Deep Cold Rolling Process on AISI 4140 Steel and Optimization of Surface Roughness by Response Surface Methodology

Transcription

1 Deep Cold Rolling Process on AISI 440 Steel and Optimization of Roughness by Response Methodology P. R. Prabhu, S. M. Kulkarni, S. S. Sharma, Jagannath K, Chandrashekhar Bhat Abstract - treatment is an important aspect of all manufacturing processes to impart special physical and mechanical properties. Deep cold rolling (DCR) process is a post-machining operation in which the surface irregularities of workpiece are compressed by the application of a ball, which produces a smooth compact surface and simultaneously induces compressive residual stress. This paper describes a systematic methodology for empirical modelling and optimization of the DCR process parameters. The design of DCR parameters is based on response surface methodology, which integrates a design of experiment, regression modelling technique for fitting a model to experimental data. Central composite design has been employed to develop a second-order surface model. Response surface methodology was employed to optimize the set of parameters to ensure a minimum surface. The optimum conditions found by RSM for the deep cold rolling process are, rolling force of 507.7N, ball diameter of mm, initial of 4.4µm and 3 number of tool passes. Keywords Deep cold rolling, Optimization, Response surface methodology, F I. INTRODUCTION ATIGUE is one of the major reasons for failure of the engineering machine components. It is of great concern for components subject to cyclical stresses, particularly where safety is paramount. It can also contribute to the failure of components such as moulds/dies, gears, bearings and shafts, and therefore have a detrimental effect on life cycle/operating costs []. It has long been recognized that fatigue cracks generally initiate from free surfaces and that performance is therefore reliant on the surface topography produced by machining []. Therefore, engineers who want to P. R. Prabhu, Asst. Professor - senior scale, Department of Mechanical & Manufacturing Engineering, Manipal Institute of Technology, Manipal (Ph: ; raghu.prabhu@manipal.edu). S. M. Kulkarni, Professor, Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal , ( smk@nitk.ac.in). S. S. Sharma, Professor, Department of Mechanical & Manufacturing Engineering, Manipal Institute of Technology, Manipal (Ph: ; ss.sharma@manipal.edu). Jagannath K, Professor, Department of Mechanical & Manufacturing Engineering, Manipal Institute of Technology, Manipal (Ph: ; jagan.korody@manipal.edu). Chandrashekhar Bhat, Professor, Department of Mechanical & Manufacturing Engineering, Manipal Institute of Technology, Manipal (Ph: ; Fax: chandra.bhat@manipal.edu). improve the life of a component will eventually have to take into consideration the surface of the component. Virtually all fatigue and corrosion related failures originate from the surface produced by a manufacturing process. The integrity of surface in resisting failure depends upon several characteristics including surface finish, residual stress, and cold working. finish has long been known to have an impact on the life of a component that undergoes cyclic loading in service [2]-[3]. That is why so much time and effort is spent on finish machining; finish grinding, honing, lapping, and polishing. The purpose of these processes is to produce a surface that is free of defects, such as gouges and scratches. A surface free of such defects has fewer flaws from which cracks can originate. A component that is free from surface defects will generally survive longer in cyclic loading conditions [2]. Deep cold rolling is one of the mechanical surface enhancement techniques that improve the surface finish of the workpiece. In deep cold rolling process, the metal on the surface of the workpiece is redistributed without material loss. Besides producing a good surface finish, the deep cold rolling process has additional advantages such as securing increased hardness, corrosion resistance and fatigue life as a result of the residual compressive stress [4]-[7]. The literature review indicates that earlier investigations concentrated on the effect of the deep cold rolling process dealing mostly with microstructure, residual stress and fatigue life of aluminium and titanium alloys []-[9]. In the present work, desirability function approach (DFA) together with response surface methodology has been used to minimize surface in deep cold rolling process. A model was developed to predict the effect of the deep cold rolling parameters on surface by using multiple regression analysis. Validation experiments were conducted on random set of experiment under optimal conditions. Deep Cold Rolling (DCR) is a surface treatment technique which is performed using a roller or ball type tool to produce a surface residual compressive stress to improve the fatigue life of materials and engineering components. As a result of the contact of a ball with the surface of a component, a longitudinal groove is created which is accompanied by a plastic region followed by an elastic zone. Upon the separation of ball, the recovery of elastic zone creates a large residual compressive stress on the surface. A number of parameters can severely influence the deep cold rolling process and consequently the near surface residual stress 25

