Three-Dimensional Transient Mold Cooling Analysis Based on Galerkin Finite Element Formulation With a Matrix-Free Conjugate Gradient Technique

Abstract

SUMMARYA methodology is presented to simulate the three-dimensional heat transfer within a mold during the injection molding process. The mold cooling analysis assists cooling channel design and paves the way for part shrinkage and warpage analysis. The transient temperature distributions in the mold and the polymer part are simultaneously computed by Galerkin Finite Element Method (GFEM) using a matrix-free Jacobi Conjugate Gradient (JCG) scheme. The numerical method presented here is efficient and has shown to require a fraction of the memory and computing time required by conventional methods. The matrix-free algorithm is initially validated using an injection mold designed to produce a plaque with a molded-in hole. Subsequently, the method is further applied to a representative automotive plastic component.

Design and FEM analysis of the milled groove insert method for cooling of plastic injection moulds

“…Although 3-D FEM results in more accurate results, the cost and time of computation may not be affordable to the manufacturers. Tang et al [9,10] reported an implicit Galerkin FEM using an element-by-element Jacobi conjugate gradient iterative solver to simulate the transient temperature distributions in the mould and the polymer part, and suggested the time accurate and efficient feature of this technique in solving the energy balance equation. It is very clear that applying 3-D FEM in cooling analysis for injection moulds is necessary, if there is considerable enhancement of computer capacity.…”

An acceleration method for the BEM-based cooling simulation of injection molding

“…The model presented by Dittus and Boetler is adopted for the heat transfer coefficient, expressed as [17] h c ¼ 0:023 k c D Re 0:8 Pr 0:4 (18) where Re is the Reynolds number, Pr the Prandtl number, k c the thermal conductivity of the coolant and D the diameter of the cooling channel. This equation is valid for 10,000oReo1,20,000 and 0.7oPro120.…”

“…At present, many studies on cooling simulation of injection mold are based on the solid geometry [11][12][13][14]. Although the cycle-averaged approach can predict well the overall performance of the cooling system, some researchers calculated the transient temperature distributions during the cooling process using the dual reciprocity boundary element method (DRBEM) [15], the Galerkin finite element method [16,17], the finite volume method [18], and other methods [19].…”

Thermo-oxidative behavior of high-temperature PMR-15 resin and composites

“…(15) is solved using a direct solution or by minimizing the residual ( ) using an iterative solution such as Jacobi Conjugate Gradient (JCG) iterative method [26] for problems with a large number of degrees of freedom. The time step, t, used for this parametric study is 1 min and the residual is minimized to a root mean square (L 2 norm) value of 1 × 10 −8 .…”