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Experimental investigation on laser transmission welding of PMMA to ABS via response surface modeling
Optics & Laser Technology 44 (2012) 1372–1383
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Experimental investigation on laser transmission welding of PMMA to ABS via response surface modeling Bappa Acherjee a,n, Arunanshu S. Kuar a, Souren Mitra a, Dipten Misra b, Sanjib Acharyya c a
Department of Production Engineering, Jadavpur University, Kolkata-700 032, India School of Laser Science & Engineering, Jadavpur University, Kolkata-700 032, India c Department of Mechanical Engineering, Jadavpur University, Kolkata-700 032, India b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 August 2011 Received in revised form 19 November 2011 Accepted 13 December 2011 Available online 31 December 2011
In this paper, an experimental investigation on diode laser transmission welding of dissimilar thermoplastics between PMMA (polymethyl methacrylate) and ABS (acrylonitrile butadiene styrene) has been carried out. The effect of the laser welding parameters such as laser power, welding speed, stand-off distance and clamp pressure on weld strength and weld width is investigated using response surface methodology (RSM). Planned experiments and subsequent analyses are carried out to develop the mathematical models to establish the correlation between the process parameters and the responses. The adequacy of the developed models is tested using the sequential F-test, lack-of-fit test and the analysis-of-variance (ANOVA) technique. A numerical multi-objective simultaneous optimization technique, in which the RSM is incorporated, is used to find the optimum solutions, according to the desired optimization criteria. In addition to that, a graphical optimization technique is, also implemented which allow identifying a region in the graphic where optimal conditions lay on. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Laser transmission welding Response surface methodology Dissimilar plastic welding
1. Introduction There is a continuously growing interest in the joining of dissimilar plastics in manufacturing industries. Joining of useful plastic combinations like PMMA (polymethyl methacrylate) to ABS (acrylonitrile butadiene styrene) and polycarbonate to ABS are already found in a number of industrial applications. They are used in automotive components like flood lights, looking mirror, dashboard components etc; displays and cabinets; and cell phone assemblies to name a few of their many applications [1,2]. PMMA is a useful, clear plastic that resembles glass, but has properties that make it superior to glass in many ways. It is chosen over glass for many reasons. It is many times stronger than glass, making it much more impact resistant and therefore safer. ABS, a copolymer, is comprised of polymerized styrene and acrylonitrile with polybutadiene, which exhibits a balanced combination of mechanical toughness, good dimensional stability, chemical resistance and electrical insulating properties. These combinations of properties make them suitable for various applications in diverse fields including automotive and computer industries. Joining of dissimilar plastics requires the application of an appropriate joining technology. In case of welding, both the materials must have chemical compatibility and the difference between the melting temperatures of those materials should not be too high [3].
n
Corresponding author. Tel.: þ91 33 2337 4125; fax: þ 91 33 2337 6331. E-mail addresses: [email protected], [email protected] (B. Acherjee).
0030-3992/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2011.12.029
Laser transmission welding is the latest addition in the field of plastic welding. Laser welding was first demonstrated on thermoplastics in the 1970s [4] but it found a place in industrial-scale situations only in the last decade. In 1987, Nakamata [5] patented the laser transmission welding technique, as a process in which, the laser beam penetrates the upper transparent plastic part and is converted into heat by the absorbing lower plastic part. The melt is created only where it is needed, in the joining area of the both partners, to form the weld. Laser transmission welding is non contact, non contaminant and flexible process, has shorter processing time, can provide consistent quality and is repeatable [2]. Literature review on laser transmission welding reveals that, the influence of the plastic composition, colorants and thickness of plastic parts on the laser transmission and absorption and finally on the mechanical performance of the weld have been studied extensively [6–11]. It is evident from the literature that the presence of reinforcement, mineral fillers, impact modifiers, color pigments and some heat stabilizers in polymer matrix lower the transmissivity of the polymer due to particulate scattering and increased absorption by colorants. It is also observed that thickness of plastic part influences the optical properties, especially in the presence of fillers, crystallites, etc. The key process parameters for laser transmission welding are: laser power, welding speed, beam spot area and clamping pressure, which control the temperature field inside the weld seam, and hence the weld quality. Material surface finish and the size of air gap have also a significant effect on the weld quality. A number of experimental programs have been carried out to study the effect of process
B. Acherjee et al. / Optics & Laser Technology 44 (2012) 1372–1383
parameters on weld quality, with various plastic materials and application strategies [12–15]. However, no comprehensive research work has been reported on laser transmission welding of PMMA to ABS. No technological database is available for laser transmission welding of such a useful material combination in open literatures. An extensive research is, therefore, needed to analyze and optimize the laser transmission welding of PMMA to ABS. To get the desired weld quality, i.e., weld bead size and weld strength, the combination of the process parameters should be selected carefully. Response surface methodology (RSM) is one of the modeling and optimization techniques currently in widespread use in describing the performance of the welding process and finding the optimum of the responses of interest [15–17]. Laser transmission welding of PMMA to ABS has been investigated in present research work. RSM is applied to the experimental data to relate the laser welding parameters (laser power, welding speed, stand-off distance and clamp pressure) with the responses (weld strength and weld width). The developed mathematical models are tested for their adequacy using analysis of variance and other adequacy measures. The effect of welding parameters on the responses is studied on the basis of the developed models. The mathematical models are further used to find optimum welding conditions to achieve the desired weld quality.
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For goal of maximum, the desirability will be defined by
di ¼
8 0; > > < > > :
yi Li Hi Li
wti
if response ðyi Þ r low value ðLi Þ ;
as response ðyi Þ varies from low ðLi Þ to high ðHi Þ if response ðyi Þ Z high value ðHi Þ
1;
ð3Þ For goal of minimum, the desirability will be defined by
di ¼
8 1; > > < > > :
Hi yi Hi Li
0;
wti
if response ðyi Þ r low value ðLi Þ ;
as response ðyi Þ varies from low ðLi Þ to high ðHi Þ if response ðyi Þ Z high value ðHi Þ
ð4Þ A weight (wt) can be assigned to a goal to emphasize the particular desirability function. Weights can be ranged between 0.1 and 10. A weight greater than 1 gives more emphasis to the goal, while weights less than 1 give less emphasis. The simultaneous objective function, D is a geometric mean of all transformed responses: !1=P n ri P Y r1 r2 rn 1= ri ri D ¼ ðd1 d1 . . . d1 Þ ¼ di ð4Þ i¼1
where n is the number of responses in the measure. Each response can be assigned an importance, relative to the other responses. Importance (ri) values varies from 1, the least important, to 5, the most important.
2. Methodology 2.1. Response surface methodology Response surface methodology is a collection of mathematical and statistical techniques that are useful for the modeling and analysis of problems in which a response of interest is influenced by several variables and the objective is to optimize the response [18]. If all variables are assumed to be measurable, the response surface can be expressed as follows: y ¼ f ðx1 ,x2 ,. . .,xk Þ
ð1Þ
where y is the response of the system, and xi the variables of action called factors. In the practical application of RSM it is necessary to develop an approximating model for the true response surface. The approximating model is based on observed data from the process or system and is an empirical model. Multiple regression analysis is a collection of statistical techniques useful for building the types of empirical models required in RSM. Usually a second order polynomial equation is used in RSM: y ¼ b0 þ
k X i¼1
bi xi þ
k X
bii xi2 þ
i¼1
where, parameters bi,j ¼ 0,1, coefficients.
k1 X k X
bij xi xj
ð2Þ
i¼1j¼2
y
k
are called the regression
2.2. Desirability function analysis The desirability function analysis method is first proposed by Derringer and Suich in 1980 [19]. This method makes use of a technique for combining multiple responses into a dimensionless measure of performance called the composite desirability function. The general approach of desirability function is to transfer each response yi into an unitless desirability function di bounded by 0 rdi r1, where, the desirable ranges are from zero to one, as least to most desirable, respectively [18].
3. Experimental work 3.1. Experimental set up Experimental investigations are performed with a continuous wave diode laser system. The system installation consists of a 30 W Coherent FAP (fiber array packaged) diode laser with a 3-axes CNC work table, coordinated with the motion system and computer interface. The diode laser is operated at 809.4 nm wavelength and the focal length used is 13 mm. The FAP system optical radiation is delivered via SMA 905 connector, which mates to an 800 mm diameter transport fiber. The photographic view of the experimental set up for present work is shown in Fig. 1. ¨ Plexiglass 6N acrylic (PMMA) granules from Evonik Rohm GmbH and Terlurans GP-22 ABS granules from BASF are used as raw materials for making of plastic plaques. Natural PMMA and opaque ABS (0.1 wt% carbon black pigmented) plaques of dimensions 80 mm 35 mm 4 mm of each are used as the work materials (having Ra value of 0.26 mm, as measured by a Surfcom 120 A stylus profilometer). They are placed on the metal plate of the holding fixture with the PMMA sample on top, with an overlap between the natural and black plaques of approximately 20 mm. The fixture is used for the repetitive work, to maintain the lapping area constant for every run and to prevent misalignment between the parts to be welded in lap joint geometry. Hydraulic clamp pressure is applied in between the workpieces to ensure the intimate contact between them. A uniform pressure on the whole length of the joint is generated by an additional transparent acrylic plaque of same size that is placed across and above the overlapping area as indicated by (A) in Fig. 1 (b). The pressure applied to the workpieces is determined from the reading of the pressure gage, fitted to the hydraulic pump, converted to the pressure experienced by the plaques based on the actual area of contact between the overlapped sections of each sample [15]. The contour welding variant of laser transmission welding is adopted for this study.
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maximum and minimum levels of the variables. The selected process parameters and their limits, units and notations are given in Table 1.
