Taguchi based Grey Relational Analysis to Optimize Face Milling Process with Multiple Performance Characteristics.

Transcription

1 Taguchi based Grey Relational Analysis to Optimize Face Milling Process with Multiple Performance Characteristics. Sadasiva Rao T., Rajesh V., *Venu Gopal A Abstract Inconel 718, a high strength, thermal resistant Nickelbased alloy, is mainly used in the aircraft industries. Due to extreme toughness and work hardening characteristic of the alloy, the problem of machining Inconel 718 is one of the ever-increasing magnitudes. The present work is focused to study the effect of process parameters such as speed, feed, depth of cut and approach angle of the cutter on cutting force, tool life and surface roughness in face milling of Inconel 718. The experiments were designed based on L 9 orthogonal array and carried out under dry conditions. Cutting force, Tool wear and surface roughness were recorded for each experiment. Grey relational analysis is used to optimize the multi performance characteristics to minimize the cutting force and surface roughness and maximize the tool life criteria. The feed was identified as the most influential process parameter on cutting force and surface roughness. Cutting speed is identified as the most influential process parameter on tool life. Keywords - ANOVA, Face milling, Grey Relational analysis, Taguchi method. I. INTRODUCTION NCONEL 718 is a nickel based super alloy which is widely I used in aerospace industry due to their exceptional thermal resistance and ability to retain mechanical properties at elevated service temperatures over 700 C [1]. However a high nickel alloy is difficult-to-cut material due to their high shear strength, work hardening ability, highly carbide particles in the micro-structure, strong tendency to weld and form built up edge and low thermal conductivity [2]-[3]. Furthermore, its low thermal conductivity results in heat concentration in the cutting edge [4]. The difficulty of machining Inconel 718 results into shorter tool life and severe surface abuse of machined surfaces [5]. A study was carried out using coated carbide inserts and ceramic inserts, it was found that coated cemented carbide inserts performed best at low speeds and federate. The ceramic insert was unsuitable for machining Inconel 718 as tool life was less than one and a half minutes for all the cutting conditions tested [6]. Sadasiva Rao Talasila., Assistant Professor is with Mechanical Engineering Department, National Institute of Technology, Warangal, INDIA. ( sadasiv@nitw.ac.in). Rajesh Valusa, was with Mechanical Engineering Department, National Institute of Technology, Warangal, INDIA. Venugopal Anne, Associate Professor is with Mechanical Engineering Department, National Institute of Technology, Warangal, INDIA. (Phone: ; Fax: , venu@nitw.ac.in). The emphasis of the previous work on the Machinability of Inconel 718 was mainly carried out considering process parameters like speed, feed and depth of cut but not much of the research is done in the area of face milling using approach angle of the cutter as the process parameter. The present work outlines the effect of approach angle along with speed, feed and depth of cut on tool life, cutting forces and surface finish produced. II. GREY RELATIONAL ANALYSIS Grey relational analysis was proposed by Deng in 1989 as cited in [10] is widely used for measuring the degree of relationship between sequences by grey relational grade. Grey relational analysis is applied by several researchers to optimize control parameters having multi-responses through grey relational grade [11]. The use of Taguchi method with grey relational analysis to optimize the face milling operations with multiple performance characteristics includes the following steps: 1. Identify the performance characteristics and cutting parameters to be evaluated. 2. Determine the number of levels for the process parameters. 3. Select the appropriate orthogonal array and assign the cutting parameters to the orthogonal array. 