Journal of Engineering and Technology

: 2014  |  Volume : 4  |  Issue : 2  |  Page : 102--109

Optimization of Fixture Layout and Artificial Neural Network (ANN) Weights of ANN-Finite Element Analysis Based Fixture Layout Model Using Genetic Algorithm

M Vasundara1, KP Padmanaban2,  
1 Department of Mechanical Engineering, PSNA College of Engineering & Technology, Dindigul, Tamil Nadu, India
2 Department of Mechanical Engineering, SBM College of Engineering & Technology, Dindigul, Tamil Nadu, India

Correspondence Address:
M Vasundara
Department of Mechanical Engineering, PSNA College of Engineering & Technology, Dindigul, Tamil Nadu


Workpiece elastic deformation in machine manufacturing may cause dimensional errors, which in turn affects the accuracy of the machined parts. Fixturing elements like locators and clamps are used to locate a workpiece with respect to the cutting tool in a given orientation such that the errors caused by workpiece elastic deformation are reduced. The optimization of locator and clamp positions is crucial in minimizing the dimensional errors in machining. In this research paper, a slot milling operation on a rectangular workpiece is considered for which the fixture layout is optimized using a hybrid system of artificial neural network (ANN) and genetic algorithm (GA). The workpiece elastic deformation for different sets of fixture layouts is calculated using finite element method (FEM) and training of ANN is done with the FEM results to develop a numerical model. To enhance the accuracy of learning in lesser time, the weights are optimized for the network using GA before the training phase. The trained ANN recognizes a pattern between the position of fixturing elements and the workpiece elastic deformation. Using the recognized pattern, GA determines the optimal position of locators and clamps to minimize the workpiece elastic deformation and thereby the dimensional errors.

How to cite this article:
Vasundara M, Padmanaban K P. Optimization of Fixture Layout and Artificial Neural Network (ANN) Weights of ANN-Finite Element Analysis Based Fixture Layout Model Using Genetic Algorithm .J Eng Technol 2014;4:102-109

How to cite this URL:
Vasundara M, Padmanaban K P. Optimization of Fixture Layout and Artificial Neural Network (ANN) Weights of ANN-Finite Element Analysis Based Fixture Layout Model Using Genetic Algorithm . J Eng Technol [serial online] 2014 [cited 2019 Sep 18 ];4:102-109
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 1. Introduction

Fixtures are used to locate, hold and support a workpiece during machining which in turn minimizes the workpiece and tooling deflections due to clamping and cutting forces. A good fixture layout constrains the workpiece fully at all times to achieve accuracy and quality during the machining operation. The workpiece location and fixture layout are crucial to product quality in terms of dimensional accuracy and precision of the part. The position of the locators and clamps, the number of locators and clamps and the value of clamping force are to be appropriately selected to minimize the workpiece deformation during machining. Several approaches have been made in the recent years to optimize the fixture layout design.

Lee and Haynes [1] were among the first to use finite element method (FEM) for the fixture design and synthesis. Siebenaler [2] , Krishnakumar and Melkote [3] and Kaya [4] developed a fixture-workpiece model and the influences of compliance of the fixture body on workpiece deformation were explored using finite element software-ANSYS version 10.0 and a built-in finite element solver. They used genetic algorithm (GA) to optimize the fixture layout so that the workpiece elastic deformation is minimized under the static machining forces. Along these same lines, a number of researchers such as Cai et al. [5] , De Meter [6] and Liao [7] developed finite element based fixture layout algorithms to control workpiece compliance for the purpose of minimizing workpiece displacement during machining. Li and Melkote [8] presented a fixture layout optimization model for improving the location accuracy of the workpiece using finite element software-ANSYS-version 5.3. Liao and Wang [9] optimized the fixture and joint positions by integrating finite element analysis (FEA) with the global optimization algorithm called mode-pursuing sampling method. The optimization is done for non-rigid sheet metal assembly to minimize the assembly variation. Sun et al. [10] used FEM to analyze the clamping forces by considering cutting forces and frictions and applied GA to optimize the fixture layout and a clamping force.