3.4. Developing the design matrix The selected design matrix, shown in Table 2, is a four factors five levels central composite rotatable design with full replications consisting of 30 sets of coded conditions and comprising a full replication of 24 ( ¼16) factorial design plus six center points and eight star points. All welding variables at the intermediate (0) level constitute the center points while the combination of each of the welding variables at either its lowest value ( 2) or its highest value ( þ2) with the other three variables at the intermediate levels constitute the star points. Thus, the 30 experimental runs allowed the estimation of the linear, quadratic and two-way interactive effects of the process parameters on the response parameters. Statistical software Design-Experts is used to code the variables and to establish the design matrix.
Table 1 Process control parameters and their limits. Parameters
Units
Power Welding speed Stand-off-distance Clamp pressure
Watt mm/s mm MPa
Notations
P S F C
Limits 2
1
0
þ1
þ2
9 4 26 0.9
12 8 32 1.5
15 12 38 2.1
18 16 44 2.7
21 20 50 3.3
Table 2 Design matrix and measured experimental results. Exp. no.
Fig. 1. (a) Pictorial, and (b) schematic view of experimental set-up.
3.2. Selection of process parameters Four independently controllable process parameters, namely: power, welding speed, stand-off distance and clamp pressure are considered as input parameters to carry out the experiments. The beam spot area on the workpiece is varied by varying the stand-offdistance i.e, the distance between laser optic and work material. 3.3. Finding the limits of process parameters Trial runs are conducted by varying one of the process parameters at a time while keeping the rest of them at constant value. The working range is decided by inspecting the weld seam for a smooth appearance and the absence of any visible defects. The upper and lower limits are coded as þ2 and 2, respectively. The coded values for intermediate values can be calculated from the relationship: 2XðX max þ X min Þ Xi ¼ 2 ð6Þ ðX max X min Þ where Xi is the required coded value of a variable X; when X is any value of the variable from Xmin to Xmax; Xmax and Xmin are the
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Welding parameter level
Measured output
P (W)
S (mm/s)
F (mm)
C (MPa)
Weld strength (N/mm)
Weld width (mm)
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 2 2 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 2 2 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 2 2 0 0 0 0 0 0
38.29 31.14 45.00 46.14 62.43 79.26 32.57 58.71 38.71 22.14 55.29 40.43 65.57 71.71 46.86 57.14 55.14 65.57 50.57 48.29 9.71 41.71 63.71 62.29 63.29 65.43 64.00 63.57 62.14 64.57
3.19 3.43 2.74 3.14 4.51 5.17 3.36 4.10 3.15 3.42 2.74 3.15 4.92 5.28 3.35 4.37 3.26 4.31 4.78 3.42 2.21 4.26 3.81 4.14 4.08 3.91 3.98 4.10 3.99 4.01
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Fig. 3. Photographs of samples after lap shear test showing (a) shear failure from weld interface, and (b) fracture of base material starting from fusion zone. Fig. 2. (a) the PMMA/ABS welded sample in lap joint geometry, and (b) the sample used for lap-shear testing.
3.5. Evaluation of responses A microprocessor controlled Instron universal testing machine with an accuracy of 70.4% of rated capacity (model: 8801, maximum capacity: 100 kN) is used for lap-shear pull test of welded specimens. The crosshead speed during the shear test is kept constant at 0.5 mm/ min. The weld strength is measured as the maximum load to failure per unit length of the weld (N/mm). Fig. 2(a) and (b) shows the welded sample in lap joint geometry and the sample used for lapshear testing, respectively. During the tensile tests, two types of breaking failure were observed: (a) shear failure from weld interface, and (b) fracture of base material starting from fusion zone, as shown in Fig. 3. An Olympus STM 6 measuring microscope is used for measuring weld seam widths. The STM6 microscope offers high performance three axis measurements of parts, with sub-micron precision. Inbuilt LED illuminator is used for reflected coaxial illumination during measurements. The average of three results of both lapshear tests and weld width are calculated and presented in Table 2.
4. Development of mathematical models Design-Experts v7 software is used for analysis of the measured responses and determining the mathematical models with best fits. The adequacy of the model is tested using the sequential f-test, lack-of-fit test and the analysis-of-variance (ANOVA) technique using the same software to obtain the best-fit model. 4.1. Analysis of weld strength The fit summary for weld strength suggests the quadratic model where the additional terms are significant and the model is not aliased [20]. The ANOVA table of the quadratic model is given in Table 3. The associated p-value of less than 0.05 for the model (i.e, a ¼0.05, or 95% confidence level) indicates that the model terms are statistically significant. The other model terms are not significant and thus, eliminated by backward elimination process to improve model adequacy. The main effect of clamp pressure (C) is added to support hierarchy. The other adequacy measures R2, adjusted R2 and predicted R2 are in reasonable agreement and are close to 1, which indicate adequacy of the model [15]. The adequate precision compares the signal to noise ratio and a ratio greater than 4 is desirable [16]. The value of adequate precision
Table 3 ANOVA analysis for the weld strength model. Sources
Sum of squares
Degrees of freedom
Mean squares
F-value
p-value
Model P S F C PS PF PC SF SC P2 S2 F2 Residual Lack of fit Pure Error Total
6931.05 75.51 41.16 2032.41 0.12 35.15 582.88 167.15 1225.00 56.25 20.94 362.26 2540.59 63.22 56.88 6.34 6994.27
12 1 1 1 1 1 1 1 1 1 1 1 1 17 12 5 29
577.59 75.51 41.16 2032.41 0.12 35.15 582.88 167.15 1225.00 56.25 20.94 362.26 2540.59 3.72 4.74 1.27
155.31 20.31 11.07 546.51 0.03 9.45 156.73 44.95 329.40 15.13 5.63 97.41 683.16
o 0.0001 0.0003 0.0040 o 0.0001 0.8582 0.0069 o 0.0001 o 0.0001 o 0.0001 0.0012 0.0297 o 0.0001 o 0.0001
3.74
0.0778
R2 ¼ 0.9910, adjusted R2 ¼0.9846, predicted R2 ¼0.9621, adequate Precision¼57.62.
ratio of 57.62 indicates adequate model discrimination. The lackof-fit F-value of 3.74 implies that the lack-of-fit is not significant relative to the pure error, as this is desirable. The final mathematical models for weld strength (Yws), which can be used for prediction within same design space, are as follows: (a) In terms of coded factors, Y ws ¼ 63:56 þ 1:77P21:31S þ9:20F þ 0:07C þ 1:48PS þ 6:04PF 23:23PC28:75SF þ 1:88SC20:86P 2 23223:60S2 29229:53F 2
ð7Þ (b) In terms of actual factors, Y ws ¼ 2425:7426:98P þ 15:43S þ 20:99F þ 17:68C þ 0:12PS þ 0:34PF
21:80PC20:37SF þ0:78SC20:10P 2
20:23S2 20220:27F 2
ð8Þ
4.2. Analysis of weld width For weld width, the fit summary recommends the quadratic model where the additional terms are significant and the model is
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Table 4 ANOVA analysis for the weld width model.
Table 5 Validation test results.
Source
Sum of squares
Degrees of freedom
Mean squares
F-value
p-value
Model P S F C PS PF SF FC P2 F2 Residual Lack of fit Pure Error Total
15.4220 1.6017 3.2561 8.4017 0.0817 0.0676 0.1332 0.6724 0.0420 0.1062 1.1218 0.1984 0.1741 0.0243 15.6204
10 1 1 1 1 1 1 1 1 1 1 19 14 5 29
1.5422 1.6017 3.2561 8.4017 0.0817 0.0676 0.1332 0.6724 0.0420 0.1062 1.1218 0.0104 0.0124 0.0049
147.7140 153.4096 311.8700 804.7218 7.8221 6.4748 12.7605 64.4033 4.0252 10.1688 107.4506
o 0.0001 o 0.0001 o 0.0001 o 0.0001 0.0115 0.0198 0.0020 o 0.0001 0.0593 0.0048 o 0.0001
2.5603
Weld strength (N/mm)
Weld width (mm)
Actual Predicted 9Error %9
53.76 50.48 6.10
4.14 3.89 6.04
1.5
Actual Predicted 9Error %9
78.44 79.41 1.24
5.23 5.10 2.49
2.7
Actual Predicted 9Error %9
22.16 21.37 3.57
3.21 3.44 7.17
Exp. No.
P (W)
S (mm/s)
F (mm)
C (MPa)
1
12
12
44
1.5
2
18
8
44
3
18
8
32
0.1529
R2 ¼0.9873, adjusted R2 ¼ 0.9806, predicted R2 ¼0.9576, adequate precision¼57.97.
not aliased. Table 4 presents the ANOVA table of the quadratic model. The ANOVA result shows the significant model terms associated with weld width. The other adequacy measures R2, adjusted R2 and predicted R2 are in reasonable agreement and are close to 1, which indicate adequate model. The value of adequate precision ratio 52.97 indicates adequate model discrimination. The lack-of-fit F-value of 2.56 implies that the lack-of-fit is not significant relative to the pure error. The final mathematical models for weld width (Yww), as determined by Design expert software are given as follows: (a) In terms of coded factors, Y ww ¼ 4:020 þ0:260P20:370S þ 0:590F þ 0:058C þ0:065PS þ 0:091PF20:210SF þ 0:051FC20:061P2 20:200F 2
ð9Þ
(b) In terms of actual factors, Y ww ¼ 28:5085 þ 0:0321P þ 0:1513S þ 0:5144F20:4438C þ 5:4167E03PS þ 5:0694E03PF28:5417E03SF þ 0:0142FC26:7882E03P 2 25:5165E03F 2
ð10Þ
4.3. Validation of the developed models To validate the developed response surface equations, derived from multiple regression analysis, three confirmation experiments are conducted with welding conditions chosen randomly within the range for which the equations are derived. The actual results are calculated as the average of three measured results for each response. The actual results, predicted values and calculated percentage error of confirmation experiments are furnished in Table 5. It is observed from the validation experiments that there is a small percentage error between the estimated and the experimental values, which indicate that the developed models can yield nearly accurate results. Fig. 4 (a) and (b) exhibit the relationship between the actual and predicted values of weld strength and weld width, respectively. These figures also indicate that the developed models are adequate and predicted results are in good agreement with measured data.
