用三维有限元求解金属淬火过程的换热系数

Solution of invert problem of heat conduct equation during quenching by three-dimensional finite element method

在金属淬火过程的数值模拟中,换热系数的正确求解是工件温度场、应力/应变场模拟结果与实际相符合的先决条件.据此研究和分析了换热系数反求法的数学模型,分别采用一维和三维有限元法对该数学模型求解.研究表明:与采用一维有限差分的求解法相比较,计算过程由一维有限元法增加到三维有限元法,与实际情况更为接近;用有限元方法求解的换热系数曲线连续且平滑,结果可靠,且编程量小;用求得的换热系数计算金属淬火试件的中心温度场变化曲线,计算结果与实测数据相吻合.

In numerical simulation of steel quenching process, the correct solution of heat transfer coefficient is the precondition of simulating the temperature field and stress/strain field. Thus a mathematical mode of inverse problem of Heat Conduct Equation was analyzed, and a solution of it by 1D and 3D Finite Element Method （FEM） was presented. Comparing with 1 D Finite Difference Method （FDM）, calculation result of 3D FEM is closer to the practice. FEM is more effective to solve differential equation than FDM. The curve of heat transfer coefficient solved by 1 D or 3 D FEM is more coherent and smoother than that solved by FDM. And the curve of central temperature field of the part was calculated, the result corresponds to the experimental data.