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Optimization of friction welding parameters using evolutionary computational techniques
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 2576–2584
journal homepage: www.elsevier.com/locate/jmatprotec
Optimization of friction welding parameters using evolutionary computational techniques P. Sathiya a,∗ , S. Aravindan b , A. Noorul Haq a , K. Paneerselvam a a b
Department of Production Engineering, National Institute of Technology, Tiruchirappalli 620015, Tamilnadu, India Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India
a r t i c l e
i n f o
a b s t r a c t
Article history:
The purpose of this study is to propose a method to decide near optimal settings of the
Received 23 July 2007
welding process parameters in friction welding of stainless steel (AISI 304) by using non
Received in revised form
conventional techniques and artificial neural network (ANN). The methods suggested in
19 May 2008
this study were used to determine the welding process parameters by which the desired
Accepted 7 June 2008
tensile strength and minimized metal loss were obtained in friction welding. This study describes how to obtain near optimal welding conditions over a wide search space by conducting relatively a smaller number of experiments. The optimized values obtained through
Keywords:
these evolutionary computational techniques were compared with experimental results.
Tensile strength
The strength and microstructural aspects of the processed joints were also analyzed to
Metal loss
validate the optimization.
Genetic algorithm (GA)
© 2008 Elsevier B.V. All rights reserved.
Simulated annealing (SA) Particle swarm optimization (PSO) Artificial neural network (ANN)
1.
Introduction
Friction welding is a solid state joining process that produces coalescence by harnessing the heat developed through controlled rubbing of the faying surfaces. Due to the heat, the material reaches the softened state, at which the plasticized material begins to form layers that intervene with one another and results in good quality weld. To produce the good quality joint it is important to set up the proper welding process parameters. The welding process is a multi-input and multi-output process in which joints are closely associated with welding parameters. Therefore, identifying the suitable combinations of process input parameters to produce the desired output require many experiments (Kalyanmoy, 1996), making this process time consuming and costly. There have been many studies on screening experiments, modeling and
∗
Corresponding author. Tel.: +91 94434 94090; fax: +91 431 2500133. E-mail address: [email protected] (P. Sathiya). 0924-0136/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2008.06.030
optimization for welding processes. However, there are few techniques to move the experimental to region near optimal welding condition. The development of mathematical models for the selection of the process parameters and the prediction of bead geometry (bead width, bead height and penetration). Factorial design was employed as a guide for optimization of process parameters (Kim et al., 2003). Statistical experimental designs were used for optimizing process parameters. Three commonly employed dissimilar metal combinations are used and only fair agreement was obtained between predicted and actual strengths for joints (Murti and Sundaresan, 1983). The selection of process parameters for obtaining optimal weld pool geometry in the tungsten inert gas welding of the stainless steel. The modified taguchi method is adopted to analyze the effect of each welding process parameters on the weld pool geometry, and to determine the process parameters
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with optimal weld pool geometry (Juang and Tarang, 2002). Response Surface Methodology (RSM) by designing a four factor, five level central composite rotatable design matrix with full replication for planning, conduction, execution and development of mathematical models. These are useful not only for selecting optimum process parameters but also for achieving the desired quality and process optimization (Gunaraj and Murugan, 1999). Neural network and multiple regression methods were used to understand the relationships between process parameters and top-bead width, and to predict the process parameters on top-bead width in robotic gas metal arc welding process (Ill-Soo et al., 2003). Polar coordinate model were established to characterize the weld pool geometry. A neural network was therefore proposed to identify the parameters in real time. By using pulsed laser elimination, clear images of the weld pool could be captured. The developed imageprocessing algorithm extracts the boundary of the weld pool in the real time, to determine the optimized welding process parameters and to obtain the desired weld bead geometry in gas metal arc welding (Zhang et al., 1996). The output variables were the bead height and depth of penetration of weld bead. These output variables were determined according to the input variables, which are the root opening, wire feed rate, welding voltage and welding speed (Kim and Rhee, 2001). Neutral network was constructed to obtain the relationship between welding process parameters and weld pool geometry in TIG welding process. An optimization algorithm called simulated annealing (SA) is then applied to the network for searching the process parameters with optimal weld pool geometry. From the observations made on the above literature, optimization of friction welding parameters will be of time consuming if the conventional technique of optimization is used, by concentrating on a single parameter whereas keeping the others as constant (Tarang et al., 1999). A hybrid intelligent method for Electric Discharge Machining process discusses on cultivating the advantages of the two methods namely artificial neural network (ANN) and genetic algorithm(GA) (Kesheng et al., 2003). The main objectives in this study are to maximize the tensile strength and minimize the metal loss. In this work to achieve the above mentioned objectives artificial neural network, is used to map the input/output relationships of the joining process, with the help of the experimental data and then genetic algorithm, simulated annealing (SA) and particle swarm optimization (PSO) are used to search the near optimal welding parameters.
2.
Table 2 – Input variable range S. no.
Input variable
1 2 3 4
Range
Heating pressure (HP) Heating time (HT) Upsetting pressure (UP) Upsetting time (UT)
15–25 bar 3–10 s 35–45 bar 3–7 s
tion and forge pressures are in the range of 15–25 bar and 35–45 bar respectively. The spindle rotating speed was kept constant at 1125 rpm and the welding was performed under the specified friction upset distance. Austenitic stainless steel (AISI 304) specimens of size 16 mm diameters and a length of 160 mm were used as parent materials in this study. The chemical composition of the specimen material is presented in Table 1. Similar austenitic stainless steel specimens were joined by friction welding process without any preheat. The range of parameters in friction welding is presented in Table 2. Friction joints are processed experimentally at randomly chosen parameters sets. For each parameter set, five joints were processed. Strength related properties of the joints were tested and the average data is presented. Theoretical optimization was carried out in order to maximize the tensile strength of the joint and to minimize the metal loss by non-traditional optimization techniques. The process was considered here as multi-input and multi-output system. The objective function was formulated by artificial neural network method.
