STUDY ON OPTIMIZATION OF MACHINING PARAMETERS IN TURNING PROCESS USING EVOLUTIONARY ALGORITHM WITH EXPERIMENTAL VERIFICATION

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1 International Journal of Mechanical Engineering and Technology (IJMET), ISSN (Print) ISSN (Online) Volume 2 Number 1, Jan - April (2011), pp IAEME, International Journal of Mechanical Engineering and Technology (IJMET), ISSN (Print), IJMET I A E M E STUDY ON OPTIMIZATION OF MACHINING PARAMETERS IN TURNING PROCESS USING EVOLUTIONARY ALGORITHM WITH EXPERIMENTAL VERIFICATION Ganesan.H Department of Mechanical Engineering, RVS College of Engineering & Technology, Coimbatore, Tamilnadu, India. ganeshmelur@yahoo.co.in ABSTRACT Mohankumar.G Park College of Engineering & Technology, Coimbatore, Tamilnadu, India.,. Optimization of cutting parameters is one of the most important elements in any process planning of metal parts. Economy of machining operation plays a key role in competitiveness in the market. Turning machines produce finished components from cylindrical bar. Finished profile from a cylindrical bar is done in two stages, rough machining and finish machining. Generally more than one passes are required for rough machining and single pass is required for finishing. The machining parameters in multipass turning are depth of cut, cutting speed and feed. The machining performance is measured either by the minimum production time or minimum cost. In this paper the optimal machining parameters for continuous profile machining turning are determined with respect to the minimum production cost, subject to a set of practical constraints, cutting force, power, dimensional accuracy and surface finish. Due to complexity of this machining optimization problem, genetic algorithm (GA) and particle swarm optimization are applied and results are compared. Key words: Optimization, multipass turning, machining parameters, genetic algorithm and particle swarm optimization. 1. INTRODUCTION It has long been recognized that conditions during cutting, such as feed rate, cutting speed and depth of cut should be selected to optimize the economics of machining operations, as assessed by productivity, total manufacturing cost per component or some other suitable criterion. Agapiou [1] formulated machining parameter optimization problem considering both multi-pass rough machining operations and single-pass finishing. Production cost and total time were taken as objectives and a weighting factor was assigned to prioritize the two objectives in the objective function. The author optimized the number of passes, depth of cut, cutting speed and feed rate in his model, through a multi-stage solution process called dynamic programming. Several physical constraints were considered and applied in this model. In his solution methodology, every cutting pass is considering as independent of the previous pass, hence the optimality for each pass is not reached simultaneously. Ruy Mesquita [2] used the Hook Jeeves search method for finding the optimum operating parameters. Shin and Joo [3] have presented a model for multipass turning in their research, only the straight turning process, i.e. cutting a component in the longitudinal direction to 11

