Optimizing cutting force for turned parts by Taguchi s parameter design approach

Transcription

1 Indian Journal of Engineering & Materials Sciences Vol., April 005, pp. 970 Optimizing cutting force for turned parts by Taguchi s parameter design approach Hari Singh a* & Pradeep Kumar b a Mechanical Engineering Department, National Institute of Technology, Kurukshetra 6 9, India b Department of Mechanical and Industrial Engineering, Indian Institute of Technology, Roorkee , India Received August 004; accepted January 005 The objective of the paper is to obtain an optimal setting of turning process parameters (cutting speed, feed and depth of cut) resulting in an optimal value of cutting force while machining En4 alloy steel (0.4%C) with TiC coated carbide inserts. The effects of the selected process parameters have been accomplished using Taguchi s parameter design approach. The results indicate that the selected process parameterscutting speed, feed and depth of cut, as well as the interaction between cutting speed and depth of cut significantly affect the mean and variance of cutting force of En4 steel turned parts. IPC Code: BG /00 The metal cutting industries in developing countries continue to suffer from a major drawback of not running the machine tools at their optimum operating conditions. The operating conditions continue to be chosen solely on the basis of the handbook values and/or manufacturer recommendations and/or worker experience. The literature survey has revealed, a little research has been conducted to obtain the optimal levels of cutting parameterscutting speed, feed and depth of cut, that yield the best machining characteristics to difficulttomachine materials 7. En4 steel is one such material which is difficulttomachine. Its typical applications are in manufacturing of automobile and machine tools parts such as axle shafts, main shafts, differential shafts, spindle gears and power transmission gears 8. Taguchi proposes an offline strategy for quality improvement in place of an attempt to inspect quality into a product on the production line. He observes that no amount of inspection can put quality back into the product; it merely treats a symptom. To achieve desirable product quality by design, Taguchi recommends a three stage process: system design, parameter design and tolerance design. While system design helps to identify the working levels of the design parameters, parameter design seeks to determine the parameter levels that produce the best performance of the product/process under study. The optimum condition is selected so that the influence of *For correspondence ( hsingh_nitk@rediffmail.com) uncontrollable factors (noise factors) causes minimum variation to system performance. The orthogonal arrays, variance and signal to noise analysis are the essential tools of parameter design. Tolerance design is a step to fine tune the results of parameter design by tightening the tolerance of parameters with significant influence on the product. The objective of the paper is to obtain an optimal setting of process parameterscutting speed, feed and depth of cut, resulting in an optimal value of cutting force while turning En4 steel with titanium carbide coated carbide inserts. The effects of the process parameters on cutting force and the subsequent optimal settings of the parameters for obtaining optimal cutting force have been accomplished using Taguchi s parameter design approach. Background of Taguchi Method Genichi Taguchi is a Japanese engineer who has been active in the improvement of Japan s industrial products and processes since the late 940s. He has developed both a philosophy and a methodology for the process or product quality improvement that depends heavily on statistical concepts and tools, especially statistically designed experiments. Many Japanese firms have achieved great success by applying his methods. Taguchi has received some of Japan s most prestigious awards for quality achievement, including the Deming prize 9. In 986, Taguchi received the most prestigious prize from the International Technology InstituteThe Willard F.

