DESIGN OF EXPERIMENTS AND RESPONSE SURFACE METHOD IN CONTEXT TO GRINDING PROCESS

DESIGN OF EXPERIMENTS AND RESPONSE SURFACE METHOD IN CONTEXT TO GRINDING PROCESS 1 Prof R. G. Jivani, 2 Prof Dr. P. M. George, 3 Prof. B. S. Patel Asso. Professor 1,2,3, B. V. M. Engg. College, V. V. Nagar, Gujarat rgjivani@yahoo.com, pmgeorge02@yahoo.com, bharatvimlapatel@yahoo.com ABSTRACT: This work reports the application of Response Surface Methodology to study the Surface Roughness of ground components, instead of the conventional one variable at a time method. With this technique the number of tests required to develop a surface roughness predicting equation can be drastically reduced. Three independent variables, viz., workspeed, traverse feed and depth of cut or infeed are selected to investigate in this work and based on the carefully planned and conducted experiments, surface roughness predictive equations can be developed. The predictability of the models can be shown by confirmatory tests. The Response Surfaces of Surface Roughness can be used to select the optimum machining conditions for a given situation. INTRODUCTION: The prediction of surface roughness during a metal removal operation is of considerable interest in planning production. In many cases surface roughness is requirement and hence it is necessary to control it. Although the general effects of the machining variables like speed, feed, depth of cut, etc on surface roughness have been described; no attempt has been made to obtain comprehensive predictive models of surface roughness. In the present work, surface roughness models are developed by a statistical approach, referred to as Response Surface Methodology (RSM), instead of the conventional one variable at a time method. With this technique, the number of tests required to develop a surface roughness predicting equation can be substantially reduced. The reliability of such an equation can also be estimated. Application of this method allows the maximum use of information at a minimum cost. RSM is a combination of mathematical and statistical techniques used in the empirical study of relationships and optimization where several independent variables or factors influence a dependent variable or response. The Response Surface Function gives a complete summary of the results of the experiment and also enables to predict the response for the combination of the values of factors that are not tested experimentally. The procedure of developing predictive models appears to be really promising. RSM was developed by Box and Wilson (1951) [1,2] while working on a chemical investigation, based on the pioneering works of R.A. Fisher (1931) in connection with agricultural experimentation. This powerful methodology has been successfully used in agricultural and chemical fields and also in production engineering works as in turning, milling, grinding, extrusion, press working, welding, etc. An attempt is made in this present investigation to develop surface roughness models for cylindrical grinding operation by utilizing RSM. Three independent variables; viz. work-

speed, feed and depth of cut are selected to be investigated in the present work and a surface roughness predictive equation can be developed by RSM. The predictability of the first order equation can be shown by confirmatory tests. THE GRINDING PROCESS: Grinding is a process of material removal in the form of small chips by the mechanical action of abrasive particles bonded together in a grinding wheel. It is basically a finishing process employed for producing close dimensional and geometrical accuracies and smooth surface finish. However, in some applications, the grinding process is also applied for higher material removal rates and is referred to as abrasive machining. Generally, in other methods of machining, the work piece is shaped by removing chips using cutting tools having defined geometry, with the tool material harder than the work material. In such type of machining the process has the following limitations: [6] 1. The difference in the hardness of the tool and that of the work is often limited, resulting in tool wear and tool failure. 2. In the process of removing the materials by way of chips, a considerable amount of heat is generated which if exceeds a specific level, affects the tool hardness. These conditions always limit the applicable cutting speed. The grinding Machines 1. Cylindrical Grinding Machines - Centre Type Cylindrical Grinding Machines (Universal, Plain Cylindrical, Plunge Cyl.) - Chucking Type Cylindrical Grinding M/cs. - Centreless Grinding Machines (Through Feed, Infeed, End Feed, Combination Infeed & Thruogh Feed) 2. Internal Grinding Machines 3. Surface Grinding Machines (Vertical Spindle, Horizontal Spindle, Rotary Table, Reciprocating Table) 4. Snagging (Floor Stand, Swing Frame, Portable, Side Grinders) 5. Special Purpose Grinding Machines (Tool and Cutter, Roll Grinders, Crank Pin Grinders, Cam Grinders, NC Grinding Machines) Advantages Of Grinding Process As compared to metal removal by cutting tools of defined geometry, grinding has the following advantages: [6] 1. Abrasives are mineral crystals with hardness much higher than that of work pieces. 2. Abrasive crystals are less sensitive to heat and can sustain higher temperatures then the conventional tool materials. This aspect permits abrasives to work at much higher cutting speeds than conventional tool materials. 3. When the Individual grains of the grinding wheel wear out during the abrasive action, the self sharpening properties of the bonded tools become effective by releasing the dulled grains and exposing new sharp ones a process which is often supported by occasional dressing or truing. 4. The simple dressing of the abrasive wheel, which is performed after the face wear has occurred, avoids the significant effect of tool edge dulling on size holding, which generally accompanies the machining process performed with cutting tools. 5. The process integrated reconditioning of the abrasive wheel, by truing with automatic position compensation; results in a degree of unattended dimensional accuracy of the work which makes it possible to achieve work size control better than that possible with conventional metal working tools.

