- Email: [email protected]
Optimization of shot peening parameters using Taguchi technique
Journal of Materials Processing Technology 153–154 (2004) 925–930
Optimization of shot peening parameters using Taguchi technique P.M. George a,∗ , Nisha Pillai b , Nisha Shah b a
Mechanical Engineering Department, B.V.M. Engineering College, Vallabh Vidyanagar, Anand District, Gujarat State 388120, India b B.V.M. Engineering College, Vallabh Vidyanagar, Anand District, Gujarat State 388120, India
Abstract Application of the Taguchi method to the optimization of the critical peening parameters is reported in this paper. The Taguchi method is used to formulate the experimental layout, to establish the order of predominance among the identified critical parameters and predict the optimal setting for each of the process parameters. The experimental results obtained confirm the adequacy and effectiveness of this approach. © 2004 Elsevier B.V. All rights reserved. Keywords: Shot peening; Taguchi technique; Analysis of variance
1. Introduction Though the discovery of shot peening was accidental it is the most widely used method for pre-stressing by mechanically induced yielding. It is nowadays used with hundreds of different components like railway and automobile leaf springs, helical springs of all types, gears, axle bearings, crankshafts, pneumatic drills, milling cutters, connecting rods, coil springs, cylinder blocks, valve springs, washers, etc. [1]. In scale and scope the variety of shot peening applications is considerable [2]. It ranges from the treatment of large aircraft undercarriage components to delicate miniaturized electronic components subjected to stress. In aerospace applications the shot peening needs to be carried out to very strict specifications to meet stringent safety requirements laid down by airline manufacturers, which demands selection and control of the peening parameters for consistent peening performance [3]. The response of the peening intensity when one process parameter is varied while keeping all others constant has been studied and established. But in the actual process carried out in the industrial environment, all parameters are varied simultaneously. The effect of simultaneous variation of the process parameters on the response is yet to be analyzed. In this paper an approach based on the Taguchi methodology is used as an efficient method to determine the factor and interaction effects as well as optimize peening intensity in
∗ Corresponding author. E-mail address: [email protected] (P.M. George).
0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.04.159
this context. The experiments required for the analysis is performed at Indabrator Ltd., Karamsad, Anand, India.
2. Description of the Taguchi method The Taguchi method is a powerful design of experiments (DOE) tool developed by G. Taguchi. It provides a simple, efficient, and systematic approach to optimize designs for performance, quality and cost. The methodology is valuable when process parameters are qualitative and discrete. He proposed that the engineering optimization of a process should be carried out in a three-step approach: system design, parameter design and tolerance design. In the system design, the engineer applies scientific and engineering knowledge to produce a basic functional prototype design. This prototype design includes the product design stage and the process design stage. Following the system design is the parameter design. The objective of the parameter design is to optimize the settings of the process parameter values. Finally, the tolerance design is used to determine and analyze tolerances around the optimal settings recommended by the parameter design. The parameter design is the key step in the Taguchi method to achieve high quality without increasing cost and the same is adopted in this paper. Taguchi method uses a special design called orthogonal arrays to study the entire parameter space with only a small number of experiments. A statistical analysis of variance (ANOVA) is performed to identify the process parameters that are statistically significant. The optimal combination of the process parameters can then be predicted based on the above analysis [4–8].
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P.M. George et al. / Journal of Materials Processing Technology 153–154 (2004) 925–930
3. The peening process
Table 1 Parameter levels and their values
Shot peening is defined as a means of cold working the surface of metal parts by means of hail or a blast of round metal or non-metal shot directed against the surface. This process induces a hemisphere of cold worked material highly stressed in compression just below the surface of the worked component, which is extremely critical fatigue wise. Since fatigue failures are cracks and cracks never open unless adjacent particles are pulled apart, it may be assumed that cracks can neither start in a compressive layer nor propagate into it. The induced residual compressive stress can neutralize a considerable portion of the tensile stress that may act on the surface of the component during service. Thus, consequently the fatigue life and in turn the part life of the component increases. The magnitude of the compressive stress induced and the depth of the induced layer depend considerably on the peening intensity. Peening intensity can be defined as a measure of the kinetic energy within a stream of peening media. Peening intensity attained can vary with shot size, shot hardness, shot speed, shot flow rate, impact angle, coverage, etc. Research is being carried out for development of non-destructive inspection for peening, but until a reliable technique is evolved, in order to have confidence in the process, it is necessary to monitor and control the process parameters closely. The process parameters can be controlled by test strips held flat and exposed to the shot beam and peened on one side. Single side exposure of the strips produce a curvature and the arc height is measured and the arc height can be used to interpret the relative shot peening intensity [9].
