International Journal of Machine Tools & Manufacture 43 (2003) 175 184

International Journal of Machine Tools & Manufacture 43 (2003) 175 184 Selection of optimal material and operating conditions in composite manufacturing. Part II: complexity, representation of characteristics and decision making S.Y. Yang a, V. Girivasan a, N.R. Singh a, I.N. Tansel a,, C.V. Kropas-Hughes b a Center for Engineering and Applied Sciences, Department of Mechanical Engineering, Florida International University, 10555 West Flagler Street, Miami, FL 33174, USA b Wright Patterson AFB, Air Force Research Laboratory, AFRL/MLLP, Building 655, R166, 2230 Tenth Street, Wright-Patterson AFB, OH 45433-7746, USA Received 16 July 2002; accepted 30 July 2002 Abstract An automated procedure is proposed to select the optimum material and processing conditions for composite materials. The complexity of the part is estimated from the STL files of the CAD/CAM programs by evaluating the angles between the triangles, which cover the surface. A correction algorithm identifies the holes and calculates the complexity without considering the triangles at their surfaces if they will be drilled later. Using multiple neural networks represented the most important characteristics of the composite material manufacturing for the user. For each considered material one genetic algorithm is assigned to select the optimal operating conditions. The optimal material is selected by comparing the good qualities of each material after the optimization. The proposed procedure is very attractive for optimization of complex systems when multiple approaches and their several characteristics are considered. 2002 Elsevier Science Ltd. All rights reserved. Keywords: Neural networks; Genetic algorithm; Composite material; STL; Optimization; Complexity 1. Introduction Composite materials have many desired characteristics including high strength, corrosion resistance, and low weight. These characteristics have allowed them to find many military and civilian applications and to be a very promising candidate for many other applications in the future. During the design stage, engineers need extensive computational help to select proper material and operating conditions, since changing design and manufacturing parameters can control many characteristics of the composite end product. The objective of this paper is to propose a human-like decision-making tool for selection of the optimal material and operating conditions in the composite material manufacture. The pro- Corresponding author. Tel.: +1-305-348-1932; fax: +1-305-348-3304. E-mail address: tanseli@fiu.edu (I.N. Tansel). posed procedure uses multiple neural networks and genetic algorithms for this purpose and can be easily adopted for many other optimization problems. Many methods have been developed for cost estimation in composite material manufacture [1 21]. Most of these studies target only cost estimation for a part by using the design parameters and an extensive database from the manufacturer. In this study, additional characteristics such as strength and manufacturing time are considered. The proposed approach could easily handle other decision-making parameters such as surface roughness and tolerances. The main objective of the developed package is to find the optimal material and processing parameters according to the priorities of the user by considering all the important decision-making parameters. The proposed procedure performs the optimization task in three stages. First, multiple neural networks are trained to estimate the most significant decision-making parameters such as cost, strength, and manufacturing time. The user can select the number and the design 0890-6955/03/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved. PII: S0890-6955(02)00133-5