6. Work-pieces in particular, or even complex profiles, which otherwise require very expensive, specially made form cutting tools; can be produced accurately by grinding with relatively inexpensive truing templates. 7. The depth of penetration of the abrasive grain into the work material can be held to a very small amount and, when necessary, chips of microscopic size can be easily removed. Thus, closer dimensional accuracies and smoother surface finish can be achieved. 8. Cutting through the hard skin of certain raw materials or forgings may require a minimum depth of cut for conventional tools, a condition which is not a factor to be considered in abrasive cheep removal. 9. There are some work materials, both in their untreated condition, and particularly after hardening, which can not be worked by conventional tool materials. The metal removal rate of the grinding process is much lower compared to other machining processes working with defined tool geometry. However, grinding is necessary to produce work pieces of high accuracy and high surface quality. LITERATURE SURVEY: The surface roughness model can be developed by utilizing Response Surface Methodology. Such powerful methodology was developed by Box and Wilson (1951) [5]- for obtaining optimum conditions in Chemical Investigations. It has been successfully applied in a wide variety of situations Application in the area of metal cutting has included research on Tool Life Testing by Wu (1964) [4] and Cutting Tool Temperature Investigations -by Wu and Meyer (1964) [5]. The method has also been applied in different areas, one of which is Biomechanics where Kaltan (1969) [3] developed reliable quantitative models for motion response. This new statistical technique views the response or dependent variable as a surface, to which a mathematical model is fitted. The RSM was used in investigations, To select a Cutting Tool to Maximize Profit by W. W. Claycombe and W. G. Sullivan (1976) [9]. The method was used for the Study of Chatter in Turning by P. Radhakrishnan (1978) [10]. Surface Roughness Prediction in Turning Using Response Surface Methodology was carried out by Dinesh G. and George P. M. at al (1984) [11]. Gupta V. K. and Parmar R. S. carried out work on Fractional Factorial Technique to Predict Dimensions of the Weld Bead in Automatic Submerged Arc Welding (1989) [12]. Study on Modeling and Optimization of Milling Low Carbon Steel was carried out by S. M. A. Sulliman and G. A. Hassan (1991) [13]. The method was used for Investigations on Through Feed Centreless Grinding Process by S. S. Pande and B. R. Lanka (1988) [14], and for Investigations on Plunge Feed Centreless Grinding Process by S. S. Pande, A.R.Naik and S. Somasundaram (1992) [15]. METHODOLOGY: Model With Three Independent Variables It is difficult to organize and evaluate research findings in the area of machining due to the large number of investigations, which have been conducted. Furthermore, these investigations have been performed under a large variety of experimental conditions. Almost all researchers have dealt with the effect of each of the independent variables on one or more outputs changing one independent variable while fixing the other independent variables at constant levels.

