Int J Adv Manuf Technol (2011) 54:445–463 DOI 10.1007/s00170-010-2958-y
ORIGINAL ARTICLE
Particle swarm optimization technique for determining optimal machining parameters of different work piece materials in turning operation S. Bharathi Raja & N. Baskar
Received: 27 January 2010 / Accepted: 20 September 2010 / Published online: 12 October 2010 # Springer-Verlag London Limited 2010
Abstract Empirical models for machining time and surface roughness are described for exploring optimized machining parameters in turning operation. CNC turning machine was employed to conduct experiments on brass, aluminum, copper, and mild steel. Particle swarm optimization (PSO) has been used to find the optimal machining parameters for minimizing machining time subjected to desired surface roughness. Physical constraints for both experiment and theoretical approach are cutting speed, feed, depth of cut, and surface roughness. It is observed that the machining time and surface roughness based on PSO are nearly same as that of the values obtained based on confirmation experiments; hence, it is found that PSO is capable of selecting appropriate machining parameters for turning operation. Keywords Turning . Machining parameters . Particle swarm optimization . Machining time . Surface roughness . Various work piece materials Nomenclature v Cutting speed m/min f Feed rate mm/rev tm Machining time seconds SR Surface roughness μm
S. Bharathi Raja (*) School of Mechanical Engineering, SASTRA University, Thanjavur, Tamil Nadu Pin 613 401, India e-mail:
[email protected] N. Baskar Department of Mechanical Engineering, M.A.M College of Engineering, Tiruchirappalli, Tamil Nadu Pin 621 105, India e-mail:
[email protected]
D d K, a, b, c L
Outside diameter mm Depth of cut mm Empirical constant Length of the part mm
1 Introduction Computerized numeric controlled (CNC) machine could able to increase its productivity or profit for the manufacturing industry because of its ability to finish a job in minimum possible time and also achieves greater savings in money. This appreciation is feasible only if the computer aided process planning (CAPP) is made to perform efficiently. The performance of CAPP mainly depends on the proper selection of machining parameters of the machine tool. Based on the information obtained from literature and industry, it is clear that the recommended machining parameters from hand books for any machining operations does not suits exactly for a particular machine tool, material and other combinations. The recommended machining parameters from handbooks are just information to perform the operation and may be helpful for researchers in doing theoretical investigation. Many researchers involved themselves in theoretical verification of optimal machining parameters found using optimization techniques over the method of selecting machining variables by handbook or by previous work experience of the operator. Very few researchers conducted experiments on a CNC machine tool to study the characteristic behavior of the machining parameters on machining time. In the present work, apart from finding optimal machining parameters using PSO, the same values have been given as cutting parameters to the CNC turning
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machine to validate the acquired values of PSO. One of the objectives of the present work is to develop a generalized optimization method for various types of materials and machining problems. This generalized method should be able to solve actual manufacturing applications and deliver a solution to the global optimum. For a turning process, the objectives of producing good surface roughness and minimum machining time are conflict in nature. The counter balance of these objectives mainly depends on exact selection of cutting speed, feed and depth of cut. The complex interrelations between the machining parameters can be studied by actually conducting experiments on a CNC lathe in order to evaluate the performance measures such as surface roughness and machining time. In this work, machining experiments were conducted on four different types of work pieces such as brass, aluminum, copper and mild steel. The tool material is tungsten carbide insert. The objectives of this work are (1) to study the effect of machining parameters on various work piece materials (2) to implement an optimization technique that could give global optimum machining parameters to minimize machining time and to achieve required surface roughness value and (3) to validate the ability of the implemented technique with a turning operation. The implemented optimization technique replaces the tedious process of machining parameters selection by trial and error method. Comparisons are made between the results of the implemented technique and the results of experiments conducted and its relation are also presented and discussed.
2 Literature review Cemal Cakir et al. [1] described a procedure to calculate the machining conditions for turning operation with minimum production cost as the objective function. The authors determined production time and cost for different work piece and tool material for the same input data. Meng et al. [2] described a machining theory to calculate optimum cutting condition in turning for minimizing cost or maximizing production rate. Lee et al. [3] developed a self-organizing adaptive modeling technique to find the relationship between cutting speed, feed, depth of cut and surface roughness, cutting force, and tool life. Wang et al. [4] verified the developed optimization strategies with CAM software and also shown the economic benefits of using optimization for single pass turning operation. RongTsu Wang et al. [5] used geometric programming principle to develop a solution method that is able to derive the interval unit production cost with interval parameters. Alakesh Manna et al. [6] described the procedure for obtain
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machining condition of turning operation by considering unit cost of production using dynamic programming technique and also investigated the influence of cutting parameters on surface roughness. James Kennedy et al. [7] developed PSO, which is a population based search procedure that could yield global optimum solution. Juan et al. [8] investigated the optimal cutting parameters for minimizing production cost on rough machining of high speed milling operation. The mathematical model was constructed based on polynominal network. Uros Zuperl et al. [9] developed neural network to describe the multi-objective optimization of cutting conditions for machining. Franci Cus et al. [10] proposed Genetic algorithm for the determination of cutting parameters to reduce production cost and time. Experimental result shows that proposed Genetic algorithm is effective and efficient for solving optimization problem. Amiolemhen et al. [11] considered multi-pass roughing operation and single pass finishing operation for facing, turning, centering, drilling, boring, chamfering, and parting operation. The proposed genetic algorithm is both effective and efficient. Ezugwu et al. [12] developed a model for the analysis and prediction of the relationship between cutting and process parameters during high speed turning of nickel-based Inconel 718 alloy. Asokan et al. [13] developed Particle swarm optimization to optimize machining parameters for surface grinding operation