外文翻译--注塑模的单浇口优化

外文翻译--注塑模的单浇口优化内容摘要：

LiA is the projector distance between ith node and node A. Ultimately, h is the maximum of the absolute value of Wi: 5 In industry, the inspection of the warpage is carried out with the help of a feeler gauge, while the measured part should be placed on a reference plat form. The value of h is the maximum numerical reading of the space between the measured part sur face and the reference platform. GATE LOCATION OPTIMIZATION PROBLEM FORMATION The quality term “warpage” means the perma nent deformation of the part, which is not caused by an applied load. It is caused by differential shrinkage throughout the part, due to the imbalance of polymer flow, packing, cooling, and crystallization. The placement of a gate in an injection mold is one of the most important variables of the total mold design. The quality of the molded part is greatly af fected by the gate location, because it influences the manner that the plastic flows into the mold cavity. Therefore, different gate locations introduce inho mogeneity in orientation, density, pressure, and temperature distribution, accordingly introducing different value and distribution of warpage. Therefore, gate location is a valuable design variable to minimize the injection molded part warpage. Because the cor relation between gate location and warpage distribu tion is to a large extent independent of the melt and mold temperature, it is assumed that the moldingconditions are kept constant in this investigation. The injection molded part warpage is quantified by the feature warpage which was discussed in the previous section. The single gate location optimization can thus be formulated as follows: Minimize: Subject to: where γ is the feature warpage。 p is the injection pressure at the gate position。 p0 is the allowable in jection pressure of injection molding machine or the allowable injection pressure specified by the designer or manufacturer。 X is the coordinate vector of the candidate gate locations。 Xi is the node on the finite element mesh model of the part for injection mold ing process simulation。 N is the total number of nodes. In the finite element mesh model of the part, every node is a possible candidate for a gate. There fore, the total number of the possible gate location Np is a function of the total number of nodes N and the total number of gate locations to be optimized n: 6 In this study, only the singlegate location problem is investigated. SIMULATED ANNEALING ALGORITHM The simulated annealing algorithm is one of the most powerful and popular metaheuristics to solve optimization problems because of the provision of good global solutions to realworld problems. The algorithm is based upon that of Metropolis et al. (1953), which was originally proposed as a means to find an equilibrium configuration of a collection of atoms at a given temperature. The connection be tween this algorithm and mathematical minimization was first noted by Pincus (1970), but it was Kirkpatrick et al.(1983) who proposed that it formed the basis of an optimization technique for bina tional (and other) problems. To apply the simulated annealing method to op timization problems, the objective function f is used as an energy function E. Instead of finding a low energy configuration, the problem bees to seek an approximate global optimal solution. The configura tions of the values of design variables are substituted for the energy configurations of the body, and the control parameter for the process is substituted for temperature. A random number generator is used as a way of generating new values for the design variables. It is obvious that this algorithm just takes the mini mization problems into account. Hence, while per forming a maximization problem the objective func tion is multiplied by (−1) to obtain a capable form. The major advantage of simulated annea ling algorithm over other methods is the ability to avoid being trapped at local minima. This algorithm em ploys a random search, which not only accepts changes that decrease objective function f, but also accepts some changes that increase it. The latter are accepted with a probability p where ∆f is the increase of f, k is Boltzman’s constant, and T is a control parameter which by analogy with the original application is known as the system “temperature” irrespective of the objective function involved. In the case of gate location optimization, the imple me nta tion of this algorithm is illustrated in , and this algorithm is detailed as follows: 7 (1) SA algorithm starts from an initial gate loca tion Xold with an assigned value Tk of the “tempera ture” parameter T (the “temperature” counter k is initially set to zero). Proper control parameter c (0c 1) in annealing process and Markov chain Ngenerate are given. (2) SA algorithm generates a new gate location Xnew in the neighborhood of Xold and the value of the objective function f(X) is calculated. (3) The new gate location will be accepted with probability determined by the acceptance function The flow chart of the simulated annealing algorithm APPLICATION AND DISCUSSION The application to a plex industrial part is presented in this section to illustrate the proposed quality measure and optimization methodology. The part is provided by a manufacturer, as shown in . In this part, the flatness of basal surface is the most important profile 8 precision requirement. Therefore, the feature warpage is discussed on basal surface, in which reference platform is specified as a horizontal plane。