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Al2O3-MMC
Optics & Laser Technology 46 (2013) 67–76
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Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Response surface method based optimization of ytterbium fiber laser parameter during machining of Al/Al2O3-MMC Arindam Ghosal, Alakesh Manna n Department of Mechanical Engineering, PEC University of Technology (Formerly: Punjab Engineering College), Chandigarh-160012, India
a r t i c l e i n f o
abstract
Article history: Received 6 February 2012 Received in revised form 8 April 2012 Accepted 21 April 2012 Available online 31 May 2012
This paper presents the investigated results on machining of Al/Al2O3-MMC by ytterbium fiber laser. The effects of the different parameters on the response characteristics are explained. A comprehensive mathematical models for correlating the interactive and higher-order influences of various machining parameters such as laser power, modulation frequency, gas pressure, wait time, pulse width on the machining performance criteria e.g., metal removal rate and tapering phenomena has been developed for achieving controlled over fiber laser machining process. The response surface methodology (RSM) is employed to achieve optimum responses i.e., minimum tapering and maximum material removal rate. The parameters wait time and modulation frequency are identified as the most significant and significant parameters for MRR. Modulation frequency range from 600 to 680 Hz taper is minimum. The optimal parametric combination for maximized MRR and minimized taper is identified as 473.12 W laser power, 604.54 Hz modulation frequency, 0.18 s wait time, 19.82 bar assist gas pressure and 93.47% of duty cycle pulse width and finally confirmation tests are conducted to validate the developed models. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Ytterbium fiber laser machining RSM Metal removal rate
1. Introduction With the rapid technological acceptance of Al/Al2O3-MMC in industrial applications, the machining of Al/Al2O3-MMC has been very important for manufacturing engineers and applied researchers working in this field. Al/Al2O3-MMC is gaining increasing industrial acceptance in the aerospace, aircraft, automobile etc. industries. Various non traditional machining processes such as AWJM, ECM, EDM, WEDM, AFF etc. have shown their scope of applications towards the machining of Al/Al2O3MMC but these processes have also their own limitations and still remain machining problems like low material removal rate, high surface roughness and poor dimensional accuracy, etc. Manufacturing of miniature and micro dimensional part of Al/Al2O3-MMC with satisfactory tolerance by any well known machining processes is still very difficult as usually this class of MMC is fabricated by casting process. Hence, a research investigation is needed for searching out a suitable non-conventional machining process for proper machining of Al–Al2O3-MMC. In nontraditional machining processes, laser machining has tremendous potential on account of the versatility of its applications and it is
n
Corresponding author. Tel.: þ91 172 275 3553; fax: þ 91 172 274 5175. E-mail addresses: [email protected], [email protected] (A. Manna). 0030-3992/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.optlastec.2012.04.030
expected that it will be successfully and commercially utilized in modern industries. The better quality of product can be produced by laser beam machining (LBM) through proper optimization and combinational control of various process parameters. Laser machining is a thermal process, the effectiveness of this process depends on thermal and optical properties of the material and hence laser machining is most suitable for materials that exhibit a high degree of brittleness, hardness and have favorable thermal properties as explained by Kacer et al. [1]. Otherwise, the laser machining is suitable for all materials. The basic material removal mechanism in laser drilling is based on the absorption of laser energy from a series of laser pulses at the same spot; material is melted and ejected to the form of hole [2–4]. Tsai and Chen [5] proposed an explanation for why the focused Nd:YAG laser is used to scribe a groove-crack on the surface of substrate and the defocused CO2 laser is used to introduce thermal stress. An excimer laser was used to study the basic mechanism roughening the surface of silicon carbide by Tonshoff and Kappel [6]. Tsai and Li [7] stated that the under water laser drilling quality of LCD glass and alumina substrates is much better than that from laser drilling in air. A three dimensional thermal model was developed for a laser assisted machining process and validated the developed model by comparing predicted surface temperature histories with measurements made using a focused laser pyrometer by Rozzi et al. [8]. A localized thermal shock is produced due to the incidence of the cold cutting
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gas-jet during laser cutting and this caused the formation of cracks whose advance was limited by the cooling of melted material which experienced visco-plastic fluency [9]. Samant and Dahotre [10] studied during Nd:YAG laser machining of MgO and concluded that the multiple reflections and energy losses associated with MgO dissociation affected the total amount of laser energy absorbed. They also stated that the evaporation of ceramic was responsible for material removal and vapour pressure ensured the formation of a clean cavity. Li et al. [11] studied for identifying the optimal laser parameter for cutting quad flat no-lead (QFN) packages by using a diode pumped solid state laser system and concluded that the best cutting quality can be achieved with optimal parameters 2 kHz frequency, 2 mm/s cutting speed, and 29 A driving current. The non uniform melts and ejection of material from the groove walls and laser power reduction as the beam propagated to the groove can be identified as causes for variation in taper angle formation and depth deviation [12,13]. The structural modifications was observed on the cut surface produced with CO2 laser cutting of commercial tiles of calcitic marble and limestone as stated by Miranda [14]. Response surface methodology (RSM) is a collection of mathematical and statistical techniques that can be applied for the modeling and analysis of problems in which a response of interest is influenced by several variables and the objective is to optimize this response [15]. Laser beam machining can be applied to a wide range of materials such as metals and non metals, soft and difficult to machine materials, and response surface methodology (RSM) is the best method for parameters optimization with reduced number of experiments without affecting the accuracy of results but qualitative variables can not be optimized [16]. Design expert software was used for optimizing the weld bead parameter by Benyounis et al. [17] and based on RSM, authors identified the optimum process parameter for maximize penetration and minimize heat input, width of heat affected zone in weldment. The RSM was used based on Box Behnkey design to optimize the CW 1.5 kW CO2 laser parameters and to develop mathematical models for penetration, welded zone width, heat affected zone for weldment by Benyounis et al. [18]. Laser cutting is a multi-input and multi-output process that needs to be judged carefully in order to get the most desirable yield. RSM is a set of mathematical and statistical techniques that are useful for modeling and predicting the response of interest to several input variables with the aim of optimizing laser cutting response [19]. The width of laser cut or kerf, quality of the cut edges and the operating cost are affected by the laser power, cutting speed, assist gas pressure, nozzle diameter and focus point position as well as the workpiece material as stated by Eltawahni et al. [20]. The application of design of experiment, evolutionary algorithms and computational network can be used to develop a mathematical relationship between the welding process input parameters and the output variables of the weld joint in order to determine the welding input parameters that lead to the desired weld quality [21]. The main objective of the paper is to develop the comprehensive statistical models for correlating the interactive and higher order influences of the various machining parameters, such as the laser power, modulation frequency, gas pressure, wait time, pulse width on the most dominant machining criteria i.e., metal removal rate and tapering phenomena for achieving controlled laser beam machining (LBM). Utilizing the experimentally obtained results, the interactive and higher order influences of the various machining
parameters are investigated during laser machining of Al/Al2O3MMC through response surface methodology. The adequacy of the developed statistical models has also been tested by the analysis of variance test. The LBM parameters are optimized for achieving an enhanced production rate with improved profile accuracy.
2. Experimental planning An ytterbium laser machine YLR 1000 with CNC system RP 3015 was used for experiments. The experimental scheme has been designed in such a way as to explore the influence of the various predominant laser machining process parameters, based on response surface methodology to obtain the optimal scheme for multi-variable experimentation and to perform investigations for exploring the interactive and higher order effects of the various parameters on the most important machining characteristics. Table 1 represents the chemical composition of stir cast Al/Al2O3-MMC sample used for experiments. Table 2 represents the physical and mechanical properties of Al/Al2O3-MMC used for experimental investigations. Fig. 1 shows ytterbium laser drilling setup used for drilling of Al/Al2O3-MMC work-piece. Table 3 represents the different parameters such as laser power, modulation frequency, gas pressure, wait time, pulse width and their levels considered for experimental investigation. The range of input variables and their initial setting values are coded for simplification of experimental data analysis. Based on some trail experiments the coded levels of different input variables are decided (Table 3). The central point i.e., the 0-level is chosen as the approximate point of optimality. Then a range of points is selected within the vicinity of the central point. For the ease simplification of the input parameters the standard relation [15] is used to determine the coded parametric values as Xk ¼
N k N0 N 1 N 0
ð1Þ
where, Nk ¼actual parametric value corresponding to the level interest i.e., natural variable for k-level, N1 ¼actual value of the parameter corresponding to the level 1 i.e., natural variable for 1-level. N0 ¼actual value corresponding to the 0 level i.e., natural variable for 0-level. The specific numbers of experiments have been carried out for different combinational values of process variables based on central composite design. The material removal rate and tapering phenomenon considered as output machining criteria. The machining is carried out for a fixed time interval. Sartorious Master Series Electronic Balance of least count 0.001 g was used to weight the work-pieces before and after each run. The material removal is determined from the difference in weight of the work-piece before and after machining. The top and bottom diameter of each micro and macro hole were measure by Olympus STM6 an optical measuring microscope of magnification 10 . The taper per unit length of the machined Table 2 Properties of Al/Al2O3-MMC used for experiment. Properties
Density (g/cc)
Material: Al/10 wt% Al2O3-MMC 2.8
Ultimate tensil Brinell e strength (MPa) hardness (BHN) 84
97
Table 1 Composition of Al/Al2O3-MMC used for experiment. Types of MMC
Types of reinforced particles
Al2O3 (wt%)
Si (wt%)
Mg (wt%)
Fe (wt%)
Cu (wt%)
Mn (wt%)
Zn (wt%)
Ti (wt%)
Al
Discontinuous MMC
Al2O3, APS: 300 mesh(50.8 mm)
10.00
7.01
0.31
0.12
0.015
0.13
0.10
0.08
Remaining
A. Ghosal, A. Manna / Optics & Laser Technology 46 (2013) 67–76
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Fig. 1. Ytterbium laser drilling is done on Al-Al2O3 MMC.
