Intelligent Fixture Design through a Hybrid System ... - Semantic Scholar
Artificial Intelligence Review (2005) 23:295–311 DOI 10.1007/s10462-004-7187-z
© Springer 2005
Intelligent Fixture Design through a Hybrid System of Artificial Neural Network and Genetic Algorithm MOHSEN HAMEDI Department of Mechanical Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran (e-mail: [email protected]) Abstract. In designing fixtures for machining operations, clamping scheme is a complex and highly nonlinear problem that entails the frictional contact between the workpiece and the clamps. Such parameters as contact area, state of contact, clamping force, wear and damage in the contact area and deformation of the component are of special interest. A viable fixture plan must include the optimum values of clamping forces. Along research efforts carried out in this area, this comprehensive problem in fixture design needs further investigation. In this study, a hybrid learning system that uses nonlinear finite element analysis (FEA) with a supportive combination of artificial neural network (ANN) and genetic algorithm (GA) is discussed. A frictional model of workpart–fixture system under cutting and clamping forces is solved through FEA. Training and querying an ANN takes advantage of the results of FEA. The ANN is required to recognize a pattern between the clamping forces and state of contact in the workpiece–fixture system and the workpiece maximum elastic deformation. Using the identified pattern, a GA-based program determines the optimum values for clamping forces that do not cause excessive deformation/stress in the component. The advantage of this work against similar studies is manifestation of exact state of contact between clamp elements and workpart. The results contribute to automation of fixture design task and computer aided process planning (CAPP). Keywords: clamping optimization, clamping simulation, fixture design, genetic algorithm
1. Introduction In machining processes, the part is accurately located, supported and constrained on the machining table. Designing fixtures as the tools to perform this job is a core process planning activity. One objective of this activity is achieving quality that is manufacturing the part within the required tolerances. Clamping scheme is determination of clamps types, their position and the force assigned to each clamp. Clamps play an important role in restraining the workpart. While they secure the component, the force exerted through them should
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not cause excessive deformation or stress. This renders clamping as a crucial aspect of the fixture design task so that it has become an important research issue in the manufacturing field. Fixture design optimization was initiated through developing analytical methodologies to study workholding problem. Asada and By (1985) presented kinematic analysis of workholding operation and developed analytical tools to design fixture layouts for complex shapes. In their model the wrokpiece was considered a rigid body. Lee and Haynes (1987) analyzed deformation of workpieces with primitive shapes under machining and clamping forces using finite element analysis (FEA). They considered friction between the clamps and the workpiece, while fixture elements were assumed rigid. Lee and Cutkosky (1991) developed a fixture-planning module to be used in a simultaneous product and process design. Considering kinematics of fixturing, force and friction analysis was used along simple geometric checks to verify sufficiency of the contact. Nee and Senthil Kumar (1991) investigated various requirements of a complete fixture design system and proposed a framework for an object/rule based fixture to partially accommodate those requirements. The works by Mittal (1991), De Meter (1994), Yeh and Liou (1999), Hurtado and Melkote (1999) and Li and Melkote (1999) address many issues of computer aided fixture planning. However, in these studies several parameters such as frictional contact, dynamic nature of cutting forces and workpiece stability need further investigation. De Meter et al. (2001) developed a model to predict the minimum clamp forces for workholding that considers deformation of workpiece and fixture. Their experimental results emphasized on significance of fixture elasticity on workpice–fixture response to machining load. Roy and Liao (2002) considered position of supporters, locators and clamps to develop an automated fixture design system that renders a stability analysis based on the extension of the screw theory proposed by Ohwovoriole (1980). Wu and Chan (1996) initially reported application of the genetic algorithm in fixture design optimization. They used the genetic algorithm (GA) in finding the most stable fixture design. Ishikawa and Aoyama (1996) used the GA to determine the optimal clamping condition for elastic workparts. Krishnakumar and Melkote (1999) applied the GA for 2-D fixturing problems without addressing clamping issue. Kulankara et al. (2002) applied GA method to optimize fixture layout and clamping force in the machining operations. In this work, maximum elastic deformation of the workpiece is taken
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into account as objective function. However, frictional contact in the workpiece–fixture system is not considered in the optimization process. In the current study, development of a hybrid method that embeds usage of nonlinear FEA in a supportive combination of artificial neural network (ANN) and GA is discussed. Applying finite element analysis to find the behavior of the workpiece–fixture contact and workpiece elastic deformation is indispensable. Since the problem is nonlinear, performing an optimization cycle combined of frictional nonlinearity and iterative nature of optimization is computationally expensive. The advantage of using the ANN is to minimize the number of solution runs that is required for each set of clamping forces. Result of the neural networks is fed into the GA as a fitness function. This leads to finding the optimal set of clamping forces that result in a secured workpiece with minimal deformation and stress. The results contribute to automation of fixture design task and computer aided process planning (CAPP).
2. ANN and the GA ANN is a system composed of many simple processing elements operating parallel wise whose function is determined by network structure, connection strengths, and the processing performed at computing elements or nodes (DARPA 1988). ANNs have been applied to an increasing number of real-world problems of considerable complexity. Their most important advantage is in solving problems that are too complex for conventional methodologies; problems that do not have an algorithmic solution or for which an algorithmic solution is too complex to be found. It seems that there is not any algorithmic solution for the problem of optimized clamping force. Published data in the literature does not display an analytical nature. Moreover, the contact status in the workpiece–fixture system has a complicated and nonalgorithmic behavior. Therefore, it is a good candidate to be tackled by ANN for recognizing a pattern in its frictional behavior. The pattern identifies the relation between the set of clamping and cutting forces from one side and contact status, deformation and stress in the workpiece from the other side. Once the ANN figures out this, the problem is to find a set of clamping forces that renders an optimum set of contact status, deformation and the stress. The GA is proven as a viable method for this optimization problem.
