本文建立了描述淬火钢圆形截面硬度分布曲线－U曲线的解析函数表达式。利用热传导微分方程解得端淬试样温度场和冷至700℃时的冷却速度方程。根据端淬曲线、冷却速度和圆截面半径关系实验曲线图及等效冷速原理，用曲线拟合法获得了硬度与试样半径和截面位置半径之间关系式。截面硬度分布函数含有从端淬试验获得的淬透性系数、最高硬度和最低硬度值，使得模型具有较高的理论性而且保证了淬透性系数与试样形状尺寸无关。检验结果表明，模拟曲线和实验值符合很好。
An analytical function for describing hardness distribution of round section in quenched steel, known as U-curve, has been established. The temperature field and cooling rate equation of Jominy at 700℃ were obtained by solving the heat conduction differential equation. The formula for expressing relations between sample radius, section position radius and section hardness was created by using the curve fitting according to the Jominy curves, cooling rate, measured section radius and cooling rate equivalent theory. This model includes hardenability coefficient, hardness maximum and hardness minimum that were obtained from Jominy test so that it displays advanced characteristic in theory and retains no correlation between hardenability and sample shape. The results show that the simulated curves are in good agreement with experimental values.
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