The Numerical Simulation On Temperature Field By FEM And Its Application To The Cooling Analysis Of Plastic Part And Mould

Temperature is one of the most important material parameters of physical science. In the field of plastic processing and molding, temperature is also one of the important key factors which affect the quality of plastic part. Then, to find out and simulate the temperature field distribution is a very cared problem at plastic processing. In this thesis the heat transfer theory and the finite element method are used to simulate the two dimension temperature field and the three dimension temperature field. 3-DOF triangular element is used to mesh the 2D temperature field and tetrahedral element is used to mesh the 3D temperature field. The weighed residual method of Galerkin is used to develop the variation equation of 2D and 3D steady-state temperature field. Corresponding to different element such as inside element, the 1st kind boundary element, the 2nd kind boundary element and the 3rd kind boundary element, the formulas about the FEM numerical simulation of temperature field are developed. When the formulas of the tetrahedral element are developed, triangular coordinates is used to develop the boundary integral part of outer boundary element. Finite difference method is used to deal with the transient-state temperature field. Differential is replaced by difference, so as to solve the transient state temperature field governing equation. There are three difference formats in this thesis. They are backward difference, Crank-Nicolson's difference and Galerkin's difference.According to the above mathematical model, programs which can simulate the steady-state and transient-state of 2D and 3D temperature fields have been wrote using Visual C++ 6.0 Language by the author. The interface programs about pre-process and post-process have been written, too. In the program, "one dimension variable-bandwidth store method" is used to store the data of global matrix so that the storage is minimal. Iteration method of Gauss-Seidel is used to solve the equation set. There are several numerical examples to verify the code and the method in this paper, including 2D, 3D, transient and stable temperature field. The simulation results by the paper's method are valid in comparison with the result of ANSYS software and analytic solution.As the application of 2D temperature field numerical simulation, the cooling procedure of thermoplastic extrusion processing has been analyzed. By the assumption, the cooling procedure of extrusion processing can be facilitated to the 2D heat conduction problem with the 3rd kind boundary condition, which can be simulated using FEM. If we consider that all the section have the same property, the temperature field distribution of same section at different time and the temperature field distributionof different section at the same time are equivalent. So the simulation of 3D temperature field during the cooling procedure of plastic extrusion is done. Comparing the results of examples, the approximate analysis solution and ANSYS results, the simulation results in this thesis are proven correct.As the application of 3D temperature field numerical simulation, the thermoplastic's cooling procedure of injection molding has been analyzed. First, the methods which are used in the cooling of injection molding CAE software are reviewed. The numerical simulation of injection molding includes four relational parts, which are filling, packing, cooling and warp. In principal injection molding CAE software, the BEM is used to the simulation of cooling, while the FEM is used to the simulation of filling, packing and warp. The analysis result of cooling is used by warp analysis. In order to use the same mesh and method, the author hopes to use FEM to simulate the transient-state temperature field during the cooling procedure of injection molding. Through the assumption, the author put forward an idea, fusion boundary, this is to ignore the boundary between mould and plastic part, the physical boundary recognized by node coordinate and its mesh size. When the stiffness matrix and heat capacity matrix is...