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Experimental study of Hole Taper in Laser Trepan Drilling of Nickel Based Super alloy Sheet
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 5 (2018) 23994–24004
www.materialstoday.com/proceedings
IConAMMA_2017
Experimental study of Hole Taper in Laser Trepan Drilling of Nickel Based Super alloy Sheet Kedari Lal Dhakera, Arun Kumar Pandeya* a
a
Mechanical Engineering Department, Jaypee University of Engineering and Technology, Raghogarh-473226, Guna (MP), India *Corresponding Author E-mail:[email protected]
Abstract This research article reports the optimum laser drilling input parameter for getting minimum hole taper and experimentally investigates the behaviour of hole taper in selected laser drilling input parameters on Inconel -718 sheet. Inconel -718 is nickel based super alloy, has diverse application in the field of manufacturing industries, including aerospace, aircraft, automotive, medical equipments, food service equipments and many others. The material is well suited for applications requiring high strength in temperature ranges from cryogenic up to 1400°F. Inconel-718 also exhibits excellent tensile and impact strength. The conventional drilling process faces difficulties to drill quality and precise holes in advanced materials due to its better mechanical properties. Making geometrical better hole is major concerned with conventional drilling process. With the help of Laser drilling process, a geometrically and dimensionally improved hole may be produced. The geometry of hole can be made further better if operating the Laser system at optimum parameters level. In this paper the effects of laser input parameters on hole taper have been investigated and optimal value of input parameters for reduced hole taper has been suggested. The experiments have been conducted by varying one parameter at a time. The experimental data are used to develop the multi regression model for hole taper. A reliable multi regression model is developed for hole taper and modern optimization tool, Genetic algorithm (GA) is used for optimization of the kerf taper. The optimal value of studied laser input parameters such as assist gas pressure, laser Current, stand-off distance, and cutting speed (Trepanning speed) have been suggested for getting lower value of hole taper. Finally, the effects of each laser input parameter of the kerf taper has been discussed. Keywords:Laser Trapan Drilling; Inconel-718, Hole Taper; Genetic Algorithm; Regression model;
*Corresponding author. Tel.: +91-`9575272128; +91-8770538640 fax: +91-7544-267011. E-mail address:[email protected] 2214-7853© 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Advances in Materials and Manufacturing Applications [IConAMMA 2017].
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1. Introduction Conventional machining processes faces the challenges due to materials properties required for technological advanced applications, very complex shapes of engineering components and durable mechanical components, in industries like aerospace, nuclear equipment manufacturing etc [1]. Therefore, in order to meet these challenges of manufacturing and machining of mechanical elements, the numbers of advanced material removal processes (Advanced machining processes) have been developed to the level of commercial application. These advanced processes are also called unconventional machining process in the sense that conventional tools are not employed for metal removal; instead, energy in its direct form is used to remove the material from the work piece. Inconel-718 is a nickel based super-alloy is known as one the most difficult –to-machine super-alloy in order to satisfy production and quality requirement [2]. The conventional machining methods for this alloy are not commercially favourable. The machined components of this material are not dimensionally accurate for advanced technological industries. Laser Beam Machining (LBM) is an advanced machining process with some specific advantage. It can machine the wide range of engineering materials, it can be applied for machining and drilling in metal, non metal, composites, ceramics and super alloys. Major advantage of Laser Beam Machining (LBM) is that it can produce complex shapes and drill micro-size holes in wide variety of engineering materials. Laser Beam Drilling (LBD) is one of the unconventional machining process in which electrical energy is converted into light energy then into thermal energy. Converted thermal energy is responsible for melting and vaporising the localised material of work piece. By ejecting melted material with the help of pressurised assist gas a hole can be created in work material. Laser Beam Drilling gives the greater scope to manufacturing industries. Manufacturing industry involved in making part, where highly dimensionally accurate component and holes are required, is adopting the LBM and LBD processes [3]. Laser Beam Drilling (LBD) is now accepted commercially where thousands of closely spaced geometrical better holes are the prime requirement. Laser Beam Drilling can be broadly categorized in two types: Laser Trepan Drilling (LTD) and Laser Percussion Drilling (LPD) as shown in Fig.1. In Laser Trepan Drilling, laser beam moves around the circumference of the hole to be drilled, and in Laser Percussion Drilling, laser beam directly ‘punched’ to work martial without any relative motion between laser beam and work material [4].
(a)
Laser Trepan Drilling
(b) Laser Percussion Drilling
Fig.1 Laser beam drilling scheme (a) Laser Trepan Drilling; (b) Laser Percussion Drilling
Laser Percussion Drilling is widely used in the industries, but this process also having many defects as compared to Laser Trepanning Drilling. The major advantage of Laser Trepanning Drilling is that it requires less energy as compared to Laser Percussion Drilling for same diameter hole. Reduced energy caused narrowed heat affected zone (HAZ) in LTP. Narrowed HAZ is always desired in any machining process [5]. The drilling time is lesser in LPD process for small hole size but geometrical quality of hole is poor in LPD process compared to LTD process [6]. All stated factors make Laser Trepan Drilling superior over Laser Percussion Drilling for getting geometrical better hole. Laser drilled holes are also associated with some geometrical defects such as circularity and hole taper, metallurgical defects, and dimensional inaccuracy in both the above stated laser drilling process. Therefore quality of hole is main issue in laser drilling process [7]. These defects can be improved by operating the laser drilling
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system at optimum parameter level. The hole taper is major geometrical defect in laser drilling because of laser beams converging-diverging nature. Although LTD produces reduced hole taper as compared to LPD process, but hole taper is still major concern in Laser Trepanning Drilling, which can be further reduced by if laser input parameters are set at optimal level. Many researchers have studied the Laser Drilling processes in different ways. Chien and Huo have experimentally investigated the recast layer in Laser Trepan Drilling on material Inconel-718. They have performed the experiments as per Taguchi based orthogonal array and suggested the reduced recast layer by Taguchi and ANOVA analysis [8]. Goyal and Dubey have developed different multi regression models for hole geometrical features (circularities and hole taper) in laser trepan drilling of titanium alloy sheet. The authors have applied the Genetic algorithm for finding the optimal value of quality parameters [9]. S. Marimuthu et al. have studied the Quasi-CW-fibre Laser Trepanning Drilling on material nickel super alloy. They have studied the recast layer, oxide layer, hole surface characteristic and fatigue performance of the laser drilled samples. There’s main findings are based on controlling the recast layer, oxide layer, hole surface and suggested the reduced recast layer thickness [10]. Tahir and Aqida have studied the kerf width and heat affected zone (HAZ) of ultra high strength 22MnB5 steel cutting in laser cutting process. They applied the response surface methodology (RSM) using three level Box-Behnken design of experiments and optimised the kerf width and HAZ formation [11]. Similarly Hajdarevic and Bijelonja have find the temperature distribution by numerical based FEM analysis and experimentally validate the result in laser drilling of tungsten alloy [12]. B. S.Yilbas et al. studied the life cycle assessment and environmental impact of the laser cutting in terms of the material waste. They formulated and predicted the kerf width using the lump parameter analysis and validate experimentally [13]. From the available literature, it can be concluded that laser drilling plays vital role in technological advanced components manufacturing. The laser drilling also associated with many defects such as, metallurgical defects and geometrical defects. Laser input parameters such as Assist gas pressure, Laser current, Stand-off distance and Cutting speed greatly affect the hole taper. The authors find very limited research available in Laser Trepan Drilling of Inconel -718 sheet and could not find any research paper for hole taper optimization during the laser trepan drilling of Inconel-718. This paper is an effort to further add an existing knowledge in laser drilling process and also to find the optimal values of laser input parameters for reduced hole taper in laser trepan drilling of nickel based super alloy sheet. Multi-Regression model has been developed for hole taper by using the data collected from experiments. The developed regression model for hole taper has been utilized for the optimization by widely used artificial intelligence based optimization technique Genetic algorithm (GA). 2.