Estimation of surface finish resulting from a metal removal operation is of considerable interest in planning production. In many cases the required surface finish may act as a constraint on the selection of work speed (or cutting speed) and feed values. In general machining variables for grinding like work-speed, feed, depth of cut, hardness, the grinding wheel, coolant, etc are known to influence the surface finish. Although the general effects of the machining variables viz., work-speed, feed and depth of cut on the surface finish have been described; very few comprehensive predictive models exist. An empirical model for surface finish, for grinding operation on cylindrical grinding machine may be developed. Independent variables considered are Work-speed (m/min), longitudinal feed (m/min), and depth of cut (mm) can be selected. After establishing the model, an approach will be made to draw contour of surface finish or roughness on plane representing feed and speed. The study of surface roughness by response surface methodology generally follows the useful, sequence of. most scientific research. This investigation will cover the following topics. 1. Postulation of the mathematical model. 2. Design of experiments. 3. Choice of actual cutting conditions. 4. Experiment 5. Estimation of the parameters 6. Check on the adequacy of the postulated model. 7. Estimation of confidence intervals. Design Of Experiments : To develop a surface roughness first order model, a design consisting of twelve experiments can be used. Eight experiments represent a 2 3 factorial design and may be represented by the numbered vertices of a cube. Standard Order Four experiments indicate the pure error. Table: First Order Design for K = 3 This design provided three levels of each independent variable, coded -1 as low level, 0 as centre level and +1 as the high level. The design matrix X 1 written as follows[7] for such arrangement can be These experiments can be performed in two blocks, each consisting of six experiments. The first block consisted of experiments 1,4,6,7,11,and 12 and the second block consisted of numbers 2,3,5,8,9 and 10. Table shows the design matrix for for such design. X = Matrix of x - Variables Design X 0 X 1 X 2 X 3 To develop a second order surface roughness model 6 more experiments can be added to form a central composite design. The additional six experimental points are star points with α = 1.682. the 18 experimental points provided five levels for each independendent variable, with their values at 0, ±1, ±1.68 in coded scale. The designed experiment numbers are shown in Fig. 1 Measured Response Y 1 1-1 -1-1 y 1 2 1 1-1 -1 y 2 3 1-1 1-1 y 3 4 1 1 1-1 y 4 5 1-1 -1 1 y 5 6 1 1-1 1 y 6 7 1-1 1 1 y 7 8 1 1 1 1 y 8 9 1 0 0 0 y 9 10 1 0 0 0 y 10 11 1 0 0 0 y 11 12 1 0 0 0 y 12

Run No. 8 5 2 4 l l c l Std. Order 1 2 3 4 Job No. 1 11 7 12 3 ØD Ød 5 6 7 8 Job No. 2 1 6 9 10 9 10 11 12 Job No. 3 Standard Order 1 to 6 : BLOCK I Standard Order 7 to 12 : BLOCK II Fig 1. Designated Experiment numbers The design procedure of response surface Y = f(x1, x2,....xk ) + ε...(1) methodology is as follows[16,7]: (i) Designing of a series of experiments for adequate and reliable measurement of the response of interest. (ii) Developing a mathematical model of the second order response surface with the best fittings. (iii) Finding the optimal set of experimental parameters that produce a maximum or minimum value of response. The goal is to optimize the response variable y. It is assumed that the independent variables are continuous and controllable by experiments with negligible errors. It is required to find a suitable approximation for the true functional relationship between independent variables and the response surface. Usually a second-order model is utilized in response surface methodology. y = β 0 + β i x i + β ii x 2 i + β ij x i x j + ε (iv) Representing the direct and interactive effects (where i = 1,... K)...(2) of process parameters through two and three dimensional plots. If all variables are assumed to be measurable, the response surface can be expressed as follows: where ε is a random error. The β coefficients, which should be determined in the second-order model, are obtained by the least square method. In general (2) can be written in matrix form.

Y = bx + E...(3) where Y is defined to be a matrix of measured values, X to be a matrix of independent variables. The matrixes b and E consist of coefficients and errors, respectively. The solution of (3) can be obtained by the matrix approach. B = (X T X ) 1 X T Y... (4) where X T is the transpose of the matrix X and (X T X) -1 is the inverse of the matrix X T X. The mathematical models were evaluated for each response by means of multiple linear regression analysis. As said previous, modelling was started with a quadratic model including linear, squared and interaction terms. The significant terms in the model were found by analysis of variance (ANOVA) for each response. Significance was judged by determining the probability level that the F-statistic calculated from the data is less than 5%. The model adequacies were checked by R 2, adjusted-r 2, predicted-r 2 and prediction error sum of squares (PRESS). A good model will have a large predicted R 2, and a low PRESS. After model fitting was performed, residual analysis was conducted to validate the assumptions used in the ANOVA. This analysis included calculating case statistics to identify outliers and examining diagnostic plots such as normal probability plots and residual plots. Maximization and minimization of the polynomials thus fitted was usually performed by desirability function method, and mapping of the fitted responses was achieved using computer software such as Design Expert. [16] The Sequencial Nature Of The Response Surface Methodology: Most applications of RSM are sequential in nature and can be carried out based on the following phases. Step 1 : At first some ideas are generated concerning which factors or variables are likely to be important in response surface study. It is usually called a screening experiment. The objective of factor screening is to reduce the list of candidate variables to a relatively few so that subsequent experiments will be more efficient and require fewer runs or tests. The purpose of this phase is the identification of the important independent variables. Step 2 : The experimenter s objective is to determine if the current settings of the independent variables result in a value of the response that is near the optimum. If the current settings or levels of the independent variables are not consistent with optimum performance, then the experimenter must determine a set of adjustments to the process variables that will move the process toward the optimum. This phase of RSM makes considerable use of the first-order model and an optimization technique called the method of steepest ascent (descent). Step 3 : Phase 2 begins when the process is near the optimum. At this point the experimenter usually wants a model that will accurately approximate the true response function within a relatively small region around the optimum. Because the true response surface usually exhibits curvature near the optimum, a second-order model (or perhaps some higher-order polynomial) should be used. Once an appropriate approximating model has been obtained, this model may be analyzed to determine the optimum conditions for the process. This sequential experimental process is usually performed within some region of the independent variable space called the operability region or experimentation region or region of interest.[16] CONCLUSION: 1. First order surface roughness model may be adequate for cylindrical grinding operation with perameters work speed, feed and depth of cut. The job dimensions and the parameters for experiments