5. Effects of process parameters on responses The effect of process parameters on weld strength and weld width of the welded sample is studied and discussed, within the scope and limitation of the present experimental investigation.
Fig. 4. Plot of actual vs. predicted response of (a) weld strength results, and (b) weld width results.
Factors interaction plots are used to present the results in graphical form. All the significant interaction terms related to weld strength and weld width models are plotted and the factor effect trends are explained in detail. 5.1. Weld strength It is observed from Fig. 5 that weld strength increases with laser power upto a certain level, and thereafter it starts to decline. This phenomenon is observed when a low or medium welding speed (S¼8–12 mm/s) is used. Whereas, weld strength increases monotonically with the laser power, when a higher welding speed (S ¼16 mm/s) is used. It can also be seen from this figure that for a
B. Acherjee et al. / Optics & Laser Technology 44 (2012) 1372–1383
Weld strength (N/mm)
70
1377
S = 8 mm/s S = 12 mm/s S = 16 mm/s
63
56
49
42 9
12
15 18 P: Power (W)
21
Fig. 5. Interaction effect of power and welding speed on weld strength, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
80
F = 32 mm
Weld strength (N/mm)
F = 38 mm F = 44 mm
65
50
35
20 9
12
15 18 P: Power (W)
21
Fig. 6. Interaction effect of power and stand-off distance on weld strength, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
lower laser power (P¼9 W); increasing the welding speed (S¼ 8–16 mm/s) decreases the weld strength. However, the trend differs when a relatively higher laser power (P¼ 12–21 W) is used. In this case, weld strength initially increases with welding speed and then gradually decreases. Such behaviors could be attributable to the following reasons. Increase of laser power with decrease of welding speed results in increase of line energy and hence a good bond is formed; accordingly, joint strength increases. Line energy is the ratio of power to welding speed, defined as laser input energy per unit length [15]. Too low line energy results in lack of penetration, poor heat transfer and poor mixing of materials, thus causing a weak weld. On the other hand, too high line energy may cause degradation of the base material. That is why optimum weld strength can be achieved at a favorable value of line energy with an appropriate combination of laser power and welding speed. According to the results furnished in Fig. 5, the appropriate combination of laser power and welding speed to obtain better weld strength is 18 W and 12 mm/s, respectively, when other parameters are kept constant at their center values. It is evident from Fig. 6 that the laser power and stand-off distance have a strong interaction effect on weld strength. The power density is directly related to the laser power and the standoff distance. In this study, the defocal portion of the laser beam is used for welding. Because of this, the beam spot diameter at the
weld interface increases with stand-off-distance, thus decreasing laser power density as it varies inversely with spot diameter. At lower stand-off distance (F¼32 mm), increasing the laser power decreases the weld strength. However, at higher stand-off distance (F¼44 mm), increasing the laser power increases the weld strength. For stand-off distance at its center value (F¼38 mm), weld strength increases with laser power until it reaches its center value and then gradually decreases. At low stand-off-distance, increasing the laser power results in a higher power density which causes overheating and partial decomposition of the material, consequently, a weak joint is formed. On the other hand, welding with low laser power and high stand-off distance would also reduce the weld strength of the joint due to the lack of full joining on a micro-scale. It can also be seen from the above figure, that for a low or medium laser power (P¼9–15 W), increasing the standoff distance initially increases the weld strength and thereafter it starts to decrease. While, the weld strength increases monotonically with the stand-off distance, when a comparatively higher laser power (P¼16–21 W) is used. The weld strength is restricted at very high power density, which causes material decomposition and a very low power density results in lack of fusion. As the results indicate, it is not recommended that very high or low power densities be used. The result indicates that by applying high
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80
C = 1.5 MPa
Welding strength (N/mm)
C = 2.1 MPa C= 2.7 MPa
65
50
35
20 9
12
15 18 P: Power (W)
21
Fig. 7. Interaction effect of power and clamp pressure on weld strength, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
80
F = 32 mm F = 38 mm
Weld strength (N/mm)
F = 44 mm
60
40
20
0 4
8
12
16
20
S: Welding speed (mm/s) Fig. 8. Interaction effect of welding speed and stand-off distance on weld strength, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
stand-off distance (F¼44 mm), the laser power should be set at its highest limit of 21 W to obtain considerably better tensile strength. In terms of the interaction effect between the laser power and clamp pressure (Fig. 7), it is evident that by using low laser power (P¼9–12 W) and high clamp pressure (C ¼2.7 MPa) or high laser power (P¼18–21 W) and low clamp pressure (C ¼1.5 MPa), the weld strength tend to increase. Clamp pressure ensures good contact between the parts to be welded. This enhances the conduction of heat from the absorptive material to the transparent part and also promotes the molten fluid flow, required for intermixing and cross linking of the polymer chains to combine towards weld formation. However, at higher levels of clamp pressure and laser power, weld strength is slightly reduced because of melt ejection from the two ends of the weld seam. Moreover, using high value of clamp pressure with high laser power would result in undesirable residual stresses that may cause the joint to be pre-stressed and thus speed up fracture. It is observed from Fig. 8, that welding speed and stand-off distance have a significant interaction effect on weld strength. For all the values of stand-off distance (F ¼32–44 mm), weld strength increases with welding speed until it reaches a threshold level and thereafter the weld strength starts to decrease. The threshold welding speed level (Sth) varies with the selected level
of stand-off distance (Sth ¼16 mm/s for F ¼32 mm; Sth ¼12 mm/s for F ¼38 mm; Sth ¼8 mm/s for F¼44 mm). It can also be seen from the above figure, that the weld strength increases monotonically with the stand-off distance, when a low or medium welding speed (S¼4–11 mm/s) is used. While, for a comparatively higher welding speed (S ¼12–20 mm/s), increasing the stand-off distance initially increases the weld strength and thereafter it starts to decrease. This is because the energy deposition and heat diffusion into the material in laser transmission welding depends on the laser power density and the irradiation time, which are in turn governed by the stand-off distance and welding speed. According to the results obtained, a lower welding speed (S ¼8 mm/s) and a higher stand-off distance (F ¼44 mm) gives comparatively better weld strength, when other parameters are kept constant at their center values. Fig. 9 shows the interaction effect of welding speed and clamp pressure on weld strength. It is seen form this figure that welding speed follows the same trend irrespective of the levels of clamp pressure used in this study. However, the trend of effect of clamp pressure varies with the levels of welding speed. At a low or medium value of welding speed (S ¼4–11 mm), the weld strength increases with clamp pressure. On the other hand, at a relatively higher value of welding speed (S ¼13–20 mm/s), increasing the clamp pressure decreases the weld strength.
B. Acherjee et al. / Optics & Laser Technology 44 (2012) 1372–1383
80
1379
C = 1.5 MPa
Weld strength (N/mm)
C = 2.1 MPa C = 2.7 MPa
65
50
35
20 4
8 12 16 S: Welding speed (mm/s)
20
Fig. 9. Interaction effect of welding speed and clamp pressure on weld strength, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
5.2
S = 8 mm/s S = 12 mm/s S = 16 mm/s
Weld width (mm)
4.4
3.6
2.8
2.0 9
12
15 18 P: Power (W)
21
Fig. 10. Interaction effect of power and welding speed on weld width, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
5.2
F = 32 mm F = 38 mm F = 44 mm
Weld width (mm)
4.4
3.6
2.8
2.0 9
12
15 18 P : Power (W)
21
Fig. 11. Interaction effect of power and stand-off distance on weld width, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
5.2. Weld width It is observed from the Fig. 10 that increasing the laser power (P¼9–21 W) and decreasing the welding speed (S ¼16–8 mm/s) increases the weld width. This effect is due to the increase of line
energy, which is directly proportional to the laser power and inversely to the welding speed. Therefore the heat input to the weld zone increases leading to more volume of the base metal being melted, consequently the width of the welded zone increase. According to the results presented in the Fig. 10, the
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B. Acherjee et al. / Optics & Laser Technology 44 (2012) 1372–1383
6.0 F = 32 mm F = 38 mm F = 44 mm
Weld width (mm)
5.0
4.0
3.0
2.0 4
8 12 16 S: Welding speed (mm/s)
20
Fig. 12. Interaction effect of welding speed and stand-off distance on weld width, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
4.8
C = 1.5 MPa C = 2.1 MPa C = 2.7 MPa
Weld width (mm)
4.1
3.4
2.7
2.0 26
32 38 44 F: Stand-off distance (mm)
50
Fig. 13. Interaction effect of stand-off distance and clamp pressure on weld width, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
maximum weld width is achieved using the laser power at higher levels i.e, 18–21 W and welding speed at lower level, i.e., 8 mm/s, when remaining parameters are at their center value. This is clear from the Fig. 11, that the interaction of higher laser power (P¼21 W) with higher stand-off distance (F¼44 mm) results in greater weld width. This effect is due to the fact that with increasing laser power, power density increases, thereby increasing the seam width. Though the increase of stand-off distance reduces power density at a constant laser power but it simultaneously increases the area of interaction due to the defocused beam. Because of this the laser power spreads onto a wide spot at the weld interface. Therefore, wide area of the base metal is melted leading to an increase in weld width or vice versa. It is evident from Fig. 12, that weld width tends to increase with slow welding speed (S ¼4 mm/s) and high stand-off distance (F¼44 mm). This implies that welding speed has a negative effect on weld width as discussed earlier. This is due to the fact that with increasing welding speed, the irradiation time reduces and less heat is delivered with consequent reduction in volume of the molten material characterized by a narrow and weak weld. Standoff distance shows a positive effect on weld width. The reason is same as that stated earlier. Fig. 13 shows the interaction effect of stand-off distance and clamp pressure on weld width. It is seen that weld width increases with the stand-off distance upto 44 mm and thereafter
it becomes almost constant. The trend does not differ with any of the level of clamp pressure that is considered in this study. It is also noticed that for a low stand-off distance (F¼26–32 mm), clamp pressure does not have significant effect on weld width. However, weld width increases with clamp pressure when a relatively higher stand-off distance (F¼ 38–50 mm) is used. According to the results obtained, interaction of higher stand-off distance (F¼50 mm) with higher clamp pressure (C ¼2.7 MPa) results in greater weld width.