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GAs are heuristic optimization methods mimicking biological reproduction processes. GAs are of particular usefulness in handling complex systems with nonlinear functions and/or large number of design variables. The solution process starts with a randomly selected population. In the search for a global optimum, a set of biologically inspired operators are used that perform specific operations on the initial population. Simulating ‘survival of the fittest’ phenomena is the core of the GA. To each member of the population a fitness value is assigned. This is done through employing a fitness function tailored to the specific problem. In this study, a supportive combination of ANN and GA is developed to combine the search power of the two methods, where the ANN assists in developing the fitness function for the GA. Consequently, reproduction, crossover and mutation processes are used to eliminate unfit members and then population evolves to the next generation. In order to increase the global fitness of the population and maximize the fitness of individuals representing the best solution, adequate number of evolutions is required. There are few parameters that control the course of the GA and its convergence. These are namely: the population size, the probability of crossover, and the probability of mutation. The solution converges in two ways. First, if the number of generations reaches a pre-defined value whilst there is no change in the best value of fitness function in a population. Second, if the number of generation reaches the specified maximum number of evolution.
3. Synopsis of the Methodology The overall approach to the problem is shown in Figure 1. A machining model provides the maximum cutting forces. A fixture schemer proposes the workholding layout that constitutes the number of fixturing elements and their positions. The information is fed to finite element software capable of modeling the frictional contact between the workpiece, locators and clamps. The FEA results are used to train the ANN. The ANN recognizes the pattern between the boundary conditions and the workpiece behavior. This pattern is used to define the clamping force optimization procedure for the GA. Modeling and solution process for the problem is shown in Figure 2. ANSYSTM software with its family of contact elements is used. Once the geometry of the component is discretized and the material properties are embedded, the boundary conditions described previously are
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Figure 1. Block diagram of the methodology.
Figure 2. Flow of activities to train ANN.
added. The clamping forces are introduced to the software through converting them to interference constants (Hamedi 2001) and assigning the result to each contact element in the clamping area. Through
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running the solution module several times, sufficient sets of input and output are derived from the pre-processing and post-processing modules of the software. The output includes maximum elastic deformation and maximum von Mises stress in the workpiece along the state of contact in the contact area, i.e. clamping and locating positions. The state of contact are given out as integer numbers for different type of contact according to ANSYSTM (Kohnke 1998): Closed contact
µ · N > Ft −−−−−−−→ Sc = 1, Sliding contact
µ · N = Ft −−−−−−−→ Sc = 2,
(1)
No contact
µ · N < Ft −−−−−−−→ Sc = 3, where µ represents coefficient of friction; N is the normal force exerted by the clamp and Ft is the tangential force acting at the clamping point. The output and input sets establish the training prodigy for the ANN program as seen in Figure 3. Following the ‘training’ phase, the ANN in the ‘querying’ phase is able to generate the same output – i.e. maximum stress and elastic deformation in the workpiece and the contact status – as FEA software. The generated output is verified through reproducing the results pertaining to a published case study (Kulankara 2002), which displays remarkable agreement. This ensures that the GA can use the pattern, identified by the ANN, confidently to form the objective function of the optimization phase. The GA program implemented in this work automatically defines three parameters: population size, the probability of crossover and the probability of mutation. In order to validate the methodology, the optimum clamp force and state of contact given out by the GA has been verified through FEA method. 4. Comparative Study to Verify the Methodolgy The methodology discussed in this article has been tested through solving few case studies. One that can display the accountability of the approach is regeneration of the results appeared in the work by Kulankara et al. (2002). The authors have combined FEA and the GA to optimize the fixture layout and clamping force. They have used commercially available FEA software, ALGOR, to build the FE model and to output the workpiece stiffness matrix. In their work the friction forces are required to exceed the tangential forces at the
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Figure 3. Procedure to define objective function for optimizing frictional clamping forces.
clamping points, which simulate the frictional constraints. Then a GAbased optimization program, with maximum workpiece deformation as the objective function, generates the optimum locating and consequently a clamping plan. Our approach for solving the problem appears in the next section, where the modeling, applying the boundary conditions and solution procedure are discussed. 4.1. Finite Element Model The geometry, feature under machining of the problem is shown in Figure 4. The box is aluminum 390 with a Poisson ration of 0.3 and Young’s modulus of 71 GPa. The inner wall of the thick-walled box is
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Figure 4. The feature under machining and position of the cutter (Kulankara 2002).
Figure 5. Finite element model of the problem (Kulankara 2002).
undergoing an end-milling process as depicted in Figure 4. In the corresponding finite element model, shown in Figure 5, a total number of 756 octahedral eight-node elements are used for discretization. 4.2. Simulation of the Milling Operation The machining parameters for this peripheral end milling operation are shown in Table 1. Based on these parameters, the maximum values of cutting forces are calculated and applied as nodal loads on the inner wall of the workpiece, at the cutter position, as displayed in Figure 4. The corresponding values for tangential, radial and axial components which are in X,Y and Z directions respectively are: Fp = 330.94 N; Fq = 398.11 N; and Fa = 22.84 N
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Table 1. Machining parameters and conditions Type of operation
End milling
Cutter diameter Number of flutes Cutter RPM Feed Radial depth of cut Axial depth of cut Radial rake angle Helix angle Projection length
25.4 mm 4 500 0.1016 mm/tooth 2.54 mm 25.4 mm 10 30 92.07 mm
Table 2. Locating and clamping coordinates (Kulankara 2002) Workholding Element
Coordinates (X, Y, Z) (mm)
Locator 1 Locator 2 Locator 3 Locator 4 Clamp 1 Clamp 2
(139.7, 0, 63.5) (38.1, 0, 63.5) (139.7, 0, 12.7) (12.7, 0, 38.1) (139.7, 127, 38.1) (12.7, 127, 25.4)
4.3. Modeling the Workpiece–Fixture Contact The fixture plan for holding the workpart in the machining operation is shown in Figure 7. This optimized workholding plan, obtained by Kulankara et al. (2002) is used for validation purposes. It uses four locators (L1, L2, L3 and L4) to locate the part and two clamps (C1, C2), acting on the opposite face, to hold it. The coordinates of the locating and clamping points are displayed in Table 2. Figure 6 shows the configuration of nodal forces that simulate the exerted cutting load on the workpart. This plan is modeled using six point-to-point contact elements. To simulate the clamping forces, interference values (Ic ) are assigned to each contact element at the clamping point according to: 1
F = kn (Ic2 + Ui2 + 2Ic Uny,i ) 2 ,
(2)
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Figure 6. Configuration of the nodal forces simuilating the milling operation (Kulankara 2002).
