JP2010042599A - Method for setting molding condition and multipurpose optimization method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a multipurpose optimization method capable of efficiently obtaining a Pareto optimal solution set by lessening an amount of calculation while using advantages of multipurpose genetic algorithm capable of searching a highly accurate optimal solution. <P>SOLUTION: This method for setting molding conditions is aimed at making a plurality of objective performances an optimal value by combining injection molding analysis and an optional technique assisted with a computer, and equipped with an optimization process to seek the Pareto optimal solution of the objective performances using the multipurpose genetic algorithm. When it is estimated that there is a search accuracy lowering part in the Pareto optimal solution from the obtained distribution of optimal solution set, a design variable is selected from the design variable of an individual of the boundary of the search accuracy lowering part by interpolating the design variable in the search accuracy lowering part, and a complement process for further searching the Pareto optimal solution is performed using the selected design variable. When it is estimated that there is no search accuracy lowering part, the complement process is not performed. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a molding condition setting method and a multipurpose optimization method for designing a resin product manufactured by, for example, an injection molding method, an injection compression molding method, an injection press molding method, or the like.

  In the selection of injection molding conditions for plastic parts, studies using CAE technology are generally performed. However, the actual condition narrowing is often advanced by trial and error based on experience and intuition. Therefore, in such work, a technique for searching for optimum conditions by combining CAE technology and CAO technology has been put into practical use, and has achieved a certain result. In particular, the method of obtaining the Pareto optimal solution set of multiple objective performances using the optimization method of the multi-objective genetic algorithm can obtain a combination of performances desired by the designer considering trade-offs, and the situation changes It is excellent in that it can be widely used.

  However, the multi-objective genetic algorithm probabilistically changes the value of the design variable without considering the correlation of the magnitude relation between the design variable and the evaluation function, so the search is inefficient and requires a lot of calculation time. It was.

JP2007-144979

  The present invention has been made in view of the above circumstances, and while utilizing the advantages of a multi-objective genetic algorithm capable of searching a plurality of optimal solutions at a time, the Pareto optimal solution set can be efficiently reduced with a reduced amount of calculation. It is an object of the present invention to provide a molding condition setting method or a multipurpose optimization method capable of obtaining the above.

  In order to achieve the above object, the molding condition setting method according to claim 1 is a molding for setting a plurality of target performances to optimum values by using a combination of an injection molding analysis and a computer-aided optimization method. The condition setting method includes an optimization step for obtaining a Pareto optimal solution of the plurality of target performances using a multi-objective genetic algorithm, and the search accuracy lowering unit is found from the distribution of the optimal solution set in the obtained optimal solution set If the design variable is estimated, the design variable is selected by interpolating the design variable inside the search accuracy degradation part from the design variable of the individual at the boundary of the search precision degradation part, and the Pareto optimization is further performed using the selected design variable. A complementing process for searching for a solution is performed, and when it is estimated that there is no search accuracy lowering part, the complementing process is not performed.

  The search accuracy reduction unit is a region where the Pareto solution is inferior to the (N-1) -dimensional boundary determined by any N points on the Pareto solution with respect to N target performances (evaluation functions). That is, in the case of two-objective optimization, when the Pareto solution is inferior to a straight line that is a one-dimensional boundary that can be determined at two arbitrary points on the Pareto solution, the inferior portion is set as a search accuracy reduction unit. Further, in the case of three-objective optimization, when the Pareto solution is inferior to a plane that is a two-dimensional boundary determined by arbitrary three points on the Pareto solution, the inferior region is set as a search accuracy reduction unit.

  In addition, the selection of design variables by interpolation is based on the assumption that the design variables and the evaluation function are correlated to some extent. Since the evaluation function is calculated from the result of analysis under the analysis condition determined by the design variable, the variation of the design variable and the variation of the evaluation function are often correlated, and this assumption is valid for many optimization problems. For example, in the injection molding analysis, if the design variable is the resin temperature and the evaluation function is the molding cycle, the design cycle and the evaluation function generally tend to be shorter when the resin temperature is lowered. Has a strong correlation. The present invention is a technique aimed at improving search efficiency in the case of following this assumption. Even if this assumption is not met, the optimization is performed according to the multi-objective genetic algorithm, so that the search accuracy is equivalent to that of the prior art. Only a few calculations are performed with the selected design variables, and almost the same efficiency as the prior art is guaranteed.