Experimental work and measurement
2.1
Work material
Inconel-718 is nickel based super alloy and is mainly used in manufacturing of equipment of the aerospace system, particularly in the high-temperature sections of gas turbine engines [14]. The composition of material by weight percent of Inconel- 718 is given in Table 1. For present research study, plate size 140x140x1.4 mm taken for conducting the experiments. Total 27 numbers of experiments have been performed according to one parameter at time variation. Table 1- Composition of material by weight percentage Cr
Ni
Mo
Nb
Ti
Fe
17.65
54.25
2.96
4.87
0.72
Remaining
2.2 Experimental setup The experiments have been conducted on Pulsed Nd:YAG laser system of 300W power at RRCAT Indore, India. In this system, the laser beam is generated at generating station and with the help of computer controlled delivery system which consists of nozzle; Laser beam is delivered to worktable. The motion of laser delivery nozzle is being controlled by CNC program and motion of nozzle in present research is along the
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circumference of 1 mm diameter. The worktable holds the sheet of Inconel -718. The assist gas used for the experimentation is compressed air. The optical scanned photograph of the different experiments conducted is shown in Fig. 2.
Fig.2-Experimental sheet after drilling
2.3 Laser input parameters and their ranges The input process parameters are selected from studying the literature available and their importance. These are assist gas pressure; laser current, stand-off distance and cutting speed (trepanning speed). These parameters greatly affect the hole’s geometrical features. For determining the range of input process parameters, exhaustive pilot experiments have been performed, in which desired hole can be drilled. After establishing the ranges of input process parameters, the experiments have been performed as per one parameter at time (OPAT) variation and each experiment is repeated once to overcome the error. The levels and ranges of different input process parameters are listed in Table 2. Table 2 -The ranges and levels of different input process parameters Symbol
Input Parameter
X1 X2 X3 X4
Assist gas pressure, GP (bar) Laser current. I (Amp) Standoff distance, SOD, (mm) Cutting (Trepanning) speed, CS, (mm/min)
Level-1
Level-2
Level-3
Level-4
Level-5
6 220 1 10
7 240 1.25 20
8 260 1.5 30
9 280 1.75 40
10 300 2 50
2.4 Measurements
Fig.3-Measument of different diametersat different intervals
After conducting the experiments for 1mm hole diameter in Inconel-718 sheet on pulsed Nd:YAG laser cutting system, 4 diameters d1, d2, d3, and d4 are measured along the circumference of each drilled hole at interval of 450 angle as shown in Fig.3. The measurements of these four diameters have been performed on
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entrance side and exit side of laser for each drilled hole. The measurements are taken on stereo optical microscope with maximum 160 x magnification. The average values of these measured diameters will gives the diameter at respective sides. After finding the top and bottom diameters of the holes, the hole taper can be calculated. 2.5 Calculation of hole taper By using the mean top (entry) and mean bottom (exit) diameters of the each hole, the hole taper have been calculated by using the Eq. (1). The calculated values of hole taper for different experimental rus are shown in Fig. 4.
tan 1 (
d ent d exit 180 )X 2t
(1)
Where; dent = Mean diameter at Entrance side of hole, dexit = Mean diameter at Exit side of hole, t = Thickness of work sheet (1.4 mm in present study), θ = Hole Taper (HT) in degree
Fig. 4 Experimental values of hole taper
3. Modeling and optimization of hole taper 3.1 Regression mathematical modelling The regression model shows the mathematical relationship between input parameters to output quality characteristics [15]. In regression modelling, data collected from experiments are used to develop the mathematical expression for output quality characteristics. In present case four laser input parameters such as assist gas pressure, laser current, stand-off distance and cutting speed have been used. The output characteristics selected for the study is hole taper (HT). In general second order regression model is preferred over first – order model because of lack of fit of first order model. The general equation of second order regression model is given as [16];
y 0
n
i 1
iX i
n
i 1
ii X 2 i
n
i 1
n
j n 1
ij X i X j
(2)
Where β = Regression coefficients, , Xi = Input parameters (Independent variables) and i = 1, 2, 3-----n are number of input parameters. y = Output parameter (dependent variable), The values of regression coefficients β in Eq. (2) require very long mathematical calculations, and can be found by least square method [17]. In this paper, The MINTAB14 software has been used to find the value of
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regression coefficients and P-value of each term of regression model. For the reliable mathematical model of hole taper, insignificant terms of the regression model have been removed from the model by the back elimination method using the P-values of different terms [16]. After removing the insignificant terms, the coefficient of different input process parameters is given in Table 3. Table 3- Regression coefficient values of significant term of model Predictor
Coef
Constant
69.11
X1
-5.210
X2
-0.043715
X3
-70.75
X4
0.15721
X1*X1
-0.02700
X2*X2
0.0008037
X3*X3
-2.615
X4*X4
-0.0005432
X1*X3
7.339
X1*X4
-0.018617
The final developed multi- regression model of hole taper after removing the insignificant terms for hole taper is as follows; H T = 1.21 0.0490X 1 0.000659X 2 0.560 X 3 0.00591X 4 0.00189X 1 X 1
