PARAMETRIC OPTIMIZATION OF FUSED DEPOSITION MODELING USING RESPONSE SURFACE METHODOLOGY A THESIS SUBMITTED IN PARTIAL FULFILLMENT FOR THE REQUIREMENT FOR THE DEGREE OF Master of Technology in Production Engineering by VEDANSH CHATURVEDI Department of Mechanical Engineering National Institute of Technology Rourkela – 8 2009 PARAMETRIC OPTIMIZATION OF FUSED DEPOSITION MODELING USING RESPONSE SURFACE METHODOLOGY A THESIS SUBMITTED IN PARTIAL FULFILLMENT FOR THE REQUIREMENT FOR THE DEGREE OF Master of Technology in Production Engineering by VEDANSH CHATURVEDI Under the guidance of Dr. S. S. MAHAPATRA Professor, Department of Mechanical Engineering Department of Mechanical Engineering National Institute of Technology Rourkela – 8 2009 National Institute of Technology Rourkela CERTIFICATE This is to certify that the thesis entitled, “PARAMETRIC OPTIMIZATION OF FUSED MODELING USING RESPONSE SURFACE METHODOLOGY” submitted by Vedansh Chaturvedi in partial fulfillment of the requirements for the award of Master of Technology Degree in Mechanical Engineering with specialization in Production Engineering at the National Institute of Technology, Rourkela (deemed University) is an authentic work carried out by him under my supervision and guidance. To the best of my knowledge, the matter embodied in the thesis has not submitted to any other University/Institute for the award of any degree or diploma. Dr. S. S. Mahapatra Date: Dept. of Mechanical Engineering National Institute of Technology Rourkela – 769008 ACKNOWLEDGEMENT I would like to express my deep sense of respect and gratitude toward my supervisor Dr. S. S. Mahapatra, who not only guided the academic project work but also stood as a teacher and philosopher in realizing the imagination in pragmatic way, I want to thank him for introducing me for the field of Optimization and giving the opportunity to work under him. His presence and optimism have provided an invaluable influence on my career and outlook for the future. I consider it my good fortune to have got an opportunity to work with such a wonderful person. I express my gratitude to Dr. R. K. Sahoo, Professor and Head, Department of Mechanical Engineering, faculty member and staff of Department of Mechanical Engineering for extending all possible help in carrying out the dissertation work directly or indirectly. They have been great source of inspiration to me and I thank them from bottom of my heart. I like to express my gratitude to Dr. Saurav Datta, Lecturer, Department of Mechanical Engineering , for his valuable advice in carrying out Literature review. I am especially indebted to my parents for their love, sacrifices and support. They are my teachers after I came to this world and have set great example for me about how to live, study and work. VEDANSH CHATURVEDI CONTENTS TITLE PAGE NO. Abstract iv List of Figures v List of Tables vii Nomenclature viii 1. An introduction of rapid prototyping process 1 1.1 Overview of rapid prototyping process 1 1.2 The basic process 2 1.3 Rapid prototyping technique 4 1.3.1 Stereolithography 4 1.3.2 Selective layer sintering 6 1.3.3 Laminated object manufacturing 8 1.3.4 Fused deposition modeling 11 1.4 Objective of Research Work 12 2. Literature review 15 3. Fused deposition modeling and ABS material 20 3.1 Fused deposition modeling 20 3.2 ABS material 23 3.3 Properties of ABS plastic 24 4. Response surface methodology 4.1 27 Response surface methodology and robust design i 30 4.2 The sequential nature of the response surface methodology 31 4.3 Building empirical models 32 4.3.1 Linear regression model 32 4.3.2 Estimation of the parameter in linear regression model 33 4.3.3 Model adequacy checking 34 4.3.4 Properties of the least square estimation regression model 34 4.3.5 Residual analysis 36 Variable selection and model building in regression 37 4.4.1 Procedure for variable selection 38 4.4.2 All possible regression 38 4.4.3 Stepwise regression analysis 39 4.4 5. Specimen preparation, Experiment and analysis 41 5.1 Specimen preparation 41 5.2 Testing of specimen 43 5.3 Analysis of experiments 47 5.4 5.3.1 Analysis of experiment for tensile test 47 5.3.2 RSA for tensile test 49 5.3.3 Analysis of experiment for flexural test 53 5.3.4 RSA for flexural test 54 5.3.5 Analysis of experiment for impact test 58 5.3.6 RSA for impact test 59 Optimization of process parameter ii 62 6. Grey- based taguchi method 64 6.1 Introduction of grey – based taguchi method 64 6.2 Grey relational analysis method 65 6.3 Response optimization of GRG and optimal parameter setting 75 7. Result, Conclusion and future scope 77 7.1 Result, Discussion 77 7.2 Conclusion 80 7.3 80 Future scope Bibliography 81 iii ABSTRACT Fused deposition modeling (FDM) is a process for developing rapid prototype (RP) objects by depositing fused layers of material according to numerically defined cross sectional geometry. The quality of FDM produced parts is significantly affected by various parameters used in the process. This dissertation work aims to study the effect of five process parameters such as layer thickness, sample orientation, raster angle, raster width, and air gap on mechanical property of FDM processed parts. In order to reduce experimental runs, response surface methodology (RSM) based on central composite design is adopted. Specimens are prepared for tensile, flexural, and impact test as per ASTM standards. Empirical relations among responses and process parameters are determined and their validity is proved using analysis of variance (ANOVA) and the normal probability plot of residuals. Response surface plots are analyzed to establish main factor effects and their interaction on responses. Optimal factor settings for maximization of each response have been determined. Major reason for weak strength of FDM processed parts may be attributed to distortion within the layer or between the layers while building the parts due to temperature gradient. Since RP parts are subjected to different loading conditions, practical implication suggests that more than one response must be optimized simultaneously. To this end, mechanical properties like tensile strength, bending strength, and impact strength of the produced component are considered as multiple responses and simultaneous optimization has been carried out with the help of response optimizer. Grey relation has been employed to convert multiple responses into a single response for optimization purpose. It is interesting to note that factor level settings for simultaneous optimization of all responses significantly differ from optimization with single response. iv LIST OF FIGURES FIGURE NO. FIGURE TITLE PAGE NO. 1.1 Stereolithography 5 1.2 Selective laser sintering 7 1.3 Laminated object manufacturing 10 1.4 Fused deposition modeling 12 3.1 FDM Vantage Machine 21 3.2 Head assembly of FDM Vantage SE 21 3.3 Showing the process parameter of FDM 23 5.1 Line diagram of specimen for tensile test 42 5.2 Line diagram of specimen for flexural test 42 5.3 Line diagram of specimen for impact test 42 5.4 Instron test of tensile specimen 44 5.5 Instron test of 3-point bending specimen 44 5.6 Charpy test of impact specimen 45 5.7 Response surface plots for tensile test 50 5.8 SEM Images of tensile failure of specimen 52 5.9 Response surface plots for flexural test 56 5.10 SEM Images of crack surface of flexural specimen 57 v 5.11 Response surface plots for impact test 61 5.12 SEM Images of broke impact test specimen 61 6.1 Sensitivity analysis for different distinguishing coefficients 72 6.2 Grey relational grade variation with number of experiments 72 vi LIST OF TABLES TABLE NO. TABLE TITLE PAGE NO. 3.1 ABS Material data sheet 25 5.1 Domain of experiments (factors and their level) 41 5.2 Experimental data obtained from the CCD runs 46 5.3 Estimated regression coefficients for tensile test 47 5.4 Analysis of variance for tensile test 48 5.5 Estimated regression coefficients for flexural test 53 5.6 Analysis of variance for flexural test 54 5.7 Estimated regression coefficients for impact test 58 5.8 Analysis of variance for impact test 59 5.9 Optimum factor levels and predicted response for individual strength 63 6.1 Normalization of the data (larger the better) 67 6.2 The deviation sequence 68 6.3 Calculation of grey relational coefficients 69 6.4 Grey relational grade 70 6.5 Response surface analysis for grey relational grade 73 6.6 Estimated regression coefficients for grey relational grade 74 6.7 Analysis of variance for grey relational grade 75 6.8 Comparison of parameter setting in individual and 76 Simultaneous optimization vii NOMENCLATURE RP Rapid prototyping STL Stereolithography FDM Fused deposition modeling ABS Acrylonitrile butadiene styrene RSM Response surface methodology CCD Central composite design ANOVA Analysis of variance SS Sum of square MS Mean sum of square DF Degree of freedom SEM Scanning electron microscope GRA Grey relational analysis GRG Grey relational grade viii CHAPTER 1 ______________________________________________________________________________ AN INTRODUCTION TO RAPID PROTOTYPING 1. Introduction 1.1 Overview of Rapid Prototyping: The term rapid prototyping (RP) refers to a class of technologies that can automatically construct physical models from Computer-Aided Design (CAD) data. These "three dimensional printers" allow designers to quickly create tangible prototypes of their designs, rather than just twodimensional pictures. Such models have numerous uses. They make excellent visual aids for communicating ideas with co-workers or customers. In addition, prototypes can be used for design testing. For example, an aerospace engineer might mount a model airfoil in a wind tunnel to measure lift and drag forces. Designers have always utilized prototypes; RP allows them to be made faster and less expensively. In addition to prototypes, RP techniques can also be used to make tooling (referred to as rapid tooling) and even production-quality parts (rapid manufacturing). For small production runs and complicated objects, rapid prototyping is often the best manufacturing process available. Of course, "rapid" is a relative term. Most prototypes require from three to seventy-two hours to build, depending on the size and complexity of the object. This may seem slow, but it is much faster than the weeks or months required to make a prototype by traditional means such as machining. These dramatic time savings allow manufacturers to bring products to market faster and more cheaply. In 1994, Pratt & Whitney achieved "an order of magnitude [cost] reduction [and] . . . time savings of 70 to 90 percent" by incorporating rapid prototyping into their investment casting process. At least six different rapid prototyping techniques are commercially available, each with unique strengths. Because RP technologies are being increasingly used in non-prototyping applications, 1 the techniques are often collectively referred to as solid free-form fabrication; computer automated manufacturing, or layered manufacturing. The latter term is particularly descriptive of the manufacturing process used by all commercial techniques. A software package "slices" the CAD model into a number of thin (~0.1 mm) layers, which are then built up one atop another. Rapid prototyping is an "additive" process, combining layers of paper, wax, or plastic to create a solid object. In contrast, most machining processes (milling, drilling, grinding, etc.) are "subtractive" processes that remove material from a solid block. RP’s additive nature allows it to create objects with complicated internal features that cannot be manufactured by other means. Of course, rapid prototyping is not perfect. Part volume is generally limited to 0.125 cubic meters or less, depending on the RP machine. Metal prototypes are difficult to make, though this should change in the near future. For metal parts, large production runs, or simple objects, conventional manufacturing techniques are usually more economical. These limitations aside, rapid prototyping is a remarkable technology that is revolutionizing the manufacturing process. 