The optimization problem in machining is highly non-linear and possessess multiple solutions. The selection and optimization of process parameters in machining are most important as it influences the production rate, tool life, surface finish etc.
Optimization during metal cutting is the determination of the optimal set of operating conditions to satisfy an objective within the operation constraints. A number of objective functions to measure the optimality of machining conditions are: (1) minimum unit production cost, (2) maximum production rate, (3) maximum profit rate and (4) weighted combination of several objective functions. Several cutting constraints are to be considered in machining such as tool-life constraint, cutting force constraint, power constraint, stable cutting region constraint, chip-tool interface temperature constraint, surface finish constraint, roughing and finishing parameter relation constraint etc. Although more numbers of papers are available in the literature on the optimization of process parameters, the selection of suitable cutting tool and cutting fluid also forms an important part of optimization.
In an earlier work, Gilbert [1950] presented a theoretical analysis of the optimization of the machining process using two criteria, maximum production rate and minimum cost for single pass turning keeping feed and depth of cut fixed. In his analysis, he did not consider the surface roughness aspect. Ermer [1971] and
Petropoulos [1973] used geometric programming for the optimization of the constrained machining economics. In a geometric programming, the objective function and constraints are expressed as posynomials. Ermer [1971] considered the minimization of unit production cost of a turning operation subjected to different constraints like available speeds, feeds and horsepower as well as desired surface finish and dimensional deviation. Petropoulos [1973] also used geometric programming for optimal selection of machining rate variables and optimize the constrained unit cost problem in turning. He considered the following constraints:
(a) the maximum cutting power available, (b) the surface roughness required, (c) the maximum cutting force permitted by the machine tool, (d) the maximum feed rate and rotational speed available from the machine tool. The author used the basic model describing the cost to produce a work piece (unit cost) by turning a job, as given by cost of operating time, tool cost and machining cost. Lambert and Walvekar [1978] used geometric programming for the optimization of machine variables to yield minimum production cost. They considered force, power and surface finish as constraints. The procedure developed by the authors provided simultaneous determination of the machining parameters that minimized the cost and satisfied constraints on the machining parameters.
Shin and Joo [1992] presented a model for the optimization of machining conditions in a multipass turning operation considering both rough and finish cutting operation. The authors adopted the minimum unit production cost as objective and cutting speed, feed and depth of cut were used as system variables. The constraints considered by them were parameter constraints (maximum and minimum values of process parameter), tool life constraints and operating constraints (cutting force constraint, power and surface finish constraint). Their model was verified with a hypothetical problem.
Gupta et al. [1995] achieved the minimization of total production cost by summation of the minimum cost of individual rough passes and finish pass. The authors used integer-programming model for obtaining the optimal subdivision of total depth of cut along with the selection of speed and feed. They used two steps for the minimization of total production cost considering fixed depth of cut and optimal combination of depth of cut for rough passes and finish pass. A new mathematical
model for determining machining parameters by minimizing total production cost in multipass turning with various constraints was presented by Al-Ahmari [2001]. The author had obtained the lowest minimum production cost compared to Shin and Joo [1992] and Gupta et al. [1995]. Yeo [1995] used sequential quadratic programming for optimizing the total production cost for obtaining optimal cutting parameters in finish pass and rough passes. Lee and Tarng [2000] used polynomial network and sequential quadratic programming to obtain the optimal cutting parameters in multipass turning. They considered the maximization of production rate and minimization of production cost.
Yang and Tang [1998] used Taguchi method, which is a special design of orthogonal array to find the optimal cutting parameters for turning operations. Signal to noise (S/N) ratio and analysis of variance (ANOVA) were used to investigate the cutting characteristics. The greatest S/N ratio level provides the optimal level of process parameters and ANOVA is performed to find out which process parameters are statistically significant.
In recent years, non-traditional optimization techniques have been applied to turning process optimization. Among the various techniques, neural network, simulated annealing, genetic algorithm, ant colony algorithm etc. have become more popular. Wang [1993] used neural network using manufacturer’s fuzzy preferences to determine the optimum cutting parameters by solving the multi-objective problem. Productivity, operation cost and cutting quality were considered the objectives. Lee et al. [1999] and Hashmi et al. [1999] used fuzzy logic model to optimize cutting conditions for machining. Chen and Tsai [1996] and Baykasoglu and Dereli [2002] applied simulated annealing algorithm in turning for obtaining optimum process parameters. They had considered several practical constraints in their model. Alberti and Perrone [1999] used fuzzy probabilistic formulation in multipass turning and optimized the resulting possibilistic model using genetic algorithm. They considered a limited number of cutting constraints in their problems. Onwubolu and Kumalo [2001] had also used genetic algorithm for determining the optimal machining parameters that minimize the production cost.
The authors had developed a new local search optimization based genetic algorithm
approach in their model. Finally, they validated the model taking some hypothetical example problems and compared their result with some other model.
An optimization technique based on ant colony algorithm was proposed by Vijaykumar et al. [2003] for solving multipass turning optimization problems.
Optimum cutting parameters were obtained by minimizing the unit production cost considering various practical constraints. Karpat and Ozel [2005] developed a multi- objective optimization model using particle swarm optimization (PSO) based neural network for the prediction of surface roughness and tool wear during single pass turning. The PSO is used to obtain optimum cutting speed, feed and tool geometry.
Sinivas et al. [2007] also used PSO technique to optimize multipass turning process to minimize total production cost using several cutting constraints. The PSO provides optimal feasible solutions within a reasonable computational time.
An optimization technique has been proposed by Amiolemhen and Ibhadode [2004] based on genetic algorithms for the determination of the cutting parameters in multi-pass machining operations by simultaneously considering multi-pass roughing and single-pass finishing operations. The optimum machining parameters are determined by minimizing the unit production cost considering many practical constraints. The model is found effective and efficient when compared with experimental results. Abburi and Dixit [2007] developed an optimization method, which is a combination of a real-coded genetic algorithm (RGA) and sequential quadratic programming (SQP) to obtain Pareto-optimal solutions to minimize the production cost and production time. The model had a major advantage that various Pareto-optimal solutions are generated without the knowledge of the cost data. Kim et al. [2008] also explored the applicability of RGA in machining optimization. Ojha et al. [2009] optimized different parameters in multipass turning using neural network, fuzzy sets and genetic algorithms. Neural network has been used for the prediction of surface finish and tool life. The developed optimization model was applied for minimization of production cost and maximization of production rate.
The optimization of machining processes has been widely investigated with a number of techniques. However, the shop floor application of these methods is still a difficult task due to lack of proper machining model. For practical applicability of
the optimization methods, the robust machining models have to be integrated with these methods. Soft computing can play an important role in this task.