0.000001 X 2 X 2 0.247X 3 X 3 0.000014 X 4 X 4 0.0059X 1 X 3 0.000648X 1 X 4 .
(3)
Where; X1= Assist gas pressure (bar), X2= Laser current (Amp), X3=Standoff distance (mm) and X4=Cutting (Trepanning) speed (mm/ min). 3.2
Adequacy of developed regression modelβ
After regression model development, it is important to confirm the goodness of fit of the developed regression model. Generally used checks of goodness of fit include the R-squared values, analyses of the pattern f residuals. The adequacy checking parameters of final reduced model are; S
= 0.006775,
R-Sq = 91%,
R-Sq(adj) = 85%
Adequacy checking parameters are sufficiently at higher value, it concludes, that data is well fitted to developed model and the model is well reliable to predict the hole taper for range of laser Input parameters taken in experiments [18]. 3.3
Optimization of hole taper by Genetic Algorithm (GA)
Numbers of artificial intelligence based optimization methods are in use for engineering design and manufacturing process optimization. Genetic algorithm (GA) is one of the artificial intelligence based optimization method, based on natural genetics principle and natural selection for searching and optimization. In general, GA is based on the inspiration of the survival of the fittest and the interbreeding population to create a new and innovative searching. This method also has specific the advantage over the other artificial intelligence based optimization methods that is it search for global optimum solution instead of a local optimum solution, if the variables precisely defined and valued [19]. Genetic algorithm is very suitable for single and multi-objective optimization problems. It has been applied in linear as well non linear optimization problem [20]. This is also suitable for multi objective optimization when different objective to be optimize simultaneously [21]. The flow diagram of the GA based optimization process is shown in Fig. 5.
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Fig.5 Procedure flow diagram of Genetic algorithm [20]
Regression Eq. (3) is the function to be minimized by the Genetic Algorithm (GA). A separate Mfile has been created for equation (3) in MATLAB2008a software. The next step in this optimization technique is selection of important parameters such as reproduction, crossover, and mutation [22]. For better performing of GA optimization the size of population is 50, type of population is double vector, crossover probability is 0.8, mutation probability is 0.2, and the number of generations 200 are taken as main parameters during the execution of GA-based optimization. After specifying all the stated parameters, in build coding of MATLAB2008a software has been run and optimization process ended when satisfying the termination criterion. The generationfitness graphs and the optimal laser input parameter values are shown in Fig. 6. It can be seen that the objective function in Eq. (3) is optimized when the mean fitness curve converges to the best fitness curve and thereafter no further change in the best fitness value has been observed. 4. Result and discussion
The result of GA based optimization is shown in Fig. 6 and it can be concluded that improvement in the best fitness value of hole taper is up to 156th generation. There after no further improvement in the best fitness value (of Hole Taper) and the best fitness (minimum) value at 156th generation has been found = 2.660 as indicated in Fig. 6. The minimum optimal value of Hole Taper, 2.660 is obtained corresponding to the optimal laser input parameters and optimal level of laser input parameters are: Assist gas pressure = 6 bar, Laser current = 220 amp, Stand-off distance= 2 mm and Cutting speed (trepanning speed) = 10 mm/min.
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Fig.6 Results of GA based optimization for Hole Taper (HT)
The optimization results shows that minimum value of hole taper is obtained at lower value of assist gas pressure, lower value of cutting speed and lower laser current, in the range taken for experiments. These facts can be justified by thermo-physical properties of material Inconel-718. The Inconel-718 are having poor thermal conductivity and poor thermal diffusivity [2]. At lower cutting speed, the time is available for heat to penetrate up to exit side of hole that make more heat is available for heating, melting of metal at exit side and by which higher mean diameter at exit is obtained, and give decreased taper hole. The assist gas’s major function is to eject the melted material from the molten pool, and assist gas also responsible for force convection heat loss. At lower assist gas pressure, force convection heat loss can be controlled and removal of melted metal will be proper on both side of hole and that’s again produced decreased taper hole. Stand-off distance is the distance between laser delivery nozzle bottom and top surface of the metal sheet. Focal point of laser beam is greatly affected by changes in stand –off distance. In present study minimum hole taper has been obtained (optimal) at higher stand-off distance. Laser beam is converging-diverging in nature. At higher stand –off distance, focal position of beam with respect to metal sheet will be increased, increased focal position produces lower mean entrance diameter which makes minimum hole taper. 5. Parametric effect 5.1
Effect of Assist gas pressure and Laser current.
The function of assist gas is to remove the molten metal from drilling area and the function of laser current is to generate the sufficient heat for melting the localised area for making drill in metal sheet. Fig. 7 shows the effect of assist gas pressure and laser current on hole taper. Behaviour of hole taper is increasing with assist gas pressure at all four level of laser current in range taken for study. The hole taper is the tangent function of difference between mean diameter at entrance and exit. Higher assist gas pressure is responsible rapid cooling (forced convection) of molten metal at exit side and sufficient heat is not reached up to the exit side, because of cooling effect of higher assist gas pressure. These facts are the reason behind decreasing mean diameter at exit with increasing assist gas pressure. Deceasing mean exit diameter is the reason for increasing hole taper as shown in fig.7. At higher laser current generated heat is more than required for melting of localised area and extra heat generated is confined to localised area due to poor thermal conductivity of material. This phenomenal create the uneven heating at entrance side of hole and larger mean entrance diameter. And the larger mean entrance diameter is responsible for higher hole taper in drilled hole of the metal sheet.
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Fig.7 Effect of Assist gas pressure and Laser current
5.2
Effect of Stand-off distance and cutting speed
The Fig. 8 shows the effect of stand-off distance (SOD) on hole taper. The hole taper decreases with increasing stand-off distance from value 1.7mm to 2mm. Position of the focal point of laser beam with respect to material sheet top surface is very important factor for forming the drilled hole geometry. Change in stand-off distance causes the change in position of focal point of laser beam. Best focal position is when focal point is within the material thickness and with increasing focal position with respect to material, entrance diameter of drilled hole decreases up to certain limit as reported by C. Y.Yeo et al.[14]. Decreasing entrance diameter of hole with increasing focal position is the explanation of presented trend of hole taper in Fig.8. Hole taper is tangential function of difference between mean entrance diameter and mean exit diameter. Decreasing mean entrance diameter is responsible for decreasing hole taper. Effect of cutting speed in comparison to SOD is very small on hole taper. Minor changes in hole taper with respect to cutting speed can be seen in fig.8. With increasing cutting speed, decreased hole taper have been observed. Cutting speed is the relative motion between work material and laser beam. As material is poor thermal conductive and at higher cutting speed chance of overheating is very limited. Heat generated at drilling area is just sufficient for proper heating and melting of work material. These facts are responsible for evenly heating of either side hole and lower the difference between entrance and exit hole diameter which causes the decreasing hole taper with increasing cutting speed.