Vallapuzha et al. [11] presented results of an extensive investigation into the relative effectiveness of various optimization methods. They showed that continuous GA yielded the best quality solutions. Fan and Senthil Kumar [12] studied the fixture locating layout with the help of robust design approach. To increase the quality of the machining workpieces and for robust layout, which is insensitive to errors, they combined the Taguchi method and the Monte-Carlo statistical method. The influence of the locators' position at different levels on the feature errors were studied by the Taguchi method. The variation of co-ordinates of the locators was simulated using Monte-Carlo method. De Meter [6] presented a finite element based support layout optimization procedure with computationally attractive qualities. They used the nonlinear optimization algorithm, but the position of locator and clamp was not considered in this work. King and Hutter [13] presented a method for optimal fixture layout design using a rigid body model of the workpiece system but accounting for the contact stiffness. They used a nonlinear optimization technique to determine a statically stable fixture layout. Tao et al. [14] determined the optimal clamping points and clamping sequence for arbitrarily shaped workpiece using geometrical reasoning methodology. In their work, only the clamp position is optimized and the position of locators is ignored. Jiang et al. [15] proposed a zonal compensation method for fixture layout optimization. They developed a surface flatness model based on high definition metrology to minimize the workpiece elastic deformation. Huang et al. [16] presented an alternative sequential space filling (SSF) strategy for optimizing fixture layout design. To search for optimal designs, the SSF strategy helps to iteratively select and shrink the candidate space. The strategy was validated through a floor span assembly case study where GA results and statistical quality control results were compared to show the effectiveness of the method. Ishikawa and Aoyama [17] determined the optimal clamping condition for an elastic workpiece using GA. Their analysis however does not consider the more general case of locator and clamp layout synthesis. Marcelin [18] has used GAs to the optimization of selecting support positions in the machining of mechanical parts. Prabhaharan et al. [19] optimized the fixture layout to minimize the dimensional and form errors. FEM was used to predict the workpiece deformation. GA and ant colony algorithm (ACA) were adopted separately for the optimization method. The performance of GA and ACA were tested and compared based on the different node systems as the workpiece deformation varies according to the node system. Padmanaban and Prabhaharan [20] optimized the fixture layout to minimize the workpiece deformation under dynamic conditions. FEM was employed to determine the workpiece elastic deformation. Different node systems were used until minimum workpiece deformation has been achieved for an optimal layout. The deformation for all the node systems were simulated in the examples considered. The evolutionary techniques, GA and ACA, were used for the optimization and the results of both the techniques were compared. Chen et al. [21] established a multi-objective optimization model to minimize the deformation and improve the uniform distribution of deformation by considering the friction and chip removal effects. The optimization process was performed through the integration of GA and FEM. Padmanaban et al. [22] optimized the machining fixture layout to minimize the workpiece elastic deformation by applying ACA based discrete and continuous optimization methods. The dynamic response of the workpiece with respect to machining and clamping forces was determined using FEM. Hamedi [23] proposed a hybrid learning system of artificial neural network (ANN) and GA in the design of machining fixture layout. The clamping forces were optimized to minimize the deformation during machining. The position of the locators and clamps were kept fixed in his work.

Most of the research work focused on FEM and GA for the optimization of the fixture layout and very few have reported on fixture problems using ANN in which one of the research works optimized the clamping forces using ANN to minimize the workpiece deformation. Very meager work has been extensively presented for the fixture layout using ANN to optimize the position of the fixturing elements. Using ANN for the prediction process helps to a great extent in reducing the computational time and moreover it would be more accurate and reliable if the weights of the network are optimized for the training phase. This can be done with any one of the optimization methods.

In this research work, a case study involving a slot milling operation on a rectangular workpiece is considered. The milling operation is performed on the assumption that the cutting force acts only along the plane and hence the workpiece response also [22] . As both the cutting force and workpiece response are only along the plane, two-dimensional (2D) workpiece geometry [4] is considered. Each and every possible fixture layout has the position of three locators and two clamps as design variables for which the values are taken within a specified range and the workpiece elastic deformation for different layouts is determined using FEA. The position of all the fixturing elements and the deformation for different layouts are used as input for ANN training, for which the optimal weights are determined using GA, to develop a numerical model. The trained ANN predicts the workpiece deformation for new different fixture layouts, which are compared with the results of FEA to validate ANN. GA, is then used to handle the fixture layout optimization problem where ANN computes the objective values for each generation of GA.