2 produce a constant part diameter was discussed. The finished component from CNC, in an FMS environment contains a continuous profile. The continuous profile consists of straight turning, facing, taper turning, convex and concave circular arcs. Yellowley et. al [4] have shown that for both turning and milling operations the optimal subdivision of depth of cut may be determined without knowledge of the relevant tool life equation. Calculation of machining parameters in turning operation using machining theory was carried out by Menget et. al [5]. The objective criteria used in this work was minimum cost. Prased et. al [ 6] have used the combination of geometric and linear programming techniques for solving multi-pass turning optimization problem as part of a PC-based generative Computer Aided Process Planning (CAPP) system. Onwubolu et.al[7] had used a genetic algorithm for optimizing multipass turning operations. Multipass turning optimization with optimal subdivision of depth of cut was developed by Gupta et al. [8]. Saravanan et al. [9] have developed a new model based on genetic algorithm and simulated annealing for optimizing machining parameters for turning operation. Bhaskara Reddy et al. [10] have used genetic algorithm to select optimal depth of cut to achieve minimum production cost in multi-pass turning operations. M. C. Chen et al. [11] have developed an optimization model for a continuous profile using simulated annealing approach. In this machining model, straight turning, taper turning, and circular turning were simultaneously considered. James Kennedy et.al. [12] have developed particle swarm optimization which is a population-based search procedure that could yield global optimum solution. K. Choudhri et al. [13] have also suggested genetic algorithm to find the optimum machining conditions in turning. In this work, two objective functions, namely unit production time and unit production cost, were optimized after satisfying few practical constraints. Ramon Quiza Sardinas et al. [14] have also used genetic algorithm for multiobjective optimization problem. The two conflicting objectives are to increase tool life and decrease operation time. Vijayakumar et al. [15] have applied ant colony algorithm to find optimal machining parameters for multi-pass turning operation and also found that the proposed algorithm outperformed the adopted genetic algorithm. Most of the researchers in the area of machining have used various techniques for finding the optimal machining parameters for single and multipass turning operations. Traditional techniques are not efficient when the practical search space is too large. Considering the drawbacks of traditional optimization techniques, The following table shows the some of the objective functions and constraints considered Sl. No. 1 Tool Used genetic algorithms (GA) Objective Functions Considered a) Minimum Production time b) Minimum Production cost Constraint Considered a) Power b) Surface finish c) Cutting force Year of Publica tions (2001) 2 GA & SA a) Minimize the cost a) Cutting speed b) Cutting force c) power d) Chip tool inter face e) Dimensional Accuracy f) Surface Finish (2003) 12

3 3 Genetic algorithm a) Minimum Production cost a) Tool life b) Cutting force c) Power d) Stable cutting region e) Dimensional accuracy (2005) 4 Genetic algorithm a) Production rate b) Tool rate a) Depth of cut b) Feed rate c) Cutting speed d) Cutting force e) Cutting power f) Surface roughness (2006) This paper attempts to determine the optimal machining parameters for machining of a continuous finished profile from bar stock to minimize the production cost using (GA) and (PSO) and the result are compared. 2. PROBLEM FORMULATION Turning is a metal cutting process in which job is held and rotated in a chuck, the cutting tool enters and leaves the work piece. The finished component is obtained by a number of rough passes and a finish pass. The roughing operation is carried out to machine the part to a size that is slightly larger than the desired size, in preparation for the finishing cut. The finishing cut is called single-pass contour machining, and is machined along the profile contour, a roughing stages and a finished stage are considered to machine the component from the bar stock. The roughing stage consists of (n-1) passes where n is the total number of roughing passes, and the last pass of roughing removes the material along the profile contour. In the finish stage material (amount of finish allowance) is removed along the contour of the profile. The machining time is considered in this work for finding the performance of the machining operations under practical constraints. The length of cutting path is calculated for each pass in the roughing and finishing stages. Then the cutting time for each pass is calculated for these stages. The objective of this research is to minimize the production cost. 2.1 Model for Machining Performance The objective of this model is to minimize the production cost which includes machining cost, machine idle cost, the tool replacement cost and the tool cost. The formula for calculating the above cost is as given by Chen and Su. Finally, by using the above mathematical processes, the unit production cost UC ($/piece) can be obtained as UC=CM + CI + CR + CT =kot M + kot1 + k o (t o T m /t l )+K t T m /t e where CM _ cutting cost ($/piece) CI _ machine idling cost ($/piece) CR _ tool replacement cost ($/piece) CT _ tool cost ($/piece) ko _ sum of direct labour cost and overhead ($/min) TM _ actual cutting time TI _ machine idle time (min) tl _ tool life (min) te _ time required to exchange a tool (min) kt _ cutting edge cost ($/edge) 13