Fig.8 Effect of Stand-off distance and cutting speed on hole taper
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6. Conclusions
Inconel-718 is the major supper alloye used in advanced technological applications. In this study, optimal parameter setting for lesser hole taper in Laser Trepan Drilling of Inconel-718 have been found. Experiments have been performed on solid state pulsed Nd:YAG laser system. The hybrid approach of multiple regression modeling and Genetic Algorithm tool have been applied successfully for modeling and optimization of hole taper. The main observations from this experimental study are listed below; 1. The second-order regression model for hole taper has been developed successfully by using the experimental data obtained in the experimentation. 2. The statistical analysis of the developed regression model has been performed and analysis shows that the developed model may be used to predict the hole taper in given range of laser input parameters. 3. The optimal (reduced)values of hole taper has been found by using the hybrid approach of multiple regression analysis and genetic algorithm. 4. The optimum input process parameters obtained by using the hybrid approach are as assist gas pressure = 6 bar, laser current = 220 amp, stand-off distance = 2 mm and cutting speed (trepanning speed) = 10 mm/min. 5. The optimum minimum value of hole taper has been found equal to 2.660, which is lowest than the all experimental values. 6. The parametric effect shows that minimum value of hole taper can be obtained at lowest value of assist gas pressure, laser current and cutting speed and highest value of stand-off distance in the range considered in this study. Acknowledgement:
The Authors are very great full to Dr. B. N. Upadhayay, SOF, Solid State Division at the RRCAT (Raja Ramanna Centre for Advanced Technology), Indore (M.P) for providing the experimental support for this work. We are also grateful to Mr. Vijay Bhardwaj for providing help in conducting the experiments. References [1] V. K. Jain, Advanced Machining Processes, Allied publisher pvt. New Delhi, 2005. [2] E.O.Ezugwu, Z.M. Wang , A.R. Machado, The machinability of nickel based alloys-a review. Journal of Materials Processing Technology, 86(1999) 1–16. [3] G. Chyryssouris, Laser Machining , Springer. New york, 2005. [4] A. K. Dubey, V. Yadava, Laser beam machining – A review, International Journal of Machine Tools & Manufacture, 48 (2008) 609-628. [5] S. Kumar, A.K. Dubey, A.K. Pandey, Computer-Aided Genetic Algorithm Based Multi-Opbjective Optimization of Laser Trapan Drilling, Internation Journal of Pricision Engineeringand Manufacuring , 14 (2013)1119-1125. [6] R. Goyal, A. K. Dubey, Quality improvement by parameter optimization in laser trepan drilling of super alloy sheet, Materials and Manufacturing Processes, 29 (2014) 1410-1416. [7] I. A. Choudhury, W. C. Chong , G.Vahid, Hole qualities in laser trepanning of polymeric materials, Optics And Lasers in Engineering,50 (2012) 1297–1305. [8] W.T. Chien, S.C. Hou , Investigating the recast layer formed during the laser trepan drilling of Inconel 718 using the Taguchi method, International Journal of Advanced Manufacturing Technology, 33( 2007) 308–316. [9] R. Goyal ,A.K. Dubey, Modeling and optimization of geometrical characteristics in laser trepan drilling of titanium alloy, Journal of Mechanical Science and Technology , 30 (3) (2016) 1281~1293. [10] S. Marimuthu, M. Antar, J. Dunleavey, D. Chantzis, W. Darlington, P. Hayward, An experimental study on quasi-CW fibre laser drilling of nickel superalloy, Optics and Laser Technology, 94 (2017) 119–127. [11] A. F. Mohd Tahira, S. N. Aqida, An investigation of laser cutting quality of 22MnB5 ultra high strength steel using response surface methodology, Optics & Laser Technology, 92 (2017) 142–149 [12] D. B. Hajdarevic, I. Bijelonja, Experimental and Numerical Investigation of Temperature Distribution and Hole Geometry during Laser Drilling Process, Procedia Engineering, 100 ( 2015 ) 384 – 393. [13] B. S.Yilbas, M. M. Shaukat, F. Ashraf, Laser cutting of various materials: Kerf width size analysis and life cycle assessment of cutting process, Optics and Laser Technology, 93 (2017) 67–73 [14] C.Y. Yeo, S. C. Tam, S. Jana, M.W.S.Lau, A technical review of the laser drilling of aerospace materials. Journal of Materials Processing Technology, 42(1994)15–49.
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[15] A. K. Pandey, A. K. Dubey, Intelligent Modeling of Laser Cutting of Thin Sheet, International Journal of Modeling and Optimization, Vol. 1(2011)107-112. [16] A. K. Pandey, A. K Dubey, Simultaneous optimization of multiple quality characteristics in laser cutting of titanium alloy sheet, Optics & Laser Technology, 44 (2012)1858–1865. [17] D.C. Montgomery, Design and analysis of experiments, John wiley and Sons hoboken, NJ, 2009. [18] M. S. Phadke, Quality engineering using robust design, Prentice-hall,NJ, 1989. [19] K. Deb , Optimization for engineering desgin. 8th ed. Prentice –hall , New Delhi, 2005. [20] R.V. Rao Advanced modeling and optimisation of manufacuring process. 1st ed. Springer, London, 2011. [21] R. N. Yadav, V. Yadava, G. K. Singh, Application of non-dominated sorting genetic algorithm for multi-objective optimization of electrical discharge diamond face grinding process, Journal of Mechanical Science and Technology, 28 (6) (2014) 2299 – 2306. [22] A.K. Pandey, A.K. Dubey, Modeling and Optimization of Kerf Taper in Pulsed Laser Cutting of Duralumin Sheet, (ASME-2012) International Manufacturing Science and Engineering Conference (MSEC2012), held at University of Notre Dame, Indiana, U.S.A, June 4-8, 2012, pp. 491-498.