with a multi-objective of minimizing production cost and maximizing production rate per work piece, besides obtaining best possible surface finish. Ramon et al. [14] used Genetic algorithm for optimizing cutting parameters and made a remark on the advantages of multi-objective optimization approach over single objective function. Tansel et al. [15] represented the relationship between the cutting condition and machine related variables. Optimal operating conditions were also calculated to obtain the best possible compromise between roughness of machined surface and the duration. Al-Ahmari [16] developed empirical model for tool life, surface roughness, and cutting force for turning operations. Data mining techniques such as response surface methodology and neural network are used to develop the machinability model. Baskar et al. [17] developed ant colony based optimization procedure to optimize wheel speed, work piece speed, depth of dressing, and lead of dressing to evaluate production cost and production time. The authors have also compared their results with genetic algorithm and geometric programming technique. Srinivas et al. [18] proposed particle swarm optimization for selecting optimized machining parameters in multi-pass turning operation for a component of continuous form. Bharathi Raja et al. [19] examined simulated annealing algorithm, genetic algorithm and PSO on three different mathematical
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models such as single pass turning operation, multi-pass turning operation, and grinding operation. The authors found that PSO outperformed other optimization techniques in all the cases. Yang et al. [20] used tungsten carbide tool to turn S45C steel bars and found the main cutting parameters that affect the cutting performance using Taguchi method. Wassila Bouzid [21] explained the feed in relation to the roughness, which depends on the cutting speed. The author has also calculated the cutting speed, which gives minimum production time. Stephene Segonds et al. [22] studied the characteristics behavior of slender work pieces under the effect of tangential cutting force during NC turning. Ramon Quiza Ersan Aslan et al. [23] outlined an experimental study on hardened steels with Al2O3 based ceramic tools and achieved a process optimization on flank wear and surface roughness. Gaitonde et al. [24] determined the most appropriate cutting speed and feed for turning of brass using K10 carbide tool. Taguchi technique has been proposed for simultaneous reduction of surface roughness and cutting force. ChorngJgh Tzeng et al. [25] found that depth of cut and cutting speed are the most significant factor for roughness average, roughness maximum, and roundness and also analyzed orthogonal array of Taguchi method using nine experimental runs. Sahin [26] used orthogonal design, signal to noise ratio, and analysis of variance for determining cutting parameters on tool life. The author concluded that percentage contribution of cutting speed, tool hardness, and feed rate on tool life are 41.63, 32.68, and 25.22, respectively. Some researchers [1–6] used traditional optimization techniques such as deterministic approach, sequential quadratic programming, and dynamic programming for solving their optimization problem. Most of the researchers [7, 9–11, 13, 14, 17–19] approached theoretically using non-traditional optimization techniques such as simulated annealing, genetic algorithm, PSO, artificial neural network, and ants colony optimization for solving machining problems. Very few researchers [8, 12, 15, 16] have done Fig. 1 LT-20 CNC lathe used
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experimental work using optimization techniques for optimizing machining parameters based on machining time, machining cost, vibrations, tool life, tool wear, cutting force surface roughness, etc. In the present work, an attempt has been made to find a technique for optimizing machining parameters that could yield minimum machining time at the same time maintaining the desired surface roughness. This is done by conducting experiments on a CNC lathe for various work piece materials such as brass, aluminum, copper, and mild steel. PSO is used to find the optimized machining parameters for obtaining the minimized machining time for the given surface roughness. The reason for selecting PSO [18, 19] as a tool for optimization is that it has been proved by many researchers that it could obtain global optimal solution very quickly and the results are comparatively better than other non-traditional optimization techniques. Then, confirmation experiments are also conducted on the machining parameters based on PSO to verify the correctness in obtaining the minimized machining time subject to the desired surface roughness. Comparisons are also made on the results of PSO and the confirmation experiments.
3 Pilot experiments The cutting experiments were conducted on LT-20 CNC lathe using tungsten carbide insert for machining the bars. The specification of the tool is CNMG 12-04-08 ISO diamond shape. The feasible range for cutting parameters is taken from machine limitations. The machining time is observed from the screen of the CNC machine excluding the tool movement between home position and the work piece. The surface roughness tester is used to measure the surface roughness of the turned work piece. The first objective of this work is to reduce the time and cost of experiments by maximizing the use of statistical data obtained from the pilot experiments [20, 26]. The number of experiments to be conducted is decided
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Fig. 2 Surface roughness tester used
from the factorial design of experiment method. Number of experiments=(y)x where y is the number of variables and x is the number of objectives. In the present work, y is 3 and x is 2. As per factorial design of experiment method, nine experiments are sufficient but ten experiments are conducted. Figure 1 shows the LT-20 CNC lathe and Fig. 2 shows the surface roughness tester used for conducting experiments (Table 1). Table 2 shows the machining time and surface roughness for different cutting speed, feed, and depth of cut for brass. The work piece material is brass. Similarly, Table 3 shows the pilot experiments conducted on aluminum work piece and the machining time and surface roughness were measured for the same machining parameters. Unlike brass, the surface roughness of aluminum is higher than that of brass material for the same machining parameters. But the time taken for machining the work piece remains the same for both brass and aluminum. Table 4 shows the value of machining time and surface roughness of copper for the given machining parameters. Copper is harder than other materials; hence, the value of feed cannot be fed more than 0.262 mm/revolution. But the surface roughness of copper is comparatively less than other proposed materials. Table 5 shows the value of machining time and surface roughness of mild steel for the same machining parameters as given for copper. Mild steel also behaves similar to copper in giving feed and the value of depth of cut cannot be given more than 1 mm. In all the cases, increase in cutting speed decreases Table 1 Specification of CNC lathe and surface roughness tester
the surface roughness and decrease in feed decreases the surface roughness but the machining time is increased.