4 Machining cost can be reduced by optimally selecting the machining parameters. In this work the equation is considered as objective function and is minimized using optimization. In this optimization, following constraints are considered. 2.2 Machining Constraints The practical constraints imposed during the roughing and finishing operations as described by Chen and Su are given below Parameter Bounds Bounds on cutting speed: V rl V r V ru where V rl and V ru are the lower and upper bounds of cutting speed in roughing, respectively. Bounds on feed: f rl < f r < f ru where f rl and f ru are the lower and upper bounds of feed in roughing, respectively. Bounds on depth of cut: d rl < d r < d ru where d rl and d ru are the lower and upper bounds of depth of cut respectively. Similarly the above parameter are also considered for finishing Cutting force The cutting force experienced by the work piece during machining will deform the work piece, try to unclamp the work piece from holding devices and also deflect the tool and tool holder. Hence the cutting force should not exceed certain value(amount) during machining. The expression for the cutting force constraint is given by Fr = kf fr F U where Fr is the cutting force during rough machining, kf, and v are the constants pertaining to a specific tool-workpiece combination, and F U is the maximum allowable cutting force (kgf) Power Constraint The power available for the spindle is limited, the power constraint is given by P r = P U where P r is the cutting power during rough machining (kw), η is the power efficiency, and P U is the maximum allowable cutting power (kw) Dimensional Accuracy Constraint The accuracy of the machined size not to be compromised beyond certain value. The regression relation for calculating the dimensional accuracy is given below: δ = f d V where δ is the dimensional accuracy, f is the feed rate per revolution, d is the depth of cut, and V is the cutting speed Surface Finish Constraint The certain amount of surface finish is to be maintained for the machined surface after finish cut. The maximum allowable surface roughness is calculated as per equation given by [ ] functional requirement. Surface roughness is influenced by the feed and the nose radius of the tool: where r is the nose radius of cutting tool (mm), R max is maximum allowable surface roughness (µ m ) and fs is the feed in finish cut. 14

5 3. SOLUTION METHODOLOGY The objective function and its constraints discussed in the previous section are non linear and complex. The optimization of machining parameter using conventional optimization technique is difficult. Genetic algorithms (GA) and Particle Swarm Optimization (PSO) are best population search based technique. 3.1 Genetic Algorithm Methodology Genetic algorithms are computerized search and optimization algorithms based on the mechanics of natural genetics and natural selection. Optimization can be done by the generation of the population. Genetic algorithms (GA) are a best population search based technique. GA are different from traditional optimizations in the following ways. 1. GA goes through solution space starting from a group of points and not from a single point. 2. GA search from a population of points and not a single point. 3. GA use information of a fitness function, not derivatives or other auxiliary knowledge. 4. GA use probabilistic transitions rules, not deterministic rules. 5. It is very likely that the expected GA solution will be a global solution. In this paper the cutting conditions are encoded as genes by binary encoding to apply GA in optimization of machining parameters. A set of genes is combined together to form chromosomes, used to perform the basic mechanisms in GA, such as crossover and mutation.. GA optimization methodology is based on machining performance predictions models developed from a comprehensive system of theoretical analysis, experimental database and numerical methods. The GA parameters along with relevant objective functions and set of machining performance constraints are imposed on GA optimization methodology to provide optimum cutting conditions. The following steps are used this methodology 1. Choose a coding to represent problem parameters, a selection operator, a crossover operator, and a mutation operator. Choose population size n, crossover probability pc, and mutation probability pm. Initialize a random population of strings of size l. Choose a maximum allowable generation number t max. Set t = Evaluate each string in the population. 3. If t tmax or other termination criteria are satisfied, terminate. 4. Perform reproduction on the population. 5. Perform crossover on pair of strings with probability pc. 6. Perform mutation on strings with probability pm. 7. Evaluate strings in the new population. Set * = t + 1 and go to Step 3. Implementation of GA with Numerical Illustration Implementation is plays an vital role in the genetic algorithm. A problem can be solved once it can be represented in the form of a solution string (chromosomes). The bits (genes) in the chromosome could be binary, real integer numbers. In this work, the cutting speed, feed rate and depth of cut are considered to be the primary parameters for the turning operation. Each of these primary variables is represented in a binary string format. The total length of the string is 18 in which first 6 bits are used for speed representation and next 6 bits represent the feed variable and the remaining 6 bits are used as depth of cut parameter. The speed, feed and depth of cut are represented as substrings in the chromosome. The strings ( ) and ( ) represent the lower and upper limits of speed, feed and depth of cut. Genetic Algorithm Parameters Population size: 32 Length of Chromosome: 6 Selection operator: Rank order Crossover operator: Single point operator Crossover probability:

6 Mutation probability: 0.1 Fitness parameter: Operation time Initialization During initialization, a solution space of a population size solution string is generated randomly between the limits of the speed, feed and depth of cut. In this work the solution space size (population size) is considered as 18 as shown in Table 1. Columns 1, Column 2 and 3 show the initial random binary population. Column 4 show the objective function output (Optimized output). Here the binary format population can be decoded by using the below formula. x i = x i (L) + (decoded decimal value) where xi is the decoded speed or feed or depth of cut, x(l) i is the lower limit of speed or feed or depth of cut, x(u) i is the upper limit of speed or feed or depth of cut, and n is the substring length (= 6). Evaluation In a GA, a fitness function value is computed for each string in the population, and the objective is to find a string with the maximum fitness function value. It is often necessary to map the underlying natural objective function to a fitness function form through one or more mappings. Since, we use a minimization objective function, the following transformation is used f(x) = where g(x) is the objective function (Operation time) and f(x) is the fitness function. In the minimization problem the string which has the higher fitness value will be the best string. Selection and Reproduction Reproduction selects good strings in a population and forms a mating pool. The reproduction operator is also called a selection operator. In this work rank order selection is used. In Table 1 Column 4 shows the output generated using this method. Column 5 is the corresponding rank of the string. A lower ranked string will have a lower fitness value or a higher objective function and vice versa. The higher cumulative probability value in the range is chosen as one of the parents. In Table 1 for the first string the generated random number is The string number (rank) 1, which has a cumulative probability of , is selected as the parent, and this process is repeated for the entire population. Crossover Crossover is a mechanism for diversification. The strings to be crossed and the crossing points are selected randomly and crossover is done with a crossover probability. A single-point crossover is used in this work. The crossover probability is The concept of crossover is explained below. Before crossover: After crossover: 1&2 9 means crossover takes place between 1st and 2nd string at (9 + 1)th cross site and after the (9 + 1)th bit all the information is exchanged between strings. The cross site number starts from zero. Hence cross site number 9 represents the 10th site Mutation Mutation is a random modification of a randomly selected string. Mutation is done with a mutation probability of 0.1. Before mutation: _0_111 16

7 After mutation: 1 9 means that mutation takes place at the 1st string at the 9th site. The mutation will invert from 0 to 1 or 1 to 0 at the particular site _1_111 The output after the first iteration is given in Table 2. The best string in the list is the chromosome rank 1 which has minimum unit production cost. This completes one iteration of the GA and the best value is stored. All the strings available at the end of first iteration will be treated as parents for the second iteration. This procedure is repeated for the number of iterations as given by the user. In this example, x (L) i = 50 for speed x (U) i = 3500 for speed x (L) i = 0.01for feed x i (U) = 0.4 for feed x (L) i =0.3 for depth of cut x (U) i = 1.5 for depth of cut Table 1 speed feed dept cut Unit Cost Table 2 speed feed dept cut Unit Cost Output Figure 1 17

