6340(Print), ISSN 0976 AND 6359(Online) TECHNOLOGY Volume 3, Issue 3, Sep- (IJMET) Dec (2012) IAEME

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1 INTERNATIONAL International Journal of Mechanical JOURNAL Engineering OF MECHANICAL and Technology (IJMET), ENGINEERING ISSN 97 4(Print), ISSN 97 AND 9(Online) TECHNOLOGY Volume, Issue, Sep- (IJMET) Dec (1) IAEME ISSN 97 4 (Print) ISSN 97 9 (Online) Volume, Issue, September - December (1), pp IAEME: Journal Impact Factor (1):.871 (Calculated by GISI) IJMET I A E M E INVESTIGATION OF POST PROCESSING TECHNIQUES TO REDUCE THE SURFACE ROUGHNESS OF FUSED DEPOSITION MODELED PARTS Addanki Sambasiva Rao 1*, Medha A Dharap, J V L Venkatesh, Deepesh Ojha 4 1 Assistant Professor, Department of Mechanical Engineering, Veermata Jijabai Technological Institute, Mumbai, India. asrao@vjti.org.in Professor, Department of Mechanical Engineering, Veermata Jijabai Technological Institute, Mumbai, India. madharap@vjti.org.in Associate Professor, Production Engineering Department, SGGSIE&T, Nanded, Maharashtra, India. meghavenkatesh@gmail.com 4 PG Student, Department of Mechanical Engineering, Veermata Jijabai Technological Institute, Mumbai, India. deepeshojha@gmail.com ABSTRACT Fused Deposition Modeling is most popular rapid prototyping process because of its faster, economical and clean technology, however it suffers from low surface finish quality. To improve its surface finish quality, various atts had been made by several researchers by controlling various process parameters. The main objective of this research is to apply chemical treatment processes through Design of Experiments using different chemicals with variant conditions like different levels of, of exposure, eratures and initial roughness, interaction effects of the process parameters have also been analyzed. ANOVA technique is used to find out the significant factors affecting the surface finish. Results show satisfactory improvement in surface finish of FDM parts (ABS) with simple inexpensive and harmless chemical treatment processes. Keywords : Acrylonitrile Butadiene Styrene (ABS), ANOVA, Chemical Treatment, Design of Experiments, Fused Deposition Modeling, Post-Processing, Surface Roughness. I. INTRODUCTION Rapid prototyping (RP) technologies provide the ability to fabricate initial prototypes from various model materials. Stratasys s Fused Deposition Modeling (FDM) is a typical RP process that can fabricate prototypes out of ABS plastic [1]. FDM rapid prototyping process is quite popular in industry for various reasons such as: different raw materials (thermo plastics) can be used as long as the appropriate hot head is available; FDM parts are very strong and hence can work as functional parts; it does not employ lasers, hence is less 1

