DEVELOPMENT OF EMPIRICAL MODEL FOR PREDICTION OF SURFACE ROUGHNESS USING REGRESSION

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International Journal of Advances in Engineering & Technology, Nov. 2013. ©IJAET ISSN: 22311963 techniques to predict the surface roughness of a product before milling in order to determine the requirement of machining parameters such as feed rate and spindle speed for obtaining a desired surface roughness and increasing product quality. II. LITERATURE SURVEY This surface roughness might be considered as the sum of two independent effects. K. Taraman et.al. developed [1] a mathematical model for the surface roughness in a turning operation. R. M. Sunderam et. al., [2] has presented the experimental development of mathematical models for predicting the surface finish of AISI 4140steel in fine turning operation using TiC coated tungsten carbide throw away tools. M.S. Chua [3] et. al., developed a process planning or NC part programming, optimal cutting conditions are to be determined using reliable mathematical models representing the machining conditions of a particular work-tool combination. Dr. Mike S. Lou [4] the author examined a new approach for finish surface prediction in end-milling operations. Used parameters spindle speed, feed rate, depth of cut. In order to develop a new technology for surface prediction, literature review of the surface texture, surface finish parameters and multiple regression analysis have been carried out. B. Sidda Reddy [5], This paper deals with the development of second order mathematical model using Response Surface Methodology (RSM) to predict the surface roughness in terms of machining parameters cutting speed, feed rate and depth of cut. The experimentation has been conducted using full factorial design in the design of experiments (DOE) on CNC turning machine with carbide cutting tool. This study deals with the development of a surface roughness prediction model for machining aluminium alloys using multiple regression and artificial neural networks. D. Hanumantha Rao [6] In this present investigation , a hybrid ANN Genetic Algorithm model is developed for predicting the SDAS values in aluminium alloy casting, Adaptation and optimization of network weights using GA is proposed as a mechanism to improve the performance of ANN model. P. Nanda Kumar [7] in this paper Al based neural network modelling approach is presented for the prediction of surface roughness of aluminium alloy products machined on CNC turning centre. Trails were made with different combinations of step size and momentum to select the best learning parameter. The best network structure with least MSE was selected among the several networks. The multiple regression models, which are most widely used as prediction methods, are considered to be compared with the developed ANN model performance. Above all the works done by Researches & Scientists considers only three working parameters mainly such as spindle speed, feed, and depth of cut from 1994 to 2013. Till time no one considers more three working parameters. All the research works cannot reach the maximum surface roughness values. This is the base for my project work by considering five parameters spindle speed, feed, depth of cut, number of flutes, and overhang length of the tool for achieving good surface values with less percentage deviation from actual. III. DESIGN OF EXPERIMENTS The factors considered were Cutting Speed, Feed Rate, Depth of Cut, Number of flutes and over hanging Length. The range of values of each factor was set at the three levels, namely low, medium and high, as shown in Table 1. Variables Designation Table 1. Values of test variables Description Values at different levels Low (L) Medium M) High (H) V Cutting Speed(rpm) 2000 2500 3000 F Feed rate (mm/min) 160 - 240 D Depth of cut(mm) 0.5 - 0.8 Nf Number of flutes 2 - 4 Ol Overhanging length(mm) 30 - 35 The number of experiments to be carried out was planned using a full factorial design [3*2*2*2*2][3,4]. Based on this setting, a total of 48 experiments, as shown in Table 2, were carried out. The experiments are conducted on CNC Milling and selected work piece material is 6082- 2042 Vol. 6, Issue 5, pp. 2041-2052
