基于有限元和最优化方法的淬火冷却过程反传热分析

INVERSE HEAT CONDUCTION ANALYSIS OF QUENCHING PROCESS BASED ON FINITE ELEMENT AND OPTIMIZATION METHOD

淬火过程换热系数的求解是反向热传导问题中的一种不适定和非线性问题.本文提出了一种求解淬火过程随温度变化的换热系数的新方法,该方法把有限元方法引入反向热传导问题,根据实验测量的温度曲线,结合使用最优化方法中的进退法和试探法确定合理的边界换热系数.为了使进退法适用于该类反传热问题,对其算法进行了改进,并用其确定换热系数优化的搜索区间,然后用试探法(黄金分割法)在搜索区间内找到换热系数的最佳值.在计算过程中,利用有限元法可以方便地计算出各个单元在整个过程的相变情况,得到各单元在相应时间段所产生相变潜热,并将各单元的相变潜热与单元温度场进行耦合计算.

The calculation of surface heat transfer coefficient during quenching process is one of the inverse heat conduction problem, and it is a nonlinear and bad-posed problem. A new method to calculate the temperature-dependent surface heat transfer coefficient during quenching process is presented, which applies finite element method (FEM), advance-retreat method and golden section method to the inverse heat conduction problem, and can calculate the surface heat transfer coefficient according to the temperature curve gained by experiments. In order to apply the advance-retreat method to inverse heat conduction problem during quenching process, the arithmetic is improved, so that the searching interval of optimization can be gained by the improved advance-retreat method. The optimum values of surface heat transfer coefficient can be easily obtained in the searching interval by golden section method. During the calculation process, the phase-transform volume and phase-transform latent heat of every element in every time interval can be calculated easily by FEM, the temperature and phase-transform volume of every element are calculated with the coupling calculation of phase-transform latent heat.