Figure 7. The optimal fixture configuration (Kulankara 2002).
where Ui represents the overall displacement of node i on the workpart and Uny,i is the displacement of node i in the clamping force direction; Kn is normal stiffness of the contact element and F is clamping force. The optimized values of the clamping forces for clamps C1 and C2 , that are applied at the position causing maximum deformation are: Fc1 = 1187.7 N, Fc2 = 1040.0N These forces are converted to interference values using the relation (2) and the procedure proposed by Hamedi (2001). The corresponding values for clamps C1 and C2 are: Ic1 = −6.96 µm, Ic2 = −6.22 µm
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Table 3. Comparing the maximum elastic deformation of the workpiece Maximum elastic deformation (µm) Current Study 5.85
Kulankara (2002) 5.42
4.4. Comparison of Results for the Two methods The finite element model of the problem described in Section 4.1 was solved by ANSYSTM . Due to nonlinear behavior of the frictional model a Newton–Rophson iterative procedure was used. The maximum elastic deformation obtained through solving the model is compared against the result of another work (Kulankara 2002) and are shown in Table 3. These two set of results are derived through different approaches, i.e. a customized program and usage of contact elements. They display 93% compatibility which presents the accountability of the method used in this study.
5. Integrated ANN and GA Approach Observing agreement between results of finite element analysis and another published work ascertained that through FEA enough set of data could be obtained for training and querying the ANN. So this step can be seen as a validation step before constructing the ANN and consequently starting the optimization procedure by using the GA. Once the ANN is created, it can be integrated into the GA. The overall procedure consists of three steps: ANN training, ANN querying and the GA programming. 5.1. Principle 3-2-1 and the ANN Training Phase In the fixture plan proposed by Kulankara et al. (2002), conventional methods for workholding prismatic parts is remarkably simplified. Therefore, to implement the current methodology and investigate its possible limitations a more practical plan is advised. It uses the conventional principle 3-2-1 for prismatic parts. The same workpiece as in Figure 4, is held on its bottom face using three locators (L1 , L2 , and L3 ) and three more locators (L4 , L5 and L6 ) restrain its two other
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Table 4. Locating and clamping coordinates according to 3-2-1 principle Workholding element
Coordinates (X, Y, Z) (mm)
Locator 1 Locator 2 Locator 3 Locator 4 Locator 5 Locator 6 Clamp 1 Clamp 2
(38.1, 0, 38.1) (114.3, 0, 38.1) (152.4, 63.5, 38.1) (12.7, 63.5, 38.1) (127,12.7,0) (88.9,114.3,0) (76.2, 114.3, 76.2) (12.7, 63.5, 76.2)
datum planes. The remaining degrees of freedom are constrained by clamps C1 and C2 . Coordinates of these fixture elements are shown in Table 4. To train the ANN, a problem with prescribed boundary conditions and equal values of cutting forces, is solved for 56 set of clamping forces. The following input and output are retrieved to train the ANN. • Input: interference values (Ic1 , Ic2 ) • Output: state of contact for clamps C1 and C2, maximum elastic deformation and maximum von Mises stress in the workpiece To determine the number of layers in the ANN, the trial begins from one layer. Deciding the number of nodes is left to the program where it reaches a number of five. A 5% error is defined as the termination criteria. A trial and error fine-tuning process terminates with six nodes as the optimum number of nodes. The finalized ANN consists of six nodes and one layer with the configuration displayed in Figure 8. Nodes 0 and 1 display the input to the ANN that are interference values. The six nodes from 2 to 7 are the ANN provisional nodes. Nodes 8–11 are the output from the ANN discussed before. 5.2. Querying Phase of the ANN Once the ANN is sufficiently trained, its querying phase involves seven investigation runs. Each run starts with introducing two interference values to the ANN and extracting the output that includes state of contact, maximum deformation and stress. The extracted results are displayed in Table 5. The results for contact status, shown as C1 and C2 status in Table 5, illustrate that predicting the contact condition
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Figure 8. The configuration of the implemented ANN. Table 5. The ANN results in the querying phase Try No.
2 12 22 31 37 47 61
C1 Status
C2 Status
Dmax (µm)
Smax (MPa)
FEA
ANN
FEA
ANN
FEA
ANN
FEA
ANN
1 1 1 1 1 1 1
1 1 1 1 1 1 1
2 2 2 2 2 2 1
2 2 2 2 2 1.9995 1.0006
15.50 14.30 11.30 9.26 7.47 5.33 4.42
15.01 14.82 12.56 10.54 7.10 5.03 4.34
3.42 3.66 3.40 3.26 2.84 3.11 3.22
3.44 3.67 3.50 3.36 3.00 3.15 3.32
between the workpart and the clamps by the ANN is in complete agreement by the FEA results. In every query run, the contact status for both clamps have the same values derived by FEA or the ANN. Therefore, the ANN confidently can predict the sate of contact between the fixture elements and the workpiece. The ANN performance for predicting maximum deflection and maximum von-Mises stress is not of lesser importance. The computed deflection results from FEA and the ANN for different query runs are displayed in Figure 9. A correlation analysis between the results yields a correlation factor of 0.986. This correlation factor for the comparable stress results, shown in Figure 10, is 0.987, which indicates a satisfactory success for the ANN in predicting the required output. Therefore, the constructed ANN can be used for optimization process with confidence and reliability.
