IJAERS/Vol. I/ Issue III/April-June, 2012/55-64
Research Article
EXPERIMENTAL INVESTIGATIONS ON OPTIMIZATION OF
ULTRASONIC WELDING PARAMETERS FOR COPPER TO
BRASS JOINTS USING RESPONSE SURFACE METHOD AND
GENETIC ALGORITHM
S Elangovan 1*, S Venkateshwaran 2, K Prakasan 3
Address for Correspondence
1
Associate Professor, 2Under Graduate Student, 3Professor
Department of Production Engineering, P.S.G College of Technology, Coimbatore – India – 641004 ABSTRACT
In this paper an effective methodology is developed to determine the optimum welding conditions that maximize the strength of joints produced by ultrasonic welding by coupling response surface method (RSM) with genetic algorithm (GA). RSM is utilized to develop an effective model to predict weld strength by incorporating process parameters such as pressure, weld time and amplitude. Experiments were conducted as per central composite face centered design for spot and seam welding of 0.2 and 0.3 mm thick copper and brass specimens. An effective second order response surface model is developed by utilizing experimental measurements. Response surface model is further interfaced with the GA to optimize the welding conditions for desired weld strength. Optimum welding conditions produced from GA is verified with the experimental results and is found to be in good agreement.
KEYWORDS Optimization, Response surface method, Genetic algorithm, Ultrasonic metal welding, Weld strength. 1. INTRODUCTION
Copper and brass alloys are extensively used in automobile industries, heat exchanger and electrical applications owing to its high thermal conductivity, strength and retention of strength at sufficiently elevated temperatures. The conventional welding process of copper and brass produces large heat affected zone (HAZ) and fusion zone (FZ), high shrinkage, variations in microstructures and properties, evaporative loss of alloying elements, high residual stress and distortion which calls for the development of a solid-state joining process in which metallurgical bonding between similar or dissimilar materials can be created without melting. One such solid-state joining process is ultrasonic metal welding (USMW).
Figure 1 Schematic representation of ultrasonic metal welding
USMW is a process in which similar or dissimilar metallic components are joined by the application of high frequency vibrations which are in plane with the interface under moderate pressure as shown in Figure 1. The high frequency relative motion between the parts leads to solid progressive shearing and plastic deformation which causes a localized joining in few seconds without producing significant amount of heat and without causing changes in the properties of work pieces. In USMW at least one part must be relatively light, as it would take tremendous amount of energy to vibrate a heavy part at the necessary
frequency which limits the applicability of the process to small components and wires.
The process modeling by RSM using statistical design of experiments based on central composite face centered design is proved to be an efficient modeling tool. This method not only reduces the cost and time but also gives the required information about the main and interaction effects. In this study, a second order response surface (RS) model for predicting weld strength of ultrasonically welded copper to brass specimens is developed. The accuracy of the RS model is verified with the experimental studies. The developed RS model is further coupled with genetic algorithm (GA) to find the optimum welding conditions leading to the maximum weld strength. The predicted optimum welding condition by GA is validated with experimental results.
The use of genetic algorithm (GA) as a tool for process optimization is rapidly becoming an established approach. The GA combines the Darwinian principle of natural selection “survival of the fittest” strategy to eliminate unfit solutions and use random information exchange, with an exploitation of knowledgecontained in old solutions, to result in a search mechanism with surprising power and speed. GA using gene information and chromosome processing to optimize the given function, proved to be an efficient optimization tool [1]. The field of ultrasonic metal welding is one of the important topics in the manufacturing of accessories used in automotive, heat exchanger and electrical applications. Many researchers have reported their research work pertaining to the mechanism of joint formation, temperature distribution at the weld interface and joint strength, etc,. Some of the important observations are presented below.
Gaitonde et al. [1] developed the second order mathematical models for minimization of burr height and burr thickness using RSM. In this study, five level half replicate second order rotatable central composite designs was adopted to study the effect of interactions. The developed RSM models were used as a fitness function in GA to optimize the process parameters ford drilling. The developed model RSM
IJAERS/Vol. I/ Issue III/April-June, 2012/55-64 model was tested through ANOVA and was found to be adequate.