8 3.2 Particle Swarm Optimization (PSO) In this proposed algorithm we are using single-objective PSO to optimization problems. PSO Algorithm 1. For i = 1 to M (M is the population size) a. Initialize P[i] randomly (P is the population of particles) b. Initialize V[i] = 0 (V is the speed of each particle) c. Evaluate P[i] d. Initialize the personal best of each particle PBESTS[i] = P[i] e. GBEST = Best particle found in P[i] 2. End For 3. Initialize the iteration counter t = 0 4. Store the vectors found in P into A (A is the external archive that stores solutions found in P) 5. Repeat a. Compute the crowding distance values of each solution in the archive A b. Sort the solutions in A in descending crowding distance values c. For i = 1 to M i. Randomly select the global best guide for P[i] from a specified top portion (e.g. top 10%) of the sorted archive A and store its position to GBEST. ii. Compute the new velocity: V[i] = W x V[i] + R1 x (PBESTS[i] P[i]) + R2 x (A[GBEST] P[i]) (W is the inertia weight equal to 0.4) (R1 and R2 are random numbers in the range [0..1]) (PBESTS[i] is the best position that the particle i have reached) (A[GBEST] is the global best guide for each solution) iii. Calculate the new position of P[i]: P[i] = P[i] + V[i] iv. If P[i] goes beyond the boundaries, then it is reintegrated by having the decision variable take the value of its corresponding lower or upper boundary and its velocity is multiplied by -1 so that it searches in the opposite direction. v. If (t < (MAXT * PMUT), then perform mutation on P[i]. (MAXT is the maximum number of iterations) (PMUT is the probability of mutation) vi. Evaluate P[i] d. End For e. Insert all new solution in P into A if they are not dominated by any of the stored solutions. All dominated solutions in the archive by the new solution are removed from the archive. If the archive is full, the solution to be replaced is determined by the following steps: i. Compute the crowding distance values of each solution in the archive A ii. Sort the solutions in A in descending crowding distance values iii. Randomly select a particle from a specified bottom portion (e.g. lower 10%) which 258 comprise the particles in the archive then replace it with the new solution f. Update best solution of each particle in P. If the current PBESTS dominates the position in memory, the particles position is updated using PBESTS[i] = P[i] g. Increment iteration counter t 6. Until maximum number of iterations is reached 18

9 Generate initial population Evaluate initial particles to get Update velocities for all the particles Update particle position Evaluate the updated particle to get No Stop criteria Yes Print the Gbest particle End Figure 2: The algorithm for Particle Swarm Optimization Global Best Selection The selection of the global best guide of the particle swarm is a crucial step in a PSO algorithm. It affects both the convergence capability of the algorithm as well as maintaining a good spread of solutions. We want to ensure that the particles in the population move towards the sparse regions of the search space. In PSO the global best guide of the particles is selected from among those solutions with the best values. Mutation The mutation operator of PSO was adapted because of the exploratory capability it could give to the algorithm by initially performing mutation on the entire population then rapidly decreasing its coverage over time. This is helpful in terms of preventing premature convergence due to existing local Pareto fronts in some optimization problems. Constraint Handling In order to handle constrained optimization problem PSO due to its simplicity in using feasibility and the solutions when comparing final output. A solution is said to constraineddominate a solution j if any of the following conditions is true: 19

10 1. Solution i is feasible and solution j is not. 2. Both solutions i and j are infeasible, but solution i has a smaller overall constraint violation. 3. Both solutions i and j are feasible and solution i dominates solutions j. When comparing two feasible particles, the particle which dominates the other particle is considered a better solution. On the other hand, if both particles are infeasible, the particle with a lesser number of constraint violations is a better solution. The Time Complexity of PSO The computational complexity of the algorithm is dominated by the objective function Operation time and Unit of Cost in the archive. If there are M objective functions and N number of solutions (particles) in the population, then the objective function computation has O(MN) computational complexity. If there are K solutions in the archive, sorting the solutions in the archive has O(M K log K) computational complexity. Output: Table 3 Unit speed feed dept cut Cost TEST EXAMPLE For testing the proposed methodology, the component shown in Fig.3 is considered. The component is to be machined with optimal speed and feed using an SUPER JOBBER LM CNC turning centre in an industry. The work piece material is EN 8 and the tool material is a carbide tip. The proposed model is run on an FANUC OI TD computer using the C++ language. Tables and graphs summaries the computational results. Number of roughing cuts - 11 Depth of cut for finishing mm Figure 3. Test Component 5. RESULTS AND DISCUSSION The GA optimization is done for 500 iterations. The results obtained from GA optimization are given in Table 1. The optimal cutting parameters such as speed, feed and depth of cut obtained from GA for the minimum cost of Figure 2 shows the fitness obtained in each iteration of the GA. The graph shows that the GA produces smooth fitness at the initial iteration and varying fitness in the subsequent iterations. The GA and PSO Optimization is coded in C++ language. The optimal cutting parameters such as speed, feed and depth of cut and constraints are considered in PSO and the result obtained with the minimum cost of shown in Table 3 20