4. Conduct the experiments based on the arrangement of the orthogonal array. 5. Normalize the experiment results of cutting force, tool life and surface roughness. 6. Perform the grey relational generating and calculate the grey relational coefficient. 7. Calculate the grey relational grade by averaging the grey relational coefficient. 8. Analyze the experimental results using the grey relational grade and statistical ANOVA. 9. Select the optimal levels of cutting parameters. 10. Verify the optimal cutting parameters through the confirmation experiment. A. Data Pre-Processing In grey relational analysis, the data pre-processing is the first step performed to normalize the random grey data with different measurement units to transform them to dimensionless parameters. Thus, data pre-processing converts the original sequences to a set of comparable sequences. Different methods are employed to pre-process grey data 166

2 depending upon the quality characteristics of the original data. The original reference sequence and pre-processed data (comparability sequence) are represented by xx 0 (0) (kk) and xx ii (0) (kk), i =1,2,.,m; k =1,2,...,n respectively, where m is the number of experiments and n is the total number of observations of data. Depending upon the quality characteristics, the three main categories for normalizing the original sequence are identified as follows: If the original sequence data has quality characteristic as larger-the-better then the original data is pre-processed as larger-the-best : xx ii (kk) = x (0) i min x (0) i min x (0) i If the original data has the quality characteristic as smallerthe better, then original data is pre-processed as smaller-thebest : xx ii (kk) = x (0) i min x (0) i However, if the original data has a target optimum value (OV) then quality characteristic is nominal-the-better and the original data is pre-processed as nominal-the-better : xx xx (0) ii (kk) = 1 ii (kk) OOOO max{max xx (0) ii (kk) OOOO, OOOO mmmmmmxx (0) ii (kk)} Also, the original sequence is normalized by a simple method in which all the values of the sequence are divided by the first value of the sequence. xx ii (kk) = xx (0) ii (kk) xx (0) ii (1) where max xx ii (0) (kk) and min xx ii (0) (kk) are the maximum and minimum values respectively of the original sequencexx ii (0) (kk). Comparable sequence xx ii (kk) is the normalized sequence of original data. B.Grey Relation Grade Next step is the calculation of deviation sequence, oooo(kk) from the reference sequence of pre-processes data xx ii (kk) and the comparability sequence xx ii (kk). The grey relational coefficient is calculated from the deviation sequence using the following relation: γγ xx 0 (kk), xx min + ξξ mmmmmm ii (kk) = oooo(kk) + ξξδmmmmmm 0 < γγ xx 0 (kk), xx ii (kk) 1 (5) where oooo(kk) is the deviation sequence of the reference sequence xx 0 (kk) and comparability sequencexx ii (kk). oooo(kk) = xx 0 (kk) xx ii (kk) Δmmmmmm = mmmmmm mmmmmm xx j i k 0 (kk) xx ii (kk) ; mmmmmm = mmmmmm mmmmmm j i k xx 0 (kk) xx ii (kk) ξξis the distinguishing coefficient ξξ [0,1]. The distinguishing coefficient (ξξ) value is chosen to be 0.5. A grey relational grade is the weighted average of the grey relational coefficient and is defined as follows: (1) (2) (3) (4) nn γγ(xx 0, xx ii ) = ββββββ( xx 0 (kk), xx ii (kk), ββββ = 1 (6) kk=1 The grey relational grade γγ(xx 0, xx ii ) represents the degree of correlation between the reference and comparability sequences. If two sequences are identical, then grey relational grade value equals unity. The grey relational grade implies that the degree of influence related between the comparability sequence and the reference sequence. In case, if a particular comparability sequence has more influence on the reference sequence than the other ones, the grey relational grade for comparability and reference sequence will exceed that for the other grey relational grades. Hence, grey relational grade is an accurate measurement of the absolute difference in data between sequences and can be applied to appropriate the correlation between sequences. III. EXPERIMENTAL DETAILS