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Figure 9. Comparing the deflection results computed by FEA and predicted by the ANN.
Figure 10. Comparing the results for von Mises Stress computed by FEA and predicted by the ANN.
5.3. The GA The satisfactory results obtained from the ANN in the querying phase lead to the GAs set-up for optimization task. Implementing the GA is required to determine the optimized values of the clamping forces. So that these forces adequately restrain the workpiece and do not cause excessive deformation or stress. The nonlinear relation between the clamping force and the workpiece deformation, obtained by the ANN is used to define the objective function for the GA. The definition of the objective function follows: i=1 Min Max(δ), (3) Sc n
given: σmax < τy ,
(4)
where δ is elastic deformation of the workpiece and Sc is the integer number representing the state of contact as in (1) for n clamps; σ is the maximum von Mises stress and τy is the yield stress of the material.
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Table 6. The results obtained from the GA and FEA Ic1 (µm)
Ic2 (µm)
GA result 4.93
5.72
δmax (µm)
Clamp force (N)
FEA
GA
C1
C2
4.17
4.60
393.6
463.7
Design variables are clamping forces at the two clamping positions. The GA program determines the controlling parameters of the optimization course i.e. the population size, the probability of crossover and the probability of mutation. The optimized set of clamping forces produced by the GA are: Ic1 = −3.93 µm, Ic2 = −4.63 µm. These values render a maximum deformation of: δmax = 4.5 µm. To increase the confidence, the problem with the above boundary condition is solved using FEA method. The results displayed in Table 6 shows agreement between the FEA solution and the GA prediction within 89.8% accuracy. An exact verification of the accuracy of the state of contact needs thorough experimental investigation. But the agreements between the results of this work and the results published by Kulankara et al. (2002) on the value of maximum deformation provides a reasonable degree of certainty.
6. Conclusion This article introduced an artificial intelligence-based procedure for optimizing the clamping forces in a machining operation. The procedure utilizes a hybrid scheme of nonlinear finite element and a supportive combination of ANN and the GA. To validate the solution, the problem of a published study was remodeled by applying the current method of using contact elements to model the frictional contact. Comparing the maximum elastic deformation in both studies displayed satisfactory agreement. This conformity led to generating adequate set of data to train an ANN consisting of one layer and six nodes. The trained ANN is able to predict the state of contact and maximum elastic deformation as well as maximum stress. The inputs to the ANN are interference values that represent clamping forces. In the querying phase, the ANN results were compared against the results of FEA and showed a remarkable agreement. The relation
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obtained from the ANN was used to define fitness function for a GA program designed to optimize the clamping forces with respect to maximum deformation and state of contact. Finally, the GA results were verified by comparing them with the results of FEA, which showed a reasonable agreement. This study contributes to automating the fixture design task in a CAPP environment. The methodology needs rigorous user interaction and the author is of the opinion that integration of FEA and the ANN will increase the efficiency of this approach. Further investigations in this area are being pursued. Moreover, usage of more efficient combinations of ANNs and GA, such as evolutionary networks are under consideration. The enhanced optimization power of these architectures should eventually enable simultaneous optimization of fixture layouts and clamping schemes. References Asada, H. & By, A. B. (1985). Kinematic Analysis of Workpart Fixturing for Flexible Assembly with Automatically Reconfigurable Fixtures. IEEE Journal of Robotics and Automation RA-1(2): 86–94. DARPA Neural Network Study, (1988). AFCEA International Press, Fairfax, VA. De Meter, E. C. (1994). Restraint Analysis of Fixtures which Rely on Surface Contact. ASME Journal of Engineering for Industry 116: 207–215. De Meter, E. C., Xi, W., Choudhuri, S., Vallapuzha, S. & Trethewey, M. (2001). A Model to Predict Minimum Required Clamp Pre-loads in Light of Fixture–Workpiece Compliance. International Journal of Machine Tools and Manufacture 41: 1031–1054. Hamedi, M. (2001). Fixture Design Optimization with Simulation of Clamp Tightness in Workpiece–Fixture System. Proceedings of the IASTED International Conference on Applied Simulation and Modeling, Spain. Ishikawa, Y. & Aoyama, T. (1996). Optimization of Fixturing Condition by Means of the Genetic Algorithm. Transactions of Japanese Society of Mechanical Engineers Series C, 65(598): 2409–2416. Kohnke, P. (1998). ANSYS version 5.6 User’s Manual. ANSYS Inc., Canonsburg, PA. Krishnakumar, K. & Melkote, S. N. (1999). Machining Fixture Layout Optimization Using the Genetic Algorithm. International Journal of Machine Tool Manufacture. 40(4): 579–598. Kulankara, K., Satyanarayana, S. & Melkote, S. N. (2002). Interactive Fixture Layout and Clamping Force Optimization Using the Genetic Algorithm. ASME Journal of Manufacturing Science and Engineering, 124: 119–125. Lee, J. D., & Haynes, L. S., (1987). Finite Element Analysis of Flexible Fixturing Systems. ASME Journal of Engineering for Industry, 113: 134–139. Mittal, R. O. (1991). Dynamic Modelling of the Fixture–Workpiece System. Robotics and Computer-Integrated Manufacturing 8(4): 201–217. Nee, A. Y. C. & Senthil Kumar, A. (1991). Framework for an Object/Rule-Based Fixture Design System. Annals of the CIRP 40: 147–151.
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Ohwovoriole, M. S. (1980). An Extension of Screw Theory and its Application to Automation of Industrial Assemblies. Ph.D. Dissertation, Stanford University, California. Roy, U. & Liao, J. (2002). Fixturing Analysis for Stability Consideration in an Automated Fixture Design System. ASME Journal of Manufacturing Science and Engineering 124: 98–104. Yeh, J. H. & Liou, F. W. (1999). Contact Condition Modelling for Machining Fixture Setup Processes. International Journal of Machine Tools and Manufacture 39: 787–803.
