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Published Journal on Plasma Arc Cutting, Optimization

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Published Journal on Plasma Arc Cutting, Optimization

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- 1. ORIGINAL ARTICLE Effect of process parameters on cut quality of stainless steel of plasma arc cutting using hybrid approach K. P. Maity & Dilip Kumar Bagal Received: 10 August 2013 /Accepted: 27 October 2014 /Published online: 5 December 2014 # Springer-Verlag London 2014 Abstract An optimization concept of the various ma- chining parameters for the plasma arc cutting procedures on AISI 316 stainless steel conducting a hybrid optimi- zation method has been carried out. A new composition of response surface methodology and grey relational analysis coupled with principal component analysis has been proposed to evaluate and estimate the effect of machining parameters on the responses. The major re- sponses selected for these analyses are kerf, chamfer, dross, surface roughness and material removal rate, and the corresponding machining parameters concentrated for this study are feed rate, current, voltage and torch height. Thirty experiments were conducted on AISI 316 stainless steel workpiece materials based on a face- centered central composite design. The experimental results obtained are applied in grey relational analysis, and the weights of the responses were evaluated by the principal component analysis and further evaluated using response surface method. The results show that the grey relational grade was significantly affected by the machining parameters directly as well as with some interactions. This method is straightforward with easy operability, and the results have also been established by running confirmation tests. The premise attributes beneficial knowledge for managing the machining pa- rameters to enhance the preciseness of machined parts by plasma arc cutting. Keywords Grey relational grade . Plasma arc cutting . Principalcomponentanalysis .Responsesurfacemethodology Abbreviations AISI American Iron and Steel Institute CNC Computer numerical control HV Vickers hardness ANN Artificial neural network QstE High-strength steel grade Hardox Abrasion-resistant steel grade MRR Material removal rate SR Surface roughness Ra Central line average roughness EN European standard steel number ISO International Organization for Standardization LB Lower-the-better HB Higher-the-better NB Nominal-the-best P Probability value ANOVA Analysis of variance PAC Plasma arc cutting A Feed rate (mm/min) B Current (ampere) C Voltage (volt) D Torch height (mm) CCD Central composite design F Statistic test value Hα Hypothesis 3D Three-dimensional RSM Response surface methodology GRA Grey relational analysis PCA Principal component analysis Nomenclature L18 Orthogonal array of 18 runs L30 Orthogonal array of 30 runs K. P. Maity (*) :D. K. Bagal Department of Mechanical Engineering, NIT Rourkela, Rourkela 769008, Odisha, India e-mail: kpmaity@gmail.com D. K. Bagal e-mail: dilipbagal90@gmail.com Int J Adv Manuf Technol (2015) 78:161–175 DOI 10.1007/s00170-014-6552-6
- 2. Y Response Xi Singular term of input variable Xii Square term of input variable XiXj Interaction term of input variable βo Regression coefficient of constant term βi Regression coefficient of singular βii Regression coefficients of square βij Regression coefficients of interaction ϵ Regression error coefficient Xi*(k) Normalized value of the kth element kth Element number ith Sequence number X0b(k) Desired value max Xi*(k) Largest value of Xi(k) min Xi*(k) Smallest value of Xi(k) Xi(k) Sequence X0(k) Reference sequence ζ Distinguishing coefficient βk Weighting value of the kth performance Cov(xi(j)) Covariance of sequence σxi(j) Standard deviation of sequence xi(j) σxi(l) Standard deviation of sequence xi(l) λ Eigenvalue λk Eigenvalue Vik Eigenvector Ym1 First principal component Ym2 Second principal component 1 Introduction Modern industry depends on the manipulation of heavy metal and alloys. Different cutting methods are used to form into specified pieces for making infrastructure and machine tools. Plasma arc cutting was developed in the mid 1950s and was primarily used to cut stainless steel and aluminium alloys. Plasma is the fourth and the most highly energized state of matter. In fact, plasma looks and behaves like a high temper- ature gas but with a capability to conduct electricity [1]. The basic principle is that the arc formed between the electrode and the work piece is constricted by a fine bore, copper nozzle. This increases the temperature and velocity of the plasma emanating from the nozzle. The temperature of the plasma is in excess of 20,000 °C, and the velocity can approach the speed of sound. When used for cutting, the plasma gas flow is increased so that the deeply penetrating plasma jet cuts through the material and molten material is removed in the efflux plasma [2]. Plasma arc cutting involves a large number of process parameters. It requires optimization of the process parameters for smooth operation of plasma arc cutting process. A