Arabian Journal of Geosciences (2020) 13:532 https://doi.org/10.1007/s12517-020-05380-0 ORIGINAL PAPER Determination of appropriate cutting parameters depending on surface roughness by Taguchi method in milling of marbles Erkan Özkan 1 & Oğuzhan Öz 2 Received: 15 August 2019 / Accepted: 28 April 2020 # Saudi Society for Geosciences 2020 Abstract Determining cutting parameters in marble machining based on computer-controlled machine (CNC) is important for product quality. The aim of this study was to use the Taguchi experiment design method to select machining parameters to improve product surface quality in CNC milling of marbles. Experimental studies were conducted with a 6-mm-diameter cutting edge on six metamorphic rocks. Experiments were performed using the Taguchi experimental design method (L9 orthogonal array). The S/N (signal/noise) ratio based on “the lower the better” approach was calculated separately for each marble sample to determine appropriate machining parameters. Statistically significant and effective machining parameters were determined using variance analysis depending on the lowest roughness value. Results show that the parameters of depth and feed rate have the greatest effect on surface roughness in the machining of marbles. Keywords Marble . Taguchi . Milling . Roughness Introduction Marble has been produced in Turkey since the Neolithic era as it has the largest marble deposits in the world (Herz 1988). Diamond wire cutting and chain saw machines are used for block production in marble quarries (Özkan et al. 2015). Blocks from marble quarries and products (slabs, plates, tablets, etc.) cut with gang saw and S/T (block cutting machines with circular diamond blade) machines in marble factories are used to produce decorative products (sculptures, carvings, reliefs, frescoes, etc.) in CNC vertical machining centers. Marble is cut deep on the x and z axis (length × depth) to produce plates with block cutting machines. Differently, CNC cutting requires a small depth cut on the x, y, and z axis, and precise machining (length × width × depth) (Sarıışık and Özkan 2016, 2017). Responsible Editor: Murat Karakus * Erkan Özkan erkanozka@gmail.com 1 Faculty of Engineering, Department of Mining, Afyon Kocatepe University, 03200ANS Campus, Afyonkarahisar, Turkey 2 Afyonkarahisar, Turkey Milling is a basic machining process commonly used in the manufacturing industry, especially in metalworking (Altintas 1994; Lee and Lin 2000). Basic cutting parameters (cutting speed, feed rate, and depth parameters) affect the surface roughness of metal materials in CNC milling (Lou et al. 1998). The Taguchi experimental design method uses fewer experiments than full factorial test design to solve the effect of basic cutting parameters on surface roughness (Ghani et al. 2004). Many researchers have, therefore, used the Taguchi method in milling metals in order to minimize surface roughness depending on basic cutting parameters (Benardos and Vosniakos 2002; Fratila and Caizar 2011; Joshi and Kothiyal 2012; Ghani et al. 2004; Zhang et al. 2007; Maiyar et al. 2013; Kıvak 2014; Quintana and Ciurana 2011). In milling under ideal conditions, surface roughness is a function of basic cutting parameters and tool geometry. However, under real conditions, cutter and workpiece vibrations, machining vibrations, or chip adhesion (built-up edge) affect surface quality. Surface roughness defines the machined surface geometry and depends on the machining parameters and the surface texture. Surface roughness formation is very dynamic, complex, and process-dependent. Consequently, surface roughness directly affects design quality and production cost (Kline et al. 1982a; Kline et al. 1982b; Smith and Tlusty 1993; Alauddin et al. 1995; Benardos and Vosniakos 532 Table 1 Page 2 of 10 Arab J Geosci (2020) 