Machining of Metal Matrix Composites pp 143162  Cite as
Computational Methods and Optimization in Machining of Metal Matrix Composites
Abstract
This chapter deals with the importance of mathematical modeling and need for optimizing the process. Further, case studies involving the various modeling and optimization techniques applied to machining of metal matrix composites are also discussed.
Keywords
Particle Swarm Optimization Artificial Neural Network Feed Rate Response Surface Methodology Metal Matrix CompositeThis chapter deals with the importance of mathematical modeling and need for optimizing the process. Further, case studies involving the various modeling and optimization techniques applied to machining of metal matrix composites are also discussed.
7.1 Introduction
The main objective of any machining process is to obtain the desired level of quality characteristic for the finished component. In order to study the machining behavior, it is essential to establish the relationship between the controlled parameters and the required quality characteristic. On the other hand, to optimize the machining process, the proper setting of control parameters (factors) on the performance measure (response) is necessary. Both modeling and optimization require efficient planning of experiments for minimizing the number of experiments, which in turn reduces the time and cost involved in the experimentation. The design of experiments (DOE) is extensively used in the planning of experiments involving several factors, where it is necessary to investigate the joint effect of the factors on a response variable [1, 2]. The DOE takes levels of several input parameters to formulate the different combinations at which the output parameters are to be observed or computed. There are several types of DOE available, which are based on statistical theory [1, 2]. The selection of proper DOE basically depends on the purpose of experimentation, which includes the development of modeling or/and optimization of machining process.
7.1.1 Importance of Mathematical Modeling
In most of the cases, true functional relationship is not known and hence an appropriate function to approximate ? is to be chosen. Normally, low order polynomial models such as first and second orders are largely used as approximating functions [1, 2] and these empirical regression equations are called as response surface models.
Identifying and fitting an appropriate response surface model from experimental data requires some knowledge of DOE, regression modeling techniques and elementary optimization methods [1, 2]. The response surface methodology (RSM) integrates all of the above. These empirical models serve to provide information about the properties of the system from which the data are taken [1, 2]. There are many other situations in which a mathematical model is used for process optimization.
There are many types of experimental designs available, which are mainly based on number of factors and their levels. The appropriate DOE to be selected is based on three criteria, namely, purpose (model development/optimization), nature of model (linear or nonlinear model) and the number of factors and the levels defined for each of the factors [3]. The DOE can be classified as fullfactorial design, fractionalfactorial design, orthogonal array, centralcomposite design and Box–Behnken design [1, 2, 3, 4].
7.1.2 Need for Optimization
The optimization of a system (product/process) design means determining the best architecture, the best parameter values and the best tolerances [4]. However, the optimization of any process still remains one of the most challenging problems because of its high complexity and nonlinearity while solving it and most of the engineering design problems are multiobjective in nature. Hence, designing the system at the required quality characteristic is an economical and technological challenge to the engineer or scientist.

Taguchi robust design optimization technique i.e., by allowing the process optimization using Taguchi technique with minimum number of experiments without the need for the development of models [4].

Modelbased optimization techniques i.e., by using the empirical models to obtain the predictions of the response of interest and then to find the best compromises among the multiobjectives for the system through the nontraditional optimization tools like genetic algorithms (GA), simulated annealing (SA), ant colony optimization (ACO) and particle swarm optimization (PSO) [5].
7.2 Modeling Approaches
The metamodels are the empirical expressions, which are used to obtain the relationships relating the control factors to the performance characteristics of interest. The data obtained from the statistical experimental design is utilized to construct the models. The advantage of the metamodel is that once it is created, it can yield large amounts of predictions. The most commonly used metamodels are response surface model, fuzzy logic, artificial neural networks and neurofuzzy inference systems. However, the models based on RSM and artificial neural network (ANN) has recently gained much attention in studying and analyzing the behavior of machining processes.
7.2.1 Modeling Based on Response Surface Methodology
The RSM using DOE proved to be an efficient mathematical modeling tool [1, 2]. The methodology not only reduces the cost and time, but also gives the required information about the main and interaction effects of the factors with reduced number of experiments. The RSM is a collection of mathematical and statistical techniques, which are useful for building the mathematical models and analyzing the problems that provide an overall perspective of the system response within the design space [1, 2]. The mathematical model of the quality characteristic to the control factors can be predicted by employing the multiple regression analysis with minimum number of experiments planned through DOE. The RSM refers not merely to the use of a response surface as a multivariate function but also to the process for determining the polynomial coefficients.