4 Mathematical model A mathematical model is formed based on the machining parameters and surface roughness of work piece. Pilot experiments was conducted on different work piece materials and based on the experimental results, new empirical relations are formulated. Although the equations framed for four materials are based on speed, feed, and depth of cut, the multiplying factors and exponents of the four materials are distinctly different. The values for the machining parameters like L, D, vmin, vmax, etc. are given in Table 6 and they are obtained from the knowledge of the machine limitations. 4.1 Formulation of objective function The objective of this work is to minimize machining time subjected to desired surface roughness values of different work piece materials and its corresponding equations is given below. Table 6 shows the minimum and maximum values of machining parameters and constant values for brass, aluminum, copper, and mild steel. tm ¼ pDL=1000vf
ð1Þ
Specification of CNC lathe
Specification of surface roughness tester
Make: ACE Designers Maximum turning diameter: 235 mm Maximum turning length: 485 mm Programming system: FANUC-OT Series Chuck diameter: 200 mm Spindle motor: 5 hp servo motor
Make: CARLZESIS Range: 0–100 μm Stylus type: DT-43827 Least count: 0.1 μm
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Table 2 Experimental results of machining time and surface roughness for the given machining parameters for Brass Experiment number
v m/min
f mm/rev
d mm
tm s
SR μm
Experiment number
v m/min
f mm/rev
d mm
tm s
SR μm
130.53 135.33 140.24 164.36 176.43
0.762 0.662 0.562 0.412 0.337
2.0 2.0 2.0 2.0 2.0
3 3 4 5 5
1.55 1.37 1.18 0.81 0.61
6 7 8 9 10
188.49 207.34 207.34 235.61 235.61
0.262 0.162 0.062 0.062 0.062
2.0 2.0 2.0 2.0 1.5
6 9 24 21 21
0.46 0.33 0.18 0.11 0.10
1 2 3 4 5
of suitable feed is necessary. Therefore, the ranges of feed for different materials are given below,
4.2 Machining parameters Although there are many machining parameters that affect the machining operation, cutting speed, feed, and depth of cut have the greatest effect on the success of a machining operation. Therefore, only these machining parameters are considered in this work. Moreover, these machining parameters also considered as the practical constraints. 4.2.1 Cutting speed In the case of carbide tool, minimum cutting speed should be maintained to avoid failure of cutting tools due to built up edge formation. Certain combinations of speed, feed and depth of cut are usually selected for easy chip removal, which are directly proportional to the type of tool and work piece material. The ranges of cutting speeds of different materials are given below, vmin i vi vmax i where i ¼ 1; 2; 3; 4 . . .
ð2Þ
4.2.2 Feed When compared to depth of cut and cutting speed, feed rate has a greater effect on machining time and surface roughness. By increasing the feed and decreasing the cutting speed, it is always possible to obtain much higher metal removal rates without affecting tool life. For obtaining good finish low feed and high cutting speed is desirable. But machining time increases heavily. To overcome this, selection
fmin i fi fmax i where i ¼ 1; 2; 3; 4 . . .
ð3Þ
4.2.3 Depth of cut Selection of depth of cut should counter balance between the tool life and metal removal rate to obtain highest permissible level of depth of cut. The depth of cut range is given below. dmin i di dmax i where i ¼ 1; 2; 3; 4 . . .
ð4Þ
4.3 Practical constraints There are always many constraints that exist in the actual cutting condition for the optimization of the objective function. For a given pass, an optimum cutting speed, feed, and depth of cut are chosen and thus balancing the conflict between the metal removal rate and tool life. The following constraints are considered for optimizing the machining parameters. vmin i vi vmax i; fmin i fi fmax i dmin i di dmax i; SRi ¼ Ki va i f b i d c i
ð5Þ
where i=1,2,3,4 and i=1 for brass, 2 for aluminum, 3 for copper, 4 for mild steel
Table 3 Experimental results of machining time and surface roughness for the given machining parameters for Aluminum Experiment number 1 2 3 4 5
v m/min
f mm/rev
d mm
tm s
SR μm
Experiment number
v m/min
f mm/rev
d mm
tm s
SR μm
130.53 135.33 140.24 164.36 176.43
0.762 0.662 0.562 0.412 0.337
2.0 2.0 2.0 2.0 2.0
3 3 4 5 5
2.43 2.41 2.38 1.20 1.10
6 7 8 9 10
188.49 207.34 207.34 235.61 235.61
0.262 0.162 0.062 0.062 0.062
2.0 2.0 2.0 2.0 1.5
6 9 24 21 21
1.00 0.87 0.57 0.34 0.25
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Table 4 Experimental results of machining time and surface roughness for the given machining parameters for copper Experiment number 1 2 3 4 5
v m/min
f mm/rev
d mm
tm s
SR μm
Experiment number
v m/min
f mm/rev
d mm
tm s
SR μm
141.37 150.79 150.79 150.79 169.64
0.262 0.262 0.200 0.150 0.150
1.0 1.0 1.0 1.0 1.0
8 8 10 14 12
1.37 1.20 0.91 0.65 0.60
6 7 8 9 10
169.64 188.49 188.49 207.34 235.61
0.100 0.050 0.050 0.030 0.010
1.0 1.0 0.5 0.5 0.3
18 33 33 50 132
0.41 0.18 0.16 0.13 0.03