Parameters
Level 1
Level 2
Time, t (min) Work height, h (mm) Shot size, d (mm) Shot flow rate, Q (kg/min)
4 508 Mix (S230 and S170) 95
6 1016 S230 207
3.1. Measuring peening intensity
4. Optimization of process parameters
Peening intensity can be measured using Almen strips and an Almen gauge. Basically, the Almen strip is a piece of spring tool steel that is blasted on one side and made to curve in response to the intensity of the impinging blast stream. By measuring the curvature, or arc height, we can interpret the relative shot peening intensity. The arc height is measured using the Almen gauge, consisting of a dial or digital indicator of least count 0.001 in., a plunger and platform area for Almen strips. The Almen strip is placed and retained magnetically against the contacts with the un-peened side towards the dial gauge stem and the arc height is read directly.
The experiment is conducted using L8 orthogonal arrays according to Taguchi methodology. The results obtained are analyzed using the software ‘Qualitek 4’.
chine manufactured by Indabrator, a WHEELABRATOR Company. Exposure time is varied by setting the timer of least count 0.5 min on the control panel of the machine. Two standard Almen blocks are positioned at the center to be in line with a vertical blast in order to make the situation as near to peening as possible. The shot flow rate is varied by adjusting the opening of the slide valve, located above the wheel abrator, at different positions. The size distribution of the shots for the two levels used, as obtained by sieve analysis carried out as per SAE specification, is as shown in Fig. 1. The effect on the response function during individual variation of the process parameters has been established. Peening intensity increases with increase in exposure and shot size. As the flow rate increases, the number of pellets striking the work surface increases which will increase the amount of work done on the surface and in turn the peening intensity. As the work height decreases, the impact of the shots on the work surface increases. Thus the energy transferred to the surface increases consequently increasing the peening intensity. This paper undertakes the study of the effect on peening intensity when the above-mentioned process parameters are varied simultaneously.
4.1. Orthogonal array experiment The selection of an appropriate orthogonal array depends on the total degrees of freedom of an experiment. Degrees of freedom are defined as the number of comparisons between
3.2. Setting the levels of the process parameters The critical process parameters that have been selected for this study, on the basis of significance are: (a) work height (distance of the component from the blade edge); (b) shot flow rate; (c) exposure time; (d) shot size. These parameters were varied at two levels as shown in Table 1. The experiments are conducted using Grade II Almen strips, satisfying the SAE specifications, from Electronic, Inc. and are peened in 72 in. swing table shot blasting ma-
Fig. 1. Size distribution of the shots used in the experiment.
P.M. George et al. / Journal of Materials Processing Technology 153–154 (2004) 925–930
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Table 2 The experimental layout according to the L8 orthogonal array
Table 4 The peening intensities recorded in terms of arc height
Trial no.
Exposure time, t (min)
Work height, h (mm)
Shot size, d (mm)
Flow rate, Q (kg/min)
Experiment no.
Reading 1 (mm)
Reading 2 (mm)
Average (mm)
1 2 3 4 5 6 7 8
1 1 1 1 2 2 2 2
1 1 2 2 1 1 2 2
1 1 2 2 2 2 1 1
1 2 1 2 1 2 1 2
1 2 3 4 5 6 7 8
0.254 0.1778 0.3683 0.381 0.2921 0.2667 0.3683 0.3429
0.2413 0.1905 0.381 0.381 0.2794 0.2667 0.3556 0.3556
0.2476 0.1841 0.3746 0.381 0.2857 0.2667 0.36195 0.34925
Table 3 Experimental layout after assigning the values of the parameters
Table 5 The average of two levels for each parameter
Experiment no.
Actual trial no.
Exposure time, t (min)
Work height, h (mm)
Shot size, d (mm)
Flow rate, Q (kg/min)
Column no.