2 4(Print), ISSN 97 9(Online) Volume, Issue, Sep- Dec (1) IAEME expensive and there are no safety related issues; It does not use liquid/powder raw materials and hence is a clean process; It can be kept in an office environment as a D printer; very easy to remove the support material; this is probably the easiest of all RP processes; this is the cheapest technology; etc. Parts produced by FDM are, however, less accurate than those produced by other rapid prototyping processes such as Stereo lithography Apparatus (SLA), Solid Ground Curing (SGC). Besides, FDM process is very slow as every point of the volume is addressed by a mechanical device. The key issue with FDM process is surface roughness because of its staircase effect (the angle between the vertical axis and surface tangents) []. The poor surface finish affects the functioning of RP parts, depending on the geometry of the enclosing surface, the building strategy, layer thickness and orientation of the part; this drawback may outweigh the advantages of RP parts []. In literature, several researchers have proposed various methods to reduce the surface roughness of the FDM parts of ABS material. One of the prominent methods is to control the process parameters like layer thickness, build orientation, raster width, raster angle, air gap etc.. In this method process parameters were optimized using statistical techniques like design of experiments and gray relational analysis have been integrated for obtaining the optimum process parameter values []. The process parameters influence the responses in a highly nonlinear manner; therefore, prediction of overall dimensional accuracy is made based on artificial neural network (ANN) [4]. Several algorithms were also developed to obtain optimum part deposition orientation for fused deposition modeling process for enhancing part surface finish and reducing build [, ]. Another method is adaptive slicing scheme in which slices of different thicknesses in different zones are produced while building the part [7-]. Daekeon Ahn et al investigated the relation between surface roughness and overlap interval [11], they also analyzed and discussed the effects of surface angle and filament section shape to the surface roughness. Debapriya Chakraborty et al introduced a new kind of deposition method called Curved layer FDM or CLFDM which offers solution to the issues of surface roughness and strength for thin curved shell-type parts, this process proposes an entirely new building paradigm for FDM, the filaments would be deposited along curved (essentially non horizontal) paths instead of planar (horizontal) paths [1]. A mathematical technique has been developed by W. Rattanawong et al to determine best part orientation based on minimum volume error (VE) in the part due to staircase effect [1]. Noshir A. Langrana et al have developed a method to fabricate the highest quality of multi-material parts. In this method, a virtual simulation system and experimental real video microscopy have been developed. In this virtual simulation, one can check or test a variety of the layered manufacturing process parameters, and make the best selection of tool path and other parameters to obtain high quality parts [14] One more method for improving surface finish is chemical treatment method which has been proposed by L.M. Galantucci et al []. In this chemical treatment method, Dimethylketone (Acetone) with 9% concentrated solution and % water was used and parts were immersed in diluted solution for minutes and also suggested that further studies need to be conducted on freeform products, also using other dimethylketone solvents such as ethylene and using designed experiments to optimize the process in terms of the solution and process. To the best of the author s knowledge, no investigations of chemical treatment method have been reported since the work of L.M. Galantucci et al. and hence the present study has been undertaken by the authors to investigate the optimum conditions for obtaining best surface finish from the chemical treatment process.

3 4(Print), ISSN 97 9(Online) Volume, Issue, Sep- Dec (1) IAEME II. PROBLEM DEFINITION L.M. Galantucci et al [] had proposed a method of chemical treatment of ABS (Acrylonitrile Butadiene Styrene) parts which yields a significant improvement of the surface finish of the treated specimens. The chemical treatment method is economical, fast and easy to use. However chemical treatment method has not been analyzed considering different types of chemicals, different levels of chemicals, effect of elevated eratures, different initial roughness of the parts, of exposure along with the underlying interaction effects for obtaining optimum surface finish. This paper reports design of experiments for analyzing chemical post processing treatment method to identify main controlling factors, side effects of the process parameter settings and disturbances to the process for ABS plastics. III.METHODOLOGY In this paper we will be optimizing the chemical treatment process using Design of Experiments (DOE). The factors affecting the chemical treatment process were identified by performing numerous trials, based on these trials, erature, of exposure and initial roughness were identified as possible main factors. These are analyzed using Design of Experiments (DOE). DOE is done for two different chemicals i.e. Dimethylketone (Acetone) and Methylethylketone (MEK), test specimen selected are shown in Fig.1(a) to Fig.1(e)... The optimization method is based on Design of Experiments (DOE) and Analysis of Variance (ANOVA). It identifies significant parameters affecting the surface finish, to which more attention must be paid in order to attain best possible results..1 Statistical Design Of Experiments Statistical DOE refers to the process of planning the experiment so that appropriate data that can be analyzed by statistical methods will be collected, resulting in valid and objective conclusions [1,1]. A statistical tool is always preferred for drawing the meaningful conclusion from a experimental design data. There are two aspects to any experimental problem; the design of the experiment and the statistical analysis of the data. When many factors control the performance of any system then it is essential to find out significant factors which need special attention either to control or optimize the system performance. Taguchi s concept of Orthogonal Array (OA) as a part of Statistical DOE is used in such situations to plan the set of experiments and ANOVA technique is used to find out the significant factors. These techniques have been used in the current study to investigate significant factors affecting the surface roughness of FDM parts (ABS P4) out of of solution C, erature of the chemical bath Tp, initial roughness of parts Ri and Time for which the parts are treated Tm. The first step in constructing an orthogonal array to fit a specific case study is to count the total degrees of freedom that tell the minimum number of experiments that must be performed to study all the chosen control factors. The number of degrees of freedom associated with a factor is equal to one less than the number of levels for that factor. In this experiment we decided to analyze surface finish for four different s of chemicals. For Acetone levels of 9%, 8%, 8%, 7% were taken and of bath of min and min were found to be suitable on the other hand for Methyl ethyl ketone of %, %, %, % were taken, also min and min were found to be suitable exposure. These chemicals have higher diffusion rate at elevated eratures so two different eratures i.e. C and C were chosen.