13:532 Names and numbers of standards used in experiments Standard names EN Standard No. Determination of knoop hardness Determination of real density and apparent density, and of total open porosity Determination of unaxial compressive strength Determination of elemental composition by XRF Determination of water absorption at atmospheric pressure Determination of flexural strength under constant moment Determination of frost resistance Determination of abrasion resistance 14205:2003 (European Standards Institute (EN) 2003) 1936: 2006 (European Standards Institute (EN) 2006a) 1926: 2006 (European Standards Institute (EN) 2006b) 15309:2007 (European Standards Institute (EN) 2007) 13755:2008 (European Standards Institute (EN) 2008a) 13161: 2008 (European Standards Institute (EN) 2008b) 12371:2010 (European Standards Institute (EN) (EN) 2010) 14157 :2017 (European Standards Institute (EN) 2017) XRF X-ray fluorescence 2002; Benardos and Vosniakos 2003; Lamikiz et al. 2004; Wang et al. 2010; Quintana and Ciurana 2011). Studies have examined the cutting forces and specific energy parameters related to the machinability of marbles and limestones on CNC with diamond-coated inserts and carbide inserts (Polini and Turchetta 2004; Turchetta et al. 2009; Turchetta 2012; Sarıışık and Özkan 2016; Sarıışık and Özkan 2017; Sarıışık and Özkan 2018). There are, however, no studies examining the quality measurement (Gálos and Gyurika 2014), average chip rate (Gyurika and Szalay 2015), chip breaking (Gyurika 2018), and effect of cutting parameters on surface roughness (Gyurika and Szalay 2019) in CNC milling of granite edges, and effect of surface roughness on CNC milling parameters with carbide tools. Carbidecoated CNC milling is widely used in the natural stone industry. Wear in cutting tools changes the surface roughness of metals. Appropriate cutting parameters play a role in reducing cutting tool wear, achieving the desired surface roughness, and improving cutting performance. Energy consumption Table 2 and tool wear are two important factors that affect operating costs in the machining of metals (Benardos and Vosniakos 2003; Ghani et al. 2004; Quintana and Ciurana 2011). Our experimental studies showed that if carbide tools start to wear, they cannot cut marbles, and break. Due to different properties and grain sizes of metamorphic origin marbles, processing parameters change. The selection of machining parameters affects tool life. In the machining of marbles, sawdust is in the form of grain and is removed with water, which prolongs tool life. Homogeneous, crack-free, and monochrome marbles were used as samples to make sense of surface roughness results. Based on cutting parameters, a Taguchi test was designed and used to measure surface roughness values (Ra). Planners and natural stone manufacturing companies can use those cutting parameters for cost analysis and milling tool operation programs in marbles. This study suggests that manufacturers use the machining parameters that provide minimum surface roughness in CNC-machined marbles. Characteristics and petrographic definitions of samples used in experiments C crack, Po pore, F fossil. Geological rock-color chart (2009) (2020) 13:532 Arab J Geosci Page 3 of 10 532 M2 M3 M5 M4 Calcite Dolomite M6 M1 Fig. 1 Cross sections of samples. CAL, calcite; DOL, dolomite Table 3 Chemical characteristics of samples Natural rock Lol (%) Na2O (%) MgO (%) Al2O3 (%) SiO2 (%) P2O5 (%) SO3 (%) Cl (%) K2O (%) CaO (%) MnO (%) Fe2O3 (%) SrO (%) F (%) M1 M2 M3 M4 M5 M6 44.0 43.6 47.2 43.0 43.6 44.3 0.011 0.015 0.018 0.020 0.007 0.029 0.177 0.760 14.4 0.348 0.327 0.875 0.129 0.100 0.049 0.048 0.020 0.047 0.126 0.090 0.062 0.065 0.030 0.054 0.006 0.004 0.010 0.003 0.010 0.002 0.007 0.009 0.011 0.008 0.004 0.014 0.004 0.006 0.008 0.008 0.014 0.026 0.019 0.006 