6. Optimization of process parameters Simultaneous optimization of multiple responses comprises of building an appropriate regression model for each of the responses and then trying to find a set of operating conditions that in some sense optimizes all the responses or at least keeps them in the desired ranges [18]. Simultaneous optimization of multiple responses can be performed numerically using desirability function analysis by selecting the desired goals for each factor and response, and graphically by overlaying critical response contours on a single contour plot. In case of dealing with many input variables, it is recommended that numerical optimization be done first, and then graphical optimization; otherwise it could be impossible to uncover a feasible region.
B. Acherjee et al. / Optics & Laser Technology 44 (2012) 1372–1383
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The same two criteria, which are used for numerical optimization, are also chosen in the graphical optimization.
6.1. Numerical optimization The optimization module in Design-experts searches for a combination of factor levels that simultaneously satisfy the requirements placed on each of the responses and factors. Numerical optimization searches the design space, using the developed regression model to find the factor settings that optimize any combination of one or more goals. The goals are combined into an overall desirability function. The numerical optimization finds a point that maximizes this desirability function. Two criteria are introduced in this numerical optimization. The first criterion is to reach maximum weld strength with no limitation on either the process parameters or the weld width. While, in the second criterion, the goal is to reach maximum weld strength and minimum weld width at relatively low-operating cost by using minimum laser power and maximum welding speed. Tables 6 and 7 summarize these two optimization criteria.
6.2. Graphical optimization A relatively straight forward approach to optimize several responses that works well when there are only a few process variables is to overlay the contours plot for each response [18]. By superimposing or overlaying critical response contours on one contour plot, it is possible to search visually for the best compromise. Graphical optimization displays the area of feasible response values in the factor space. Regions that do not fit the optimization criteria are shaded [20]. The response limits, lower and/or upper for each response are included according to the numerical optimization results. The same two criteria, which are used for numerical optimization, are implemented in the graphical optimization. 6.3. Results and discussion
Table 6 The first criterion of numerical optimization. Parameter or response
P, W S, mm/s F, mm C, MPa Weld strength, N/mm Weld width, mm
Goal
Limit
Is in range Is in range Is in range Is in range Maximize Is in range
Importance
Lower
Upper
9 4 26 0.9 9.71 2.21
21 20 50 3.3 79.00 5.28
3 3 3 3 5 5
Table 7 The second criterion of numerical optimization. Parameter or response
P, W S, mm/s F, mm C, MPa Weld strength, N/mm Weld width, mm
Goal
Limit
Minimize Maximize Is in range Is in range Maximize Minimize
Importance
Lower
Upper
9 4 26 0.9 9.71 2.21
21 20 50 3.3 79.00 5.28
3 3 3 3 5 5
Table 8 presents the optimal welding conditions according to the first criterion that would lead to maximum weld strength of about 88.89 N/mm, which is better than that achieved with experimental trials. The above table furnishes five set of the pareto-optimal solutions. In view of the fact that none of the solutions in the pareto-optimal outcome is definitely better than others, each of them is an acceptable solution. According to the first criterion, the optimum parametric range for the laser power has to be 18.28–20.89 W, welding speeds has to be 6.18–8.18 mm/s and stand-off-distance within the range of 43.45–44.86 mm using a clamping pressure of 0.95–1.61 MPa. Otherwise, putting constraints by the second criteria, the minimum laser power is always to be set at 9.62–9.87 W, then the welding speed reaches to its maximum value at 18.48–19.00 mm/s when the stand-off distance and clamp pressure are set around the 32.09–32.19 mm and 3.29–3.30 MPa, respectively. Using the second criterion, the minimum weld width achieved is 2.28 mm and the maximum attainable weld strength is 63.47 N/mm, as can be seen in Table 9. For both the criteria, the parameter combinations with highest desirability values are selected as the best laser transmission welding conditions, accordingly. Graphical optimization results into overlay contours plots, which allow quick visual inspection of the area of feasible response values in the factor space to choose the optimum welding parameter combination. The bright areas on the overlay
Table 8 Optimal welding condition based on the first criterion. Sol. No.
P (W)
S (mm/s)
F (mm)
C (MPa)
Weld strength (N/mm)
Weld width (mm)
Desirability
1 2 3 4 5
19.89 19.26 19.36 18.28 17.85
8.17 6.18 8.91 8.18 7.81
44.34 43.45 46.43 44.86 42.35
1.05 0.95 1.14 1.04 1.01
88.89 87.94 85.40 83.77 80.86
5.10 5.24 5.12 5.06 4.90
1.000 selected 1.000 1.000 1.000 1.000
Table 9 Optimal welding condition based on the second criterion. Sol. No.
P (W)
S (mm/s)
F (mm)
C (MPa)
Weld strength (N/mm)
Weld width (mm)
Desirability
1 2 3 4 5
9.87 9.69 9.76 9.78 9.62
18.98 18.48 19.00 19.00 18.81
32.09 32.09 32.14 32.10 32.19
3.30 3.30 3.30 3.29 3.30
63.47 63.50 63.45 63.37 63.76
2.28 2.29 2.29 2.28 2.31
0.914 Selected 0.914 0.914 0.913 0.913
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of verification tests. A fair agreement between the predicted and experimental results is observed.
Overlay Plot
10.00
7. Conclusion
Welding speed
9.00
The following conclusions can be drawn from the experimental investigation carried out within the factor range considered in this study and for the specified materials combinations:
Weld width: 5.08
8.00 Weld width: 5.15
7.00
Weld strength: 87 Weld strength: 89
6.00 16.00
17.00
18.00 Power
19.00
20.00
12.00
13.00
Overlay Plot
20.00 Weld width: 2.28
Weld width: 2.32
Welding speed
19.00
18.00
17.00
Weld strength: 63.4 Weld strength: 63.7
16.00 9.00
10.00
11.00 Power
Fig. 14. Overlay plot shows the region of the optimal working condition (a) based on the first criterion at stand-off distance¼ 44.34 mm and clamp pressure¼ 1.05 MPa, and (b) based on the second criterion at stand-off distance¼32.09 mm and clamp pressure¼ 3.30 MPa.
1. The developed response surface models can predict the responses adequately within the limits of welding parameters being used, 2. Laser power, welding speed and stand-off distance have a strong interaction effect on weld strength and weld width. These parameters control the heat input to the weld zone and thus the quality of the weld, 3. The weld strength is limited by very high heat input, which causes overheating and partial decomposition of the material. A very low heat input, on the other hand results in lack of fusion. 4. It can be observed from the ANOVA tables that the stand-off distance has the maximum effect on weld strength, followed by laser power and welding speed. Clamp pressure has statistically insignificant effect on the weld strength. 5. According to the results of ANOVA, stand-off distance is the most important factor affecting the weld width, and it is followed by welding speed, laser power, and clamp pressure. 6. The optimal welding condition can be determined effectively using the numerical optimization technique, which results in a set of pareto-optimal solution according to the desired optimization criteria. 7. Graphical optimization results into overlay contours plots, which allow quick visual inspection of the area of feasible response values in the factor space to choose the optimum welding parameter combination.
Appendix A. Supporting materials Supplementary data associated with this article can be found in the online version at doi:10.1016/j.optlastec.2011.12.029.
Table 10 Results of verification experiments (according to first criterion). Results
Predicted
Experimental
9Error (%)9
Weld strength (N/mm) Weld width (mm)
88.89 5.10
83.46 5.23
6.12 2.51
References
Table 11 Results of verification experiments (according to second criterion). Results
Predicted
Experimental
9Error (%)9
Weld strength (N/mm) Weld width (mm)
63.47 2.28
60.43 2.33
4.79 2.19
plots in Fig. 14 (a) and (b) are the regions that meet the proposed criteria. 6.4. Verification tests Finally, for each criterion, three additional experiments are conducted at the optimal parameters setting and average of those three is used for verification. Tables 10 and 11 present the results
[1] Russek UA, Poggel M, Otto G, Koeppe A. Advances in laser beam welding of polymers and automotive prospects. Proceedings of the 9th International Conference: TPOs in Automotive, Maastricht, the Netherlands. 2003. 51–60. [2] Acherjee B, Kuar AS, Mitra S, Misra D. Laser transmission welding: a novel technique in plastic joining. In: Klein RJ, editor. Welding: Processes, Quality, and Applications. New York: Nova Science Publishers, Inc; 2010. p. 365–88. [3] Baylis B. Welding thermoplastic elastomers to polypropylene with a diode laser, Proceedings of the 21st ICALEO, Scottsdale, AZ, USA, 2002. [4] Silvers Jr. HJ, Wachtell S. Perforating, welding and cutting plastic films with a continuous CO2 lase. In: Pennsylvania State University, Engineering Proceedings, 1970. p. 88–97. [5] Nakamata H. Process for joining different kinds of synthetic resins, US Patent, 4636609 (1987). [6] Kagan VA, Bray R, Chambers A. Forward to better understanding of optical characterization and development of colored polyamides for the infra-red/ laser welding: part I – efficiency of polyamides for infra-red welding. Journal of Reinforced Plastics and Composites 2003;22(6):533–47. [7] Kagan VA, Chambers A, Bray R. Forward to better understanding of optical characterization and development of colored polyamides for the infra-red/ laser welding, part II – family of colored polyamides. Journal of Reinforced Plastics and Composites 2003;22(7):593–603. [8] Jansson A, Kouvo S, Kujanpa¨ a¨ V. Preliminary investigations of laser welding of plastics in massproduction, Proceedings of the 23rd ICALEO, San Francisco, CA, USA, vol. 97, 2004.