4 4(Print), ISSN 97 9(Online) Volume, Issue, Sep- Dec (1) IAEME Table 1 Factors and their levels for experiment Levels Sr. No. Control Factors C (% of ) Chemical Chemical Tp ( C) Ri (Initial Roughness, µm) Tm(Time of exposure in Min.) Chemical Chemical Initial roughness of the parts was taken as roughness corresponding to.4 layer thickness and. layer thickness. Time of exposure was also identified as factor affecting the results of chemical treatment process. Therefore degrees of freedom (DOF) of factors are (C(), Tm(1), Ri(1), Tm(1). Degrees of freedom of their interactions are (C&Tp (), C&Tm(), Tm&Tp(1). Considering all the factors and their interactions there are 1 degrees of freedom. Hence this experiment is carried out using L1, orthogonal array for 4 factors one at 4 level and at levels to design the experiments for finding out the surface roughness of given parts under the simultaneous variation of 4 different parameters at different levels as shown in Table 1. Figure1(a) Test Specimen with.4 mm Figure1(b) Test specimen with. mm layer thickness layer thickness of Sample1/A1 Figure 1(c) Sample /A Figure 1(d) Sample Figure 1(e) Sample 4 In total, L1 has 1 degrees of freedom. The remaining (1-1) two degrees of freedom are used for error. The design of experiments based on the L1 array for the present case is shown in Table. Inability to distinguish effect of factors and interactions is called confounding [1]. As it is expected that factors C, Tm, Tp to interact, no factors are assigned to columns, and 7. This is done to avoid confounding. The results of surface roughness value of various FDM samples with combinations of parameters for chemical 1 are shown in Table. Similar results for chemical is shown in Table 4

5 4(Print), ISSN 97 9(Online) Volume, Issue, Sep- Dec (1) IAEME Table Orthogonal Array L1 with results of trials for chemical 1 C(1) Tp() Ri() Tm(4) CxTp() CxTm() TpxTm(7) A11 A1 A1 A

6 4(Print), ISSN 97 9(Online) Volume, Issue, Sep- Dec (1) IAEME Trials were carried out according to the various combinations of parameters displayed in the Orthogonal Array and the results for surfaces roughness values were recorded. Three readings were taken on sample1, A11 correspondence to the top surface, A1 correspondence to the reading along the build direction, A1 correspondence to the reading perpendicular to the build direction. These were then analyzed to obtain the optimum condition using MINITAB software. The Data Means plot for main effects and interaction plots for Chemical 1 is shown in Fig..The S-N ratio plot for main effects and interaction plots for Chemical 1 is shown in Fig. The experimental data was solved using both Data Means and S-N Ratio. The condition was S-N Ratio taken was Smaller is Better hence we will be accepting the higher value as preferred value from the graph where as in means graph lower value will be taken as preferred value. Results from both Data Means and S-N Ratio give the same optimized condition. Data Means plot for main effects and interaction plots for Chemical is shown in Fig.4 and S-N ratio plot for main effects and interactions is shown in Fig.. Main Effects Plot (data means) for Means Interaction Plot (data means) for Means Mean of Means roughness Figure- (a) Figure- (b) Figure -Main effects and Interaction Plots for data means Main Effects Plot (data means) for SN ratios Interaction Plot (data means) for SN ratios concentr ation Mean of SN ratios roughness Signal-to-noise: Smaller is better Figure- (a) Signal-to-noise: Smaller is better Figure- (b) Figure -Main effects and Interaction Plots for S-N Ratio

7 4(Print), ISSN 97 9(Online) Volume, Issue, Sep- Dec (1) IAEME Table Orthogonal Array L1 with results of trials for chemical C(1) Tp() Ri() Tm(4) CxTp() CxTm() TpxTm(7) M11 M1 M Main Effects Plot (data means) for Means Interaction Plot (data means) for Means Mean of Means roughness 4 4 concentr ation 4..4 Figure-4 (a). Figure-4 (b) Figure 4-Main effects and Interaction Plots for Means (MEK) Mean of SN ratios Main Effects Plot (data means) for SN ratios Interaction Plot (data means) for SN ratios roughness Signal-to-noise: Smaller is better Signal-to-noise: Smaller is better Figure- (a) Figure- (b) Figure -Main effects and Interaction Plots for S-N Ratio (MEK) 7