number of investigators have carried out the research in this direction [3]. Bhuvenesh et al. investigated the surface roughness and material removal rate of AISI-1017 mild steel using manual plasma arc cutting machining by Taguchi methodology [4]. They observed that the relationship between average material removal rate and average surface roughness is inversely pro- portional to each other. Kechagias and Billis modeled a para- metric design of computer numerical control (CNC)-con- trolled plasma arc cutting process of St. 37 carbon steel and AISI steel plates by using robust design of orthogonal array L18 (21 ×37 ) [5, 6]. Arc ampere is the most significant factor. The standoff distance is the most significant parameter. The plate thickness is the least significant parameter in plasma arc cutting process. Gullu and Atici investigated the consequence of plasma arc parameters on the structure variation of AISI-304 and St. 52 steel plates by Panasonic digital PRIOR optic microscope and Vicker hardness measurement device for heat affected zone and hardness, respectively. It was evident from the statistical analysis that the cutting speed was the most significant factor which affects the surface roughness [7]. After cutting, it is seen that hardness increases in the areas near the surface of part i.e. around 250–350 HVand decreases towards the core of the material [8]. Özek et al. performed a Fuzzy model for predicting surface roughness in plasma cutting of AISI-4140 steel plate [7]. Radovanovic and Madic modeled a parametric design of plasma arc cutting process by using ANN to predict surface roughness. It is observed that surface roughness in- creases with increase in cutting speed, but decreases with increase in cutting arc current. Good surface finish can be achieved in plasma arc cutting process of 8-mm thick plate when cutting current and cutting speeds are set nearer to their high and low level of the experimental range, respectively [9–11]. The proficiency of a manufacturing practice to produce a desired quality of cut and material removal rate depends on various parameters. The factors that bias output responses are machining parameters, tool and workpiece material properties and cutting conditions. Therefore, it is important for the re- searchers to model and appraise the relationship among roughness and the parameters affecting its value. The deter- mination of this correlation remains an open field of research, mainly on account of the advances in machining and material technology and the feasible modeling techniques. In machin- ability review investigations, statistical design of experiments is used quite extensively. Statistical design of experiments assign to the process of planning the experiments so that the adequate data can be examined by statistical methods, resulting in precise and objective conclusions [12]. Nemchinsky and Severance discussed the fundamentals of plasma arc cutting process with physical reasoning [13]. Salonitis and Vatousianos recently carried out an experimental investigation of the plasma arc cutting process [14]. Yun and Na carried out an experiment about the real time control of plasma arc cutting process by using 162 Int J Adv Manuf Technol (2015) 78:161–175
- 3. intensity measurements of ejected plasma gas. They observed that the amount of the attached dross substan- tially reduced by a simple controlled speed [15]. Zhang and Zhang gave the various aspects of keyhole through- out the plasma arc cutting process. Their experimental results revealed that once the keyhole is established, the width of the keyhole does not change with the changes in the welding current and the welding speed, but it does change with the changes in the flow rate of the plasma gas and the diameter of the orifice [16]. Xu et al. carried out an experiment to reduce the kerf width and to improve the kerf quality by using the hydro- magnetically confined plasma arc on engineering ceram- ic plates. They concluded that for a given diameter of nozzle, a high-quality cut can be produced by using a lower arc current than it is usually required in conven- tional plasma arc cutting process, while ensuring a fine arc shape and capability of cutting simply by employing hydro-magnetic constriction [17]. Asiabanpour et al. optimized the quality of 18 parts manufactured by the automated plasma cutting process by using response surface method and desirability func- tions. They concluded that the high value of current and pressure is necessary for quality cut due to plasma arc cutting process [18]. Similarly, Ferreira et al. optimized the input parameters of plasma arc cutting process using QstE-380 and Hardox 450 alloy steel plate by using response surface method. They observed that there is increase in cutting speed to 65 % from 35 % with reduction in cost around 28 % [19]. Hatala et al. de- scribed the effect of technological factors on roughness parameters Ra and heat-affected zone of the steel sur- face European Standard Steel Number (EN) Internation- al Organization for Standardization (ISO) S355 by using planned experiment and regression model analysis. They concluded