Padmanaban and Balasubramanian [2] developed an empirical relationship using RSM to predict tensile strength of laser beam welded AZ31B magnesium alloy. The authors have used three factor, three level central composite face centered design to optimize the parameters. They identified that the welding speed has the greatest influence on tensile strength, followed by laser power and focal position.
Research by Nuran Bradley [3] emphasized on design, modeling and analysis of RSM and explained the first-order, the second-order, and three- level fractional factorial in depth. The author explained the advantages and limitations of each models numerically and graphically.
Kumar et al. [4] proposed a methodology to improve the mechanical properties of AA 5456 aluminum alloy welds in magnetic arc oscillation welding process. The authors have used Taguchi’s method to optimize the process parameters. The percentage of error between experimental and predicted values was found to be very small. Microstructures of all the welds were studied and correlated with the mechanical properties.
Research by De Vries [5] discussed the mechanics and mechanism of USMW. Temperature was measured for the welding of aluminum by infrared camera for different welding conditions. It was found that interface temperature varied from 40 to 80 percentage of the melting point depending on the value of the parameters used for welding.
Watanabe et al.[6] investigated the effect of welding conditions on the mechanical properties and the interface microstructure of the welded joint while joining mild steel sheet to aluminum alloy sheet containing magnesium. From the experimental results it is observed that weld strength decreases with increasing of clamping force, because the excessive clamping force reduced the frictional action at the interface.
Meran [7] developed the Genetic Algorithm Welding Current/Velocity Estimation Models (GAWCEM/GAWVEM) to optimize the parameters like weld current and weld velocity in tungsten inert gas (TIG) welding. The developed models are compared with experimental data and are found to be in good agreement.
Onwubolu and Shivendra Kumar [8] presented a mathematical model for correlating the interaction of drilling parameters and their effect on the cutting tool using RSM in CNC drilling process. In this work, three level full factorial designs were chosen for experiments. The optimam combinations of these parameters from RSM were useful for minimizing the axial force and torque eduring drilling operations. Elangovan et al. [9] made a systematic study on ultrasonic welding of copper to optimize of the process parameters using Taguchi method. L27 Orthogonal array was chosen for this study by considering the control factors and their interactions. Through ANOVA it was shown that pressure, amplitude and time are the important welding parameters that influence weld strength.
Canyurt et al. [10] developed the genetic algorithm weld strength estimation model (GAWSEM) to
estimate the weld strength of brass using hybrid laser welding. The estimated results indicated that GAWSEM model can be used as an estimation technique to predict the weld parameters which give the quality welds for brass material.
Habib [11] discussed the development of a comprehensive mathematical for correlating the interactive and higher order influences of various parameters in electrical discharge machining through RSM utilizing relevant experimental data. The adequacy of the above proposed models has been tested through ANOVA.
Thus, from the literature review it is observed that weld pressure, amplitude and weld time are critical parameters in deciding the weld strength and quality of the weld. Many researchers have developed second order mathematical model using RSM for different processes like drilling, Tungsten Inert Gas (TIG) welding, laser hybrid welding and electric discharge machining. Then the mathematical model is used in genetic algorithm as a fitness function to optimize the process parameters. It seems that no work has been reported in ultrasonic welding of copper - brass wherein welding parameters for maximizing weld strength using RSM and GA is considered. So optimization of parameters while joining copper – brass specimens using USMW by RSM and GA has been attempted in this work. 2. EXPERIMENTAL PROCEDURES 2.1 Plan of Experiments
An important stage in response surface model generation by RSM is the planning of experiments. From the literature survey, factors which have a significant influence on weld strength of ultrasonic metal welding were identified. They are weld pressure, weld time and amplitude of vibration of horn.