5 Implementation of optimization technique The second objective of this work is to find the optimal machining parameters to minimize the machining time for the given surface roughness value by using optimization technique. The result of pilot experiments has revealed that decrease in feed rate improved surface finish but machining time gets increased. Use of higher cutting speed may enhance surface finish but the tool life is lost. So an optimization technique is required to solve this machining problem. The machining parameters are identified and the best combinations of parameters are selected by using optimization technique. Different optimization techniques are used to solve the mathematical models for machining problems. Based on the previous literatures, PSO technique [18, 19] has always yielded best result as compared to other techniques. So, PSO technique is implemented to solve the mathematical model in this work. 5.1 Particle swarm optimization James Kennedy and Russell C. Eberhart first described PSO in 1995. PSO is a stochastic, population-based search procedure non-traditional optimization technique and one of the direct search methods. A stochastic process is a nondeterministic one whose subsequent state is determined based on random element. Direct search method proceeds to the next state based on objective function information. Nontraditional optimization technique is generally evolved from social behavior and social learning. PSO is one such method based on swarm intelligence where all the swarms in a group
could reach the available food comfortably. The intelligence of swarm is based on the principle of personal, social and psychological behavior of the swarm. PSO could able to find near optimal solution when the search space is large. In a minimization optimization problem, “best” means the position of the particle with smallest objective function value. Each swarm is called as “particle” and they are made to move in multi-directional space. Each particle has its own position and velocity. Particles in a population communicate each other and adjust their position and velocity in order to obtain good position. The better the present particle, it moves on its own way. The better the neighbor’s way, the present particle tend to follow the neighbor’s way. All the particles have to undergo the following criteria to attain the best position. 1. Global best is termed as “gbest,” where the new best position is formed based on any particle in the population so far. 2. Local best or particle best is termed as “pbest,” where the best particle position is identified by the same particle itself. For each particle, the particle velocity and updating of particle position is calculated using Eqs. 6 and 7. V ½ ¼ c1 randðÞ ðpbest½ present½ Þ þ c2 randðÞ ðgbest½ present½ Þ
ð6Þ
p½ ¼ V ½ þ present½
ð7Þ
V [ ] is the particle velocity, present is the current particle, pbest and gbest are defined as stated before, rand ( ) is the
Table 5 Experimental results of machining time and surface roughness for the given machining parameters for mild steel v m/min
f mm/rev
d mm
tm s
SR μm
Experiment number
v m/min
f mm/rev
d mm
tm s
SR μm
1 2 3
141.37 150.79 150.79
0.262 0.262 0.200
1.0 1.0 1.0
8 8 10
1.91 1.67 1.41
6 7 8
169.64 188.49 188.49
0.100 0.050 0.050
1.0 1.0 0.5
18 33 33
0.67 0.53 0.22
4 5
150.79 169.64
0.150 0.150
1.0 1.0
14 12
1.06 0.81
9 10
207.34 235.61
0.030 0.010
0.5 0.3
50 132
0.19 0.09
Experiment number
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Table 6 Values of machining parameters Brass
Aluminum
Copper
Mild Steel
Parameters L
Values 55 MM
Parameters D
Values 38 mm
Parameters
Values
Parameters
Values
vmin vmax fmin fmax dmin dmax K1 a1 b1 c1
50 m/min 240 m/min 0.062 mm/rev 0.762 mm/rev 1.5 mm 2.0 mm 2700 −1.39 0.79 0.25
vmin vmax fmin fmax dmin dmax K1 a1 b1 c1
50 m/min 240 m/min 0.062 mm/rev 0.762 mm/rev 1.5 mm 2.0 mm 2750 −1.40 0.80 0.25
vmin vmax fmin fmax dmin dmax K1 a1 b1 c1
50 m/min 240 m/min 0.010 mm/rev 0.262 mm/rev 0.3 mm 1.0 mm 9550 −1.52 1.004 0.25
vmin vmax fmin fmax dmin dmax K1 a1 b1 c1
50 m/min 240 m/min 0.010 mm/rev 0.262 mm/rev 0.3 mm 1.0 mm 13000 −1.52 1.004 0.25
random number between 0 and 1, c1, c2 are learning factors usually varies from 1 to 4, p [ ] is new particle position. An important feature of PSO is that it has very few parameters to adjust. In the past several years, PSO has been successfully applied [13, 18, 19] in many engineering researches and application areas. It has been proven by many researchers that PSO could yield best result and in a faster way compared to other optimization methods. One of the advantages of PSO is that it takes real number as particles. The searching is a repeat process and the stop criteria are that the maximum iteration is reached or the minimum error condition is satisfied. The various parameters in PSO are number of particles, dimension of particles, and range of particles, learning factor, stop condition, and global Vs local version. 5.2 Algorithm Step 1 Create a uniformly distributed population of particles. Step 2 Position of each particle is evaluated based on objective function. Step 3 Particle’s current position is updated when the present is better than the previous position.
Step 4 Best particle is determined based on particle’s previous best positions. Step 4 Particle velocity is updated. Step 5 Particles are moved to their new positions. Step 6 Go to step 2 until stopping criteria is satisfied. Step 7 End 5.3 Parameters of PSO Initially, 100 iterations were executed with 100 populations for experiment number 1. The convergence to near optimal solution is obtained in 37th iteration itself. The values obtained after 37th iteration to 100th iteration are same. In order to check for any further improvement, number of iterations is increased up to 1,000. But there was no change in the objective function value with respect to 37th iteration value. While executing the PSO program, the iteration number of convergence to near optimal solution varies in each run. This is because; the selection of random numbers varies in every run of the same program. Based on the previous literature [19] and also to avoid missing the best optimal solution (if any) at the later stage, the program is executed for 1,000 iterations for safer side. When the search space is large, it is always better to have huge population
Table 7 Optimized machining parameters for the given surface roughness for Brass Experiment number 1 2 3 4 5
SR μm
v m/min
f mm/rev
d mm
tm s
Experiment number
SR μm
v m/min
f mm/rev
d mm
tm s
