钢的U曲线数学模型

MATHEMATICAL MODEL OF U-CURVE OF STEELS

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．首先求得端淬试样冷至700℃时的冷却速率计算公式．根据端淬曲线、冷却速率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上所处位置半径之间关系式．截面硬度分布函数含有从端淬实验曲线获得的淬透性系数、最高硬度和最低硬度值,使得模型具有较高的合理性且保证了淬透性系数与试样形状无关．实验验证结果表明,根据本文模型模拟所得结果与实验测试值符合很好．

An analytical function for describing hardness distribution in round section of quenched steel, known as U-curve, has been established. First of all, the cooling rate equation of Jominy test sample at 700 ℃ were obtained. The formula expressing relation between rod-like sample radius, section position radius and hardness was fitted according to the Jominy curves, experiment chart of cooling rate-section radius and equivalent cooling rate principle. This model included hardenability coefficient, hardness maximum and hardness minimum, which were obtained from Jominy test curve, so displayed higher reasonability in theory and retains no correlation between hardenability and sample shape. The validation experiments show that the simulated curves are in good agreement with experimental ones.