Large numbers of trial runs were carried out using 0.2 and 0.3 mm thick copper-brass specimens to determine maximum and minimum values of ultrasonic welding parameters. In this study, experiments are planned as per Central Composite Face Centered (CCF) design with the star points at the center of each face of factorial space was used for spot and seam welding of 0.2 and 0.3 mm thick copper – brass joints. This design fits the second order response surface very accurately [2]. From the trial runs the most suitable parameters were identified which is listed in Table 1.
Table 1 Range of variables for joining of Cu -brass specimens
2.2 Experimental details
The experimental setup for the USMW is shown in Figure 2 with data acquisition system (DAQ). Welding was carried out using a conventional ultrasonic metal welding machine (2500 W, 20 kHz) for different ranges of weld parameters. Experiments are carried out using the design matrix as developed in Table 1. In this work horn made of hardened steel with diamond knurl pattern (seam and spot) and anvil
Factor Notation Unit Factor Level
-1 0 +1
Pressure (x1) p bar 3.0 3.5 4.0
Weld time(x2) t sec 2.5 3.0 3.5
IJAERS/Vol. I/ Issue III/April-June, 2012/55-64 made of steel with serrations on top surface were used. The horn is serrated near the tip for preventing the workpiece from sliding during welding. The specimens (0.2mm and 0.3mm thick pure copper and brass) were prepared according to ASTM standard (D 1002 – 01) [12] for testing strength of the joint by tensile loading. Before welding, samples were cleaned with acetone to remove the surface impurities as it may affect the bond strength. Figure 3 shows the
standard size of specimen as per ASTM standard. Figures 4 and 5 show the actual spot and seam welded samples of copper - brass work pieces. A computerized tensile testing machine was used to determine the weld strengths. During the tensile testing, ductile fracture was observed at weld interface for most of the welded samples and some of the fractured samples were shown in figure 6.
Figure 2 Experimental set up for ultrasonic metal welding
Figure 3 ASTM standard (D 1002 – 01) for weld specimen
IJAERS/Vol. I/ Issue III/April-June, 2012/55-64
Figure 5 Seam welded specimens of Cu-brass (0.2 mm thick)
Figure 6 Spot welded specimens after tensile test (0.2 mm thick) 3.3 Response surface model for weld strength
The Response Surface Methodology (RSM) is a collection of mathematical and statistical techniques useful for the modeling and analysis of problems in which a response of interest isinfluenced by several variables and the objective is to optimize this response [13]. The second order mathematical models have been developed to predict the weld strength. The polynomial equation for three factors considered in the present case is
∑
∑
∑∑
= = <+
+
+
=
q j q j i j j i ij j jj j j ix
x
x
x
1 1 2 0y
β
β
β
β
(1)where
y
i is the response, i.e. weld strength; xi represents pressure, weld time and amplitude; β0 ,βj ,βjjand βijrepresent the constant, linear, quadratic and interaction terms respectively.In this work, the CCF design is used which fits the second order response very accurately [2]. The axial and star points in CCF design allow quadratic terms included in the model which gives efficient estimation of response with curvature surfaces [3]. All coefficients are obtained by applying CCF using Minitab software package and second order mathematical model for predicting weld strength is developed. The developed mathematical model for spot and seam welding of 0.2 and 0.3 mm thick copper to brass joints are given below.
0.2 mm seam welding Weld strength= -8.358 + 1.757x1 + 1.641x2 + 0.139x3 – 0.035x12 -0.161x22 + 0.00034 x32 + 0.089 x1x2 – 0.022 x1x3 – 0.026x2 x3 (2a) 0.2 mm spot welding Weld strength= -44.490 + 14.408 x1 + 33.375x2 -0.927x3 – 0.658x12 -3.492x22 + 0.0042x32 – 3.95x1x2 +0.1038x1x3+0.0672x2x3 (2b) 0.3 mm seam welding Weld strength= -55.752 + 19.350x1 + 15.534x2 +0.144x3 – 1.955x12 -2.354x22 - 0.0005x32 – 1.076x1x2 – 0.071x1x 3+ 0.053x2x3 (2c) 0.3 mm spot welding Weld strength= 32.716 + 8.831x1 – 32.019x2 + 0.129x3 –3.246x12 +3.768x22 + 0.0044x32 + 3.282x1x2 +0.109x1x3– 0.026x2 x3 (2d) where, x1- weld pressure; x2 – weld time; x3 – amplitude of vibration of horn.
