Prediction of 3D grinding temperature field based on meshless method considering infinite element

  • Zixuan WangEmail author
  • Yan Li
  • Tianbiao Yu
  • Ji Zhao
  • P. H. WenEmail author


A three-dimensional numerical model to calculate the grinding temperature field distribution is presented. The finite block method, which is developed from meshless method, is used to deal with the stationary and the transient heat conduction problems in this paper. The influences of workpiece feed velocity, cooling coefficient, and the depth of cut on temperature distribution are considered. The model with temperature-dependent thermal conductivity and specific heat is presented. The Lagrange partial differential matrix from the heat transfer governing equation is obtained by using Lagrange series and mapping technique. The grinding wheel-workpiece contact area is assumed as a moving distributed square heat source. The Laplace transformation method and Durbin’s inverse technique are employed in the transient heat conduction analysis. The results of the developed model are compared with others’ finite element method solutions and analytical solutions where a good agreement is demonstrated. And the finite block method was proved a better convergence and accuracy than finite element method by comparing the ABAQUS results. In addition, the three-dimensional infinite element is introduced to perform the thermal analysis, and there is a great of advantages in the simulation of large boundary problems.


Meshless finite block method Infinite element Mapping technique Differential matrix Grinding processes Heat transfer 


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Funding information

The work was funded by China Scholarship Council, the Fundamental Research Funds for the Central Universities (N160306006), National Natural Science Foundation of China (51275084), and Science and technology project of Shenyang (18006001).


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical Engineering and AutomationNortheastern UniversityShenyangPeople’s Republic of China
  2. 2.School of Mechanics and EngineeringSouthwest Jiaotong UniversityChengduPeople’s Republic of China
  3. 3.Department of MathematicsCity University of Hong KongKowloon TongHong Kong
  4. 4.School of Engineering and Materials ScienceQueen Mary University of LondonLondonUK

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