Table 3 Machining parameters, actual setting values and their coded levels. Sr. No.
1 2 3 4 5
Machining parameters
Laser power (W) Modulation frequency(Hz) Gas pressure (bar) Wait time (s) Pulse width (%)
Symbol
x1 x2 x3 x4 x5
Units
Watt Hz bar s %
Level 2
1
0
1
2
400 600 15 0.1 75
500 700 16 0.15 80
700 800 17 0.2 90
900 900 18 0.25 95
1000 1000 20 0.3 100
hole was determined by utilizing the relation as given below. ðMeasured diameter at entrance of holeÞ2ðMeasured diameter at exit of holeÞ 2ðThickness of the work-pieceÞ ðDdÞ Taper ¼ 2t Taper ¼
where, D¼Measured diameter at top of the machined hole, mm; d¼Measured diameter at bottom of the machined hole, mm; t¼Thickness of the work-piece, mm. ðDdÞ p : : ð3Þ Taper, radian ¼ Tan1 2:t 180 A well-designed experimental plan can substantially reduce the total number of experiments. In the present set of analysis, the laser power (x1), modulation frequency (x2), gas pressure (x3), wait time (x4) and pulse width (x5) are considered as the controllable variables and their effects on material removal rate (MRR) and tapering phenomena are investigated through a set of planned experiments. Here, the central composite second-order rotatable design [15] consists of a 2k factorial, where number of variables, k¼5, with nf runs in factorial block, 2k axial or star runs and nc center runs is used and the experimental size is reduced by using half replication of 2k factorial design. With half replication, a becomes 2(k 1)/4. Hence a ¼2(5 1)/4 ¼21 ¼2.000 and according to this central composite second-order rotatable design, the total number of points in the design is 33; 6 observations for center in factorial block and 1 observation for centre in axial block are repeated. Hence, total 31 runs have been conducted for experimental investigation.
3. Mathematical modeling and process optimization Response surface methodology is utilized to determine the relationship between various process parameters and machining characteristics e.g., material removal rate and taper angle. A second-order response surface model is used to evaluate the parametric effects on material removal rate and taper angle. A
ð2Þ
second order response surface model can be written as y ¼ bo þ
k X i¼1
bi xi þ
k X i¼1
bii x2i þ
XX
bij xi xj þ e
ð4Þ
ioj
The terms bo ,bi are the second order regression coefficients and bii , bij represent the pure second order or quadratic effects. xi, xj represent the interactive terms which deal the interactive effects of the process parameters, k represents the number of machining parameters i.e., variables considered for the research investigation, y represents the corresponding response of the machining characteristics, ‘e’ is an error term. An experimental plan for studying the relationship between the controllable parameters and the various machining criteria has been made based on central composite second-order rotatable design is shown in Table 4. Table 4 also represents the experimentally obtained results for response 1 and response 2, i.e., MRR and hole taper, respectively. 3.1. Mathematical models for MRR and taper Considering 5 variables (Table 3) and utilizing the experimental results from 63 experiments (i.e., 31 experiments 3-replication of each experiment), and according to Eq. (4) the mathematical models for MRR and taper angle are developed. The developed mathematical model based on RSM for correlating the MRR with various predominant laser machining process parameters as considered in the experimental design as follows, Y MRR ¼ 0:253080:01099x1 0:03074x2 þ 0:01069x3 0:03347x4 0:00509x5 þ 0:05411x1 x2 0:0214x1 x3 þ 0:00423x1 x4 þ 0:06398x1 x5
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0:11923x2 x3 þ 0:03647x2 x4 þ0:00161x2 x5
Similarly, the developed mathematical model for taper is
0:04898x3 x4 0:05825x3 x5 0:00352x4 x5 0:0056x1 2 0:01269x2 2 0:01462x3 2 þ 0:00116x4 2 0:0044x5 2 ,
ð5Þ
Y Taper ¼ 0:00449þ 0:00039x1 þ 0:00064x2 0:000337x3 0:000102x4 þ 0:00027x5 0:000857x1 x2 þ0:00119x1 x3 0:000686x1 x4 þ 0:0000095x1 x5 þ 0:001486x2 x3 0:000943x2 x4 0:000219x2 x5 0:000287x3 x4 þ 0:001003x3 x5
Table 4 Plan for CCD; different controlling parameters and results.
0:00071x4 x5 0:000289x1 2 0:000283x2 2 0:000475x3 2 0:000133x4 2 þ 0:000059x5 2 ,
Run
x1
x2
x3
x4
x5
MRR, g/s (Response 1)
Taper, radian (Response 2)
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 31
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 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 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 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 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0
0.2404 0.1701 0.2357 0.3184 0.3126 0.2988 0.2272 0.2272 0.2299 0.2346 0.2316 0.2346 0.2312 0.2356 0.2351 0.2332 0.2334 0.2363 0.2321 0.2330 0.2344 0.2325 0.2604 0.2324 0.2372 0.2381 0.2399 0.2391 0.2416 0.2761 0.2824
0.0040 0.0043 0.0049 0.0040 0.0030 0.0050 0.0046 0.0048 0.0052 0.0042 0.0043 0.0038 0.0036 0.0042 0.0044 0.0042 0.0040 0.0048 0.0042 0.0045 0.0040 0.0041 0.0047 0.0043 0.0045 0.0049 0.0046 0.0047 0.0047 0.0044 0.0043
ð6Þ
3.2. Analysis of variance and model fitment test The analysis of variance (ANOVA) test has been performed to test the adequacy of the developed models for establishing the mathematical link between the response and the machining parameters of laser machining process. The ANOVA test module has been designed to estimate the sum of squares of the response into the contribution due to the second order and a lack of fit component which measures the deviations of the responses from the fitted surface as well as a measure of the experimental errors. Table 5 represents the ANOVA for MRR. From Table 5, it is clear that the ytterbium fiber laser parameters such as wait time and modulation frequency are the most significant and significant parameters, respectively for MRR. The interaction between ‘laser power and pulse width’; and ‘modulation frequency and N2 gas pressure’ are the most significant and significant interaction, respectively for MRR. Similarly, laser power and modulation frequency are the most significant and significant parameters with 8.86714 and 7.25794 F-test value, respectively for taper. However, N2-gas pressure also shows its significance for taper with F-test value 3.93472 at 95% confidence level. The interaction between ‘laser power and N2 gas pressure’ and ‘modulation frequency and N2 gas pressure’ are the most significant and significant interaction, respectively for taper. From Table 6, it is concluded that the laser power, modulation frequency, gas pressure, wait time, pulse width are significantly influencing for controlling MRR and taper as the P-value for both
Table 5 ANOVA for MRR. Sum of Source Model A: Laser power B: Modulation frequency C: Assist gas pressure (N2) D: wait time E: pulse width AB AC AD AE BC BD BE CD CE DE A2 B2 C2 D2 E2 Residual Lack of Fit Pure Error Total
Squares 0.02064 0.00048 0.00115 0.00027 0.00280 3.7819E-05 0.00302 0.00040 1.9585E-05 0.00498 0.00355 0.00077 1.7835E-06 0.00119 0.00107 8.4296E-06 7.3588E-05 0.00028 0.00037 2.3677E-06 3.4497E-05 0.00339 0.00153 0.00185 0.02403
df 20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10 6 4 30
Mean
F
p-value
Square 0.00103 0.00048 0.00115 0.00027 0.00280 3.7819E-05 0.00302 0.00040 1.9585E-05 0.00498 0.00355 0.00077 1.7835E-06 0.00119 0.00107 8.4296E-06 7.3588E-05 0.00028 0.00037 2.3677E-06 3.4497E-05 0.00033 0.00025 0.00046 –
Value 3.04239 1.42406 3.40837 0.80712 8.25490 0.11147 8.90321 1.19074 0.05772 14.69615 10.46528 2.27589 0.00525 3.50805 3.16479 0.02484 0.21690 0.83417 1.11228 0.00697 0.10168 – 0.55195 – –
Prob 4F 0.03710 0.26030 0.09460 0.39011 0.01660 0.74541 0.01371 0.30081 0.81500 0.00331 0.00891 0.16231 0.94361 0.09060 0.10560 0.87791 0.65141 0.38261 0.31641 0.93511 0.75640 – 0.75460 – –
– Significant – – – – – – – – – – – – – – – – – – – – – Not significant –
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Table 6 Results of analysis of variance for MRR and Taper. Source of variation
Second-order terms Lack of fit Experimental errors Total
d.o.f.