3.
Problem formulation
The friction welding parameters such as heating pressure (HP), heating time (HT), upsetting pressure (UP), and upsetting time (UT) are highly influencing the mechanical properties of the weld in turn dictate the qualities of the joints. Increased tensile strength and reduced metal loss are the objectives of this study.
Experimental details
A continuous drive friction welding machine (KUKA, Germany) with a maximum 150 kN load was used for welding. The fric-
Fig. 1 – Structure of ANN model to predict tensile strength and metal loss.
Table 1 – Base material chemical composition Element
%
C
Si
Mn
P
Cr
Ni
Co
Mo
As
Pb
Ti
0.046
0.344
1.31
0.018
17.8
8.28
0.078
0.01
0.015
0.0007
0.035
Fe Balance
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So the combined objective function is to maximize J, which is given as follows J=
w T w M 1 0 2 0 Td
−
(1)
Md
where J is the combined objective function, T0 is obtained tensile strength in MPa, M0 is obtained metal loss in mm, Td is desired tensile strength in MPa (696 MPa, 120% of parent material strength), Md is desired metal loss in mm (4 mm, 2.5% of total length of the joint); w1 is weight for obtained tensile strength (0.8); w2 is weight for obtained metal loss (0.2) (values of Md , Td , w1 and w2 were chosen arbitrarily).
3.1.
General model
Process modeling and optimization are very important issues in welding engineering. Welding processes are usually too complicated to warrant appropriate analytical models and most of the time, analytical models are developed based on many assumptions, which contradict reality. More importantly, it is sometimes difficult to adjust the parameters of the models according to the actual situation of the welding process. Because of the complexity of the welding process, optimization and optimal control are difficult to perform. Therefore, artificial neural network is used, which can map the input/output relationships of joining process. The back-propagation network is the most commonly used neural network because there exists a mathematically strict learning scheme to train the network and guarantee mapping between inputs and outputs. Back-propagation neural network (Haykin, 1999) is usually referred to as feed forwarded, multi-layered network with a number of hidden layers, trained with a gradient descent technique as explained in Fig. 1. Preliminary trials on friction welding were performed on a random manner within the available range. The tensile strength and the metal loss of the processed joints were determined. The input parameters and the output parameters of the processed joints were presented in Table 3. These parameters were used to train the ANN model. Fig. 2 explains the accuracy of the developed model with the number of iterations. From the figure, it is observed that the training were planned
Fig. 2 – Number of iterations vs percentage errors.
to perform upto 9,000 iterations which are necessary to obtain minimized mean standard error, but we obtained minimum mean standard error of 4.90479e−914 at 8552 iterations itself. The developed ANN model is integrated with optimization algorithm as explained in the flow chart, presented in Fig. 3.
3.2.
Welding constraints
The practical constraints imposed during the welding operations are stated as follows. Parameter bounds: • Bounds on heating pressure HPL ≤ HP ≤ HPU
(1)
where HPL and HPU are the lower and upper bounds of heating pressure, respectively.
Table 3 – Experimental values of friction processed joints S. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Heating pressure (HP) (bar) 15 20 20 15 16 17 18 19 20 21 22 23 24 25
Heating time (HT) (s) 3 5 8 5 5 6 6 7 7 8 8 9 9 10
Upsetting pressure (UP) (bar) 40 40 45 35 36 37 38 39 40 41 42 43 44 45
Upsetting time (UT) (s) 5 7 3 3 3 4 4 5 5 6 6 7 7 7
Tensile strength (MPa)
Metal loss (mm)
596.7 581.3 542.7 585.0 580.7 574.0 562.7 551.3 542.3 535.0 533.7 523.0 524.8 524.0
9.56 11.38 10.7 9.86 12.62 12.87 12.86 13.15 13.87 13.92 13.94 13.65 13.95 14.1
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4.1.
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Genetic algorithm methodology
Genetic algorithms are computerized search and optimization algorithms based on the mechanics of natural genetics and natural selection. GA is very different from traditional search and optimization methods used in engineering problems. Because of its simplicity, ease of operation, minimum requirements and global perspective, GA has been successfully used in a wide variety of problems (Kalyanmoy, 1996). The general optimization procedure using a genetic algorithm is shown in Fig. 4.
4.1.1.
• Step 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 tmax . Set t = 0. • Step 2: Evaluate each string in the population. • Step 3: If t > tmax or other termination criteria is satisfied, terminate. • Step 4: Perform reproductions on the population.
Fig. 3 – Flow chart for general model usage with optimization algorithms.
• Bounds on heating time HTL ≤ HT ≤ HTU
Steps in genetic algorithm
(2)
where HTL and HTU are the lower and upper bounds of heating time, respectively. • Bounds on upsetting pressure UPL ≤ UP ≤ UPU
(3)
where UPL and UPU are the lower and upper bounds of upsetting pressure, respectively. • Bounds on upsetting time UTL ≤ UT ≤ UTU
(4)
where UTL and UTU are the lower and upper bounds of upsetting time, respectively.
4.