The coefficient of determination (R2)is used to find the closeness of the experimental and predicted values and is calculated using the following expression [4].
∑
−∑
− = 2 2 2 ) ( / ) (Yp Ya Ye Ya R (3) where Yp is the predicted weld strength (using the above model); Ye is the experimental weld strength; and Ya is the average of experimental values. The coefficient of determination (R2) values are presented in the result and discussion section.2.4 Optimization problem formulation and solution
Genetic algorithms are more likely to converge to global optimum than conventional optimization techniques, since they search from a population of points, and are based on probabilistic rules. The conventional optimization techniques are ordinarily based on deterministic hill-climbing methods, which
IJAERS/Vol. I/ Issue III/April-June, 2012/55-64 may find local optima. The genetic algorithm solves optimization problem iteratively based on biological evolution process in nature (Darwin’s theory of survival of the fittest). In the solution procedure, a set values of parameter is randomly selected and the best combination of parameters leading to maximum weld strength is determined. New combination of parameters is generated from the best combination by simulating biological mechanisms of offspring, crossover and mutation.
This process is repeated until weld strength with new combination of parameters cannot be further increased. The final combination of parameters is considered as the optimum solution.
The principal steps in GA based optimization are listed below:
Step 1: Randomly generate an initial chromosome population.
Step 2: Decode the genes namely pressure, weld time and amplitude of vibration for all chromosomes. Step 3: With specified values of sheet thickness, evaluate the predicted value of weld strength using the models based on RSM for weld strength.
Step4: Determine the fitness of all chromosomes and obtain the maximum (fitmax).
Step 5: If fit max ≤required fitness (fit required), then carryout following genetic operations:
(a) Selection based on expected number control method,
(b) Crossover, and
(c) Mutation, to generate new chromosome population and go to step 2.
else stop.
In this work, maximization of weld strength must be formulated in the standard mathematical format as given below for Cu- brass specimens.
Find: p, t, a, to Maximize: Y(p, t, a) with respect to the constraints
3 bar ≤ p ≤ 4 bar (4a) 2.5 sec ≤ t ≤ 3.5 sec (4b) 28 µm ≤ a ≤ 57 µm (4c) where Y = weld strength, p = pressure, w = weld time and a = amplitude of vibration of horn
Using Matlab optimization toolbox, several combinations of values for welding conditions to obtain optimal results were tried. The best combination of these values for welding conditions will lead to the maximum weld strength. A number of trials were conducted with different settings to achieve the maximum weld strength using Matlab optimization toolbox.
The critical parameters in GA are the size of the population, mutation rate and crossover rate. Their values are given in table 2.
Table 2 Combination of GA parameters for optimal solution.
3. RESULTS AND DISCUSSIONS 3.1 Experimental study and RSM
Totally twenty (20) experiments are conducted at different levels of parameters (Table 1) to obtain ultrasonic seam and spot welded joints of 0.2 and 0.3 mm thick copper and brass sheets using USMW. The values of weld strength obtained from experiments and those predicted from response surface model along with design matrix are tabulated as in table 3 and 4 for seam and spot welding of 0.2 and 0.3 mm thick copper - brass joints. While comparing the predicted values of strength with experimental values, it was observed that the deviations are minimum except for a few combination of parameters. The average of deviation (%) between theoretical weld strength and experimental weld strength for seam and spot welded joints of copper-brass sheets are minimum. Hence the adequacy of the developed model.