1.2 The Basic Process Although several rapid prototyping techniques exist, all employ the same basic five-step process. The steps are: 1. Create a CAD model of the design 2. Convert the CAD model to STL format 3. Slice the STL file into thin cross-sectional layers 4. Construct the model one layer atop another 5. Clean and finish the model 2 CAD Model Creation: First, the object to be built is modeled using a Computer-Aided Design (CAD) software package. Solid modelers, such as Pro/ENGINEER, tend to represent 3-D objects more accurately than wire-frame modelers such as AutoCAD, and will therefore yield better results. The designer can use a pre-existing CAD file or may wish to create one expressly for prototyping purposes. This process is identical for all of the RP build techniques. Conversion to STL Format: The various CAD packages use a number of different algorithms to represent solid objects. To establish consistency, the STL (stereolithography), the first RP technique) format has been adopted as the standard of the rapid prototyping industry. The second step, therefore, is to convert the CAD file into STL format. This format represents a threedimensional surface as an assembly of planar triangles, "like the facets of a cut jewel." The file contains the coordinates of the vertices and the direction of the outward normal of each triangle. Because STL files use planar elements, they cannot represent curved surfaces exactly. Increasing the number of triangles improves the approximation, but at the cost of bigger file size. Large, complicated files require more time to pre-process and build, so the designer must balance accuracy with manageability to produce a useful STL file. Since the .stl format is universal, this process is identical for all of the RP build techniques. Slice the STL File: In the third step, a pre-processing program prepares the STL file to be built. Several programs are available, and most allow the user to adjust the size, location and orientation of the model. Build orientation is important for several reasons. First, properties of rapid prototypes vary from one coordinate direction to another. For example, prototypes are usually weaker and less accurate in the z (vertical) direction than in the x-y plane. In addition, part orientation partially determines the amount of time required to build the model. Placing the shortest dimension in the z direction reduces the number of layers, thereby shortening build time. 3 The pre-processing software slices the STL model into a number of layers from 0.01 mm to 0.7 mm thick, depending on the build technique. The program may also generate an auxiliary structure to support the model during the build. Supports are useful for delicate features such as overhangs, internal cavities, and thin-walled sections. Each PR machine manufacturer supplies their own proprietary pre-processing software. Layer by Layer Construction: The fourth step is the actual construction of the part. Using one of several techniques (described in the next section) RP machines build one layer at a time from polymers, paper, or powdered metal. Most machines are fairly autonomous, needing little human intervention. Clean and Finish: The final step is post-processing. This involves removing the prototype from the machine and detaching any supports. Some photosensitive materials need to be fully cured before use. Prototypes may also require minor cleaning and surface treatment. Sanding, sealing, and/or painting the model will improve its appearance and durability. 1.3 Rapid Prototyping Techniques Most commercially available rapid prototyping machines use one of six techniques. At present, trade restrictions severely limit the import/export of rapid prototyping machines, so this guide only covers systems available in the U.S. 1.3.1 Stereolithography: Stereolithography is an additive fabrication process utilizing a vat of liquid UV-curable photopolymer "resin" and a UV laser to build parts a layer at a time. On each layer, the laser beam traces a part cross-section pattern on the surface of the liquid resin. Exposure to the UV laser light cures, or, solidifies the pattern traced on the resin and adheres it to the layer below. 4 After a pattern has been traced, the SLA's elevator platform descends by a single layer thickness, typically 0.05 mm to 0.15 mm (0.002" to 0.006"). Then, a resin-filled blade sweeps across the part cross section, re-coating it with fresh material. On this new liquid surface the subsequent layer pattern is traced, adhering to the previous layer. A complete 3-D part is formed by this process. After building, parts are cleaned of excess resin by immersion in a chemical bath and then cured in a UV oven. Stereolithography requires the use of support structures to attach the part to the elevator platform and to prevent certain geometry from not only deflecting due to gravity, but to also accurately hold the 2-D cross sections in place such that they resist lateral pressure from the re-coater blade. Supports are generated automatically during the preparation of 3-D CAD models for use on the stereolithography machine, although they may be manipulated manually. Supports must be removed from the finished product manually; this is not true for all rapid prototyping technologies. Figure 1.1 Stereolithography Application Range Parts used for functional tests. 5 Manufacturing of medical models. Form –fit functions for assembly tests. Advantages Possibility of manufacturing parts which are impossible to be produced conventionally in a single process. Can be fully atomized and no supervision is required. High Resolution. Disadvantages Necessity to have a support structure. Require labor for post processing and cleaning. 1.3.2 Selective Laser Sintering: Selective laser sintering is an additive rapid manufacturing technique that uses a high power laser (for example, a carbon dioxide laser) to fuse small particles of plastic, metal, ceramic, or glass powders into a mass representing a desired 3-dimensional object. The laser selectively fuses powdered material by scanning cross-sections generated from a 3-D digital description of the part (for example from a CAD file or scan data) on the surface of a powder bed. After each cross-section is scanned, the powder bed is lowered by one layer thickness, a new layer of material is applied on top, and the process is repeated until the part is completed.Compared to other rapid manufacturing methods, SLS can produce parts from a relatively wide range of commercially available powder materials, including polymers (nylon, also glass-filled or with other fillers, and polystyrene), metals (steel, titanium, alloy mixtures, and composites) and green sand. The physical process can be full melting, partial melting, or liquid-phase sintering. And, 6 depending on the material, up to 100% density can be achieved with material properties comparable to those from conventional manufacturing methods. In many cases large numbers of parts can be packed within the powder bed, allowing very high productivity.SLS is performed by machines called SLS systems; the most widely known model of which is the Sinterstation SLS system. SLS technology is in wide use around the world due to its ability to easily make very complex geometries directly from digital CAD data. While it began as a way to build prototype parts early in the design cycle, it is increasingly being used in limited-run manufacturing to produce end-use parts. One less expected and rapidly growing application of SLS is its use in art. SLS was developed and patented by Dr. Carl Deckard at the University of Texas at Austin in the mid-1980s, under sponsorship of DARPA. A similar process was patented without being commercialized by R.F. Housholder in 1979.Unlike some other Rapid Prototyping processes, such as Stereolithography (SLA) and Fused Deposition Modeling (FDM), SLS does not require support structures due to the fact that the part being constructed is surrounded by unsintered powder at all times. Figure 1.2 Selective laser sintering 7 Application Range Visual Representation models. Functional and tough prototypes. cast metal parts. Advantages Flexibility of materials used. No need to create a structure to support the part. Parts do not require any post curing except when ceramic is used. Disadvantages During solidification, additional powder may be hardened at the border line. The roughness is most visible when parts contain sloping (stepped) surfaces. 1.3.3 Laminated object manufacturing: Profiles of object cross sections are cut from paper or other web material using a laser. The paper is unwound from a feed roll onto the stack and first bonded to the previous layer using a heated roller which melts a plastic coating on the bottom side of the paper. The profiles are then traced by an optics system that is mounted to an X-Y stage. After cutting of the layer is complete, excess paper is cut away to separate the layer from the web. Waste paper is wound on a take-up roll. The method is self-supporting for overhangs and undercuts. Areas of cross sections which are to be removed in the final object are heavily cross-hatched with the laser to facilitate removal. It can be time consuming to remove extra material for some geometry, however. In general, the finish, accuracy and stability of paper objects are not as good as for materials used with other RP methods. However, material costs are very low, and objects have the look and feel 8 of wood and can be worked and finished in the same manner. This has fostered applications such as patterns for sand castings. While there are limitations on materials, work has been done with plastics, composites, ceramics and metals. Some of these materials are available on a limited commercial basis. Variations on this method have been developed by many companies and research groups. For example, Kira's Paper Lamination Technology (PLT) uses a knife to cut each layer instead of a laser and applies adhesive to bond layers using the xerographic process. Solido Ltd. of Israel (formerly Solidimension) also uses a knife, but instead bonds layers of plastic film with a solvent. There are also variations which seek to increase speed and/or material versatility by cutting the edges of thick layers diagonally to avoid stair stepping. The principal US commercial provider of laser-based LOM systems, Helisys, ceased operation in 2000. However the company's products are still sold and serviced by a successor organization, Cubic Technologies. The process is performed as follows: 1. Sheet is adhered to a substrate with a heated roller. 2. Laser traces desired dimensions of prototype. 3. Laser cross hatches non-part area to facilitate waste removal. 4. Platform with completed layer moves down out of the way. 5. Fresh sheet of material is rolled into position. 6. Platform moves up into position to receive next layer. 7. The process is repeated. 9 Figure 1.3 Laminated object manufacturing Application Range Visual Representation models Large Bulky models as sand casting patterns Advantages Variety of organic and inorganic materials such as paper, plastic, ceramic, composite can be used Process is faster than other processes No internal stress and undesirable deformations LOM can deal with discontinuities, where objects are not closed completely Disadvantages The stability of the object is bonded by the strength of the glued layers. Parts with thin walls in the z direction can not be made using LOM Hollow parts can not be built using LOM 10 1.3.4 Fused Deposition Modeling Fused deposition modeling, which is often referred to by its initials FDM, is a type of additive fabrication or (sometimes called rapid prototyping/rapid manufacturing (RP or RM)) technology commonly used within engineering design[1]. The technology was developed by S. Scott Crump in the late 1980s and was commercialized in 1990. The FDM technology is marketed commercially by Stratasys, which also holds a trademark on the term. Like most other additive fabrication processes (such as 3D printing and stereolithography) FDM works on an "additive" principle by laying down material in layers. A plastic filament or metal wire is unwound from a coil and supplies material to an extrusion nozzle which can turn on and off the flow. The nozzle is heated to melt the material and can be moved in both horizontal and vertical directions by a numerically controlled mechanism, directly controlled by a computeraided manufacturing (CAM) software package [2]. The model or part is produced by extruding small beads of thermoplastic material to form layers as the material hardens immediately after extrusion from the nozzle. Several materials are available with different trade-offs between strength and temperature properties. As well as acrylonitrile butadiene styrene (ABS) polymer, the FDM technology can also be used with polycarbonates, polycaprolactone, polyphenylsulfones and waxes. A "watersoluble" material can be used for making temporary supports while manufacturing is in progress[3]. Marketed under the name Waterworks by Stratasys, this soluble support material is quickly dissolved with specialized mechanical agitation equipment utilizing a precisely heated sodium hydroxide solution. 11 Figure 1. 4 Fused deposition modeling Application Range Conceptual modeling Fit, form applications and models for further manufacturing procedures Investment casting and injection molding Advantages Quick and cheap generation of models There is no worry of exposure to toxic chemicals, lasers or a liquid chemical bath. Disadvantages Restricted accuracy due to the shape of material used, wire is 1.27 mm diameter. 