 2. Materials and Methods

The proposed methodology for the optimization of fixture layout to minimize the workpiece elastic deformation is shown in [Figure 1].{Figure 1}

 3. Fixture Layout Optimization Case Study

3.1 Illustration

The case study [4] considered in this paper is to demonstrate the proposed fixture layout optimization method. The 2D workpiece geometry, in which the end milling operation is performed, is shown in [Figure 2]. The workpiece-fixture system consists of three locators, L1 , L2 and L3 and two clamps C1 and C2 . The machining forces for performing end milling operation are 100 N (←) and 286 N (Ϳ). The clamping forces acting at clamp C1 and C2 are 200 N and 350 N respectively.{Figure 2}

The range of values for the design variables are as follows:

5 < L1 < 148 mm

5 < L2 < 148 mm

5 < L3 < 85 mm

5 < C1 < 65 mm

5 < C2 < 125 mm

3.2 FEA

FEA is used widely to determine the deformation at any point on the workpiece. In this research work, the clamping forces to restrain the workpiece and the machining forces required are kept unchanged throughout the milling operation. The position of locators and clamps are varied to predict the fixture layout to minimize the workpiece elastic deformation. Hence, the position of the locators and clamps are assumed as the design variables. For the 2D geometry considered in the research work, the fixture layout consists of three locators and two clamps. The FEA software ANSYS has been employed to determine the workpiece deformation for the defined fixture layouts. In the analysis, the element death technique has been adopted with respect to tool movement and chip removal.

The meshed finite element model of the workpiece and the deformed model are shown in [Figure 3] and [Figure 4], respectively. In the ANSYS model, shown in [Figure 3] and [Figure 4], the positions of the locators L1 , L2 and L3 are 78.25 mm, 44.0 mm and 10.94 mm, respectively. The degrees of freedom for the locators L1 and L2 are arrested along y-axis and for the locator L3 , it is arrested along x-axis. The forces of 200 N and 350 N are applied by the clamps C1 and C2 in y-axis and x-axis respectively at the positions 55.79 mm and 114.91 mm. The randomly generated fixture layouts and the corresponding deformation values form the database for training ANN.{Figure 3}{Figure 4}

3.3 GA based weight optimization for ANN

ANN solves problems by learning the relationship between inputs and outputs. The widely used learning algorithm is backpropagation network (BPN), which is a gradient descent technique with backward error propagation. In the GA based weight optimization, also called as neuro-genetic hybrid system, the weights of a multilayer feed forward network are optimized using GA. ANN needs sufficient training to learn the input-output relationship, whereas overtraining the network may lead to undesired effects. The weights are determined based on a gradient search technique and hence there is a risk of encountering the local minimum problem. GA has been found to be good at finding acceptably good solutions to problems acceptably quickly. By hybridizing BPN and GA, the necessary weights can be optimized in order to enhance the speed of training.

The workpiece-fixture system considered in this research work consists of five fixturing elements, i.e., three locators and two clamps. So, a BPN is considered with one input layer consisting of five nodes, one hidden layer of five nodes and one output layer with one node. GA is used to find the optimum weights of BPN. These optimum weights are applied to BPN to infer the output. The parameters used to train and infer the neuro-genetic hybrid system are given in [Table 1].{Table 1}

3.3.1 Coding

The parameters representing the solution of a problem are called as genes. These genes are joined together in the form of string of values referred as a chromosome. For a BPN with l-m-n network configuration, i.e., l input neurons, m hidden neurons and n output neurons, the number of weights to be determined are (l + n)m. If the gene length (the number of digits in weight) is assumed to be d, then the chromosome (string S) length is L = (l + n)md. In the problem considered, there are five input nodes, five hidden nodes and one output node. Therefore, the total number of weights to be calculated is 30. Each weight is represented by five digits so that the length of the chromosome is 150. An initial population of 100 chromosomes is generated randomly.

3.3.2 Weight extraction

The weights are extracted from each of chromosomes to determine the fitness values for each of the chromosomes. The weight extraction is performed using the following equations:


where Wk is the actual weight, X1 , X2 , …, Xd represent a chromosome and Xkd+1 , Xkd+2 , …, X(k+1)d represent the kth gene in the chromosome.

3.3.3 Fitness function

A fitness function must be calculated for each problem to be solved. It is determined using the root mean square of the errors. The root mean square of the error is


where Ei is the error value for the sets, i = 1, 2, 3, …, N is the number of sets of input-output pairs for the problem.

The fitness value for each of the individual chromosome is


3.3.4 Reproduction

Reproduction is the selection operator applied on the population to select the chromosomes. The selected chromosomes act as parents to crossover and produce offspring. Before reproduction, a mating pool is formed with good strings from the population. In the mating pool, the chromosome with least fitness is excluded and replaced with a duplicate copy of the chromosome with the highest fitness value. After forming the mating pool, the parents are selected in pairs at random to apply other operators.