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[9] Grewell D, Rooney P, Kagan VA. Relationship between optical properties and optimized processing parameters for through-transmission laser welding of thermoplastics. Journal of Reinforced Plastics and Composites 2004;23(3):239–47. [10] Haberstroh E, Hoffmann WM, Poprawe R, Sari F. 3 laser transmission joining in microtechnology. Microsystem Technologies 2006;12:632–9. [11] Chen M, Zak G, Bates PJ. Effect of carbon black on light transmission in laser welding of thermoplastics. Journal of Materials Processing Technology 2011;211:43–7. [12] Douglass DM, Wu C.Y. Laser welding of polyolefin elastomers to thermoplastic polyolefin, Proceedings of the 22nd ICALEO, Jacksonville, FL, USA, vol. 95, 2003. LMP Sec-A, pp. 118–123. [13] Russek UA, Staub H, Palmen A, Kind H. Simultaneous laser beam welding of thermoplastics—innovations and challenges, Proceedings of the 22nd ICALEO, Jacksonville, Florida, USA, vol. 95, 2003. LMP Sec-A, pp. 99–107. [14] Prabhakaran R, Kontopoulou M, Zak G, Bates PJ, Baylis BK. Contour laser–laser transmission welding of glass reinforced nylon. Journal of Thermoplastic Composite Materials 2006;19:427–39.
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[15] Acherjee B, Misra D, Bose D, Venkadeshwaran K. Prediction of weld strength and seam width for laser transmission welding of thermoplastic using response surface methodology. Optics & Laser Technology 2009;41(8): 956–67. [16] Benyounis KY, Olabi AG, Hashmi MSJ. Effect of laser welding parameters on the heat input and weld-bead profile. Journal of Materials Processing Technology 2005;164–165:978–85. [17] Ruggiero A, Tricarico L, Olabi AG, Benyounis KY. Weld-bead profile and costs optimization of the CO2 dissimilar laser welding process of low carbon steel and austenitic steel AISI316. Optics & Laser Technology 2011;43:82–90. [18] Montgomery DC. Design and Analysis of Experiments.5th edn. New York: Wiley; 2001. [19] Derringer G, Suich R. Simultaneous optimization of several response variables. Journal of Quality Technology 1980;12(4):214–9. [20] Design-Expert software, v7, User’s Guide – Technical Manual. Minneapolis: Stat-Ease, Inc.
Contents lists available at SciVerse ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Experimental investigation on laser transmission welding of PMMA to ABS via response surface modeling Bappa Acherjee a,n, Arunanshu S. Kuar a, Souren Mitra a, Dipten Misra b, Sanjib Acharyya c a
Department of Production Engineering, Jadavpur University, Kolkata-700 032, India School of Laser Science & Engineering, Jadavpur University, Kolkata-700 032, India c Department of Mechanical Engineering, Jadavpur University, Kolkata-700 032, India b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 August 2011 Received in revised form 19 November 2011 Accepted 13 December 2011 Available online 31 December 2011
In this paper, an experimental investigation on diode laser transmission welding of dissimilar thermoplastics between PMMA (polymethyl methacrylate) and ABS (acrylonitrile butadiene styrene) has been carried out. The effect of the laser welding parameters such as laser power, welding speed, stand-off distance and clamp pressure on weld strength and weld width is investigated using response surface methodology (RSM). Planned experiments and subsequent analyses are carried out to develop the mathematical models to establish the correlation between the process parameters and the responses. The adequacy of the developed models is tested using the sequential F-test, lack-of-fit test and the analysis-of-variance (ANOVA) technique. A numerical multi-objective simultaneous optimization technique, in which the RSM is incorporated, is used to find the optimum solutions, according to the desired optimization criteria. In addition to that, a graphical optimization technique is, also implemented which allow identifying a region in the graphic where optimal conditions lay on. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Laser transmission welding Response surface methodology Dissimilar plastic welding
1. Introduction There is a continuously growing interest in the joining of dissimilar plastics in manufacturing industries. Joining of useful plastic combinations like PMMA (polymethyl methacrylate) to ABS (acrylonitrile butadiene styrene) and polycarbonate to ABS are already found in a number of industrial applications. They are used in automotive components like flood lights, looking mirror, dashboard components etc; displays and cabinets; and cell phone assemblies to name a few of their many applications [1,2]. PMMA is a useful, clear plastic that resembles glass, but has properties that make it superior to glass in many ways. It is chosen over glass for many reasons. It is many times stronger than glass, making it much more impact resistant and therefore safer. ABS, a copolymer, is comprised of polymerized styrene and acrylonitrile with polybutadiene, which exhibits a balanced combination of mechanical toughness, good dimensional stability, chemical resistance and electrical insulating properties. These combinations of properties make them suitable for various applications in diverse fields including automotive and computer industries. Joining of dissimilar plastics requires the application of an appropriate joining technology. In case of welding, both the materials must have chemical compatibility and the difference between the melting temperatures of those materials should not be too high [3].
n
Corresponding author. Tel.: þ91 33 2337 4125; fax: þ 91 33 2337 6331. E-mail addresses: [email protected], [email protected] (B. Acherjee).
0030-3992/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2011.12.029
Laser transmission welding is the latest addition in the field of plastic welding. Laser welding was first demonstrated on thermoplastics in the 1970s [4] but it found a place in industrial-scale situations only in the last decade. In 1987, Nakamata [5] patented the laser transmission welding technique, as a process in which, the laser beam penetrates the upper transparent plastic part and is converted into heat by the absorbing lower plastic part. The melt is created only where it is needed, in the joining area of the both partners, to form the weld. Laser transmission welding is non contact, non contaminant and flexible process, has shorter processing time, can provide consistent quality and is repeatable [2]. Literature review on laser transmission welding reveals that, the influence of the plastic composition, colorants and thickness of plastic parts on the laser transmission and absorption and finally on the mechanical performance of the weld have been studied extensively [6–11]. It is evident from the literature that the presence of reinforcement, mineral fillers, impact modifiers, color pigments and some heat stabilizers in polymer matrix lower the transmissivity of the polymer due to particulate scattering and increased absorption by colorants. It is also observed that thickness of plastic part influences the optical properties, especially in the presence of fillers, crystallites, etc. The key process parameters for laser transmission welding are: laser power, welding speed, beam spot area and clamping pressure, which control the temperature field inside the weld seam, and hence the weld quality. Material surface finish and the size of air gap have also a significant effect on the weld quality. A number of experimental programs have been carried out to study the effect of process
B. Acherjee et al. / Optics & Laser Technology 44 (2012) 1372–1383
parameters on weld quality, with various plastic materials and application strategies [12–15]. However, no comprehensive research work has been reported on laser transmission welding of PMMA to ABS. No technological database is available for laser transmission welding of such a useful material combination in open literatures. An extensive research is, therefore, needed to analyze and optimize the laser transmission welding of PMMA to ABS. To get the desired weld quality, i.e., weld bead size and weld strength, the combination of the process parameters should be selected carefully. Response surface methodology (RSM) is one of the modeling and optimization techniques currently in widespread use in describing the performance of the welding process and finding the optimum of the responses of interest [15–17]. Laser transmission welding of PMMA to ABS has been investigated in present research work. RSM is applied to the experimental data to relate the laser welding parameters (laser power, welding speed, stand-off distance and clamp pressure) with the responses (weld strength and weld width). The developed mathematical models are tested for their adequacy using analysis of variance and other adequacy measures. The effect of welding parameters on the responses is studied on the basis of the developed models. The mathematical models are further used to find optimum welding conditions to achieve the desired weld quality.
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For goal of maximum, the desirability will be defined by
di ¼
8 0; > > < > > :
yi Li Hi Li
wti
if response ðyi Þ r low value ðLi Þ ;
as response ðyi Þ varies from low ðLi Þ to high ðHi Þ if response ðyi Þ Z high value ðHi Þ
1;
ð3Þ For goal of minimum, the desirability will be defined by
di ¼
8 1; > > < > > :
Hi yi Hi Li
0;
wti
if response ðyi Þ r low value ðLi Þ ;
as response ðyi Þ varies from low ðLi Þ to high ðHi Þ if response ðyi Þ Z high value ðHi Þ
ð4Þ A weight (wt) can be assigned to a goal to emphasize the particular desirability function. Weights can be ranged between 0.1 and 10. A weight greater than 1 gives more emphasis to the goal, while weights less than 1 give less emphasis. The simultaneous objective function, D is a geometric mean of all transformed responses: !1=P n ri P Y r1 r2 rn 1= ri ri D ¼ ðd1 d1 . . . d1 Þ ¼ di ð4Þ i¼1
where n is the number of responses in the measure. Each response can be assigned an importance, relative to the other responses. Importance (ri) values varies from 1, the least important, to 5, the most important.
2. Methodology 2.1. Response surface methodology Response surface methodology is a collection of mathematical and statistical techniques that are useful for the modeling and analysis of problems in which a response of interest is influenced by several variables and the objective is to optimize the response [18]. If all variables are assumed to be measurable, the response surface can be expressed as follows: y ¼ f ðx1 ,x2 ,. . .,xk Þ
ð1Þ
where y is the response of the system, and xi the variables of action called factors. In the practical application of RSM it is necessary to develop an approximating model for the true response surface. The approximating model is based on observed data from the process or system and is an empirical model. Multiple regression analysis is a collection of statistical techniques useful for building the types of empirical models required in RSM. Usually a second order polynomial equation is used in RSM: y ¼ b0 þ
k X i¼1
bi xi þ
k X
bii xi2 þ
i¼1
where, parameters bi,j ¼ 0,1, coefficients.
k1 X k X
bij xi xj
ð2Þ
i¼1j¼2
y
k
are called the regression
2.2. Desirability function analysis The desirability function analysis method is first proposed by Derringer and Suich in 1980 [19]. This method makes use of a technique for combining multiple responses into a dimensionless measure of performance called the composite desirability function. The general approach of desirability function is to transfer each response yi into an unitless desirability function di bounded by 0 rdi r1, where, the desirable ranges are from zero to one, as least to most desirable, respectively [18].