1.55 1.37 1.18 0.81 0.61
157.67 164.37 172.84 196.18 215.84
0.511 0.470 0.425 0.330 0.272
1.5 1.5 1.5 1.5 1.5
4 4 4 5 5
6 7 8 9 10
0.46 0.33 0.18 0.11 0.10
237.35 240.00 240.00 240.00 240.00
0.225 0.151 0.070 0.045 0.040
1.5 1.5 1.5 0.8 0.8
6 9 19 29 32
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Table 8 Optimized machining parameters for the given surface roughness for aluminum Experiment number 1 2 3 4 5
SR μm
v m/min
f mm/rev
d mm
tm s
Experiment number
SR μm
v m/min
f mm/rev
d mm
tm s
2.43 2.41 2.38 1.20 1.10
133.98 134.35 134.91 169.50 174.49
0.708 0.704 0.698 0.442 0.417
1.5 1.5 1.5 1.5 1.5
3 3 3 4 4
6 7 8 9 10
1.00 0.87 0.57 0.34 0.25
180.12 188.68 217.24 240.00 240.00
0.393 0.357 0.269 0.168 0.114
1.5 1.5 1.5 1.5 1.5
4 5 5 8 11
size to converge to a global optimum solution very quickly. For uniformity and comparison, 100 population size and 1,000 iterations are performed in all the experiments. The learning factor c1 and c2 are also tested for 64 combinations (c1 = 0.5,1.0,1.5,2.0,2.5,3.0,3.5,4.0 and c2 = 0.5,1.0,1.5,2.0,2.5,3.0,3.5,4.0) and it was found that except for three combinations ([c1=0.5, c2=0.5], [c1=0.5, c2= 1.0], and [c1=1.0, c2=0.5]), all other combinations have yielded better and same result. Based on the above findings, the following parameters are chosen for executing PSO for all the work piece materials. Number of iterations performed: 1,000 Population : 100 Learning Factor c1 :2 Learning Factor c2 :2
5.4.2 Calculation of feed Similarly feed is also calculated randomly within the limits using Eq. 9 f ¼ fmin þ ðfmax fmin Þ randðÞ
ð9Þ
5.4.3 Calculation of depth of cut Similarly depth of cut is also calculated randomly within the limits using Eq. 10 d ¼ dmin þ ðdmax dmin Þ randðÞ
ð10Þ
5.4.4 Checking the constraint
5.4 Numerical illustration of PSO The procedure of PSO is explained below with respect to the first particle in the first iteration. Similarly, the remaining 99 particles are executed by the same procedure. This constitutes iteration 1. The remaining 999 iterations are executed in the same manner. 5.4.1 Calculation of cutting speed
The values obtained using Eqs. 8, 9, and 10 are substituted in the surface roughness constraint Eq. 11 to check for the given surface roughness value obtained from the pilot experiment. Otherwise, the above steps should be repeated with new random numbers. Kðva f b d c Þ ¼ SR
ð11Þ
5.4.5 Calculation of objective function
Cutting speed is calculated randomly within the limits using Eq. 8. v ¼ vmin þ ðvmax vmin Þ randðÞ
ð8Þ
After satisfying Eq. 11, the optimized machining parameter values are substituted in machining time Eq. 12 tm ¼ pDL=1000vf
ð12Þ
Table 9 Optimized machining parameters for the given surface roughness for Copper Experiment number 1 2 3 4 5
SR μm
v m/min
f mm/rev
d mm
tm s
Experiment number
SR μm
v m/min
f mm/rev
d mm
tm s
1.37 1.20 0.91 0.65 0.60
149.00 158.50 163.48 178.59 175.93
0.262 0.262 0.253 0.178 0.149
1.5 1.3 0.6 1.1 1.5
8 7 8 10 12
6 7 8 9 10
0.41 0.18 0.16 0.13 0.03
189.64 199.38 201.48 205.00 210.00
0.120 0.072 0.061 0.055 0.011
1.2 0.5 0.6 0.5 0.5
14 22 25 28 135
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Table 10 Optimized machining parameters for the given surface roughness for Mild Steel Experiment number 1 2 3 4 5
SR μm
v m/min
f mm/rev
d mm
tm s
Experiment number
SR μm
v m/min
f mm/rev
d mm
tm s
1.91 1.67 1.41 1.06 0.82
146.55 158.23 163.48 138.76 175.93
0.262 0.262 0.253 0.148 0.149
1.5 1.4 1.0 1.0 1.5
8 8 8 15 12
6 7 8 9 10
0.67 0.53 0.22 0.15 0.09
189.45 174.12 188.49 192.10 198.00
0.139 0.094 0.050 0.031 0.012
1.4 1.5 0.9 1.5 1.5
12 19 33 52 131
5.4.6 Calculation of pbest value The minimum machining time for each initial solution is considered as the pbest value. This is the best value of the particular solution only. 5.4.7 Calculation of gbest value The minimum machining time for the initial solution or for the whole iteration is considered as the gbest value. 5.4.8 Calculation in first iteration For cutting speed
depth of cut for the desired surface roughness are given in Tables 7, 8, 9, and 10. The surface roughness obtained from the pilot experiment is kept constant and 1,000 iterations with 100 populations were executed to get optimized machining parameters and its corresponding minimized machining time. This is the result of the experiment number 1. Similarly, ,1000 iterations with 100 populations’ runs are executed for remaining nine experiments. Tables 7, 8, 9, and 10 show the optimized machining parameters for the given surface roughness for brass, aluminum, copper, and mild steel using PSO technique.
6 Confirmation experiments
V ½ ¼ c1 randðÞfpbest½v present½vg þ c2 randðÞfgbest½v present½vg
ð13Þ
where present [±] is the cutting speed value for the first particle of the initial random solution. p½v ¼ present½v þ V ½
The optimum machining parameters obtained from PSO are validated by conducting experiments on brass, aluminum, copper and mild steel materials. Tables 11, 12, 13, and 14 show the experimental results obtained for the above work piece materials.
ð14Þ
The cutting speed value is replaced by p [ ]. Similarly the feed and depth of cut values are calculated and minimized machining time is obtained subjected to the required surface roughness value. 5.5 Computational result of PSO The minimized machining time and its corresponding machining parameters values of cutting speed, feed, and
7 Results and discussions Brass, aluminum, copper, and mild steel are identified for conducting experiments, as they are the most commonly used materials in manufacturing industry. The effect of machining parameters on the machining time was considered. Ten experiments on ten work pieces of same dimensions were conducted and their corresponding machining time and surface roughness values were observed.