ScienceDirect Materials Today: Proceedings 5 (2018) 23994–24004
www.materialstoday.com/proceedings
IConAMMA_2017
Experimental study of Hole Taper in Laser Trepan Drilling of Nickel Based Super alloy Sheet Kedari Lal Dhakera, Arun Kumar Pandeya* a
a
Mechanical Engineering Department, Jaypee University of Engineering and Technology, Raghogarh-473226, Guna (MP), India *Corresponding Author E-mail:[email protected]
Abstract This research article reports the optimum laser drilling input parameter for getting minimum hole taper and experimentally investigates the behaviour of hole taper in selected laser drilling input parameters on Inconel -718 sheet. Inconel -718 is nickel based super alloy, has diverse application in the field of manufacturing industries, including aerospace, aircraft, automotive, medical equipments, food service equipments and many others. The material is well suited for applications requiring high strength in temperature ranges from cryogenic up to 1400°F. Inconel-718 also exhibits excellent tensile and impact strength. The conventional drilling process faces difficulties to drill quality and precise holes in advanced materials due to its better mechanical properties. Making geometrical better hole is major concerned with conventional drilling process. With the help of Laser drilling process, a geometrically and dimensionally improved hole may be produced. The geometry of hole can be made further better if operating the Laser system at optimum parameters level. In this paper the effects of laser input parameters on hole taper have been investigated and optimal value of input parameters for reduced hole taper has been suggested. The experiments have been conducted by varying one parameter at a time. The experimental data are used to develop the multi regression model for hole taper. A reliable multi regression model is developed for hole taper and modern optimization tool, Genetic algorithm (GA) is used for optimization of the kerf taper. The optimal value of studied laser input parameters such as assist gas pressure, laser Current, stand-off distance, and cutting speed (Trepanning speed) have been suggested for getting lower value of hole taper. Finally, the effects of each laser input parameter of the kerf taper has been discussed. Keywords:Laser Trapan Drilling; Inconel-718, Hole Taper; Genetic Algorithm; Regression model;
*Corresponding author. Tel.: +91-`9575272128; +91-8770538640 fax: +91-7544-267011. E-mail address:[email protected] 2214-7853© 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Advances in Materials and Manufacturing Applications [IConAMMA 2017].
Arun Kumar Pandey / Materials Today: Proceedings 5 (2018) 23994–24004
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1. Introduction Conventional machining processes faces the challenges due to materials properties required for technological advanced applications, very complex shapes of engineering components and durable mechanical components, in industries like aerospace, nuclear equipment manufacturing etc [1]. Therefore, in order to meet these challenges of manufacturing and machining of mechanical elements, the numbers of advanced material removal processes (Advanced machining processes) have been developed to the level of commercial application. These advanced processes are also called unconventional machining process in the sense that conventional tools are not employed for metal removal; instead, energy in its direct form is used to remove the material from the work piece. Inconel-718 is a nickel based super-alloy is known as one the most difficult –to-machine super-alloy in order to satisfy production and quality requirement [2]. The conventional machining methods for this alloy are not commercially favourable. The machined components of this material are not dimensionally accurate for advanced technological industries. Laser Beam Machining (LBM) is an advanced machining process with some specific advantage. It can machine the wide range of engineering materials, it can be applied for machining and drilling in metal, non metal, composites, ceramics and super alloys. Major advantage of Laser Beam Machining (LBM) is that it can produce complex shapes and drill micro-size holes in wide variety of engineering materials. Laser Beam Drilling (LBD) is one of the unconventional machining process in which electrical energy is converted into light energy then into thermal energy. Converted thermal energy is responsible for melting and vaporising the localised material of work piece. By ejecting melted material with the help of pressurised assist gas a hole can be created in work material. Laser Beam Drilling gives the greater scope to manufacturing industries. Manufacturing industry involved in making part, where highly dimensionally accurate component and holes are required, is adopting the LBM and LBD processes [3]. Laser Beam Drilling (LBD) is now accepted commercially where thousands of closely spaced geometrical better holes are the prime requirement. Laser Beam Drilling can be broadly categorized in two types: Laser Trepan Drilling (LTD) and Laser Percussion Drilling (LPD) as shown in Fig.1. In Laser Trepan Drilling, laser beam moves around the circumference of the hole to be drilled, and in Laser Percussion Drilling, laser beam directly ‘punched’ to work martial without any relative motion between laser beam and work material [4].
(a)
Laser Trepan Drilling
(b) Laser Percussion Drilling
Fig.1 Laser beam drilling scheme (a) Laser Trepan Drilling; (b) Laser Percussion Drilling
Laser Percussion Drilling is widely used in the industries, but this process also having many defects as compared to Laser Trepanning Drilling. The major advantage of Laser Trepanning Drilling is that it requires less energy as compared to Laser Percussion Drilling for same diameter hole. Reduced energy caused narrowed heat affected zone (HAZ) in LTP. Narrowed HAZ is always desired in any machining process [5]. The drilling time is lesser in LPD process for small hole size but geometrical quality of hole is poor in LPD process compared to LTD process [6]. All stated factors make Laser Trepan Drilling superior over Laser Percussion Drilling for getting geometrical better hole. Laser drilled holes are also associated with some geometrical defects such as circularity and hole taper, metallurgical defects, and dimensional inaccuracy in both the above stated laser drilling process. Therefore quality of hole is main issue in laser drilling process [7]. These defects can be improved by operating the laser drilling
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system at optimum parameter level. The hole taper is major geometrical defect in laser drilling because of laser beams converging-diverging nature. Although LTD produces reduced hole taper as compared to LPD process, but hole taper is still major concern in Laser Trepanning Drilling, which can be further reduced by if laser input parameters are set at optimal level. Many researchers have studied the Laser Drilling processes in different ways. Chien and Huo have experimentally investigated the recast layer in Laser Trepan Drilling on material Inconel-718. They have performed the experiments as per Taguchi based orthogonal array and suggested the reduced recast layer by Taguchi and ANOVA analysis [8]. Goyal and Dubey have developed different multi regression models for hole geometrical features (circularities and hole taper) in laser trepan drilling of titanium alloy sheet. The authors have applied the Genetic algorithm for finding the optimal value of quality parameters [9]. S. Marimuthu et al. have studied the Quasi-CW-fibre Laser Trepanning Drilling on material nickel super alloy. They have studied the recast layer, oxide layer, hole surface characteristic and fatigue performance of the laser drilled samples. There’s main findings are based on controlling the recast layer, oxide layer, hole surface and suggested the reduced recast layer thickness [10]. Tahir and Aqida have studied the kerf width and heat affected zone (HAZ) of ultra high strength 22MnB5 steel cutting in laser cutting process. They applied the response surface methodology (RSM) using three level Box-Behnken design of experiments and optimised the kerf width and HAZ formation [11]. Similarly Hajdarevic and Bijelonja have find the temperature distribution by numerical based FEM analysis and experimentally validate the result in laser drilling of tungsten alloy [12]. B. S.Yilbas et al. studied the life cycle assessment and environmental impact of the laser cutting in terms of the material waste. They formulated and predicted the kerf width using the lump parameter analysis and validate experimentally [13]. From the available literature, it can be concluded that laser drilling plays vital role in technological advanced components manufacturing. The laser drilling also associated with many defects such as, metallurgical defects and geometrical defects. Laser input parameters such as Assist gas pressure, Laser current, Stand-off distance and Cutting speed greatly affect the hole taper. The authors find very limited research available in Laser Trepan Drilling of Inconel -718 sheet and could not find any research paper for hole taper optimization during the laser trepan drilling of Inconel-718. This paper is an effort to further add an existing knowledge in laser drilling process and also to find the optimal values of laser input parameters for reduced hole taper in laser trepan drilling of nickel based super alloy sheet. Multi-Regression model has been developed for hole taper by using the data collected from experiments. The developed regression model for hole taper has been utilized for the optimization by widely used artificial intelligence based optimization technique Genetic algorithm (GA). 2.