3. Experimental work 3.1. Experimental set up Experimental investigations are performed with a continuous wave diode laser system. The system installation consists of a 30 W Coherent FAP (fiber array packaged) diode laser with a 3-axes CNC work table, coordinated with the motion system and computer interface. The diode laser is operated at 809.4 nm wavelength and the focal length used is 13 mm. The FAP system optical radiation is delivered via SMA 905 connector, which mates to an 800 mm diameter transport fiber. The photographic view of the experimental set up for present work is shown in Fig. 1. ¨ Plexiglass 6N acrylic (PMMA) granules from Evonik Rohm GmbH and Terlurans GP-22 ABS granules from BASF are used as raw materials for making of plastic plaques. Natural PMMA and opaque ABS (0.1 wt% carbon black pigmented) plaques of dimensions 80 mm 35 mm 4 mm of each are used as the work materials (having Ra value of 0.26 mm, as measured by a Surfcom 120 A stylus profilometer). They are placed on the metal plate of the holding fixture with the PMMA sample on top, with an overlap between the natural and black plaques of approximately 20 mm. The fixture is used for the repetitive work, to maintain the lapping area constant for every run and to prevent misalignment between the parts to be welded in lap joint geometry. Hydraulic clamp pressure is applied in between the workpieces to ensure the intimate contact between them. A uniform pressure on the whole length of the joint is generated by an additional transparent acrylic plaque of same size that is placed across and above the overlapping area as indicated by (A) in Fig. 1 (b). The pressure applied to the workpieces is determined from the reading of the pressure gage, fitted to the hydraulic pump, converted to the pressure experienced by the plaques based on the actual area of contact between the overlapped sections of each sample [15]. The contour welding variant of laser transmission welding is adopted for this study.
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maximum and minimum levels of the variables. The selected process parameters and their limits, units and notations are given in Table 1.
3.4. Developing the design matrix The selected design matrix, shown in Table 2, is a four factors five levels central composite rotatable design with full replications consisting of 30 sets of coded conditions and comprising a full replication of 24 ( ¼16) factorial design plus six center points and eight star points. All welding variables at the intermediate (0) level constitute the center points while the combination of each of the welding variables at either its lowest value ( 2) or its highest value ( þ2) with the other three variables at the intermediate levels constitute the star points. Thus, the 30 experimental runs allowed the estimation of the linear, quadratic and two-way interactive effects of the process parameters on the response parameters. Statistical software Design-Experts is used to code the variables and to establish the design matrix.
Table 1 Process control parameters and their limits. Parameters
Units
Power Welding speed Stand-off-distance Clamp pressure
Watt mm/s mm MPa
Notations
P S F C
Limits 2
1
0
þ1
þ2
9 4 26 0.9
12 8 32 1.5
15 12 38 2.1
18 16 44 2.7
21 20 50 3.3
Table 2 Design matrix and measured experimental results. Exp. no.
Fig. 1. (a) Pictorial, and (b) schematic view of experimental set-up.
3.2. Selection of process parameters Four independently controllable process parameters, namely: power, welding speed, stand-off distance and clamp pressure are considered as input parameters to carry out the experiments. The beam spot area on the workpiece is varied by varying the stand-offdistance i.e, the distance between laser optic and work material. 3.3. Finding the limits of process parameters Trial runs are conducted by varying one of the process parameters at a time while keeping the rest of them at constant value. The working range is decided by inspecting the weld seam for a smooth appearance and the absence of any visible defects. The upper and lower limits are coded as þ2 and 2, respectively. The coded values for intermediate values can be calculated from the relationship: 2XðX max þ X min Þ Xi ¼ 2 ð6Þ ðX max X min Þ where Xi is the required coded value of a variable X; when X is any value of the variable from Xmin to Xmax; Xmax and Xmin are the
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Welding parameter level
Measured output
P (W)
S (mm/s)
F (mm)
C (MPa)
Weld strength (N/mm)
Weld width (mm)
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 2 2 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 2 2 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 2 2 0 0 0 0 0 0
38.29 31.14 45.00 46.14 62.43 79.26 32.57 58.71 38.71 22.14 55.29 40.43 65.57 71.71 46.86 57.14 55.14 65.57 50.57 48.29 9.71 41.71 63.71 62.29 63.29 65.43 64.00 63.57 62.14 64.57
3.19 3.43 2.74 3.14 4.51 5.17 3.36 4.10 3.15 3.42 2.74 3.15 4.92 5.28 3.35 4.37 3.26 4.31 4.78 3.42 2.21 4.26 3.81 4.14 4.08 3.91 3.98 4.10 3.99 4.01
B. Acherjee et al. / Optics & Laser Technology 44 (2012) 1372–1383
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Fig. 3. Photographs of samples after lap shear test showing (a) shear failure from weld interface, and (b) fracture of base material starting from fusion zone. Fig. 2. (a) the PMMA/ABS welded sample in lap joint geometry, and (b) the sample used for lap-shear testing.
3.5. Evaluation of responses A microprocessor controlled Instron universal testing machine with an accuracy of 70.4% of rated capacity (model: 8801, maximum capacity: 100 kN) is used for lap-shear pull test of welded specimens. The crosshead speed during the shear test is kept constant at 0.5 mm/ min. The weld strength is measured as the maximum load to failure per unit length of the weld (N/mm). Fig. 2(a) and (b) shows the welded sample in lap joint geometry and the sample used for lapshear testing, respectively. During the tensile tests, two types of breaking failure were observed: (a) shear failure from weld interface, and (b) fracture of base material starting from fusion zone, as shown in Fig. 3. An Olympus STM 6 measuring microscope is used for measuring weld seam widths. The STM6 microscope offers high performance three axis measurements of parts, with sub-micron precision. Inbuilt LED illuminator is used for reflected coaxial illumination during measurements. The average of three results of both lapshear tests and weld width are calculated and presented in Table 2.
4. Development of mathematical models Design-Experts v7 software is used for analysis of the measured responses and determining the mathematical models with best fits. The adequacy of the model is tested using the sequential f-test, lack-of-fit test and the analysis-of-variance (ANOVA) technique using the same software to obtain the best-fit model. 4.1. Analysis of weld strength The fit summary for weld strength suggests the quadratic model where the additional terms are significant and the model is not aliased [20]. The ANOVA table of the quadratic model is given in Table 3. The associated p-value of less than 0.05 for the model (i.e, a ¼0.05, or 95% confidence level) indicates that the model terms are statistically significant. The other model terms are not significant and thus, eliminated by backward elimination process to improve model adequacy. The main effect of clamp pressure (C) is added to support hierarchy. The other adequacy measures R2, adjusted R2 and predicted R2 are in reasonable agreement and are close to 1, which indicate adequacy of the model [15]. The adequate precision compares the signal to noise ratio and a ratio greater than 4 is desirable [16]. The value of adequate precision
Table 3 ANOVA analysis for the weld strength model. Sources
Sum of squares
Degrees of freedom
Mean squares
F-value
p-value
Model P S F C PS PF PC SF SC P2 S2 F2 Residual Lack of fit Pure Error Total
6931.05 75.51 41.16 2032.41 0.12 35.15 582.88 167.15 1225.00 56.25 20.94 362.26 2540.59 63.22 56.88 6.34 6994.27
12 1 1 1 1 1 1 1 1 1 1 1 1 17 12 5 29
577.59 75.51 41.16 2032.41 0.12 35.15 582.88 167.15 1225.00 56.25 20.94 362.26 2540.59 3.72 4.74 1.27
155.31 20.31 11.07 546.51 0.03 9.45 156.73 44.95 329.40 15.13 5.63 97.41 683.16
o 0.0001 0.0003 0.0040 o 0.0001 0.8582 0.0069 o 0.0001 o 0.0001 o 0.0001 0.0012 0.0297 o 0.0001 o 0.0001
3.74
0.0778
R2 ¼ 0.9910, adjusted R2 ¼0.9846, predicted R2 ¼0.9621, adequate Precision¼57.62.
ratio of 57.62 indicates adequate model discrimination. The lackof-fit F-value of 3.74 implies that the lack-of-fit is not significant relative to the pure error, as this is desirable. The final mathematical models for weld strength (Yws), which can be used for prediction within same design space, are as follows: (a) In terms of coded factors, Y ws ¼ 63:56 þ 1:77P21:31S þ9:20F þ 0:07C þ 1:48PS þ 6:04PF 23:23PC28:75SF þ 1:88SC20:86P 2 23223:60S2 29229:53F 2
ð7Þ (b) In terms of actual factors, Y ws ¼ 2425:7426:98P þ 15:43S þ 20:99F þ 17:68C þ 0:12PS þ 0:34PF
21:80PC20:37SF þ0:78SC20:10P 2
20:23S2 20220:27F 2
ð8Þ
4.2. Analysis of weld width For weld width, the fit summary recommends the quadratic model where the additional terms are significant and the model is
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Table 4 ANOVA analysis for the weld width model.
Table 5 Validation test results.
Source
Sum of squares
Degrees of freedom
Mean squares
F-value
p-value
Model P S F C PS PF SF FC P2 F2 Residual Lack of fit Pure Error Total
15.4220 1.6017 3.2561 8.4017 0.0817 0.0676 0.1332 0.6724 0.0420 0.1062 1.1218 0.1984 0.1741 0.0243 15.6204
10 1 1 1 1 1 1 1 1 1 1 19 14 5 29
1.5422 1.6017 3.2561 8.4017 0.0817 0.0676 0.1332 0.6724 0.0420 0.1062 1.1218 0.0104 0.0124 0.0049
147.7140 153.4096 311.8700 804.7218 7.8221 6.4748 12.7605 64.4033 4.0252 10.1688 107.4506
o 0.0001 o 0.0001 o 0.0001 o 0.0001 0.0115 0.0198 0.0020 o 0.0001 0.0593 0.0048 o 0.0001
2.5603
Weld strength (N/mm)
Weld width (mm)
Actual Predicted 9Error %9
53.76 50.48 6.10
4.14 3.89 6.04
1.5
Actual Predicted 9Error %9
78.44 79.41 1.24
5.23 5.10 2.49
2.7
Actual Predicted 9Error %9
22.16 21.37 3.57
3.21 3.44 7.17
Exp. No.