0.003 - 55.4 55.2 38.1 56.5 55.9 54.6 0,008 - 0.029 0.065 0.018 0.030 0.037 0.028 0.008 0.019 0.016 0.020 0.017 0.029 0.093 0.052 - Lol loss on ignition Table 4 Physical and mechanical properties of samples Natural rock AD (kg/m3) OP (%) WA (%) HK HS UCS (MPa) FS (MPa) AR (cm3/50 cm2) M1 M2 2686 2653 0.24 0.22 0.10 0.06 141.15 144.18 48.9 46.3 68.74 94.12 14.81 13.31 25.41 20.45 M3 M4 M5 M6 2673 2710 2650 2664 0.12 0.33 0.26 0.21 0.10 0.20 0.12 0.07 157.33 140.43 143.90 145.28 49.1 42.5 44.1 50.2 69.04 58.84 66.85 76.20 10.89 5.23 10.54 21.37 29.60 32.36 21.09 14.77 AD apparent density, OP open porosity, HK knoop hardness, HS shore hardness, WA water absorption, UCS uniaxial compressive strength, FS flexural strength, AR abrasion strength 532 Page 4 of 10 Arab J Geosci (2020) 13:532 Fig. 2 CNC stone milling machine (a general view, b Maltese cross system top view, and c Maltese cross system side view) In CNC machinability, the processing parameters as well as the crystal structures and grain dimensions of natural stones should be taken into account in order to achieve surface quality in natural stones. Taguchi method The Taguchi method is a statistical method that allows for selection of experimental design based on well-defined parameters in a working environment. This method is based on orthogonal array used to combine machining parameters that reduce and affect process variability. The greatest advantage of this method is that it performs a few experiments instead of all possible setting of experiments and therefore provides time and cost savings. S (signal value) is the actual value of the Table 5 system and N (noise factor) is the share of unwanted factors in the measured value. A series of statistics, referred to as the S/N ratio defining performance characteristics, are used in a Taguchi experimental design to reduce system variation. The S/N ratio approximates characteristic values to target values and ensures minimum deviation. The performance characteristic analysis in the S/N ratio has three categories: (1) Nominal is the best, (2) Larger is the better, and (3) Smaller is the better. The appropriate level of a process parameter for each of these categories is the level that results in the maximum value of the S/N ratio (Dehnad 1989; Taguchi et al. 2004; Roy 2010; Kıvak 2014). Cutting parameters were determined to use to minimize surface roughness. Equation 1 is used for calculations.   S 1 ¼ −10log ∑ni¼1 y2i ð1Þ N n Technical features of CNC marble vertical processing machine Technical feature Unit Value Spindle motor Number of axis Motor speed Processing speed Motor × axis feed speed Coolant Automatic number of teams kW Number rpm rpm mm/min l/min Number 9 4 24,000 24,000 80,000 3 8 Fig. 3 Milling tool for stone cutting (2020) 13:532 Arab J Geosci Table 6 Technical features of mill cutting tool Page 5 of 10 532 Technical feature Value Code Cutting tool diameter Stem diameter Cutting length End length MFR-6 6 mm 6 mm 25 mm 63 mm Milling end Edge number Helix angle 36,657 4 25° Table 8 Exp. No. The steps for selecting the appropriate parameter in the Taguchi experimental design are as follows: (1) defining performance characteristics and select machining parameters, (2) determining the number of levels for machining parameters and the possible interactions between machining parameters, (3) determining the orthogonal array and assign machining parameters to it, (4) conducting experiments based on orthogonal arrangement, (5) calculating total loss function and S/N ratio, (6) using the multiple-response S/N ratio and variance analysis (ANOVA) to analyze experimental results, and (7) selecting levels of appropriate machining parameters (Nalbant et al. 2007). T1 T2 T3 T4 T5 T6 T7 T8 T9 Experimental layout using an L9 orthogonal array Factor level A B C V f a 1 1 1 2 2 