Solution methodology
Most of the researchers have used traditional optimization techniques for solving engineering problems. The traditional methods of optimization and search do not perform well over a broad spectrum of problem domains. Traditional techniques are not efficient when practical search space is too large. These algorithms are not robust. Traditional techniques such as geometric programming, dynamic programming and branch and bound techniques found hard to solve these problem and they are inclined to obtain a local optimal solution. Based on the merits of non-traditional optimization techniques over traditional techniques, this paper has proposed to compare three non-traditional techniques (GA, SA and PSO) in solving welding optimization problem.
Fig. 4 – The general structure of the genetic algorithm.
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• Step 5: Perform crossovers on pair of strings with probability pc . • Step 6: Perform mutations on strings with probability pm . • Step 7: Evaluate strings in the new population. Set = t + 1 and go to Step 3.
4.1.2.
Genetic algorithm parameters
The parameters used for GA is given below. Population size Length of chromosome Selection operator Crossover operator Crossover probability Mutation probability Fitness parameter
100 40 Roulette method Single point operator 0.9 0.01 Tensile strength and metal loss
4.2.
Simulated annealing algorithm
The flow chart for the simulated annealing algorithm is shown in Fig. 5. The algorithm begins with an initial point x1 (HP1 , HT1 , UP1 , and UT1 ) and a high temperature T. A second point x2 (HP2 , HT2 , UP2 , and UT2 ) is created using Gaussian distribution and the differences in the function values (E) at these points are calculated. If the second point has a smaller value, the point is accepted. Otherwise the point is accepted with a probability exp (−E/t). This completes one iteration of the simulated annealing procedure. The algorithm is terminated when a sufficiently small temperature is obtained or a small enough change in function value is obtained (Kalyanmoy, 1996).
4.2.1.
Simulated annealing steps
Step 1: Choose an initial point x1 , Set T as a sufficiently high value. Cooling rate C. And set, t = 0.
Fig. 5 – Flow chart for the simulated annealing algorithm.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 2576–2584
Step 2: Calculate a neighboring point using Gaussian distribution
x2 = x1 +
n i=1
n ri − 2
where
= varaince =
maximum value of parameter −mininum value of parameter 6
n: number of random numbers; ri : random numbers. Step 3: If E = E(x(t+1) )–E(x(t) ) > 0, i.e. if the difference in the fitness value ispositive then, set T = T*C; else create an random number (r) in the range (0, 1). If the r ≤ exp(E/T) set T = T*C; else go to Step 2. Step 4: If the temperature is small, terminate. Else go to Step 2. The parameters used in the simulated annealing algorithm are given as: the initial temperature Ts = 1000 ◦ C, the final temperature Te = 1 ◦ C and the decaying ratio Cr = 0.95.
4.3.
tions and searches for optimum by updating generations. However, unlike GA, PSO has no evolution operators such as crossover and mutation. In PSO, the solutions, called particles, are “flown” through the problem space by following the current optimum particles. The flow chart for the particle swarm optimization algorithm is shown in Fig. 6.
4.3.1. .
Particle swarm optimization
Particle swarm optimization (PSO) is an evolutionary computation technique was developed in 1995, inspired by social behavior of bird flocking or fish schooling (Haykin, 1999). Similar to GA, PSO is a population based optimization tool. The system is initialized with a population of random solu-
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PSO parameter control
In PSO following parameters are needed to be tuned. Here is a list of the parameters and their typical values. (a) The number of particles The typical range is 20–40. Actually for most of the problems, 10 particles is large enough to get good results. For some difficult or special problems, one can try 100 or 200 particles as well. (b) Dimension of particles Dimension of particles is determined by the problem to be optimized. Here, heating pressure (HP), heating time (HT), upsetting pressure (UP) and upsetting time (UT) are taken as the dimension of particles. (c) Range of particles Range of particles is determined by the problem to be optimized. (d) Learning factors c1 and c2 are learning factors usually equals to 2. However, other settings can be also used in different process. But usually c1 equals to c2 and ranges from 0 to 4. (e) The stop condition
Fig. 6 – Flow chart describing the particle swarm optimization (PSO) algorithm.
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The stop condition depends on the problem to be optimized. The maximum number of iteration that the PSO can execute is termed as the stop condition. (f) Inertia weight It is the weight given to the previous velocity. It’s value equals to 0.5 for the best result.
4.3.2.
PSO algorithm
PSO is initialized with a group of random particles (solutions) and then searches for optimum by updating generations. In every iteration, each particle is updated by the following two “best” values. The first one is the best solution (fitness) it has achieved so far. (The fitness value is also stored). This value is called pbest. Another “best” value that is tracked by the particle swarm optimizer is the best value among the current and previous pbest values, obtained so far by any particle in the population. This best value is a global best and hence it is called as gbest. Fig. 6 shows the flow chart for the particle swarm optimization algorithm. The following equations are used to update the velocity and position of the algorithm,
Fig. 7 – Friction-welded sample.
v [ ] = w ∗ v[] + c1 ∗ rand( ) ∗ (pbest[ ] − present[ ]) + c2 ∗ rand( ) ∗ (gbest[ ] − present[ ])
(5) Fig. 8 – Tensile tested sample.
present[ ] = persent[ ] + v[ ]
(6)
where v[ ] is the particle velocity; persent[ ] is the current particle (solution), pbest[ ] is the particle’s best, gbest[ ] is the global best, rand( ) is a random number between (0, 1), c1 , c2 are learning factors. Usually c1 = c2 = 2.
5.