176 S.Y. Yang et al. / International Journal of Machine Tools & Manufacture 43 (2003) 175 184 parameters of interest according to his needs. In the second stage, the complexity of the part is evaluated from the STL output files of the CAD/CAM automatically. In the last stage, the genetic algorithm selects the optimum processing parameters for each material by using neural networks. When multiple materials are considered, the best one is selected by comparing the merits of each according to the user s selected criteria. Most of the manufacturers save the CAD files of completed parts. Precisely located, perfectly round holes of the parts are usually drilled after the composite parts are manufactured. If the complexity of the part is estimated by considering the surfaces of holes, the value drastically increases with the number of holes. Similarly, cost and manufacturing time estimates will artificially increase. If the parts are large and contain many holes, the cost and manufacturing time estimates are completely unrealistic. Instead of removing the holes from the CAD drawing manually and preparing the STL files of the parts without holes, a correction algorithm is necessary to identify the triangles at the surfaces of the holes and to ignore them during the complexity estimation. To evaluate the performance of the proposed procedure, a graphic utility, neural network training, and an optimization program were developed using a Visual Basic program. This evaluation package was called Composite Material Selection Advisor (CoMaSA). 2. Previous work In this section the available cost and complexity estimation methods are outlined. 2.1. Cost estimation in composite material manufacturing Hundreds of different operations are performed by thousands of people to manufacture complex military hardware such as airplanes. During the optimization of design and material selection, engineers should know the actual cost of already produced similar parts but they need some computational tools to estimate the cost of their new designs. Manufacturing cost [1 4] is calculated by using either the traditional methods or activity-based costing (ABC). Traditional methods use volume-based measures including the labor hours, which normally becomes the most influential part of the calculated cost. Since composite part manufacture is labor intensive, costs are usually calculated unfairly compared to the cost estimates of massproduced parts. ABC is preferred in composite material manufacturing to be able to evaluate the overhead costs more accurately and to obtain the cost of composite parts precisely. Parametric cost models (PCM) or manufacturing process cost models (MPCM) can be used for the estimation of the cost of the composite parts [4 6]. Development and procurement costs for aircraft (DAPCA IV) [7] is a PCM. Advanced composite cost estimating model (ACCEM) [8], manufacturing cost model for composites (MCMC) [9] and composite optimization software for transport aircraft design evaluation (COSTADE) [10] are MPCM. DAPCA IV is primarily prepared from relatively old information, and validity of the estimations is questionable for composites. Most of the MPCM are prepared by considering the operation and needs of specific companies by using their database and are very complicated. The accuracy of the models could be limited when used by other companies.[4,5]. A totally integrated manufacturing cost estimating system (TIMCES) estimates the cost of parts from the design inputs [11] following a well-structured methodology. This approach separately estimates the cost of material, labor, machinery, operations, and overheads. A theoretical cost model [12] was developed for composite fabrication by using first-order models and considering the complexity of the part. Eaglesham [4] proposed a decision support system, which arranges the existing accounting data and uses intelligent search methods to estimate the cost at the conceptual design stage. NASA [13] has given links to many cost estimation resources including books, government reports, periodicals, references, software, and technical reports on their web page. However, most of these resources are not directed to composite material manufacture. 2.2. Complexity estimation in composite material manufacturing Complexity of a part represents the difficulty of creating the required shape, achieving the expected characteristics and meeting the necessary tolerances. Complexity should be considered during the cost estimation of composite materials since the manufacturing time and necessary support will be directly related to the projections. ACCEM [8] uses correction factors in cost estimation to make the necessary adjustments by considering the geometric features of the part. For the theoretical cost model [12] a series of features was used to estimate the complexity including bending of fibers in composite materials [14], number of nonredundant dimensions on a part drawing [15], and shear and ply stacking [16]. In addition, the complexity of parts was also studied by considering other manufacturing applications including assembly and mold making [17 20]. The level of discontinuity [17], the number of dimensions in the drawing [18], and symmetry [19] were used to obtain the complexity. Parametric consultants evaluate the complexity by considering the known cost of similar equipment [13,20]. Li et al. [21] recently indicated the importance

S.Y. Yang et al. / International Journal of Machine Tools & Manufacture 43 (2003) 175 184 177 of the curvature angle(s) of the part on the complexity and proposed collection of the information from the outputs of the commercial packages. 3. Selection of the optimum material and operating conditions In the following sections, automated evaluation of the CAD/CAM files to estimate the complexity of the part, correction of the estimation if there are vertical holes, structure of the optimization, and operation of the proposed system will be presented. 3.1. Estimation of complexity from CAD/CAM files Almost all the sophisticated CAD/CAM programs save their data by using different formats. In this study, the use of STL files was selected to transfer the data from CAD/CAM program to CoMaSA since almost all the commercial solid-modeling programs have the option to save the data as a STL file. In addition, STL files are much easier to use to evaluate the geometric characteristics of the parts. The CoMaSA graphic utility program was developed to read the STL file to calculate the volume and complexity of a part automatically. In this study, all the CAD drawings of the parts were prepared by using the Parametric Corporation s Pro-E package. The calculated volume and estimated complexity were written to the FixedInput.txt file, which contains the value of all fixed inputs that are used in the general optimization program. The complexity of a part is calculated according to the following equation [22]: q i L i (Part)/ q k L k (1) (Cube having the same surface area as the part) where θ i is the angle between the normal vectors of two adjacent triangles of the STL file of the part, L i is the length of their common side, and θ k,l k are the same parameters defined for the cube. Fig. 1 demonstrates parameters used in the complexity calculation. Fig. 2. User interface of the graphics utility program of the CoMaSA package. According to the formula, if the normal of neighboring triangles are parallel to each other or have very small angles, complexity will be a small number. Larger angles will increase the calculated complexity. Triangles make 90-degree angles at the edges of the part. Normally, manufacturing of these edges is easier. The algorithm checks the angles and reduces the calculated complexity for that edge if the normals are perpendicular to each other. The user interface of the graphic utility program is presented in Fig. 2. The demonstrated part had 556 triangles. The program calculated the volume and complexity as 61.87 in. 3 and 3.77 respectively. Part rotation, imaging solid object, wire-frame model presentation, and hidden line removal capabilities are added to the graphic utility program for convenience of the user. 3.2. Complexity correction algorithm for holes After the program receives all the information from the STL file, the part is cut with a horizontal test plane at the middle (Fig. 3) to determine the triangles at the surfaces of the holes. Fig. 1. Parameters used in complexity calculation. Fig. 3. Part with a hole is cut with a horizontal test plane.