The calculated value of R2 using equation (3) for seam and spot welded joints of 0.2 and 0.3 mm thick copper to brass joints are listed in table 5. It is observed that, the coefficients of determination (R2) for the entire developed models are found to be higher which indicated that a high correlation exists between experimental and predicted values. Hence significance of the developed model.
IJAERS/Vol. I/ Issue III/April-June, 2012/55-64
Table 4 Comparison of weld strengths from experiments and RSM (spot welds)
Table 5 Coefficient of determination (R2) values for seam and spot welding
Table 6 Comparison of optimum weld strength from experiments, RSM and GA for Cu and brass specimens
Figures 7, 8, 9 and 10 show the comparison of weld strengths obtained from experiments and predicted weld strengths for seam and spot welded samples of copper - brass sheets. From the graphs, it can be observed that difference between weld strength obtained from experiments and those predicted by RSM are minimum. Also, it can be noticed that weld strength of spot welded joints are more than that of seam welded joints for similar combination of parameters, because of reduced weld area.
Figure 7 Comparison of weld strengths of Cu-brass joints (0.2 mm, seam weld)
Figures 11 shows the estimated response surface and contour plot for weld strength of 0.3 mm thick copper and brass sheets joined by ultrasonic spot welding with varying values of pressure and weld time keeping amplitude of vibration of horn constant. It can be seen from this figure that weld strength
increases with increase of weld time for any value of pressure. This may be because increase in weld time gives sufficient time to disrupt the contaminants which causes a good metal to metal contact. The close contact of the surfaces allows van der Waals forces to take effect which leads to better bonding and increase of weld strength.
Figure 8 Comparison of weld strengths of Cu-brass joints (0.3 mm, seam weld)
Figures 12 shows the estimated response surface and contour plot for weld strength of 0.3 mm thick copper and brass sheets joined by ultrasonic spot welding with varying values of amplitude of horn and weld time keeping pressure constant. It can be seen from this figure that weld strength increases with increase of amplitude and weld time. This may be because increase in amplitude gives increased area for welding action between the metal surfaces leading to better bonding and increase of weld strength.
IJAERS/Vol. I/ Issue III/April-June, 2012/55-64 Figure 9 Comparison of weld strengths of
Cu-brass joints (0.2 mm, spot weld)
Figure 10 Comparison of weld strengths of Cu-brass joints (0.3 mm, spot weld)
Figure 11 Effect of pressure and weld time on weld strength (0.3 mm, spot weld)
Figures 13 shows the estimated response surface and contour plot for weld strength of 0.3 mm thick copper and brass sheets joined by ultrasonic spot welding with varying values of amplitude of horn and pressure keeping weld time constant. It can be seen from this figure that weld strength increases with increase of amplitude and pressure. This may be because increase in clamping force (pressure) causes asperities of the two surfaces come in contact. But contamination still prevents the parts from bonding, because pressure alone is not sufficient to cause plastic deformation and local cleaning of the surfaces. So the combination of increase in amplitude and pressure leads to better bonding and increase of weld strength.
Figure 12 Effect of amplitude and weld time on weld strength (0.3 mm, spot weld)
Figure 13 Effect of amplitude and pressure on weld strength (0.3 mm, spot weld)
Figures 14 shows the estimated response surface and contour plot for weld strength of 0.3 mm thick copper and brass sheets joined by ultrasonic seam welding with varying values of pressure and weld time keeping amplitude constant. It can be seen from this figure that weld strength increases up to 3.0 sec. Beyond 3.0 sec, weld strength starts decreasing for any value of pressure. This may be because at initial stage of welding, asperities present on the metal surfaces get welded to make pure metal contact. After that (beyond 3.0 sec) increased weld time disturbs the contact and changes the orientation of the bonding and they get stretched and inclined (a possible
IJAERS/Vol. I/ Issue III/April-June, 2012/55-64 situation is shown in Figure 15). This can be further investigated by microstructural studies and can be undertaken as the work for future. Figures 16 shows the estimated response surface and contour plot for weld strength of 0.3 mm thick copper and brass sheets joined by ultrasonic seam welding with varying values of amplitude and weld time keeping pressure constant. It can be seen from this figure that weld strength increases with increase of weld time for any value of amplitude. The increase in weld time gives sufficient time to disrupt the contaminants which causes a good metal to metal contact leading to better bonding and increase of weld strength.