Results and discussion
Investigations were carried out already to assess the relationship of microstructure/property relationships of similar and dissimilar joints of stainless steel by various welding processes (Eberhart and Kennedy, 1995; Mohandas et al., 1999; Ramazan and Orhan, 2004; Hisoshi et al., 1997). The effects of joining process parameters on metallurgical and mechanical properties of friction-welded (304 austenitic stainless steel) joints were investigated, and the correlation between the microstructure and the joint strength was carried out (Sathiya et al., 2005). Due to the difficulties associated with conventional way of optimization, we used evolutionary computational techniques to get maximized tensile strength and minimized metal loss. Typical macrograph of the friction-
Fig. 9 – Fracture surface of the friction-welded tensile sample.
welded specimen is presented in Fig. 7. The friction welding experiments were conducted with a random change of parameters with in the range specified in Table 2. The processed joints were subjected to tensile testing to evaluate the strength related aspects of joints. The process parameters for the
Table 4 – Comparison of results of various algorithms Algorithm
Genetic algorithm (GA) Simulated annealing (SA) Particle swarm optimization (PSO)
Heating pressure (HP) (bar) 17.7028 16.0535 16.1598
Heating time (HT) (s) 4.2663 4.3096 6.3566
Upsetting pressure (UP) (bar) 35.1078 39.7534 37.1210
Upsetting time (UT) (s) 4.0250 5.7388 5.9542
Metal loss (M0 ) (mm) 8.9114 9.1401 9.0694
Tensile strength (T0 ) (MPa) 591.9098 591.8333 591.6310
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Fig. 10 – SEM photograph of the fracture surface for tensile test specimen (500×). Table 5 – Comparison between theoretical and experimental input and output values Input parameters Heating pressure (HP) (bar) Theoretically optimized parameters by GA Experimentally used parameters
Output parameters
Upsetting pressure (UP) (bar)
17.7028
4.2663
35.1078
4.0250
8.9114
591.9098
17
4
35
4
9.8
586
joints and the associated strength and metal loss are presented in Table 4. These experimental input and output values were utilized to train the general ANN model (explained in Section 3) developed using MATLAB. The flow chart (Fig. 3) explains the general procedure of optimization. The program is constructed in such a way that the trained ANN will take random input parameters from the optimization algorithm (GA/SA/PSO) and the output of ANN is again presented to algorithm for optimization and finally the respective optimized outputs are obtained separately. The results obtained from the optimization algorithm (GA/SA/PSO) are presented in Table 4. The table presents the optimized parameters for the maximized strength and minimized metal loss. From the Table 4, it can be observed that for this friction processed joints, among the optimization techniques used, GA, give the best results in terms of maximized tensile strength and minimized metal loss. The best input parameters obtained through GA, were used to process the friction joints experimentally. The tensile strength and metal loss of those joints were evaluated. Typical tensile tested specimen which was machined from the joint processed at the optimized input parameters by genetic algorithm is presented in Fig. 8. The macrograph of the fractured specimen is presented in Fig. 9. From the macrograph presented above, it can be understood that the joints failed mostly at the nearby joint zone and partly through the parent material. Fig. 10 shows the SEM micrographs of the fractured surface of the tensile tested specimen. The shear flow of material observed in the micrographs is the mechanism behind the failure of joint. Micrographs also reveal smaller dimple like structures which confirm the ductile mode failure of the joints. Table 5 presents the theoretical and experimental input and output parameters of the friction processed similar joints of stainless steel (AISI 304). The very close agree-
Upsetting time (UT) (s)
Metal loss (M0 ) (mm)
Tensile strength (T0 ) (MPa)
Heating time (HT) (s)
ment between theoretical and experimental data confirms the potential applicability of these evolutionary computational techniques for the industrial problems.
6.
Conclusion
The following conclusions are drawn from this work. • Investigation on the implementation of friction welding of similar stainless steel (AISI 304) joints is carried out. The relationship between the input parameters such as heating pressure, heating time, upsetting pressure and upsetting time with the output parameters like tensile strength and metal loss is modeled through ANN. The developed ANN model is suitably integrated with optimization algorithms. To optimize the welding parameters, GA, SA and PSO techniques were employed. Among the three algorithms GA outperforms well for this friction welding process. • For the optimized welding parameters of GA, the friction welding joints were processed. Joints exhibit higher quality. The good agreement between the theoretically predicted (GA) and experimentally obtained tensile strength and metal loss confirms the applicability of these evolutionary computational techniques for optimization of process parameters in the welding process.
references
Eberhart, D., Kennedy, J., 1995. Particle swarm optimization. Proceedings of IEEE International Conference on Neural Networks, 1942–1948.
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Gunaraj, V., Murugan, N., 1999. Application of response surface methodology for predicting weld bead quality in submerged arc welding of pipes. Journal of Material Processing Technology 88, 266–275. Haykin, S., 1999. Neural Network. In: A Comprehensive Foundation. Macmillan, New York. Hisoshi, Y., Koishi, O., Toshiro, K., Yoshinao, T., 1997. Evaluation of friction welded joint performance. International Journal of the Japan Society for Precision Engineering 31, 10–14. Ill-Soo Kim, Joon-Sik Son, Prasad Yarlagadda, K.D.V., 2003. A study on the quality improvement of robotic GMA welding process, Robotics and Computer Integrated Manufacturing 19, 567– 572. Juang, S.C., Tarang, Y.S., 2002. Process Parameter selection for optimizing the weld pool geometry in the tungsten inert gas welding of stainless steel. Journal of Materials Processing Technology 122, 33–37. Kalyanmoy, D., 1996. Optimizations for Engineering Design – Algorithm and Examples. Prentice Hall of India, New Delhi, pp. 290–333. Kesheng, W., Hirpa, L., Gelgele, Y., Qingfeng, Y., Minglung, F., 2003. A hybrid intelligent method for modeling the EDM process. International Journal of Machine Tools & Manufacture 43, 995–999. Kim, D., Rhee, S., 2001. Optimization of arc welding process parameters using a genetic algorithm. Welding Journal, 184–189.