Factors
Level 1 (mm)
Level 2 (mm)
Level 2 − Level 1 (mm)
1 2 3 4 5 6 7 8
5 8 1 4 2 3 6 7
4 4 4 4 6 6 6 6
508 508 1016 1016 508 508 1016 1016
Mix Mix S230 S230 S230 S230 Mix Mix
95 207 95 207 95 207 95 207
1 2 3 4
t (min) h (mm) d (mm) Q (kg/min)
0.296 0.245 0.285 0.316
0.315 0.366 0.326 0.294
0.019 0.120 0.041 −0.230
process parameters that need to be made to determine which level is better and specifically how much better it is. For example, a two-level process parameter counts for one degree of freedom. The degrees of freedom associated with interaction between two process parameters are given by the product of the degrees of freedom for the two process parameters. In the present study, three interactions between the parameters are taken into account. There are four sets of peening parameters being considered for this study. Therefore, there will be seven degrees of freedom in total. The degrees of freedom for the orthogonal array should be greater than or at least equal to those for the experiment. In this study, the standard L8 orthogonal array is used. The experimental layout for the peening parameters using the L8 orthogonal array is shown in Table 2. The experimental layout after assigning the values of the parameters is shown in Table 3. Complete randomization within blocks is used to minimize the influence of the variation of any unknown and uncontrolled factor. The trials are conducted randomly, in
two blocks, i.e., experiment numbers 3–6 in block 1 and the remaining in block 2. The peening intensities recorded in terms of arc height based on the experimental layout are as shown in Table 4. 4.2. Effect of simultaneous variation on response The grand average of the peening performance is found to be 0.305 mm. Table 5 indicates the average of two levels for each parameter. The graphs in Fig. 2(a) and (b) show the effect of parameters time and height, with respect to the grand performance average, and symbolizes that peening intensity increases with respect to time and height. The graphs in Fig. 3 (a) and (b) symbolizes that peening intensity increases with respect to shot size and shot flow rate. This is in accordance with established relations. 4.3. Analysis of variance The ANOVA table derived for this study is as shown in Table 6. The degree of freedom signifies the extent of influence of error to experimental results. The greater is the number of degrees of freedom, the greater will be its influence.
Fig. 2. Variation of peening intensity with respect to time and height.
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Fig. 3. Variation of peening intensity with respect to shot size and shot flow rate.
The sum of squares provides a measure of the total variation present. The largest contribution to the total sum of squares is of factor ‘h’ followed by factor ‘s’ and then ‘Q’. The larger is the contribution of a particular factor to the total sum of squares, the larger is its ability to influence its quality characteristic. It can be seen that the contribution of error to the total sum of squares is zero, i.e., very small, which indicates that error has almost negligible effect on the quality characteristic. The larger is the variance of a factor, the larger is its ability to influence the quality characteristic. Error variance is a measure of the variation due to all the uncontrolled parameters, including measurement error involved in a particular experiment (set of data collected). Referring to the ANOVA table, it can be seen that the error variance in this case is very small. So it can be inferred that the variation due to all the uncontrolled and unknown parameters is almost negligible. In addition, the F-test can also be used to determine which process parameters have a significant effect on the quality characteristic. Usually, when the F-value is greater than 4, it means that the change of the process parameter has a significant effect on the quality characteristic. The value of F can also be used to rank order the factors. From the ANOVA table, it can be inferred that the work height, shot size and shot flow rate have a significant effect on the peening intensity. The factor ‘t’ has an F-ratio of less than 4. The most significant factor is the work height followed by shot size, shot flow rate and exposure time. Pure sum is used to calculate the percentage contribution of a factor to the total variation. The portion of the total variation observed in an experiment attributed to each significant factor and/or interaction is reflected in the percent contribution. The percent contribution is a function of the sums of squares for each significant item. The percent contribution indicates the relative power of a
factor and/or interaction to reduce variation. If the factor and/or interaction levels were controlled precisely, then the total variation could be reduced by the amount indicated by the percent contribution. The percent contribution due to error provides an estimate of the adequacy of the experiment. As the percent contribution due to error is low, 15% or less, then it is assumed that no important factors were omitted from the experiment [9]. In this study the error contribution is only 8.642 and hence the experiment has been sufficient in terms that all critical process parameters have been evaluated and variations in conditions and measurement was a minimum. 4.4. Optimization of peening parameters Table 7 shows the settings of the levels to obtain an optimum peening intensity. The contribution of each factor to increase the peening intensity to the optimum is also indicated. It is seen that there is a 32.45% increase in the peening intensity at the optimum conditions. It is seen that the contribution of work height is most significant to increase peening Table 7 The settings of the levels of variables to obtain optimum peening intensity Column no.