Experimental work and measurement
2.1
Work material
Inconel-718 is nickel based super alloy and is mainly used in manufacturing of equipment of the aerospace system, particularly in the high-temperature sections of gas turbine engines [14]. The composition of material by weight percent of Inconel- 718 is given in Table 1. For present research study, plate size 140x140x1.4 mm taken for conducting the experiments. Total 27 numbers of experiments have been performed according to one parameter at time variation. Table 1- Composition of material by weight percentage Cr
Ni
Mo
Nb
Ti
Fe
17.65
54.25
2.96
4.87
0.72
Remaining
2.2 Experimental setup The experiments have been conducted on Pulsed Nd:YAG laser system of 300W power at RRCAT Indore, India. In this system, the laser beam is generated at generating station and with the help of computer controlled delivery system which consists of nozzle; Laser beam is delivered to worktable. The motion of laser delivery nozzle is being controlled by CNC program and motion of nozzle in present research is along the
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circumference of 1 mm diameter. The worktable holds the sheet of Inconel -718. The assist gas used for the experimentation is compressed air. The optical scanned photograph of the different experiments conducted is shown in Fig. 2.
Fig.2-Experimental sheet after drilling
2.3 Laser input parameters and their ranges The input process parameters are selected from studying the literature available and their importance. These are assist gas pressure; laser current, stand-off distance and cutting speed (trepanning speed). These parameters greatly affect the hole’s geometrical features. For determining the range of input process parameters, exhaustive pilot experiments have been performed, in which desired hole can be drilled. After establishing the ranges of input process parameters, the experiments have been performed as per one parameter at time (OPAT) variation and each experiment is repeated once to overcome the error. The levels and ranges of different input process parameters are listed in Table 2. Table 2 -The ranges and levels of different input process parameters Symbol
Input Parameter
X1 X2 X3 X4
Assist gas pressure, GP (bar) Laser current. I (Amp) Standoff distance, SOD, (mm) Cutting (Trepanning) speed, CS, (mm/min)
Level-1
Level-2
Level-3
Level-4
Level-5
6 220 1 10
7 240 1.25 20
8 260 1.5 30
9 280 1.75 40
10 300 2 50
2.4 Measurements
Fig.3-Measument of different diametersat different intervals
After conducting the experiments for 1mm hole diameter in Inconel-718 sheet on pulsed Nd:YAG laser cutting system, 4 diameters d1, d2, d3, and d4 are measured along the circumference of each drilled hole at interval of 450 angle as shown in Fig.3. The measurements of these four diameters have been performed on
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entrance side and exit side of laser for each drilled hole. The measurements are taken on stereo optical microscope with maximum 160 x magnification. The average values of these measured diameters will gives the diameter at respective sides. After finding the top and bottom diameters of the holes, the hole taper can be calculated. 2.5 Calculation of hole taper By using the mean top (entry) and mean bottom (exit) diameters of the each hole, the hole taper have been calculated by using the Eq. (1). The calculated values of hole taper for different experimental rus are shown in Fig. 4.
tan 1 (
d ent d exit 180 )X 2t
(1)
Where; dent = Mean diameter at Entrance side of hole, dexit = Mean diameter at Exit side of hole, t = Thickness of work sheet (1.4 mm in present study), θ = Hole Taper (HT) in degree
Fig. 4 Experimental values of hole taper
3. Modeling and optimization of hole taper 3.1 Regression mathematical modelling The regression model shows the mathematical relationship between input parameters to output quality characteristics [15]. In regression modelling, data collected from experiments are used to develop the mathematical expression for output quality characteristics. In present case four laser input parameters such as assist gas pressure, laser current, stand-off distance and cutting speed have been used. The output characteristics selected for the study is hole taper (HT). In general second order regression model is preferred over first – order model because of lack of fit of first order model. The general equation of second order regression model is given as [16];
y 0
n
i 1
iX i
n
i 1
ii X 2 i
n
i 1
n
j n 1
ij X i X j
(2)
Where β = Regression coefficients, , Xi = Input parameters (Independent variables) and i = 1, 2, 3-----n are number of input parameters. y = Output parameter (dependent variable), The values of regression coefficients β in Eq. (2) require very long mathematical calculations, and can be found by least square method [17]. In this paper, The MINTAB14 software has been used to find the value of
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regression coefficients and P-value of each term of regression model. For the reliable mathematical model of hole taper, insignificant terms of the regression model have been removed from the model by the back elimination method using the P-values of different terms [16]. After removing the insignificant terms, the coefficient of different input process parameters is given in Table 3. Table 3- Regression coefficient values of significant term of model Predictor
Coef
Constant
69.11
X1
-5.210
X2
-0.043715
X3
-70.75
X4
0.15721
X1*X1
-0.02700
X2*X2
0.0008037
X3*X3
-2.615
X4*X4
-0.0005432
X1*X3
7.339
X1*X4
-0.018617
The final developed multi- regression model of hole taper after removing the insignificant terms for hole taper is as follows; H T = 1.21 0.0490X 1 0.000659X 2 0.560 X 3 0.00591X 4 0.00189X 1 X 1