8 4(Print), ISSN 97 9(Online) Volume, Issue, Sep- Dec (1) IAEME. Analysis of variance The results obtained for surface roughness data from the white light interferometer (WLI) data are analyzed by using the statistical tool ANOVA. It determines the relative effect of the individual factors and their interactions on the surface roughness of parts. The analysis by using ANOVA technique is done analytically. An equation for total variation may be written as SS T = + SS C + SS + SS + SS + SS SS + Tp Ri Tm TmxC TpxC SS TmxTp (1) where SS T is total sum of squares, SS C, SS Tp, SS Ri, SS Tm, are sum of squares for Concentration C, Temperature Tp, Initial roughness Ri, Time Tm. SS Tmxc, SS Tpxc,, SS TmXTp are sum of squares of Concentration-Temperature, Concentration -Time and Time-Temperature interactions respectively and SS E is sum of square of the error. If T is the sum of all (N) Surface roughness values, the total sum of squares is given by SS T N = Fi i = 1 T N () Sum of squares of Concentration(C) factor is given as SS C N = i = 1 Ci N Ci T N () where, N is the number of levels of Concentration factor, C i and N Ci are the sum and number of observations respectively under i th level. Similarly, sum of squares of other five factors can also be calculated. Sum of squares of interaction of C and Tm is given by SS CXTm = n i = ( CXTm N 1 ( CXTm ) i ) i T N SS C SS Tm (4) where (C xtm) i and N (CXTm)i are the sum and number of observations (surface roughness) respectively under i th condition of the combinations of factors C and Tm and n is the number of possible combinations of the interacting factors C and Tm. Similarly, the sum of squares for other two interactions can also be found out. The results obtained from ANOVA for chemical 1 and chemical are given in Table 4 and Table respectively. 8

9 4(Print), ISSN 97 9(Online) Volume, Issue, Sep- Dec (1) IAEME Table-4 ANOVA table for Chemical 1 Source DF Seq SS Percent contribution Concentration 9..9 Temp Initial roughness Time Concentration*Temp Concentration*Time Temp*Time Residual Error Total Table- ANOVA table for Chemical Source DF Seq SS Percent contribution Concentration Temp Initial roughness Time Concentration*Temp Concentration*Time Temp*Time Residual Error 1..7 Total

10 4(Print), ISSN 97 9(Online) Volume, Issue, Sep- Dec (1) IAEME IV. RESULTS All the test sample from group 1 to 1 having average minimum and maximum roughness. micron and.7 micron respectively had experienced reduced roughness value after the chemical treatment. The minimum average roughness observed is equal to.17 micron and maximum average roughness equal to.47 micron for Chemical 1 and average minimum.14 micron and maximum.8 micron for chemical. Fig. shows effect of chemical treatment on average roughness value for chemical 1 and chemical. The roughness values are analyzed on the basis on DOE and ANOVA for both the chemicals. Following are the detailed explanation of results:- 4.1 CHEMICAL 1 From the ANOVA table (Table 4) we find that for chemical 1 the most important factor is contributing.9%, -erature interaction is the second most important factor contributing 11.1% followed by initial roughnesss 7.% of exposure is the least significant factor. Fig. and Fig. also display the similar results Ra(initial) Ra(acetone) Ra(MEK) Ra(initial) Ra(acetone) Ra(MEK) Figure Effect of chemical treatment on average roughness value of Group1-1 It is observed from Fig.(a) and Fig.(a) that the optimum condition is C4-Tp- Ri1-Tm1 i.e. level 4 for (9%), level for erature ( C), level 1 for initial roughness (corresponding to layer thickness.4 mm) and level 1 for exposure ( min.) is the optimum condition without taking interaction into account. Since it is clear from the results from ANOVA that -erature interaction is the second most important factor contributing 11.1% so when considering interactions CxTp and Tp xtm we can conclude from Fig.(b) and Fig.(b) that the optimum condition is C-Tp- Ri1-Tm1. 4