1.4 Objective of Research Work The competition in world market for manufactured product has intensified tremendously in recent years. It has become important for new products to reach the market as early as possible. As a result reduction of product development cycle time is a major concern in industries for achieving competitive advantage. Now days the focus of industries has shifted from traditional product development methodology to accelerated or rapid fabrication techniques. Some of the 12 latest developments within the automotive industry have shown how emerging rapid prototyping and manufacturing (RP&M) technologies can be used to reduce lead time in the prototype development process. The main benefit rapid prototyping (RP) technologies offer as compared to conventional subtractive and formative manufacturing process is that virtually any complex geometry can be built in a layer wise manner directly from CAD model of part without the need for tooling using a nearly fully automated process. This ability to fabricate complex geometry at no extra cost is virtually unheard in traditional manufacturing, where there is direct link between cost of component and complexity of design. On the other hand absence of tooling means that manufacturing inputs are not required in order to design parts and products . For example if RP is used to manufactured the part which was conventionally manufactured by injection moulding, considerations for draft angles, ejection pins and gates marks, wall thickness, sharp corners, weld lines and parting lines is not important for part design. This directly means whatever can be designed it can be manufactured. That is optimal design can be selected for manufacturing without considering the feasibility of their production in terms of available manufacturing technology. Incorporating features such as undercuts, blind holes, screws in process like injection moulding often requires expensive tooling, extensive tool setups and testing runs and inevitably leads to undesirable lead times and costs. Also there is a threshold limit for minimum production level which has to be cross to offset the cost of tooling. This result in high volume manufacturing to compensate the tooling cost. Whereas the possibility of producing highly complex, cost effective custom parts is apparent in RP . Another noted advantage of RP is their ability to produce functional assembly by consolidating sub assemblies into single unit at the computer aided design (CAD) stage thus reducing the part count, handling time storage requirement and without considering the mating and fit problem. RP allows the deposition of 13 multiple materials in any location or combination that the designer requires. This has potentially enormous implications for the functionality and aesthetics that can be designed into parts . Having such enormous advantages one of the biggest hindrance in the full scale application of RP technologies is available materials and their properties, which substantially differ from the properties of generally used materials. To overcome this limitation one approach is to develop new materials which can be used by RP machines and have properties superior or as par with conventional materials. Another procedure is to suitably adjust the process parameters for RP part fabrication for maximum improvement in the properties. Number of researchers contributed in this second approach. Their works reveal that properties of RP parts are function of various process related parameters and can be significantly improved with their proper adjustment. Since mechanical strength is an important requirement for the functional part there is great need to improve them. With this aim in mind the present study focus on the mechanical properties viz. tensile, flexural and impact strength of part fabricated using fused deposition modeling (FDM) technology and derive the quantitative relation between the processing parameters and mechanical strength so that the mechanical response of the processed part must be predictable over the allowable range of parameter. 14 CHAPTER 2 ______________________________________________________________________________ A BRIEF LITERATURE REVIEW 2. Literature review Ahn et al. [4] Uses design of experiment method and concluded that the air gap and raster orientation affect the tensile strength of FDM processes part where as raster width, model temperature and colour have little effect. They further compare the measured tensile strength of FDM part processed at different raster angles and air gap with the tensile strength of injection moulded part. Material use for both type of fabrication is ABSP400. With zero air gap FDM specimen tensile strength lies between 10%-73% of injection moulded part with maximum at 0° and minimum at 90° raster orientation with respect to loading direction. But with negative air gap there is significant increase in strength at respective raster orientation but still it is less than the injection moulded part. All specimens failed in transverse direction except for specimen whose alternate layer raster angle varies between 45° and -45°. This type of specimen failed along the 45° line. Compression test on the specimen build at two different orientations revealed that this strength is higher than the tensile strength and lies between 80 to 90% of those for injection moulded part. Also specimen build with axis perpendicular to build table shows less compressive strength as compared to specimen build with axis parallel to build table. Based on these observations it was concluded that strength of FDM processed part is anisotropic. Es Said et al. [5] Study the effect of raster angle on the tensile, bending and impact properties of FDM ABSP400 part made using FDM1650 machine. There observations indicate that raster orientation effect the strength as polymer molecules align themselves along the direction of flow. Also FDM follows phase change for constructing solid model from solid filament extruded from nozzle tip in semi molten state and solidify in a chamber maintain at particular temperature. As a 15 result volumetric shrinkage takes place which results in weak interlayer bonding and cause porosity which reduce the load bearing area. Lee et al. [6] Performed experiments on cylindrical parts made using three RP processes FDM, 3D printer and nano composite deposition (NCDS) to study the effect of build direction on the compressive properties. Experimental results show that compressive strength is 11.6% higher for axial FDM specimen as compared to transverse FDM specimen. In 3D printing, diagonal specimen possesses maximum compressive strength in comparison to axial specimen. For NCDS, axial specimen showed compressive strength 23.6% higher than that of transverse specimen. Out of three RP technologies, parts built by NCDS are most affected by the build direction. Khan et al. [7] concluded that layer thickness, raster angle and air gap are found to be significantly affect the elastic performance of the compliant FDM ABS prototype. Wang et al. [8], in their work, has mentioned that as extruded material from nozzle cools from its glass transition temperature to chamber temperature inner stresses will develop particularly due to uneven deposition speed. These inner stresses will cause the inter layer and the intra layer deformation which will result in cracking, de-lamination or even part fabrication failure. Thus affect the part strength and size. They propose the mathematical model to study the effect of total number of layers, stacking section length, and chamber temperature on the above mentioned deformations. They concluded that as the total number of layers increase deformation will decrease rapidly but decreasing tendency will become slow after certain number of layers, higher stacking section lengths will produce large deformations and as chamber temperature will increase deformation will decrease and become zero at the glass transition temperature of 16 material. Based on these results they propose that material use for part fabrication must have lower glass transition temperature and linear shrinkage rate. Also the extruded fiber length must be small. Bellehumeur et al. [9] experimentally assessed the bond quality between adjacent filaments and their failure under flexural loading. Experimental results showed that both the envelope temperature and variations in the convective conditions with in the building chamber have strong effect on the meso-structure and the overall quality of bond strength. On line measurements of the cooling temperature profiles reveals that temperature profile of bottom layers rises above the glass transition temperature followed by rapid decrease as the extrusion head moves away from the position of placement of thermoset and minimum temperature increase with the number of layers. Microphotograph of the cross sectional area shows diffusion of adjacent filaments is more in lower layers as compared to upper layers for the face of specimen with higher number of layers. Chou and Zang [10], in their work, simulated the FDM process using finite element analysis (FEA) and analyzes the effect of tool path patterns on residual stresses and part distortions. At each layer stress starts to accumulate at the locations of initial deposition and at tool path turning point. During the deposition process, the residual stress is smallest for most recently activated elements as compare to earlier activated element. The residual effect on the bottom surface of each layer corresponds to stress concentration pattern of its bottom layer. For the long raster pattern stress concentration characteristic is aligned along the length side and along the width side for the short raster deposition. Thus the maximum stress zone shifts from the center of the part towards the length side and width side for the long and short raster pattern respectively. Simulated results are found to be in agreement with experimental results of the distortion in part 17 except the magnitude of distortion is more than the expected and this may be due to simplified material properties and boundary conditions assumed during simulation. Above mention work reveals that the mechanical properties of FDM processed part exhibit anisotropy and are sensitive to the processing parameters that affect the meso-structure and fibreto-fibre bond strength. Also un-even heating and cooling cycles due to inherent nature of FDM build methodology results in stress accumulation in the build part and these stress concentration regions will also affect the strength. It is also observed that all the researches in FDM strength modeling is basically devoted to study the effect of processing conditions on the part strength with no significant effort made to develop the strength model in terms of FDM process parameters so as to predict in advance the strength of component for practical application. Anitha et al. [11], in their result, revealed several interesting features of the FDM process Only the layer thickness is effective to 49.37% at 95% level of significance. But on pooling, it was found that the layer thickness is effective to 51.57% at 99% level of significance. The other factors, road width and speed , contributes to 15.57 and 15.83% at 99% level of significance, respectively. The significance of layer thickness is further strengthened by the correlation analysis. Which indicates a strong inverse relationship with surface roughness. According to the S/N analysis, the layer thickness is most effective when it is at level 3(0.3556mm), the road width at level 1(0.537mm) and the speed of deposition at level 3 (200mm).According to this trials , sample 18 was found to give the best results. Agrawal et al. [12] In this work, the concept of stochastic modelling of tolerances and clearances has been extended to RP processes. Using the uniﬁed approach for RP processes, the mechanical error in the FD process has been studied. A methodology has been developed to analyse the mechanical error at the nozzle tip of the FD process for input values of the tolerances 18 and clearances, where the links and hinges are produced on a mass scale. Closed-form expressions have been derived to ﬁnd the mechanical error in the coordinates of a point on the work surface. It is observed that the inﬂuence coeﬃcients of the z coordinate of a point on the work surface have a larger magnitude than those of the x and y coordinates. The three-sigma bands obtained in tracing a few example curves by the nozzle tip are plotted. The variances and their sum are listed in a table to show their variation across the work surface. The overall error is found to vary appreciably across the work surface. The error is minimum at the front-left end of the work surface and maximum at the rear-right end. The methodology can be extended for the optimal allocation of tolerances and clearances to reduce the cost of manufacturing. Pandey et al. [13] In this research they found Orientation for part deposition is one of the important factors as it aﬀects average part surface roughness and production time. In the present work, two objective functions, namely average part surface roughness and build time, are formulated. NSGA-II is successfully used to determine a set of pareto optimal solutions for part deposition orientation for the two contradicting objectives. It can be seen from the results obtained for diﬀerent parts that there exist two limiting situations. One is minimum average part surface roughness with maximum production time and another is minimum production time with maximum average part surface roughness. The developed system of part deposition orientation determination also gives a set of intermediate solutions in which any solution can be used depending upon the pre- ference of user for the two objectives. The present system can be used for any class of component, which may be a freeform or a regular object. 