178 S.Y. Yang et al. / International Journal of Machine Tools & Manufacture 43 (2003) 175 184 The program calculates all of the intersection points between the horizontal plane and the edges of the triangles that cover the part surface.the equation of the horizontal plane is z C, - x +,and - y + (2) where C is a constant and is equal to half the total height of the part.the equation of a line in triangle is x x1 x1 x2 y y1 y2 y1 z z1 z2 z1. (3) To determine if the edges of each triangle are cut by the plane, f(z) = z C is used. Coordinates from the beginning (x1, y1, z1) and the end of the line (x2, y2, z2) are substituted in the f(z) expression. A sign change when the beginning and end-points are used indicates that the line had been cut by the test plane (Fig. 4). After this inspection, the program calculates the exact coordinates of the intersection by substituting Z = C into the line equations (eq. (3)) so that: x c y1 (x1 x2) x1andy (4) y2 y1 c y1 (y1 y2) y1. y2 y1 This procedure is repeated until all intersections between the horizontal plane and the edges of the triangles are identified. Two intersections are obtained for each triangle if the plane intersects it. Since the triangles cover the surface of the part completely, two neighboring triangles will always have identical intersections with the horizontal test plane. The neighboring triangles are sorted by using this property. If no neighboring triangle is found, and there are extra intersections, one of them is randomly taken and the procedure is then followed until no points are left. Inspection of the array starts from the second point of the last triangle in the array. Algorithms follow the sequence until the coordinates of the starting point are encountered. For each hole and outer surface of the part, there will be one loop. The number of holes is equal to number of loops minus one. The largest loop is the intersection of the test plane with the outer surface of the part. The other loops are checked to determine if they are round. If they are round, their radius and center locations are calculated. For correction of the complexity estimation, the triangles which intersect with the horizontal plane do not belong to the outer shell of the part and are not used during the complexity calculation. 3.3. Structure of the optimization program The structure of the optimization program is presented in Fig. 5 when m decision parameters of n different composites are considered to select the best material and optimum operating conditions. When a part is considered, the volume and complexity of the part are the fixed parameters. Depending on the application, surface finish, optical characteristics, and many other properties may be added to the list. If these characteristics affect the estimated decision parameters, neural networks should be selected to take these values as inputs. The operating conditions could be the filler percentage, process temperature, and other adjustable parameters. The allowable ranges of these parameters would be given to the program. One genetic algorithm is assigned for each composite material. The genetic algorithm gives the fixed parameters of the part and various values for each operating condition parameter to the neural networks as input. Neural networks estimate the decision parameters such as cost, manufacturing time, strength, and others. Each genetic algorithm tries to obtain the optimum operating conditions for one composite material. After all the genetic algorithms reach the optimal solution, the process is stopped. The composite material that offers the lowest or highest value for the objective function according to the problem is selected. The estimated optimum operating conditions for that material will be used. The developed package does not have limitations on the number of n, and m could be a maximum of 6; however, very large n values require very long optimization times, while a large value of m will need very a extensive training process. The package allows the user to select one design parameter to be maximized or minimized, and to determine the acceptable range for all. In addition, it is possible to give an optimization function that considers multiple design parameters. 3.4. Operation of the proposed package Fig. 4. Determination of the intersection between the horizontal plane and each triangle. In addition to the graphic utility and optimization programs, the CoMaSA package contains a neural network trainer. All the neural networks are the back-propagation type. All the constants and parameters of the operating condition are the inputs. To estimate each decision-making parameter one neural network with one output is assigned. Interaction of the CoMaSA with the user is presented in Fig. 6.

S.Y. Yang et al. / International Journal of Machine Tools & Manufacture 43 (2003) 175 184 179 Fig. 5. Structure of the optimization program of the CoMaSA. 4. Case study To evaluate the performance of the CoMaSA, optimization was repeated with three different objectives. In the optimizations, three composite materials were considered. For the composite materials the following nine equations were assumed to represent the manufacturing time, cost, and strength of the prepared product: material1:time 0.113f 0.85 v 0.65 c 1.15 (h.), (5) Cost 3.08f 0.8 v 0.7 c 1.1 ($), (6) Strength 226f 0.8 (kpa), (7) material2:time 0.145f 0.82 v 0.67 c 1.27 (h.), (8) material2:time 0.145f 0.82 v 0.67 c 1.27 (h.), (9) Strength 332f 0.82 (kpa), (10) material3:time 0.152f 0.84 v 0.69 c 1.32 (h.), (11) Cost 3.25f 0.82 v 0.66 c 1.31 ($), (12) Strength 345f 0.85 (kpa) (13) where v is volume of a part, c is the complexity of the part, and f is the fiber volume to be used. The actual characteristics of the composite materials were not used in this study since the material suppliers and manufacturers did not want to distribute their priority information. The volume and complexity of the part were constant. The optimization was repeated three times with the following objectives: Minimum manufacturing time, lowest