  The molding condition setting method described in claim 2 is characterized in that, in the invention described in claim 1, after performing the complementing step, an optimization step using a multi-purpose genetic algorithm is performed again.

  The multi-objective optimization method according to claim 3 is a multi-objective optimization method for setting a plurality of objective performances to an optimum value by using a combination of computer analysis and an optimization technique, and using a multi-objective genetic algorithm. An optimization step for obtaining a Pareto optimal solution of the plurality of objective performances, and in the obtained optimal solution set, when it is estimated that there is a search accuracy reduction unit from the distribution of the optimal solution set, the search accuracy reduction unit The design variable is selected by interpolating the design variable in the search accuracy reduction part from the design variable of each individual, and a supplementary step of further searching for the Pareto optimal solution using the selected design variable is performed, and the search accuracy reduction part In the case where it is estimated that there is no compensation, the complementing process is not performed.

  In the case of combining the analysis by the computer and the optimization method, the variation of the design variable and the variation of the evaluation function are often correlated, and this assumption is valid in many cases. Even if this assumption is not met, the optimization is performed according to the multi-objective genetic algorithm, so that the search accuracy is equivalent to that of the prior art. Only a few calculations are performed with the selected design variables, and almost the same efficiency as the prior art is guaranteed. Computer analysis includes, but is not limited to, structural analysis, impact analysis, various forming analysis, fluid analysis, vibration analysis, fatigue analysis, and the like.

  According to the first to third aspects of the invention, a multi-purpose genetic algorithm capable of searching for a plurality of optimum solutions at a time by estimating and complementing a search accuracy lowering portion from the distribution of the optimum solution set. Thus, it is possible to provide a molding condition setting method or a multi-purpose optimization method capable of efficiently performing optimization calculation while reducing the amount of calculation.

Hereinafter, an embodiment in which the multipurpose optimization method of the present invention is used as a molding condition setting method when designing a resin product will be described with reference to the drawings.
In this embodiment, a combination of numerical analysis for calculating the injection molding process of a plastic part and a computer-aided optimization method obtains molding conditions (design variables) that optimize the two target performances related to the plastic part. .

  FIG. 1 is a flowchart for explaining the steps of the multi-objective optimization method of this embodiment. First, in Step 1, an analytical shape model for analyzing the resin flow in the injection molding process is created. In this embodiment, it is a rectangular (aspect ratio = 4/5) flat plate-like member as shown in FIG. 2, and a rectangular opening is formed in a part of the flat plate so that resin flows evenly into the cavity. Is a difficult shape.

  The product gives a thickness distribution in four parts as shown in FIG. 3, which is one of the design variables. The resin injection port is disposed at substantially the center of the flat plate and at the center of the side end close to the opening. Each injection port is provided with a hot runner, a tapered sprue, or a cold runner, through which resin from the injection machine is supplied.

For the numerical analysis for calculating the injection molding process, Moldflow Plastics Insight version 6.1 (trade name, manufactured by Moldflow Corporation), which is an injection molding analysis software, was used. The material used was Sumitomo Noblen AZ564 (trade name, manufactured by Sumitomo Chemical Co., Ltd.), which is a polypropylene resin. The melt flow rate (MFR) measured by the method specified in JIS-K7210 is 30 [g / 10min,
230 ° C.] and the specific gravity is 0.9.

  Next, in step 2, the target performance is selected and an evaluation function is created. Here, the clamping force and the molding cycle were selected as the target performance. The mold clamping force is an index indicating the scale of the injection molding machine, and the molding cycle is an index indicating the production efficiency of the apparatus. Therefore, the smaller one can reduce the manufacturing cost, which is economically advantageous. is there. Clamping force (CF) is at 98% filling, and molding cycle (CT) is the sum of injection time (design variable: it), cooling time (response value) and product removal time (fixed value: 10 seconds). . The cooling time was the maximum solidification time (excluding the runner part).