19 CHAPTER 3 ______________________________________________________________________________ FUSED DEPOSITION MODELLING AND ABS MATERIAL 3. Fused deposition modeling and ABS material 3.1 Fused Deposition Modeling FDM is one of the RP technology developed by Stratasys, USA (Figure 3.1). But unlike other RP systems which involve an array of lasers, powders, resins, this process uses heated thermoplastic filaments which are extruded from the tip of nozzle in a temperature controlled environment. For this there is a material deposition subsystem known as head (Figure 3.2) which consist of two liquefier tips. One tip for model material and other tip for support material deposition both of which works alternatively. The article forming material is supplied to the head in the form of a flexible strand of solid material from a supply source (reel). One pair of pulleys or rollers having a nip in between are utilized as material advance mechanism to grip a flexible strand of modeling material and advance it into a heated dispensing or liquefier head. The material is heated above its solidification temperature by a heater on the dispensing head and extruded in a semi molten state on a previously deposited material onto the build platform following the designed tool path. The head is attached to the carriage that moves along the X-Y plane. The build platform moves along the Z direction. The drive motion are provided to selectively move the build platform and dispensing head relative to each other in a predetermined pattern through drive signals input to the drive motors from CAD/CAM system. The fabricated part takes the form of a laminate composite with vertically stacked layers, each of which consists of contiguous material fibres or rasters with interstitial voids. Fibre-to-fibre bonding within and between layers occurs by a thermally-driven diffusion bonding process during solidification of the semi-liquid extruded fibre [14]. 20 FDM Vantage uses insight software to import STL file automatically slice the file, generate necessary support structure and material extrusion path [15]. Power required - 230 V,AC Motor - 50/60 Hz,3Ф Max. room temperature Size of the system - 29.3oC - 1277mm wide X 874 mm deep X 1950 mm hight Figure 3.1 FDM Vantage machine SE Inlet passage Roller Support liquefier Model liquefier Support tip Model tip Figure 3.2 Head Assembly of FDM Vantage SE 21 Main process parameters involved in part fabrication are [3.3]: 1. Orientation: Part builds orientation or orientation referrers to the inclination of part in a build platform with respect to X, Y, Z axis. Where X and Y-axis are considered parallel to build platform and Z-axis is along the direction of part build. 2. Layer thickness: It is a thickness of layer deposited by nozzle and depends upon the type of nozzle used. 3. Part Fill Style: Determines the manner in which nozzle will deposit the material in a single layer of a part. There are two types of part fill methods: Perimeter Raster: Outer boundary is contour (perimeter) and internal is filled with raster. Contours to depth: Other then the outer contour additional contours are provided to fill the inner region and remaining inner region is filled with raster. The number of additional contours is determined by the depth of contours value. By default depth of contour is twice the contour width to produce one contour. 4. Contour width: The width of contour deposited by nozzle. 5. Part raster width (raster width): Width of raster pattern used to fill interior regions of part curves. 6. Part interior style: Determine how the interior area in each layer is filled. There are two methods: Solid normal: Fills the part completely Sparse: Semi hollow interior (honeycomb structure), minimize the amount of material used. 7. Visible surface: This feature improves the part external appearance. 8. Raster angle: It is a direction of raster relative to the x-axis of build table. 22 9. Shrinkage factor: Shrinkage factor applied in the x, y and z direction. 10. Perimeter to raster air gap: The gap between inner most contours and the edge of the raster fill inside of the contour. 11. Raster to raster gap (air gap): It is the gap between two adjacent rasters on same layer. Figure 3.3 showing process parameter of FDM 3.2 ABS (Acrylonitrile butadiene styrene) material: Acrylonitrile Butadiene Styrene (ABS) chemical formula (C8H8· C4H6·C3H3N)n) is a common thermoplastic used to make light, rigid, molded products such as piping (for example Plastic Pressure Pipe Systems), musical instruments (most notably recorders and plastic clarinets), golf club heads (used for its good shock absorbance), automotive body parts, wheel covers, enclosures, protective head gear, buffer edging for furniture and joinery panels, airsoft BBs and toys, including Lego bricks. ABS plastic ground down to an average diameter of less than 1 micrometer is used as the colorant in some tattoo inks. Tattoo inks that use ABS are extremely vivid. This vividness is the most obvious indicator that the ink contains ABS, as tattoo inks rarely list their ingredients [4] . It is a copolymer made by polymerizing styrene and acrylonitrile in the presence of polybutadiene. The proportions can vary from 15 to 35% acrylonitrile, 5 to 30% butadiene and 23 40 to 60% styrene. The result is a long chain of polybutadiene criss-crossed with shorter chains of poly(styrene-co-acrylonitrile). The nitrile groups from neighboring chains, being polar, attract each other and bind the chains together, making ABS stronger than pure polystyrene. The styrene gives the plastic a shiny, impervious surface. The butadiene, a rubbery substance, provides resilience even at low temperatures. ABS can be used between −25 and 60 °C. The properties are created by rubber toughening, where fine particles of elastomer are distributed throughout the rigid matrix. Production of 1 kg of ABS requires the equivalent of about 2 kg of oil for raw materials and energy. It can also be recycling. 3.3 Properties of ABS plastic ABS is derived from acrylonitrile, butadiene, and styrene. Acrylonitrile is a synthetic monomer produced from propylene and ammonia; butadiene is a petroleum hydrocarbon obtained from the C4 fraction of steam cracking; styrene monomer is made by dehydrogenation of ethyl benzene a hydrocarbon obtained in the reaction of ethylene and benzene. The advantage of ABS is that this material combines the strength and rigidity of the acrylonitrile and styrene polymers with the toughness of the polybutadiene rubber. The most important mechanical properties of ABS are resistance and toughness. A variety of modifications can be made to improve impact resistance, toughness, and heat resistance. The impact resistance can be amplified by increasing the proportions of polybutadiene in relation to styrene and also acrylonitrile although this causes changes in other properties. Impact resistance does not fall off rapidly at lower temperatures. Stability under load is excellent with limited loads [7]. Even though ABS plastics are used largely for mechanical purposes, they also have good electrical properties that are fairly constant over a wide range of frequencies. These properties 24 are little affected by temperature and atmospheric humidity in the acceptable operating range of temperatures. The final properties will be influenced to some extent by the conditions under which the material is processed to the final product; for example, molding at a high temperature improves the gloss and heat resistance of the product whereas the highest impact resistance and strength are obtained by molding at low temperature. ABS polymers are resistant to aqueous acids, alkalis, concentrated hydrochloric and phosphoric acids, alcohols and animal, vegetable and mineral oils, but they are swollen by glacial acetic acid, carbon tetrachloride and aromatic hydrocarbons and are attacked by concentrated sulfuric and nitric acids. They are soluble in esters, ketones and ethylene dichloride. The aging characteristics of the polymers are largely influenced by the polybutadiene content, and it is normal to include antioxidants in the composition. On the other hand, while the cost of producing ABS is roughly twice the cost of producing polystyrene, ABS is considered superior for its hardness, gloss, toughness, and electrical insulation properties. However, it will be degraded (dissolve) when exposed to acetone. ABS is flammable when it is exposed to high temperatures, such as a wood fire. It will "boil", then burst spectacularly into intense, hot flames. Table 3.1 ABS material data sheet Properties Specifications Amorphous 1.05 0.27 20 29.64 62.05 63.43 2068.48 8.94 R110 Excellent Structure Specific density Water absorption rate (%) Elongation (%) Tensile strength (MPa) Compression strength (MPa) Flexural strength (MPa) Flexural modulus (MPa) Impact (joules) Hardness Ultrasonic welding 25 Bonding Machining Min. utilization temperature (deg. C) Max. utilization temperature (deg .C) Melting point (deg.C) Coefficient of expansion Arc resistance Dielectric strength (KV/mm) Transparency UV Resistance Chemical resistance Excellent Good -40 90 105 0.000053 80 16 Translucent Poor Good 26 CHAPTER 4 ______________________________________________________________________________ RESPONSE SURFACE METHODOLOGY 4. Response surface methodology Response surface methodology is very useful and modern technique for the prediction and optimization of machining performances. In the present study, the strength of ABS material part made by fused deposition modelling machine has been predicted and also process parameters have been optimized by RSM. In this chapter, overview of RSM has been discussed. Response surface methodology (RSM) is a collection of statistical and mathematical techniques useful for developing, improving, and optimizing processes. The most extensive applications of RSM are in the particular situations where several input variable potentially influence some performance measure or quality characteristic of the process. This performance measure or quality characteristic is called the response. The input variables are sometimes called independent variables. The field of response surface methodology consists of the experimental strategy for exploring the space of the process or independent variables, Empirical statistical modelling to develop an approximated relationship between the yield and the process variables. Also, with the help of response surface methodology, optimization can be done for finding the values of the process variables that produce desirable values of the response [16]. In general, the relationship between the response y and independent variables ξ1, ξ2, …., ξk is, Y= f(ξ1,ξ2,………………ξk) + ε ………….……………(4.1) where ε includes effects such as measurement error on the response, background noise, the effect of other variables, and so on. Usually ε is treated as a statistical error, often assuming it to have a normal distribution with mean zero and variance σ2. Then, E(y) = η =E[f(ξ1,ξ2,…………ξk)] + E(ε) =f(ξ1, ξ2,………..ξk) 27 ……………...(4.2) The variables ξ1, ξ2,…., ξk in equation (4.2) are usually called the natural variables, because they are expressed in the natural units of measurement, such as degrees Celsius, pounds per square inch, etc. In much RSM work, it is convenient to transform the natural variables to coded variables x1, x2, …. ,xk, which are usually defined to be dimensionless with mean zero and the same standard deviation. In terms of the coded variables, the response function equation (4.2) can be written as, η =f(x1,x2……….xk) …………………………….(4.3) Because the form of the true response function is unknown, it should be approximated. In fact, successful use of RSM is critically dependent upon the experimenter’s ability to develop a suitable approximation. Usually, a low-order polynomial in some relatively small region of the independent variable space is appropriate. In many cases, either a first-order or a second-order model is used. The first-order model is likely to be appropriate when the experimenter is interested in approximating the true response surface over a relatively small region of the independent variable space in a location where there is little curvature in response function. For the case of two independent variables, the first-order model in terms of the coded variables is given by, η = β0 +β1x1 +β2x2 …………………………….…………….. (4.4) The form of the first-order model in equation (4.4) is sometimes called a main effects model, because it includes only the main effects of the two variables x1 and x2. If there is an interaction between these variables, it can be added to the model easily as expressed below: η = β0 +β1x1 +β2x2+β12x1x2 28 ……………………….……… (4.5) This is the first-order model with interaction. Adding the interaction term introduces curvature into the response function. Often the curvature in the true response surface is strong enough that the first-order model (even with the interaction term included) is inadequate. A second-order model will likely be required in these situations. For the case of two variables, the second-order model is: η = β0 +β1x1 +β2x2+β11x21+β22x2 2+β12x1x2 ……………………..…… (4.6) This model would likely be useful as an approximation to the true response surface in a relatively small region. The second-order model is widely used in response surface methodology for several reasons: the second-order model is very flexible. It can take on a wide variety of functional forms, so it will often work well as an approximation to the true response surface. It is easy to estimate the parameters in the second-order model. The method of least Squares can be used for this purpose. There is considered to be practical experience indicating that second-order models work well in solving real response surface problems. In general, the first-order model is: η = β0 +β1x1 +β2x2+…………+βkxk …………………………….