Factor
Level description
Level
Contribution
1 2 3 4
t h d Q
6 1016 Level 2 95
2 2 2 1
0.009 0.06 0.02 0.01
Total contribution from all factors to increase the peening intensity = 0.099 mm; current grand average of performance = 0.305 mm; expected result at optimum condition = 0.404 mm; percent increase in intensity after optimization = ((0.404 − 0.305)/0.305) × 100 = 32.45%.
Table 6 The ANOVA table Column no.
Factor
Degrees of freedom (f)
Sum of squares (SS)
Variance (V)
F-ratio (F)
Pure sum (S)
1 2 3 4 Other error
t h d Q –
1 1 1 1 3
0 0.058 0.006 0.002 0
0 0.058 0.006 0.002 0
1.603 202.411 23.209 7.027 –
0 0.058 0.006 0.001 –
Total
–
7
0.035
–
–
–
Percent contribution, P (%) 0.744 80.842 8.344 1.428 8.642 100
P.M. George et al. / Journal of Materials Processing Technology 153–154 (2004) 925–930 Table 8 Table of interaction of variables Sr. no.
Interacting factor pairs
Columns interaction
Severity index, SI (%)
Optimum levels
1 2 3
d×Q t×Q h×Q
3×4 1×4 2×4
24.99 15.43 13.50
2, 1 2, 1 2, 1
intensity to the optimum followed by shot size, shot flow rate and exposure time. 4.5. Interaction effects The synergistic effect of two or more factors in a factorial experiment where effect of one factor depends on
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the variation of another is called interaction and the same are shown in Table 8. The severity index is the measure of the extent of the interaction between two chosen parameters. It can be inferred from the values indicated in the table, that the factors shot size and shot flow rate have the maximum interaction between them. The optimum level for each of the factors of the interacting pair to achieve the optimum peening intensity is also indicated in the table. A histogram depicting the severity index of the interacting pairs is shown in Fig. 4. The graphs showing the interactions of the parameters have been plotted in Fig. 5(a)–(c). As the severity index increases, the lines in the above graphs tend to intersect each other at right angles and as it decreases the lines tend to be parallel to each other.
5. Conclusion
Fig. 4. Histogram depicting the severity index of interacting pairs.
From the percent contribution of each factor indicated in the ANOVA table (Table 6) it could be inferred that work height is the most predominant factor. The critical process parameters, according to their relative significance, are work height, shot size, shot flow rate and exposure time. The study indicates that the effect on the peening intensity, when the parameters are varied simultaneously, is quite different from that observed when parameters are varied individually. This is attributed to the interactions that exist between the parameters when they are varied simultaneously. It is found that peening intensity increases with respect to work height while it decreases with respect to shot flow rate. The optimum peening intensity is obtained by setting work height at 1016 mm, shot flow rate at 95 kg/min, exposure time at 6 min and shot size at S230. The peening intensity is found to increase by 32.45% at this optimum level. The interaction effects are also studied and the graphs shown in Fig. 8, establishes that shot size and shot flow rate interact maximum. Based on these results, it can be inferred that for optimum intensity, the amount of shot required is comparatively less. The designers of the peening machines can use the order of predominance established, while designing the machines. It can also be used to fulfil specific requirements raised by the quality and economy conscious customers. Applying the optimized results derived in this study can also enhance the performance level.
References
Fig. 5. The graphs showing the interactions of the parameters.
[1] Society of Automotive Engineers Handbook, SAE Publications, 1964. [2] L. Wagner, Response of light alloys to shot peening: comparison of magnesium and aluminium alloy, Met. Finish. News 3 (2002) 12– 13. [3] G. Levasseur, Peen forming feature possibility for wing skin fabrication, Met. Finish. News 3 (2002) 4–5.
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[4] A. Garcia-Diaz, D.T. Philips, Principles of Experimental Design and Analysis, Chapman & Hall, 1995. [5] D.R. Cox, N. Reid, The Theory of the Design of Experiments, Chapman & Hall/CRC, 2000. [6] C. Douglas, Montgomery, Design and Analysis of Experiments, Wiley, 2001.
[7] R.A. Johnson, Miller and Freund’s Probability and Statistics for Engineers, PHI, 2001. [8] P.J. Ross, Taguchi Techniques for Quality Engineering, McGraw-Hill, 1989. [9] A.H. Burr, J.B. Cheathan, Mechanical Analysis and Design, PHI India Pvt. Ltd, 1997.