  Next, in step 3, design variables are set. In this embodiment, the thickness of each part is set to pt1 to pt4. These plate thicknesses are in the range of 2.0 mm to 4.0 mm and take discrete values with a pitch of 0.1 mm.

Next, in step 4, initial design variables (first generation genes) of N individuals of the first generation are selected using an appropriate method. Here, the first generation (table 1) is created by combining two conditions, the maximum wall thickness condition (pt1 to pt4 = 4mm) and the minimum wall thickness condition (pt1 to pt4 = 2mm) and the 18 sampling conditions described below. 1).
・ Sampling method:
Experimental design; Optimal Latin Hypercubes (optimal Latin hypercube experiment)

  Next, a process using a multi-purpose genetic algorithm is performed. In this embodiment, iSIGHT version 10.0 (trade name, manufactured by Engineous Software Inc.) is used as the optimization support software. As an optimization method, a neighborhood culture genetic algorithm (NCGA), which is one of Multi Objective Genetic Algorithm (MOGA), was used. The number of set analyzes was 20 with 20 individuals and 10 generations.

  First, in step 5, each first generation individual is analyzed using analysis software. In step 6, the value of each evaluation function is obtained. Next, in steps 7 to 11, an evolution operation step is performed. That is, the design variables of the previous generation individual set are converted to genes in step 7, crossover and mutation operations are performed with a predetermined probability in step 8, each individual is analyzed in step 9, and an evaluation function is calculated. And get fitness. Then, the individual having good fitness obtained in step 10 is selected as the next generation parent. After performing Steps 8 to 10 for the set number of generations, Step 11 creates a Pareto optimal solution (hereinafter referred to as “provisional Pareto solution”) based on the evaluation of individuals of each generation. If there is a Pareto optimal solution obtained in Steps 13 to 19 described later, a provisional Pareto solution may be created.

  Here, it is determined in step 12 whether or not the preset condition for ending the molding condition setting method of this embodiment is satisfied. In the present embodiment, the process is terminated when step 11 is reached for the third time, but the termination condition is not limited to this. If the end condition is satisfied, the calculation is ended with this as the final Pareto solution. In step 21, the Pareto solution is analyzed, design variables that meet the condition are selected, and molding is performed.

  On the other hand, when it is determined in step 12 that the provisional Pareto solution does not satisfy the termination condition, a Pareto optimal solution set complementing process, which is a feature of the present invention, is performed in steps 13 to 19 described below. The Pareto optimal solution set complementing step determines whether or not there is a portion (hereinafter referred to as “search accuracy lowering portion”) for which the Pareto solution obtained at that time point is determined to have insufficient search accuracy, If there is a search accuracy lowering part, it is a step of complementing it by a predetermined method. If the search accuracy lowering part is not found, the process proceeds to the next step without performing the complementing process.

  Here, the “search accuracy lowering portion” is used in the sense that the Pareto solution obtained by using the optimization method is a portion where the search is insufficient and the optimum solution is not yet reached. For example, when it is desired to reduce the two evaluation functions, if the multi-objective genetic algorithm search is insufficient for the downward Pareto optimal solution as shown by the solid line in FIG. ”Can be obtained. In the present invention, in step 11, when a provisional Pareto solution in which a part is “upwardly convex” as shown by a broken line in FIG. 4A is obtained, “downwardly convex” indicated by a solid line is obtained. Assuming that the curve is the optimal solution (first assumption), this “upwardly convex” portion is set as the search accuracy decreasing portion.

Specifically, in step 13, in the case of a two-evaluation function, as shown in FIG. 4B, a straight line that contacts the lower side of the provisional Pareto solution is drawn, and a portion between the contact points is a “search accuracy reduction unit”. And In calculation, a straight line connecting any two points on the provisional Pareto solution may be compared with the provisional Pareto solution, and a straight line may be calculated such that the provisional Pareto solution is inferior at all points. Area _{(F i min j ≦ F i} ≦ F i max j) part of the interim Pareto solutions in between the interim Pareto solutions and the straight line intersection (contact) is "search accuracy reduction unit". If there are two or more “upwardly convex” portions as shown in FIG. 4C, each range is set as a search accuracy decreasing portion.