2 98 INDIAN J. ENG. MATER. SCI., APRIL 005 Rockwell Medal for Excellence in Technology. Taguchi s major contribution has involved combining engineering and statistical methods to achieve rapid improvements in cost and quality by optimizing product design and manufacturing processes. Since 98, after Taguchi s association with the top companies and institutes in USA (AT & T Bell Laboratories, Xerox, Lawrence Institute of Technology (LIT), Ford Motor Company etc.), Taguchi methods have been called a radical approach to quality, experimental design and engineering 0. The term Taguchi method refers to the parameter design, tolerance design, the quality loss function, design of experiments using orthogonal arrays, and methodology applied to evaluate measuring systems 9. Pignatiello identifies two separate aspects of the Taguchi method (TM): the strategy of Taguchi and the tactics of Taguchi. Taguchi tactics refer to the collection of specific methods and techniques used by Genichi Taguchi and Taguchi strategy is the conceptual framework or structure for planning a product or process design experiment. Taguchi addresses design and engineering (offline) as well as manufacturing (online) quality. This fundamentally differentiates TM from statistical process control (SPC), which is purely an online quality control method,. Taguchi ideas can be distilled into two fundamental concepts: (i) Quality losses must be defined as deviation from target, not conformance to arbitrary specifications. (ii) Achieving high system quality levels economically requires quality to be designed into the product. Quality is designed, not manufactured, into the product 4,5. Taguchi methods represent a new philosophy 6. Quality is measured by the deviation of a functional characteristic from its target value. Noises (uncontrolled variables) can cause such deviations resulting in loss of quality. Taguchi methods seek to remove the effect of noises. The heart of the Taguchi philosophy is the quality loss function 7. The loss function is based on the concept that loss is incurred when a product s functional quality characteristic deviates from its target value regardless of the amount of deviations 8. Taguchi defines quality loss via his loss function. While a loss function may take on many different forms, Taguchi has found that a simple quadratic function (a parabola) approximates the behaviour of loss in many cases 0. When the quality characteristic of interest is to be maximized or minimized, the loss function may become a half parabola 9. The loss function promotes efforts to continually reduce the variation in a product s functional characteristics. Taguchi s concept of loss sets the Taguchi methods apart from the traditional SPC approach to quality which defines the cost of poor quality chiefly as cost of scrap, rework and warranty repair. Loss occurs not only when the product is outside of specifications, but also when product falls within specifications 0. This brings TM s view of the world in line with the view of the consumer. Taguchi recommends the use of the criteria he calls SignaltoNoise (S/N)ratios as performance statistics. The change in quality characteristic of a product under investigation in response to a factor introduced in the experimental design is the signal of the desired effect. The effect of the external factors (uncontrollable factors) on the outcome of the quality characteristic under test is termed the noise. The signal to noise ratio measures the sensitivity of the quality characteristic being investigated in a controlled manner, to those external influencing factors (noise factors) not under control. The S/N ratio is basically a transformed figure of merit, created from the loss function. To use the loss function as a figure of merit an appropriate loss function with its constant value must first be established which is not always cost effective and easy. Taguchi recognized this dilemma early in the development of his methodologies and created the transform for the loss function, which is named S/N ratio 7. The S/N is a concurrent statistic which is able to look at two characteristics of a distribution and roll these characteristics into a single number or figure of merit. The S/N ratio combines both the parameters (the mean level of the quality characteristic and variation around this mean) in a single metric. Taguchi has developed over 70 distinct S/N ratios. Each of these is a customized measure of the performance characteristic in term of location (mean) and dispersion (variation) 7. The aim in any experiment is always to determine the highest possible S/N ratio for the result irrespective of the type of the quality characteristics. A high value of S/N implies that signal is much higher than the random effects of noise factors 0,. Turning Process Parameters In order to identify the process parameters that may affect the machining characteristics of turned parts, an