20 6 4 30
Sum of squares
Mean square
D 0.28
MRR
B 0.26
E
Taper (Eq. (6))
MRR (Eq. (5))
Taper (Eq. (6))
MRR (Eq. (5))
Taper (Eq. (6))
MRR (Eq. (5))
Taper (Eq. (6))
0.02064 0.00154 0.00186 0.02404
5.3429E 06 5.5855E 07 0.0132E 05 6.0335E 06
1.032E 03 0.000256 0.4650E 03 –
2.6715E 07 9.3093E 08 0.0033E 05 –
3.0424 – – –
3.8686 – – –
0.0371 – – –
0.0161 – –
Design-Expert® Software Factor Coding: Actual MRR Actual Factors A: Laser power = 700.00 B: Modulation frequency = 800.00 C: Assist gas pressure(Nitrogengen) = 17.50 D: wait time = 0.20 E: pulse width = 87.50
A C E A
0.24 C
D
0.22
B 0.2 -1.000
P-value
MRR (Eq. (5))
Perturbation 0.3
F-value
-0.500 0.000 0.500 1.000 Deviation from Reference Point (Coded Units)
Fig. 2. Perturbation plot shows the effect of ytterbium fiber laser process parameters on MRR.
the responses are less than 0.05. The F-test values for both the responses at 95% confidence level are 3.0424 and 3.8686, respectively. The R2 value for both the responses i.e., MRR and taper are 0.86 and 0.88, respectively. The value of R2(adj) for MRR and taper are 0.61 and 0.66, respectively. These values are above the average value and developed second order models fits the data, therefore, the data for both the response are well fitted in the developed second order models.
4. Parametric analysis on machining characteristics of ytterbium fiber laser The influences of the various process parameters of ytterbium fiber laser on both the responses i.e., MRR and taper during laser machining of 5 mm thick Al/10 wt% Al2O3-MMC have been analyzed based on the developed mathematical models established utilizing response surface methodology (RSM). 4.1. Parametric influences on MRR The perturbation plot for the MRR is shown in Fig. 2. The effect of different parameters of ytterbium fiber laser can compare with respect to a particular point in a design space. This particular point is known as centre point. The lines represent by the different factors A (laser power), B (modulation frequency), C (N2 gas pressure), D (wait time) and E (pulse width) represent their individual behaviors on MRR keeping other parameters constant. From Fig. 2, it is clear that the MRR increases with increase in N2 gas pressure, which agrees with [20]. Similarly, MRR decreases with increase in wait time and modulation frequency. The parameters laser power and pulse width both
has a small effect on MRR, on increase of both the parameters up to certain limit i.e., 400 to 500 W laser power and 75 to 80% pulse width MRR slightly decreases. Fig. 3 shows the combined effects of wait time and modulation frequency on MRR. The parameters laser power, N2 gas pressure and pulse width are hold at 700 W, 17.50 bar and 87.5% of duty cycle, respectively. From Fig. 3, it is clear that the MRR is high at low modulation frequency and low wait time. MRR increases with decrease of wait time and maximum MRR observed with in the range of 0.15 to 0.10 s. MRR also increases with decrease in modulation frequency. It is observe that the best range of modulation frequency is 680 to 600 Hz for optimal MRR. The experimental results revels that comparatively low modulation frequency and low wait time are found to be favorable for higher MRR because of higher cutting speed. It is also due to the less wait time causes less heat losses from the drilling spot as a results material removal rate increase by quick vaporization of the work-piece material. The combined effects of pulse width and laser power on MRR have been shown in Fig. 4. The response surface plot Fig. 4 reflects that the pulse width has a moderate effect on MRR. At constant parametric setting e.g., 800 Hz modulation frequency, 17.5 bar H2 gas pressure, 0.20 s wait time with low pulse width range from 75 to 80% of duty cycle and laser power range 400 to 475 W the MRR is high as compared with moderate pulse width and laser power setting. The combined effects of assisted gas pressure and modulation frequency on MRR have been shown in Fig. 5. The response surface plot Fig. 5 reflects that the assisted gas pressure and modulation frequency both have moderate effect on MRR. At high assisted gas pressure and low modulation frequency i.e., ranges towards from 18 to 20 bar and 680 to 600 Hz, respectively with constant 700 W laser power, 0.20 s wait time, 87.5% of duty cycle pulse width the MRR is high as compared to the parameters setting at low assisted gas pressure with high modulation frequency.
4.2. Parametric influences on taper The minimization of laser hole deviation is highly needed for maintaining quality and accuracy of hole. The combined effect of different parameters of Yitterbium fiber laser on hole taper has been analyzed through different graphs. The combined effects of modulation frequency and laser power on taper have been shown in Fig. 6. The response surface plot Fig. 6 reflects that the modulation frequency and laser power both have great effect on taper. At high modulation frequency and laser power the taper is high as compared with low modulation frequency and laser power. Minimum taper observed at laser power range in between 400 and 475 W. Taper also increase with increase on modulation frequency and minimum taper is obtained at low modulation frequency i.e., range between 600 and 680 Hz with other parameters remain hold as 17.5 bar assisted gas pressure, 0.20 s wait time, 87.5% of duty cycle pulse width. The optimal MRR and taper is obtained within the range of laser power 700 W and modulation frequency 680 Hz.
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Design-Expert® Software Factor Coding: Actual MRR 0.31844 0.169876 X1 = B: Modulation frequency X2 = D: wait time Actual Factors A: Laser power = 700.00 C: Assist gas pressure(Nitrogengen) = 17.50 E: pulse width = 87.50 0.6 0.5
MRR
0.4 0.3 0.2 0.1 0 -0.1
0.30 0.25 0.20 D: wa it ti me
0.15
1000.00 920.00 840.00 y enc 760.00 equ r f 680.00 on lati odu 0.10 600.00 M B:
Fig. 3. Response surface plot of MRR with wait time and modulation frequency.
Design-Expert® Software Factor Coding: Actual MRR 0.31844 0.169876 X1 = A: Laser power X2 = E: pulse width Actual Factors B: Modulation frequency = 800.00 C: Assist gas pressure(Nitrogengen) = 17.50 D: wait time = 0.20 0.6 0.5
MRR
0.4 0.3 0.2 0.1 0 -0.1
100.00
1000 .00 92 850. 5.00 0 0 7 7 90.00 700.0 5.00 E: 0 r 85.00 6 pu we 550. 25.00 lse 80.00 po 00 r 475. wid se 75.00 400.00 00 th La A:
95.00
Fig. 4. Response surface plot of MRR with pulse width and laser power.
The combined effects of assisted gas pressure and laser power on taper have been shown in Fig. 7. The response surface plot Fig. 7 reflects that the assisted gas pressure and laser power both
have significant effect on taper. At high assisted gas pressure with low laser power the taper is low as compared with low assisted gas pressure and laser power. The experimental results revels that
A. Ghosal, A. Manna / Optics & Laser Technology 46 (2013) 67–76
Design-Expert® Software Factor Coding: Actual MRR 0.31844 0.169876 X1 = B: Modulation frequency X2 = C: Assist gas pressure(Nitrogengen) Actual Factors A: Laser power = 700.00 D: wait time = 0.20 E: pulse width = 87.50
0.6 0.5 0.4 MRR
0.3 0.2 0.1 0 -0.1
20.00
1000.00 19.00 920.00 18.00 ssis 840.00 y t ga enc 17.00 s pr 760.00 equ ess r f 16.00 ure 680.00 n (Nit atio rog dul eng 15.00 600.00 o M en) B:
C: A
Fig. 5. Response surface plot of MRR with assisted gas pressure and modulation frequency.
Design-Expert® Software Factor Coding: Actual taper 0.0052 0.003 X1 = A: Laser power X2 = B: Modulation frequency Actual Factors C: Assist gas pressure(Nitrogengen) = 17.50 D: wait time = 0.20 E: pulse width = 87.50 0.008 0.006
taper
0.004 0.002 0 -0.002
1000.00 1 92 000 920.00 .00 5. 8 50 0 7 B: M 840.00 70 75.0 .00 0 odu 0 0 62 latio 760.00 5. .00 5 n fr er 475 50.00 00 equ 680.00 pow enc r 600.00 400.0 .00 e 0 y Las A: Fig. 6. Response surface plot of taper with modulation frequency and laser power.