The construction of RSM models involves three main steps, namely, choosing a functional form for the model representation, fitting the model to the observed data and the statistical validation for the response surface [3].
After conducting a set of experiments to obtain the quality characteristics or outputs according to the experimental designs, the next step is to take the vectors of input control factors (x) and the corresponding responses (y) for fitting the appropriate model. Typical response surface model limits the order of polynomial to one or two since the lowdegree models contain fewer terms than the higherdegree models and thus, require fewer experiments to be performed [1, 2, 3].
The secondorder model can take on a wide variety of functional forms, so it will often work well as an approximation to the true response surface.
The analysis of variance (ANOVA) [1, 2] technique is used to check the adequacy of the developed model for the desired confidence interval. The ANOVA table includes the sum of squares (SS), the degrees of freedom (DF) and the mean square (MS). In ANOVA, the contribution for SS is from the first order terms, the secondorder terms and the residual error. The MS are obtained by dividing the SS of each of the sources of variation by the respective DF. The Fisher’s variance ratio is the ratio of MS of regression to MS of residual error. As per ANOVA, the model developed is adequate within the desired confidence interval, if Fisher’s variance ratio of regression exceeds the standard tabulated value of Fratio.
7.2.1.1 Case Study: RSM Model Development for Machining of MMC
The study presented here describes the development of secondorder RSMbased models to predict some aspects of machinability, namely, machining force (F _{m}), cutting power (P) and specific cutting force (K _{s}) during turning of metal matrix composites (MMC) [6]. Aluminum alloy reinforced with 20% of silicon carbide (SiC) particulates (A356/20/SiCpT6) work material was used throughout the investigation. The chemical composition of A356 aluminum matrix is with 7% Si and 0.4% Mg. The average dimension of SiC particles is about 20 ?m.
Process parameters and their levels
Parameters  Unit  Levels  

1  2  3  4  
Cutting speed (v)  m/min  50  100  200  – 
Feed rate (f)  mm/rev  0.05  0.10  0.15  0.20 
Experimental layout plan and the machinability characteristics
Trial number  Levels of process parameters  Actual values of process parameters  Machinability characteristics  

v  f  v (m/min)  f (mm/rev)  F _{ m }(N)  P(W)  K _{ s } (MPa)  
1  1  1  50  0.05  216.2  145  1,744.3 
2  1  2  50  0.1  326.9  224  1,346.2 
3  1  3  50  0.15  440.2  305  1,221.0 
4  1  4  50  0.2  551.3  385  1,156.0 
5  2  1  100  0.05  220.3  274  1,643.4 
6  2  2  100  0.1  328.8  433  1,299.1 
7  2  3  100  0.15  429.5  582  1,163.2 
8  2  4  100  0.2  515.9  717  1,074.8 
9  3  1  200  0.05  212.8  522  1,565.5 
10  3  2  200  0.1  309.0  812  1,218.1 
11  3  3  200  0.15  389.8  1,071  1,071.2 
12  3  4  200  0.2  461.5  1,308  980.9 
Summary of ANOVA for machining force, cutting power and specific cutting force models
Response  Sum of squares  Degrees of freedom  Mean square  Fratio  

Regression  Residual  Regression  Residual  Regression  Residual  
Machining force (Fm)  1,49,186  136  5  6  29,837  23  1,312.00 
Cutting power (P)  13,88,586  536  5  6  2,77,717  89  3,111.35 
Specific cutting force (K _{ s })  6,38,456  5,657  5  6  1,27,691  243  135.44 
7.2.2 Modeling Based on Artificial Neural Networks
The model development by RSM is a method, which requires minimum number of experiments to be conducted, but restricted to only small range of input variables and hence not suitable for complex and highly nonlinear processes. On the other hand, the development of higher order RSM model requires more number of experiments to be performed and hence costlier. This poses a limitation on the use of RSM models for highly nonlinear process and these constraints led to the development of model based on ANN.
The ANN is a fast, efficient, accurate and cost effective processmodeling tool in which the biological neurons are represented by a mathematical model [7]. The ability of ANN to capture any complex input–output relationships from the limited data set is valuable in machining process, where a huge experimental data for processmodeling is difficult and further expensive to obtain. The ANN is a flexible modeling tool with an aptitude to learn the mapping between input and output variables [7].