Table 11 Experimental result of machining time and surface roughness for the optimized machining parameters of brass v m/min
f mm/rev
d mm
tm s
SR μm
Experiment number
v m/min
f mm/rev
d mm
tm s
SR μm
1 2 3
157.67 164.37 172.84
0.511 0.470 0.425
1.5 1.5 1.5
4 4 4
1.53 1.33 1.15
6 7 8
237.35 240.00 240.00
0.225 0.151 0.070
1.5 1.5 1.5
6 9 19
0.66 0.37 0.21
4 5
196.18 215.84
0.330 0.272
1.5 1.5
5 5
0.92 0.69
9 10
240.00 240.00
0.045 0.040
0.8 0.8
29 32
0.17 0.14
Experiment number
454
Int J Adv Manuf Technol (2011) 54:445–463
Table 12 Experimental result of machining time and surface roughness for the optimized machining parameters of aluminum Experiment number 1 2 3 4 5
v m/min
f mm/rev
d mm
tm s
SR μm
Experiment number
v m/min
f mm/rev
d mm
tm s
SR μm
133.98 134.35 134.91 169.50 174.49
0.708 0.704 0.698 0.442 0.417
1.5 1.5 1.5 1.5 1.5
3 3 3 4 4
2.69 2.51 2.48 1.27 1.05
6 7 8 9 10
180.12 188.68 217.24 240.00 240.00
0.393 0.357 0.269 0.168 0.114
1.5 1.5 1.5 1.5 1.5
4 5 5 8 11
0.95 0.79 0.55 0.41 0.29
Then optimization based on PSO was executed using MATLAB software in which 1,000 iterations with 100 populations were used to run the program. The program is executed to get optimized machining parameters for minimizing machining time subject to the required surface roughness values obtained from pilot experiments. The PSO program was executed ten times for the corresponding ten pilot experiments for a material. The computational time for execution of single run in a Core 2 Duo processor computer are observed to be 4 s in an average. Then once again experiments were conducted ten times based on the recommended machining parameters of PSO. Table 15 shows the average deviation and accuracy rate of predicted and actual surface roughness value of the proposed four work materials. The accuracy rate of the predicted surface roughness to the actual surface roughness in finding the optimal machining parameters (for all the four materials) for minimizing machining time are found to be 85% in an average. 7.1 Graphical representation of robustness of PSO The third objective of the present work is to validate the ability of PSO in finding optimal machining parameters to minimize the machining time subject to the desired surface roughness. The optimized machining parameters are taken from the result of PSO and given as the cutting parameters to a CNC machine. It is observed from the following figures that the machining time increases with a decrease in feed and the feed has a greater effect on machining time when compared to the contribution of cutting speed and depth of cut. All the following figures
attempts to show the closeness of predicted value obtained by PSO and actual values obtained by confirmation experiments. It is obvious from the following figures that the predicted values of PSO technique is very close to the actual values. Figure 3 shows the relationship between cutting speed, machining time and surface roughness of brass based on pilot experiments, PSO, and confirmation experiments. For the same cutting speed, the machining times obtained by PSO and confirmation experiments are same. At the same time, the surface roughness obtained by PSO and confirmation experiments has deviation. This is the compromise in obtaining the same machining time based on PSO and confirmation experiments. Figure 4 shows the relationship between feed, machining time and surface roughness obtained by brass based on pilot experiments, PSO, and confirmation experiments. For the same feed, the machining times obtained by PSO and confirmation experiments are same but the surface roughness obtained by PSO and confirmation experiments has small deviations. Surface roughness is directly proportional to feed and inversely proportional to cutting speed. Experimentally, when cutting speed is increased, surface roughness gets decreased. But when feed is simultaneously increased, surface roughness also increases overcoming the effect of cutting speed. This fact could be clearly seen from Figs. 3 and 4 that the effect of feed on machining time and surface roughness is comparatively more than the cutting speed. Figure 5 shows the relationship between depth of cut, machining time, and surface roughness of brass based on
Table 13 Experimental result of machining time and surface roughness for the optimized machining parameters of copper Experiment number 1 2 3 4 5
v m/min
f mm/rev
d mm
tm s
SR μm
Experiment number
v m/min
f mm/rev
d mm
tm s
SR μm
149.00 158.50 163.48 178.59 175.93
0.262 0.262 0.253 0.178 0.149
1.5 1.3 0.6 1.1 1.5
8 7 8 10 12
1.30 1.28 1.01 0.76 0.71
6 7 8 9 10
189.64 199.38 201.48 205.00 210.00
0.120 0.072 0.061 0.055 0.011
1.2 0.5 0.6 0.5 0.5
14 22 25 28 135
0.58 0.20 0.18 0.16 0.08
Int J Adv Manuf Technol (2011) 54:445–463
455
Table 14 Experimental result of machining time and surface roughness for the optimized machining parameters of mild steel Experiment number 1 2 3 4 5
v m/min
f mm/rev
d mm
tm s
SR μm
Experiment number
v m/min
f mm/rev
d mm
tm s
SR μm
146.55 158.23 163.48 138.76 175.93
0.262 0.262 0.253 0.148 0.149
1.5 1.4 1.0 1.0 1.5
8 8 8 15 12
1.94 1.71 1.37 0.98 0.87
6 7 8 9 10
189.45 174.12 188.49 192.10 198.00
0.139 0.094 0.050 0.031 0.012
1.4 1.5 0.9 1.5 1.5
12 19 33 52 131
0.73 0.68 0.36 0.24 0.14