73
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A. Ghosal, A. Manna / Optics & Laser Technology 46 (2013) 67–76
Design-Expert® Software Factor Coding: Actual taper 0.0052 0.003 X1 = A: Laser power X2 = C: Assist gas pressure(Nitrogengen) Actual Factors B: Modulation frequency = 800.00 D: wait time = 0.20 E: pulse width = 87.50 0.008 0.006
taper
0.004 0.002 0 -0.002
92
00
00
0.
5.
85
10 20.00 00 C: A 19.00 .0 77 ssis 0 18.00 t ga 5. 7 00 62 00. sp 17.00 res 5 5.0 00 16.00 sur er 47 50. 0 e(N ow 15.00 400 5.00 00 itro rp e gen .00 s La gen A: ) Fig. 7. Response surface plot of taper with assisted gas pressure and laser power.
Design-Expert® Software Factor Coding: Actual taper 0.0052 0.003 X1 = B: Modulation frequency X2 = C: Assist gas pressure(Nitrogengen) Actual Factors A: Laser power = 700.00 D: wait time = 0.20 E: pulse width = 87.50 taper
20.00 C: Assist gas pressure(Nitrogengen)
0.002
19.00
0.003 0.005 0.004
18.00 Fig. 9. SEM of a drilled hole shows the laser entry surface.
17.00
16.00 0.004
15.00 600.00
680.00
760.00 840.00 920.00 B: Modulation frequency
1000.00
Fig. 8. Effect graphs of assist gas pressure and modulation frequency on taper.
comparatively low gas pressure and high laser power are found to be favorable for lower taper because the higher assisted gas pressure cools the localized heating zone causing slower rate of
material removal by penetrate up to the whole thickness of the work piece. During experiments it is also observed that the required drilling time is more when through hole drilling was done at high H2 gas pressure with low laser power. In this case laser beam energy strike for a longer period causing material removal from large area of the top surface of drilled hole, resulting an increase in taper with increase of assist gas pressure. From the graph, it is clear that the range of N2 gas pressure from 18 to 20 bar and 400 to 550 W laser power the hole taper can be minimized. The combined effects of assist gas pressure and modulation frequency on taper have been shown in Fig. 8. The effect graphs Fig. 8 reflects that the assisted gas pressure and modulation
A. Ghosal, A. Manna / Optics & Laser Technology 46 (2013) 67–76
75
Table 7 Optimal values of process parameters for maximized MRR and minimized Taper. Experimental validity search on MRR
Experimental validity search on taper
Process parameters
Actual values of parametric combination
Value obtained from Eq. (2)
Value obtained from experi-ment
Error
Actual values of parametric combination
Value obtained from Eq. (3)
Value obtained from experi-ment
Error
Laser power (W) Modulation frequency (Hz) Gas pressure (bar) Wait time (s) Pulse width (%)
473.12 604.54
0.40965
0.39162
0.01803
473.12 604.54
0.00012
0.00083
0.00071
19.82
19.82
0.18 93.47
0.18 93.47
frequency both have moderate effect on taper. From Fig. 8 it is clear that the taper is minimum at range between 18 and 20 bar Nitrogen gas pressure. Modulation frequency in between 920 and 1000 Hz taper is minimum. At very low modulation frequency the beam energy is slightly high but time between two successive beams is more, therefore material has been removed only from the narrow focusing spot on the top surface of work piece. At high assist gas pressure a very narrow localized heating has been occurred as a result low taper hole is generated. Again, at high modulation frequency with high gas pressure, beam energy is less but the time between two successive incident beams is very small, therefore the top surface gets heated rapidly and generated larger taper of micro hole. Hence for low taper, recommended combination is 700 W laser power, 0.20 s wait time, 87.5% of duty cycle pulse width with high assist gas pressure range from 18 to 20 bar and low modulation frequency range from 600 to 680 Hz. Fig. 9 shows the scanning electron microscopy photograph of a drilled hole having 822.857 mm minimum opening and 828.650 mm maximum opening when leaser machining was performed with parametric combination 700 W laser power, 600 Hz modulation frequency, 19 bar gas pressure, 0.20 s wait time and 87.5% of duty cycle pulse width. Here, average deviation at entrance is 0.70% on diameter of a drilled hole of 5 mm thick work piece.
6. Conclusions The ytterbium fiber laser has a capability to perform successful quality hole generation on Al/Al2O3-MMC. The ytterbium fiber laser process parameter can be possibly controlled for effective drilling of Al/Al2O3-MMC. Based on the investigation during machining of Al/Al2O3-MMC by ytterbium fiber laser and developed mathematical models the following outcome can be concluded as listed below: (i) The material removal rate increases with increase of N2 gas pressure and maximum material removal rate observed with in the range of 400 to 475 W laser power. (ii) The developed mathematical models for material removal rate and taper are successfully proposed for effective machining of Al/Al2O3-MMC. These developed models can help directly for evaluation of material removal rate and taper angle under various parametric setting during ytterbium fiber laser machining of Al/Al2O3-MMC. (iii) The minimum taper angle on machined hole is observed at parametric setting range from 18 to 20 bar gas (nitrogen) pressure and 600 to 680 Hz modulation frequency. (iv) The optimal parametric combination for maximized MRR and minimized taper is 473.12 W laser power, 604.54 Hz modulation frequency, 19.82 bar nitrogen gas pressure, 0.18 s wait time and 93.47% pulse width.
5. Confirmation and optimality search Based on the developed second order response equations, optimality searches i.e., searching of optimal parametric setting values for maximum material removal rate and minimum taper can be obtained. This searching can help to identify the parametric combinational effects on the desired response criteria. The developed program in Design Expert Software was utilized to obtain the parametric values for maximized material removal rate and minimized taper phenomenon. The optimal parametric values are considered and different experiments are carried out for optimality test. Table 7 shows the actual values of the process parameters corresponding to the optimal parametric combination for maximum material removal rate and minimum taper during machining of Al/Al2O3-MMC. Table 7 also shows the experimentally obtained values for MRR and taper phenomenon as well as calculated values from the developed mathematical models with estimated error. The estimated error for MRR is only 0.01803. This error is projected based on the experimentally obtained MRR and the MRR from the developed mathematical model, Eq. (2). Similarly, estimated error for taper based on experimental value over developed mathematical model (Eq. (3)) is only 0.00071. From Table 7, it is clear that the optimal parametric combinations of process parameters are satisfied and bear a good agreement with the experimental results.
References [1] Kacer K, Muthe M, AKman E, Demir A, Candan L, Canel T, Gunay V, Sinmazcelek T. Characterization of drilling alumina ceramic using Nd:YAG pulsed laser. Journal of Materials Processing Technology 2009;209(4): 2008–14. [2] Meijer J. Laser beam machining state of the art and new opportunities. Journal of Materials Processing Technology 2004;149:2–17. [3] Tiwari G, Sarin Sundar JK, Sundarajan G, Joshi SV. Influence of process parameters during pulsed Nd:YAG laser cutting of nickel-base superalloys. Journal of Materials Processing Technology 2005;170:229–39. [4] Biswas R, Kuar AS, Sarkar S, Mitra S. A parametric study of pulsed Nd:YAG laser micro-drilling of gamma-titanium aluminide. Optics and Laser Technology 2010;42:23–31. [5] Tsai Chwan Huei, Hong-Wen Chen. Laser cutting of thick ceramic substrates by controlled technique. Journal of Materials Processing Technology 2003;136:166–73. [6] Tonshoff HK, Kappel H. Surface modification of ceramics by laser machining. Annals of CIRP 1998;47(1):471–4. [7] Tsai Chwan Huei, Li Chang-Cheng. Investigation of underwater laser drilling for brittle substrate. Journal of Materials Processing Technology 2009;209: 2838–46. [8] Rozzi Jay C, Pfefferkorn Frank E, Incropera Frank P, Shin Yung C. Transient three dimensional heat transfer model for laser assisted machining of silicon Nitride: I. Comparison of prediction with measured surface temperature historic. International Journal of Heat and Mass Transfer 2000;41:1409–24. [9] Pascual-Cosp J, Ramirezdel Valle AJ, Garcia-Fortea J, Sanchez-Soto PJ. Laser cutting of high vitrified ceramic materials: development of a method using a
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Nd:YAG laser to avoid catastrophic breakdown;. Materials Letters 2002;55: 274–80. Samant Anoop N, Dahotre Narendra B. An integrated computational approach to sngle dimensional laser machining of magnesia. Optics and Lasers in Engineering 2009;47:570–7. Li Chen-Hao, Tsai Meng-Jong, Yang Ciann-Dong. Study of optical laser parameters for cutting QFN packages by Taguchi’s matrix method. Optics and Laser Technology 2007;39:786–95. Lallemanda G. Grooving by Nd:YAG laser treatment. Journal of Materials Processing Technology 2000;99:32–7. Dhupal D, Doloi B, Bhattacharyya B. Parametric analysis and optimization of Nd:YAG laser micro-grooving of aluminum titanate (Al2TiO5) ceramics. International Journal of Advanced Manufacturing Technology 2008;36: 883–93. Miranda RM. Structural analysis of heat affected zone of marble and lime stone tiles cut by CO2 laser. Materials Characterization 2004;53:411–7. Montgomery DC. Design and Analysis of Experiments. 4th ed. John Wiley and Sons; 1997.
