Multi Response Optimization of Ultrasonic Machining Parameters Using Weighted Principal Component Analysis

Transcription

1 5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12 th 14 th, 2014, IIT Guwahati, Assam, India Multi Response Optimization of Ultrasonic Machining Parameters Using Weighted Principal Component Analysis N.D.Badgayan 1, P.S. Rama Sreekanth 1* 1 National Institute of Science and Technology,Odisha, ,nitesh.badgayan@gmail.com, * p.sreekanth@nist.edu Abstract In this paper, based on historical data three parameters i.e. Grit size, Power and Tool type were varied to investigate its effect on responses i.e Material Removal Rate (MRR),Tool Wear Rate (TWR) and Surface Roughness (Ra) for work piece machined by Ultrasonic Machining(USM) process An attempt has been made to find optimal solution for the responses using Weighted Principal Component Analysis (WPCA).Analysis of data has found that responses were highly correlated with correlation coefficient (r=0.905) which justifies the application of WPCA as an optimization tool. The optimal parameter setting obtained after analysis was exonerated with valid altercation. Keywords: Ultrasonic Machining, Weighted Principal Component Analysis, Multi Output Performance Index 1. Introduction USM is a Non Traditional Machining (NTM) process in which abrasive contained in slurry are driven against work by tool oscillating at low amplitude and high frequency. Titanium Grade 1which is taken as work material as based on historical data, has a melting point of 1670 C with low thermal conductivity of 16 W/mK.It has got tendency to weld to cutting tool during machining and also its low thermal conductivity increases the temperature of tool work interface leading to premature tool failure making it cumbersome to machine by conventional machining. Principal Component Analysis (PCA) is a statistical procedure that uses orthogonal transformation to convert a set of observation of possible correlated variable into set of value of linearly uncorrelated variable called principal components. The main advantage of PCA is that once pattern in data have been identified the data can be compressed i.e. by reducing number of dimension without much loss of information, Johnson and Winchen (2002).The drawback with PCA method was it only assign weight to principal components depending on their Accountability Proportion (AP), Qiuming et al. (2010).But in WPCA total principal components are used and a Multi Output Performance Index (MOPI) is generated and a higher value of MOPI is taken into consideration. To the best of author s knowledge no work has been reported on the context of Multi response Optimization of USM Parameters using WPCA. Depending on industry reckoning of optimal parameter setting for a process sometimes become exigent, say for an example in a CNC manufacturing unit during machining Inconel- 718 super alloy, the output parameters such as Metal Removal Rate and Surface Roughness may be evaluated taking different input factors (e.g. speed of rotation, feed and depth of cut) at different levels. The same can perpetrate with any Design of Experiment (DOE) approach but finding optimal parameter setting become unwieldy as techniques like Grey Relational Analysis (GRA),Desirability Approach (DA) and The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) all takes responses to be independent of each other which is observed as a severe flaw as in cases of correlated responses but the same is overcome with Weighted Principal Component Analysis takes the responses to be dependent on each other and after thorough correlation analysis it reaches to any findings. 2. Mathematical Formulation. Signal to Noise Ratio (Higher is Better): = 10 og,..(1) Signal to Noise Ratio (Lower is Better): = 10log,.. (2) Where m= Number of Trials, y= Response or Output Normalized S/N Ratio (X IJ ):..(3) = f,. = Maximum of,

2 Multi Response Optimization of Ultrasonic Machining Parameters Using Weighted Principal Component Analysis Start B Grit Size C Power Calculate S/N Ratio for MRR (Higher is better equation 1), for TWR and Ra (Lower is Better equation 2) Normalize S/N ratio as formula given in equation 3 Carry out Correlation Analysis on the Normalized Value to Check Reponse Correlation After Normalizing put the value in MINITAB Software for Principal Component Analysis (Table 4) Generate Principal components as per formula Z 1=-0.681MRR TWR+0.307Ra,Z 2=0.160 MRR-0.274TWR+0.948Ra, Z 3=0.715MRR+0.695TWR+0.080Ra Generate MOPI (Multi Objective Performance Index) from Table 5 Figure 1 Sequential steps involved in WPCA 3.Optimization of USM Parameters End Three parameters i.e. Grit Size, Power and Tool Type, each kept at different level (Table 1) had been varied to investigate its effect on Material Removal Rate (MRR), Tool Wear Rate (TWR) and Surface Roughness (Ra).The complete experimental design matrix along with the responses were depicted in Table 2.The data in both Table 1 and Table 2 were historical data whose reference was cited.wpca had been used to find optimal solution for the responses i.e. MRR, TWR and Ra.Prior to WPCA, response correlation analysis was carried out (r=0.905).in order to nullify noise effect on the data the run order were completely randomized Table 1 Variable Parameters and their s Jatinder,K. et al. (2008) Sym. Factor Work Mat. A Tool Mat. Titanium Grade 1 High Carbon Steel Table 2 Experimental Design Matrix, Jatinder k. et al (2008) R UN Tool Material Grit Size (Sieve Numb er) Power (Watt) MRR (mg/m in) TWR (mg/m in) Roughn ess (CLA Microns ) 1 Ti HCS HCS Ti Ti HCS Ti \ HCS Ti HCS HCS Ti Ti HCS Ti HCS HCS HCS Ti HCS Ti HCS Ti Ti Results and Discussions The signal to noise ratio of responses were generated based on eqn. 1 and eqn. 2.S/N ratio for MRR was generated using eqn. 1 as MRR needs to be as high as possible but for other two responses TWR and Ra S/N ratio was generated using eqn.2 as both of the responses need to be as low as possible. After generation of S/N ratio values were normalized using eqn.3.after generating normalized log s Value using eqn 3, MINITAB 16 software was used to generate Principal Components Z 1,Z 2,Z 3 and the generated principal components were independent and free from any correlation. MOPI was calculated from the steps depicted in Fig.1.Table 3 depicts the WPCA results of responses. Table 4and Table 5 depicts Eigen analysis on normalized value and level average MOPI calculated respectively 661-2