Kim, I.S., Son, K.J., Yang, Y.S., Yaragada, P.K.D.V., 2003. Sensitivity analysis for process parameters in GMA welding processes using a factorial design method. International Journal of Machine Tools & Manufacture 43, 763–769. Mohandas, T., Madhusudhan Reddy, G., Mohammad, N., 1999. A comparative evaluation of gas tungsten and shielded metal arc welds of a ferritic stainless steel. Journal of Material Processing Technology 94, 133–140. Murti, K.G.K., Sundaresan, S., 1983. Parameter optimization in friction welding dissimilar materials. Metal Construction, 331–335. Ramazan, K., Orhan, B., 2004. An investigation of microstructure/properties relationships in dissimilar welds between martensitic and austenitic stainless steel. Materials and Design 25, 317–329. Sathiya, P., Aravindan, S., Noorul Haq, A., 2005. Mechanical and metallurgical properties of friction welded AISI 304 stainless steel. International Journal of Advanced Manufacturing Technology 26, 501–511. Tarang, Y.S., Tsai, H.L., Yeh, S.S., 1999. Modeling optimization and classification of weld quality in tungsten inert gas welding. International Journal of Machine Tools & Manufacture 39, 1427–1438. Zhang, Y.M., Kovacevic, R., Li, L., 1996. Characterization and real-time measurement of geometrical appearance of the weld pool. International Journal of Machine tools & Manufacture 136, 799–816.
journal homepage: www.elsevier.com/locate/jmatprotec
Optimization of friction welding parameters using evolutionary computational techniques P. Sathiya a,∗ , S. Aravindan b , A. Noorul Haq a , K. Paneerselvam a a b
Department of Production Engineering, National Institute of Technology, Tiruchirappalli 620015, Tamilnadu, India Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India
a r t i c l e
i n f o
a b s t r a c t
Article history:
The purpose of this study is to propose a method to decide near optimal settings of the
Received 23 July 2007
welding process parameters in friction welding of stainless steel (AISI 304) by using non
Received in revised form
conventional techniques and artificial neural network (ANN). The methods suggested in
19 May 2008
this study were used to determine the welding process parameters by which the desired
Accepted 7 June 2008
tensile strength and minimized metal loss were obtained in friction welding. This study describes how to obtain near optimal welding conditions over a wide search space by conducting relatively a smaller number of experiments. The optimized values obtained through
Keywords:
these evolutionary computational techniques were compared with experimental results.
Tensile strength
The strength and microstructural aspects of the processed joints were also analyzed to
Metal loss
validate the optimization.
Genetic algorithm (GA)
© 2008 Elsevier B.V. All rights reserved.
Simulated annealing (SA) Particle swarm optimization (PSO) Artificial neural network (ANN)
1.
Introduction
Friction welding is a solid state joining process that produces coalescence by harnessing the heat developed through controlled rubbing of the faying surfaces. Due to the heat, the material reaches the softened state, at which the plasticized material begins to form layers that intervene with one another and results in good quality weld. To produce the good quality joint it is important to set up the proper welding process parameters. The welding process is a multi-input and multi-output process in which joints are closely associated with welding parameters. Therefore, identifying the suitable combinations of process input parameters to produce the desired output require many experiments (Kalyanmoy, 1996), making this process time consuming and costly. There have been many studies on screening experiments, modeling and
∗
Corresponding author. Tel.: +91 94434 94090; fax: +91 431 2500133. E-mail address: [email protected] (P. Sathiya). 0924-0136/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2008.06.030
optimization for welding processes. However, there are few techniques to move the experimental to region near optimal welding condition. The development of mathematical models for the selection of the process parameters and the prediction of bead geometry (bead width, bead height and penetration). Factorial design was employed as a guide for optimization of process parameters (Kim et al., 2003). Statistical experimental designs were used for optimizing process parameters. Three commonly employed dissimilar metal combinations are used and only fair agreement was obtained between predicted and actual strengths for joints (Murti and Sundaresan, 1983). The selection of process parameters for obtaining optimal weld pool geometry in the tungsten inert gas welding of the stainless steel. The modified taguchi method is adopted to analyze the effect of each welding process parameters on the weld pool geometry, and to determine the process parameters
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with optimal weld pool geometry (Juang and Tarang, 2002). Response Surface Methodology (RSM) by designing a four factor, five level central composite rotatable design matrix with full replication for planning, conduction, execution and development of mathematical models. These are useful not only for selecting optimum process parameters but also for achieving the desired quality and process optimization (Gunaraj and Murugan, 1999). Neural network and multiple regression methods were used to understand the relationships between process parameters and top-bead width, and to predict the process parameters on top-bead width in robotic gas metal arc welding process (Ill-Soo et al., 2003). Polar coordinate model were established to characterize the weld pool geometry. A neural network was therefore proposed to identify the parameters in real time. By using pulsed laser elimination, clear images of the weld pool could be captured. The developed imageprocessing algorithm extracts the boundary of the weld pool in the real time, to determine the optimized welding process parameters and to obtain the desired weld bead geometry in gas metal arc welding (Zhang et al., 1996). The output variables were the bead height and depth of penetration of weld bead. These output variables were determined according to the input variables, which are the root opening, wire feed rate, welding voltage and welding speed (Kim and Rhee, 2001). Neutral network was constructed to obtain the relationship between welding process parameters and weld pool geometry in TIG welding process. An optimization algorithm called simulated annealing (SA) is then applied to the network for searching the process parameters with optimal weld pool geometry. From the observations made on the above literature, optimization of friction welding parameters will be of time consuming if the conventional technique of optimization is used, by concentrating on a single parameter whereas keeping the others as constant (Tarang et al., 1999). A hybrid intelligent method for Electric Discharge Machining process discusses on cultivating the advantages of the two methods namely artificial neural network (ANN) and genetic algorithm(GA) (Kesheng et al., 2003). The main objectives in this study are to maximize the tensile strength and minimize the metal loss. In this work to achieve the above mentioned objectives artificial neural network, is used to map the input/output relationships of the joining process, with the help of the experimental data and then genetic algorithm, simulated annealing (SA) and particle swarm optimization (PSO) are used to search the near optimal welding parameters.