Optimization of shot peening parameters using Taguchi technique P.M. George a,∗ , Nisha Pillai b , Nisha Shah b a
Mechanical Engineering Department, B.V.M. Engineering College, Vallabh Vidyanagar, Anand District, Gujarat State 388120, India b B.V.M. Engineering College, Vallabh Vidyanagar, Anand District, Gujarat State 388120, India
Abstract Application of the Taguchi method to the optimization of the critical peening parameters is reported in this paper. The Taguchi method is used to formulate the experimental layout, to establish the order of predominance among the identified critical parameters and predict the optimal setting for each of the process parameters. The experimental results obtained confirm the adequacy and effectiveness of this approach. © 2004 Elsevier B.V. All rights reserved. Keywords: Shot peening; Taguchi technique; Analysis of variance
1. Introduction Though the discovery of shot peening was accidental it is the most widely used method for pre-stressing by mechanically induced yielding. It is nowadays used with hundreds of different components like railway and automobile leaf springs, helical springs of all types, gears, axle bearings, crankshafts, pneumatic drills, milling cutters, connecting rods, coil springs, cylinder blocks, valve springs, washers, etc. [1]. In scale and scope the variety of shot peening applications is considerable [2]. It ranges from the treatment of large aircraft undercarriage components to delicate miniaturized electronic components subjected to stress. In aerospace applications the shot peening needs to be carried out to very strict specifications to meet stringent safety requirements laid down by airline manufacturers, which demands selection and control of the peening parameters for consistent peening performance [3]. The response of the peening intensity when one process parameter is varied while keeping all others constant has been studied and established. But in the actual process carried out in the industrial environment, all parameters are varied simultaneously. The effect of simultaneous variation of the process parameters on the response is yet to be analyzed. In this paper an approach based on the Taguchi methodology is used as an efficient method to determine the factor and interaction effects as well as optimize peening intensity in
∗ Corresponding author. E-mail address: [email protected] (P.M. George).
0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.04.159
this context. The experiments required for the analysis is performed at Indabrator Ltd., Karamsad, Anand, India.
2. Description of the Taguchi method The Taguchi method is a powerful design of experiments (DOE) tool developed by G. Taguchi. It provides a simple, efficient, and systematic approach to optimize designs for performance, quality and cost. The methodology is valuable when process parameters are qualitative and discrete. He proposed that the engineering optimization of a process should be carried out in a three-step approach: system design, parameter design and tolerance design. In the system design, the engineer applies scientific and engineering knowledge to produce a basic functional prototype design. This prototype design includes the product design stage and the process design stage. Following the system design is the parameter design. The objective of the parameter design is to optimize the settings of the process parameter values. Finally, the tolerance design is used to determine and analyze tolerances around the optimal settings recommended by the parameter design. The parameter design is the key step in the Taguchi method to achieve high quality without increasing cost and the same is adopted in this paper. Taguchi method uses a special design called orthogonal arrays to study the entire parameter space with only a small number of experiments. A statistical analysis of variance (ANOVA) is performed to identify the process parameters that are statistically significant. The optimal combination of the process parameters can then be predicted based on the above analysis [4–8].
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P.M. George et al. / Journal of Materials Processing Technology 153–154 (2004) 925–930
3. The peening process
Table 1 Parameter levels and their values
Shot peening is defined as a means of cold working the surface of metal parts by means of hail or a blast of round metal or non-metal shot directed against the surface. This process induces a hemisphere of cold worked material highly stressed in compression just below the surface of the worked component, which is extremely critical fatigue wise. Since fatigue failures are cracks and cracks never open unless adjacent particles are pulled apart, it may be assumed that cracks can neither start in a compressive layer nor propagate into it. The induced residual compressive stress can neutralize a considerable portion of the tensile stress that may act on the surface of the component during service. Thus, consequently the fatigue life and in turn the part life of the component increases. The magnitude of the compressive stress induced and the depth of the induced layer depend considerably on the peening intensity. Peening intensity can be defined as a measure of the kinetic energy within a stream of peening media. Peening intensity attained can vary with shot size, shot hardness, shot speed, shot flow rate, impact angle, coverage, etc. Research is being carried out for development of non-destructive inspection for peening, but until a reliable technique is evolved, in order to have confidence in the process, it is necessary to monitor and control the process parameters closely. The process parameters can be controlled by test strips held flat and exposed to the shot beam and peened on one side. Single side exposure of the strips produce a curvature and the arc height is measured and the arc height can be used to interpret the relative shot peening intensity [9].