3 SINGH & KUMAR: OPTIMAL SETTING OF TURNING PROCESS PARAMETERS 99 Ishikawa causeeffect diagram was constructed and is shown in Fig.. The identified process parameters affecting the characteristics of turned parts are 5 : (i) cutting tool parameterstool geometry and tool material, (ii) work piece related parametersmetallography, hardness, (iii) cutting parameterscutting speed, feed, depth of cut, and (iv) environment parametersdry cutting and wet cutting. En4 steel is a difficulttomachine material and finds its typical applications in the manufacturing of automobile and machine tool parts. Because of its wide application En4 steel has been selected as the work material in this work. The recently developed tool materials like coated carbides have improved the productivity levels of difficulttomachine materials. The following process parameters were thus selected for the present work 6 : cutting speed (A), feed (B), depth of cut (C), tool material Widadur TG inserts, work material En4 steel, and environment dry cutting. The ranges of the selected turning process parameters (cutting speed, feed and depth of cut) were ascertained by conducting some preliminary experiments using one variable at a time approach. The following parameters were kept constant in the entire scheme of experimentation 6 : Work material : En4 steel Cutting tool : Widadur TG Insert geometry : SPUN 0 08 (ISO designation) Tool holder : CSBPR 55H (ISO designation) Tool overhang : 0 mm Cutting conditions : Dry Fig. Ishikawa causeeffect diagram of a turning process Selection of an orthogonal array (OA) In selecting an appropriate OA, the prerequisites are : (i) selection of process parameters and interactions to be evaluated, and (ii) selection of number of levels for the selected parameters. The nonlinear behaviour of the process parameters, if exists, can only be revealed if more than two levels of the parameters are investigated 9. Therefore, each parameter was analyzed at three levels. The process parameters along with their values at three levels are given in Table. It was also decided to study the two factor interaction effects on the cutting force. The selected interactions were: (i) between cutting speed and feed (A B), (ii) between feed and depth of cut (B C), and (iii) between cutting speed and depth of cut (A C). With three parameters each at three levels and three secondorder interactions the total degree of freedom (DOF) required is 8, since a three level parameter has DOF (number of levels) and each second order interaction has 4 DOF (product of DOF of interacting parameters). As per Taguchi s method the total DOF of the selected OA must be greater than or equal to the total DOF required for the experiment. So, an L 7 ( ) OA (a standard level orthogonal array) having 6 DOF was selected for the present work. The L 7 OA with process parameters and interactions assigned is given in Table. The parameters and interactions have been assigned to specific column of the array using linear graphs 7. Experimental analysis En4 alloy steel rods of 90 mm diameter and 500 mm length were turned on an H centre lathe of H.M.T. TiC coated carbide inserts were used to machine En4 steel (0.4%C) of 0 BHN. The trial conditions are given in Table. Three specimens for each trial condition were prepared using randomization technique. Thus 8 specimens were turned and the cutting force was measured for each specimen using a threedimensional turning dynamometer. The results of the experiments for twentyseven trial conditions with three repetitions are reported in Table. Table Process parameters with their values at three levels Process Parameters Levels parameters designation L L L Cutting speed A (m/min) Feed B (mm/rev) Depth of cut C (mm)

4 INDIAN J. ENG. MATER. SCI., APRIL The selected quality characteristic, cutting force, is a lower the better type and the signal to noise (S/N) ratio for lower the better type of response was used as given below 0 : S/N ratio (in db) = ( ) 0 log... n y y y n () where y, y y n are the responses of quality characteristic for a trial condition repeated n times. The S/N ratios were computed using Eq. () for each of the 7 trials and the values are reported in Table along with the raw data. The mean response refers to the average value of the performance characteristic for each parameter at different levels. The average values of cutting force for each parameter at levels, and were calculated and are plotted in Fig.. The average values of S/N ratios of various parameters at different levels are also plotted in Fig.. It is clear from Fig. that cutting force is minimum at the rd level of parameter A (cutting speed), st level of parameter B (feed) and st level of parameter C (depth of cut). The S/N ratio analysis (Fig. ) also suggests the same levels of the parameters (A, B and C ) as the best levels for minimum cutting force of En4 steel turned parts. The interaction graph between cutting speed and depth of cut (not shown) reveals that A C is the best treatment combination to give minimum cutting force. Thus the interaction analysis reinforces the selection of rd level of cutting speed (A ) and st level of depth of cut (C ) based on their individual effects. In order to study the significance of the parameters in affecting the quality characteristic of interest (cutting force), analysis of variance (ANOVA) was Table L 7 ( ) Orthogonal array (process parameters and interactions assigned) with responses (raw data & S/N ratios) Column A B A B A B C A C A C B C B C Trial