11 6. CONCLUSION All types of CNC machines have been used to produce continuous finished profiles. A continuous finished profile has many types of operations such as facing, taper turning and circular turning. To model the machining process, several important operational constraints have been considered. These constraints were taken to account in order to make the model more realistic. A model of the process has been formulated with non-traditional algorithms; GA and PSO have been employed to find the optimal machining parameters for the continuous profile. PSO produces better results. Using this technique production cost can be further minimized. The results show that the production cost is minimized by using the optimized machining parameter. REFERENCES 1. Agapiou,( 1992) The optimization of machining operations based on a combined criterion, Part-1: the use of combined objectives in single pass operations, ASME Journal of Engineering for Industry, 114, pp ,. 2. Ruy Mesquita et al.(1995), Computer aided selection of optimum machining parameters in multi pass turning, International Journal of Advanced Manufacturing technology, 10, pp Y. C. Shin, Y. S. Joo, (1992)"Optimization of machining conditions with practical constraints", Int. J. Prod. Res., vol. 30, no. 12, pp ,. 4. I. Yellowley et al.( 1992), The optimal subdivision of cut in multi pass machining operation, International Journal of Material Processing Technology, 27, pp ,. 5.Q. Meng et al. (2000), Calculation of optimum cutting condition for turning operation using a machining theory, International Journal of Machine Tool and Manufacture, 40,pp ,. 6 A. V. S. R. K. Prasad et al.( 1997), Optimal selection of process parameters for turning operations in a CAPP system, International Journal of Production Research, 35, pp ,. 7. G. C. Onwubolu et al. (2001), Multi-pass turning operations optimisation based on genetic algorithms, Proceedings of Institution of Mechanical Engineers, 215, pp , 8. R. Gupta et al.,(1995) Determination of optimal subdivision of depth of cut in multi-pass turning with constraints, International Journal of Production Research, 33(9), pp , 9.R. Saravanan et.al (2003)Machining Parameters Optimisation for Turning Cylindrical Stock into a Continuous Finished Profile Using Genetic Algorithm (GA) and Simulated Annealing (SA) Int J Adv Manuf Technol 21:1 9, 10. Bhaskara Reddy SV, Shunmugam MS, Narendran TT (1998) Optimal subdivision of the depth of cut to achieve minimum production cost in multi-pass turning using a genetic algorithm. J Mater Process Technol 79: , 11.M. C. Chen and C. T. Su,(1998) Optimization of machining conditions for turning cylindrical stocks into continuous finished profiles, International Journal of Production Research, 36(8), pp , 12. James Kennedy and Russell Eberhart (2000)"Particle swarm optimization", Proceeding of IEEE International Conference on Neural Networks, IV, pp. 1,942 1, Choudhri K, Prathinar DK, Pal DK, (2002) Multi objective optimization in turning using a genetic algorithm. J Inst Eng 82:37 44, 14.Ramon Quiza Sardinas, Santana MR, Brindis EA (2006) Genetic algorithm-based multiobjective optimization of cutting parameters in turning processes Published in Engineering Applications of Artificial Intelligence Vijayakumar K, Prabhaharan G, Asokan P, Saravanan R (2003) Optimization of multipass turning operations using ant colony system. Int J Mach Tools Manuf 43: , 16.Kalyanmoy Deb, (1996). Optimizations for engineering design Algorithm and examples, Prentice-Hall of India, New Delhi 21