can be fixed after selecting the machine, the work material and the grinding wheel. 2. A second-order response surface model for surface roughness can be developed from the observed data. This will give 95% confidence level for the model. 3. Response surface methodology provides a large amount of information with a small amount of experimentation. REFERENCES: 1. Box G.E.P., Multilayer Design of first First Order, Biometrics, 39,1952,pp.49-57 2. Box G.E.P. and Hunter J. S., Multifactor Experimental Designs for Exploring Response Surface, Ann. Math. Statist., 28, 1957, pp 195-241. 3. Kaltan A., Quantitative Models of Human Motion by Response Surface Methodology, ASME Paper, 69-WA/BHF-5, 1969. 4. Wu. S. M., Tool Life Testing by Response Surface Methodology Pt. I and II, J. Engng. Ind. Trans. ASME, Vol. 86, 1964, pp 105-116. 5. Wu S. M. and Meyer R. N., Cutting Tool Temperature Predicting Equation by Response Surfaae Methodology, Jengng. Ind. Trans. ASME, Vol. 86, 1964,pp 150-156. 6. Hindustan Machine Tools, Banglore, Production Technology, Tata McGraw-Hill Publishing Co. Ltd., New Delhi, 1995, pp 249-287. 7. D.C. Montgomery. 2005, Design and analysis of experiments. New York: John Wiley and Sons. 8. Kolarik W. J., Creating Quality Concepts, Systems, Strategies and tools, McGraw Hill Inc.,New York,1995, pp 435-522, 532-564. 9. Claycombe W. W. and Sullivan W. G., Use of Response Surface Methodology to selsct a cutting tool to Maximize Profit, Transactions of the ASME Journal of Engineering for Industry, Feb., 1976, pp 63-65. 10. Rathakrishnan P., Venkatraman K., Response Surface Approach to the study of Chatter in Turning, Proceedings of the 8 th AIMTDR Conference, I.I.T., Bombay, 1978. 11. Dinesh G. and George P. M., Surface Roughness Prediction Using Response Surface Methodology Project Report, 1984. 12. Gupta V. K. and Parmar R. S., Fractional Factorial Technique to Predict Dimensions of the Weld Bead in Automatic Submerged Arc Welding, Journal of IE (India), Mech. Engg. Division, Vol. 70Part MC-4, Nov.,1989. 13. Sulliman S. M. A., and Hassan G. A., Modelling Optimization and Response Curvesof Milling Low Carbon Steel, Int. J. Prod. Res., 1991, Vol29, No. 4, pp 725-737. 14. Pande S. S., Naik A. R. and S. Somasundaram, Some Invastigations on Plunge Feed Centreless Grinding Process, Int. J. Prod. Res., 1992, Vol. 30, No. 12, pp. 2825-2838. 15. Pande S. S., Lanka B. R., Invastigations on the Through-feed Centreless Grinding Process, Int. J. Prod. Res., 1992, Vol. 27, No. 7, pp. 1195-1208. 16. S. Raissi and R. Eslami Farsani, Statistical Process Optimization Through Multi-Response Surface Methodology,Int. Journal of Computational and Mathemetical Sciences, June 2009, pp 291-295