…………(4.7) And the second-order model is η = β0 + + ………………….………………. (4.8) + Finally, it should be noted that there is a close connection between RSM and linear regression analysis. For example, say, the following model is considered: η = β0 +β1x1 +β2x2+…………+βkxk + ε 29 ……………..………………(4.9) The β’s are a set of unknown parameters. To estimate the values of these parameters, the experimental data must be needed. 4.1. Response Surface Methodology and Robust Design: RSM is an important branch of experimental design. It is also a critical technology in developing new processes and optimizing their performance. The objectives of quality improvement, including reduction of variability and improved process and product performance, can often be accomplished directly using RSM. It is well known that variation in key performance characteristics can result in poor process and product quality. During the 1980s, considerable attention was given to process quality, and methodology was developed for using experimental design, specifically for the following: For designing or developing products and processes so that they are robust to component variation. For minimizing variability in the output response of a product or a process around a target value. For designing products and processes so that they are robust to environment conditions. By robust means that the product or process performs consistently on target and is relatively insensitive to factors that are difficult to control. Professor Genichi Taguchi used the term robust parameter design (RPD) to describe his approach to this important problem. Essentially, robust parameter design prefers to reduce process or product variation by choosing levels of controllable factors (or parameters) that make the system insensitive (or robust) to changes in a set of uncontrollable factors. These uncontrollable factors represent most of the sources of variability. Taguchi referred to these uncontrollable factors as noise factors. In RSM, it is assumed that these noise factors are 30 uncontrollable in the field, but can be controlled during process development for purposes of a designed experiment. Considerable attention has been focused on the methodology advocated by Taguchi, and a number of flaws in his approach have been discovered. However, the framework of response surface methodology allows easily incorporate many useful concepts in his philosophy. 4.2 The Sequential Nature of the Response Surface Methodology: Most applications of RSM are sequential in nature. They are briefly discussed below: Phase 0: At first, some ideas should be generated concerning which factors or variables are likely to be important in response surface study. It is usually known as a screening experiment. The objective of factor screening is to reduce the list of candidate variables to a relatively few so that subsequent experiments will be more efficient and require fewer runs or tests. The purpose of this phase is the identification of the important independent variables. Phase 1: The objective of the experiment is to determine if the current settings of the independent variables result in a value of the response that is near the optimum. If the current settings or levels of the independent variables are not consistent with optimum performance, then a set of adjustments must be done to the process variables that will move the process toward the optimum. This phase of RSM makes considerable use of the first-order model and an optimization technique called the method of steepest ascent /descent. Phase 2: When the process is near the optimum, it is required to develop a model that will accurately approximate the true response function within a relatively small region around the optimum. As the true response surface usually exhibits curvature near the optimum, a secondorder model (or perhaps some higher-order polynomial) should be used. Once an appropriate approximated model has been obtained, this model may be analyzed to determine the optimum 31 conditions for the process. This sequential experimental process is usually performed within some region of the independent variable space called the operability region or experimentation region or region of interest. 4.3 Building Empirical Models: 4.3.1 Linear regression model: In the practical application of RSM, it is necessary to develop an approximated model for the true response surface. The true response surface is typically driven by some unknown physical mechanism. The approximated model is based on observed data from the process or system and it is an empirical model. Multiple regressions is a collection of statistical techniques useful for building the types of empirical models required in RSM. The first-order multiple linear regression models with two independent variables is: Y = β0+β1x1+β2x2+ε ………………………….………………….(4.10) The independent variables are often called predictor variables or regressors. The term “linear” is used because equation (4.10) is a linear function of the unknown parameters β0, β1 and β2. In general, the response variable y may be related to k regressor variables. The model is given by: Y = β0+β1x1+β2x2 +……..+ βkxk+ε ………………………………..(4.11) This is called a multiple linear regression model with k regressor variables. The parameters βj, j=0,l, ...k, are called the regression coefficients. Models those are more complex in appearance than equation (4.11) may often be analyzed by multiple linear regression techniques. For example, adding an interaction term to the first-order model in two variables, the model becomes: Y= βo+β1x1+β2x2+β12x1x2+ε ……………………..………………(4.12) 32 As another example, considering the second-order response surface model in two variables, the model becomes: η = β0 +β1x1 +β2x2+β11x21+β22x2 2+β12x1x2 + ε ……………………(4.13) In general, any regression model that is linear in the parameters (the β-values) is a linear regression model, regardless of the shape of the response surface that it generates. 4.3.2 Estimation of the parameters in linear regression models: The method of least squares is typically used to estimate the regression coefficients in a multiple linear regression model. It is, say, supposed that n > k observations on the response variable are available: y1, y2,…., yn. Along with each observed response yi, each regressor variable has to be observed, xij denotes the i-th observation or level of variable xj. The model in terms of the observations may be written in matrix notation as: y = Xβ + ε ……………………………………(4.14) Where, y is an n x 1 vector of the observations, X is an n x p matrix of the levels of the independent variables, β is a p x 1 vector of the regression coefficients, and ε is an n x 1 vector of random errors. It is required to find the vector of least squares estimators, b, that minimizes: L= …………………….………....(4.15) ε12 = ε’ε = (y-Xβ)’(y-Xβ) After some simplifications, the least squares estimator of β is: b= (x’x) -1 x’y …………………………………(4.16) It is easy to see that X’X is a p x p symmetric matrix and X’y is a p x 1 column vector. The matrix X’X has the special structure. The diagonal elements of X’X are the sums of squares of 33 the elements in the columns of X, and the off-diagonal elements are the sums of cross-products of the elements in the columns of X. Furthermore, the elements of X’y are the sums of crossproducts of the columns of X and the observations {yi}. The fitted regression model is: Ŷ=Xb …………………………..(4.17) The difference between the observation yi and the fitted value ei = yi – Ŷ is a residual, …………………………..(4.18) The n x 1 vector of residuals is denoted by: e=y–Ŷ …………………………(4.19) 4.3.3 Model adequacy checking: It is always necessary to Examine the fitted model to ensure that it provides an adequate approximation to the true system. Verify that none of the least squares regression assumptions are violated. 4.3.4 Properties of the least square estimators: The method of least squares produces an unbiased estimator of the parameter β in the multiple linear regression models. The important parameter is the sum of squares of the residuals SSE = (yi-Ŷi )2 = ei2 = e’e ………………………….……(4.20) Because X'Xb = X’y, a computational formula for SSE can be derived as: SSE = y’y – b’X’y ……………………………(4.21) Equation (4.21) is called the error or residual sum of squares. 34 It can be shown that an unbiased estimator of σ2 is: …………...……...……..(4.22) σ2= Where, n is a number of observations and p is a number of regression coefficients. The total sum of squares is: SST = y’y – – = ....……………….…….(4.23) Then the coefficient of multiple determination R2 is defined as: ………………….(4.24) R 2 =1- R2 is a measure of the amount of reduction in the variability of y obtained by using the regressor variables x1,x2,...,xk in the model. From inspection of the analysis of variance identity equation However, a large value of R2 does not necessarily (Equation (4.24)) can see that imply that the regression model is good one. Adding a variable to the model will always increase R2, regardless of whether the additional variable is statistically significant or not. Thus it is possible for models that have large values of R2 to yield poor predictions of new observations or estimates of the mean response. Because R2 always increases as terms are added to the model, it is preferable to use an adjusted R2 statistic defined as: R adj2 = = 1- (1-R 2) …………………..……(4.25) In general, the adjusted R2 statistic will not always increase as variables are added to the model. In fact, if unnecessary terms are added, the value of R2adj will often decrease. When R2 35 and R2adj differ dramatically, there is a good chance that non significant terms have been included in the model. However, testing hypotheses on the individual regression coefficients are very much important. Such tests would be useful in determining the value of each of the regressor variables in the regression model. For example, the model might be more effective with the inclusion of additional variables, or perhaps with the deletion of one or more of the variables already in the model. Adding a variable to the regression model always causes the sum of squares for regression to increase and the error sum of squares to decrease. It must be decided whether the increase in the regression sum of squares is sufficient to warrant using the additional variable in the model. Furthermore, adding an unimportant variable to the model can actually increase the mean square error, thereby decreasing the usefulness of the model [17]. 4.3.5 Residual analysis: The residuals from the least squares fit, defined by play an important role in judging model adequacy. It is preferable to work with scaled residuals, in contrast to the ordinary least squares residuals. These scaled residuals often convey more information than do the ordinary residuals. The standardizing process scales the residuals by dividing them by their average standard deviation. In some data sets, residuals may have standard deviations that differ greatly. There is some other way of scaling that takes this into account. The vector of fitted values yˆI corresponding to the observed values yi is Ŷ = Xb = X(X’X) -1 X’y =Hy 36 …………………………….(4.26) The n x n matrix H = X(X’X)-1 X’ is usually called the hat matrix because it maps the vector of observed values into a vector of fitted values. The hat matrix and its properties play a central role in regression analysis. e = y – Xb =y - Hy =(1-H)y ……………………………… (4.27) The prediction error sum of squares provides a useful residual scaling: ………………… (4.28) PRESS = From Equation (5.28) it is easy to see that the PRESS residual is just the ordinary residual weighted according to the diagonal elements of the hat matrix hii. Generally, a large difference between the ordinary residual and the PRESS residual will indicate a point where the model fits the data well, but a model built without that point predicts poorly. 4.4 Variable Selection and Model Building in Regression: In response surface analysis, it is customary to fit the full model corresponding to the situation at hand. It means that in steepest ascent, the full first-order model is usually fitted, and in the analysis of the second-order model, the full quadratic is usually fitted. Nevertheless, in some cases, where the full model may not be appropriate; that is, a model based on a subset of the regressors in the full model may be superior. Variable selection or model-building techniques usually is used to identify the best subset of regressors to include in a regression model Now, it is assumed that there are K candidate regressors denoted x1,x2,...,xk and a single response variable y. All models will have an intercept term β0, so that the full model has (K + 1) parameters. It is shown that there is a strong motivation for correctly specifying the regression model: Leaving out important regressors introduces bias into the parameter estimates, while including unimportant variables weakens the prediction or estimation capability of the model. 