[16] Dubey Avanishkr, Yadava Vinod. Experimental study of Nd:YAG laser beam machining: a review. Journal of Materials Processing Technology 2008;195:15–26. [17] Benyounis KY, Olabi AG, Hashm MSJ. Optimizing the laser welded butt joints of medium carbon steel using RSM. Journal of Materials Processing Technology 2005;164–165:986–9. [18] Benyounis KY, Olabi AG, Hashm MSJ. Effect of laser welding parameters on the heat input and weld bead profile. Journal of Materials Processing Technology 2005;164–165:978–85. [19] Eltawahni HA, Olabi AG, Benyounis KY. Investigating the CO2 laser cutting parameters of MDF wood composite material. Optices and Laser Technology 2011;43(3):648–59. [20] Eltawahni HA, Hagino M, Benyounis KY, Inoue T, Olabi AG. Effect of CO2 laser cutting process parameters on edge quality and operating cost of AISI316L. Optices and Laser Technology 2012;44(4):1068–82. [21] Benyounis KY, Olabi AG. Optimization of different welding processes using statistical and numerical approaches: a reference guide. Advances in Engineering Software 2008;39(6):483–96.
Contents lists available at SciVerse ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Response surface method based optimization of ytterbium fiber laser parameter during machining of Al/Al2O3-MMC Arindam Ghosal, Alakesh Manna n Department of Mechanical Engineering, PEC University of Technology (Formerly: Punjab Engineering College), Chandigarh-160012, India
a r t i c l e i n f o
abstract
Article history: Received 6 February 2012 Received in revised form 8 April 2012 Accepted 21 April 2012 Available online 31 May 2012
This paper presents the investigated results on machining of Al/Al2O3-MMC by ytterbium fiber laser. The effects of the different parameters on the response characteristics are explained. A comprehensive mathematical models for correlating the interactive and higher-order influences of various machining parameters such as laser power, modulation frequency, gas pressure, wait time, pulse width on the machining performance criteria e.g., metal removal rate and tapering phenomena has been developed for achieving controlled over fiber laser machining process. The response surface methodology (RSM) is employed to achieve optimum responses i.e., minimum tapering and maximum material removal rate. The parameters wait time and modulation frequency are identified as the most significant and significant parameters for MRR. Modulation frequency range from 600 to 680 Hz taper is minimum. The optimal parametric combination for maximized MRR and minimized taper is identified as 473.12 W laser power, 604.54 Hz modulation frequency, 0.18 s wait time, 19.82 bar assist gas pressure and 93.47% of duty cycle pulse width and finally confirmation tests are conducted to validate the developed models. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Ytterbium fiber laser machining RSM Metal removal rate
1. Introduction With the rapid technological acceptance of Al/Al2O3-MMC in industrial applications, the machining of Al/Al2O3-MMC has been very important for manufacturing engineers and applied researchers working in this field. Al/Al2O3-MMC is gaining increasing industrial acceptance in the aerospace, aircraft, automobile etc. industries. Various non traditional machining processes such as AWJM, ECM, EDM, WEDM, AFF etc. have shown their scope of applications towards the machining of Al/Al2O3MMC but these processes have also their own limitations and still remain machining problems like low material removal rate, high surface roughness and poor dimensional accuracy, etc. Manufacturing of miniature and micro dimensional part of Al/Al2O3-MMC with satisfactory tolerance by any well known machining processes is still very difficult as usually this class of MMC is fabricated by casting process. Hence, a research investigation is needed for searching out a suitable non-conventional machining process for proper machining of Al–Al2O3-MMC. In nontraditional machining processes, laser machining has tremendous potential on account of the versatility of its applications and it is
n
Corresponding author. Tel.: þ91 172 275 3553; fax: þ 91 172 274 5175. E-mail addresses: [email protected], [email protected] (A. Manna). 0030-3992/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.optlastec.2012.04.030
expected that it will be successfully and commercially utilized in modern industries. The better quality of product can be produced by laser beam machining (LBM) through proper optimization and combinational control of various process parameters. Laser machining is a thermal process, the effectiveness of this process depends on thermal and optical properties of the material and hence laser machining is most suitable for materials that exhibit a high degree of brittleness, hardness and have favorable thermal properties as explained by Kacer et al. [1]. Otherwise, the laser machining is suitable for all materials. The basic material removal mechanism in laser drilling is based on the absorption of laser energy from a series of laser pulses at the same spot; material is melted and ejected to the form of hole [2–4]. Tsai and Chen [5] proposed an explanation for why the focused Nd:YAG laser is used to scribe a groove-crack on the surface of substrate and the defocused CO2 laser is used to introduce thermal stress. An excimer laser was used to study the basic mechanism roughening the surface of silicon carbide by Tonshoff and Kappel [6]. Tsai and Li [7] stated that the under water laser drilling quality of LCD glass and alumina substrates is much better than that from laser drilling in air. A three dimensional thermal model was developed for a laser assisted machining process and validated the developed model by comparing predicted surface temperature histories with measurements made using a focused laser pyrometer by Rozzi et al. [8]. A localized thermal shock is produced due to the incidence of the cold cutting
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gas-jet during laser cutting and this caused the formation of cracks whose advance was limited by the cooling of melted material which experienced visco-plastic fluency [9]. Samant and Dahotre [10] studied during Nd:YAG laser machining of MgO and concluded that the multiple reflections and energy losses associated with MgO dissociation affected the total amount of laser energy absorbed. They also stated that the evaporation of ceramic was responsible for material removal and vapour pressure ensured the formation of a clean cavity. Li et al. [11] studied for identifying the optimal laser parameter for cutting quad flat no-lead (QFN) packages by using a diode pumped solid state laser system and concluded that the best cutting quality can be achieved with optimal parameters 2 kHz frequency, 2 mm/s cutting speed, and 29 A driving current. The non uniform melts and ejection of material from the groove walls and laser power reduction as the beam propagated to the groove can be identified as causes for variation in taper angle formation and depth deviation [12,13]. The structural modifications was observed on the cut surface produced with CO2 laser cutting of commercial tiles of calcitic marble and limestone as stated by Miranda [14]. Response surface methodology (RSM) is a collection of mathematical and statistical techniques that can be applied for the modeling and analysis of problems in which a response of interest is influenced by several variables and the objective is to optimize this response [15]. Laser beam machining can be applied to a wide range of materials such as metals and non metals, soft and difficult to machine materials, and response surface methodology (RSM) is the best method for parameters optimization with reduced number of experiments without affecting the accuracy of results but qualitative variables can not be optimized [16]. Design expert software was used for optimizing the weld bead parameter by Benyounis et al. [17] and based on RSM, authors identified the optimum process parameter for maximize penetration and minimize heat input, width of heat affected zone in weldment. The RSM was used based on Box Behnkey design to optimize the CW 1.5 kW CO2 laser parameters and to develop mathematical models for penetration, welded zone width, heat affected zone for weldment by Benyounis et al. [18]. Laser cutting is a multi-input and multi-output process that needs to be judged carefully in order to get the most desirable yield. RSM is a set of mathematical and statistical techniques that are useful for modeling and predicting the response of interest to several input variables with the aim of optimizing laser cutting response [19]. The width of laser cut or kerf, quality of the cut edges and the operating cost are affected by the laser power, cutting speed, assist gas pressure, nozzle diameter and focus point position as well as the workpiece material as stated by Eltawahni et al. [20]. The application of design of experiment, evolutionary algorithms and computational network can be used to develop a mathematical relationship between the welding process input parameters and the output variables of the weld joint in order to determine the welding input parameters that lead to the desired weld quality [21]. The main objective of the paper is to develop the comprehensive statistical models for correlating the interactive and higher order influences of the various machining parameters, such as the laser power, modulation frequency, gas pressure, wait time, pulse width on the most dominant machining criteria i.e., metal removal rate and tapering phenomena for achieving controlled laser beam machining (LBM). Utilizing the experimentally obtained results, the interactive and higher order influences of the various machining
parameters are investigated during laser machining of Al/Al2O3MMC through response surface methodology. The adequacy of the developed statistical models has also been tested by the analysis of variance test. The LBM parameters are optimized for achieving an enhanced production rate with improved profile accuracy.