Parameters
Level 1
Level 2
Time, t (min) Work height, h (mm) Shot size, d (mm) Shot flow rate, Q (kg/min)
4 508 Mix (S230 and S170) 95
6 1016 S230 207
3.1. Measuring peening intensity
4. Optimization of process parameters
Peening intensity can be measured using Almen strips and an Almen gauge. Basically, the Almen strip is a piece of spring tool steel that is blasted on one side and made to curve in response to the intensity of the impinging blast stream. By measuring the curvature, or arc height, we can interpret the relative shot peening intensity. The arc height is measured using the Almen gauge, consisting of a dial or digital indicator of least count 0.001 in., a plunger and platform area for Almen strips. The Almen strip is placed and retained magnetically against the contacts with the un-peened side towards the dial gauge stem and the arc height is read directly.
The experiment is conducted using L8 orthogonal arrays according to Taguchi methodology. The results obtained are analyzed using the software ‘Qualitek 4’.
chine manufactured by Indabrator, a WHEELABRATOR Company. Exposure time is varied by setting the timer of least count 0.5 min on the control panel of the machine. Two standard Almen blocks are positioned at the center to be in line with a vertical blast in order to make the situation as near to peening as possible. The shot flow rate is varied by adjusting the opening of the slide valve, located above the wheel abrator, at different positions. The size distribution of the shots for the two levels used, as obtained by sieve analysis carried out as per SAE specification, is as shown in Fig. 1. The effect on the response function during individual variation of the process parameters has been established. Peening intensity increases with increase in exposure and shot size. As the flow rate increases, the number of pellets striking the work surface increases which will increase the amount of work done on the surface and in turn the peening intensity. As the work height decreases, the impact of the shots on the work surface increases. Thus the energy transferred to the surface increases consequently increasing the peening intensity. This paper undertakes the study of the effect on peening intensity when the above-mentioned process parameters are varied simultaneously.
4.1. Orthogonal array experiment The selection of an appropriate orthogonal array depends on the total degrees of freedom of an experiment. Degrees of freedom are defined as the number of comparisons between
3.2. Setting the levels of the process parameters The critical process parameters that have been selected for this study, on the basis of significance are: (a) work height (distance of the component from the blade edge); (b) shot flow rate; (c) exposure time; (d) shot size. These parameters were varied at two levels as shown in Table 1. The experiments are conducted using Grade II Almen strips, satisfying the SAE specifications, from Electronic, Inc. and are peened in 72 in. swing table shot blasting ma-
Fig. 1. Size distribution of the shots used in the experiment.
P.M. George et al. / Journal of Materials Processing Technology 153–154 (2004) 925–930
927
Table 2 The experimental layout according to the L8 orthogonal array
Table 4 The peening intensities recorded in terms of arc height
Trial no.
Exposure time, t (min)
Work height, h (mm)
Shot size, d (mm)
Flow rate, Q (kg/min)
Experiment no.
Reading 1 (mm)
Reading 2 (mm)
Average (mm)
1 2 3 4 5 6 7 8
1 1 1 1 2 2 2 2
1 1 2 2 1 1 2 2
1 1 2 2 2 2 1 1
1 2 1 2 1 2 1 2
1 2 3 4 5 6 7 8
0.254 0.1778 0.3683 0.381 0.2921 0.2667 0.3683 0.3429
0.2413 0.1905 0.381 0.381 0.2794 0.2667 0.3556 0.3556
0.2476 0.1841 0.3746 0.381 0.2857 0.2667 0.36195 0.34925
Table 3 Experimental layout after assigning the values of the parameters
Table 5 The average of two levels for each parameter
Experiment no.
Actual trial no.
Exposure time, t (min)
Work height, h (mm)
Shot size, d (mm)
Flow rate, Q (kg/min)
Column no.
