Thermal field model driven by heat anisotropy and computational stability analysis in grinding of MgF2 crystals

Abstract

Developing an accurate and efficient model of thermal field is crucial for optimizing process parameters and achieving high removal accuracy in grinding of difficult-to-machine materials, especially for brittle and anisotropic solids. However, ensuring both the accuracy and computational efficiency of the model remains challenging, as it is highly sensitive to computational stability, the selection of an appropriate heat flux model, and the anisotropic nature of heat conduction. In this work, a comprehensive thermal model of grinding of MgF₂ crystals was developed based on the principle of energy conservation and Fourier's Law of heat conduction, explicitly incorporating the anisotropy of heat conduction. Then, a rigorous computational stability analysis of the grinding thermal field was performed using the Gerschgorin circle theorem, enabling the determination of the optimal time step. Finally, the proposed model was compared with the traditional thermal field model and validated through grinding experiments. The results demonstrate a strong agreement between simulation and experiment, with the triangular heat flux model achieving an average simulation error of 10.37 %, outperforming other heat flux models. The results contribute to elucidating the sensitivity of thermal anisotropy to heat generation during the grinding of anisotropic solids, thereby providing a theoretical basis for optimizing process parameters.