The purpose of ANN development is to imitate human brain so as to implement the various functions such as association, selforganization and generalization. The ANNs are parallel computer models of processes and the mechanisms, which constitute biological nerve systems. The ANNs are attractive in view of their highexecution speed and modest computer hardware requirements in addition to an adaptive nature and capability in solving complex and nonlinear problems. The ANN is made up of neurons connected via links. The information is processed within the neurons and is propagated to other neurons through the links connecting neurons.
 For output layer:$$ \delta_{pk} = (d_{kp}  o_{kp} )(1  o_{kp} );\;k = 1, \ldots K $$(7.15)
 For hidden layer:$$ \delta_{pj} = o_{pj} (1  o_{pj} )\,\sum {\delta_{pk} w_{kj} } ;\;j \, = 1, \ldots J $$(7.16)
 1.
The network weights are initialized to small random values.
 2.
The input/desired output pairs are presented one by one, updating the weights each time.
 3.The MSE due to all outputs and NP number of patterns is computed as:$$ MSE = \frac{1}{NP}\sum\limits_{p = 1}^{NP} {\,\,\sum\limits_{k = 1}^{K} {\left( {d_{kp}  o_{kp} } \right)^{2} } } $$(7.17)
 4.
If (MSE < specified tolerance) or (epochs > (epochs)_{max})
Then stop.
Else, go to Step 2.
7.2.2.1 Case Study: ANN Model Development for Machining of MMC
A case study of ANNbased modeling of surface roughness in turning of AlSiC (20p) using coarse grade polycrystalline diamond (PCD) inserted under different cutting conditions is considered in this section [8]. A multilayer perceptron (MLP) model has been constructed with EBPTA to capture the relationship between cutting speed (v), feed rate (f) and depth of cut (d) on surface roughness (R _{a}) of turned component. The inputoutput data required for development of ANN model has been obtained through FFD. The experimental results were obtained by turning of MMC’s of type A356/SiC/20p (aluminum with 7.5% silicon, 2.44% magnesium, reinforced with 20% volume particles of SiC).
A medium duty lathe of 2 kW spindle power has been employed for dry turning of 30 trials of parameter combinations. The CNMA 120408 inserts with PCLNR 25 X25 M12 tool holder with PCD were used to turn the billets of 150 mm diameter. The tool geometry of PCD inserts employed was, top rake angle of 0º and nose radius of 0.8 mm. The work material was machined at five different cutting speeds ranging from 100 to 600 m/min with two feed rates of 0.108 and 0.200 mm/rev and depth of cut as 0.25, 0.50 and 0.75 mm. Each experimental trial was carried out for 3 min duration.
The average surface roughness (R _{a}) in the direction of tool movement was measured in three different places of machined surface using a surface roughness tester, Mitutoyo Surf test301 with a cutoff and transverse length of 0.8, and 2.5 mm, respectively. The average surface roughness (R _{ a }) for three different locations was considered for each trial.
The ANN training was performed using 18 inputoutput patterns and other 12 data sets were then utilized for ANN validation. The network was trained by using suitable scaling factor for input parameters. The ANN designed for the present study takes depth of cut, cutting speed and feed rate as the input parameters; surface roughness as the output parameter. The ANN architecture selected for the surface roughness force model is 3101, number of epochs is set to 2000, transfer function is sigmoid, learning factor is 0.6 while momentum factor is 1.0.
Validation of results for surface roughness obtained using ANN
Reading number  Experimental surface roughness (?m)  ANN predicted surface roughness (?m)  Error (%) 

1  3.94  3.96  0.75 
2  2.27  2.25  0.50 
3  4.21  4.30  2.17 
4  3.87  3.88  0.27 
5  4.50  4.45  1.10 
6  2.49  2.52  1.42 
7  6.19  6.10  1.44 
8  5.05  5.03  0.39 
9  5.39  5.13  4.78 
10  2.93  2.86  2.26 
11  5.75  5.66  1.48 
12  4.57  4.60  0.84 
7.3 Optimization Methods
The robust parameter design (RPD) as suggested by Taguchi [2, 4] is an engineering methodology that emphasizes proper choice of levels of control factors in a process. The principle of choice of levels focuses mainly on variability around a target for the quality characteristic. The majority of variability around a target is caused by uncontrollable parameters known as noise factors. Hence, RPD entails designing the system by selecting the optimal levels of control factors so as to achieve robustness of system response to inevitable changes in the noise factors [2, 4]. The noise factors may be, and often are, controlled at research or development level but they cannot be controlled at the production or product use level [4].