PSO and confirmation experiments. For the same depth of cut, the machining times obtained by PSO and confirmation experiments are same. At the same time, the surface roughness obtained by PSO and confirmation experiments has deviation. This is the compromise in obtaining the same machining time based on PSO and confirmation experiments. Figure 6 shows the relationship between cutting speed, machining time, and surface roughness of aluminum based on pilot experiments, PSO, and confirmation experiments. For the same cutting speed, the machining times obtained by PSO and confirmation experiments are same. At the same time, the surface roughness obtained by PSO and confirmation experiments has deviation. This is the compromise in obtaining the same machining time based on PSO and confirmation experiments Figure 7 shows the relationship between feed, machining time, and surface roughness obtained by aluminum based on pilot experiments, PSO, and confirmation experiments. For the same feed, the machining times obtained by PSO and confirmation experiments are same but the surface roughness obtained by PSO and confirmation experiments has small deviations. Surface roughness is directly proportional to feed and inversely proportional to cutting speed. Experimentally, when cutting speed is increased, surface roughness gets decreased. But when feed is simultaneously increased, surface roughness also increases overcoming the effect of cutting speed. This fact could be clearly seen from Figs. 6 and 7 that the effect of feed on machining time and surface roughness is comparatively more than the cutting speed. Figure 8 shows the relationship between depth of cut, machining time, and surface roughness of aluminum based on PSO and confirmation experiments. For the same depth of cut, the machining times obtained by PSO and
Table 15 Average deviation and accuracy rate of predicted and actual surface roughness
confirmation experiments are same. At the same time, the surface roughness obtained by PSO and confirmation experiments has deviation. This is the compromise in obtaining the same machining time based on PSO and confirmation experiments. Figure 9 shows the relationship between cutting speed, machining time, and surface roughness of copper based on pilot experiments, PSO, and confirmation experiments. For the same cutting speed, the machining times obtained by PSO and confirmation experiments are same. At the same time, the surface roughness obtained by PSO and confirmation experiments has deviation. This is the compromise in obtaining the same machining time based on PSO and confirmation experiments Figure 10 shows the relationship between feed, machining time, and surface roughness obtained by copper based on pilot experiments, PSO, and confirmation experiments. For the same feed, the machining times obtained by PSO and confirmation experiments are same but the surface roughness obtained by PSO and confirmation experiments has small deviations. Surface roughness is directly proportional to feed and inversely proportional to cutting speed. Experimentally, when cutting speed is increased, surface roughness gets decreased. But when feed is simultaneously increased, surface roughness also increases overcoming the effect of cutting speed. This fact could be clearly seen from Figs. 9 and 10 that the effect of feed on machining time and surface roughness is comparatively more than the cutting speed. Figure 11 shows the relationship between depth of cut, machining time, and surface roughness of copper based on PSO and confirmation experiments. For the same depth of cut, the machining times obtained by PSO and confirmation experiments are same. At the same time, the
S. o
Work piece material
1 2 3 4
Brass Aluminum Copper Mild steel
Average deviation in μm
Accuracy rate (%)
0.07 0.08 0.08 0.08
85.04 92.37 81.71 80.90
456
Int J Adv Manuf Technol (2011) 54:445–463 Brass
Machining time in seconds
35 30
Predicted & actual machining time
25 20 15
Pilot Experiment
10 5 0 120
140
160
180
200
220
240
Surface roughness in microns
Cutting speed in m/min 1.6 1.4 1.2 1
Actual roughness
0.8
Pilot Experiment
0.6
Predicted roughness
0.4 0.2 0 120
140
160
180
200
220
240
Cutting speed in m/min
Fig. 3 Cutting speed versus machining time and surface roughness for brass
surface roughness obtained by PSO and confirmation experiments has deviation. This is the compromise in obtaining the same machining time based on PSO and confirmation experiments.
Figure 12 shows the relationship between cutting speed, machining time, and surface roughness of mild steel based on pilot experiments, PSO, and confirmation experiments. For the same cutting speed, the machining
Machining time in seconds
Brass 35 30
Predicted and actual Machining time
25 20 15
Pilot Experiment
10 5 00
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.6
0.7
0.8
Surface roughness in microns
Feed in mm/revolution
1.6 1.4
Predicted roughness
1.2 1 0.8
Actual roughness
0.6
Pilot Experiment
0.4 0.2 0
0
0.1
0.2
0.3
0.4 Feed in mm/revolution
Fig. 4 Feed versus machining time and surface roughness for brass
0.5
Int J Adv Manuf Technol (2011) 54:445–463
457 Brass
Machining time in seconds
35 Predicted machining time Actual machining time
30 25 20 15 10 5 0 0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
Depth of cut in mm
Surface roughness in microns
1.6 Predicted roughness Actual roughness
1.4 1.2 1 0.8 0.6 0.4 0.2 0
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
Depth of cut in mm
Fig. 5 Depth of cut versus machining time and surface roughness for brass
Aluminium Machining time in seconds
25 20
Pilot Experiment
15
Actual machining time
10
Predicted machining time
5 0 120
140
160
180
200
220
240
200
220
240
Surface roughness in microns
Cutting speed in m/min. 3 2.5
Pilot Experiment
2 1.5
Actual roughness Predicted roughness
1 0.5 0 120
140
160
180
Cutting speed in m/min.