3 5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12 th 14 th, 2014, IIT Guwahati, Assam, India Sl No Table 3 WPCA on response data log s Value Normalized log s Value Z 1 Z 2 Z 3 MOPI MRR TWR Ra MRR TWR Ra After WPCA analysis on responses, Eigen analysis was carried out normalized value and level average MOPI was calculated which was depicted in Table 4 and Table 5 respectively Table 4 Eigen Analysis of normalized value Princip al Compo nent Eige n Val ue Z Z Z Expla ined Variat ion (%) Cumu lative Variat ion (%) Eigen Vector (MRR,TWR Ra) { ,0.665,0.3 07} {0.160, ,0.948} [0.715,0.695,0. 080] Table 5 Average MOPI Symbol Factor A Tool B Grit size C Power

4 Multi Response Optimization of Ultrasonic Machining Parameters Using Weighted Principal Component Analysis The following graphs Figure 2 (A, B, C) were plotted taking average of Power,Grit Size and Tool Type with average MOPI from Table 5 a b The optimal Process Parameters were found from Fig 2 (A,B,C) to be A2, B3 & C3 (Table 6), which bouts the twenty third observation on Table 2, taken from historical data.the surface Roughness (Ra) was found to be 0.35 microns with MRR 0.87 mg/min and TWR 0.73 mg/min.the bouting of optimal process Parameter setting and observedexperimental data (Obs 23), Table 2 can be justified with following point enumerated here under: 1. Out of all twenty four observation Table 2 the Optimal Ra value was least,0.35 microns with difference of % from highest value of Ra attained (Obs 1) and its difference between next succeeding observation (Obs 17) was found to be 74.28% 2. The Optimal TWR was found to be 0.73 micron which was % higher then lowest value (Obs 12) and approximately 9 times lower than highest value (Obs 22) with lowest TWR of 0.16 mg/min (Obs 12) the Ra was found to be 13 % more then value attained with optimal setting 3. The Optimal MRR was 0.87 mg/min which was % less then highest MRR attained (Obs 2) and % higher then the lowest MRR(Obs 12) The following Table 6 depicts the comparison of initial process parameters and optimal process parameters Table 6 Initial and Optimal conditions Initial Conditions Value Optimal Conditions Tool Type Ti Titanium Grade 5 Grit Size Power MRR(mg/min) TWR(mg/min) Ra(micron,CLA) c Figure 2 (a): Tool level Vs MOPI, (b): Grit Vs MOPI, (c): Power Vs MOPI 5. Conclusion The optimal parameter setting obtained from WPCA was found bouting with an experimental observation. The attained value of MRR (0.87 mg/min) was quite appreciable along with attaining lowest Surface Roughness of 0.35 microns and TWR of 0.73 mg/min.as MRR was always in contra with TWR and Ra;higher the MRR the more Roughness and TWR would be (Obs 2).The attained parameter setting obtained from WPCA was completely 661-4

5 5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12 th 14 th, 2014, IIT Guwahati, Assam, India exonerating on grounds of attaining a moderate MRR & TWR along with lowest Ra References 1. Johnson, R.A. and Winchen, D.W. (2002), Applied Multivariate Statistical Analysis Prentice Hall Incl Englewood Cliffs,New Jersey 2. Jatinder,K., Khamba, J.S. and Mohapatra S.K.(2008), An investigation into the machining characteristics of titanium using ultrasonic Machining, International Journal of Machining and Machinability of Materials,Vol.3, pp Qiuming,C., Wenlei, W.,Shenyung,Z. and Xia, Q. (2010),A spatially weighted principal componenet analysis for multi element geochemical data for mapping location of felsic intrusion in the Gejiu mineral district of Yunnan, China, Computers and Geosciences Vol.27,pp