Traditionally, mathematical programing techniques like linear programing, integer programing, dynamic programing and geometric programing have been used to solve the optimization problems in machining processes. However, the traditional techniques are not ideal for solving these problems, as they tend to obtain a local optimal solution. Considering the drawbacks of the traditional optimization techniques, attempts are being made to optimize the machining problem using heuristic search algorithms like GA, SA, ACO and PSO [5].
7.3.1 Taguchi Robust Design
Taguchibased optimization technique has produced a unique and powerful optimization discipline that differs from the traditional practises. Taguchi optimization technique is based on concept of “robust design”, which aims at obtaining the solutions that make the design less sensitive to noise factors. Taguchi technique [4] has been widely applied in the process design, wherein the mathematical models for the performance do not exist and the experiments are typically conducted to determine the optimum settings for the design and process variables.
Taguchi robust design principle is based on matrix experiments. The traditional experimental design methods are too complex and are not easy to use. If the number of parameters is more, a large number of experiments have to be performed. This problem is overcome in the Taguchi technique, which uses a special design of orthogonal arrays (OA) [4, 9] to study the entire parameter space with small number of experiments. The OA is a major tool used in the robust design, which is used to study many design parameters by means of a quality characteristic. The purpose of conducting an experiment based on OA is to determine the optimum level for each parameter and to establish the relative significance of individual parameters in terms of their main effects on the quality characteristic. The OA gives acceptable estimates of factor effects with reduced number of experiments when compared to the traditional methods.
Taguchi has tabulated 18 standard OAs, each comprising N _{0} (?N _{min}) number of trials for different numbers of factors and their levels, which can be directly used for the experimental plan [9]. However, Taguchi design allows defining different number of levels for each factor. In such situations, the mixed level OA need to be selected for the experimentation purpose. After a simple analysis and processing of the output results from experiments as per OA, an optimum combination of the factor values can be obtained. It is demonstrated in statistics that although the number of experiments is dramatically reduced, the optimal result obtained from OA usage is very close to that obtained from FFD.
The principle behind Taguchi robust design is to control the effect of variations caused by noise factors on product quality characteristic rather than controlling the source of noise itself [4, 9]. In order to minimize the variations in the quality characteristic, Taguchi introduced a method to transform the repetition data to signaltonoise (S/N) ratio (?), which is a measure of variation present in the scattered response data [4, 9]. The maximization of S/N ratio simultaneously optimizes the quality characteristic and minimizes the effect of noise factors.
 Smallerthebetter type:$$ \begin{aligned} \eta_{i} =  10\log &_{10} \left[ {\frac{1}{n}\sum\limits_{j = 1}^{n} {y_{j}^{2} } } \right]\;{\text{dB}} \\ {\text{ if }}y\,{\text{needs to be minimized}} .\\ \end{aligned} $$(7.19)
 Largerthebetter type:$$ \begin{aligned} \eta_{i} =  10\log &_{10} \left[ {\frac{1}{n}\sum\limits_{j = 1}^{n} {y_{j}^{  2} } } \right]\;{\text{dB}} \\ {\text{ if }}y\,{\text{needs to be maximized}}. \\ \end{aligned} $$(7.20)
Taguchi optimization procedure consists of analysis of means (ANOM) and ANOVA on S/N ratio of OA [4]. The ANOM is used to identify the optimal factor level combinations and to estimate the main effects of each factor. ANOM is also employed to find the effect of a factor level, which is the deviation it causes from the overall mean response. The optimal level for a parameter is the level, which results in highest value of S/N ratio in the experimental region. The ANOVA is used to estimate the error variance for the effects and variance of the prediction error. ANOVA is performed on S/N ratio to obtain the contribution of each of the factors.
After selecting the optimal levels of process parameters, the final step is to predict and verify the adequacy of the model for determining the optimum response [4, 9]. The confirmation experiments under the optimal conditions are then performed and the results with the predictions are compared. In order to judge the closeness of observed value of signaltonoise ratio with that of the predicted value, the variance of prediction error is determined and the corresponding twostandard deviation confidence limits for the prediction error of S/N ratio are calculated. If the prediction error is outside these limits, one should suspect the possibility that the additive model is not adequate. Otherwise, the additive model is adequate [4, 9].
7.3.1.1 Case Study: Taguchi Robust Design for Machining of MMC
Results of ANOVA of surface roughness
Cutting parameters  Degrees of freedom  Sum of squares  Mean square  Ftest  Percent contribution 

Cutting speed  2  60.70  30.38  28  12 
Feed rate  2  35.70  17.90  6.2  51 
Depth of cut  2  16.90  8.40  18.80  30 
Error  20  45.20  1.125  –  7 
Total  26  158.50  –  –  100 
7.3.2 Heuristic Search Algorithms
The heuristic algorithms are the modelbased optimization techniques i.e., by using the metamodels to obtain predictions of the phenomena of interest and then to find the best compromises among the objectives for the system through the latest nontraditional optimization tools like GA, SA, ACO and PSO.