© Springer 2005
Intelligent Fixture Design through a Hybrid System of Artificial Neural Network and Genetic Algorithm MOHSEN HAMEDI Department of Mechanical Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran (e-mail: [email protected]) Abstract. In designing fixtures for machining operations, clamping scheme is a complex and highly nonlinear problem that entails the frictional contact between the workpiece and the clamps. Such parameters as contact area, state of contact, clamping force, wear and damage in the contact area and deformation of the component are of special interest. A viable fixture plan must include the optimum values of clamping forces. Along research efforts carried out in this area, this comprehensive problem in fixture design needs further investigation. In this study, a hybrid learning system that uses nonlinear finite element analysis (FEA) with a supportive combination of artificial neural network (ANN) and genetic algorithm (GA) is discussed. A frictional model of workpart–fixture system under cutting and clamping forces is solved through FEA. Training and querying an ANN takes advantage of the results of FEA. The ANN is required to recognize a pattern between the clamping forces and state of contact in the workpiece–fixture system and the workpiece maximum elastic deformation. Using the identified pattern, a GA-based program determines the optimum values for clamping forces that do not cause excessive deformation/stress in the component. The advantage of this work against similar studies is manifestation of exact state of contact between clamp elements and workpart. The results contribute to automation of fixture design task and computer aided process planning (CAPP). Keywords: clamping optimization, clamping simulation, fixture design, genetic algorithm
1. Introduction In machining processes, the part is accurately located, supported and constrained on the machining table. Designing fixtures as the tools to perform this job is a core process planning activity. One objective of this activity is achieving quality that is manufacturing the part within the required tolerances. Clamping scheme is determination of clamps types, their position and the force assigned to each clamp. Clamps play an important role in restraining the workpart. While they secure the component, the force exerted through them should
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not cause excessive deformation or stress. This renders clamping as a crucial aspect of the fixture design task so that it has become an important research issue in the manufacturing field. Fixture design optimization was initiated through developing analytical methodologies to study workholding problem. Asada and By (1985) presented kinematic analysis of workholding operation and developed analytical tools to design fixture layouts for complex shapes. In their model the wrokpiece was considered a rigid body. Lee and Haynes (1987) analyzed deformation of workpieces with primitive shapes under machining and clamping forces using finite element analysis (FEA). They considered friction between the clamps and the workpiece, while fixture elements were assumed rigid. Lee and Cutkosky (1991) developed a fixture-planning module to be used in a simultaneous product and process design. Considering kinematics of fixturing, force and friction analysis was used along simple geometric checks to verify sufficiency of the contact. Nee and Senthil Kumar (1991) investigated various requirements of a complete fixture design system and proposed a framework for an object/rule based fixture to partially accommodate those requirements. The works by Mittal (1991), De Meter (1994), Yeh and Liou (1999), Hurtado and Melkote (1999) and Li and Melkote (1999) address many issues of computer aided fixture planning. However, in these studies several parameters such as frictional contact, dynamic nature of cutting forces and workpiece stability need further investigation. De Meter et al. (2001) developed a model to predict the minimum clamp forces for workholding that considers deformation of workpiece and fixture. Their experimental results emphasized on significance of fixture elasticity on workpice–fixture response to machining load. Roy and Liao (2002) considered position of supporters, locators and clamps to develop an automated fixture design system that renders a stability analysis based on the extension of the screw theory proposed by Ohwovoriole (1980). Wu and Chan (1996) initially reported application of the genetic algorithm in fixture design optimization. They used the genetic algorithm (GA) in finding the most stable fixture design. Ishikawa and Aoyama (1996) used the GA to determine the optimal clamping condition for elastic workparts. Krishnakumar and Melkote (1999) applied the GA for 2-D fixturing problems without addressing clamping issue. Kulankara et al. (2002) applied GA method to optimize fixture layout and clamping force in the machining operations. In this work, maximum elastic deformation of the workpiece is taken
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into account as objective function. However, frictional contact in the workpiece–fixture system is not considered in the optimization process. In the current study, development of a hybrid method that embeds usage of nonlinear FEA in a supportive combination of artificial neural network (ANN) and GA is discussed. Applying finite element analysis to find the behavior of the workpiece–fixture contact and workpiece elastic deformation is indispensable. Since the problem is nonlinear, performing an optimization cycle combined of frictional nonlinearity and iterative nature of optimization is computationally expensive. The advantage of using the ANN is to minimize the number of solution runs that is required for each set of clamping forces. Result of the neural networks is fed into the GA as a fitness function. This leads to finding the optimal set of clamping forces that result in a secured workpiece with minimal deformation and stress. The results contribute to automation of fixture design task and computer aided process planning (CAPP).
2. ANN and the GA ANN is a system composed of many simple processing elements operating parallel wise whose function is determined by network structure, connection strengths, and the processing performed at computing elements or nodes (DARPA 1988). ANNs have been applied to an increasing number of real-world problems of considerable complexity. Their most important advantage is in solving problems that are too complex for conventional methodologies; problems that do not have an algorithmic solution or for which an algorithmic solution is too complex to be found. It seems that there is not any algorithmic solution for the problem of optimized clamping force. Published data in the literature does not display an analytical nature. Moreover, the contact status in the workpiece–fixture system has a complicated and nonalgorithmic behavior. Therefore, it is a good candidate to be tackled by ANN for recognizing a pattern in its frictional behavior. The pattern identifies the relation between the set of clamping and cutting forces from one side and contact status, deformation and stress in the workpiece from the other side. Once the ANN figures out this, the problem is to find a set of clamping forces that renders an optimum set of contact status, deformation and the stress. The GA is proven as a viable method for this optimization problem.
