A Fast Algorithm Of Temperature Field Optimization In Linear Heat Condunction And Application In Electric Heating-Plate Optimization

In the field of heat transfer, the study on the traditional forward problem is relatively complete in theory, algorithm and application, but the corresponding inverse problem is more complex and difficult. Under certain condition, some inverse problems can be transformed into optimization problems, however, the calculation needed is large and the efficiency is low.Heating plate is the key component in injection molding machine. For the generally used heating plate, the electric heating tube is installed in a proper place of the plate as the heating source. The main performance criterion of heating plate is to require the surface temperature difference as small as possible. However, the practical plate is very difficult to achieve the requirements. Heating-plate problem is a typical inverse problem, and also a typical problem of the linear heat conduction problem. Studies on the rapid and efficient solutions to the problem are of important value.This paper studies the basic characteristics of the problem of linear heat conduction. In this paper, a superposition principle of the linear heat conduction problem is put forward, on the basis of it, a fast temperature optimization algorithm of the linear heat conduction is purposed. The heating-plate problem, as a typical application example of the new algorithm, is analyzed and optimized by the new algorithm and finite element method, and is conpared with traditional method such as orthogonal test. Then a practical experiment is designed and carried out to verify the results of the optimization. The research result solved the heating-plate problem, and provided a reference to other linear heat conduction problems of temperature field optimization.The main research contents include:1. Superposition principle of the linear heat conduction.The superposition principle of the linear heat conduction is derived based on the general characteristics of linear systems. In linear heat conduction system, when the initial condition and boundary condition exists at the same time, they can be separately considered, and then superimposed up.2. Fast temperature field optimization algorithm in linear heat conduction.On the basis of the superposition principle, a fast temperature optimization algorithm of the linear heat conduction is purposed. In the traditional optimization way, it needs to search and iterate the solution in the entire solution space of the problem. In each iteration, it needs to solve the finite element model of the problem, so the calculation is very large. The fast temperature field optimization algorithm takes full advantage of the principle of superposition of the linear heat conduction. It just needs to solve some specific FE model, which based on the optimization goal variables, and then the optimization result can be obtained by solving a simple algebraic equation set. Therefore, the computational efficiency will be greatly enhanced.3. Heating-plate temperature analysis uses finite element method.A heating-plate FEM analysis model is been set up, including geometric modeling, model simplification, load and boundary conditions. It lies the foundation for the next phase of optimization.4. Optimization of the heating-plate temperature field.The fast algorithm is applied to optimize the plate's electric power distribution, and to be contrasted with orthogonal experimental method. The results showed that the correct and effective of new fast algorithm, it greatly improved the efficiency in comparision with the orthogonal experimental method. 5. Heat-plate temperature field experiment.The experimental program is designed, an experimental platform is set up. The first experimental results validate the accuracy of the results of CAE finite element analysis, and the second experimental results validate the fast algorithm.