2.
Table 2 – Input variable range S. no.
Input variable
1 2 3 4
Range
Heating pressure (HP) Heating time (HT) Upsetting pressure (UP) Upsetting time (UT)
15–25 bar 3–10 s 35–45 bar 3–7 s
tion and forge pressures are in the range of 15–25 bar and 35–45 bar respectively. The spindle rotating speed was kept constant at 1125 rpm and the welding was performed under the specified friction upset distance. Austenitic stainless steel (AISI 304) specimens of size 16 mm diameters and a length of 160 mm were used as parent materials in this study. The chemical composition of the specimen material is presented in Table 1. Similar austenitic stainless steel specimens were joined by friction welding process without any preheat. The range of parameters in friction welding is presented in Table 2. Friction joints are processed experimentally at randomly chosen parameters sets. For each parameter set, five joints were processed. Strength related properties of the joints were tested and the average data is presented. Theoretical optimization was carried out in order to maximize the tensile strength of the joint and to minimize the metal loss by non-traditional optimization techniques. The process was considered here as multi-input and multi-output system. The objective function was formulated by artificial neural network method.
3.
Problem formulation
The friction welding parameters such as heating pressure (HP), heating time (HT), upsetting pressure (UP), and upsetting time (UT) are highly influencing the mechanical properties of the weld in turn dictate the qualities of the joints. Increased tensile strength and reduced metal loss are the objectives of this study.
Experimental details
A continuous drive friction welding machine (KUKA, Germany) with a maximum 150 kN load was used for welding. The fric-
Fig. 1 – Structure of ANN model to predict tensile strength and metal loss.
Table 1 – Base material chemical composition Element
%
C
Si
Mn
P
Cr
Ni
Co
Mo
As
Pb
Ti
0.046
0.344
1.31
0.018
17.8
8.28
0.078
0.01
0.015
0.0007
0.035
Fe Balance
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So the combined objective function is to maximize J, which is given as follows J=
w T w M 1 0 2 0 Td
−
(1)
Md
where J is the combined objective function, T0 is obtained tensile strength in MPa, M0 is obtained metal loss in mm, Td is desired tensile strength in MPa (696 MPa, 120% of parent material strength), Md is desired metal loss in mm (4 mm, 2.5% of total length of the joint); w1 is weight for obtained tensile strength (0.8); w2 is weight for obtained metal loss (0.2) (values of Md , Td , w1 and w2 were chosen arbitrarily).
3.1.
General model
Process modeling and optimization are very important issues in welding engineering. Welding processes are usually too complicated to warrant appropriate analytical models and most of the time, analytical models are developed based on many assumptions, which contradict reality. More importantly, it is sometimes difficult to adjust the parameters of the models according to the actual situation of the welding process. Because of the complexity of the welding process, optimization and optimal control are difficult to perform. Therefore, artificial neural network is used, which can map the input/output relationships of joining process. The back-propagation network is the most commonly used neural network because there exists a mathematically strict learning scheme to train the network and guarantee mapping between inputs and outputs. Back-propagation neural network (Haykin, 1999) is usually referred to as feed forwarded, multi-layered network with a number of hidden layers, trained with a gradient descent technique as explained in Fig. 1. Preliminary trials on friction welding were performed on a random manner within the available range. The tensile strength and the metal loss of the processed joints were determined. The input parameters and the output parameters of the processed joints were presented in Table 3. These parameters were used to train the ANN model. Fig. 2 explains the accuracy of the developed model with the number of iterations. From the figure, it is observed that the training were planned
Fig. 2 – Number of iterations vs percentage errors.
to perform upto 9,000 iterations which are necessary to obtain minimized mean standard error, but we obtained minimum mean standard error of 4.90479e−914 at 8552 iterations itself. The developed ANN model is integrated with optimization algorithm as explained in the flow chart, presented in Fig. 3.
3.2.
Welding constraints
The practical constraints imposed during the welding operations are stated as follows. Parameter bounds: • Bounds on heating pressure HPL ≤ HP ≤ HPU
(1)
where HPL and HPU are the lower and upper bounds of heating pressure, respectively.
Table 3 – Experimental values of friction processed joints S. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Heating pressure (HP) (bar) 15 20 20 15 16 17 18 19 20 21 22 23 24 25
Heating time (HT) (s) 3 5 8 5 5 6 6 7 7 8 8 9 9 10
Upsetting pressure (UP) (bar) 40 40 45 35 36 37 38 39 40 41 42 43 44 45
Upsetting time (UT) (s) 5 7 3 3 3 4 4 5 5 6 6 7 7 7
Tensile strength (MPa)
Metal loss (mm)
596.7 581.3 542.7 585.0 580.7 574.0 562.7 551.3 542.3 535.0 533.7 523.0 524.8 524.0
9.56 11.38 10.7 9.86 12.62 12.87 12.86 13.15 13.87 13.92 13.94 13.65 13.95 14.1
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4.1.