180 S.Y. Yang et al. / International Journal of Machine Tools & Manufacture 43 (2003) 175 184 Fig. 7. Part plotted with varying number of triangles (The surface of the half sphere on the left is represented by 2060 triangles while only 106 triangles were used for the one on the right). Fig. 6. Proposed procedure for selection of optimal material and operating conditions. Fig. 8. Variation of complexity with number of triangles. cost, and maximum strength. In each optimization the acceptable range of the two other design parameters were selected. Fiber volume was the only parameter of the operating condition to be determined during the optimization. The allowable range of it was selected between 0.1 and 0.9 in this study to see if it would be able to use the whole range. In the practical cases the volume percentage of the filler is selected well below 90%. 5. Results and discussion In this section the validity of the proposed complexity estimation procedure, correction of complexity by removing the round holes, and performance of the optimization process will be discussed. complexity for the same part with minimal deviation for the number of triangles. A hemisphere is presented in Fig. 7 when its surface is covered with 2060 and 106 triangles. Both drawings were prepared using the Pro-E package. The variation of the complexity with the number of triangles for the same part is presented in Fig. 8. The complexity changed very slightly when the number of triangles changed twenty times. Stringers are parts that are widely used in the structures of aircraft, especially in the fuselage. Fig. 9 shows the variation of the complexity parameter with the length for various stringer shapes. The complexity of the part also increases with the length. It is more expensive to build longer composite parts than the shorter ones. The ACCEM manual also indicates a similar relationship. 5.1. Validity of the proposed complexity estimation procedure To evaluate the validity of the proposed complexity calculation procedure, the relationship between the characteristics of the parts and the calculated values are compared. Ideally, the complexity should be constant when the part geometry is represented at different resolutions; however, it should increase when the length and bend angle increase. According to the desired part resolution, CAD/CAM packages use different numbers of triangles to represent the parts. A valid procedure should estimate the same Fig. 9. Variation of complexity with length.

S.Y. Yang et al. / International Journal of Machine Tools & Manufacture 43 (2003) 175 184 181 The proposed system correctly estimated the increase of the complexity with the length. In addition to the complexity, the volume of the part also increases with length. The cost of the longer parts will not only be the function of the increasing complexity but also the increasing volume. Fig. 10 shows the variation of the complexity with the bend angle. Bend angles increase the difficulty of manufacturing a part and its cost. Beams with rectangular cross-sections and varying bend angle (angle between the end planes) were modeled by using Pro-Engineer and analyzed using the complexity estimation system. The estimated complexity had an almost linear relationship with the bend angle of the part. In this study decision-making parameters are calculated by using neural networks. Since the neural networks are capable of representing even very non-linear characteristics, identical trends between complexity and decision-making parameters, such as cost, are not necessary. Table 1 Complexity of a part with holes and when the correction algorithm removed the triangles at the surfaces of round holes Complexity No. of holes Before holes removed After holes removed 1 1.69 0.9998 2 2.33 0.9966 3 2.93 0.9924 4 3.54 0.9944 5 4 0.9834 6 4.5 0.978 9 6.22 0.9841 12 7.63 0.9788 5.2. Correction of complexity estimation with round hole removal procedure To evaluate the accuracy of the proposed complexity correction process by round hole removal, a cube was created with 5 in. edges. The STL file of the part was prepared when the part had 1 to 12 holes with diameters of 0.50 in. and 1.00 in.. The complexity of the part was calculated with holes. When the correction algorithm was not used, part complexity changed between 1.69 and 7.63 (Table 1 and Fig. 11). Complexity increased with each extra hole. When the complexity was estimated after the round holes were removed, almost the same complexity values were obtained as the part with no holes. There was a small decrease in the complexity since the number of holes used for the part were reduced. The complexity of the part without any holes was 1.00. The user interface of the program is presented in Fig. 12. The correction algorithm also found the location of the holes and their diameter. The accuracy of both the estimated position and radius is satisfactory (Table 2) to estimate the drilling cost accurately. Fig. 11. Complexity of the part increases with the number of holes. Proposed correction algorithm eliminates the error. Fig. 10. Variation of complexity with the bend angle. Fig. 12. The user interface of the complexity estimation program with correction algorithm with round hole removal.