2 3 3 3 1 2 3 1 2 3 1 2 3 1 2 3 2 3 1 3 1 2 169 169 169 188 188 188 207 207 207 2000 2500 3000 2000 2500 3000 2000 2500 3000 1 2 3 2 3 1 3 1 2 at least 99.7% dolomite mineral consisting of 38.1% CaO and 14.4% MgO. Table 3 shows the chemical analysis of the samples. Shore hardness was carried out in the Accredited Natural Stone Analysis Laboratory (DAL) of the Mining Engineering Department of the Faculty of Engineering of Afyon Kocatepe Experimental methods Rocks used in experimental studies Six types (Afyon White, Bursa Kemalpasa White, Marmara White, Mugla White, Usak White, and Kutahya Gray) of polished metamorphic rock samples of 300 × 300 × 20 mm were used in the experiments. Table 1 presents the physicomechanical tests and standards of the samples. Table 2 shows the mineralogical and petrographical descriptions of the samples, while the grain sizes, textures, and minerals of the samples are shown in the thin sections in Fig. 1. Data were analyzed using X-ray fluorescence method. The samples were composed of at least 98.8% calcite minerals ranging from 54.60 to 56.50% with CaO. Marmara White is composed of Table 7 Factors and levels used in experiments Factor Cutting feed Feed rate Depth of cut Symbol V f a Unit m/min mm/min mm Code A B C Level 1 2 3 169 2000 1 188 2500 2 207 3000 3 Assigned factor value Fig. 4 Machining process plan 532 Page 6 of 10 Arab J Geosci (2020) 13:532 Fig. 5 Milling of samples and surface roughness measurements (a leveling of the surface, b surface treatment, c machined surface appearance, and d surface roughness measurement) University. Table 4 shows the physical and mechanical properties of the samples. Milling tests and surface roughness measurements Milling was performed at the CNC stone vertical machining center in the Laboratory of the Mining Engineering Department of the Engineering Faculty of Afyon Kocatepe University. Figure 2 and Table 5 show, respectively, the image and technical features of the CNC stone vertical machining center. Figure 3 and Table 6 show, respectively, the image and technical features of the carbide milling bit used in the machining experiments. A new carbide milling tool was used to level the marbles and process the marble samples. Table 9 V (m/min) 169 169 169 188 188 188 207 207 207 Alpham program was used in modeling and assigning machining parameters. The experimental study was designed in three dimensions as three squares of 40 × 40 mm on a marble of 300 × 300 × 20 mm. The machining parameters were 1, 2, and 3 mm of depths; 169, 188, and 207 m/min of cutting speeds; and 2000, 2500, and 3000 mm/min of feed rates. The Taguchi method was used to determine appropriate machining parameters. Cutting depth, cutting speed, and progress (control parameters) are designed at 3 different levels. Taguchi’s “smaller is the better” approach was used to appropriate the machining parameters of surface roughness. Table 7 shows the L9 orthogonal array of the Taguchi method. Table 8 shows the L9 orthogonal array applied according to the machining parameters. The Taguchi method uses the S/N ratio to analyze performance criteria. The objective of the S/N ratio is to determine Experimental results for Ra and S/N ratio f (m/min) 2000 2500 3000 2000 2500 3000 2000 2500 3000 a (m/min) 1 2 3 2 3 1 3 1 2 M1 M2 M3 M4 M5 M6 Ra S/N Ra S/N Ra S/N Ra S/N Ra S/N Ra S/N 6.10 7.79 7.86 8.62 11.69 8.72 8.70 9.20 8.92 − 15.70 − 17.83 − 17.91 − 18.71 − 21.35 − 18.81 − 18.79 − 19.28 − 19.01 6.01 5.77 5.85 5.60 5.76 5.55 6.29 6.57 5.96 − 15.58 − 15.23 − 15.34 − 14.96 − 15.22 − 14.88 − 15.98 − 16.35 − 15.50 3.65 3.54 3.74 4.12 4.25 4.32 4.65 4.54 4.91 − 11.26 − 10.98 − 11.45 − 12.30 − 12.56 − 12.71 − 13.35 − 13.14 − 13.82 6.90 6.44 6.34 7.06 7.14 6.44 7.50 7.46 6.92 − 16.77 − 16.18 − 16.04 − 16.98 − 17.07 − 16.17 − 17.50 − 17.46 − 16.81 4.84 5.53 5.57 