AND RESULTS All experiments have been carried out in dry conditions on three axis vertical milling machine tool of Bharat Fritz Werner Ltd. The workpiece material used was Inconel 718. The dimension of the workpiece was 100 mm 90 mm 75 mm. The chemical composition and mechanical properties of Inconel 718 are shown in Table I and II respectively. TABLE I CHEMICAL COMPOSITION OF INCONEL 718 Element C Si Mn Ti Co Cr Fe Mo Nb Al Ni Wt (%) nn kk=1 TABLE II MECHANICAL PROPERTIES OF INCONEL 718 Property Value Tensile strength (MPa) 1310 Yield strength (MPa) 1110 Elastic modulus (GPa) 206 Hardness (HRC) 38 Density (g/cm 3 ) 8.19 Thermal conductivity(w/m K) 11.4 The cutting inserts used in the machining test was Widia SPMW TN 7535 and the cutter used was a Widia M400 face milling cutter of diameter 150 mm. The insert has three layers of CVD coatings TiN-TiCN-Al 2 O 3 on a substrate of cemented carbide. The top coating of TiN decreases a friction coefficient between the chip and the tool. Al 2 O 3 coating in the middle layer is for adhesion resistance while TiCN is coating for abrasion resistance. Three cartridges have been designed for M400 milling cutter for different approach angles and single tip seat design. The axial rake angle -6º and radial rake angle -8º are used for design. These two angles are provided on the tip seat of the cartridge. The design is carried for all the cartridges by maintaining the same axial and radial rake angle and only the approach angle is varied. In full factorial design, the number of experimental runs exponentially increases with the increase in the number of 167

3 factors as well as their levels. This results in huge experimentation cost and considerable time period [11].So, in order to compromise these two adverse factors and to search for the optimal process condition through a limited number of experimental runs Taguchi s L9 orthogonal array consisting of 9 sets of data was selected to optimize the multiple performance characteristics of the face milling. Experiments were conducted with the process parameters as given in Table III. TABLE III EXPERIMENTAL FACTORS AND THEIR LEVELS Symbol Cutting parameters Unit Level 1 Level 2 Level 3 A Cutting speed m/min B Feed rate mm/rev C Depth of cut mm D Approach Angle Degrees Selected design matrix shown in Table III based on the Taguchi L9 orthogonal array consisting of 9 sets of coded conditions and the experimental results for the responses of cutting force (F), tool life (TL) and surface roughness (Ra). All these data are used for the analysis and evaluation of the optimal parameters combination. TABLE IV ORTHOGONAL ARRAY L 9 (3 4 ) OF THE EXPERIMENTAL RUNS AND RESULTS Parameter level Experimental Results F TL Run No R (N) a (µm) (Min) The response variables measured were cutting force, tool life and surface roughness. Kistler Dynamometer type 9272 is used to measure the cutting force during face milling operation. The signals of the forces generated during the machining were fed into the Kistler 5070 multichannel charge amplifier connected to the dynamometer and a data acquisition system after each pass. Handy surf (E-35 A) is used to measure average surface roughness with 0.8 mm as cut-off length. Tool wear is measured by using Mitutoyo Toolmaker s Microscope TM-500 with a magnification of 15x fitted with digital micrometer XY table with the resolution of mm. The Tools were examined at regular intervals of cutting time until the tool failed. Tool rejection criteria 0.35mm flank wear was used in accordance with ISO standard 3685 for tool life testing [12]. IV. ANALYSIS OF RESULTS A. Best experimental run The experimental results for cutting force (F), Tool life (TL) and surface roughness (R a ) are listed in the Table IV. Typically, smaller values of F, R a and larger values of T are desirable. Thus the data sequences have the smaller-the-better characteristic, the smaller-the-better methodology, i.e. Equation (2), was employed for data pre-processing. The values of the F, T and Ra are set to be the reference (0) sequence xx 0, k =1 3.Moreover, the