0.000001 X 2 X 2 0.247X 3 X 3 0.000014 X 4 X 4 0.0059X 1 X 3 0.000648X 1 X 4 .
(3)
Where; X1= Assist gas pressure (bar), X2= Laser current (Amp), X3=Standoff distance (mm) and X4=Cutting (Trepanning) speed (mm/ min). 3.2
Adequacy of developed regression modelβ
After regression model development, it is important to confirm the goodness of fit of the developed regression model. Generally used checks of goodness of fit include the R-squared values, analyses of the pattern f residuals. The adequacy checking parameters of final reduced model are; S
= 0.006775,
R-Sq = 91%,
R-Sq(adj) = 85%
Adequacy checking parameters are sufficiently at higher value, it concludes, that data is well fitted to developed model and the model is well reliable to predict the hole taper for range of laser Input parameters taken in experiments [18]. 3.3
Optimization of hole taper by Genetic Algorithm (GA)
Numbers of artificial intelligence based optimization methods are in use for engineering design and manufacturing process optimization. Genetic algorithm (GA) is one of the artificial intelligence based optimization method, based on natural genetics principle and natural selection for searching and optimization. In general, GA is based on the inspiration of the survival of the fittest and the interbreeding population to create a new and innovative searching. This method also has specific the advantage over the other artificial intelligence based optimization methods that is it search for global optimum solution instead of a local optimum solution, if the variables precisely defined and valued [19]. Genetic algorithm is very suitable for single and multi-objective optimization problems. It has been applied in linear as well non linear optimization problem [20]. This is also suitable for multi objective optimization when different objective to be optimize simultaneously [21]. The flow diagram of the GA based optimization process is shown in Fig. 5.
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Fig.5 Procedure flow diagram of Genetic algorithm [20]
Regression Eq. (3) is the function to be minimized by the Genetic Algorithm (GA). A separate Mfile has been created for equation (3) in MATLAB2008a software. The next step in this optimization technique is selection of important parameters such as reproduction, crossover, and mutation [22]. For better performing of GA optimization the size of population is 50, type of population is double vector, crossover probability is 0.8, mutation probability is 0.2, and the number of generations 200 are taken as main parameters during the execution of GA-based optimization. After specifying all the stated parameters, in build coding of MATLAB2008a software has been run and optimization process ended when satisfying the termination criterion. The generationfitness graphs and the optimal laser input parameter values are shown in Fig. 6. It can be seen that the objective function in Eq. (3) is optimized when the mean fitness curve converges to the best fitness curve and thereafter no further change in the best fitness value has been observed. 4. Result and discussion
The result of GA based optimization is shown in Fig. 6 and it can be concluded that improvement in the best fitness value of hole taper is up to 156th generation. There after no further improvement in the best fitness value (of Hole Taper) and the best fitness (minimum) value at 156th generation has been found = 2.660 as indicated in Fig. 6. The minimum optimal value of Hole Taper, 2.660 is obtained corresponding to the optimal laser input parameters and optimal level of laser input parameters are: Assist gas pressure = 6 bar, Laser current = 220 amp, Stand-off distance= 2 mm and Cutting speed (trepanning speed) = 10 mm/min.
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Fig.6 Results of GA based optimization for Hole Taper (HT)
The optimization results shows that minimum value of hole taper is obtained at lower value of assist gas pressure, lower value of cutting speed and lower laser current, in the range taken for experiments. These facts can be justified by thermo-physical properties of material Inconel-718. The Inconel-718 are having poor thermal conductivity and poor thermal diffusivity [2]. At lower cutting speed, the time is available for heat to penetrate up to exit side of hole that make more heat is available for heating, melting of metal at exit side and by which higher mean diameter at exit is obtained, and give decreased taper hole. The assist gas’s major function is to eject the melted material from the molten pool, and assist gas also responsible for force convection heat loss. At lower assist gas pressure, force convection heat loss can be controlled and removal of melted metal will be proper on both side of hole and that’s again produced decreased taper hole. Stand-off distance is the distance between laser delivery nozzle bottom and top surface of the metal sheet. Focal point of laser beam is greatly affected by changes in stand –off distance. In present study minimum hole taper has been obtained (optimal) at higher stand-off distance. Laser beam is converging-diverging in nature. At higher stand –off distance, focal position of beam with respect to metal sheet will be increased, increased focal position produces lower mean entrance diameter which makes minimum hole taper. 5. Parametric effect 5.1
Effect of Assist gas pressure and Laser current.
The function of assist gas is to remove the molten metal from drilling area and the function of laser current is to generate the sufficient heat for melting the localised area for making drill in metal sheet. Fig. 7 shows the effect of assist gas pressure and laser current on hole taper. Behaviour of hole taper is increasing with assist gas pressure at all four level of laser current in range taken for study. The hole taper is the tangent function of difference between mean diameter at entrance and exit. Higher assist gas pressure is responsible rapid cooling (forced convection) of molten metal at exit side and sufficient heat is not reached up to the exit side, because of cooling effect of higher assist gas pressure. These facts are the reason behind decreasing mean diameter at exit with increasing assist gas pressure. Deceasing mean exit diameter is the reason for increasing hole taper as shown in fig.7. At higher laser current generated heat is more than required for melting of localised area and extra heat generated is confined to localised area due to poor thermal conductivity of material. This phenomenal create the uneven heating at entrance side of hole and larger mean entrance diameter. And the larger mean entrance diameter is responsible for higher hole taper in drilled hole of the metal sheet.
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Fig.7 Effect of Assist gas pressure and Laser current
5.2
Effect of Stand-off distance and cutting speed
The Fig. 8 shows the effect of stand-off distance (SOD) on hole taper. The hole taper decreases with increasing stand-off distance from value 1.7mm to 2mm. Position of the focal point of laser beam with respect to material sheet top surface is very important factor for forming the drilled hole geometry. Change in stand-off distance causes the change in position of focal point of laser beam. Best focal position is when focal point is within the material thickness and with increasing focal position with respect to material, entrance diameter of drilled hole decreases up to certain limit as reported by C. Y.Yeo et al.[14]. Decreasing entrance diameter of hole with increasing focal position is the explanation of presented trend of hole taper in Fig.8. Hole taper is tangential function of difference between mean entrance diameter and mean exit diameter. Decreasing mean entrance diameter is responsible for decreasing hole taper. Effect of cutting speed in comparison to SOD is very small on hole taper. Minor changes in hole taper with respect to cutting speed can be seen in fig.8. With increasing cutting speed, decreased hole taper have been observed. Cutting speed is the relative motion between work material and laser beam. As material is poor thermal conductive and at higher cutting speed chance of overheating is very limited. Heat generated at drilling area is just sufficient for proper heating and melting of work material. These facts are responsible for evenly heating of either side hole and lower the difference between entrance and exit hole diameter which causes the decreasing hole taper with increasing cutting speed.