5.93 6.24 6.81 6.66 7.30 6.82 − 13.70 − 14.86 − 14.92 − 15.46 − 15.90 − 16.66 − 16.47 − 17.26 − 16.68 6.15 5.83 6.09 6.79 7.66 6.98 7.39 7.34 7.43 − 15.78 − 15.32 − 15.70 − 16.64 − 17.69 − 16.88 − 17.38 − 17.31 − 17.42 Arab J Geosci Table 10 (2020) 13:532 Page 7 of 10 532 Response table mean S/N ratio for Ra factor M1 Level (Ra) 1 2 3 Delta Rank V (A) -18.50 -19.52 -19.36 0.87 3 Appropriate parameter A1:B1:C1 M3 Level (Ra) V (A) 1 -12.37 2 -12.37 3 -12.46 Delta 0.09 Rank 3 Appropriate parameter A1:B2:C1 M5 Level (Ra) V (A) 1 -15.88 2 -15.67 3 -15.77 Delta 0.21 Rank 3 Appropriate parameter A2:B1:C1 f (B) -18.30 -19.49 -18.58 1.19 2 a (C) -17.15 -19.63 -19.03 1.91 1 f (B) -12.31 -12.23 -12.67 0.44 2 a (C) -11.23 -12.53 -13.44 2.21 1 f (B) -15.22 -16.01 -16.09 0.88 2 a (C) -14.50 -16.01 -16.81 2.31 1 the appropriate parameter with minimum deviation. In this study, the S/N ratio was used to determine appropriate cutting parameters against minimum surface roughness. The closest cutting parameters for minimum surface roughness (smaller S/ N ratios and levels) were calculated using Eq. 1. In the first stage, surface leveling operations were performed. In the second stage, pocket milling was performed according to the machining parameters. In the third stage, surface leveling operations were performed on sections other than the already processed ones. Figure 4 presents the image of the machining steps. The three-parameter and three-level Taguchi experimental design yielded nine surfaces (L9 orthogonal array). The roughness of those surfaces was measured using a surface roughness measuring instrument (Mahr-Perthometer M2). The surfaces were divided into 4 equal squares and 36 measurements were made for each square. Figure 5 shows the images of the machining steps and surface roughness measurement. Results and discussion Tables 9 and 10 show the S/N ratios relative to each level of the machining parameters and the mean S/N response for Ra, respectively (Öz 2018). The greatest values in Tables 9 and 10 indicate the parameter levels with the lowest probability of variance to achieve the desired Ra values. The parameter with the highest delta value for M2 Level (Ra) 1 2 3 Delta Rank V (A) -15.61 -15.23 -15.52 0.38 2 Appropriate parameter A2:B3:C2 M4 Level (Ra) V (A) 1 -16.81 2 -16.66 3 -16.88 Delta 0.22 Rank 3 Appropriate parameter A2:B3:C1 M6 Level (Ra) V (A) 1 -16.66 2 -16.46 3 -16.93 Delta 0.46 Rank 2 Appropriate parameter A2: B3: C1 f (B) -15.51 -15.60 -15.25 0.36 3 a (C) -15,39 -15,03 -15,95 0,92 1 f (B) -17.09 -16.91 -16.35 0.74 2 a (C) -16.34 -16.75 -17.26 0.92 1 f (B) -16.60 -16.78 -16.67 0.18 3 a (C) -15.60 -17.08 -17.38 1.77 1 each level of samples has the greatest effect on roughness. Table 10 shows the rank of effect, indicating that the possible combination of parameters is A1:B1:C1 to obtain an Ra value for the sample M1. Figure 6 shows the Ra S/ N response graphs of the samples. The highest slopes in the graphs indicate the effectiveness levels of parameters. Describing the effects of parameters on quality characteristics more clearly and numerically allows us to select parameter levels more precisely. In this study, analysis of variance was used to determine parameter effectiveness rates. Table 11 shows the analysis results. In variance analysis, whether a parameter has an effect on response is determined by P (significance/probability) value. P < 0.05 (5% significance value) at the 95% level of confidence suggests the effect of the parameter on the response. The rightmost column of Table 10 shows the contribution (%) of each factor to total variation. Since F values in depth factor are greater than F0,05;2;8 = 4.46 in variance analysis based on F hypothesis, it has an effect on Ra surface roughness. The most effective parameter for Ra for the samples M2, M3, M5, and M6 is 72.48%, 94.29%, 80.39%, and 89.18% depth, respectively (Table 10). However, depth, cutting speed, and feed rate have an effect of 55.01%, 21.42%, and 22.96% in the sample M1, respectively. Depth and feed rate have an effect of 53.56% and 37.56% in the sample M4, respectively. Analysis of variance shows that cutting speed has the least effect on Ra roughness. 