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GAs are heuristic optimization methods mimicking biological reproduction processes. GAs are of particular usefulness in handling complex systems with nonlinear functions and/or large number of design variables. The solution process starts with a randomly selected population. In the search for a global optimum, a set of biologically inspired operators are used that perform specific operations on the initial population. Simulating ‘survival of the fittest’ phenomena is the core of the GA. To each member of the population a fitness value is assigned. This is done through employing a fitness function tailored to the specific problem. In this study, a supportive combination of ANN and GA is developed to combine the search power of the two methods, where the ANN assists in developing the fitness function for the GA. Consequently, reproduction, crossover and mutation processes are used to eliminate unfit members and then population evolves to the next generation. In order to increase the global fitness of the population and maximize the fitness of individuals representing the best solution, adequate number of evolutions is required. There are few parameters that control the course of the GA and its convergence. These are namely: the population size, the probability of crossover, and the probability of mutation. The solution converges in two ways. First, if the number of generations reaches a pre-defined value whilst there is no change in the best value of fitness function in a population. Second, if the number of generation reaches the specified maximum number of evolution.
3. Synopsis of the Methodology The overall approach to the problem is shown in Figure 1. A machining model provides the maximum cutting forces. A fixture schemer proposes the workholding layout that constitutes the number of fixturing elements and their positions. The information is fed to finite element software capable of modeling the frictional contact between the workpiece, locators and clamps. The FEA results are used to train the ANN. The ANN recognizes the pattern between the boundary conditions and the workpiece behavior. This pattern is used to define the clamping force optimization procedure for the GA. Modeling and solution process for the problem is shown in Figure 2. ANSYSTM software with its family of contact elements is used. Once the geometry of the component is discretized and the material properties are embedded, the boundary conditions described previously are
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Figure 1. Block diagram of the methodology.
Figure 2. Flow of activities to train ANN.
added. The clamping forces are introduced to the software through converting them to interference constants (Hamedi 2001) and assigning the result to each contact element in the clamping area. Through
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running the solution module several times, sufficient sets of input and output are derived from the pre-processing and post-processing modules of the software. The output includes maximum elastic deformation and maximum von Mises stress in the workpiece along the state of contact in the contact area, i.e. clamping and locating positions. The state of contact are given out as integer numbers for different type of contact according to ANSYSTM (Kohnke 1998): Closed contact
µ · N > Ft −−−−−−−→ Sc = 1, Sliding contact
µ · N = Ft −−−−−−−→ Sc = 2,
(1)
No contact
µ · N < Ft −−−−−−−→ Sc = 3, where µ represents coefficient of friction; N is the normal force exerted by the clamp and Ft is the tangential force acting at the clamping point. The output and input sets establish the training prodigy for the ANN program as seen in Figure 3. Following the ‘training’ phase, the ANN in the ‘querying’ phase is able to generate the same output – i.e. maximum stress and elastic deformation in the workpiece and the contact status – as FEA software. The generated output is verified through reproducing the results pertaining to a published case study (Kulankara 2002), which displays remarkable agreement. This ensures that the GA can use the pattern, identified by the ANN, confidently to form the objective function of the optimization phase. The GA program implemented in this work automatically defines three parameters: population size, the probability of crossover and the probability of mutation. In order to validate the methodology, the optimum clamp force and state of contact given out by the GA has been verified through FEA method. 4. Comparative Study to Verify the Methodolgy The methodology discussed in this article has been tested through solving few case studies. One that can display the accountability of the approach is regeneration of the results appeared in the work by Kulankara et al. (2002). The authors have combined FEA and the GA to optimize the fixture layout and clamping force. They have used commercially available FEA software, ALGOR, to build the FE model and to output the workpiece stiffness matrix. In their work the friction forces are required to exceed the tangential forces at the
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Figure 3. Procedure to define objective function for optimizing frictional clamping forces.
clamping points, which simulate the frictional constraints. Then a GAbased optimization program, with maximum workpiece deformation as the objective function, generates the optimum locating and consequently a clamping plan. Our approach for solving the problem appears in the next section, where the modeling, applying the boundary conditions and solution procedure are discussed. 4.1. Finite Element Model The geometry, feature under machining of the problem is shown in Figure 4. The box is aluminum 390 with a Poisson ration of 0.3 and Young’s modulus of 71 GPa. The inner wall of the thick-walled box is
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Figure 4. The feature under machining and position of the cutter (Kulankara 2002).
Figure 5. Finite element model of the problem (Kulankara 2002).
undergoing an end-milling process as depicted in Figure 4. In the corresponding finite element model, shown in Figure 5, a total number of 756 octahedral eight-node elements are used for discretization. 4.2. Simulation of the Milling Operation The machining parameters for this peripheral end milling operation are shown in Table 1. Based on these parameters, the maximum values of cutting forces are calculated and applied as nodal loads on the inner wall of the workpiece, at the cutter position, as displayed in Figure 4. The corresponding values for tangential, radial and axial components which are in X,Y and Z directions respectively are: Fp = 330.94 N; Fq = 398.11 N; and Fa = 22.84 N
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Table 1. Machining parameters and conditions Type of operation
End milling
Cutter diameter Number of flutes Cutter RPM Feed Radial depth of cut Axial depth of cut Radial rake angle Helix angle Projection length
25.4 mm 4 500 0.1016 mm/tooth 2.54 mm 25.4 mm 10 30 92.07 mm
Table 2. Locating and clamping coordinates (Kulankara 2002) Workholding Element
Coordinates (X, Y, Z) (mm)
Locator 1 Locator 2 Locator 3 Locator 4 Clamp 1 Clamp 2
(139.7, 0, 63.5) (38.1, 0, 63.5) (139.7, 0, 12.7) (12.7, 0, 38.1) (139.7, 127, 38.1) (12.7, 127, 25.4)
4.3. Modeling the Workpiece–Fixture Contact The fixture plan for holding the workpart in the machining operation is shown in Figure 7. This optimized workholding plan, obtained by Kulankara et al. (2002) is used for validation purposes. It uses four locators (L1, L2, L3 and L4) to locate the part and two clamps (C1, C2), acting on the opposite face, to hold it. The coordinates of the locating and clamping points are displayed in Table 2. Figure 6 shows the configuration of nodal forces that simulate the exerted cutting load on the workpart. This plan is modeled using six point-to-point contact elements. To simulate the clamping forces, interference values (Ic ) are assigned to each contact element at the clamping point according to: 1
F = kn (Ic2 + Ui2 + 2Ic Uny,i ) 2 ,
(2)
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Figure 6. Configuration of the nodal forces simuilating the milling operation (Kulankara 2002).