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Genetic algorithm methodology
Genetic algorithms are computerized search and optimization algorithms based on the mechanics of natural genetics and natural selection. GA is very different from traditional search and optimization methods used in engineering problems. Because of its simplicity, ease of operation, minimum requirements and global perspective, GA has been successfully used in a wide variety of problems (Kalyanmoy, 1996). The general optimization procedure using a genetic algorithm is shown in Fig. 4.
4.1.1.
• Step 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 tmax . Set t = 0. • Step 2: Evaluate each string in the population. • Step 3: If t > tmax or other termination criteria is satisfied, terminate. • Step 4: Perform reproductions on the population.
Fig. 3 – Flow chart for general model usage with optimization algorithms.
• Bounds on heating time HTL ≤ HT ≤ HTU
Steps in genetic algorithm
(2)
where HTL and HTU are the lower and upper bounds of heating time, respectively. • Bounds on upsetting pressure UPL ≤ UP ≤ UPU
(3)
where UPL and UPU are the lower and upper bounds of upsetting pressure, respectively. • Bounds on upsetting time UTL ≤ UT ≤ UTU
(4)
where UTL and UTU are the lower and upper bounds of upsetting time, respectively.
4.
Solution methodology
Most of the researchers have used traditional optimization techniques for solving engineering problems. The traditional methods of optimization and search do not perform well over a broad spectrum of problem domains. Traditional techniques are not efficient when practical search space is too large. These algorithms are not robust. Traditional techniques such as geometric programming, dynamic programming and branch and bound techniques found hard to solve these problem and they are inclined to obtain a local optimal solution. Based on the merits of non-traditional optimization techniques over traditional techniques, this paper has proposed to compare three non-traditional techniques (GA, SA and PSO) in solving welding optimization problem.
Fig. 4 – The general structure of the genetic algorithm.
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• Step 5: Perform crossovers on pair of strings with probability pc . • Step 6: Perform mutations on strings with probability pm . • Step 7: Evaluate strings in the new population. Set = t + 1 and go to Step 3.
4.1.2.
Genetic algorithm parameters
The parameters used for GA is given below. Population size Length of chromosome Selection operator Crossover operator Crossover probability Mutation probability Fitness parameter
100 40 Roulette method Single point operator 0.9 0.01 Tensile strength and metal loss
4.2.
Simulated annealing algorithm
The flow chart for the simulated annealing algorithm is shown in Fig. 5. The algorithm begins with an initial point x1 (HP1 , HT1 , UP1 , and UT1 ) and a high temperature T. A second point x2 (HP2 , HT2 , UP2 , and UT2 ) is created using Gaussian distribution and the differences in the function values (E) at these points are calculated. If the second point has a smaller value, the point is accepted. Otherwise the point is accepted with a probability exp (−E/t). This completes one iteration of the simulated annealing procedure. The algorithm is terminated when a sufficiently small temperature is obtained or a small enough change in function value is obtained (Kalyanmoy, 1996).
4.2.1.
Simulated annealing steps
Step 1: Choose an initial point x1 , Set T as a sufficiently high value. Cooling rate C. And set, t = 0.
Fig. 5 – Flow chart for the simulated annealing algorithm.
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Step 2: Calculate a neighboring point using Gaussian distribution
x2 = x1 +
n i=1
n ri − 2
where
= varaince =
maximum value of parameter −mininum value of parameter 6
n: number of random numbers; ri : random numbers. Step 3: If E = E(x(t+1) )–E(x(t) ) > 0, i.e. if the difference in the fitness value ispositive then, set T = T*C; else create an random number (r) in the range (0, 1). If the r ≤ exp(E/T) set T = T*C; else go to Step 2. Step 4: If the temperature is small, terminate. Else go to Step 2. The parameters used in the simulated annealing algorithm are given as: the initial temperature Ts = 1000 ◦ C, the final temperature Te = 1 ◦ C and the decaying ratio Cr = 0.95.
4.3.
tions and searches for optimum by updating generations. However, unlike GA, PSO has no evolution operators such as crossover and mutation. In PSO, the solutions, called particles, are “flown” through the problem space by following the current optimum particles. The flow chart for the particle swarm optimization algorithm is shown in Fig. 6.
4.3.1. .
Particle swarm optimization
Particle swarm optimization (PSO) is an evolutionary computation technique was developed in 1995, inspired by social behavior of bird flocking or fish schooling (Haykin, 1999). Similar to GA, PSO is a population based optimization tool. The system is initialized with a population of random solu-
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PSO parameter control
In PSO following parameters are needed to be tuned. Here is a list of the parameters and their typical values. (a) The number of particles The typical range is 20–40. Actually for most of the problems, 10 particles is large enough to get good results. For some difficult or special problems, one can try 100 or 200 particles as well. (b) Dimension of particles Dimension of particles is determined by the problem to be optimized. Here, heating pressure (HP), heating time (HT), upsetting pressure (UP) and upsetting time (UT) are taken as the dimension of particles. (c) Range of particles Range of particles is determined by the problem to be optimized. (d) Learning factors c1 and c2 are learning factors usually equals to 2. However, other settings can be also used in different process. But usually c1 equals to c2 and ranges from 0 to 4. (e) The stop condition
Fig. 6 – Flow chart describing the particle swarm optimization (PSO) algorithm.
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The stop condition depends on the problem to be optimized. The maximum number of iteration that the PSO can execute is termed as the stop condition. (f) Inertia weight It is the weight given to the previous velocity. It’s value equals to 0.5 for the best result.
4.3.2.