37 4.4.1 Procedures for variable selection: Now, it is required to find several of the more widely used methods for selecting the appropriate subset of variables for a regression model. The approach is also made on the optimization procedure used for selecting the best model from the whole set of models and finally it is required to discuss and illustrate several of the criteria that are typically used to decide which subset of the candidate regressors leads to the best model. 4.4.2 All possible regression: This procedure requires that all the regression equations are fitted involving one-candidate regressors, two-candidate regressors, and so on. These equations are evaluated according to some suitable criterion, and the best regression model selected. If it is assumed that the intercept term β0 is included in all equations, then there are K candidate regressors and there are 2 K total equations to be estimated and examined. For example, if K = 4, then there are 24= 16 possible equations, whereas if K = 10, then there are210 = 1024. Clearly the number of equations to be examined increases rapidly as the number of candidate regressors increases. Usually, the candidate variables are restricted for the model to those in the full quadratic polynomial and it is required that all models obey the principal of hierarchy. A model is said to be hierarchical if the presence of higher-order terms (such as interaction and second-order terms) requires the inclusion of all lower-order terms contained within those of higher order. For example, this would require the inclusion of both main effects, if a two-factor interaction term was in the model. Many regression model builders believe that hierarchy is a reasonable model-building practice while fitting polynomials. 38 4.4.3 Stepwise regression methods: As the evaluation of all possible regressions can be burdensome, various methods have been developed for evaluating only a small number of subset regression models by either adding or deleting regressors one at a time. These methods are generally referred to as stepwise-type procedures. They can be classified into three broad categories: a) Forward selection, b) Backward elimination, and c) Stepwise regression, which is a popular combination of procedures (a) and (b). a) Forward selection: This procedure begins with the assumption that there are no regressors in the model other than the intercept. An effort is made to find an optimal subset by inserting regressors into the model one at a time. The first regressor selected for entry into the equation is the one that has the largest simple correlation with the response variable y. If it is supposed that the first regressor is x1, then the regressor will produce the largest value of the F-statistic for testing significance of regression. This regressor is entered, if the F-statistic exceeds a pre-selected F-value, say, Fin (or F-to-enter). The second regressor chosen for entry is the one that now has the largest correlation with y after adjusting for the effect of the first regressor entered (x 1) on y. It is referred as partial correlations. In general, at each step the regressor having the highest partial correlation with y (or equivalently the largest partial F-statistic given the other regressors already in the model) is added to the model, if its partial F-statistic exceeds the pre-selected entry level Fin. The procedure terminates either when the partial F-statistic at a particular step does not exceed Fin or when the last candidate regressor is added to the model. 39 b) Backward elimination: Forward selection begins with no regressors in the model and attempts to insert variables until a suitable model is obtained. Backward elimination attempts to find a good model by working in the opposite direction. That is, it is required to start a model that includes all K Candidate regressors. Then the partial F-statistic (or a t-statistic, which is equivalent) is computed for each regressor, as if, it were the last variable to enter the model. The smallest of these partial Fstatistics is compared with a pre-selected value, Fout (or F-to-remove); and if the smallest partial F-value is less than Fout, that regressor is removed from the model. Now, a regression model with (K – 1) regressors is fitted, the partial F-statistic for this new model calculated, and the procedure repeated. The backward elimination algorithm terminates, when the smallest partial F-value is not less than the pre-selected cut-off value Fout. c) Stepwise regression: The two procedures described above suggest a number of possible combinations. One of the most popular is the stepwise regression algorithm. This is a modification of forward selection in which at each step all regressors, entered into the model previously, are reassessed via their partial F-or t-statistics. A regressor added at an earlier step may now be redundant because of the relationship between it and regressors now in the equation. If the partial F-statistic for a variable is less than Fout, that variable is dropped from the model. Stepwise regression requires two cutoff values, Fin and Fout. Sometimes, it is preferred to choose Fin = Fout, although this is not necessary. Sometimes, it is also chosen that Fin > Fout, making it more difficult to add a regressor than to delete one. In the present study, some of the concepts of RSM have been used for predicting the FDM response viz, Tensile Strength, Flexural strength, and Impact strength. Also, the optimization of process parameters has been done by RSM. 40 CHAPTER 5 ______________________________________________________________________________ SPECIMEN PREPARATION, EXPERIMENT AND ANALYS 5.1. Specimen preparation Tensile test specimens having dimensions 60 mm x 20 mm x 5 mm. Flexural test specimens were 80 mm x 10 mm x 4 mm, and impact test specimens 80 mm x 10 mm x 4 mm, and V notch of radius 0.25 mm. Since orientation is an important parameter for part strength, tests have been conducted by changing the orientation for measuring Tensile strength (ASTMD 638), Flexural strength (ASTMD 790) and Impact strength (ASTM D256). The part are modeled in CATIAV5 software and exported as STL file. STL file is imported to FDM software (Insight). Here, factors are set as per experiment plan. Three parts per experiment are fabricated using FDM Vantage SE machine[18]. The material use for part fabrication is ABS P400. Parts are modeled and experiment is conducted as per ISO R527:1966, ISO 178:1975 and ISO 180:1982 for tensile, flexural and impact tests respectively. And part made according to response surface design 32 runs. Table 5.1 Domain of experiments Level Factor Symbol Unit Lowest(-2) Low(-1) Middle(0) High(1) Highest(2) Layer A Mm 0.127 0.158 0.190 0.222 0.254 B degree 0 15 30 45 60 Raster angle C degree 0 15 30 45 60 Raster width D Mm 0.4064 0.4264 0.4464 0.4664 0.4864 Air gap E Mm 0 0.002 0.004 0.006 0.008 thickness Sample orientation 41 Figure 5.1 Line diagram of specimen for tensile test Figure 5.2 Line diagram of specimen for flexural test Figure 5.3 Line diagram of specimen for izod test After making the test specimen According to response surface design 32 runs on the FDM Vantage SE (RP) machine, these specimens were tested. Tensile test and 3-point bending test 42 (flexural test) were conducted on Instron 1195 machine and Impact test was on Instron - Wolpert Pendulum Impact Testing Machine. 5.2. Testing of specimens: Tensile strength at break is determined according to ISO R527:1966. Shows the shape of the test specimens. Flexural strength at yield of test specimen is determined as per ISO R178:1975 standard. Three point bending test is used for flexural strength determination. For this specimen is supported by two supports and loaded in the middle by force, until the test specimen fractures [19]. The tensile testing and three-point bending tests were performed using an Instron 1195 series IX automated material testing system with crosshead speeds of 1mm/s and 2mm/s respectively. Charpy impact test performed in Instron Wolpert pendulum impact test machine is used to determine the impact strength of specimen as per ISO/179:1982. During impact testing specimen is subjected to quick and intense blow by hammer pendulum striking the specimen with a speed of 3.8 m/s. The impact energy absorbed is measure of the toughness of material and it is calculated by taking the difference in potential energies of initial and final position of hammer. following condition were taken during the different test: Machine parameter of Instron 1195 tensile test: Sample type : ASTM Sample rate (pts/sec) : 9.103 Cross head speed (mm/min) : 1.000 Full scale loading range(KN) : 20.00 Humidity (%) : 50% Temperature (deg.F) : 73 43 (a) Figure of tensile test (b) specimen after fracture Figure 5.4 Instron test of tensile specimen Machine parameter of Instron 1195 flexural test : Sample type : ASTM Sample rate (pts/sec) : 9.103 Cross head speed(mm/min) : 2.00 Full scale load range (KN) : 5.00 Humidity (%) : 50% Temperature ( deg. F) : 73 (c) Figure of flexural test (d) Specimen after bending Figure 5.5 3-point bending test of specimen 44 Machine parameter Instron - Wolpert Pendulum Impact Testing Machine: Sample type : ASTM Impact test striking velocity : 3.8 m/sec Pendulum fall angle : 160o pendulum fall height : 0.757 m length of pendulum : 390 mm (e) Figure of impact test (f) specimen after break Figure 5.6 Impact test of specimen In order to build empirical model for Tensile strength, flexural strength and impact strength, experiments were conducted based on central composite design (CCD). The CCD is capable of fitting second order polynomial and is preferable if curvature is assumed to be present in the system. To reduce the experiment run, half factorial (two levels) is considered. Maximum and minimum value of each factor is coded into +2 and -2 respectively using, so that all input factors are represented in same range [17]. 45 xij - (xi,max+xi,min)/2 = 2 x ______________ (xi,max-xi,min)/2 ξij where ij and xij are coded and actual value of j th level of i th factor respectively. Table 5.2 Experimental data obtained from the CCD runs Run Order 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Factor(coded units) A -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -2 2 0 0 0 0 0 0 0 0 0 0 0 B -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 0 0 -2 2 0 0 0 0 0 0 0 0 0 C -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 0 0 0 0 -2 2 0 0 0 0 0 0 0 D -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 -2 2 0 0 0 0 0 E 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 0 0 0 0 0 0 0 0 -2 2 0 0 0 46 Tensile Flexural Impact strength strength strength (MPa) (MPa) (Joules) 11.54 31.70 11.80 17.76 31.40 11.30 11.04 25.00 10.50 13.69 26.50 14.00 12.29 31.90 10.85 12.35 42.00 11.35 11.15 32.10 12.85 12.29 38.80 11.60 16.73 30.10 10.79 16.17 31.60 13.80 11.04 29.70 10.90 11.86 19.20 11.90 12.94 31.80 12.80 15.60 31.90 10.40 11.05 35.70 11.70 16.31 34.00 11.37 11.14 39.70 11.50 16.10 39.10 12.14 16.55 32.00 10.80 11.04 24.20 12.30 15.60 21.30 13.40 12.30 34.20 12.30 12.26 37.50 11.40 16.40 36.00 12.40 13.98 39.70 11.50 12.40 39.80 14.30 15.20 42.20 14.90 16.30 40.10 15.50 15.90 41.60 14.70 30 31 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16.40 15.50 15.90 41.10 42.30 41.80 15.00 15.10 14.90 5.3 Analysis of experiments: Analysis of the experimental data obtained from CCD design runs is done on MINITAB R14 software using full quadratic response surface model as given by . y k 0 i 1 i xi k xx i 1 ii i i i j x xj ij i Where y is the response, xi is i th factor For significance check F value given in ANOVA table is used. Probability of F value greater than calculated F value due to noise is indicated by p value. If p value is less than 0.05, significance of corresponding term is established. For lack of fit p value must be greater the 0.05. An insignificant lack of fit is desirable as it indicates anything left out of model is not significant and develop model fits. Based on analysis of variance (ANOVA) test full quadratic model was found to be suitable for tensile strength, flexural strength and impact strength with regression p-value less than 0.05 and lack of fit more then 0.05. 5.3.1 Analysis of experiment for tensile test: Table 5.3 Estimated regression coefficients for tensile test Term Constant A B C D E A*A B*B C*C Coef. 15.8469 1.1737 -1.1654 -0.5188 -0.7446 -0.2746 -0.5419 -0.4982 -0.4594 SE Coef. 0.2408 0.1232 0.1232 0.1232 0.1232 0.1232 0.1115 0.1115 0.1115 47 T 65.814 9.525 -9.458 -4.210 6.042 -2.228 -4.862 -4.470 -4.122 P 0.000 0.000 0.000 0.001 0.000 0.048 0.001 0.001 0.002 D*D E*E A*B A*C A*D A*E B*C B*D B*E C*D C*E D*E -0.3644 -0.6494 0.0931 -0.0006 -0.1181 0.3406 0.7619 -0.3381 0.9581 0.3781 0.4044 0.3669 S =0.6037 0.1115 0.1115 0.1509 0.1509 0.1509 0.1509 0.1509 0.1509 0.1509 0.1509 0.1509 0.1509 -3.270 -5.826 0.617 -0.004 -0.783 2.257 5.048 -2.240 6.349 2.505 2.679 2.431 R2 = 97.4% 0.007 0.000 0.550 0.997 0.450 0.045 0.000 0.047 0.000 0.029 0.021 0.033 R2 (adj) = 92.7% In tensile test analysis all the factors and interaction A*A, B*B, C*C, D*D, E*E, A*E, B*C, B*D, B*E, C*D, C*E, and D*E interactions are important because their P value is less than 0.05. The coefficient of determination (R2) which indicates the goodness of fit for the model so the value of R2 =97.4% which indicate the high significance of the model. With the above analysis we found the following regression equation:Ts = 15.8469+1.1737A -1.1654B -0.5188C +0.7446D -0.2746E -0.5419(A*A) - 0.4982(B*B) 0.4594(C*C) -0.3644(D*D) - 0.6494(E*E) + 0.3406(A*E) +0.7619(B*C) – 0.3381(B*D) + 0.9581(B*E) + 0.3781(C*D) + 0.404(C*E) + 0.3669(D*E). Table 5.4 Analysis of variance for tensile test Source DF Regression 20 Linear 5 Square 5 Interaction 10 Residual 11 Lack of fit 6 Pure error 5 Total 31 DF=degree of freedom Tensile strength MS 7.5761 17.4470 5.8413 3.5081 0.3644 0.4926 0.2107 SS 151.522 87.235 29.206 35.081 4.009 2.955 1.053 155.530 SS= sum of square 48 F 20.79 47.87 16.03 9.63 p 0.000 0.000 0.000 0.000 2.34 0.185 MS=mean sum of square In the above table we can see P value of all the term is less than 0.05, so these all term are significant, and non significance lack of fit is desired in this case value of LOF is 0.185 which is more than 0.05 and non significant. 