2 among which the rolling force is proved to be the most important. It is also known that only optimized rolling process can improve the fatigue strength, too low rolling forces have no significant influence on the fatigue behaviour and too high ones may even aggravate it, by inducing micro cracks []. The DCR process is widely used in automobile and aero industry for improving the fatigue resistance of crank shafts and turbine blades. A. Material II. APPARATUS AND METHOD The sample material was AISI 440 steel in the form of round bars with 2mm diameter as shown in Fig. (ASM standard E 4). The chemical composition of AISI 440 steel in mass% is as follows: C, 0.27Si, 0.Mn, 0.055P, 0.04S,.20Cr, 0.25Mo, 0.Ni. This steel is especially recommended for the manufacture of transmission shaft, gear shaft, crank shaft and also for a wide variety of automotive type applications []. Fig. Workpiece geometry (mm) B. DCR parameters and surface measurements The experiments were carried out using a conventional lathe (PSG type A 4). In this study, four factors were studied and their low-middle-high values are given in Table. However in all experiments lubricant (brake oil), feed rate (3 mm/min), ball material (tungsten carbide) were taken as fixed values. After the experiments, surface measurements were carried out by using Surtronic Taylor Hobson Talysurf measuring instrument. TABLE I FACTORS AND LEVELS OF EXPERIMENTATION Symbol Factor Unit Level Level 2 Level 3 A Ball Diameter mm B Rolling Force N C Initial Roughness µm D No. of Passes 2 3 C. Response surface methodology Often engineering experimenters wish to find the conditions under which a certain process attains the optimal results. That is, we want to determine the levels of the design parameters at which the response reaches its optimum. The optimum could be either a maximum or a minimum of a function of the design parameters. One of the methodologies for obtaining the optimum is response surface technique. Response surface methodology is a collection of statistical and mathematical methods that are useful for the modeling and analyzing engineering problems [2]. In this technique, the main objective is to optimize the response surface that is influenced by various process parameters. Response surface methodology also quantifies the relationship between the controllable input parameters and the obtained response surfaces [3]. D. Experimental design In RSM design, there should be at least three levels for each factor. In this way, the factor values that are not actually tested using fewer experimental combinations and the combinations themselves can be estimated [3]. The results are expressed in 3D series or counter map. The arrangement of experiments carried out in this work based on the central composite design (CCD). The experimental parameters used and the corresponding responses are given in Table 2. The first column of the table is assigned to the ball diameter (A), the second to the rolling force (B), the third to the initial (C) and the fourth to number of tool passes (D). The measurement results are given in the right end column. TABLE II DCR PROCESSING PARAMETERS AND AVERAGE MEASURED SURFACE ROUGHNESS VALUES Factors Exp. No. A B C D (µm) E. Treatment method In most RSM problems, there is a functional relation between responses and independent variables and this relation can be explained using the model below [4]. 0 k k 2 i Xi ii Xi ij XX i j i= i= i j η = β + β + β + β + ε () 2

3 Where η is the estimated response (surface ), β 0 is constant, β i, β ii, and β ij represent the coefficients of linear, quadratic and cross-product terms, respectively. X reveals the coded variables that correspond to the DCR parameters such as ball diameter (A), rolling force (B), initial (C) and number of tool passes (D). The tests for significance of the regression and individual model coefficients were performed to verify the goodness of fit for the obtained model. The analysis of variance (ANOVA) was applied to summarize these tests. Additionally, plot of main effects, interactions, normal probability and 3D response surface corresponding to ANOVA analysis were constructed. These plots were used to investigate the influences of DCR parameters on the surface, and are illustrated in Figs is an index used to check the adequacy of the model in which calculated value of F should be greater than the F-table value. Interaction Plot for Roughness Data Means Rolling force Initial Ball diameter RollingBall force Rolling Initial Normal Probability Plot (response is Roughness) Fig. 4 Interaction plot for surface Percent Residual Fig. 2 Normal probability plot for surface Contour Plot of Roughness vs, Hold Values Rolling force 500 Initial Main Effects Plot for Roughness Data Means Fig. 5 Contour plot of surface Rolling force Optimal D High Cur Low Ball dia Rolling Initial No of pa [.0] [ ] [4.40] [3.0] Mean Initial Composite Desirability Fig. 3 Main effects plot for surface 3 Roughnes Minimum y = d = Analysis of variance essentially consists of partitioning the total variation in an experiment into components ascribable to the controlled factors and error. The statistical significance of the fitted second order model was evaluated by the P-values of ANOVA. Table 3 shows the results of ANOVA. In ANOVA table, the sum of squares is used to estimate the square of deviation from the grand mean. Mean squares are estimated by dividing the sum of squares by degrees of freedom. F-ratio Fig. Response optimization plot for surface The model is adequate at 95% confidence level since the F calculated value is greater than the F-table value. When P- values are less than 0.05 (or 95% confidence), the obtained models are considered to be statistically significant. It demonstrates that the terms chosen in the model have significant effects on the responses. The other important coefficient is the determination coefficient, R 2, which is 27