that for achieving higher quality of cut sur- face, it is recommended to use higher pressures of plasma gas and appropriate feed rate of plasma torch. For getting lower heat-affected zone value, the cutting speed and power should be controlled [20]. It is evident from the literature review that most of the investigators have investigated material removal rate and surface roughness by simple Taguchi method and response surface method [21, 22]. In general, plasma arc cutting process involves a large number of response parameters. In the present investigation, a number of response parameters have been optimized with respect to the number of process parameters using response surface methodology combined with grey relational analysis and principal component analysis. The quality of cut and material removal rate is taken as the re- sponses [23]. The feed rate, current, voltage and torch height are acquired as the process parameters. 2 Experimental details The whole experiment of plasma arc cutting process is carried out by the MESSER Company built CNC plasma machine named as BURNY 1250, where the cutting process is con- ducted in Hypertherm environment. The parameters of oxy- gen supply, fuel gas supply and power supply are fixed at 20 MPa, 1.2 MPa and 400 VDC, respectively. The material of AISI 316 stainless steel is taken for experimentation whose thickness is 120 mm. The values of process parameters are given in Table 1. Feed rate, current, voltage and torch height are taken as the input process parameters. The quality of cut and material removal rate are measured as the major responses, and the corresponding data are tabulated in Appendix 1. Surface roughness is measured using Talysurf. Material removal rate is calculated by weight measurement. The value of dross and chamfer is calculated by the help of Vernier caliper and protractor. 3 Analysis method 3.1 Experimental design with response surface method As per Montgomery, response surface method is a collection of mathematical and statistical techniques that are helpful for modeling and analysis of problems in which response is influenced by several input variables, and the main objective is to find the correlation between the response and the vari- ables inspected [23]. Response surface method has many advantages and has effectively been applied to study and optimize the processes. It offers enormous information from a small number of experiments. In addition, it is possible to detect the interaction effect of the independent parameters on the response. The model easily clarifies the effect for binary combination of the independent process parameters. Further- more, the empirical model that related the response to the independent variables is used to obtain information. Accord- ing to Pradhan, it has been widely used in analyzing various processes, designing the experiment, building models, evalu- ating the effects of several factors and searching for optimum conditions to give desirable responses and reduce the number of experiments [24–26]. The experimental values are ana- lyzed, and the mathematical model is then developed that Table 1 Values of input process parameters Process parameters Units Code L (1) L (2) L (3) Feed rate mm/min A 920 945 970 Current A B 40.0 42.5 45.0 Voltage V C 100 120 140 Torch height mm D 2.0 2.5 3.0 Int J Adv Manuf Technol (2015) 78:161–175 163
- 4. illustrates the relationship between the process variable and response. The following second-order model explains the behavior of the system: Y ¼ β0 þ X i¼1 k βiXi þ X i¼1 k βiiX2 i þ X i;j¼1;i≠j k βijXiX j þ ∈ ð1Þ where Y is the corresponding response, Xi is the input variables and Xii and XiXj are the squares and interaction terms, respectively, of these input variables. The unknown regression coefficients are β0, βi, βij and βii, and the error in the model is depicted as ϵ [25]. The response surface method design of matrix form is given in Appendix 1. The output responses of plasma arc cutting as per response surface meth- od are given in Appendix 2. 3.2 Data preprocessing According to Fung, data preprocessing is the method of trans- ferring the original sequence to a comparable sequence, where the original data normalize to a range of 0 and 1 [28]. Gener- ally, three different kinds of data normalizations are carried out to render the data, whether the lower-the-better (LB), the higher-the-better (HB) or nominal-the-best (NB). For ‘higher- the-better’, characteristics such as productivity or material removal rate, the original sequence can be HB and should be normalized as follows [27]: Xi Ã kð Þ ¼ Xi kð Þ−minXi kð Þ maxXi kð Þ−minXi kð Þ ð2Þ However, if the expectancy is as small as possible for the quality of cut such as mean surface roughness, chamfer, dross and kerf, then the original sequence should be normalized as ‘lower-the-better’: Xi Ã kð Þ ¼ maxXi kð Þ−Xi kð Þ maxXi kð Þ−minXi kð Þ ð3Þ Conversely, if a specific target value is to be achieved, then the original sequence will be normalized by the following equation of NB: Xi Ã kð Þ ¼ 1− Xi kð Þ−minX0b kð Þj j maxXi kð Þ−X0b kð Þ ð4Þ where i=1,2,…,n; k=1,2,…,p; Xi*(k) is the normalized value of the kth element in the ith sequence; X0b(k) is the desired value of the kth quality characteristic; max Xi*(k) is the largest value of Xi(k); min Xi*(k) is the smallest value of Xi(k); n is the number of experiments; and p is the number of quality characteristics [28]. According to the type of characteristic, type of responses normalize the Appendix 2 as per above equation and the outcomes are tabulated in Appendix 3. As the responses are of LB and HB types, there is no use of Eq. (4) in the present calculation. 