5 SINGH & KUMAR: OPTIMAL SETTING OF TURNING PROCESS PARAMETERS 0 Table Experimental data of cutting force and signal to noise ratio Trial Cutting force (N) S/N Ratio (db) No. R R R Total T CF = Overall mean of CF = N CF = Cutting force performed. The pooled ANOVA of the raw data (cutting force) is given in Table 4. The S/N ANOVA (pooled version) is given in Table 5. It is clear from ANOVAs (Tables 4 and 5) that the parameters A, B and C (cutting speed, feed and depth of cut respectively) and the interaction between cutting speed and depth of cut (A C) significantly affect both the mean value as well as the variation of the cutting force. The percent contributions of factors as quantified under column P of Tables 4 and 5 reveal that the relative power of depth of cut (C) and feed (B) in controlling the mean and variation is significantly larger than the relative power of cutting speed (A). Fig. Effects of process parameters on cutting force (raw data) and S/N data (main effects) Table 4 ANOVA (raw data: cutting force) Source SS DOF V F ratio SS / P A B C A B B C A C T e (pooled) (05) (48) (494) (70) SS = Sum of squares, DOF = Degrees of Freedom, V = Variance, T = Total SS / = pure sum of squares, P = Percent contribution, e = error, Tabulated Fratio at 95% confidence level: F 0.05; ; 70 =.; F 0.05;4;70 =.50 * Significant at 95% confidence level. 6.58* 79.0* 7.45* 8.*

6 0 INDIAN J. ENG. MATER. SCI., APRIL 005 Table 5 S/N ANOVA (raw data: cutting force) Source SS DOF V F ratio SS / P A B C A B B C A C T e (pooled) (0.089) ( ) (0.4964) (6) * 5.8* * 5.5* Tabulated Fratio at 95% confidence level: F 0.05; ; 6 =.6; F 0.05; 4; 6 =.0 * Significant at 95% confidence level. Estimating Optimal Cutting Force The optimal cutting force (μ CF ) is predicted at the selected optimal setting of process parameters. The significant parameters with optimal levels are already selected as: A, B and C. The interaction effect is not being considered in estimating mean and confidence interval around the estimated mean due to poor additivity between parameters and interaction 0. The estimated mean of the response characteristic can be computed as 0 : μ CF = A + B + C T CF () where T CF = overall mean of cutting force = 45.56N (Table ); A, B and C are the mean values of cutting force with parameters at optimum levels. From Fig. : A = 46 N, B = 45 N, C = 8 N Hence, μ CF = = 4.88 N A confidence interval for the predicted mean on a confirmation run can be calculated using the following equation 0 : C.I. = Fα (, fe) Ve + n eff R () where, F α (, f e ) is the F ratio required for α, α is the risk, f e is the error DOF, V e is the error variance, n eff is the effective number of replications and is equal to N, +[Total DOF associated in the estimate of mean] R is the number of repetitions for confirmation experiment and N is the total number of experiments. Using the values V e = and f e = 70 from Table 4, the C.I. was calculated. Total DOF associated with the mean (μ CF ) = = 6 Total trials = 7; N = 7 = 8; n eff = =.57; α = 0.05 F 0.05 (, 70) =.98 (tabulated) The calculated C.I. is: C.I. = ± 8.57 The predicted mean of the cutting force is: μ CF = 4.88 N The 95% confidence interval of the predicted optimal cutting force is: (μ CF C.I.) < μ CF (N)<(μ CF + C.I.) 96. <μ CF (N)< 5.45 Confirmation experiment Three confirmation experiments were conducted at the optimal setting of turning process parameters recommended by the investigation. The average value of cutting force was found to be 4N. This result was within the C.I. of the predicted optimal cutting force. Conclusions. The percent contributions of parameters in affecting variation in cutting force while machining En4 steel with carbide inserts of ISO designation SPUN 008 are: depth of cut (70.50%), feed (9.44%), and cutting speed (4.50%).. The optimal setting of process parameters for optimal cutting force are: cuting speed (0 m/min), feed (0.4 mm/rev), and depth of cut (0.70 mm).. The percent contribution of interaction between cutting speed and depth of cut (A C) to the variation of cutting force is.64% while the other interactions: between cutting speed and feed (A B),

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