Fig. 6 Cutting speed versus machining time and surface roughness for aluminum
458
Int J Adv Manuf Technol (2011) 54:445–463 Aluminium
Machining time in seconds
25 20 Pilot Experiment
15 10 Predicted & Actual machining time
5 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Feed in mm/revolution
Surface roughness in microns
3 2.5 2 Pilot Experiment
Actual roughness Predicted roughness
1.5 1 0.5 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Feed in mm/revolution
Fig. 7 Feed versus machining time and surface roughness for aluminum
Aluminium Machining time in seconds
11 Predicted machining time Actual machining time
10 9 8 7 6 5 4 3
0.5
1
1.5
2
2.5
Surface roughness in microns
Depth of cut in mm 3 Predicted roughness Actual roughness
2.5 2 1.5 1 0.5 0 0.5
1
1.5
Depth of cut in mm
Fig. 8 Depth of cut versus machining time and surface roughness for aluminum
2
2.5
Int J Adv Manuf Technol (2011) 54:445–463
459
Machining time in seconds
Copper 140 120 100
Predicted & actual machining time
80
Pilot Experiment
60 40 20 0 140
150
160
170
180
190
200
210
220
230
240
200
210
220
230
240
Surface roughness in microns
Cutting speed in m/min 1.4 Actual roughness
1.2 1
Pilot Experiment
0.8
Predicted roughness
0.6 0.4 0.2 0 140
150
160
170
180
190
Cutting speed in m/min
Fig. 9 Cutting speed versus machining time and surface roughness for copper
times obtained by PSO and confirmation experiments are same. At the same time, the surface roughness obtained by PSO and confirmation experiments has deviation. This is the compromise in obtaining the same machining time based on PSO and confirmation experiments
Figure 13 shows the relationship between feed, machining time, and surface roughness obtained by mild steel based on pilot experiments, PSO, and confirmation experiments. For the same feed, the machining times obtained by PSO and confirmation experiments are same
Machining time in seconds
Copper 140 120 100 Predicted and actual machining time
80 60
Pilot Experiment
40 20 0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Surface roughness in microns
Feed in mm/revolution 1.4 Pilot Experiment
1.2 1
Predicted roughness
0.8
Actual roughness
0.6 0.4 0.2 0 0
0.05
0.1
0.15
0.2
Feed in mm/revolution
Fig. 10 Feed versus machining time and surface roughness for copper
0.25
0.3
0.35
460
Int J Adv Manuf Technol (2011) 54:445–463 Copper
Machining time in seconds
140 120 100 80 60 40
Predicted machining time Actual machining time
20 0 0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.2
1.3
1.4
1.5
Surface roughness in microns
Depth of cut in mm 1.4 1.2 1
Actual roughness 0.8 0.6
Predicted roughness
0.4 0.2 0 0.5
0.6
0.7
0.8
0.9
1
1.1
Depth of cut in mm
Fig. 11 Depth of cut versus machining time and surface roughness for copper
but the surface roughness obtained by PSO and confirmation experiments has small deviations. Surface roughness is directly proportional to feed and inversely proportional to cutting speed. Experimentally, when cutting speed is increased, surface roughness gets decreased. But when feed is simultaneously increased, surface roughness also increases overcoming the effect of cutting speed. This fact could be clearly seen from Figs. 12 and 13 that the effect of feed on machining time and surface roughness is comparatively more than the cutting speed. Figure 14 shows the relationship between depth of cut, machining time, and surface roughness of mild steel based on PSO and confirmation experiments. For the same depth of cut, the machining times obtained by PSO and confirmation experiments are same. At the same time, the surface roughness obtained by PSO and confirmation experiments has deviation. This is the compromise in obtaining the same machining time based on PSO and confirmation experiments.
8 Conclusions For the given component, it is not possible to exactly mention the value of cutting speed, feed, and depth of cut in a process planning sheet for the given time of
machining and surface roughness value. Proper selection of machining parameters can minimize machining time and also could obtain desired surface finish. But desired surface roughness can be achieved by trial and error method of giving various combinations of machining parameters. But it is time consuming and material is unnecessarily wasted for this purpose. So, there is a need to develop a model that could able to find the optimum machining parameters for minimizing the machine time subjected to the desired surface finish. The results of confirmation experiment proved that the optimized machining parameters of PSO could yield the same machining time and near surface roughness value for a given component. Even though there is slight deviation in surface roughness of experiment value from the PSO value, the deviation can be justified based on the effects of vibration, spindle run-out, and work-piece material property. In order to help the machinist in judicious selection of machining parameters, we have approached using empirical data to predict the optimal machining parameters for effective turning. The following points were observed as conclusions from the present work: &
PSO provides a simple, systematic, and efficient methodology for optimization of machining parameters.
Int J Adv Manuf Technol (2011) 54:445–463
461 Mild Steel
Machining time in seconds
140 120 100 Predicted & actual machining time
80
Pilot experiment
60 40 20 0 140
150
160
170
180
190
200
210
220
230
240
210
220
230
240
Surface roughness in microns
Cutting speed in m/min
2
1.5 Predicted roughness
1 Actual roughness
Pilot experiment
0.5
0 140
150
160
170
180
190
200
Cutting speed in m/min
Fig. 12 Cutting speed versus machining time and surface roughness for mild steel
& &
Confirmation experiments verified the effectiveness of the present approach in finding optimal machining parameters. Since the proposed technique could obtain a global optimum solution within a reasonable execution time on
&
a personal computer, the algorithm can be used on online systems for the selection of optimal machining parameters. The software is completely generalized and problem independent, so that it can be easily modified to optimize other machining operations such as milling,
Machining time in seconds
Mild Steel
140 120 100 80 60
Predicted & actual machining time
40
Pilot Experiment
20 0 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.3
0.35
Feed in mm/revolution
Surface roughness in microns
2 Pilot Experiment
1.5
Actual roughness
1
0.5 Predicted roughness 0
0
0.05
0.1
0.15
0.2
Feed in mm/revolution
Fig. 13 Feed versus machining time and surface roughness for mild steel
0.25
462
Int J Adv Manuf Technol (2011) 54:445–463 Mild Steel
Machining time in seconds
140 120 100 80
Predicted & actual machining time
60 40 20 0 0.9
1
1.1
1.2
1.3
1.4
1.5
1.3
1.4
1.5
Surface roughness in microns
Depth of cut in mm 2
1.5
1
0.5
0 0.9
Actual roughness
Predicted roughness
1
1.1
1.2
Depth of cut in mm
Fig. 14 Depth of cut versus machining time and surface roughness for mild steel
&
& &
& &
grinding, etc. under various economic criteria and numerous practical constraints. The surface roughness equation developed for machining brass, aluminum, copper, and mild steel using tungsten carbide insert can be used for industrial applications to get optimal machining parameters. Surface roughness can be improved by the proposed approach instead of engineering judgment. Deviations between actual and predicted surface roughness are very small, and the overall accuracy rate of the present approach is found to be 85 % in an average for all the considered work piece materials. Use of higher cutting speed, lower feed, and depth of cut is recommended to obtain better surface roughness for the given range. Feed has greater influence on machining time and surface roughness when compared to cutting speed and depth of cut.
8.1 Scope for future work In the present work, machining time is minimized subject to the desired surface roughness value based on PSO and confirmed the same by conducting experiments using the same parameters. But, metal machining is a complex
phenomenon and so inclusion of many other machining parameters and constraints may enhance the end result. Multi-pass turning or component-based attempts can be carried out to show ability and effectiveness of nontraditional optimization techniques.
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