3.3.5 Crossover

Crossover operator is applied to the mating pool to create a new better string from the good strings produced by reproduction. Two parent chromosomes are selected randomly to create a new better chromosome. Here, a single point crossover operator has been used where two random positions are chosen and the strings are exchanged between these two positions to create an offspring.

3.3.6 Mutation

The strings are subjected to mutation after performing crossover. Mutation of a bit involves flipping it, with a mutation probability Pm . The best individuals (with high fitness value) are selected from the existing population to form a new generation of possible solutions to the problem. The new generation formed contains better characteristics than their parents. Proceeding in this way, after many generations, the entire population inherits the best characteristics due to exchange of good characteristics. The final population gives the best fit solutions to the problem.

3.4 Development of numerical model using ANN

The structure of ANN consists of interconnected artificial neurons arranged in layers. The architecture of the ANN used in this research work is shown in [Figure 5]. With the help of the optimized weights calculated using GA, the neural network is trained and tested.{Figure 5}

3.4.1 Training phase of ANN

A MATLAB R2010a (Mathworks software for programming) based ANN training phase was conducted using FEA simulation results to obtain the co-ordinate positions of milling fixture layout. The training phase is continued for different layouts and the design variables and their maximum deformations are made available as data base for ANN.

The network is fed with 80 sets of known input and output values for training. For the given input, the output obtained from the network is compared with the target value. The various control parameters for the ANN is given in [Table 2].{Table 2}

The trained neural network with known inputs and output generates output values of maximum workpiece elastic deformation for all the input layouts. The results of ANN are compared with that of the FEA results.

3.4.2 Testing phase of ANN

The trained network is able to predict the maximum workpiece elastic deformation for different fixture layouts. By defining the minimum and maximum value for each design variable, 20 sets of new fixture layouts are randomly generated within the specified range. The new randomly generated 20 fixture layouts are given as input to the trained ANN and the results are compared with that of FEA to ensure the reliability of ANN. The comparison between the FEA results and the ANN results during the testing phase is shown in [Figure 6].{Figure 6}

3.5 Optimization of fixture layout using GA

GA is directed search algorithms based on the mechanics of biological evolution for finding the global optimum solution for an optimization problem. They operate on a population of potential solutions adopting the principle of survival of the fittest to successively produce better approximations to a solution. At each generation of a GA, a new set of individuals is selected according to their fitness level to create a new set of approximations. The individuals are then reproduced using the operators to evolve populations of individuals that are better suited to their environment.

In this research work, the fixture layout and the position of fixturing elements are taken as design variables for GA. The position of each fixturing element is referred to a gene. A fixture layout is referred to a string or chromosome, which is a collection of genes. In this fixture layout problem, the number of genes in each chromosome is five to represent three locators and two clamps. The number of chromosomes referred to as the population is taken as 40. The objective function in the fixture layout optimization problem is to minimize the workpiece elastic deformation. The objective function is mapped to fitness function value F(x), which is evaluated for each chromosome using the following equation:


where f(x) is the objective function value. The deformation values are calculated using the numerical model developed with the help of ANN.

The convergence of GA is controlled by the crossover probability (Pc ) and the mutation probability (Pm ). The effects of control parameters used in GA are studied and it is proved from the results shown in [Figure 7], [Figure 8], [Figure 9], [Figure 10], [Figure 11], [Figure 12] that the choice of crossover probability Pc = 0.9 and mutation probability Pm = 0.04 is the optimal one. The GA input parameters for the fixture layout problem is given in [Table 3].{Figure 7}{Figure 8}{Figure 9}{Figure 10}{Figure 11}{Figure 12}{Table 3}

The GA results of the fixture layout for 15 runs are shown in [Table 4]. Run 7 gives the optimal fixture layout, i.e., the positions of the fixturing elements, which have the minimum workpiece deformation.{Table 4}

 4. Conclusion

In this research work, GA-ANN hybrid system has been adopted to minimize the maximum workpiece elastic deformation. The major advantage of using the ANN for the fixture layout design to predict the workpiece deformation is the less computation time. The neural network is trained with adequate sets of fixture layouts and their respective workpiece elastic deformation. To improve the learning efficiency of the network, the weights are optimized using GA. A numerical model developed from the trained network is used to predict the workpiece elastic deformation for any fixture layout within the given range. The numerical model developed using ANN defines the objective function for GA. The computational time is reduced to a great extent as the developed numerical model is used to calculate the workpiece deformation for GA. Finally by hybridizing ANN and GA, the machining fixture layout has been optimized.


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