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根据实验的实际条件，考虑对流、辐射等复杂边界条件，给出了有限尺寸、移动热源的激光相变硬化三维温度场数学模型；应用有限差分法，对温度场进行计算；讨论不同参数对激光相变硬化的影响，发现温度峰值随给定功率或移动速度不同而变化．本模型可以用来预测相变硬化的宽度、深度，分析组织变化的规律，为深入研究激光相变硬化的机理和优化工艺参数提供理论依据．
According to the experimental conditions, considering the complicated boundary conditions such as convection and radiation, the mathematical model of laser phase-change hardening temperature field with finite size and moving heat source is given. The temperature field is calculated by finite difference method. The effect of phase change hardening and found that the peak temperature with a given power or moving speed varies. The model can be used to predict the width and depth of phase-change hardening and to analyze the regularity of the microstructural changes. It provides a theoretical basis for further study on the mechanism of laser phase-change hardening and optimization of process parameters.