  The occurrence of the search accuracy degradation part is thought to be due to the fact that the multi-purpose genetic algorithm changes the design variable stochastically, and the “search precision degradation part” is due to unlucky probabilistic elements and insufficient number of searches. It is done. Depending on the optimization problem, there may be a case where the curve having the “convex upward” portion shown in FIG. 5A is actually the Pareto optimal solution, and further, as shown in FIG. In some cases, the curve may be convex. In the case shown in FIGS. 5A and 5B, the method of the present invention cannot obtain an effect. Therefore, even if the following Pareto optimal solution set complementing process is performed, the solution does not move in the direction of convergence, and a better result cannot be obtained. That is, a useless process is performed. If there is no effect, only a small amount of time is required for the calculation compared to the search by the multi-objective algorithm. On the other hand, if the effect is effective, a large amount of calculation time is required for the multi-objective genetic algorithm. In view of the fact that it can be significantly reduced, the usefulness of the present invention can be fully evaluated.

ｉ：ｉ番目の目的性能に関する添え字
ａ_ｉ：定数
ｂ：定数
Ｆ_ｉ：評価関数
以下の、式２で表される範囲に含まれるすべての暫定パレート解が式１で定義される境界より劣っている場合、式２の範囲を探索精度低下部とする。他の探索精度低下部に内包される探索精度低下部がある場合は、その探索精度低下部に関する補完工程を省略するため、内包する最も範囲の大きい探索精度低下部のみを代表して特定する。
Ｆ_imin≦Ｆ_ｉ≦Ｆ_imax （式２）
Ｆ_imin_ｉ：式２を満たす評価関数値の内の最小値
Ｆ_imax_ｉ：式２を満たす評価関数値の内の最大値 In the above description, the case of two evaluation functions has been described. However, the present invention is theoretically applicable to an arbitrary multi-evaluation function. In general, in the case of N evaluation functions, “provisional pareto” A “straight line connecting any two points on the solution” is defined as “an (N−1) -dimensional boundary connecting any N points on the provisional Pareto solution”. Such an (N-1) -dimensional boundary is expressed by the following formula (1).

i: Subscript related to the i-th target performance a _i : Constant b: Constant F _i : Evaluation function All the provisional Pareto solutions included in the range represented by Equation 2 below are inferior to the boundary defined by Equation 1 If it is, the range of Expression 2 is set as the search accuracy reduction unit. In the case where there is a search accuracy reduction part included in another search accuracy reduction part, only the search accuracy reduction part with the largest range included is specified as a representative in order to omit the complementing process related to the search accuracy reduction part.
F _i min ≦ F _i ≦ F _i max (Formula 2)
F _i min _i : Minimum value among evaluation function values satisfying expression 2 F _i max _i : Maximum value among evaluation function values satisfying expression 2

In this way, after searching for the search accuracy lowering portion in step 13, it is determined in step 14 whether or not the search accuracy lowering portion exists, and if it is determined that the search accuracy lowering portion does not exist, Pareto optimal Without performing the solution set complementation process, the process goes to the individual set creation process of step 20 to perform the normal multi-purpose genetic algorithm process. If it is determined in step 14 that there is a search accuracy lowering portion, a Pareto solution set complementing process in the search accuracy lowering portion is executed. That is, in step 15, as shown in FIG. 6, interpolated values from both ends are calculated in the search accuracy reduction unit for each design variable. In this example, the interpolation point is divided into four by three points. For example, for the first design variable pt1, the interpolation points C, D, and E are based on the design variables of the end points A and B as follows. Calculated.
pt1C = (pt1B−pt1A) / 4 + pt1A
pt1D = (pt1B−pt1A) / 4 × 2 + pt1A
pt1E = (pt1B−pt1A) / 4 × 3 + pt1A
In this optimization, the design variable is defined as a discrete variable in increments of 0.1, so the second decimal place is rounded off.

  In step 16, an analysis is executed using the prepared design variable, and in step 17 an evaluation function is calculated using the analysis result. This Pareto solution set complementing process is based on the assumption that the design variable and the evaluation function are correlated to some extent (second assumption). This assumption, like the first assumption, is not necessarily valid for all problems, but is assumed to be valid in many cases.