Figures 17 shows the estimated response surface and contour plot for weld strength of 0.3 mm thick copper and brass sheets joined by ultrasonic seam welding with varying values of amplitude and pressure keeping weld time constant. It can be seen from this figure, that weld strength increases considerably up to 3.5 bar. Beyond 3.5 bar, weld strength again starts decreasing for any value of amplitude. This may be because increase in clamping force (pressure) reduces the relative motion between surfaces leading to reduced area of contact and hence reduced strength. Similar observations were found for 0.2 mm thick seam and spot welding of copper and brass sheets.
Figure 14 Effect of pressure and weld time on weld strength (0.3 mm, seam weld)
Figure 15 Effect of excessive weld time on weld strength
Figure 16 Effect of amplitude and weld time on weld strength (0.3 mm, seam weld)
IJAERS/Vol. I/ Issue III/April-June, 2012/55-64 3.2 Results and discussion for GA
Using the fitness function formulated in Eq. (2a), (2b), (2c) and (2d), the constraints of welding conditions formulated in Eq. (4a), (4b) and (4c) and the parameters for GA given in Table 2, optimization of weld strength was attempted. For this MATLAB optimization tool box is used. Results are shown in figure 18, 19, 20 and 21. These pertain to seam and spot welding of Cu-brass specimens with thickness values of 0.3 mm respectively. Figures 18 and 20 represent the convergence of fitness value to the optimum level after 50 iterations and the converged values of optimum parameters for seam and spot welding of 0.3 mm thick Cu – brass specimens are shown in Figures 19 and 21. Converged values are (1) pressure, (2) weld time and (3) amplitude.
Figure18 Convergence of fitness values (0.3 mm, seam weld)
Figure 19 Converged values of parameters (0.3 mm, seam weld)
Figure 20 Convergence of fitness values (0.3 mm, spot weld)
By solving the optimization problem, GA gives the optimum combinations of parameters for maximum weld strength compared to the initial set of welding parameters. The optimum welding conditions leading to the maximum weld strength is shown in Table 6 for seam and spot welding of 0.2mm and 0.3mm
thick copper and brass specimens. The optimum welding conditions predicted by RSM and GA are further compared with experimental results for the same set of parameters.
Figure 21 Converged values of parameters (0.3 mm, spot weld)
From Table 6, it is seen that results obtained from RSM and GA based optimization are in good agreement with experimental observations. The maximum variation between weld strengths obtained using GA and experiments for seam welding of 0.2 mm thick Cu – brass specimens is 0.25%. For spot welding of 0.2 mm thick Cu – brass specimens the variation is 3.99%. Similarly, maximum variation between weld strengths obtained using GA and experiments for seam welding of 0.3 mm thick is Cu – brass specimens is 5.37%. For spot welding of 0.3 mm thick Cu – brass specimens the variation is 0.17%. These studies clearly show that spot welded joints of 0.2 and 0.3 mm thick specimens of Cu and brass yield the highest strength.
4. CONCLUSIONS
In this study, a second order mathematical model using RSM was developed to predict the maximum weld strength of seam and spot welds produced by USMW using 0.2 mm 0.3 mm thick copper-brass sheets. The developed RS model was further coupled with GA to find the optimum welding conditions leading to maximize the strength. Further, the optimum welding condition obtained from GA was compared with experimental results. It was found that the optimum conditions obtained from GA correlates very well with the experimental results. The difference was found to be less than 6%. This indicates that the optimization methodology proposed in this study by coupling the developed RS model and the GA is effective.