5.3.2 Response surface analysis for tensile test: Surface Plot of tensile vs B, A Surface Plot of tensile vs C, A Hold Values C 0 D 0 E 0 Hold Values B 0 D 0 E 0 17.5 15 tensile 15.0 tensile 12 9 10.0 2 6 0 -2 A 0 2 12.5 B 2 0 -2 -2 A Surface Plot of tensile vs D, A 0 2 C -2 Surface Plot of tensile vs E, A Hold Values B 0 C 0 E 0 Hold Values B 0 C 0 D 0 18 15 15 tensile tensile 12 12 9 9 2 0 -2 A 0 2 2 6 D 0 -2 -2 A 49 0 2 -2 E Surface Plot of tensile vs C, B Surface Plot of tensile vs D, B Hold Values A 0 D 0 E 0 Hold Values A 0 C 0 E 0 20 tensile 17.5 15.0 15 tensile 12.5 10 2 0 -2 B 0 0 -2 -2 2 2 10.0 C B Surface Plot of tensile vs E, B 0 2 D -2 Surface Plot of tensile vs D, C Hold Values A 0 C 0 D 0 Hold Values A 0 B 0 E 0 16 15 14 tensile tensile 10 10 2 5 0 -2 0 B 12 E -2 2 2 0 -2 C Surface Plot of tensile vs E, C 0 D -2 2 Surface Plot of tensile vs E, D Hold Values A 0 B 0 D 0 Hold Values A 0 B 0 C 0 16 15.0 14 tensile tensile 12.5 12 10.0 10 2 0 -2 C 0 2 2 E 0 -2 -2 D 0 2 Figures 5.7 Surface plots for tensile strength 50 -2 E From response surface it is observed that strength first decrease and then increase with layer thickness (A) increase. The reason may be that at smaller layer thickness numbers of layers are more resulting in increase in heat conduction towards the bottom layers therefore strong bonding between adjacent rasters is expected. But this also increases the distortion in bottom layers which is responsible for weak bond strength, so with increase in layer thickness distortion in layer thickness decreased and tensile strength increased. Response surface shows the decreasing trend of strength with respect to increase in orientation (B).this may be due to the stepped effect in which one layer does not coincide with the next layer exactly this ultimately reduce the strength of the part. Number of layers also increases with increase in orientation for same layer thickness as a result distortion in part will increase resulting in less bond strength. Tensile strength is decreasing with respect to raster angle ,the reason may be that at small angle raster deposited have long length due to this inter bonding of the part is good and also number of layer is less. So, with increase in raster angle this inters bonding gets weak and decreases the strength. Tensile strength is increase with increasing the raster width (D) , the reason may be that at small raster width number of layer are more so the distortion chances are higher, so with increase in raster width strength increase. Tensile strength is increased up to certain level and after that level it decrease, this is due to that If raster deposition is much closed the melt material can overlap to next raster and it can lose Its strength. But this air gap should be maintain, if air gap is large there will be a gap between two raster and it can also reduce the strength. 51 (a) Horizontal position of specimen (b) vertical position of specimen Figure 5.8 SEM image of tensile failure of specimen The above SEM images are shown for two position of tensile fracture (a) is a horizontal position of fractured specimen and (b) is vertical position of fractured specimen. We have 32 specimens for each test, so randomly we have chosen one specimen of parametric combination, and choose the specimen of parametric combination of 19 for the SEM image which will give the behavior of specimen after different test. In Image (a) the circle portion shows the fracture on the specimen, This is the ABS P400 (acrylonitrilebutadine-styrene) material, and we can see there is no or negligible elongation in the specimen while we do the tensile test and material behavior like a brittle material and image (b) shows the different points from where fracture occurred. 52 5.3.3 Analysis of experiment for flexural test: Table 5.5 Estimated regression coefficients for flexural test Term Constant A B C D E A*A B*B C*C D*D E*E A*B A*C A*D A*E B*C B*D B*E C*D C*E D*E S = 1.320 Coef. 41.7159 0.2583 -1.5417 3.2833 -0.7667 0.6500 -0.7284 -3.5534 -3.6409 -1.3909 -0.6409 -0.9625 1.4375 -1.7875 0.6375 1.7125 0.4875 -0.5125 -0.4625 -0.7625 0.3125 SE Coef. 0.5264 0.2694 0.2694 0.2694 0.2694 0.2694 0.2437 0.2437 0.2437 0.2437 0.2437 0.3299 0.3299 0.3299 0.3299 0.3299 0.3299 0.3299 0.3299 0.3299 0.3299 T 79.248 0.959 -5.723 12.188 -2.846 2.413 -2.989 -14.583 -14.942 -5.708 -2.630 -2.917 4.357 -5.418 1.932 5.190 1.478 -1.553 -1.402 -2.311 0.947 R2 = 98.5% P 0.000 0.358 0.000 0.000 0.016 0.034 0.012 0.000 0.000 0.000 0.023 0.014 0.001 0.000 0.079 0.000 0.168 0.149 0.189 0.041 0.364 R2(adj) = 95.7% In flexural test we can see by the above table factors B, C, D, E and interaction A*A, B*B, C*C, D*D, E*E, A*B, A*C, A*D, B*C, and C*E are most important because they are having P value less than 0.05. The coefficient of determination (R2) which indicates the goodness of fit for the model so the value of R2 =98.5% which indicate the high significance of the model. With the above analysis we found the following regression equation:- 53 Fs = 41.7159– 1.5417B + 3.2833C – 0.7667D + 0.6500E – 0.7284(A*A) – 3.5534 (B*B) – 3.6409 (C*C) – 1.3909 (D*D) – 0.6409 (E*E) – 0.9625 (A*B) + 1.4375(A*C) -1.7875 (A*D) + 1.7125(B*C) – 0.7625(C*E). Table 5.6 ANOVA analysis for flexural test Source Regression Linear Square Interaction Residual Lack of fit Pure error Total DF 20 5 5 10 11 6 5 31 Flexural strength MS F 61.922 35.55 68.323 39.23 144.420 82.92 17.473 10.03 1.742 2.635 3.94 0.670 SS 1238.44 341.62 722.10 174.73 19.16 15.81 3.35 1257.60 DF =degree of freedom SS = sum of square p 0.000 0.000 0.000 0.000 0.077 MS = mean sum of square In the above table we can see P value of all the term is less than 0.05, so these all term are significant, and non significance lack of fit is desired in this case value of LOF is 0.077 which is more than 0.05 and non significant. 5.3.4 Response surface analysis for flexural test: Surface Plot of flexural vs B, A Surface Plot of flexural vs C, A Hold Values C 0 D 0 E 0 Hold Values B 0 D 0 E 0 40 flexural 40 flexural 30 30 20 2 20 0 -2 A 0 2 2 10 B 0 -2 -2 A 54 0 2 -2 C Surface Plot of flexural vs D, A Surface Plot of flexural vs E, A Hold Values B 0 C 0 E 0 Hold Values B 0 C 0 D 0 42 40 39 35 flexural flexural 36 30 2 25 0 -2 0 A 0 -2 -2 2 2 33 D 0 A 2 E -2 Surface Plot of flexural vs D, B Surface Plot of flexural vs C, B Hold Values A 0 C 0 E 0 Hold Values A 0 D 0 E 0 45 40 30 flexur al flexur al 15 2 0 0 -2 0 B 2 30 2 20 C 0 -2 -2 B Surface Plot of flexural vs E, B 0 D -2 2 Surface Plot of flexural vs D, C Hold Values A 0 C 0 D 0 Hold Values A 0 B 0 E 0 40 flexural 40 flexural 30 20 2 20 0 -2 B 0 2 30 E 2 0 -2 -2 C 55 0 2 -2 D Surface Plot of flexural vs E, D Surface Plot of flexural vs E, C Hold Values A 0 B 0 C 0 Hold Values A 0 B 0 D 0 40 flexural 40 30 flexural 35 20 2 10 0 -2 C 0 2 2 30 E 0 -2 -2 D 0 2 E -2 Figure 5.9 Surface plots of flexural test Flexural strength response surface shows that flexural strength monotonously increases with increase in layer thickness (A) .The reason may be that for flexural strength measurement load is applied perpendicular to length of specimen. Therefore thicker part will show more strength as compared to thinner part. Hence, if part is made with thicker layer then each individual layer will show more resistance against the failure as compared to part of same thickness made with thinner layer. Flexural strength of the material is first increasing with respect to sample orientation (B) and after certain level it gets decrease, this is may be due to the stepped effect, in this layer deposited over another layer so due the sample orientation there may be some portion is vacant this lead to the weak strength of material. At lower raster angle (C) not only the length of individual raster is more but their inclination along the length of specimen is also more as result strength will be more. Combine effect of long raster and thick layer is responsible for monotonous increase in strength at small raster angle value with increase in layer thickness. But long rasters have more distortion as compare to short rasters as a result strength will increase on increasing the raster angle. 56 Higher width (D) reducing the number of rasters due to which the rasters are not able to give much resistance for the applied load. Higher raster not only reduces the number of rasters but also inputting more heat into the system as a result strength will decrease. Flexural strength is increased with increasing the air gap (E), this is due to that, at min. air gap two raster will be very close and this decreases the heat dissipation and increase the chance of residual stress accumulation. This lead to reduce the strength at low level of air gap. (c) Crack formation in flexural specimen (d) specimen after cracking Figure 5.10 SEM image of crack surface of flexural specimen SEM image of 3-point bending test specimen is shown in Image (c) and (d) respectively. Image (c) shows the crack occurred after bending test, in fig we can see that the cracking length is max, where max. Load is applied .and in Image (d) the horizontal position of the cracked specimen is shown, although ABS P400 (acrylonitrile-butadine-styrene) is a brittle material so we can see in the Image (d) no or negligible elongation took place. 57 5.3.5 Analysis of experiment for impact test: Table 5.7 Estimated regression coefficients for impact test Term Constant A B C D E A*A B*B C*C D*D E*E A*B A*C A*D A*E B*C B*D B*E C*D C*E D*E S = 0.3835 Coef. 14.9724 0.2004 0.1971 -0.1779 0.0588 0.6429 -0.7549 -0.8224 -0.4974 -0.7349 -0.4849 0.1444 -0.6556 -0.0606 0.0506 0.1569 -0.3481 -0.1869 -0.0106 -0.1369 -0.1044 SE Coef. 0.15296 0.07828 0.07828 0.07828 0.07828 0.07828 0.07081 0.07081 0.07081 0.07081 0.07081 0.09587 0.09587 0.09587 0.09587 0.09587 0.09587 0.09587 0.09587 0.09587 0.09587 T P 97.884 2.560 2.518 -2.273 0.751 8.213 -10.661 -11.614 -7.025 -10.379 -6.848 1.506 -6.838 -0.632 0.528 1.636 -3.631 -1.949 -0.111 -1.428 -1.089 R2 = 97.9% 0.000 0.027 0.029 0.044 0.469 0.000 0.000 0.000 0.000 0.000 0.000 0.160 0.000 0.540 0.608 0.130 0.004 0.077 0.914 0.181 0.300 R2 (adj) =94.0% With the above analysis we found factors A, B, C, E and interaction A*A, B*B, C*C, D*D, E*E, A*C, B*D. The coefficient of determination (R2) which indicates the goodness of fit for the model so the value of R2 =97.9% which indicate the high significance of the model. With the above analysis we found the following regression equation:Is = 14.9724 + 0.2004A + 0.1971B – 0.1779C + 0.6429E – 0.7549(A*A) – 0.8224(B*B) 0.4974 (C*C) – 0.7349 (D*D) - 0.4849 (E*E) – 0.6556 (A*C) – 0.3481(B*D) . 58 Table 5.8 Analysis of variance for impact test Source DF Regression 20 Linear 5 Square 5 Interaction 10 Residual 11 Lack of fit 6 Pure error 5 Total 31 DF =degree of freedom SS 74.2303 12.6590 50.8931 10.6783 1.6177 1.2494 0.3683 75.8480 SS = sum of square Tensile strength MS 3.7115 2.5318 10.1786 1.0678 0.1471 0.2082 0.0737 F 25.24 17.22 69.21 7.26 p 0.000 0.000 0.000 0.001 2.83 0.137 MS = mean sum of square In the above table we can see P value of all the term is less than 0.05, so these all term are significant, and non significance lack of fit is desired in this case value of LOF is 0.077 which is more than 0.05 and non significant. 