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NATARAJAN U A. C.C.E.T

Multi-response Optimization in Micro-electric discharge (Micro-EDM) machining using Taguchi’s Quality loss function and Principal component analysis. NATARAJAN U A. C.C.E.T. CONTENTS. INTRODUCTION METHODOLOGY Taguchi Quality Loss Method

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NATARAJAN U A. C.C.E.T

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  1. Multi-response Optimization in Micro-electric discharge (Micro-EDM) machining using Taguchi’s Quality loss function and Principal component analysis NATARAJAN U A. C.C.E.T

  2. CONTENTS • INTRODUCTION • METHODOLOGY • Taguchi Quality Loss Method • Principal Component Analysis • IMPLEMENTATION • RESULTS and • FUTURE WORK

  3. INTRODUCTION • In this work, Polarity, Peak current, Ignition voltage, Pulse on- time, Pulse off-time, Capacitance, Gap and Gain are to be taken as input parameters. Surface roughness and Metal Removal Rate and Tool wear ratio are considered as responses. • Using the Taguchi’s Quality loss function and Principal component analysis, optimal parameters are to be determined

  4. INPUT PARAMETERS AND OUTPUTS( RESPONSES) Polarity A Peak current Gain B H Metal Removal rate Surface roughness Tool wear ratio Gap Ignition voltage C G Capacitance Pulse on time F Pulse off time D E

  5. PROPOSED METHODOLOGY • To identify the signal and noise factors which influence the responses • To determine the type of responses or quality characteristics to be optimized • Smaller-the-better responses • Larger-the-better responses • Nominal is the better responses • To compute the quality loss(QL) for each response • To compute the normalized quality loss (NQL) • Perform Principal Component Analysis(PCA) on the NQL data • To determine the optimal condition • Perform a confirmatory experiment

  6. S/N RATIO for Single Objective Problem • S/N ratio (db) = -10 log [ 1/n∑ni (Di2)] ( FOR LOWER-THE-BETTER TYPE ) • S/N ratio (db) = -10 log [ 1/n∑ ni (1/Di2)] ( FOR HIGHER-THE-BETTER TYPE ) where Di is the response value for a trial condition repeated ‘ n’ times.

  7. MULTIPLE SIGNAL-TO-NOISE RATIO for Multiple Objective Problem The Normalized quality loss can be computed as below: yiJ = LiJ / Li* where LiJ=Quality loss for the ith quality characteristic at the jth trial condition Li* = Maximum quality loss for the ith quality characteristic among all the trial conditions The Total Normalized Quality Loss (Yi) Yi = Σik wi yiJ Multiple Signal-to-Noise Ratio(MSNR) = ηJ = -10 log(YJ)

  8. PRINCIPAL COMPONENT ANALYSIS - Methodology • PCA is the one of the multi-variate analysis techniques, introduced by Karl Pearson (1901) and developed by Hotelling(1933) • With the advent of electronic computers, it iswidely usednowadays in the various research fields likeImage processing, Data compression, Medical field etc. • The central idea of PCA is to reduce the dimensionality of a data setin which there are a large number of interrelated variables, while retaining as much as possible variation present in the data set • The reduction is achieved by transforming to a new set of variables, the principal components, which are uncorrelated and which are ordered so that the first few retain most of the variation present in all of the original variables • Other synonymous terms for PCA :Empirical Orthogonal functions Factor analysis

  9. Let Y1, Y2 , …..,Yp be a set of variables. Using PCA, the following uncorrelated linear combinations are obtained as follows: WhereΩ1is the first principal component and Ω2is the second principal component

  10. (x1, x2) A Plot of 50 observations on two variables X1 and X2

  11. Ω2 Ω1 A Plot of 50 observations with respect to their Principal Components

  12. Y- axis X -axis

  13. IMPLEMENTATION - Taguchi Quality Loss Method Factors and their Levels

  14. Machine used

  15. EXPERIMENTAL READINGS (DATA) with L-18 Orthogonal Array

  16. Normalized Quality Loss values of selected Quality characteristics

  17. MULTIPLE SIGNAL-TO-NOISE RATIO FOR VARIOUS FACTORS

  18. MULTIPLE SIGNAL-TO-NOISE RATIO FOR VARIOUS FACTORS

  19. ANOVA on the Multiple Signal-to-Noise Ratio (MSNR) before Pooling

  20. ANOVA on the Multiple Signal-to-Noise Ratio (MSNR) after Pooling Pure Sum of squares ( S’ ) S’A = SSA – [( DOFA) * Ve ] = 132.467 – [ 1 * 4.2983] = 128.1687 Percentage Contribution PA = S’A / ST = 128.1687 / 303.4606 = 0.4224*100 =42.24 From F-tables: F0.05,2,11 = 3.98 F0.10,2,11 = 2.86 * factor is significant at both 5% and 10% significance levels

  21. PRINCIPAL COMPONENT ANALYSIS -Implementation MINITAB RESULTS EIGEN ANALYSIS OF THE CORRELATION MATRIX Eigenvalue 1.8790 0.8818 0.2392 Proportion 0.626 0.294 0.080 Cumulative 0.626 0.920 1.000 Variable PC1 PC2 PC3 C1 -0.519 -0.705 0.484 C2 0.517 -0.709 -0.480 C3 0.681 0.001 0.732 PCA 1 = -0.519 (MRR) + 0.517 (SR) + 0.681 (TWR)

  22. RESULTS Significant Factors for the Taguchi method: A E D G A - Polartiy E - Pulse off time D - Pulse on time G - Gap Significant Factors for the PCA : A F H C A - Polarity F - Capacitance H - Gain C - Ignition voltage Optimal Settings of Factor Level for Taguchi method : A2-B1-C3-D2-E1-F1-G2-H1 Optimal Settings of Factor Level for PCA method : A1 –B1-C3-D1-E2-F2-G2-H2

  23. PREDICTION AND COMPARISON OF S/N RATIOS

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