3.3 Grey relational coefficient and grey relational grade After normalizing the data, usually grey relational coefficient is calculated to display the relationship between the optimal and actual normalized experimental results. The grey relation- al coefficient can be expressed as [29–31]: γi kð Þ ¼ γ X0 kð Þð − Xi kð Þð Þ ¼ Δmin þ ζΔmax Δ0;i kð Þ þ ζΔmax i ¼ 1; 2; 3; …; n; k ¼ 1; 2; 3; …; p ð5Þ where is Δ0,i(k)=|X0(k)−Xi(k)| the difference of the abso- lute value called deviation sequence of the reference sequence X0(k) and comparability Xi(k). ζ is the distinguishing coeffi- cient or identification coefficient in which the value range is 0 ≤ ζ ≤1. In general, it is set to 0.5 as optimistic value in normal distribution; hence, same is adopted in this study. The aim of defining the grey relational coefficient is to express the rela- tional degree between the reference sequence X0(k) and the comparability sequences Xi(k), where i=1,2,…,m and k= 1,2,…,n with m=30 and n=3 in this study [32]. The computed deviation sequences of the normalized values are tabulated in Appendix 4. The grey relational grade is a weighting sum of the grey relational coefficients and it is defined as [31]: γ x0; xið Þ ¼ X k¼1 n βk x0; xið Þ ð6Þ where βk represents the weighting value of the kth perfor- mance characteristic and [32] Xk¼1 n βk ¼ 1 ð7Þ 3.4 Principal component analysis Principal component analysis is a mathematical approach that converts a set of observations of probably correlated variables into a set of values of uncorrelated variables. It was invented very early and later mostly used as a tool in investigative data analysis and for the formation of predictive models. Principal component analysis can be done by eigenvalue decomposition of a data covariance matrix or singular value decomposition of a data matrix. It is used for identifying patterns in data and expressing the data in such a way as to highlight their similarities and differences [33]. The main advantage of principal compo- nent analysis is that once the patterns in data have been identi- fied, the data can be compressed, i.e. by reducing the number of 164 Int J Adv Manuf Technol (2015) 78:161–175
- 5. dimensions, without much loss of information. The explicit goals of principal component analysis are the following: 1. To extract the most significant information from the data, 2. To squeeze the size of the data set by keeping only the significant, 3. To simplify the explanation of the data set, and 4. To analyze the structure of the observations and the variables. The procedure is described as follows [33]: 1. The original multiple quality characteristic array X ¼ x1 1ð Þ x1 2ð Þ … … x1 nð Þ x2 1ð Þ x2 2ð Þ … … x2 nð Þ : : … … : : : … … : xm 1ð Þ xm 2ð Þ … … xm nð Þ 2 6 6 6 6 4 3 7 7 7 7 5 ð8Þ i=1,2,…,m; j=1,2,…,n [34] where m is the number of experiment and n is the number of the response. In the present work, x is the grey relational coefficient of each response and m=30 and n=3. 2. Correlation coefficient array The correlation coefficient array is evaluated as follows: Rjl ¼ Cov xi jð Þ; xi lð Þð Þ σxi jð Þ Â σxi lð Þ j ¼ 1; 2; 3; …; m l ¼ 1; 2; 3; …; n ð9Þ where Cov(xi(j)), xi(l) is the covariance of se- quences xi(l) and xi(l), σxi(j) is the standard devia- tion of sequence xi(j) and σxi(l) is the standard deviation of sequence xi(l). 3. Determining the eigenvalues and eigenvectors The eigenvalues and eigenvectors are determined from the correlation coefficient array: R−λkImð ÞVik ¼ 0 ð10Þ where λ is the eigenvalue ∑ k¼1 n λk ¼ n; k ¼ 1; 2; 3; …; n and Vik=[ak1,ak2,ak3,…,akm]T is the eigenvectors cor- responding to the eigenvalue λk. The eigenvalues and its variation are shown in (Table 2 as per Eq. 10 ). 4. Principal components The uncorrelated principal component is formulated as: Ymk ¼ X i¼1 n xm ið Þ⋅Vik ð11Þ where Ym1 is called the first principal component, Ym2 is called the second principal component and so on. The principal components are aligned in descending order with respect to variance, and therefore, the first principal component Ym1 accounts for most variance in the data. The eigenvectors and its contributions are displayed in Appendix 5. By using Eq. 5, the grey relational coefficients are computed and the results are written in Appendix 6. The total average of the grey relational grade value for all the 30 experiments is computed and listed in Appendix 6. The optimization design is accom- plished relating to a single grey relational grade instead of complex multi-response characteristic. Fundamentally, the larger the grey relational grade, the better is the mul- tiple performance