4 defined as the ratio of the explained variation to the total variation and is a measure of the degree of fit. The more R 2 approaches to unity, the better the response model fits the actual data. TABLE III THE ANOVA TABLE FOR SURFACE ROUGHNESS Source DF SS MS F P PC (%) A B C D AB AC AD BC BD CD Residual Total 30 *PC percentage contribution TABLE IV ESTIMATED REGRESSION COEFFICIENTS FOR SURFACE ROUGHNESS (UNCODED UNITS) Factors Reg. Coeff. P R 2 Constant % A B C D AB AC AD BC BD CD III. RESULTS & DISCUSSIONS The linear and interactive factors that can affect the surface parameter, the arithmetic mean of absolute are given in Table 3. The most significant factor on the surface is number of tool pass (D), which explains.22% contribution of total variation. The next contribution on surface is from the ball diameter (A) with.35% contribution. It is clearly observed that in Fig. 3, number of tool pass has largest effect on surface. Actually this case is commonly expected. In this study, it is found out that, as the number of tool pass and ball diameter increases, the surface decreases. This case can be explained as the increase in ball diameter value increases the contact area of ball-workpiece during processing. Similarly as the number of tool pass increases, the peaks and valleys are compressed, results in decreasing the surface. A. model Estimated regression coefficients for surface using data in uncoded units are shown in Table 4. The regression equation in terms of actual factors for surface is, Ra = A B C D AB AC AD BC BD CD (2) B. Response surface analysis We consider a measure of the model s overall performance referred to as the coefficient of determination and denoted by R 2. In the model, R 2 is obtained equal to 9.9% for surface. The R 2 value indicates that the deep cold rolling parameters explain 9.9% of variance in surface. The normal probability plot of the residuals is shown in Fig. 2. The predicted values were found to be statistically similar to the actual measured values, based on the probability plot. A check on the plot in Fig. 2 shown that the residuals generally fall on a straight line implying that the errors are distributed normally. The standardized residual versus observation order plot is shown in Fig. 2. It is revealed that it has no obvious pattern and unusual structure. This implies that the model proposed is adequate. The comparison of experimental results with the RSM predictions is presented in Table 5. As seen in Table 5, the fits between experimental surface values and model surface values are very good. The comparisons of experimental results with the RSM predictions have been depicted in terms of percentage absolute error for validation set of experiments. In the prediction of surface values the average absolute error for RSM is found to be as about 5.3%. TABLE V REGRESSION DATA SHOWING ACTUAL, FIT AND RESIDUAL VALUES (µm) Exp. No % Measured Fit Error

5 C. Optimization of response RSM and DFA have been demonstrated to be efficient to optimize deep cold rolling process parameters for surface. In this study, the target for the response is a minimum value; the transformation of surface is smaller-the-better problem. One of the most important aims of experiments related to manufacturing is to achieve the desired surface of the optimal deep cold rolling parameters. Response surface optimization is an ideal technique for determination of best processing parameter combination in deep cold rolling. Here the goal is to minimize the surface. RSM optimization result for surface is shown in Fig. and Table respectively. TABLE VI RESPONSE OPTIMIZATION FOR SURFACE ROUGHNESS Optimum combination Parameters Goal D. Validation experiments Ball diameter (mm) Rolling Force (N) Initial Ra No. of Pass Minimum The purpose of the validation experiment is to validate accuracy of the predictive model. The final step of the RSM after selecting the optimum parameter combination is to predict and verify the improvement of the performance characteristics with the selected optimum parameters. Validation experiments were conducted and the results are shown in Table 7. Response TABLE VII VALIDATION EXPERIMENTS AND RESULTS A (mm) Optimum combination B (N) C (µm) Based on the experimental work, the absolute average error between the experimental and predicted values at the optimal combination of parameter settings for surface is calculated as 2.54%. The experimental results at the optimum process parameter combination confirm the effectiveness of the response surface model for optimum deep cold rolling parameters. IV. CONCLUSIONS Measured (µm) Predicted (HV) % Error In this experimental study, the evaluations of the four variables rolling force, ball diameter, initial of the work piece and number of passes on AISI 440steel were investigated by RSM. The results of the research are given below: D The significant factors on the surface were determined as number of tool pass and ball diameter with.22% and.35% contribution in the total variability of the model. The average absolute error between experimental and predicted values was calculated as about 5.3% to confirm the high predictive power of model. The experimental results at the optimum process parameter combination confirm the effectiveness of the response surface models for optimum deep cold rolling parameters. Using response optimization the optimal combination of processing parameters are (mm, N, 4.4µm, 3) for ball diameter, rolling force, initial of the workpiece and number of tool passes respectively for surface. V. REFERENCES [] G. F. Bush, J. O. Almen, L. A. Danse, J. P. Heise, How, when and by whom was mechanical prestressing discovered, Society of automotive engineers ISTC, Div. 20 meeting, SAE, Colorado Springs, Colorado 92. [2] Thomas S. Migala and Terry L. 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