Predicting spindle displacement caused by heat using the general regression neural network

  • Bo-Lin Jian
  • Cheng-Chi Wang
  • Chin-Tsung Hsieh
  • Ying-Piao Kuo
  • Mao-Chin Houng
  • Her-Terng YauEmail author


Machine tools may be affected by room temperature, the heat generated by the process, and many other factors. These cause the temperature of the spindle, motor, lead screw, and other parts to rise, and this causes thermal deformation. The main purpose of this study was an exploration of the relationship between the temperature of the spindle and thermal deformation. Measurements were made of the increases in temperature of a CNC lathe spindle, and the related axial displacements involved, at spindle speeds of 1000, 2000, and 3000 rpm. Multiple regression analysis and a general regression neural network were used to establish the relationship between thermal deformation and temperature change individually. The results showed the coefficient of determination of the multiple regression analysis to be 0.9275, while the general regression determined by the neural network was 1. The fitting result of the regression neural network was better than that of multiple regression analysis, and the maximum error was less than 0.1 μm. In addition, this study also used COMSOL simulation analysis software to analyze features of the thermal behavior generated by the spindle structure. A trial and error method was used to adjust the boundary conditions. Results showed that the maximum error in temperature rise determination of simulation and experiment was less than 1 °C.


Multiple regression analysis General regression neural network Finite element analysis 


Funding information

We would like to acknowledge the Ministry of Science and Technology’s “Spindle Peripheral Smart Function Technology Development for Domestic Lathe Machine Tools” project (project number: MOST107-2218-E-167-001-) for assisting with funding for this study.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical EngineeringNational Chin-Yi University of TechnologyTaichungTaiwan
  2. 2.Graduate Institute of Precision ManufacturingNational Chin-Yi University of TechnologyTaichungTaiwan

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