2. Experimental planning An ytterbium laser machine YLR 1000 with CNC system RP 3015 was used for experiments. The experimental scheme has been designed in such a way as to explore the influence of the various predominant laser machining process parameters, based on response surface methodology to obtain the optimal scheme for multi-variable experimentation and to perform investigations for exploring the interactive and higher order effects of the various parameters on the most important machining characteristics. Table 1 represents the chemical composition of stir cast Al/Al2O3-MMC sample used for experiments. Table 2 represents the physical and mechanical properties of Al/Al2O3-MMC used for experimental investigations. Fig. 1 shows ytterbium laser drilling setup used for drilling of Al/Al2O3-MMC work-piece. Table 3 represents the different parameters such as laser power, modulation frequency, gas pressure, wait time, pulse width and their levels considered for experimental investigation. The range of input variables and their initial setting values are coded for simplification of experimental data analysis. Based on some trail experiments the coded levels of different input variables are decided (Table 3). The central point i.e., the 0-level is chosen as the approximate point of optimality. Then a range of points is selected within the vicinity of the central point. For the ease simplification of the input parameters the standard relation [15] is used to determine the coded parametric values as Xk ¼
N k N0 N 1 N 0
ð1Þ
where, Nk ¼actual parametric value corresponding to the level interest i.e., natural variable for k-level, N1 ¼actual value of the parameter corresponding to the level 1 i.e., natural variable for 1-level. N0 ¼actual value corresponding to the 0 level i.e., natural variable for 0-level. The specific numbers of experiments have been carried out for different combinational values of process variables based on central composite design. The material removal rate and tapering phenomenon considered as output machining criteria. The machining is carried out for a fixed time interval. Sartorious Master Series Electronic Balance of least count 0.001 g was used to weight the work-pieces before and after each run. The material removal is determined from the difference in weight of the work-piece before and after machining. The top and bottom diameter of each micro and macro hole were measure by Olympus STM6 an optical measuring microscope of magnification 10 . The taper per unit length of the machined Table 2 Properties of Al/Al2O3-MMC used for experiment. Properties
Density (g/cc)
Material: Al/10 wt% Al2O3-MMC 2.8
Ultimate tensil Brinell e strength (MPa) hardness (BHN) 84
97
Table 1 Composition of Al/Al2O3-MMC used for experiment. Types of MMC
Types of reinforced particles
Al2O3 (wt%)
Si (wt%)
Mg (wt%)
Fe (wt%)
Cu (wt%)
Mn (wt%)
Zn (wt%)
Ti (wt%)
Al
Discontinuous MMC
Al2O3, APS: 300 mesh(50.8 mm)
10.00
7.01
0.31
0.12
0.015
0.13
0.10
0.08
Remaining
A. Ghosal, A. Manna / Optics & Laser Technology 46 (2013) 67–76
69
Fig. 1. Ytterbium laser drilling is done on Al-Al2O3 MMC.
Table 3 Machining parameters, actual setting values and their coded levels. Sr. No.
1 2 3 4 5
Machining parameters
Laser power (W) Modulation frequency(Hz) Gas pressure (bar) Wait time (s) Pulse width (%)
Symbol
x1 x2 x3 x4 x5
Units
Watt Hz bar s %
Level 2
1
0
1
2
400 600 15 0.1 75
500 700 16 0.15 80
700 800 17 0.2 90
900 900 18 0.25 95
1000 1000 20 0.3 100
hole was determined by utilizing the relation as given below. ðMeasured diameter at entrance of holeÞ2ðMeasured diameter at exit of holeÞ 2ðThickness of the work-pieceÞ ðDdÞ Taper ¼ 2t Taper ¼
where, D¼Measured diameter at top of the machined hole, mm; d¼Measured diameter at bottom of the machined hole, mm; t¼Thickness of the work-piece, mm. ðDdÞ p : : ð3Þ Taper, radian ¼ Tan1 2:t 180 A well-designed experimental plan can substantially reduce the total number of experiments. In the present set of analysis, the laser power (x1), modulation frequency (x2), gas pressure (x3), wait time (x4) and pulse width (x5) are considered as the controllable variables and their effects on material removal rate (MRR) and tapering phenomena are investigated through a set of planned experiments. Here, the central composite second-order rotatable design [15] consists of a 2k factorial, where number of variables, k¼5, with nf runs in factorial block, 2k axial or star runs and nc center runs is used and the experimental size is reduced by using half replication of 2k factorial design. With half replication, a becomes 2(k 1)/4. Hence a ¼2(5 1)/4 ¼21 ¼2.000 and according to this central composite second-order rotatable design, the total number of points in the design is 33; 6 observations for center in factorial block and 1 observation for centre in axial block are repeated. Hence, total 31 runs have been conducted for experimental investigation.
3. Mathematical modeling and process optimization Response surface methodology is utilized to determine the relationship between various process parameters and machining characteristics e.g., material removal rate and taper angle. A second-order response surface model is used to evaluate the parametric effects on material removal rate and taper angle. A
ð2Þ
second order response surface model can be written as y ¼ bo þ
k X i¼1
bi xi þ
k X i¼1
bii x2i þ
XX
bij xi xj þ e
ð4Þ
ioj
The terms bo ,bi are the second order regression coefficients and bii , bij represent the pure second order or quadratic effects. xi, xj represent the interactive terms which deal the interactive effects of the process parameters, k represents the number of machining parameters i.e., variables considered for the research investigation, y represents the corresponding response of the machining characteristics, ‘e’ is an error term. An experimental plan for studying the relationship between the controllable parameters and the various machining criteria has been made based on central composite second-order rotatable design is shown in Table 4. Table 4 also represents the experimentally obtained results for response 1 and response 2, i.e., MRR and hole taper, respectively. 3.1. Mathematical models for MRR and taper Considering 5 variables (Table 3) and utilizing the experimental results from 63 experiments (i.e., 31 experiments 3-replication of each experiment), and according to Eq. (4) the mathematical models for MRR and taper angle are developed. The developed mathematical model based on RSM for correlating the MRR with various predominant laser machining process parameters as considered in the experimental design as follows, Y MRR ¼ 0:253080:01099x1 0:03074x2 þ 0:01069x3 0:03347x4 0:00509x5 þ 0:05411x1 x2 0:0214x1 x3 þ 0:00423x1 x4 þ 0:06398x1 x5
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A. Ghosal, A. Manna / Optics & Laser Technology 46 (2013) 67–76
0:11923x2 x3 þ 0:03647x2 x4 þ0:00161x2 x5
Similarly, the developed mathematical model for taper is
0:04898x3 x4 0:05825x3 x5 0:00352x4 x5 0:0056x1 2 0:01269x2 2 0:01462x3 2 þ 0:00116x4 2 0:0044x5 2 ,
ð5Þ
Y Taper ¼ 0:00449þ 0:00039x1 þ 0:00064x2 0:000337x3 0:000102x4 þ 0:00027x5 0:000857x1 x2 þ0:00119x1 x3 0:000686x1 x4 þ 0:0000095x1 x5 þ 0:001486x2 x3 0:000943x2 x4 0:000219x2 x5 0:000287x3 x4 þ 0:001003x3 x5
Table 4 Plan for CCD; different controlling parameters and results.