Figure 7. The optimal fixture configuration (Kulankara 2002).
where Ui represents the overall displacement of node i on the workpart and Uny,i is the displacement of node i in the clamping force direction; Kn is normal stiffness of the contact element and F is clamping force. The optimized values of the clamping forces for clamps C1 and C2 , that are applied at the position causing maximum deformation are: Fc1 = 1187.7 N, Fc2 = 1040.0N These forces are converted to interference values using the relation (2) and the procedure proposed by Hamedi (2001). The corresponding values for clamps C1 and C2 are: Ic1 = −6.96 µm, Ic2 = −6.22 µm
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Table 3. Comparing the maximum elastic deformation of the workpiece Maximum elastic deformation (µm) Current Study 5.85
Kulankara (2002) 5.42
4.4. Comparison of Results for the Two methods The finite element model of the problem described in Section 4.1 was solved by ANSYSTM . Due to nonlinear behavior of the frictional model a Newton–Rophson iterative procedure was used. The maximum elastic deformation obtained through solving the model is compared against the result of another work (Kulankara 2002) and are shown in Table 3. These two set of results are derived through different approaches, i.e. a customized program and usage of contact elements. They display 93% compatibility which presents the accountability of the method used in this study.
5. Integrated ANN and GA Approach Observing agreement between results of finite element analysis and another published work ascertained that through FEA enough set of data could be obtained for training and querying the ANN. So this step can be seen as a validation step before constructing the ANN and consequently starting the optimization procedure by using the GA. Once the ANN is created, it can be integrated into the GA. The overall procedure consists of three steps: ANN training, ANN querying and the GA programming. 5.1. Principle 3-2-1 and the ANN Training Phase In the fixture plan proposed by Kulankara et al. (2002), conventional methods for workholding prismatic parts is remarkably simplified. Therefore, to implement the current methodology and investigate its possible limitations a more practical plan is advised. It uses the conventional principle 3-2-1 for prismatic parts. The same workpiece as in Figure 4, is held on its bottom face using three locators (L1 , L2 , and L3 ) and three more locators (L4 , L5 and L6 ) restrain its two other
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Table 4. Locating and clamping coordinates according to 3-2-1 principle Workholding element
Coordinates (X, Y, Z) (mm)
Locator 1 Locator 2 Locator 3 Locator 4 Locator 5 Locator 6 Clamp 1 Clamp 2
(38.1, 0, 38.1) (114.3, 0, 38.1) (152.4, 63.5, 38.1) (12.7, 63.5, 38.1) (127,12.7,0) (88.9,114.3,0) (76.2, 114.3, 76.2) (12.7, 63.5, 76.2)
datum planes. The remaining degrees of freedom are constrained by clamps C1 and C2 . Coordinates of these fixture elements are shown in Table 4. To train the ANN, a problem with prescribed boundary conditions and equal values of cutting forces, is solved for 56 set of clamping forces. The following input and output are retrieved to train the ANN. • Input: interference values (Ic1 , Ic2 ) • Output: state of contact for clamps C1 and C2, maximum elastic deformation and maximum von Mises stress in the workpiece To determine the number of layers in the ANN, the trial begins from one layer. Deciding the number of nodes is left to the program where it reaches a number of five. A 5% error is defined as the termination criteria. A trial and error fine-tuning process terminates with six nodes as the optimum number of nodes. The finalized ANN consists of six nodes and one layer with the configuration displayed in Figure 8. Nodes 0 and 1 display the input to the ANN that are interference values. The six nodes from 2 to 7 are the ANN provisional nodes. Nodes 8–11 are the output from the ANN discussed before. 5.2. Querying Phase of the ANN Once the ANN is sufficiently trained, its querying phase involves seven investigation runs. Each run starts with introducing two interference values to the ANN and extracting the output that includes state of contact, maximum deformation and stress. The extracted results are displayed in Table 5. The results for contact status, shown as C1 and C2 status in Table 5, illustrate that predicting the contact condition
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Figure 8. The configuration of the implemented ANN. Table 5. The ANN results in the querying phase Try No.
2 12 22 31 37 47 61
C1 Status
C2 Status
Dmax (µm)
Smax (MPa)
FEA
ANN
FEA
ANN
FEA
ANN
FEA
ANN
1 1 1 1 1 1 1
1 1 1 1 1 1 1
2 2 2 2 2 2 1
2 2 2 2 2 1.9995 1.0006
15.50 14.30 11.30 9.26 7.47 5.33 4.42
15.01 14.82 12.56 10.54 7.10 5.03 4.34
3.42 3.66 3.40 3.26 2.84 3.11 3.22
3.44 3.67 3.50 3.36 3.00 3.15 3.32
between the workpart and the clamps by the ANN is in complete agreement by the FEA results. In every query run, the contact status for both clamps have the same values derived by FEA or the ANN. Therefore, the ANN confidently can predict the sate of contact between the fixture elements and the workpiece. The ANN performance for predicting maximum deflection and maximum von-Mises stress is not of lesser importance. The computed deflection results from FEA and the ANN for different query runs are displayed in Figure 9. A correlation analysis between the results yields a correlation factor of 0.986. This correlation factor for the comparable stress results, shown in Figure 10, is 0.987, which indicates a satisfactory success for the ANN in predicting the required output. Therefore, the constructed ANN can be used for optimization process with confidence and reliability.
