機(jī)械類外文翻譯--運(yùn)用線性規(guī)劃對注塑模澆口位置優(yōu)化的研究（英文）

1、ORIGINAL ARTICLEA study of gate location optimization of plastic injection molding using sequential linear programmingMing Zhai & Ying XieReceived: 18 August 2009 /Accepted: 13 October 2009 # Springer-Verlag London L

2、imited 2009Abstract A gate location is one of the most important design variables controlling the product quality of injection molding. In this paper, the numerical simulation of injection mold filling process is combine

3、d with the design optimization method to find the optimum gate location to achieve balanced flow. The objective function is expressed in terms of the difference between the maximum and minimum times of boundary filling.

4、The coordinates of gate are chosen as design variables, and a constraint is employed to limit the clamp force lower than the reference value. The optimization problem is solved with the sequential linear programming algo

5、rithm, and design sensitivities are evaluated via the finite difference approximation. Finally, numerical examples are given to demonstrate the effect of proposed methods.Keywords Injection molding . Gate location .Optim

6、al design . Flow balance1 IntroductionInjection molding is by far the most popular process for the production of plastic parts. As the injection molding produc- tion is dominated by complex process dynamics, it is diffic

7、ult to fully understand and predict the final part quality that is related to various molding parameters. In the past three decades, the numerical simulation of injection molding has been greatly developed by clear under

8、standing characteristics of flowing and heat transfer of polymer melts to predicate the quality characteristics of injection-molded parts without actually fabricating a mold. However, the computer aidedengineering (CAE)

9、simulation requires the mold designer to run the simulation, perform the design evaluation, and redesign based on experience, until a satisfactory design is obtained. This manual design process does not guarantee the opt

10、imal design solution and so has led to increasing interest in the utilization of design optimization techniques in the mold design procedure.Several studies reported have investigated the optimiza-tion of the injection m

11、olding process. Pandelidis and Zhou [1] presented the optimization of gate location using the combined scheme of a simulated annealing and hill- climbing method. The quality of a gating design was presented as an additiv

12、e function of a temperature differ- ential term and an overpack term, with appropriate weighting term. Young [2] developed a method of gate location optimization based on the minimization of the mold filling pressure, un

13、even filling pattern, and tempera- ture difference during the mold filling process. Ye et al. [3] developed a scheme to optimize the part quality in injection molding. A mathematical definition of part warpage is present

14、ed, and simulated annealing method is used to search for optimum process condition. Chang et al. [4] combined the usage of Taguchi approach and CAE flow simulation software for optimal design of injection molding process

15、 parameters. Irani et al. [5] developed a system that automates the process of gate design. The gate design is performed in two stages, global search followed by a local search. During the global search, the candidate ga

16、ting plans are generated using feature connectivity information. These gating plans are evaluated and redesigned in iterative until the best cavity inlet conditions for each plan is obtained. Then, the best in the trial

17、set is perturbed locally in a search for a better gating plan. The limitation of this system is that the features used are very simple geometry. Zhai et al. [6–9] has investigated the objective function and search scheme

18、M. Zhai (*): Y. Xie Department of Engineering Mechanics, Zhengzhou University, Zhengzhou 450002, People’s Republic of China e-mail: mmzhai@hotmail.comInt J Adv Manuf TechnolDOI 10.1007/s00170-009-2376-1the most important

19、 variables of the total mold design, and it is necessary to search for an optimum gate location to improve part quality. In this context, the optimization of gate location is studied. A gate is modeled as point sources,

20、and coordinates of the gate location are selected as design variables. To apply optimization theory to the injection molding process, quantitative measure of the part quality first need to be developed since the ultimate

21、 goal in optimizing the injection molding design is to improve part quality. The part quality can be described with many end product properties such as mechanical, thermal, electrical, optical, or geometrical properties.

22、 There are two types of part quality measures: direct and indirect method. Direct method can determine the measurable quantities that characterize a product. In contrast, an indirect measure of quality is a quantity that

23、 is correlated but does not produce a direct estimate of that quality. The indirect quality measures used in this paper are those related to warpage. Part warpage, a dimensional distortion that causes structural unfitnes

24、s and esthetic problems, is one of the critical quality issues for injection molded parts. When the molded part does not satisfy a dimensional tolerance, it is useless as the final product. A major cause of part warpage

25、is the residual stresses induced by unbalanced filling. When such residual stress has no chance to relax, the plastic parts will gradually warp upon ejection as time passes. For this reason, achieving balanced flow is th

26、e objective of the optimization scheme in this study. Lam et al. [13, 14] have developed the flow path concept for cavity balancing. For plastic injection molding, flow path is defined as the path traced by a melt partic

27、le when it is first injected into a cavity until the mold cavity has been completely filled. It may be visualized as the trajectory from the injection gate to the extremities of the cavity. An automatic flow path generat

28、ion routine was developed [15, 16]. For the part with uniform thickness, balanced flow is achieved if all flow paths are of equal length. However, equal flow path length cannot be achieved practically. Instead, the varia

29、tion between the lengths of the flow path is adopted as a measure of the uniformity of fill. The lesser the variation between the lengths of the flow paths indicates that the more balanced is the flow. Thus, Lam and Jin

30、[16] used the standard deviation of the flow path lengths as the objective function for gate location optimization to achieve a balanced flow. However, for the part with nonuniform thickness, the filling time for each el

31、ement will vary even though the other conditions are the same for all elements. This means that the length of flow path is no longer proportional to the filling time, and the standard deviation of flow lengths cannot be

32、used as the measurement of the uniformity of the fill pattern. It is, therefore, better to employ the standard deviation of filling times for all boundary nodesdirectly [16]. Later, Zhai et al. [8] employ injection press

33、ure as a proxy to a balanced flow. The injection pressure for a design with a nonuniform flow pattern will be higher than that for a uniform flow pattern, as an unbalanced flow will lead to overpacking and thus, higher i

34、njection pressure. Therefore, uniform flow pattern can be achieved through minimizing injection pressure under constant injection rate. Although the standard deviation of filling time describes the overall variation of t

35、he filling time and thus, uniformity of fill, it does not directly reflect the difference between the maximum and minimum boundary filling time. The difference between the maximum and minimum boundary filling time could

36、also be employed to reflect the uniformity of fill and is used as an objective function in this paper. Thus, the gate location optimization based on the difference between the maximum and minimum boundary filling time ca

37、n be stated as: MinimizeFðXÞ ¼ tBoundaryNode ? ?max ? tBoundaryNode ? ?min ð6ÞSubject toGðXÞ ? GclampX 2 Ω ð7Þwhere F(X) is the objective function, X=[x, y, z], x, y, z are th

38、e coordinates of the corresponding gate, Ω is the feasible search space, G is the calculated clamp force, and Gclamp is the maximum clamp force. The constraint function limits the clamp force below a reference value. tBo

39、undaryNode is the time when the polymer melt reaches a boundary node in a finite element model, and the subscript max and min refer to the maximum and minimum time of polymer melt reaching the boundary nodes, respectivel

40、y. In a mold filling simulation, the time of resin flow reaching each boundary node can be determined by the control volume finiteFig. 1 Melt front advancement of initial design (at the time, t=0.619 s)Int J Adv Manuf Te