532 Page 8 of 10 M1 Data Means V M2 Data Means f V a f a -15,0 Mean of S/N ratios -17,5 Mean of S/N ratios (2020) 13:532 Arab J Geosci -18,0 -18,5 -19,0 -15,2 -15,4 -15,6 -15,8 -19,5 -16,0 169 188 207 2000 2500 3000 1 2 169 3 188 207 f a V -11,0 3000 1 2 3 f a -16,2 Mean of S/N ratios Mean of S/N ratios 2500 M4 Data Means M3 Data Means V 2000 -11,5 -12,0 -12,5 -13,0 -16,4 -16,6 -16,8 -17,0 -17,2 -13,5 169 188 207 2000 2500 3000 1 2 3 169 188 207 f a 3000 1 2 3 V f a -15,5 Mean of S/N ratios -14,5 Mean of S/N ratios 2500 M6 Data Means M5 Data Means V 2000 -15,0 -15,5 -16,0 -16,5 -17,0 -16,0 -16,5 -17,0 -17,5 169 188 207 2000 2500 3000 1 2 3 169 188 207 2000 2500 3000 1 2 3 Fig. 6 The graphic of mean of S/N ratios versus factor levels (Ra) Conclusion First, appropriate machining parameters were determined using the Taguchi experimental design method as a result of milling six types of marbles based on CNC parameters. Second, variance analysis was carried out to calculate the effects (%) of statistically significant machining parameters. Some results were obtained for sample marbles and CNC machine tool working conditions. As described in this article, Taguchi’s robust orthogonal array design method is suitable for analyzing the surface roughness problem of marbles. The Taguchi method is a systematic, simple, and efficient method that can be used to analyze surface roughness during milling and to find the most appropriate parameter with experimental design. The combination of the factorial design of 3 parameters and 3 levels required 27 experiments. However, the L9 Taguchi orthogonal array reduced it to 9. The preparation time required for Arab J Geosci Table 11 Ra V f a Error Total (2020) 13:532 Page 9 of 10 532 Results of the analysis of variance for Ra M1 M2 M3 M4 M5 M6 % Effect F % Effect F % Effect F % Effect F % Effect F % Effect F 21.42 22.96 55.01 0.61 100 35.49 38.05 91.18 13.29 11.15 72.48 3.08 100 4.30 3.60 23.45 0.21 4.2 94.29 1.29 100 0.15 3.23 72.64 3.18 37.56 53.56 5.70 100 0.55 6.58 9.39 0.65 13.51 80.39 5.45 100 0.11 2.47 14.74 5.46 0.82 89.18 4.54 100 0.17 1.20 19.64 appropriate parameter selection in CNC machining of marbles has been minimized and machining performance and product quality have been improved. According to the graphs of the mean S/N ratios, the appropriate parameter combinations for Ra are A1:B1:C1, A2:B3:C2, A1:B2:C1, A2:B3:C1, A2:B1:C1, and A2:B3:C1 for the samples M1, M2, M3, M4, M5, and M6, respectively. Analysis of variance was used to determine the effects of parameters on Ra. The results show that the most effective parameter for Ra for the samples M2, M3, M5, and M6 is 72.48%, 94.29%, 80.39%, and 89.18% depth, respectively. However, depth, cutting speed, and feed rate have an effect of 55.01%, 21.42%, and 22.96% in the sample M1, respectively. Depth and feed rate have an effect of 53.56% and 37.56% in the sample M4, respectively. Depth generally has an effect on surface quality. Low depth (1 mm) results in the best surface quality. Furthermore, the less the depth, the better the surface quality. The shape, clamping, and orientation of the M2 sample’s grains to each other are different compared with other samples. For this reason, better surface quality results were obtained at a depth of 2 mm. Marbles differ by surface roughness texture and grain size, and therefore, it is recommended that future studies use a larger database. 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