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Figure 9. Comparing the deflection results computed by FEA and predicted by the ANN.
Figure 10. Comparing the results for von Mises Stress computed by FEA and predicted by the ANN.
5.3. The GA The satisfactory results obtained from the ANN in the querying phase lead to the GAs set-up for optimization task. Implementing the GA is required to determine the optimized values of the clamping forces. So that these forces adequately restrain the workpiece and do not cause excessive deformation or stress. The nonlinear relation between the clamping force and the workpiece deformation, obtained by the ANN is used to define the objective function for the GA. The definition of the objective function follows: i=1 Min Max(δ), (3) Sc n
given: σmax < τy ,
(4)
where δ is elastic deformation of the workpiece and Sc is the integer number representing the state of contact as in (1) for n clamps; σ is the maximum von Mises stress and τy is the yield stress of the material.
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Table 6. The results obtained from the GA and FEA Ic1 (µm)
Ic2 (µm)
GA result 4.93
5.72
δmax (µm)
Clamp force (N)
FEA
GA
C1
C2
4.17
4.60
393.6
463.7
Design variables are clamping forces at the two clamping positions. The GA program determines the controlling parameters of the optimization course i.e. the population size, the probability of crossover and the probability of mutation. The optimized set of clamping forces produced by the GA are: Ic1 = −3.93 µm, Ic2 = −4.63 µm. These values render a maximum deformation of: δmax = 4.5 µm. To increase the confidence, the problem with the above boundary condition is solved using FEA method. The results displayed in Table 6 shows agreement between the FEA solution and the GA prediction within 89.8% accuracy. An exact verification of the accuracy of the state of contact needs thorough experimental investigation. But the agreements between the results of this work and the results published by Kulankara et al. (2002) on the value of maximum deformation provides a reasonable degree of certainty.
6. Conclusion This article introduced an artificial intelligence-based procedure for optimizing the clamping forces in a machining operation. The procedure utilizes a hybrid scheme of nonlinear finite element and a supportive combination of ANN and the GA. To validate the solution, the problem of a published study was remodeled by applying the current method of using contact elements to model the frictional contact. Comparing the maximum elastic deformation in both studies displayed satisfactory agreement. This conformity led to generating adequate set of data to train an ANN consisting of one layer and six nodes. The trained ANN is able to predict the state of contact and maximum elastic deformation as well as maximum stress. The inputs to the ANN are interference values that represent clamping forces. In the querying phase, the ANN results were compared against the results of FEA and showed a remarkable agreement. The relation
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obtained from the ANN was used to define fitness function for a GA program designed to optimize the clamping forces with respect to maximum deformation and state of contact. Finally, the GA results were verified by comparing them with the results of FEA, which showed a reasonable agreement. This study contributes to automating the fixture design task in a CAPP environment. The methodology needs rigorous user interaction and the author is of the opinion that integration of FEA and the ANN will increase the efficiency of this approach. Further investigations in this area are being pursued. Moreover, usage of more efficient combinations of ANNs and GA, such as evolutionary networks are under consideration. The enhanced optimization power of these architectures should eventually enable simultaneous optimization of fixture layouts and clamping schemes. References Asada, H. & By, A. B. (1985). Kinematic Analysis of Workpart Fixturing for Flexible Assembly with Automatically Reconfigurable Fixtures. IEEE Journal of Robotics and Automation RA-1(2): 86–94. DARPA Neural Network Study, (1988). AFCEA International Press, Fairfax, VA. De Meter, E. C. (1994). Restraint Analysis of Fixtures which Rely on Surface Contact. ASME Journal of Engineering for Industry 116: 207–215. De Meter, E. C., Xi, W., Choudhuri, S., Vallapuzha, S. & Trethewey, M. (2001). A Model to Predict Minimum Required Clamp Pre-loads in Light of Fixture–Workpiece Compliance. International Journal of Machine Tools and Manufacture 41: 1031–1054. Hamedi, M. (2001). Fixture Design Optimization with Simulation of Clamp Tightness in Workpiece–Fixture System. Proceedings of the IASTED International Conference on Applied Simulation and Modeling, Spain. Ishikawa, Y. & Aoyama, T. (1996). Optimization of Fixturing Condition by Means of the Genetic Algorithm. Transactions of Japanese Society of Mechanical Engineers Series C, 65(598): 2409–2416. Kohnke, P. (1998). ANSYS version 5.6 User’s Manual. ANSYS Inc., Canonsburg, PA. Krishnakumar, K. & Melkote, S. N. (1999). Machining Fixture Layout Optimization Using the Genetic Algorithm. International Journal of Machine Tool Manufacture. 40(4): 579–598. Kulankara, K., Satyanarayana, S. & Melkote, S. N. (2002). Interactive Fixture Layout and Clamping Force Optimization Using the Genetic Algorithm. ASME Journal of Manufacturing Science and Engineering, 124: 119–125. Lee, J. D., & Haynes, L. S., (1987). Finite Element Analysis of Flexible Fixturing Systems. ASME Journal of Engineering for Industry, 113: 134–139. Mittal, R. O. (1991). Dynamic Modelling of the Fixture–Workpiece System. Robotics and Computer-Integrated Manufacturing 8(4): 201–217. Nee, A. Y. C. & Senthil Kumar, A. (1991). Framework for an Object/Rule-Based Fixture Design System. Annals of the CIRP 40: 147–151.
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Ohwovoriole, M. S. (1980). An Extension of Screw Theory and its Application to Automation of Industrial Assemblies. Ph.D. Dissertation, Stanford University, California. Roy, U. & Liao, J. (2002). Fixturing Analysis for Stability Consideration in an Automated Fixture Design System. ASME Journal of Manufacturing Science and Engineering 124: 98–104. Yeh, J. H. & Liou, F. W. (1999). Contact Condition Modelling for Machining Fixture Setup Processes. International Journal of Machine Tools and Manufacture 39: 787–803.