7.3.2.1 Genetic Algorithms
The GA are nontraditional search algorithms that emulate the adaptive processes of natural biological systems [10]. Based on the survival and reproduction of the fittest, they continually search for new and better solutions without any preassumptions such as continuity and unimodality. The GA has been applied in many complex optimization and search problems, outperforming the traditional optimization and search methods.
The solution of the problem that GAs attempt to solve is coded into a string of binary numbers known as chromosomes. Each chromosome contains the information of a set of possible process parameters. Initially, a population of chromosomes are formed randomly. The fitness of each chromosome is then evaluated using an objective function after the chromosome has been decoded. Upon completion of the evaluation, either a roulette wheel method or selected control method is used to select randomly pairs of chromosomes to undergo genetic operations such as crossover and mutation to produce offspring for fitness evaluation. This process continues until a near optimal solution is found.
7.3.2.2 Simulated Annealing
The SA is also one of the nontraditional search and optimization techniques, which resembles the cooling process of molten metals through annealing [11]. The SA procedure simulates this process of annealing to achieve the minimization function value in a problem.
The algorithm begins with an initial point, m _{1} and a high temperature, T. A second point, m _{2} is created using a Gaussian distribution and the difference in the function values at these points (?E), is calculated. If the second point has a smaller value, the point is accepted; otherwise the point is accepted with a probability e ^{(–E/T)} [11]. This completes an iteration of the SA procedure. The algorithm is terminated when a sufficiently small temperature is obtained or a small enough change in the function value is observed.
7.3.2.3 Ant Colony Algorithm
The natural metaphor on which ant algorithms are based is ant colonies. The researchers are fascinated by seeing the ability of nearblind ants in establishing the shortest route from their nest to the food source and back. These ants secrete a substance, called pheromone, and use its trial as a medium for communicating information [12]. The probability of the trial being followed by other ants is enhanced by further deposition by others following the trial. This cooperative behavior of ants inspired the new computational paradigm for optimizing reallife systems, which is suited for solving largescale problems.
In the first step of ant colony algorithm (ACO), hundred solutions are generated randomly with parameters that satisfy the constraints. The initial solutions are classified as superior and inferior solutions. The following three operations are performed on the randomly generated initial solution: (1) random walk or cross over—90% of the solutions (randomly chosen) in the inferior solutions are replaced with randomly selected superior solutions, (2) mutation—the process whereby randomly adding or subtracting a value is done to each variable of the newly created solutions in the inferior region with a mutation probability and (3) trial diffusion—applied to inferior solutions that were not considered during random walk and mutation stages.
7.3.2.4 Particle Swarm Optimization
The PSO is a populationbased stochastic optimization technique, inspired by social behavior of bird flocking or fish schooling [13]. The PSO shares many similarities with evolutionary computation techniques such as GA. The system is initialized with a population of random solutions and searches for optima by updating generations. However, unlike GA, PSO has no evolution operators such as crossover and mutation.
In PSO, the potential solutions, called particles, fly through the problem space by following current optimum particles. Each particle keeps track of its coordinates in the problem space, which are associated with the best solution (fitness) it has achieved so far and the fitness value is stored. This value is called “pbest”. Another “best” value that is tracked by the particle swarm optimizer is the best value, obtained so far by any particle in the neighbors of the particle. This location is called “lbest”. When a particle takes all the population as its topological neighbors, the best value is a global best and is called “gbest”. The PSO concept consists of, at each time step, changing the velocity of (accelerating) each particle toward its “pbest” and “lbest” locations (local version of PSO). Acceleration is weighted by a random term, with separate random numbers being generated for acceleration toward “pbest” and “lbest” locations.
7.3.2.5 Case Study: Genetic AlgorithmsBased Optimization for Machining of MMC
This case study addresses the application of GA for optimizing the cutting conditions during turning of PMMC’s of type A356/20/SiCpT6 (continuous casting) in which the matrix is aluminum with 7% silicon, 0.4% magnesium, reinforced with 20% volume particles of SiC [14]. The material was subjected to heat treatment (solutionizing and aging T65h at 154°C). The average dimension of SiC particle is 20 microns.
