3D grinding temperature field can be simulated by the finite difference method. When the finite difference method is used to calculate the temperature field, the boundary conditions need to be considered. Unfortunately, the difference equations for internal nodes and boundary nodes are not the same. For cuboid computing domains, there are twenty-six types of boundary nodes. This reduces the calculation efficiency to a certain extent. An improved finite difference method for the 3D grinding temperature field was proposed to solve this problem in this paper. By adding auxiliary nodes, the boundary nodes are converted into internal nodes, and the difference equations of the boundary nodes and internal nodes are unified. In this paper, the improved algorithm was used to simulate the 3D grinding temperature field. The temperature distribution characteristics of the grinding temperature field were analyzed. Then, the effects of heat source type, space step size, and convective heat transfer coefficient on the temperature field were studied. The results show that the improved algorithm can well simulate the 3D grinding temperature field. Finally, compared with the original algorithm, the calculation results were completely consistent, and the efficiency is improved by about 20%.

可以通过有限差分法模拟3D研磨温度场。当使用有限差分法计算温度场时，需要考虑边界条件。不幸的是，内部节点和边界节点的差分方程式并不相同。对于长方体计算域，有26种边界节点。这在一定程度上降低了计算效率。为解决这一问题，提出了一种改进的3D磨削温度场有限差分法。通过添加辅助节点，将边界节点转换为内部节点，统一边界节点与内部节点的差分方程。本文采用改进算法对3D磨削温度场进行仿真。分析了磨削温度场的温度分布特征。然后，研究了热源类型，空间步长和对流传热系数对温度场的影响。结果表明，改进算法可以很好地模拟3D磨削温度场。最后，与原始算法相比，计算结果完全一致，效率提高了约20％。