Factors
Level 1 (mm)
Level 2 (mm)
Level 2 − Level 1 (mm)
1 2 3 4 5 6 7 8
5 8 1 4 2 3 6 7
4 4 4 4 6 6 6 6
508 508 1016 1016 508 508 1016 1016
Mix Mix S230 S230 S230 S230 Mix Mix
95 207 95 207 95 207 95 207
1 2 3 4
t (min) h (mm) d (mm) Q (kg/min)
0.296 0.245 0.285 0.316
0.315 0.366 0.326 0.294
0.019 0.120 0.041 −0.230
process parameters that need to be made to determine which level is better and specifically how much better it is. For example, a two-level process parameter counts for one degree of freedom. The degrees of freedom associated with interaction between two process parameters are given by the product of the degrees of freedom for the two process parameters. In the present study, three interactions between the parameters are taken into account. There are four sets of peening parameters being considered for this study. Therefore, there will be seven degrees of freedom in total. The degrees of freedom for the orthogonal array should be greater than or at least equal to those for the experiment. In this study, the standard L8 orthogonal array is used. The experimental layout for the peening parameters using the L8 orthogonal array is shown in Table 2. The experimental layout after assigning the values of the parameters is shown in Table 3. Complete randomization within blocks is used to minimize the influence of the variation of any unknown and uncontrolled factor. The trials are conducted randomly, in
two blocks, i.e., experiment numbers 3–6 in block 1 and the remaining in block 2. The peening intensities recorded in terms of arc height based on the experimental layout are as shown in Table 4. 4.2. Effect of simultaneous variation on response The grand average of the peening performance is found to be 0.305 mm. Table 5 indicates the average of two levels for each parameter. The graphs in Fig. 2(a) and (b) show the effect of parameters time and height, with respect to the grand performance average, and symbolizes that peening intensity increases with respect to time and height. The graphs in Fig. 3 (a) and (b) symbolizes that peening intensity increases with respect to shot size and shot flow rate. This is in accordance with established relations. 4.3. Analysis of variance The ANOVA table derived for this study is as shown in Table 6. The degree of freedom signifies the extent of influence of error to experimental results. The greater is the number of degrees of freedom, the greater will be its influence.
Fig. 2. Variation of peening intensity with respect to time and height.
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P.M. George et al. / Journal of Materials Processing Technology 153–154 (2004) 925–930
Fig. 3. Variation of peening intensity with respect to shot size and shot flow rate.
The sum of squares provides a measure of the total variation present. The largest contribution to the total sum of squares is of factor ‘h’ followed by factor ‘s’ and then ‘Q’. The larger is the contribution of a particular factor to the total sum of squares, the larger is its ability to influence its quality characteristic. It can be seen that the contribution of error to the total sum of squares is zero, i.e., very small, which indicates that error has almost negligible effect on the quality characteristic. The larger is the variance of a factor, the larger is its ability to influence the quality characteristic. Error variance is a measure of the variation due to all the uncontrolled parameters, including measurement error involved in a particular experiment (set of data collected). Referring to the ANOVA table, it can be seen that the error variance in this case is very small. So it can be inferred that the variation due to all the uncontrolled and unknown parameters is almost negligible. In addition, the F-test can also be used to determine which process parameters have a significant effect on the quality characteristic. Usually, when the F-value is greater than 4, it means that the change of the process parameter has a significant effect on the quality characteristic. The value of F can also be used to rank order the factors. From the ANOVA table, it can be inferred that the work height, shot size and shot flow rate have a significant effect on the peening intensity. The factor ‘t’ has an F-ratio of less than 4. The most significant factor is the work height followed by shot size, shot flow rate and exposure time. Pure sum is used to calculate the percentage contribution of a factor to the total variation. The portion of the total variation observed in an experiment attributed to each significant factor and/or interaction is reflected in the percent contribution. The percent contribution is a function of the sums of squares for each significant item. The percent contribution indicates the relative power of a
factor and/or interaction to reduce variation. If the factor and/or interaction levels were controlled precisely, then the total variation could be reduced by the amount indicated by the percent contribution. The percent contribution due to error provides an estimate of the adequacy of the experiment. As the percent contribution due to error is low, 15% or less, then it is assumed that no important factors were omitted from the experiment [9]. In this study the error contribution is only 8.642 and hence the experiment has been sufficient in terms that all critical process parameters have been evaluated and variations in conditions and measurement was a minimum. 4.4. Optimization of peening parameters Table 7 shows the settings of the levels to obtain an optimum peening intensity. The contribution of each factor to increase the peening intensity to the optimum is also indicated. It is seen that there is a 32.45% increase in the peening intensity at the optimum conditions. It is seen that the contribution of work height is most significant to increase peening Table 7 The settings of the levels of variables to obtain optimum peening intensity Column no.