0:00071x4 x5 0:000289x1 2 0:000283x2 2 0:000475x3 2 0:000133x4 2 þ 0:000059x5 2 ,
Run
x1
x2
x3
x4
x5
MRR, g/s (Response 1)
Taper, radian (Response 2)
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 31
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 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 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 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 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0
0.2404 0.1701 0.2357 0.3184 0.3126 0.2988 0.2272 0.2272 0.2299 0.2346 0.2316 0.2346 0.2312 0.2356 0.2351 0.2332 0.2334 0.2363 0.2321 0.2330 0.2344 0.2325 0.2604 0.2324 0.2372 0.2381 0.2399 0.2391 0.2416 0.2761 0.2824
0.0040 0.0043 0.0049 0.0040 0.0030 0.0050 0.0046 0.0048 0.0052 0.0042 0.0043 0.0038 0.0036 0.0042 0.0044 0.0042 0.0040 0.0048 0.0042 0.0045 0.0040 0.0041 0.0047 0.0043 0.0045 0.0049 0.0046 0.0047 0.0047 0.0044 0.0043
ð6Þ
3.2. Analysis of variance and model fitment test The analysis of variance (ANOVA) test has been performed to test the adequacy of the developed models for establishing the mathematical link between the response and the machining parameters of laser machining process. The ANOVA test module has been designed to estimate the sum of squares of the response into the contribution due to the second order and a lack of fit component which measures the deviations of the responses from the fitted surface as well as a measure of the experimental errors. Table 5 represents the ANOVA for MRR. From Table 5, it is clear that the ytterbium fiber laser parameters such as wait time and modulation frequency are the most significant and significant parameters, respectively for MRR. The interaction between ‘laser power and pulse width’; and ‘modulation frequency and N2 gas pressure’ are the most significant and significant interaction, respectively for MRR. Similarly, laser power and modulation frequency are the most significant and significant parameters with 8.86714 and 7.25794 F-test value, respectively for taper. However, N2-gas pressure also shows its significance for taper with F-test value 3.93472 at 95% confidence level. The interaction between ‘laser power and N2 gas pressure’ and ‘modulation frequency and N2 gas pressure’ are the most significant and significant interaction, respectively for taper. From Table 6, it is concluded that the laser power, modulation frequency, gas pressure, wait time, pulse width are significantly influencing for controlling MRR and taper as the P-value for both
Table 5 ANOVA for MRR. Sum of Source Model A: Laser power B: Modulation frequency C: Assist gas pressure (N2) D: wait time E: pulse width AB AC AD AE BC BD BE CD CE DE A2 B2 C2 D2 E2 Residual Lack of Fit Pure Error Total
Squares 0.02064 0.00048 0.00115 0.00027 0.00280 3.7819E-05 0.00302 0.00040 1.9585E-05 0.00498 0.00355 0.00077 1.7835E-06 0.00119 0.00107 8.4296E-06 7.3588E-05 0.00028 0.00037 2.3677E-06 3.4497E-05 0.00339 0.00153 0.00185 0.02403
df 20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10 6 4 30
Mean
F
p-value
Square 0.00103 0.00048 0.00115 0.00027 0.00280 3.7819E-05 0.00302 0.00040 1.9585E-05 0.00498 0.00355 0.00077 1.7835E-06 0.00119 0.00107 8.4296E-06 7.3588E-05 0.00028 0.00037 2.3677E-06 3.4497E-05 0.00033 0.00025 0.00046 –
Value 3.04239 1.42406 3.40837 0.80712 8.25490 0.11147 8.90321 1.19074 0.05772 14.69615 10.46528 2.27589 0.00525 3.50805 3.16479 0.02484 0.21690 0.83417 1.11228 0.00697 0.10168 – 0.55195 – –
Prob 4F 0.03710 0.26030 0.09460 0.39011 0.01660 0.74541 0.01371 0.30081 0.81500 0.00331 0.00891 0.16231 0.94361 0.09060 0.10560 0.87791 0.65141 0.38261 0.31641 0.93511 0.75640 – 0.75460 – –
– Significant – – – – – – – – – – – – – – – – – – – – – Not significant –
A. Ghosal, A. Manna / Optics & Laser Technology 46 (2013) 67–76
71
Table 6 Results of analysis of variance for MRR and Taper. Source of variation
Second-order terms Lack of fit Experimental errors Total
d.o.f.
20 6 4 30
Sum of squares
Mean square
D 0.28
MRR
B 0.26
E
Taper (Eq. (6))
MRR (Eq. (5))
Taper (Eq. (6))
MRR (Eq. (5))
Taper (Eq. (6))
MRR (Eq. (5))
Taper (Eq. (6))
0.02064 0.00154 0.00186 0.02404
5.3429E 06 5.5855E 07 0.0132E 05 6.0335E 06
1.032E 03 0.000256 0.4650E 03 –
2.6715E 07 9.3093E 08 0.0033E 05 –
3.0424 – – –
3.8686 – – –
0.0371 – – –
0.0161 – –
Design-Expert® Software Factor Coding: Actual MRR Actual Factors A: Laser power = 700.00 B: Modulation frequency = 800.00 C: Assist gas pressure(Nitrogengen) = 17.50 D: wait time = 0.20 E: pulse width = 87.50
A C E A
0.24 C
D
0.22
B 0.2 -1.000
P-value
MRR (Eq. (5))
Perturbation 0.3
F-value
-0.500 0.000 0.500 1.000 Deviation from Reference Point (Coded Units)
Fig. 2. Perturbation plot shows the effect of ytterbium fiber laser process parameters on MRR.
the responses are less than 0.05. The F-test values for both the responses at 95% confidence level are 3.0424 and 3.8686, respectively. The R2 value for both the responses i.e., MRR and taper are 0.86 and 0.88, respectively. The value of R2(adj) for MRR and taper are 0.61 and 0.66, respectively. These values are above the average value and developed second order models fits the data, therefore, the data for both the response are well fitted in the developed second order models.
4. Parametric analysis on machining characteristics of ytterbium fiber laser The influences of the various process parameters of ytterbium fiber laser on both the responses i.e., MRR and taper during laser machining of 5 mm thick Al/10 wt% Al2O3-MMC have been analyzed based on the developed mathematical models established utilizing response surface methodology (RSM). 4.1. Parametric influences on MRR The perturbation plot for the MRR is shown in Fig. 2. The effect of different parameters of ytterbium fiber laser can compare with respect to a particular point in a design space. This particular point is known as centre point. The lines represent by the different factors A (laser power), B (modulation frequency), C (N2 gas pressure), D (wait time) and E (pulse width) represent their individual behaviors on MRR keeping other parameters constant. From Fig. 2, it is clear that the MRR increases with increase in N2 gas pressure, which agrees with [20]. Similarly, MRR decreases with increase in wait time and modulation frequency. The parameters laser power and pulse width both
has a small effect on MRR, on increase of both the parameters up to certain limit i.e., 400 to 500 W laser power and 75 to 80% pulse width MRR slightly decreases. Fig. 3 shows the combined effects of wait time and modulation frequency on MRR. The parameters laser power, N2 gas pressure and pulse width are hold at 700 W, 17.50 bar and 87.5% of duty cycle, respectively. From Fig. 3, it is clear that the MRR is high at low modulation frequency and low wait time. MRR increases with decrease of wait time and maximum MRR observed with in the range of 0.15 to 0.10 s. MRR also increases with decrease in modulation frequency. It is observe that the best range of modulation frequency is 680 to 600 Hz for optimal MRR. The experimental results revels that comparatively low modulation frequency and low wait time are found to be favorable for higher MRR because of higher cutting speed. It is also due to the less wait time causes less heat losses from the drilling spot as a results material removal rate increase by quick vaporization of the work-piece material. The combined effects of pulse width and laser power on MRR have been shown in Fig. 4. The response surface plot Fig. 4 reflects that the pulse width has a moderate effect on MRR. At constant parametric setting e.g., 800 Hz modulation frequency, 17.5 bar H2 gas pressure, 0.20 s wait time with low pulse width range from 75 to 80% of duty cycle and laser power range 400 to 475 W the MRR is high as compared with moderate pulse width and laser power setting. The combined effects of assisted gas pressure and modulation frequency on MRR have been shown in Fig. 5. The response surface plot Fig. 5 reflects that the assisted gas pressure and modulation frequency both have moderate effect on MRR. At high assisted gas pressure and low modulation frequency i.e., ranges towards from 18 to 20 bar and 680 to 600 Hz, respectively with constant 700 W laser power, 0.20 s wait time, 87.5% of duty cycle pulse width the MRR is high as compared to the parameters setting at low assisted gas pressure with high modulation frequency.
4.2. Parametric influences on taper The minimization of laser hole deviation is highly needed for maintaining quality and accuracy of hole. The combined effect of different parameters of Yitterbium fiber laser on hole taper has been analyzed through different graphs. The combined effects of modulation frequency and laser power on taper have been shown in Fig. 6. The response surface plot Fig. 6 reflects that the modulation frequency and laser power both have great effect on taper. At high modulation frequency and laser power the taper is high as compared with low modulation frequency and laser power. Minimum taper observed at laser power range in between 400 and 475 W. Taper also increase with increase on modulation frequency and minimum taper is obtained at low modulation frequency i.e., range between 600 and 680 Hz with other parameters remain hold as 17.5 bar assisted gas pressure, 0.20 s wait time, 87.5% of duty cycle pulse width. The optimal MRR and taper is obtained within the range of laser power 700 W and modulation frequency 680 Hz.
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Design-Expert® Software Factor Coding: Actual MRR 0.31844 0.169876 X1 = B: Modulation frequency X2 = D: wait time Actual Factors A: Laser power = 700.00 C: Assist gas pressure(Nitrogengen) = 17.50 E: pulse width = 87.50 0.6 0.5
MRR
0.4 0.3 0.2 0.1 0 -0.1
0.30 0.25 0.20 D: wa it ti me
0.15
1000.00 920.00 840.00 y enc 760.00 equ r f 680.00 on lati odu 0.10 600.00 M B:
Fig. 3. Response surface plot of MRR with wait time and modulation frequency.