11 4(Print), ISSN 97 9(Online) Volume, Issue, Sep- Dec (1) IAEME 4. CHEMICAL From Table we find that for chemical,, - erature interaction, erature and - interaction are the most significant factor contributing 7.78%, 1.9%, 14.1% and 14.% respectively. From Fig4.(a) and Fig.(a) we find that the optimum condition for chemical is C-Tp- Ri1-Tm1 i.e. %, C erature of bath, initial roughness corresponding to.4 mm layer thickness and minutes exposure. It is obvious from ANOVA analysis that - erature interaction is the most dominant factor after factor in this chemical treatment process contributing 1.9% followed by - interaction. Considering both C xtm and CxTp interactions we find from Fig.4 (b) and Fig. (b) that the optimum condition is C-Tp-Ri1-Tm. Samples were treated at both the conditions without interaction and with interaction for both the chemicals 1 & chemical. Table shows the tabulated results and roughness values at optimum levels. It is clear from Table that optimum condition with interaction gives better results for both chemical 1 and chemical. Condition 1 refers to the optimum condition without taking account for interaction while condition refers to optimum condition when taking account for interactions. Table Results for optimum condition and roughness values at optimum levels. Factors Acetone Methyl Ethyl Ketone Condition 1 (C4-Tp- Ri1-Tm1) Condition (C-Tp- Ri1-Tm1) Condition 1 (C-Tp-Ri1-Tm1) Condition (C-Tp-Ri1-Tm) C(% of ) 9 8 Tp( C) Ri (Initial Roughness, µm) Tm(Time of exposure in Min.) Average roughness value, Ra ( µm) Further a comparison is made between results obtained with chemical 1 and chemical on four different samples which were manufactured on Stratasys s Dimension SST 1 FDM machine. Sample 1 is a cube as shown in Fig.1(a) & Fig.1(b), sample is shown in Fig.1(c), sample is shown in Fig.1(d) and sample 4 is shown in Fig.1(e).The results with comparisons for chemical 1 and chemical is shown in Table 7. Fig.7 shows the original part where as Fig.8 and Fig.9 show the parts treated with Chemical 1 and Chemical respectively at their optimum conditions. 41

12 4(Print), ISSN 97 9(Online) Volume, Issue, Sep- Dec (1) IAEME Table 7 Comparison between Chemical 1 and Chemical Chemical 1( Acetone) Chemical ( Methylethylketone) Samples Roughness at optimum cond. µm Aesthetic appearance Curing Time hrs % change in dimensions Roughness at optimum cond. µm Aesthetic appearance Curing Time hrs % change in dimensions Sample 1.17 Very smooth 1 Less than.%.14 Glossy Less than 1% Sample 1.1 Very smooth 1 Less than.%.98 Glossy Less than 1% Sample.847 Very smooth 1 Less than.%.49 Glossy Less than 1% Sample 4. Very smooth 1. Less than.%.1 Glossy Less than 1% Figure 7(original) Figure 8(Chemical1) Figure 9(Chemical) The original part as shown in Fig.7 is made of ABS material in white & blue color, but the chemically treated parts as shown in Fig.8 and Fig.9 are made of ABS material in white color. The size of the specimen was measured before and after the chemical treatment process in order to account for the variation in dimensions due to chemical treatment process. Base lengths were taken as l1 and l, height of the specimen was taken as H. Readings were taken by ACCURATE SPECTRA co-ordinate measuring machine. The results show less than 1% deviation. Detailed results are shown in Table 8. 4

13 4(Print), ISSN 97 9(Online) Volume, Issue, Sep- Dec (1) IAEME Table 8 Average change in dimension after chemical treatment process. Length L1 Length L Height H (mm) (mm) (mm) Chemical 1 Average Variance Chemical Average Variance The cost of the chemical treatment process is compared with the commercially available systems and the same is listed in the Table 9. It is observed from the Table 9 that the proposed system is economical to use and has very small setup cost as compared to the commercial system available in the market. Table 9 Cost comparison of proposed chemical treatment process with other available commercial system. Capital Cost, Depreciation, INR(Approx.) INR Sr. No 4 Raw Material cost per part*, INR Power Consumption cost per hour, INR Labour Cost per hour, INR 1 Acetone process.78 per day MEK process.78 per day 1 Commercial system, 99 per day 4 1 * for part size xx mm V.CONCLUSION In this paper the surface roughness of FDM prototype parts is addressed, the parameters that have significant effect on the surface roughness (Ra) value in the chemical treatment process have been identified. The chemical treatment process is optimized in terms of solution, of exposure, initial roughness and erature of the chemical bath using Design of Experiments and ANOVA. Two different chemical were taken, i.e. Dimethyl ketone (Acetone) and Methyl ethyl ketone (MEK), in case of Acetone it was observed that the solution, -erature interaction and the initial roughness are the most significant factors. For Methyl ethyl ketone chemical treatment process, it was observed that the, - erature interaction and - interaction are the most important factors, surprisingly for MEK the initial roughness and of exposure have negligible effect on the process. The process was applied for simple parts to complex free form parts. The optimum levels for the parameters for chemical treatment process are found out which shows drastic improvement in surface finish. The appearance of the finished parts is comparable to plastic moulded parts, the parts have glossy finish and the maximum curing is about to 4 hours. The process is very much economical compared to other commercial systems available in the market. Further studies can be carried out to commercialize this process to make it available in the market at an affordable price.