characteristics. Thus, the overall grey relational grade of each combination is ranked as per value [35–37]. The regression coefficient values, standard deviations, T values and probability (p) values are given in Appendix 7. Regression analysis is performed to find out the relationship between the input factors and the response grey relational grade. Here, 0.80 is the maximum value of overall grey relational grade, and hence, it is ranked as 1. The analysis of parameters is carried out by using analysis of variance (ANOVA), and the data are shown in (Table 3). Once the optimal level of the cutting parameters is recog- nized, which is acquired from the analysis, it is customary to validate the responses. The confirmation experiments are per- formed to assist the verification of the plasma arc cutting process at its optimum condition of input parameters. The results of the confirmation runs for the responses are tabulated in Appendix 3. The following equations of plasma arc cutting (PAC) output responses are given below: Mean material removal rate ¼ 6921:73 þ 0:0311833 Ã Feed Rate − 39:8295 Â Current − 2:71381 Â Voltage − 71:8525 Â Torch Height; ð12Þ Table 2 The eigenvalues and explained variation for principal components Principal components Eigenvalue Explained variations (%) First 1.31 26.20 Second 1.28 25.70 Third 1.00 20.00 Fourth 0.82 16.40 Fifth 0.59 12.70 Int J Adv Manuf Technol (2015) 78:161–175 165
- 6. Mean surface roughness ¼ 9:1349 þ 0:0503167 Â Feed Rate − 1:52617 Â Current− 0:171021 Â Voltage þ 4:2075 Â Torch Height; Chamfer ¼ 1:82142 − 0:00045 Â Feed Rate − 0:00683333 Â Current − 0:00139583 Â Voltage þ 0:220833 Â Torch Height; Dross ¼ 46:2527 − 0:0262 Ã Feed Rate − 0:381667 Â Current − 0:020625 Â Voltage þ 1:08833 Â Torch Height; Table 3 The ANOVA table *p≤0.05 Sources DF Seq. SS Adj. SS Adj. MS F P Percent contribution Regression 14 0.30 0.30 0.02 1.07 0.45 49.90 Linear 4 0.13 0.12 0.03 1.52 0.25 22.65 A 1 0.02 0.02 0.02 0.88 0.36 3.51 B 1 0.02 0.03 0.03 1.46 0.25 3.39 C 1 0.01 0.00 0.00 0.02 0.89 1.05 D 1 0.09 0.09 0.09 4.62 0.05* 14.70 Square 4 0.06 0.06 0.01 0.71 0.60 9.53 A×A 1 0.00 0.01 0.01 0.45 0.51 0.50 B×B 1 0.03 0.04 0.04 1.98 0.18 5.48 C×C 1 0.00 0.00 0.00 0.03 0.86 0.00 D×D 1 0.02 0.02 0.02 1.06 0.32 3.55 Interaction 6 0.11 0.11 0.02 0.88 0.53 17.71 A×B 1 0.01 0.01 0.01 0.34 0.57 1.12 A×C 1 0.00 0.00 0.00 0.04 0.84 0.15 A×D 1 0.09 0.09 0.09 4.53 0.05* 15.13 B×C 1 0.00 0.00 0.00 0.02 0.89 0.00 B×D 1 0.00 0.00 0.00 0.02 0.90 0.00 C×D 1 0.01 0.01 0.01 0.36 0.56 1.19 Residual error 15 0.30 0.30 0.02 5.10 Lack-of-fit 10 0.20 0.20 0.02 0.98 0.54 33.22 Pure error 5 0.10 0.10 0.02 16.89 Total 29 0.60 166 Int J Adv Manuf Technol (2015) 78:161–175 4%4% 1% 16% 1% 0% 17% 0% 0% 1% 56% % Contibution of parameters on overall grey grades FEED RATE CURRENT VOLTAGE TORCH HEIGHT FEED RATE*CURRENT FEED RATE*VOLTAGE FEED RATE*TORCH HEIGHT CURRENT*VOLTAGE CURRENT*TORCH HEIGHT VOLTAGE*TORCH HEIGHT Residual Error Fig. 1 3D pie chart of percentage contribution of input variables on overall grey relational grades ð13Þ ð14Þ ð15Þ
- 7. Int J Adv Manuf Technol (2015) 78:161–175 167 3210-1-2-3 99 95 90 80 70 60 50 40 30 20 10 5 1 Standardized Residual Percent Normal Probability Plot (response is Overall Grey Relational Grade) 0.70.60.50.40.3 2 1 0 -1 -2 Fitted Value StandardizedResidual Versus Fits (response is Overall Grey Relational Grade) (a) (b) 0.20.10.0-0.1-0.2 10 8 6 4 2 0 Standardized Residual Frequency Histogram (response is Overall Grey Relational Grade) 30282624222018161412108642 2 1 0 -1 -2 Observation Order StandardizedResidual Versus Order (response is Overall Grey Relational Grade) (c) (d) Fig. 2 Plot of residuals of overall grey relational grade 995970945920895 0.7 0.6 0.5 0.4 0.3 47.545.042.540.037.5 16014012010080 0.7 0.6 0.5 0.4 0.3 3.53.02.52.01.5 Feed Rate Mean Current Voltage Torch Height Main Effects Plot for Overall Grey Relational GradeFig. 3 Main effect plot of overall grey relational grade
- 8. Kerf ¼ 10:436 − 0:00596667 Â Feed Rate − 0:0693333 Â Current − 0:00075 Â Voltage þ 0:435 Â Torch Height; ð16Þ 4 Results and discussions Cutting the stainless steel plates is still more defying than that of other steel metals due to the difference in the physical, mechanical and metallurgical properties of the metals to be cut. Proper choice of mechanism and process variables are, 168 Int J Adv Manuf Technol (2015) 78:161–175 Feed Rate Current 990980970960950940930920910900 47 46 45 44 43 42 41 40 39 38 Voltage 120 Torch Height 2.5 Hold Values – – – 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.8 Grade Relational Grey Overall Contour Plot of Overall Grey Relational Grade vs Current, Feed Rate Feed Rate Voltage 990980970960950940930920910900 160 150 140 130 120 110 100 90 80 Current 42.5 Torch Height 2.5 Hold Values – – – – – – 0.450 0.450 0.475 0.475 0.500 0.500 0.525 0.525 0.550 0.550 0.575 0.575 0.600 0.600 Grade Relational Overall Grey Contour Plot of Overall Grey Relational Grade vs Voltage, Feed Rate (a) (b) Feed Rate TorchHeight 990980970960950940930920910900 3.5 3.0 2.5 2.0 1.5 Current 42.5 Voltage 120 Hold Values – – – – 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 