PSO algorithm
PSO is initialized with a group of random particles (solutions) and then searches for optimum by updating generations. In every iteration, each particle is updated by the following two “best” values. The first one is the best solution (fitness) it has achieved so far. (The fitness value is also stored). This value is called pbest. Another “best” value that is tracked by the particle swarm optimizer is the best value among the current and previous pbest values, obtained so far by any particle in the population. This best value is a global best and hence it is called as gbest. Fig. 6 shows the flow chart for the particle swarm optimization algorithm. The following equations are used to update the velocity and position of the algorithm,
Fig. 7 – Friction-welded sample.
v [ ] = w ∗ v[] + c1 ∗ rand( ) ∗ (pbest[ ] − present[ ]) + c2 ∗ rand( ) ∗ (gbest[ ] − present[ ])
(5) Fig. 8 – Tensile tested sample.
present[ ] = persent[ ] + v[ ]
(6)
where v[ ] is the particle velocity; persent[ ] is the current particle (solution), pbest[ ] is the particle’s best, gbest[ ] is the global best, rand( ) is a random number between (0, 1), c1 , c2 are learning factors. Usually c1 = c2 = 2.
5.
Results and discussion
Investigations were carried out already to assess the relationship of microstructure/property relationships of similar and dissimilar joints of stainless steel by various welding processes (Eberhart and Kennedy, 1995; Mohandas et al., 1999; Ramazan and Orhan, 2004; Hisoshi et al., 1997). The effects of joining process parameters on metallurgical and mechanical properties of friction-welded (304 austenitic stainless steel) joints were investigated, and the correlation between the microstructure and the joint strength was carried out (Sathiya et al., 2005). Due to the difficulties associated with conventional way of optimization, we used evolutionary computational techniques to get maximized tensile strength and minimized metal loss. Typical macrograph of the friction-
Fig. 9 – Fracture surface of the friction-welded tensile sample.
welded specimen is presented in Fig. 7. The friction welding experiments were conducted with a random change of parameters with in the range specified in Table 2. The processed joints were subjected to tensile testing to evaluate the strength related aspects of joints. The process parameters for the
Table 4 – Comparison of results of various algorithms Algorithm
Genetic algorithm (GA) Simulated annealing (SA) Particle swarm optimization (PSO)
Heating pressure (HP) (bar) 17.7028 16.0535 16.1598
Heating time (HT) (s) 4.2663 4.3096 6.3566
Upsetting pressure (UP) (bar) 35.1078 39.7534 37.1210
Upsetting time (UT) (s) 4.0250 5.7388 5.9542
Metal loss (M0 ) (mm) 8.9114 9.1401 9.0694
Tensile strength (T0 ) (MPa) 591.9098 591.8333 591.6310
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Fig. 10 – SEM photograph of the fracture surface for tensile test specimen (500×). Table 5 – Comparison between theoretical and experimental input and output values Input parameters Heating pressure (HP) (bar) Theoretically optimized parameters by GA Experimentally used parameters
Output parameters
Upsetting pressure (UP) (bar)
17.7028
4.2663
35.1078
4.0250
8.9114
591.9098
17
4
35
4
9.8
586
joints and the associated strength and metal loss are presented in Table 4. These experimental input and output values were utilized to train the general ANN model (explained in Section 3) developed using MATLAB. The flow chart (Fig. 3) explains the general procedure of optimization. The program is constructed in such a way that the trained ANN will take random input parameters from the optimization algorithm (GA/SA/PSO) and the output of ANN is again presented to algorithm for optimization and finally the respective optimized outputs are obtained separately. The results obtained from the optimization algorithm (GA/SA/PSO) are presented in Table 4. The table presents the optimized parameters for the maximized strength and minimized metal loss. From the Table 4, it can be observed that for this friction processed joints, among the optimization techniques used, GA, give the best results in terms of maximized tensile strength and minimized metal loss. The best input parameters obtained through GA, were used to process the friction joints experimentally. The tensile strength and metal loss of those joints were evaluated. Typical tensile tested specimen which was machined from the joint processed at the optimized input parameters by genetic algorithm is presented in Fig. 8. The macrograph of the fractured specimen is presented in Fig. 9. From the macrograph presented above, it can be understood that the joints failed mostly at the nearby joint zone and partly through the parent material. Fig. 10 shows the SEM micrographs of the fractured surface of the tensile tested specimen. The shear flow of material observed in the micrographs is the mechanism behind the failure of joint. Micrographs also reveal smaller dimple like structures which confirm the ductile mode failure of the joints. Table 5 presents the theoretical and experimental input and output parameters of the friction processed similar joints of stainless steel (AISI 304). The very close agree-
Upsetting time (UT) (s)
Metal loss (M0 ) (mm)
Tensile strength (T0 ) (MPa)
Heating time (HT) (s)
ment between theoretical and experimental data confirms the potential applicability of these evolutionary computational techniques for the industrial problems.
6.
Conclusion
The following conclusions are drawn from this work. • Investigation on the implementation of friction welding of similar stainless steel (AISI 304) joints is carried out. The relationship between the input parameters such as heating pressure, heating time, upsetting pressure and upsetting time with the output parameters like tensile strength and metal loss is modeled through ANN. The developed ANN model is suitably integrated with optimization algorithms. To optimize the welding parameters, GA, SA and PSO techniques were employed. Among the three algorithms GA outperforms well for this friction welding process. • For the optimized welding parameters of GA, the friction welding joints were processed. Joints exhibit higher quality. The good agreement between the theoretically predicted (GA) and experimentally obtained tensile strength and metal loss confirms the applicability of these evolutionary computational techniques for optimization of process parameters in the welding process.
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