A methodology is presented for the design of optimal cooling systems for injection mold tooling which models the mold cooling as a nonlinear constrained optimization problem. The design constraints and objective function are evaluated using Finite Element Analysis (FEA). The objective function for the constrained optimization problem is stated as minimization of both a function related to part average temperature and temperature gradients throughout the polymeric part. The goal of this minimization problem is to achieve reduction of undesired defects as sink marks, differential shrinkage, thermal residual stress built-up, and part warpage primarily due to non-uniform temperature distribution in the part. The cooling channel size, locations, and coolant flow rate are chosen as the design variables. The constrained optimal design problem is solved using Powell’s conjugate direction method using penalty function. The cooling cycle time and temperature gradients are evaluated using transient heat conduction simulation. A matrix-free algorithm of the Galerkin Finite Element Method (FEM) with the Jacobi Conjugate Gradient (JCG) scheme is utilized to perform the cooling simulation. The optimal design methodology is illustrated using a case study.
Optimality and duality in nonsmooth vector optimization with non-convex feasible set