1.0 1.0 Grade Relational Grey Overall Contour Plot of Overall Grey Relational vs Torch Height, Feed Rate Current Voltage 47464544434241403938 160 150 140 130 120 110 100 90 80 Feed Rate 945 Torch Height 2.5 Hold Values – – – – – 0.45 0.45 0.50 0.50 0.55 0.55 0.60 0.60 0.65 0.65 0.70 0.70 Grade Relational Overall Grey Contour Plot of Overall Grey Relational Grade vs Voltage, Current (c) (d) Current TorchHeight 47464544434241403938 3.5 3.0 2.5 2.0 1.5 Feed Rate 945 Voltage 120 Hold Values – – – – 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.8 0.9 0.9 Grade Relational Grey Overall Contour Plot of Overall Grey Relational Grade vs Torch Height, Current Voltage TorchHeight 1601501401301201101009080 3.5 3.0 2.5 2.0 1.5 Feed Rate 945 Current 42.5 Hold Values – – – 0.4 0.4 0.5 0.5 0.6 0.6 0.7 0.7 Grade Relational Grey Overall Contour Plot of Overall Grey Relational Grade vs Torch Height, Voltage (e) (f) Fig. 4 Contour plot of interaction terms vs. overall grey relational grade
- 9. therefore, obligatory to make the cuts with good quality. Therefore, plasma arc cutting of stainless steel metals has increasing demand due to the higher penetration rates and with the benefits of high cutting speed providing higher productivity. This paper demonstrated a bid for devel- opment of mathematical models of the plasma arc cut- ting process based on response surface methodology. Parameter design of response surface methodology be- ing simple and cheap is adopted for in-depth study to understand process parameters and their interaction ef- fects on responses like accuracy of dimensions in dif- ferent directions of PAC built parts with minimum ex- perimental runs [38]. To maintain a high production rate and admissible quality of cut devices, the machining process parameters of PAC must be optimized [39]. From the design of experiments and due to a broad range of input process parameters, the present work is contoured to four factors, three levels and an L30 orthogonal array design matrix to simplify the present dilemma. In this present study, 30 experiments are carried out based on response surface method with a face-centered central composite design (CCD). Here, the MINITAB version 16 software is used to optimize the experimental data, and this software is a well- efficient statistical tool which helps to analyze the influence of input parameters on output responses of whole experimental design. Int J Adv Manuf Technol (2015) 78:161–175 169 48 440.4 0.6 40900 0.8 950 1000 Current GRG Feed Rate Voltage 120 Torch Height 2.5 Hold Values Surface Plot of Overall GRG vs Current, Feed Rate 1600.45 120 0.50 0.55 900 0.60 80950 1000 GRG Voltage Feed Rate Current 42.5 Torch Height 2.5 Hold Values Surface Plot of Overall GRG vs Voltage, Feed Rate 3.6 3.0 0.3 2.4 0.6 90 0.9 1.8 950 1000 GRG Torch Height Feed Rate Current 42.5 Voltage 120 Hold Values Surface Plot of Overall GRG vs Torch Height, Feed Rate 160 120 0.5 0.6 40 0.7 8044 48 GRG Voltage Current Feed Rate 945 Torch Height 2.5 Hold Values Surface Plot of Overall GRG vs Voltage, Current (a) (b) (c) (d) (e) (f) 3.6 3.00.4 2.4 0.6 0.8 40 1.8 44 48 GRG Torch Height Current Feed Rate 945 Voltage 120 Hold Values Surface Plot of Overall GRG vs Torch Height, Current 3.6 3.00.4 2.4 0.5 0.6 80 0.7 1.8120 160 GRG Torch Height Voltage Feed Rate 945 Current 42.5 Hold Values Surface Plot of Overall GRG vs Torch Height, Voltage Fig. 5 Surface plot of interaction terms vs. overall grey relational grade
- 10. The regression analysis is carried out to inspect how much is the goodness of relationship in between process variables and the overall grey relational grade in the experiment. From Appendix 7, it can be concluded that the torch height and the interaction of feed rate and torch height are the most influenc- ing character as the P value comes 0.05. The ANOVA analysis is applied to test the adequacy of the design by observing the P value for the F statistic under the 95 % confidence interval. According to the null hypothesis, if the value of P is less than or equal to 0.05, then it is concluded that the Hα is very much exact and the treatments have statistically significant effect on experiment. From the last column of Appendix 2, it is seen that the torch height is the most significant term due to its maximum percentage contribution, i.e. 14.70 % followed by feed rate with 3.51 % and current and voltage with 3.39 and 1.05 %, respectively. Similarly, analysis is carried out to determine the percentage contribution of the square and the interaction terms of input process parameters from this table. Again, from this column of Appendix 7, it can be predicted that the residual error of experiment has only 5.10 % contri- bution to the experiment. Then, the percentage of contribution of lack-of-fit and pure error is listed as 33.22 and 16.89 %, respectively, which shows the deficiency in fitting the data. From the 3D pie chart of Fig. 1, it is indicated that the torch height has the highest impact on experimental results. The residual plots of input variable of plasma arc cutting process have been plotted in Fig. 3. From Fig. 2a of normal