Optimizing boundary conditions for thermal analysis of the spindle system using dynamic metamodel assisted differential evolution method

  • Feng TanEmail author
  • Congying Deng
  • Haiqiong Xie
  • Guofu Yin


Contributing up to 40~70% of total errors deteriorating the machining quality of machine tools, thermal errors need to be decreased. Building the accurate thermal simulation model of spindle system is the premise to study its thermal characteristics and further reduce its thermal errors. However, the accuracy of the thermal simulation model mainly rests with the accuracy of the boundary conditions since the mesh model is accurate enough. In overcoming the poor consistency between the thermal experiment and thermal simulation, thus obtaining the accurate thermal simulation model, the empirically calculated boundary conditions should be optimized, which is essentially an inverse problem. Treating the heat generation rates and the convective heat transfer coefficients as the optimization objects, and the simulation difference as the objective function, a dynamic metamodel assisted differential evolution (DMDE) method is adopted to efficiently search the optimal boundary conditions. The metamodel generated on the already executed data can prescreen out the most promising trial data to speed up the convergence of the differential evolution. And the scoring strategy is used to select the top high possible trial data to further accelerate the convergence. Results demonstrate that the optimal boundary conditions can be obtained using this method with maximum temperature simulation error reduced from 85.6 to 4.9% and thermal extension simulation error reduced from 60.9 to− 3.5%. Furthermore, the number of executions of thermal simulation analysis is reduced from 2000 needed by genetic algorithm or differential evolution to an average of 206 needed by the adopted method.


Spindle system Thermal simulation analysis Boundary conditions Metamodel Differential evolution 


Funding information

This research was financially supported by the Chongqing Research Program of Basic Research and Frontier Technology (grant no. cstc2019jcyj-msxmX0540), the National Natural Science Foundation of China (grant no. 51705058), the National Science and Technology Major Project of China (grant no. 2017ZX04020001-005), and the CAS “Light of West China” Program.


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Copyright information

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

Authors and Affiliations

  • Feng Tan
    • 1
    Email author
  • Congying Deng
    • 1
  • Haiqiong Xie
    • 1
  • Guofu Yin
    • 2
  1. 1.School of Advanced Manufacturing EngineeringChongqing University of Posts and TelecommunicationsChongqingPeople’s Republic of China
  2. 2.School of Manufacturing Science and EngineeringSichuan UniversityChengduPeople’s Republic of China

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