  Next, in step 18, these evaluation functions are compared with the provisional Pareto solution. If even some of the supplementary calculation values are better than the provisional Pareto solution, the part is replaced in step 19 and the provisional Pareto solution is updated. As it is, the next multi-objective genetic algorithm optimization process is entered.

  That is, in step 20, a next generation individual set is created. Here, the solution for the number of individuals is selected from the Pareto optimal solutions obtained so far, and the design variable is set as the next generation parent. At this time, if an updated solution exists, it is selected with priority. In addition, according to the updated solution, the design variable of the Pareto optimal solution end in the design variable space and the design variable of the solution where the density of the Pareto optimal solution is sparse may be given priority as the next generation parent, The present invention is not limited to this. When the number of Pareto optimal solutions is small and the number of individuals is insufficient, design variables are determined and added randomly. Next, the process after step 8 is repeated using the obtained new generation individual set, and an optimization process using a multi-purpose genetic algorithm is performed.

  As described above, in the multi-objective optimization method of this embodiment, efficient optimization is performed by using a combination of the multi-objective genetic algorithm optimization process and the Pareto solution set complement process in the search accuracy reduction unit. can do. Of course, since this method is based on the above two assumptions, no improvement can be obtained in the case of a problem in which these assumptions are not satisfied. However, the calculation of the Pareto solution set complementing process is performed by the number of interpolation points, and the increase in the amount of calculation is slight, which does not impose a heavy burden. And in many cases, a large calculation process shortening effect can be obtained. Therefore, it can be said that the method is effective as a whole. If the update process in step 18 is not continuously executed, it may be determined that this method is not effective, and the subsequent Pareto solution set complement process may not be executed.

  FIG. 7 shows a result of an example of the optimization method according to the present embodiment compared with a result of a conventional method (optimization process using only a multi-purpose genetic algorithm). Compared to the Pareto optimal solution set candidates that required 50 generations (1000 analysis) with the conventional optimization method, this optimization method has 30 generations (600 analysis of evolution operation steps + 32 additional analysis of Pareto optimal solution set interpolation steps) At the time of exploring better solutions. Therefore, the optimization method of the present invention has obtained better results with a smaller amount of calculation, and it has been found that this optimization method has high search efficiency.

It is a flowchart explaining the setting method of the molding conditions of embodiment of this invention. It is a figure which shows the cavity for describing embodiment of this invention. Similarly, it is a figure which shows the thickness distribution of a cavity. It is a figure explaining the principle of embodiment of this invention. Similarly, it is a figure explaining the principle of embodiment of this invention. It is a figure explaining the method of embodiment of this invention. It is a graph which shows the result of having implemented the method of this embodiment.

Claims (3)

Using a combination of injection molding analysis and computer-aided optimization methods, in the setting method of molding conditions to optimize multiple target performance,
An optimization step for obtaining a Pareto optimal solution of the plurality of objective performances using a multi-objective genetic algorithm;
In the obtained optimal solution set, if it is estimated that there is a search accuracy degradation part from the distribution of the optimal solution set, the design variable inside the search accuracy degradation part is interpolated from the individual design variable of the search accuracy degradation boundary. To select a design variable, and to perform a complementing process for searching for the Pareto optimal solution using the selected design variable. A method for setting the characteristic molding conditions.   The molding condition setting method according to claim 1, wherein after performing the complementing step, an optimization step using a multi-purpose genetic algorithm is performed again. In a multi-objective optimization method to optimize multiple target performances using a combination of computer analysis and optimization methods,
An optimization step for obtaining a Pareto optimal solution of the plurality of objective performances using a multi-objective genetic algorithm,
In the obtained optimal solution set, if it is estimated that there is a search accuracy degradation part from the distribution of the optimal solution set, the design variable inside the search accuracy degradation part is interpolated from the individual design variable of the search accuracy degradation boundary. To select a design variable, and to perform a complementing process for searching for the Pareto optimal solution using the selected design variable. Feature multi-objective optimization method.

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