probability plot, it can be understood that all the data follow a normal distribution as all the points were placed near the straight line. It can be seen that the process parameters of plasma arc cutting pro- cess have a fruitful significance on experiment as there is a large angled slope of straight line in the graph. The fitted value vs. standardized residual of overall grey relational grade is plotted in Fig. 2b where a random distribution is observed for the model. Here, the stan- dardized residual distribution pursues that the indepen- dent patterns are normally placed on each side of the reference line. Now, from the histogram plot of stan- dardized residuals in Fig. 2c, it is inferred that all the columns are performed in a normal distribution with its mean and standard deviation. Figure 2d shows that the plot in between the observed run order and the stan- dardized residuals in which it can be visually under- stood that the maximum and minimum influence of process parameters on responses occurred at the 17th and 25th run order, respectively. The main effect plot of overall grey relational grade is presented in Fig. 3. This obtains the optimal para- metric setting of process parameters in plasma arc cut- ting machining operation. From the main effect plot, it is concluded that the optimistic overall grey relational grade can be achieved with feed rate=970 mm/min, current=47.5 A, voltage=140 V and torch height= 1.5 mm respectively. The counter plots of interaction terms at their average level vs. overall grey relational grade are found in Fig. 4. Mainly, the shapes of counter plots might be elliptical or saddle form which indicates that the combination of each variable is significant except voltage vs. current plot be- cause of the lowest value of overall grey relational grade obtained in the middle region of current, which can be seen in Fig. 4d. Similarly, the 3D surface plot of the abovementioned inter- action terms can be exerted in Fig. 5. It is to be noted that all other terms are taken into account at their average value. Finally, the confirmation test has been carried out at the optimum condition of plasma arc cutting process parameters which is to confirm the feasibility of the correct optimal setting on responses of the experiment. The outcomes of the confirmation test for the mean material removal rate and the quality of cut values are computed in Table 4. Here, the distance between nozzle of torch and workpiece is the crucial factor in this experiment. From the ANOVA analysis, it is evident that the interaction of feed rate and torch height is also influenced to the abovementioned outputs. From the above descriptive analysis, evidently, the best design is becoming one primary challenge of technology market. In this paper, the optimal values of process parameters have been numerically found out using the quadratic model of response surface methodology (RSM). Since time and cost are comprised while operating the experimental runs, it is relevant to reduce the number of runs while not compromising the desired goals [40]. 5 Conclusion This paper furnishes the findings of an experimental investigation into the effect of feed rate, current, voltage Table 4 Conformation results for mean material removal rate and the quality of cut Best combination Experimental value Predicted value Mean MRR (mm2 /min) Mean SR (μm) Chamfer (mm) Dross (mm2 ) Kerf (mm) Mean MRR (mm2 /min) Mean SR (μm) Chamfer (mm) Dross (mm2 ) Kerf (mm) A B C D 970 47.50 140 1.5 3987.47 62.94 1.48 1.72 1.95 4572.4 32.18 1.20 1.45 1.90 170 Int J Adv Manuf Technol (2015) 78:161–175
- 11. and torch height on the characteristic of cut when ma- chining AISI 316 stainless steel by plasma. The specific problems of PAC have been analyzed. Response surface method coupled with grey relational analysis and prin- cipal component analysis has been carried out to opti- mize plasma arc cutting processes with multi-objective criteria. The best possible optimum conditions of this process are the following: 970 mm/min of feed rate, 47.5 A of current, 140 V of voltage and 1.5 mm of torch height. Torch height as well as interaction of torch height with feed rate is the most influencing parameters in plasma arc cutting machining. The shortened quadrat- ic models developed using the combinatorial plea of RSM and grey relational analysis (GRA) with principal component analysis (PCA) were reasonably accurate and can be used for prediction within the limits of the factors investigated. Appendix 1 Appendix 2 Table 6 Output responses of plasma arc cutting process Run order Mean material removal rate Mean surface roughness Chamfer Dross Kerf 1 4891.10 58.16 1.83 3.63 2.73 2 3992.62 46.49 1.01 0.80 3.44 3 5541.59 51.81 1.52 9.57 2.64 4 4494.18 25.82 1.42 4.26 2.70 5 5497.43 71.42 1.88 8.26 3.53 6 5082.01 41.88 1.00 7.00 3.30 7 3842.59 62.86 1.05 4.29 2.38 8 4865.14 69.52 1.64 7.63 3.41 9 5345.53 51.13 1.52 8.52 2.61 10 5678.41 32.08 1.83 0.45 2.73 11 3061.77 37.48 1.24 3.00 3.48 12 3929.05 63.29 1.47 1.74 1.93 13 3905.86 72.62 1.58 4.56 2.39 14 5670.24 52.73 1.05 5.25 2.63 15 3489.34 35.60 1.62 2.73 3.73 16 4995.12 63.60 1.10 6.34 