182 S.Y. Yang et al. / International Journal of Machine Tools & Manufacture 43 (2003) 175 184 Table 2 Hole locations and radiuses. Actual and calculated values are presented. Measurements are in inches Hole no. Actual coordinates Calculated coordinates Hole no. Actual radius Calculated radius 1 X 1.500 1.513 1 0.25 0.26 2 0.25 0.26 Z 1.500 1.498 3 0.25 0.26 2 X 1.500 1.513 4 0.25 0.26 5 0.25 0.26 Z 0.000 0.002 6 0.25 0.26 3 X 0.500 0.513 7 0.25 0.26 8 0.25 0.26 Z 1.500 1.498 9 0.25 0.26 4 X 0.500 0.513 10 0.25 0.26 11 0.25 0.26 Z 0.000 0.002 12 0.25 0.3 5 X 0.500 0.487 Z 1.500 1.498 6 X 0.500 0.487 Z 0.000 0.002 7 X 1.500 1.487 Z 1.500 1.498 8 X 1.500 1.487 Z 0.000 0.002 9 X 1.500 1.487 Z 1.500 1.502 10 X 0.500 0.487 Z 1.500 1.502 11 X 0.500 0.513 Z 1.500 1.502 12 X 1.500 1.522 Z 1.500 1.456 Table 3 Selected optimal material and operating conditions Minimize Cost Minimize Time Maximize Strength Ranges of output Time 2 to 8 (h.) Cost 100 to 200 ($) Cost 50 to 220 ($) Strength 150 to 350 (kpa) Strength 170 to 350 (kpa) Time 3 to 12 (h.) Optimized values 118.3 ($) 5.037 (h.) 302.669 (kpa) Other outputs Time 5.631 (h.) Cost 143.912 ($) Cost 219.965 ($) Strength 150.0 (kpa) Strength 170.0 (kpa) Time 11.702 (h.) Iterations 345 175 230 Fiber volume 0.376 0.698 0.854 Fittest material Material 2 Material 1 Material 3 5.3. Selection of the optimal material and operating conditions Nine back-propagation-type neural networks were trained to represent the manufacturing time, cost, and strength characteristics of three composite materials. Each neural network had three inputs. The inputs were the volume, complexity, and fiber volume percentage. The organization of the neural networks and genetic algorithms is presented in Fig. 13. Optimization was repeated three times to obtain the minimum cost, the shortest manufacturing time, and maximum strength.

S.Y. Yang et al. / International Journal of Machine Tools & Manufacture 43 (2003) 175 184 183 Fig. 14. volume). Selected optimum material and operating condition (fiber Structure of the optimization composite material manufac- Fig. 13. ture. The user interface of the program after the completion of the optimization task is presented in Fig. 14. The selected optimal material and operating conditions after the optimization process are presented in Table 3. The accuracy of the neural network training program and optimization programs were demonstrated in the previous paper [23]. 6. Conclusion In this paper, the representation of the characteristics of the composite materials by using neural networks, and selection of the optimal material and operating conditions by using the genetic algorithms is proposed. To evaluate the accuracy of the proposed automated procedure, the Composite Material Selection Adviser (CoMaSA) package was developed. The package uses three separate programs. These programs train the neural networks to represent the characteristics of the parts, estimate complexity from the STL files, and optimum material and process parameters are selected by using multiple neural networks and genetic algorithms. The programs require minimum user input as almost all the critical values are obtained automatically. The proposed complexity estimation procedure automatically estimates the part complexity. If the part has holes to be drilled after the manufacturing of the composite part is completed, correction algorithms estimate the complexity of the part automatically after the round holes are removed. This algorithm also reports the size and location of the holes. The complexity estimation procedure was not sensitive to the number of the triangles, which cover the part surface. The estimated complexity increased proportionately when the length and the bend angle changed. In all the studied cases, the optimal conditions were obtained without converging to local minimums. The proposed multi-neural network system estimated three important decision-making parameters of composite material manufacturing very conveniently. It is possible to increase the number of parameters. Once the parameters to be optimized were selected or an optimization function was determined, genetic algorithms found the optimal material and operating conditions within the selected boundaries. The proposed procedure is very convenient also to model and optimize other complex systems. Acknowledgements This work was partially supported by the Air Force Research Laboratory (contract # F33615-99-C5703), and National Research Council Summer Fellowship. The authors thank AFPL/MLLP, and NRC for the support.

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