Factor
Level description
Level
Contribution
1 2 3 4
t h d Q
6 1016 Level 2 95
2 2 2 1
0.009 0.06 0.02 0.01
Total contribution from all factors to increase the peening intensity = 0.099 mm; current grand average of performance = 0.305 mm; expected result at optimum condition = 0.404 mm; percent increase in intensity after optimization = ((0.404 − 0.305)/0.305) × 100 = 32.45%.
Table 6 The ANOVA table Column no.
Factor
Degrees of freedom (f)
Sum of squares (SS)
Variance (V)
F-ratio (F)
Pure sum (S)
1 2 3 4 Other error
t h d Q –
1 1 1 1 3
0 0.058 0.006 0.002 0
0 0.058 0.006 0.002 0
1.603 202.411 23.209 7.027 –
0 0.058 0.006 0.001 –
Total
–
7
0.035
–
–
–
Percent contribution, P (%) 0.744 80.842 8.344 1.428 8.642 100
P.M. George et al. / Journal of Materials Processing Technology 153–154 (2004) 925–930 Table 8 Table of interaction of variables Sr. no.
Interacting factor pairs
Columns interaction
Severity index, SI (%)
Optimum levels
1 2 3
d×Q t×Q h×Q
3×4 1×4 2×4
24.99 15.43 13.50
2, 1 2, 1 2, 1
intensity to the optimum followed by shot size, shot flow rate and exposure time. 4.5. Interaction effects The synergistic effect of two or more factors in a factorial experiment where effect of one factor depends on
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the variation of another is called interaction and the same are shown in Table 8. The severity index is the measure of the extent of the interaction between two chosen parameters. It can be inferred from the values indicated in the table, that the factors shot size and shot flow rate have the maximum interaction between them. The optimum level for each of the factors of the interacting pair to achieve the optimum peening intensity is also indicated in the table. A histogram depicting the severity index of the interacting pairs is shown in Fig. 4. The graphs showing the interactions of the parameters have been plotted in Fig. 5(a)–(c). As the severity index increases, the lines in the above graphs tend to intersect each other at right angles and as it decreases the lines tend to be parallel to each other.
5. Conclusion
Fig. 4. Histogram depicting the severity index of interacting pairs.
From the percent contribution of each factor indicated in the ANOVA table (Table 6) it could be inferred that work height is the most predominant factor. The critical process parameters, according to their relative significance, are work height, shot size, shot flow rate and exposure time. The study indicates that the effect on the peening intensity, when the parameters are varied simultaneously, is quite different from that observed when parameters are varied individually. This is attributed to the interactions that exist between the parameters when they are varied simultaneously. It is found that peening intensity increases with respect to work height while it decreases with respect to shot flow rate. The optimum peening intensity is obtained by setting work height at 1016 mm, shot flow rate at 95 kg/min, exposure time at 6 min and shot size at S230. The peening intensity is found to increase by 32.45% at this optimum level. The interaction effects are also studied and the graphs shown in Fig. 8, establishes that shot size and shot flow rate interact maximum. Based on these results, it can be inferred that for optimum intensity, the amount of shot required is comparatively less. The designers of the peening machines can use the order of predominance established, while designing the machines. It can also be used to fulfil specific requirements raised by the quality and economy conscious customers. Applying the optimized results derived in this study can also enhance the performance level.
References
Fig. 5. The graphs showing the interactions of the parameters.
[1] Society of Automotive Engineers Handbook, SAE Publications, 1964. [2] L. Wagner, Response of light alloys to shot peening: comparison of magnesium and aluminium alloy, Met. Finish. News 3 (2002) 12– 13. [3] G. Levasseur, Peen forming feature possibility for wing skin fabrication, Met. Finish. News 3 (2002) 4–5.
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[4] A. Garcia-Diaz, D.T. Philips, Principles of Experimental Design and Analysis, Chapman & Hall, 1995. [5] D.R. Cox, N. Reid, The Theory of the Design of Experiments, Chapman & Hall/CRC, 2000. [6] C. Douglas, Montgomery, Design and Analysis of Experiments, Wiley, 2001.
[7] R.A. Johnson, Miller and Freund’s Probability and Statistics for Engineers, PHI, 2001. [8] P.J. Ross, Taguchi Techniques for Quality Engineering, McGraw-Hill, 1989. [9] A.H. Burr, J.B. Cheathan, Mechanical Analysis and Design, PHI India Pvt. Ltd, 1997.