International Journal of Advances in Engineering & Technology, Nov. 2013. ©IJAET ISSN: 22311963 Aluminium alloy (Si-0.6 to 1.3, Fe-0.6, Cu-0.1, Mn-0.4 to 1.0, Cr-0.25, Zi-0.1, Ti-0.2, and Mg-0.4 to 1.2). The cutting tool with carbide inserts (CCMW 9030) is used to machine the work piece material. The response of surface roughness was measured by using Mitutoyo Surftest-211 instrument and the results are tabulated in table 2. Test No. v(rpm) f(mm/r ev) d (mm) Table 2: Experimental Results (Train Data) nf ol (mm) Ra (μm) 2043 Vol. 6, Issue 5, pp. 2041-2052 Test No. v(rpm) f(mm/ rev) d (mm) nf ol (mm ) 1 2000 160 0.5 2 35 1.747 25 2000 160 0.5 4 35 4.777 2 2000 160 0.8 2 35 1.537 26 2000 160 0.8 4 35 4.773 3 2000 240 0.8 2 35 1.717 27 2000 240 0.8 4 35 7.087 4 2000 240 0.5 2 35 1.563 28 2000 240 0.5 4 35 6.31 5 2500 160 0.5 2 35 1.46 29 2500 160 0.5 4 35 3.947 6 2500 160 0.8 2 35 1.513 30 2500 160 0.8 4 35 4.403 7 2500 240 0.8 2 35 1.677 31 2500 240 0.5 4 35 5.393 8 2500 240 0.5 2 35 1.653 32 2500 240 0.8 4 35 5.75 9 3000 160 0.8 2 35 0.823 33 3000 160 0.8 4 35 3.213 10 3000 160 0.5 2 35 0.587 34 3000 160 0.5 4 35 2.797 11 3000 240 0.8 2 35 1.623 35 3000 240 0.8 4 35 2.707 12 3000 240 0.5 2 35 1.657 36 3000 240 0.5 4 35 2.54 13 2000 160 0.8 2 30 2.497 37 2000 160 0.8 4 30 2.04 14 2000 160 0.5 2 30 2.49 38 2000 160 0.5 4 30 2.353 15 2000 240 0.5 2 30 3 39 2000 240 0.5 4 30 2.847 16 2000 240 0.8 2 30 4.07 40 2000 240 0.8 4 30 3.167 17 2500 160 0.5 2 30 1.58 41 2500 160 0.8 4 30 1.21 18 2500 160 0.8 2 30 1.5 42 2500 160 0.5 4 30 0.97 19 2500 240 0.5 2 30 4.193 43 2500 240 0.8 4 30 2.437 20 2500 240 0.8 2 30 4.057 44 2500 240 0.5 4 30 2.73 21 3000 160 0.5 2 30 2.55 45 3000 160 0.8 4 30 0.947 22 3000 160 0.8 2 30 2.493 46 3000 160 0.5 4 30 1.257 23 3000 240 0.8 2 30 3.86 47 3000 240 0.5 4 30 2.86 24 3000 240 0.5 2 30 4.26 48 3000 240 0.8 4 30 3.203 IV. SURFACE ROUGHNESS MODEL The purpose of developing the mathematical models relating the machining responses and their machining factors is to facilitate a functional relationship between surface roughness and the independent variables (v, f, d, nf, ol). The following models are considered in this section. 4.1 Multiple Regression Model The multiple regression models were developed by using the independent variables (v, f, d, nf, ol) and the dependent variable (Ra). The experimental results were modeled using multiple regression methodology and respective models excluding and including interaction terms were developed. The equation excluding interaction terms using independent variables [5]. For simplicity, equation is re-written as algebraic representation of regression line can be represented by Ra = b0+b1x1+b2x2+b3x3+b4x4+b5x5 ……………(1) Where, Ra is surface roughness; x1,x2,x3,x4,x5 are predictors and b0,b1,b2,b3,b4,b5 are the regression coefficients. Using the experimental data, the analysis consisted of estimating these five variables first for first order model. If the first order model demonstrates any statistical evidence of lack of fit, a second order model can then be developed using additional data, this model is an algebraic model with interaction terms are considered. The Multiple regression equation of second order model with interaction terms can be represented by the fallowing equation. R=b0+b1x1+b2x2+b3x3+b4x4+b5x5+b6x1x2+b7x1x3+b8x1x4+b9x1x5+b10x2x3+b11x2x4+b12x2 x5+b13x3x4+b14x3x5+b15x4x5+b16x12+b17x22+b18x32+b19x42+b20x52 …………………..(2) Ra (μm)
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DEVELOPMENT OF EMPIRICAL MODEL FOR PREDICTION OF SURFACE ROUGHNESS USING REGRESSION

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