Fig.8 Effect of Stand-off distance and cutting speed on hole taper
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6. Conclusions
Inconel-718 is the major supper alloye used in advanced technological applications. In this study, optimal parameter setting for lesser hole taper in Laser Trepan Drilling of Inconel-718 have been found. Experiments have been performed on solid state pulsed Nd:YAG laser system. The hybrid approach of multiple regression modeling and Genetic Algorithm tool have been applied successfully for modeling and optimization of hole taper. The main observations from this experimental study are listed below; 1. The second-order regression model for hole taper has been developed successfully by using the experimental data obtained in the experimentation. 2. The statistical analysis of the developed regression model has been performed and analysis shows that the developed model may be used to predict the hole taper in given range of laser input parameters. 3. The optimal (reduced)values of hole taper has been found by using the hybrid approach of multiple regression analysis and genetic algorithm. 4. The optimum input process parameters obtained by using the hybrid approach are as assist gas pressure = 6 bar, laser current = 220 amp, stand-off distance = 2 mm and cutting speed (trepanning speed) = 10 mm/min. 5. The optimum minimum value of hole taper has been found equal to 2.660, which is lowest than the all experimental values. 6. The parametric effect shows that minimum value of hole taper can be obtained at lowest value of assist gas pressure, laser current and cutting speed and highest value of stand-off distance in the range considered in this study. Acknowledgement:
The Authors are very great full to Dr. B. N. Upadhayay, SOF, Solid State Division at the RRCAT (Raja Ramanna Centre for Advanced Technology), Indore (M.P) for providing the experimental support for this work. We are also grateful to Mr. Vijay Bhardwaj for providing help in conducting the experiments. References [1] V. K. Jain, Advanced Machining Processes, Allied publisher pvt. New Delhi, 2005. [2] E.O.Ezugwu, Z.M. Wang , A.R. Machado, The machinability of nickel based alloys-a review. Journal of Materials Processing Technology, 86(1999) 1–16. [3] G. Chyryssouris, Laser Machining , Springer. New york, 2005. [4] A. K. Dubey, V. Yadava, Laser beam machining – A review, International Journal of Machine Tools & Manufacture, 48 (2008) 609-628. [5] S. Kumar, A.K. Dubey, A.K. Pandey, Computer-Aided Genetic Algorithm Based Multi-Opbjective Optimization of Laser Trapan Drilling, Internation Journal of Pricision Engineeringand Manufacuring , 14 (2013)1119-1125. [6] R. Goyal, A. K. Dubey, Quality improvement by parameter optimization in laser trepan drilling of super alloy sheet, Materials and Manufacturing Processes, 29 (2014) 1410-1416. [7] I. A. Choudhury, W. C. Chong , G.Vahid, Hole qualities in laser trepanning of polymeric materials, Optics And Lasers in Engineering,50 (2012) 1297–1305. [8] W.T. Chien, S.C. Hou , Investigating the recast layer formed during the laser trepan drilling of Inconel 718 using the Taguchi method, International Journal of Advanced Manufacturing Technology, 33( 2007) 308–316. [9] R. Goyal ,A.K. Dubey, Modeling and optimization of geometrical characteristics in laser trepan drilling of titanium alloy, Journal of Mechanical Science and Technology , 30 (3) (2016) 1281~1293. [10] S. Marimuthu, M. Antar, J. Dunleavey, D. Chantzis, W. Darlington, P. Hayward, An experimental study on quasi-CW fibre laser drilling of nickel superalloy, Optics and Laser Technology, 94 (2017) 119–127. [11] A. F. Mohd Tahira, S. N. Aqida, An investigation of laser cutting quality of 22MnB5 ultra high strength steel using response surface methodology, Optics & Laser Technology, 92 (2017) 142–149 [12] D. B. Hajdarevic, I. Bijelonja, Experimental and Numerical Investigation of Temperature Distribution and Hole Geometry during Laser Drilling Process, Procedia Engineering, 100 ( 2015 ) 384 – 393. [13] B. S.Yilbas, M. M. Shaukat, F. Ashraf, Laser cutting of various materials: Kerf width size analysis and life cycle assessment of cutting process, Optics and Laser Technology, 93 (2017) 67–73 [14] C.Y. Yeo, S. C. Tam, S. Jana, M.W.S.Lau, A technical review of the laser drilling of aerospace materials. Journal of Materials Processing Technology, 42(1994)15–49.
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[15] A. K. Pandey, A. K. Dubey, Intelligent Modeling of Laser Cutting of Thin Sheet, International Journal of Modeling and Optimization, Vol. 1(2011)107-112. [16] A. K. Pandey, A. K Dubey, Simultaneous optimization of multiple quality characteristics in laser cutting of titanium alloy sheet, Optics & Laser Technology, 44 (2012)1858–1865. [17] D.C. Montgomery, Design and analysis of experiments, John wiley and Sons hoboken, NJ, 2009. [18] M. S. Phadke, Quality engineering using robust design, Prentice-hall,NJ, 1989. [19] K. Deb , Optimization for engineering desgin. 8th ed. Prentice –hall , New Delhi, 2005. [20] R.V. Rao Advanced modeling and optimisation of manufacuring process. 1st ed. Springer, London, 2011. [21] R. N. Yadav, V. Yadava, G. K. Singh, Application of non-dominated sorting genetic algorithm for multi-objective optimization of electrical discharge diamond face grinding process, Journal of Mechanical Science and Technology, 28 (6) (2014) 2299 – 2306. [22] A.K. Pandey, A.K. Dubey, Modeling and Optimization of Kerf Taper in Pulsed Laser Cutting of Duralumin Sheet, (ASME-2012) International Manufacturing Science and Engineering Conference (MSEC2012), held at University of Notre Dame, Indiana, U.S.A, June 4-8, 2012, pp. 491-498.