Design-Expert® Software Factor Coding: Actual MRR 0.31844 0.169876 X1 = A: Laser power X2 = E: pulse width Actual Factors B: Modulation frequency = 800.00 C: Assist gas pressure(Nitrogengen) = 17.50 D: wait time = 0.20 0.6 0.5
MRR
0.4 0.3 0.2 0.1 0 -0.1
100.00
1000 .00 92 850. 5.00 0 0 7 7 90.00 700.0 5.00 E: 0 r 85.00 6 pu we 550. 25.00 lse 80.00 po 00 r 475. wid se 75.00 400.00 00 th La A:
95.00
Fig. 4. Response surface plot of MRR with pulse width and laser power.
The combined effects of assisted gas pressure and laser power on taper have been shown in Fig. 7. The response surface plot Fig. 7 reflects that the assisted gas pressure and laser power both
have significant effect on taper. At high assisted gas pressure with low laser power the taper is low as compared with low assisted gas pressure and laser power. The experimental results revels that
A. Ghosal, A. Manna / Optics & Laser Technology 46 (2013) 67–76
Design-Expert® Software Factor Coding: Actual MRR 0.31844 0.169876 X1 = B: Modulation frequency X2 = C: Assist gas pressure(Nitrogengen) Actual Factors A: Laser power = 700.00 D: wait time = 0.20 E: pulse width = 87.50
0.6 0.5 0.4 MRR
0.3 0.2 0.1 0 -0.1
20.00
1000.00 19.00 920.00 18.00 ssis 840.00 y t ga enc 17.00 s pr 760.00 equ ess r f 16.00 ure 680.00 n (Nit atio rog dul eng 15.00 600.00 o M en) B:
C: A
Fig. 5. Response surface plot of MRR with assisted gas pressure and modulation frequency.
Design-Expert® Software Factor Coding: Actual taper 0.0052 0.003 X1 = A: Laser power X2 = B: Modulation frequency Actual Factors C: Assist gas pressure(Nitrogengen) = 17.50 D: wait time = 0.20 E: pulse width = 87.50 0.008 0.006
taper
0.004 0.002 0 -0.002
1000.00 1 92 000 920.00 .00 5. 8 50 0 7 B: M 840.00 70 75.0 .00 0 odu 0 0 62 latio 760.00 5. .00 5 n fr er 475 50.00 00 equ 680.00 pow enc r 600.00 400.0 .00 e 0 y Las A: Fig. 6. Response surface plot of taper with modulation frequency and laser power.
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Design-Expert® Software Factor Coding: Actual taper 0.0052 0.003 X1 = A: Laser power X2 = C: Assist gas pressure(Nitrogengen) Actual Factors B: Modulation frequency = 800.00 D: wait time = 0.20 E: pulse width = 87.50 0.008 0.006
taper
0.004 0.002 0 -0.002
92
00
00
0.
5.
85
10 20.00 00 C: A 19.00 .0 77 ssis 0 18.00 t ga 5. 7 00 62 00. sp 17.00 res 5 5.0 00 16.00 sur er 47 50. 0 e(N ow 15.00 400 5.00 00 itro rp e gen .00 s La gen A: ) Fig. 7. Response surface plot of taper with assisted gas pressure and laser power.
Design-Expert® Software Factor Coding: Actual taper 0.0052 0.003 X1 = B: Modulation frequency X2 = C: Assist gas pressure(Nitrogengen) Actual Factors A: Laser power = 700.00 D: wait time = 0.20 E: pulse width = 87.50 taper
20.00 C: Assist gas pressure(Nitrogengen)
0.002
19.00
0.003 0.005 0.004
18.00 Fig. 9. SEM of a drilled hole shows the laser entry surface.
17.00
16.00 0.004
15.00 600.00
680.00
760.00 840.00 920.00 B: Modulation frequency
1000.00
Fig. 8. Effect graphs of assist gas pressure and modulation frequency on taper.
comparatively low gas pressure and high laser power are found to be favorable for lower taper because the higher assisted gas pressure cools the localized heating zone causing slower rate of
material removal by penetrate up to the whole thickness of the work piece. During experiments it is also observed that the required drilling time is more when through hole drilling was done at high H2 gas pressure with low laser power. In this case laser beam energy strike for a longer period causing material removal from large area of the top surface of drilled hole, resulting an increase in taper with increase of assist gas pressure. From the graph, it is clear that the range of N2 gas pressure from 18 to 20 bar and 400 to 550 W laser power the hole taper can be minimized. The combined effects of assist gas pressure and modulation frequency on taper have been shown in Fig. 8. The effect graphs Fig. 8 reflects that the assisted gas pressure and modulation
A. Ghosal, A. Manna / Optics & Laser Technology 46 (2013) 67–76
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Table 7 Optimal values of process parameters for maximized MRR and minimized Taper. Experimental validity search on MRR
Experimental validity search on taper
Process parameters
Actual values of parametric combination
Value obtained from Eq. (2)
Value obtained from experi-ment
Error
Actual values of parametric combination
Value obtained from Eq. (3)
Value obtained from experi-ment
Error
Laser power (W) Modulation frequency (Hz) Gas pressure (bar) Wait time (s) Pulse width (%)
473.12 604.54
0.40965
0.39162
0.01803
473.12 604.54
0.00012
0.00083
0.00071
19.82
19.82
0.18 93.47
0.18 93.47
frequency both have moderate effect on taper. From Fig. 8 it is clear that the taper is minimum at range between 18 and 20 bar Nitrogen gas pressure. Modulation frequency in between 920 and 1000 Hz taper is minimum. At very low modulation frequency the beam energy is slightly high but time between two successive beams is more, therefore material has been removed only from the narrow focusing spot on the top surface of work piece. At high assist gas pressure a very narrow localized heating has been occurred as a result low taper hole is generated. Again, at high modulation frequency with high gas pressure, beam energy is less but the time between two successive incident beams is very small, therefore the top surface gets heated rapidly and generated larger taper of micro hole. Hence for low taper, recommended combination is 700 W laser power, 0.20 s wait time, 87.5% of duty cycle pulse width with high assist gas pressure range from 18 to 20 bar and low modulation frequency range from 600 to 680 Hz. Fig. 9 shows the scanning electron microscopy photograph of a drilled hole having 822.857 mm minimum opening and 828.650 mm maximum opening when leaser machining was performed with parametric combination 700 W laser power, 600 Hz modulation frequency, 19 bar gas pressure, 0.20 s wait time and 87.5% of duty cycle pulse width. Here, average deviation at entrance is 0.70% on diameter of a drilled hole of 5 mm thick work piece.
6. Conclusions The ytterbium fiber laser has a capability to perform successful quality hole generation on Al/Al2O3-MMC. The ytterbium fiber laser process parameter can be possibly controlled for effective drilling of Al/Al2O3-MMC. Based on the investigation during machining of Al/Al2O3-MMC by ytterbium fiber laser and developed mathematical models the following outcome can be concluded as listed below: (i) The material removal rate increases with increase of N2 gas pressure and maximum material removal rate observed with in the range of 400 to 475 W laser power. (ii) The developed mathematical models for material removal rate and taper are successfully proposed for effective machining of Al/Al2O3-MMC. These developed models can help directly for evaluation of material removal rate and taper angle under various parametric setting during ytterbium fiber laser machining of Al/Al2O3-MMC. (iii) The minimum taper angle on machined hole is observed at parametric setting range from 18 to 20 bar gas (nitrogen) pressure and 600 to 680 Hz modulation frequency. (iv) The optimal parametric combination for maximized MRR and minimized taper is 473.12 W laser power, 604.54 Hz modulation frequency, 19.82 bar nitrogen gas pressure, 0.18 s wait time and 93.47% pulse width.
5. Confirmation and optimality search Based on the developed second order response equations, optimality searches i.e., searching of optimal parametric setting values for maximum material removal rate and minimum taper can be obtained. This searching can help to identify the parametric combinational effects on the desired response criteria. The developed program in Design Expert Software was utilized to obtain the parametric values for maximized material removal rate and minimized taper phenomenon. The optimal parametric values are considered and different experiments are carried out for optimality test. Table 7 shows the actual values of the process parameters corresponding to the optimal parametric combination for maximum material removal rate and minimum taper during machining of Al/Al2O3-MMC. Table 7 also shows the experimentally obtained values for MRR and taper phenomenon as well as calculated values from the developed mathematical models with estimated error. The estimated error for MRR is only 0.01803. This error is projected based on the experimentally obtained MRR and the MRR from the developed mathematical model, Eq. (2). Similarly, estimated error for taper based on experimental value over developed mathematical model (Eq. (3)) is only 0.00071. From Table 7, it is clear that the optimal parametric combinations of process parameters are satisfied and bear a good agreement with the experimental results.
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