results of nine experiments were the comparability sequences xx (0) ii, i=1, , k =1 3. Table V listed all of the sequences after implementing the data preprocessing using Equation (2). The reference and the comparability sequences were denoted as xx 0 and xx ii, respectively. TABLE V DATA PRE-PROCESSING RESULTS Comparability Reference sequence sequence Run No F TL R a No No No No No No No No No Also, the deviation sequences, max and min for i =1 9, k =1 3 can be calculated. The deviation sequences 01 (1) using Equation (6) can be calculated as follows: o1 (1) = x 0 (1) x 1 (1) = = The distinguishing coefficient can be substituted for the Grey relational coefficient in Equation (5). If all the process parameters have equal weighting, is set to be 0.5. Table VII listed the s and the grade for all nine comparability sequences. TABLE VI DEVIATION SEQUENCES Comparability Sequence Reference Sequence Run No F TL R a No No No No No No No No No

4 TABLE VII CALCULATED GREY RELATIONAL COEFFICIENT AND GREY RELATIONAL GRADE Orthogonal Array Grade Exp. Run Grey Relational Coefficient Grey Order L 9 (3 4 ) F TL R a This investigation employs the response table of the Taguchi method to calculate the average Grey relational grades for each factor level, as illustrated in Table VII. Since the s represented the level of correlation between the reference and the comparability sequences, the larger means the comparability sequence exhibiting a stronger correlation with the reference sequence. Based on this study, one can select a combination of the levels that provide the largest average response. In Table VIII, the combination of A 1, B 1, C 1, and D 2 shows the largest value of the for the factors A, B, C and D, respectively. Therefore, A 1 B 1 C 1 D 2 with a cutting speed of 40 m/min, a feed rate of 0.16 mm/rev, a depth of cut of 0.10 mm, and approach angle of 45º is the optimal parameter combination for the face milling operation. TABLE VIII RESPONSE TABLE FOR GREY RELATIONAL GRADE Levels Factors Average of Grey Relational Grade = B. Most influential factor Grey relational analysis was applied to find the most influential factor among the milling process parameters that affect the cutting force, tool life and surface roughness. The values of the factor level in nine experimental runs are set to be the comparability sequences for four controllable factors as shown in Table IX. Data preprocessing was employed according to Equation (4), and the normalized results were tabulated in Table IX. The deviation sequences were calculated using the same method above with the help of Equation (6). To obtain the grey relational coefficients, the deviation sequences and the distinguishing coefficient were substituted in Equation (5). Additionally, the grey relational coefficients are averaged using equal weighting to obtain grey relational grade. TABLE IX SEQUENCES AFTER DATA PREPROCESSING FOR REFERENCE AND COMPARABILITY SEQUENCES Exp. No Comparability sequences Reference sequences F TL R a TABLE X CALCULATED GREY RELATIONAL COEFFICIENT AND GREY RELATIONAL GRADE FOR THE EXPERIMENTAL FACTORS TO EXPERIMENTAL RESULT OF F Table X shows the grey relational coefficients and grey relational grade for the cutting force. Similarly Table XI and Table XII show the grey relational coefficients and grey relational grade for the tool life and surface roughness respectively. The grey relational grades in Table X-XII can be further arranged in a matrix form shown as follows: γ(f, A) γ(f, B) γ(f, C) γ(f, D) γγ = γ(tl, A) γ(tl, A) γ(tl, A) γ(tl, A) γ(ra, A) γ(ra, A) γ(ra, A) γ(ra, A) = TABLE XI THE CALCULATED GREY RELATIONAL COEFFICIENT AN GREY RELATIONAL GRADE FOR THE EXPERIMENTAL FACTORS TO EXPERIMENTAL RESULT OF TL