P (W)
S (mm/s)
F (mm)
C (MPa)
1
12
12
44
1.5
2
18
8
44
3
18
8
32
0.1529
R2 ¼0.9873, adjusted R2 ¼ 0.9806, predicted R2 ¼0.9576, adequate precision¼57.97.
not aliased. Table 4 presents the ANOVA table of the quadratic model. The ANOVA result shows the significant model terms associated with weld width. The other adequacy measures R2, adjusted R2 and predicted R2 are in reasonable agreement and are close to 1, which indicate adequate model. The value of adequate precision ratio 52.97 indicates adequate model discrimination. The lack-of-fit F-value of 2.56 implies that the lack-of-fit is not significant relative to the pure error. The final mathematical models for weld width (Yww), as determined by Design expert software are given as follows: (a) In terms of coded factors, Y ww ¼ 4:020 þ0:260P20:370S þ 0:590F þ 0:058C þ0:065PS þ 0:091PF20:210SF þ 0:051FC20:061P2 20:200F 2
ð9Þ
(b) In terms of actual factors, Y ww ¼ 28:5085 þ 0:0321P þ 0:1513S þ 0:5144F20:4438C þ 5:4167E03PS þ 5:0694E03PF28:5417E03SF þ 0:0142FC26:7882E03P 2 25:5165E03F 2
ð10Þ
4.3. Validation of the developed models To validate the developed response surface equations, derived from multiple regression analysis, three confirmation experiments are conducted with welding conditions chosen randomly within the range for which the equations are derived. The actual results are calculated as the average of three measured results for each response. The actual results, predicted values and calculated percentage error of confirmation experiments are furnished in Table 5. It is observed from the validation experiments that there is a small percentage error between the estimated and the experimental values, which indicate that the developed models can yield nearly accurate results. Fig. 4 (a) and (b) exhibit the relationship between the actual and predicted values of weld strength and weld width, respectively. These figures also indicate that the developed models are adequate and predicted results are in good agreement with measured data.
5. Effects of process parameters on responses The effect of process parameters on weld strength and weld width of the welded sample is studied and discussed, within the scope and limitation of the present experimental investigation.
Fig. 4. Plot of actual vs. predicted response of (a) weld strength results, and (b) weld width results.
Factors interaction plots are used to present the results in graphical form. All the significant interaction terms related to weld strength and weld width models are plotted and the factor effect trends are explained in detail. 5.1. Weld strength It is observed from Fig. 5 that weld strength increases with laser power upto a certain level, and thereafter it starts to decline. This phenomenon is observed when a low or medium welding speed (S¼8–12 mm/s) is used. Whereas, weld strength increases monotonically with the laser power, when a higher welding speed (S ¼16 mm/s) is used. It can also be seen from this figure that for a
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Weld strength (N/mm)
70
1377
S = 8 mm/s S = 12 mm/s S = 16 mm/s
63
56
49
42 9
12
15 18 P: Power (W)
21
Fig. 5. Interaction effect of power and welding speed on weld strength, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
80
F = 32 mm
Weld strength (N/mm)
F = 38 mm F = 44 mm
65
50
35
20 9
12
15 18 P: Power (W)
21
Fig. 6. Interaction effect of power and stand-off distance on weld strength, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
lower laser power (P¼9 W); increasing the welding speed (S¼ 8–16 mm/s) decreases the weld strength. However, the trend differs when a relatively higher laser power (P¼ 12–21 W) is used. In this case, weld strength initially increases with welding speed and then gradually decreases. Such behaviors could be attributable to the following reasons. Increase of laser power with decrease of welding speed results in increase of line energy and hence a good bond is formed; accordingly, joint strength increases. Line energy is the ratio of power to welding speed, defined as laser input energy per unit length [15]. Too low line energy results in lack of penetration, poor heat transfer and poor mixing of materials, thus causing a weak weld. On the other hand, too high line energy may cause degradation of the base material. That is why optimum weld strength can be achieved at a favorable value of line energy with an appropriate combination of laser power and welding speed. According to the results furnished in Fig. 5, the appropriate combination of laser power and welding speed to obtain better weld strength is 18 W and 12 mm/s, respectively, when other parameters are kept constant at their center values. It is evident from Fig. 6 that the laser power and stand-off distance have a strong interaction effect on weld strength. The power density is directly related to the laser power and the standoff distance. In this study, the defocal portion of the laser beam is used for welding. Because of this, the beam spot diameter at the
weld interface increases with stand-off-distance, thus decreasing laser power density as it varies inversely with spot diameter. At lower stand-off distance (F¼32 mm), increasing the laser power decreases the weld strength. However, at higher stand-off distance (F¼44 mm), increasing the laser power increases the weld strength. For stand-off distance at its center value (F¼38 mm), weld strength increases with laser power until it reaches its center value and then gradually decreases. At low stand-off-distance, increasing the laser power results in a higher power density which causes overheating and partial decomposition of the material, consequently, a weak joint is formed. On the other hand, welding with low laser power and high stand-off distance would also reduce the weld strength of the joint due to the lack of full joining on a micro-scale. It can also be seen from the above figure, that for a low or medium laser power (P¼9–15 W), increasing the standoff distance initially increases the weld strength and thereafter it starts to decrease. While, the weld strength increases monotonically with the stand-off distance, when a comparatively higher laser power (P¼16–21 W) is used. The weld strength is restricted at very high power density, which causes material decomposition and a very low power density results in lack of fusion. As the results indicate, it is not recommended that very high or low power densities be used. The result indicates that by applying high
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80
C = 1.5 MPa
Welding strength (N/mm)
C = 2.1 MPa C= 2.7 MPa
65
50
35
20 9
12
15 18 P: Power (W)
21
Fig. 7. Interaction effect of power and clamp pressure on weld strength, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
80
F = 32 mm F = 38 mm
Weld strength (N/mm)
F = 44 mm
60
40
20
0 4
8
12
16
20
S: Welding speed (mm/s) Fig. 8. Interaction effect of welding speed and stand-off distance on weld strength, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
stand-off distance (F¼44 mm), the laser power should be set at its highest limit of 21 W to obtain considerably better tensile strength. In terms of the interaction effect between the laser power and clamp pressure (Fig. 7), it is evident that by using low laser power (P¼9–12 W) and high clamp pressure (C ¼2.7 MPa) or high laser power (P¼18–21 W) and low clamp pressure (C ¼1.5 MPa), the weld strength tend to increase. Clamp pressure ensures good contact between the parts to be welded. This enhances the conduction of heat from the absorptive material to the transparent part and also promotes the molten fluid flow, required for intermixing and cross linking of the polymer chains to combine towards weld formation. However, at higher levels of clamp pressure and laser power, weld strength is slightly reduced because of melt ejection from the two ends of the weld seam. Moreover, using high value of clamp pressure with high laser power would result in undesirable residual stresses that may cause the joint to be pre-stressed and thus speed up fracture. It is observed from Fig. 8, that welding speed and stand-off distance have a significant interaction effect on weld strength. For all the values of stand-off distance (F ¼32–44 mm), weld strength increases with welding speed until it reaches a threshold level and thereafter the weld strength starts to decrease. The threshold welding speed level (Sth) varies with the selected level
of stand-off distance (Sth ¼16 mm/s for F ¼32 mm; Sth ¼12 mm/s for F ¼38 mm; Sth ¼8 mm/s for F¼44 mm). It can also be seen from the above figure, that the weld strength increases monotonically with the stand-off distance, when a low or medium welding speed (S¼4–11 mm/s) is used. While, for a comparatively higher welding speed (S ¼12–20 mm/s), increasing the stand-off distance initially increases the weld strength and thereafter it starts to decrease. This is because the energy deposition and heat diffusion into the material in laser transmission welding depends on the laser power density and the irradiation time, which are in turn governed by the stand-off distance and welding speed. According to the results obtained, a lower welding speed (S ¼8 mm/s) and a higher stand-off distance (F ¼44 mm) gives comparatively better weld strength, when other parameters are kept constant at their center values. Fig. 9 shows the interaction effect of welding speed and clamp pressure on weld strength. It is seen form this figure that welding speed follows the same trend irrespective of the levels of clamp pressure used in this study. However, the trend of effect of clamp pressure varies with the levels of welding speed. At a low or medium value of welding speed (S ¼4–11 mm), the weld strength increases with clamp pressure. On the other hand, at a relatively higher value of welding speed (S ¼13–20 mm/s), increasing the clamp pressure decreases the weld strength.
