. Wang, and Q. Huang, "Modeling method of spindle axial thermal error model based on machine tool power", Patent: CN115017829A, 2022.
[66]
K. Liu, H.B. Liu, and T. Li, "Application method of “thermal error-temperature ring of CNC machine tool spindle"", Patent: WO2020006851A1, 2018.
[67]
G.F. Yin, Q.H. Liao, and L. Wang, "Modeling method for selecting thermal key points of CNC machine tool spindle system based on time characteristics", Patent: CN110543140A, 2020.
[68]
F. Fang, S.T. Xiang, C. Liu, W.J Min, and Z.P. Luo, "A training method of thermal error modeling of NC machine tool spindle based on image threshold setting", Patent: CN109709895A, 2021.
[69]
G.L. Li, Z.Y. Wang, Z.Y. Li, K. Xu, X.Y. Chen, and Y. Xiao, "Sectional modeling method of thermal error of NC machine tool spindle considering thermal hysteresis", Patent: CN114896771A, 2022.
[70]
K. Liu, Y.Q. Wang, H.B. Liu, T. Li, H.N. Liu, and D.W. Li, "Modeling and compensation method for radial thermal drift error of spindle of horizontal numerical control lathe", Patent: CN107942934A, 2019.
[71]
K. Liu, H.B. Liu, T. Li, Y.Q. Wang, Z.Y. Jia, and D.M. Guo, "Method for testing and modeling origin thermal drift error of semi-closed loop feed shaft of numerical control machine tool", Patent: CN107168242A, 2019.
[72]
C.F. Xi, and W.J. Cheng, "Thermal displacement error measuring device and modeling method of numerical control machine tool", Patent: CN111123835A, 2019.
[73]
X.H. Shan, "Thermal deformation correction method and thermal deformation correction device of numerical control machine tool", Patent: JP2006116654A, 2004.
[74]
C. Ma, J.L. Liu, H.Q. Gui, and S.L. Wang, "Establishment method of grinding comprehensive error model and geometric-thermal error control method of gear grinding machine", Patent: CN113589757A, 2021.
[75]
D.Q. Zeng, H.Y. Chen, H.F. Yin, and Z.G. Li, "Machine tool thermal error compensation method, device, computer equipment, system and machine tool", Patent: CN114660992A, 2022.
[76]
Z.H. Zu, Y.Y. Huang, M. Yu, G. Chen, J.H. Zhao, and M.Y. Qiu, "Method for compensating thermal error of machining equipment, device, system, medium and terminal thereof", Patent: CN112147951A, 2020.
[77]
T. Tao, Y.X. Liu, Z.Z. Yan, H.Y. Du, H. Shi, J.X. Fan, C.P. Jiang, and X.S. Mei, "Data acquisition and thermal error compensation system of CNC machine tool edge based on internet of things", Patent: CN112034788A, 2020.
[78]
X.Y. Wei, Y.C. Chen, W.D. Hu, Q.S. Pan, E.M. Miao, and X.G. Feng, "Method for compensating thermal error of machine tools in different regions", Patent: CN114895627A, 2022.
[79]
X.J. Tao, X.J. Shi, and Y.J. Zhou, "Measuring system and method for thermal error of gear hobbing machine bed", Patent: CN114115122A, 2021.
[80]
W.G. Gao, W. Li, D.L. Ni, D.W. Zhang, L.N. Wang, and K. Shi, "Device and method for testing thermal error of machine tool spindle", Patent: CN112276673A, 2020.
[81]
B.J. Li, H.J. Cao, and H.L. Zheng, "Analysis-based comprehensive energy efficiency test method for CNC machine tools", Patent: CN113010980A, 2021.
[82]
M.T. Lu, R.L. Diao, and X.Y. Jiang, "Thermal error control structure of numerical control machine tool", Patent: CN114310478A, 2022.
[83]
L. Hao, J. Hao, H.T. Wang, G.L. Zhang, Z. Xue, and J.T. Duan, "Thermal error control structure and method of numerical control machine tool", Patent: CN107378637A, 2017.
[84]
K. Liu, Y.M. Cui, L. Song, H.N. Liu, W. Han, and Y.Q. Wang, "Self-adaptive compensation method for thermal error of numerical control machine tool", Patent: CN113009882A, 2021.
[85]
K. Liu, S.F. Wang, and Z.Y. Ban, "Self-healing method for spindle accuracy of numerical control machine tool", Patent: CN114019903A, 2021.
[86]
Y. Dai, X.S. Tao, Z.L. Li, Y.D. Bao, Y.D. Bao, and G.D. Liu, "Method and system for compensating thermal error of numerical control milling head", Patent: CN113721548A, 2021.
[87]
Y. Yang, C.H. Yang, D.Y. Liu, and L.W. Zeng, "Automatic displacement compensation method and system for thermal deformation of worm gear hobbing machine", Patent: CN114002999A, 2022.
[88]
D.H. Jin, "Method and system for measuring and correcting thermal displacement of machine tool spindle", Patent: JP2004154907A, 2002.