2.53 17 5427.69 34.60 1.53 1.74 3.58 18 4223.34 56.61 1.08 6.43 2.65 19 4854.34 71.30 1.63 3.83 3.41 20 5030.29 54.97 1.38 5.27 2.64 21 4072.35 62.76 1.97 8.57 2.34 22 5448.16 34.18 1.68 4.56 2.57 23 4402.74 43.74 1.47 8.43 2.62 24 5470.08 52.35 1.64 9.03 3.73 25 4415.95 66.97 1.78 5.89 2.93 26 5520.10 26.57 1.93 8.52 2.28 27 4649.92 45.13 1.43 3.67 2.04 28 3805.88 44.59 1.67 7.27 3.16 29 5453.33 63.04 1.24 5.79 2.27 30 5538.55 61.25 1.52 8.53 3.07 Table 5 Response surface method design with input parameters Std. order Run order Feed rate Current Voltage Torch height 18 1 945 42.5 120 2.5 7 2 920 45.0 140 2.0 20 3 945 42.5 120 2.5 3 4 920 45.0 100 2.0 9 5 920 40.0 100 3.0 5 6 920 40.0 140 2.0 2 7 970 40.0 100 2.0 11 8 920 45.0 100 3.0 19 9 945 42.5 120 2.5 4 10 970 45.0 100 2.0 17 11 945 42.5 120 2.5 8 12 970 45.0 140 2.0 13 13 920 40.0 140 3.0 16 14 970 45.0 140 3.0 15 15 920 45.0 140 3.0 12 16 970 45.0 100 3.0 14 17 970 40.0 140 3.0 6 18 970 40.0 140 2.0 10 19 970 40.0 100 3.0 1 20 920 40.0 100 2.0 29 21 945 42.5 120 2.5 30 22 945 42.5 120 2.5 25 23 945 42.5 80 2.5 23 24 945 37.5 120 2.5 Table 5 (continued) Std. order Run order Feed rate Current Voltage Torch height 22 25 995 42.5 120 2.5 26 26 945 42.5 160 2.5 24 27 945 47.5 120 2.5 28 28 945 42.5 120 3.5 27 29 945 42.5 120 1.5 21 30 895 42.5 120 2.5 Int J Adv Manuf Technol (2015) 78:161–175 171
- 12. Appendix 3 Appendix 4 Table 7 Normalized values for mean material removal rate and the quality of cut Run order Mean material removal rate Mean surface roughness Chamfer Dross Kerf 1 0.70 0.31 0.15 0.65 0.56 2 0.36 0.56 1.00 0.96 0.16 3 0.95 0.44 0.46 0.00 0.61 4 0.55 1.00 0.57 0.58 0.58 5 0.93 0.03 0.09 0.14 0.11 6 0.77 0.66 1.00 0.28 0.24 7 0.30 0.21 0.95 0.58 0.75 8 0.69 0.07 0.34 0.21 0.18 9 0.87 0.46 0.46 0.12 0.63 10 1.00 0.87 0.15 1.00 0.56 11 0.00 0.75 0.76 0.72 0.14 12 0.33 0.20 0.52 0.86 1.00 13 0.32 0.00 0.41 0.55 0.74 14 1.00 0.42 0.95 0.47 0.61 15 0.16 0.79 0.36 0.75 0.00 16 0.74 0.19 0.90 0.35 0.67 17 0.90 0.81 0.46 0.86 0.08 18 0.44 0.34 0.92 0.34 0.60 19 0.69 0.03 0.36 0.63 0.18 20 0.75 0.38 0.61 0.47 0.61 21 0.39 0.21 0.00 0.11 0.77 22 0.91 0.82 0.30 0.55 0.64 23 0.51 0.62 0.52 0.13 0.62 24 0.92 0.43 0.34 0.06 0.00 25 0.52 0.12 0.20 0.40 0.45 26 0.94 0.98 0.05 0.11 0.81 27 0.61 0.59 0.56 0.65 0.94 28 0.28 0.60 0.31 0.25 0.31 29 0.91 0.20 0.75 0.41 0.81 30 0.95 0.24 0.47 0.11 0.37 Table 8 The deviation sequences for mean material removal rate and the quality of cut Run order Mean material removal rate Mean surface roughness Chamfer Dross Kerf 1 0.30 0.69 0.85 0.35 0.44 2 0.64 0.44 0.00 0.04 0.84 3 0.05 0.56 0.54 1.00 0.39 4 0.45 0.00 0.43 0.42 0.42 5 0.07 0.97 0.91 0.86 0.89 6 0.23 0.34 0.00 0.72 0.76 7 0.70 0.79 0.05 0.42 0.25 8 0.31 0.93 0.66 0.79 0.82 9 0.13 0.54 0.54 0.88 0.37 10 0.00 0.13 0.85 0.00 0.44 11 1.00 0.25 0.24 0.28 0.86 12 0.67 0.80 0.48 0.14 0.00 13 0.68 1.00 0.59 0.45 0.26 14 0.00 0.58 0.05 0.53 0.39 15 0.84 0.21 0.64 0.25 1.00 16 0.26 0.81 0.10 0.65 0.33 17 0.10 0.19 0.54 0.14 0.92 18 0.56 0.66 0.08 0.66 0.40 19 0.31 0.97 0.64 0.37 0.82 20 0.25 0.62 0.39 0.53 0.39 21 0.61 0.79 1.00 0.89 0.23 22 0.09 0.18 0.70 0.45 0.36 23 0.49 0.38 0.48 0.87 0.38 24 0.08 0.57 0.66 0.94 1.00 25 0.48 0.88 0.80 0.60 0.55 26 0.06 0.02 0.95 0.89 0.19 27 0.39 0.41 0.44 0.35 0.06 28 0.72 0.40 0.69 0.75 0.69 29 0.09 0.80 0.25 0.59 0.19 30 0.05 0.76 0.53 0.89 0.63 172 Int J Adv Manuf Technol (2015) 78:161–175
- 13. Appendix 5 Appendix 6 Table 9 The eigenvectors for principal components and contribution Outputs Eigenvectors Principal component analysis (1) Principal component analysis (2) Principal component analysis (3) Principal component analysis (4) Principal component analysis (5) % Mean material removal rate −0.59 0.27 0.05 0.67 −0.34 35 Mean surface roughness 0.04 0.76 −0.11 0.06 0.63 00 Chamfer 0.53 −0.23 0.41 0.66 0.25 29 Dross 0.58 0.49 −0.07 −0.01 −0.65 33 Kerf 0.16 −0.22 −0.90 0.33 0.07 03 Table 10 Grey relational coefficient, grey relational grade and rank of the mean material removal rate and the quality of cut Sl. no. Grey relational coefficient Overall grey relational grade Rank Material removal rate Surface roughness Chamfer Dross Kerf 1 0.62 0.42 0.37 0.59 0.53 0.53 16 2 0.44 0.53 0.99 0.93 0.37 0.74 4 3 0.91 0.47 0.48 0.33 0.56 0.49 19 4 0.52 1.00 0.54 0.54 0.54 0.57 13 5 0.88 0.34 0.36 0.37 0.36 0.41 26 6 0.69 0.59 1.00 0.41 0.40 0.66 6 7 0.42 0.39 0.91 0.54 0.67 0.59 11 8 0.62 0.35 0.43 0.39 0.38 0.42 23 9 0.80 0.48 0.48 0.36 0.57 0.50 18 10 1.00 0.79 0.37 1.00 0.53 0.75 2 11 0.33 0.67 0.68 0.64 0.37 0.46 20 12 0.43 0.38 0.51 0.78 1.00 0.58 12 13 0.42 0.33 0.46 0.53 0.66 0.43 22 14 0.99 0.47 0.90 0.49 0.56 0.80 1 15 0.37 0.71 0.44 0.67 0.33 0.41 24 16 0.66 0.38 0.84 0.44 0.60 0.66 7 17 0.84 0.73 0.48 0.78 0.35 0.74 3 18 0.47 0.43 0.86 0.43 0.56 0.55 15 19 0.61 0.34 0.44 0.57 0.38 0.56 14 20 0.67 0.45 0.56 0.49 0.56 0.62 9 21 0.45 0.39 0.33 0.36 0.69 0.20 30 22 0.85 0.74 0.42 0.53 0.58 0.61 10 23 0.51 0.57 0.51 0.36 0.57 0.39 27 24 0.86 0.47 0.43 0.35 0.33 0.45 21 25 0.51 0.36 0.38 0.46 0.47 0.39 28 Int J Adv Manuf Technol (2015) 78:161–175 173
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