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80
1379
C = 1.5 MPa
Weld strength (N/mm)
C = 2.1 MPa C = 2.7 MPa
65
50
35
20 4
8 12 16 S: Welding speed (mm/s)
20
Fig. 9. Interaction effect of welding speed and clamp pressure on weld strength, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
5.2
S = 8 mm/s S = 12 mm/s S = 16 mm/s
Weld width (mm)
4.4
3.6
2.8
2.0 9
12
15 18 P: Power (W)
21
Fig. 10. Interaction effect of power and welding speed on weld width, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
5.2
F = 32 mm F = 38 mm F = 44 mm
Weld width (mm)
4.4
3.6
2.8
2.0 9
12
15 18 P : Power (W)
21
Fig. 11. Interaction effect of power and stand-off distance on weld width, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
5.2. Weld width It is observed from the Fig. 10 that increasing the laser power (P¼9–21 W) and decreasing the welding speed (S ¼16–8 mm/s) increases the weld width. This effect is due to the increase of line
energy, which is directly proportional to the laser power and inversely to the welding speed. Therefore the heat input to the weld zone increases leading to more volume of the base metal being melted, consequently the width of the welded zone increase. According to the results presented in the Fig. 10, the
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6.0 F = 32 mm F = 38 mm F = 44 mm
Weld width (mm)
5.0
4.0
3.0
2.0 4
8 12 16 S: Welding speed (mm/s)
20
Fig. 12. Interaction effect of welding speed and stand-off distance on weld width, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
4.8
C = 1.5 MPa C = 2.1 MPa C = 2.7 MPa
Weld width (mm)
4.1
3.4
2.7
2.0 26
32 38 44 F: Stand-off distance (mm)
50
Fig. 13. Interaction effect of stand-off distance and clamp pressure on weld width, while the remaining parameters are at their respective center values (Inset figure: 3-D response surface plot).
maximum weld width is achieved using the laser power at higher levels i.e, 18–21 W and welding speed at lower level, i.e., 8 mm/s, when remaining parameters are at their center value. This is clear from the Fig. 11, that the interaction of higher laser power (P¼21 W) with higher stand-off distance (F¼44 mm) results in greater weld width. This effect is due to the fact that with increasing laser power, power density increases, thereby increasing the seam width. Though the increase of stand-off distance reduces power density at a constant laser power but it simultaneously increases the area of interaction due to the defocused beam. Because of this the laser power spreads onto a wide spot at the weld interface. Therefore, wide area of the base metal is melted leading to an increase in weld width or vice versa. It is evident from Fig. 12, that weld width tends to increase with slow welding speed (S ¼4 mm/s) and high stand-off distance (F¼44 mm). This implies that welding speed has a negative effect on weld width as discussed earlier. This is due to the fact that with increasing welding speed, the irradiation time reduces and less heat is delivered with consequent reduction in volume of the molten material characterized by a narrow and weak weld. Standoff distance shows a positive effect on weld width. The reason is same as that stated earlier. Fig. 13 shows the interaction effect of stand-off distance and clamp pressure on weld width. It is seen that weld width increases with the stand-off distance upto 44 mm and thereafter
it becomes almost constant. The trend does not differ with any of the level of clamp pressure that is considered in this study. It is also noticed that for a low stand-off distance (F¼26–32 mm), clamp pressure does not have significant effect on weld width. However, weld width increases with clamp pressure when a relatively higher stand-off distance (F¼ 38–50 mm) is used. According to the results obtained, interaction of higher stand-off distance (F¼50 mm) with higher clamp pressure (C ¼2.7 MPa) results in greater weld width.
6. Optimization of process parameters Simultaneous optimization of multiple responses comprises of building an appropriate regression model for each of the responses and then trying to find a set of operating conditions that in some sense optimizes all the responses or at least keeps them in the desired ranges [18]. Simultaneous optimization of multiple responses can be performed numerically using desirability function analysis by selecting the desired goals for each factor and response, and graphically by overlaying critical response contours on a single contour plot. In case of dealing with many input variables, it is recommended that numerical optimization be done first, and then graphical optimization; otherwise it could be impossible to uncover a feasible region.
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The same two criteria, which are used for numerical optimization, are also chosen in the graphical optimization.
6.1. Numerical optimization The optimization module in Design-experts searches for a combination of factor levels that simultaneously satisfy the requirements placed on each of the responses and factors. Numerical optimization searches the design space, using the developed regression model to find the factor settings that optimize any combination of one or more goals. The goals are combined into an overall desirability function. The numerical optimization finds a point that maximizes this desirability function. Two criteria are introduced in this numerical optimization. The first criterion is to reach maximum weld strength with no limitation on either the process parameters or the weld width. While, in the second criterion, the goal is to reach maximum weld strength and minimum weld width at relatively low-operating cost by using minimum laser power and maximum welding speed. Tables 6 and 7 summarize these two optimization criteria.
6.2. Graphical optimization A relatively straight forward approach to optimize several responses that works well when there are only a few process variables is to overlay the contours plot for each response [18]. By superimposing or overlaying critical response contours on one contour plot, it is possible to search visually for the best compromise. Graphical optimization displays the area of feasible response values in the factor space. Regions that do not fit the optimization criteria are shaded [20]. The response limits, lower and/or upper for each response are included according to the numerical optimization results. The same two criteria, which are used for numerical optimization, are implemented in the graphical optimization. 6.3. Results and discussion
Table 6 The first criterion of numerical optimization. Parameter or response
P, W S, mm/s F, mm C, MPa Weld strength, N/mm Weld width, mm
Goal
Limit
Is in range Is in range Is in range Is in range Maximize Is in range
Importance
Lower
Upper
9 4 26 0.9 9.71 2.21
21 20 50 3.3 79.00 5.28
3 3 3 3 5 5
Table 7 The second criterion of numerical optimization. Parameter or response
P, W S, mm/s F, mm C, MPa Weld strength, N/mm Weld width, mm
Goal
Limit
Minimize Maximize Is in range Is in range Maximize Minimize
Importance
Lower
Upper
9 4 26 0.9 9.71 2.21
21 20 50 3.3 79.00 5.28
3 3 3 3 5 5
Table 8 presents the optimal welding conditions according to the first criterion that would lead to maximum weld strength of about 88.89 N/mm, which is better than that achieved with experimental trials. The above table furnishes five set of the pareto-optimal solutions. In view of the fact that none of the solutions in the pareto-optimal outcome is definitely better than others, each of them is an acceptable solution. According to the first criterion, the optimum parametric range for the laser power has to be 18.28–20.89 W, welding speeds has to be 6.18–8.18 mm/s and stand-off-distance within the range of 43.45–44.86 mm using a clamping pressure of 0.95–1.61 MPa. Otherwise, putting constraints by the second criteria, the minimum laser power is always to be set at 9.62–9.87 W, then the welding speed reaches to its maximum value at 18.48–19.00 mm/s when the stand-off distance and clamp pressure are set around the 32.09–32.19 mm and 3.29–3.30 MPa, respectively. Using the second criterion, the minimum weld width achieved is 2.28 mm and the maximum attainable weld strength is 63.47 N/mm, as can be seen in Table 9. For both the criteria, the parameter combinations with highest desirability values are selected as the best laser transmission welding conditions, accordingly. Graphical optimization results into overlay contours plots, which allow quick visual inspection of the area of feasible response values in the factor space to choose the optimum welding parameter combination. The bright areas on the overlay
Table 8 Optimal welding condition based on the first criterion. Sol. No.
P (W)
S (mm/s)
F (mm)
C (MPa)
Weld strength (N/mm)
Weld width (mm)
Desirability
1 2 3 4 5
19.89 19.26 19.36 18.28 17.85
8.17 6.18 8.91 8.18 7.81
44.34 43.45 46.43 44.86 42.35
1.05 0.95 1.14 1.04 1.01
88.89 87.94 85.40 83.77 80.86
5.10 5.24 5.12 5.06 4.90
1.000 selected 1.000 1.000 1.000 1.000
Table 9 Optimal welding condition based on the second criterion. Sol. No.
P (W)
S (mm/s)
F (mm)
C (MPa)
Weld strength (N/mm)
Weld width (mm)
Desirability
1 2 3 4 5
9.87 9.69 9.76 9.78 9.62
18.98 18.48 19.00 19.00 18.81
32.09 32.09 32.14 32.10 32.19
3.30 3.30 3.30 3.29 3.30
63.47 63.50 63.45 63.37 63.76
2.28 2.29 2.29 2.28 2.31
0.914 Selected 0.914 0.914 0.913 0.913
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of verification tests. A fair agreement between the predicted and experimental results is observed.
Overlay Plot
10.00
7. Conclusion
Welding speed
9.00
The following conclusions can be drawn from the experimental investigation carried out within the factor range considered in this study and for the specified materials combinations:
Weld width: 5.08
8.00 Weld width: 5.15
7.00
Weld strength: 87 Weld strength: 89
6.00 16.00
17.00
18.00 Power
19.00
20.00
12.00
13.00
Overlay Plot
20.00 Weld width: 2.28
Weld width: 2.32
Welding speed
19.00
18.00
17.00
Weld strength: 63.4 Weld strength: 63.7
16.00 9.00
10.00
11.00 Power
Fig. 14. Overlay plot shows the region of the optimal working condition (a) based on the first criterion at stand-off distance¼ 44.34 mm and clamp pressure¼ 1.05 MPa, and (b) based on the second criterion at stand-off distance¼32.09 mm and clamp pressure¼ 3.30 MPa.
1. The developed response surface models can predict the responses adequately within the limits of welding parameters being used, 2. Laser power, welding speed and stand-off distance have a strong interaction effect on weld strength and weld width. These parameters control the heat input to the weld zone and thus the quality of the weld, 3. The weld strength is limited by very high heat input, which causes overheating and partial decomposition of the material. A very low heat input, on the other hand results in lack of fusion. 4. It can be observed from the ANOVA tables that the stand-off distance has the maximum effect on weld strength, followed by laser power and welding speed. Clamp pressure has statistically insignificant effect on the weld strength. 5. According to the results of ANOVA, stand-off distance is the most important factor affecting the weld width, and it is followed by welding speed, laser power, and clamp pressure. 6. The optimal welding condition can be determined effectively using the numerical optimization technique, which results in a set of pareto-optimal solution according to the desired optimization criteria. 7. Graphical optimization results into overlay contours plots, which allow quick visual inspection of the area of feasible response values in the factor space to choose the optimum welding parameter combination.
Appendix A. Supporting materials Supplementary data associated with this article can be found in the online version at doi:10.1016/j.optlastec.2011.12.029.
Table 10 Results of verification experiments (according to first criterion). Results
Predicted
Experimental
9Error (%)9
Weld strength (N/mm) Weld width (mm)
88.89 5.10
83.46 5.23
6.12 2.51
References
Table 11 Results of verification experiments (according to second criterion). Results
Predicted
Experimental
9Error (%)9
Weld strength (N/mm) Weld width (mm)
63.47 2.28
60.43 2.33
4.79 2.19
plots in Fig. 14 (a) and (b) are the regions that meet the proposed criteria. 6.4. Verification tests Finally, for each criterion, three additional experiments are conducted at the optimal parameters setting and average of those three is used for verification. Tables 10 and 11 present the results
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