Further, it is concluded that weld strength increases with increases of amplitude because increase in amplitude gives increased area for rubbing action between the metallic surfaces that leads better bonding and increase of weld strength. Also, weld strength increases with increase of pressure because increase in pressure causes asperities of the two surfaces come in to close contact which allows van der Waals forces to take effect which leads to better bonding and increase of weld strength. In some cases weld strength increases up to 3.0 sec. Beyond 3.0 sec weld time, the weld strength start decreasing for any value of pressure and amplitude because excessive weld time affects the existing molecular bond in the joint.
In some cases weld strength increases considerably up to 3.5 bar. Beyond 3.5 bar, the weld strength again start decreasing for any value of amplitude. This is
IJAERS/Vol. I/ Issue III/April-June, 2012/55-64 because increase in clamping force (pressure) reduces the relative motion between surfaces leading to reduced area of contact and hence reduced strength.
ACKNOWLEDGEMENTS
The authors express their sincere thanks to the Management and to the Principal, PSG College of Technology, Coimbatore, for providing necessary support and infrastructure to carry out this work. We are grateful to AICTE, New Delhi for funding this research work under research promotion scheme. (F.No:8023/ BOR/RID/RPS – 136/2007-08)
REFERENCES
1. V.N. Gaitonde, S.R. Karnik, B.T. Achyutha and B.
Siddeswarappa, “Genetic algorithm-based burr size minimization in drilling of AISI 316L stainless steel,” Journal of materials processing technology, Vol.197, 2008, pp.225- 236.
2. Padmanaban,G., Balasubramanian,V., Optimization of
laser beam welding process parameters to attain maximum tensile strength in AZ31B magnesium alloy, Journal of Optics & Laser Technology, Vol.42, 2010, pp.1253-1260.
3. Nuran Bradley, ‘‘The Response Surface Methodology”,
Dissertation, Indiana University South Bend, 2007.
4. A. Kumar, P. Shailesh, and S. Sundarrajan,
“Optimization of magnetic arc oscillation process parameters on mechanical properties of AA 5456 Aluminum alloy weldments,” Journal of Materials and Design, Vol.29, 2008, pp.1904-1913.
5. E. DeVries, “Mechanics and Mechanism of Ultrasonic Metal Welding,” Ph.D. Dissertation, The Ohio State University, 2004.
6. T.Watanabe, H. Sakuyama, and A. Yanagisawa,
“Ultrasonic welding between mild steel sheet and Al– Mg alloy sheet,” Journal of Materials Processing Technology, Vol.34, 2009, pp.1107-1111.
7. Cemal Meran, “Prediction of the optimized welding parameters for the joined brass plates using genetic algorithm,” Journal materials & design, Vol.27, 2006, pp.356-363.
8. G.C. Onwubolu and Shivendra Kumar, “Response
surface methodology-based approach to CNC drilling
operations,” Journal of materials processing
technology, Vol. 171, 2006, pp.41-47.
9. S. Elangovan, K. Prakasan and V. Jaiganesh,
“Optimization of ultrasonic welding parameters for copper to brass joints using design of experiments,” International journal of Advanced Manufacturing Technology, Vol.51, 2010, pp. 163 – 171.
10. O. E. Canyurt, H. R. Kim and K. Y. Lee, “Estimation of laser hybrid welded joint strength by using genetic algorithm approach,” Mechanics of Materials, Vol.40, 2008, pp.825-831.
11. S. S. Habib, “Study of the parameters in electrical
discharge machining through response surface
methodology approach,” Journal of Applied
Mathematical modeling, Vol.33, 2009, pp.4397-4407
12. ASTM International Codes, “Standard Test Method for
Apparent Shear Strength of Single-Lap-Joint
Adhesively Bonded Metal Specimens by Tension Loading (Metal-to-Metal),” ASTM International, Vol. 01, 2005, pp. 52-55.
13. D. C. Montgomery, Design and Analysis of
Experiments, 4th Edition, John Wiley and Sons, New York, 1997.