Turning cutting conditions with PCD
S. No.  Cutting speed (m/min)  Feed rate (mm/rev) 

1  250  0.1 
2  350  0.1 
3  500  0.1 
4  700  0.1 
5  500  0.2 
6  500  0.05 
A Kistler piezoelectric dynamometer with appropriate load amplifier was used. Different programs for data acquisition have been developed and used based on Lab VIEW software. They allow continuous recording and simultaneous graphical visualization of evolution of cutting force, feed force and depth force. The tool wear was measured according to ISO 3685 with a Mitutoyo optical microscope, which has 30× magnification and 1 micron resolution. The surface roughness of turned workpiece was evaluated according to ISO 4287/1 with a HomeltesterT500 profilometer. The details of experimental results and discussion are given in Antonio and Davim [14].
The aim of the numerical model was to obtain the cutting conditions using GA. The controlled variables cutting speed (v), feed (f) and cutting time (t) assume the following discrete values: v = (v _{1}, v _{2}, …, v _{n}); f = (f _{1}, f _{2}, …, f _{n}) and t = (t _{1}, t _{2},…, t _{n}) with a genetic code to define. As reported in Antonio and Davim [14], the time interval is 39 min with fractions of 1 min and hence the design space is a typical discrete and nonconvex search domain. Each chromosome has three genes and each gene represents code value for each variable on a turning operation according to above discrete values. The various outputs considered in this study are cutting force (F _{c}), feed force (F _{f}), depth force (F _{d}), tool wear (V _{b}), average surface roughness (R _{a}) and peak to valley height (R _{t}).
Subject to constraints, V _{b} < 0.3 mm; R _{a} < 1 ?m.
Where, \( t^{*} = \frac{t}{{t^{\max } }} \)is the normalized cutting time.
The details of genetic operations, namely, selection, crossover and mutation are given in Antonio and Davim [14]. A population of eight chromosomes are considered in GA and search is based on best solutions with N _{A} = 2 and N _{c} = 1 is considered for mutation operator. The constraints are penalized by ? _{0} = 1% and ? _{1} = 5%. The constraint violations considered are: For V _{b}, d _{0} = 0.003 mm, d _{1} = 0.03 mm; For R _{a}, d _{0} = 0.05 microns, d _{1} = 0.1 microns. The optimal cutting conditions are found to be cutting speed (v) = 350 m/mi, feed (f) = 0.1 mm/rev and cutting time (t) = 19 min. It was concluded that the optimal cutting conditions of turning operation obtained through GA optimization demonstrate the potential of mixed numericalexperimental mode.
7.4 Conclusion
The modeling based on RSM and ANN have been extensively used in the machining processes. The RSM coupled with DOE is a collection of mathematical and statistical technique not only reduces the cost and time, but also gives the required information about the main and interaction effects of the factors with minimum number of experiments. On the other hand, ANN is a powerful modeling tool; mainly deals with complex and nonlinear problems and can provide accurate results in machining process.
Two case studies based on modeling approaches involving the machinability investigations during turning of MMC with PCD tool were presented. The first investigation is on RSM modeling to study the influence of cutting speed and feed on machining force, cutting power and specific cutting force. The twofactor interaction effects on machinability characteristics were studied by generating 3D response surface plots. The ANNbased modeling for predicting the surface roughness during turning of MMC is detailed in the second case study. A MLP model trained by EBPTA has been used to capture the relationship between cutting speed, feed and depth of cut on surface roughness.
The main advantage of Taguchi robust design (TRD) is to make the process performance measure less sensitive to noise factors. The TRD employs OA for conducting the experiments and signaltonoise (S/N) ratio as the objective function for optimization. In Taguchi method, analysis of means (ANOM) is used to identify the optimum level factor combinations and ANOVA is employed to estimate the relative significance of each factor on performance measure. The case study demonstrating the application of Taguchi method for determining the optimal process parameter settings of cutting speed, feed rate and depth of cut to minimize the surface roughness during turning of MMC is presented in this chapter.
The conventional optimization techniques such as gradientbased methods do not function effectively and are not suitable for solving multiobjective optimization problems. Hence, a number of heuristic algorithms such as GA, SA, ACO and PSO have been proposed for obtaining optimal solutions for multiobjective problems. The multiobjective optimization in machining of MMC using GA concept is illustrated in this chapter, which consists of a stochastic strategy of direct search that stimulates the genetic process of evolution.
Notes
Acknowledgements
The authors would like to thank Elsevier and SAGE publications for granting permission for reuse of the published materials.
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