5 TABLE XII THE CALCULATED GREY RELATIONAL COEFFICIENT AN GREY RELATIONAL GRADE FOR THE EXPERIMENTAL FACTORS TO EXPERIMENTAL RESULT OF R A In grey relation analysis, the maximum value in each row represents the most influential factor that affect the output variable. By comparing Row 1, Row 2 and Row 3, some conclusion can be drawn from this matrix. In the first row, γ(f, B) > γ(f, C) > γ(f, A) > γ(f, D), it means that the order of importance for the controllable factors to F, in sequence is the factor B, C, A and D. In the second row, γ(f, A) > γ(f, C) > γ(f, B) > γ(f, D), the order of importance for the controllable factors to TL, in sequence is the factor A, C, B and D. Similarly, based on the third row, γ(ra, B) > γ(ra, A) > γ(ra, D) > γ(ra, C), the order of importance for the controllable factors to R a, in sequence is the factor B, A, D and C. Additionally, Table XIII gives the results of the analysis of variance (ANOVA) for the F, T and R a using the calculated values from the of Table VII and the response of Table VIII. According to Table XIII, the factor B i.e. feed with 37.08% of contribution is the most significant controlled parameters for the face milling operation, the cutting speed with 16.76% contribution, the depth of cut with 25.43% and approach angle with contribution of 20.73% for the minimization of the cutting force, surface roughness and maximization of tool life, if simultaneously considered. TABLE XIII ANOVA RESULTS FOR F, T AND R A Factor Level 1 Level 2 Level 3 DOF SS MS % P A B C D Total error V. CONCLUSION The present work has successfully demonstrated the application of Taguchi based Grey relational analysis for multi objective optimization of process parameters in Face milling Inconal 718 metal based super alloy. The conclusions can be drawn from the present work are as follows 1. The highest of was observed for the experimental run 1, shown in response table (Table No. VII) of the average Grey relational grade, which indicates that the optimal combination of control factors and their levels are 40 m/min cutting speed, 0.16 mm/rev feed, 0.1 mm depth of cutand 35 0 approch angle. 2. The order of importance for the controllable factors to the minimum force, in sequence, is the feed, depth of cut cutting speed and approach angle; order to the maximum tool life,in sequence is the speed, depth of cut,feedand approach angle; the order to minimum surface roughness, in sequence, is the feed, speed, approach angle and depth of cut. 3. However, it is observed through ANOVA that the cutting speed is the most influential control factor among the four face milling process parameters investigated in the present work, when minimization of cutting forces, maximization of tool life and minimization of surface roughness are simultaneously considered. REFERENCES [1] M. Balazinski, V. Songmene, Improvement of tool life through variable feed milling of Inconel 600, Ann. CIRP 44 (1) (1995) [2] N. Natural, Y. Yamaha, High speed machining of Inconel 718 with ceramics tools, Ann. CIRP 42 (1) (1993) [3] M. Alauddin, M.A. EI Baradie, M.S.J. Hashmi, End milling machinability of Inconel 718, J. Eng. Manuf. 210 (1996) [4] T.I. Elwardany, E. Mohammed, M.A. Elbestawi, Cutting temperature of ceramic tools in high speed machining of difficultto cut materials, Int. Journal of mechanical Tool Manufact 36 (5) (1996) [5] E.O.Ezugwu, Z.M. Wang, A.R. Machado, The machinability of nickel-based alloys: a review, J. Mater. Process. Technol. 86(1999) [6] B. S. Yeo, The Machinability of Inconel 718, [7] Sahoo P, Pal SK. Tribological performance optimization of electroless Ni P coatings using the Taguchi method and grey relational analysis, Triboletters 2007;28: [8] Datta S, Bandyopadhyay A, Pal PK. Solving multi-criteria optimization problem in submerged arc welding consuming a mixture of fresh flux and fused slag. Int J AdvManufTechnol 2008;35: C.Confirmation Test The optimal parameter combination for the achieving minimum F, minimum R a and maximum TL is obtained using grey relational analysis as A 1 B 1 C 1 D 2 i.e. cutting speed of 40m/min; feed 0.16 mm/rev; depth of cut 0.15 mm and approach angle 45. Confirmation test was carried out by using A 1 B 1 C 1 D 2 optimal setting. The results of the confirmation test were cutting force( F) of 209 N, surface roughness (R a ) of 0.98 µm and tool life (TL) of min. The confirmation test result is better than the experiments in Table IV. 170