14 4(Print), ISSN 97 9(Online) Volume, Issue, Sep- Dec (1) IAEME REFERENCES [1] Sung-Hoon Ahn, Caroline S. Lee, Woobyok Jeong, (4), Development of translucent FDM parts by post-processing, Rapid Prototyping Journal, Vol. Iss: 4 pp [] L.M. Galantucci, Lavecchia M, Percoco FG, (9), Experimental study aiming to enhance surface finish of fused deposition modeled parts, CIRP Annals Manufacturing Technology 8(9): [] Che Chung Wang, Ta-Wei Lin, Shr-Shiung Hu, (7), Optimizing the rapid prototyping process by integrating the Taguchi method with the Gray relational analysis, Rapid Prototyping Journal, Vol. 1 Iss: pp [4] Anoop Kumar Sood, R.K. Ohdar, S.S. Mahapatra, (9), Improving dimensional accuracy of Fused Deposition Modelling processed part using grey Taguchi method, Materials and Design (9) [] K. Thrimurthulu, Pulak M. Pandey, N. Venkata Reddy, (4), Optimum part deposition orientation in fused deposition modeling, International Journal of Machine Tools & Manufacture 44 (4) 8 94 [] Hong-Seok Byun, Kwan H. Lee, (), Determination of the optimal build direction for different rapid prototyping processes using multi-criterion decision making, Robotics and Computer-Integrated Manufacturing, () 9 8. [7] P.M. Pandey, N.V. Reddy, S.G. Dhande, (), Real Adaptive Slicing for Fused Deposition Modeling, International Journal of Machine Tools & Manufacture 4 () [8] Sarat Singamneni, Roger Anak Joe, and Bin Huang (1) Adaptive Slicing for Fused Deposition Modeling and Practical Implementation Schemes, Trans Tech Publications, Switzerland, Advanced Materials Research Vol. 48 (1) pp [9] Justin Tyberg, Jan Helge BøhnU,(1999) FDM systems and local Adaptive Slicing, Materials and Design (1999)77-8. [] K.P. Karunakaran, P. Vivekananda Shanmuganathan, Sanjay Janardhan Jadhav, Prashant Bhadauria, Ashish Pandey, () Rapid prototyping of metallic parts and moulds, Journal of Materials Processing Technology () [11] Daekeon Ahn, Jin-Hwe Kweon, Jin-Ho Choi and Seok-Hee Lee,(11) Relation between surface roughness and overlap interval in Fused Deposition Modeling Trans Tech Publications, Switzerland, Advanced Materials Research Vols. 4- (11) pp 1-1. [1] Debapriya Chakraborty, B. Aneesh Reddy, A. Roy Choudhury, (8), Extruder path generation for Curved Layer Fused Deposition Modeling, Computer-Aided Design 4 (8) 4. [1] W. Rottanawong, S. H. Masood, P. Lovenitti, (1), A volumetric approach to part build orientations in rapid prototyping, Journal of Material Processing Technology 119(1), 48-. [14] Noshir A. Langrana, Dan Qiu, Evan Bossett, Stephen C. Danforth, () Mohsen Jafari, Ahmad Safari, Virtual simulation and video microscopy for fused deposition Methods, Materials and Design 1()7-8. [1] Montgomery DC () Design and Analysis of Experiments. New Delhi: Wiley India (P) Ltd. [1] Phadke MS (1989) Quality Engineering and Robust Design. New Delhi: Tata McGraw-Hill. 44