5.3.6 Response analysis for impact test: Surface Plot of impact vs B, A Surface Plot of impact vs C, A Hold Values C 0 D 0 E 0 Hold Values B 0 D 0 E 0 14 impact 14 12 impact 12 10 10 2 8 0 -2 A 0 2 2 8 B 0 -2 -2 A 59 0 2 -2 C Surface Plot of impact vs D, A Surface Plot of impact vs E, A Hold Values B 0 C 0 E 0 Hold Values B 0 C 0 D 0 16 14 impact 14 12 impact 10 10 2 8 0 -2 A 0 12 D -2 2 2 0 -2 0 A Surface Plot of impact vs C, B E -2 2 Surface Plot of impact vs D, B Hold Values A 0 D 0 E 0 Hold Values A 0 C 0 E 0 14 14 impact 12 impact 12 10 10 8 2 8 0 -2 0 B C -2 2 2 0 -2 B Surface Plot of impact vs E, B 0 D -2 2 Surface Plot of impact vs D, C Hold Values A 0 C 0 D 0 Hold Values A 0 B 0 E 0 14 impact 14 12 impact 10 2 8 0 -2 B 0 2 12 2 10 E 0 -2 -2 C 60 0 2 -2 D Surface Plot of impact vs E, C Surface Plot of impact vs E, D Hold Values A 0 B 0 D 0 Hold Values A 0 B 0 C 0 16 14 14 impact impact 12 12 10 2 10 0 -2 C 0 2 2 8 E 0 -2 -2 D 0 2 E -2 Figure 5.11 Surface plots of impact test With the above graphs we can see that behavior of all the factors are similar and up to level 0 of the factors strength is increasing and after that level its decreasing, this is may be due to the reason which we have discussed in tensile strength analysis and flexural strength analysis. (e) Horizontal position of broke specimen (f) vertical position of broke specimen Figure 5.12 SEM image of broke impact test specimen 61 In above SEM image two image shown (e) and (f) respectively for horizontal and vertical position of the impact specimen. Image (e) shows the behavior of material after breaking. In this test material directly break from the notch portion with the help of pendulum. And it is the ABS P400 (acrylonitrile-butadine-styrene) material which behaves as a brittle material, this directly break and no elongation takes place, this we can see in image (e) and (d) that the material broke at different place due to sudden impact load, but no change or elongation in any dimension of the shape took place. With the above three analysis we see that tensile strength is higher in experiment no. 2, flexural strength is higher in experiment no. 31, and impact strength is higher in experiment no. 28. And factors and interactions which are affecting the strength are different in three cases. So to optimize all the response simultaneously by converting multiple response into single response Gery-taguchi method is used. 5.4 Optimization of process parameters Above discussion shows that FDM process involves large number of conflicting factors and complex part building phenomena making it difficult to predict the output characteristics based on simple analysis of factor variation. Hence, to determine the optimal setting of process parameters that will maximize the tensile strength, flexural strength and impact strength respectively, desirability function (DF) given by Equation (5.1) is used n 1/ n DF d i 1 wi i wi i 1 ………………..……………………(5.1) where di is the desirability defined for the ith targeted output. For a goal to find a maximum, di is calculated as shown in Equation (5.2). 62 di 0 Yi if Low i Yi low i High i low i di di if 1 if Yi low i Yi High i ……………....(5.2) High i where Yi is the found value of the ith output during optimization process, and the lowi, Highi are the minimum and maximum values respectively of the experimental data for the ith output. Since all the strengths are equally important therefore value of weight wi is taken as 1.Optimum factor levels that will maximize the desirability function are calculated and are given in Table (5.10) for respective strength together with its predicted value. Table 5.9 Optimum factor and predicted response for individuals strength Response Goal Tensile strength Low High wi Maximum 11.04 17.76 1 Flexural strength Maximum 19.2 42.3 1 Impact strength Maximum 10.4 15.5 1 63 Factor level (Coded units) A=2; B=-2; C=2; D= -2; E=-2 A=0; B=0; C=0; D=0; E=0.4968 A=0; B=0; C=0; D=0; E=0.6835 Predicted response 19.43 DF 1.0000 41.88 0.98185 15.1853 0.93829 CHAPTER 6 ______________________________________________________________________________ GREY – BASED TAGUCHI METHOD 6. Grey-based taguchi method 6 .1 Introduction : Taguchi’s philosophy, developed by Dr. Genichi Taguchi, is an efficient tool for the design of high quality manufacturing system [30]. It is a method based on Orthogonal Array experiments which provides much-reduced variance for the experiment resulting optimal setting of process control parameters. Orthogonal Array provides a set of well-balanced experiments with less number of experimental runs. In order to evaluate the optimal parameter setting, Taguchi method uses a statistical measure of performance called signal-to-noise ratio that takes both the mean and the variability into account. The S/N ratio is the ratio of the mean (signal) to the standard deviation (noise). The ratio depends on the quality characteristics of the product/process to be optimized. The standard S/N ratios generally used are Nominal-is-Best (NB), lower-the-better (LB) and Higher-the-Better (HB). The optimal setting is the parametric combination, which has the highest S/N ratio. However, traditional Taguchi method cannot solve multi-objective optimization problem. This can be achieved by grey based Taguchi method. In grey relational analysis, experimental data i.e. measured features of quality characteristics of the product are first normalized ranging from zero to one. This process is known as grey relational generation. Next, based on normalized experimental data, grey relational coefficient is calculated to represent the correlation between the desired and actual experimental data. Then, overall grey relational grade is determined by averaging the grey relational coefficient corresponding to selected responses. The overall performance characteristic of the multiple response process depends on the calculated overall grey relational grade. This approach converts a multipleresponse process optimization problem into a single response optimization situation with the objective function is overall grey relational grade. Using grey-Taguchi method, the optimal parametric combination is then evaluated by maximizing the S/N ratio of the overall grey relational grade. 64 6.2 Grey-relational analysis: Data preprocessing: Grey data processing must be performed before Grey correlation coefficients can be calculated. A series of various units must be transformed to be dimensionless. Usually, each series is normalized by dividing the data in the original series by their average. Let the original reference sequence and sequence for comparison be represented as xo(k) and xi (k), i =1, 2, ...,m; k =1, 2, ..., n, respectively, where m is the total number of experiment to be considered, and n is the total number of observation data. Data preprocessing converts the original sequence to a comparable sequence [30]. Several methodologies of preprocessing data can be used in Grey relation analysis, depending on the characteristics of the original sequence. If the target value of the original sequence is “the-larger-the-better”, then the original sequence is normalized as follows: If the expectancy is smaller- the –better, then the original sequence should be normalized as follow. However, there is a definite target value to be achieved; the original sequence will be normalized in the form. 65 or the original sequence can be simply normalized by the most basic methodology, i.e. let the values of original sequence be divided by the ﬁrst value of sequence: where x*i(k) is the value after the grey relational generation (data pre-processing), max x0i (k) is the largest value of x0i (k), min x0i (k) is the smallest value of x0i (k) and x0 is the desired value. Grey relational coefficient and grey relational grade: Following data pre-processing, a grey relational coefficient is calculated to express the relationship between the ideal and actual normalized experimental results. The grey relational coefficient can be expressed as follows: where Δ0i(k)is the deviation sequence of the reference sequence x*0(k) and the comparability sequence x*i(k), namely ξ is distinguishing or identiﬁcation coefficient: ξ ε [0,1]. ξ =0.5 is generally used. After obtaining the grey relational coefficient, we normally take the average of the grey relational coefficient as the grey relational grade. The grey relational grade is defined as follows: 66 However, since in real application the effect of each factor on the system is not exactly same. Eq. (6) can be modified as follow: Where wk represents the normalized weighting value of factor k. Given the same weights, Eqs. (6) and (7) are equal. In the grey relational analysis, the grey relational grade is used to show the relationship among the sequences. If the two sequences are identical, then the value of grey relational grade is equal to 1. The grey relational grade also indicates the degree of inﬂuence that the comparability sequence could exert over the reference sequence. There- fore, if a particular comparability sequence is more important than the other comparability sequences to the reference sequence, then the grey relational grade for that comparability sequence and reference sequence will be higher than other grey relational grades [31] . In this analysis we are considering three responses tensile strength, flexural strength, impact strength, these response should be high, so we normalizing the data according to larger -thebetter(LB). Table 6.1 . Normalization of the data (larger-the-better) (x*I (k)) Experiment no. Ideal condition 1 2 3 4 5 6 7 Tensile strength 1.00000 Flexural strength Impact strength 1.00000 1.00000 0.07440 1.00000 0.00000 0.39435 0.18601 0.19494 0.01637 0.54113 0.52814 0.25108 0.31602 0.54978 0.98701 0.55844 67 0.27451 0.17647 0.01961 0.70588 0.08824 0.18627 0.48039 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 0.18601 0.84673 0.76339 0.00000 0.12202 0.28274 0.67857 0.00149 0.78423 0.01488 0.75298 0.81994 0.00000 0.67857 0.18750 0.18155 0.79762 0.43750 0.20238 0.61905 0.78274 0.72321 0.79762 0.66369 0.72321 0.84848 0.47186 0.53680 0.45455 0.00000 0.54545 0.54978 0.71429 0.64069 0.88745 0.86147 0.55411 0.21645 0.09091 0.64935 0.79221 0.72727 0.88745 0.89177 0.99567 0.90476 0.96970 0.94805 1.00000 0.97835 0.23529 0.07647 0.66667 0.09804 0.29412 0.47059 0.00000 0.25490 0.19020 0.21569 0.34118 0.07843 0.37255 0.58824 0.37255 0.19608 0.39216 0.21569 0.76471 0.88235 1.00000 0.84314 0.90196 0.92157 0.88235 Table 6.2 The deviation sequence (Δo,i(k)) Experiment no. 1 2 3 4 5 6 Tensile strength, Flexural strength, Impact strength, Δo,i(1) Δo,i(2) Δo,i(3) 0.92560 0.45887 0.72549 0.00000 0.47186 0.82353 1.00000 0.74892 0.98039 0.60565 0.68398 0.29412 0.81399 0.45022 0.91176 0.80506 0.01299 0.81373 68 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 0.98363 0.81399 0.15327 0.23661 1.00000 0.87798 0.71726 0.32143 0.99851 0.21577 0.98512 0.24702 0.18006 1.00000 0.32143 0.81250 0.81845 0.20238 0.56250 0.79762 0.38095 0.21726 0.27679 0.20238 0.33631 0.27679 0.44156 0.15152 0.52814 0.46320 0.54545 1.00000 0.45455 0.45022 0.28571 0.35931 0.11255 0.13853 0.44589 0.78355 0.90909 0.35065 0.20779 0.27273 0.11255 0.10823 0.00433 0.09524 0.03030 0.05195 0.00000 0.02165 0.51961 0.76471 0.92353 0.33333 0.90196 0.70588 0.52941 1.00000 0.74510 0.80980 0.78431 0.65882 0.92157 0.62745 0.41176 0.62745 0.80392 0.60784 0.78431 0.23529 0.11765 0.00000 0.15686 0.09804 0.07843 0.11765 Table 6.3 Calculation of grey relational coefficients(ξi (k)) Tensile strength Flexural Experimental no. (MPa) strength(MPa) Impact strength(joules) 1 0.35073 0.52145 0.40800 2 1.00000 0.51448 0.37778 3 0.33333 0.40035 0.33775 4 0.45222 0.42230 0.62963 5 0.38052 0.52619 0.35417 6 0.38312 0.97468 0.38000 7 0.33701 0.53103 0.49038 8 0.38052 0.76744 0.39535 69 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 0.76538 0.67879 0.33333 0.36285 0.41076 0.60869 0.33366 0.69855 0.33667 0.66933 0.73523 0.33333 0.60869 0.38095 0.37923 0.71187 0.47059 0.38532 0.56757 0.69710 0.64367 0.71187 0.59786 0.64367 0.48632 0.51910 0.47826 0.33333 0.52381 0.52619 0.63637 0.58186 0.81626 0.78305 0.52860 0.38954 0.35484 0.58779 0.70642 0.64706 0.81626 0.82206 0.99141 0.84000 0.94286 0.90588 1.00000 0.95850 Table 6.4 Grey- relational grade (γi) γi 0.42672 0.63075 0.35714 0.50138 0.42029 0.57926 0.45280 0.51443 0.53431 0.59929 0.38941 Ex. No. 1 2 3 4 5 6 7 8 9 10 11 70 0.35124 0.60000 0.35664 0.41463 0.48572 0.33333 0.40157 0.38174 0.38931 0.43147 0.35172 0.44348 0.54839 0.44348 0.38346 0.45133 0.38931 0.68000 0.80952 1.00000 0.76120 0.83606 0.86441 0.80952 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 0.37027 0.47343 0.48940 0.45720 0.55405 0.51408 0.62795 0.53851 0.38878 0.50397 0.47074 0.48970 0.60342 0.55872 0.62912 0.78950 0.84570 0.78257 0.81793 0.82075 0.80389 71 Figure 6.1. Sensitivity analysis for different distinguishing coefficients(ξ) Figure 6.2 . Grey relational grade variation with number of experiment(ξ=0.5) 72 The purpose of distinguish coefficient is to expand or compress the range of the grey relational coefficient. The distinguishing coefficient can be selected by decision maker judgement, and different distinguishing coefficients usually provide different results in GRA. Sensitivity analysis for different distinguishing coefficients (Figure 19) shows that impact of their variation on grey relation coefficient is very small. They all led to the same optimum factor levels. In this case distinguishing coefficient is taken as 0.5. Table 6.5 Response surface analysis for grey relational grade S.N. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 A B -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -2 2 0 0 0 0 0 0 0 0 C -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 0 0 -2 2 0 0 0 0 0 0 D -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 0 0 0 0 -2 2 0 0 0 0 E -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 -2 2 0 0 73 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 0 0 0 0 0 0 0 0 -2 2 Grey-relational grade 0.42672 0.63075 0.35714 0.50138 0.42029 0.57926 0.45280 0.51443 0.53431 0.59929 0.38941 0.37027 0.47343 0.48940 0.45720 0.55405 0.51408 0.62795 0.53851 0.38878 0.50397 0.47074 0.48970 0.60342 0.55872 0.62912 27 28 29 30 31 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.78950 0.84570 0.78257 0.81793 0.82075 0.80389 Table 6.6 Estimated Regression coefficients for grey relational grade Term Constant A B C D E A*A B*B C*C D*D E*E A*B A*C A*D A*E B*C B*D B*E C*D C*E D*E S= 0.03359 Coef. 0.806193 0.039803 -0.035677 0.002714 0.008833 0.014307 -0.055893 -0.082735 -0.076808 -0.062007 -0.050166 -0.010024 -0.003793 -0.025638 0.015982 0.036812 -0.005890 0.012165 0.001875 0.009618 0.007965 SE Coef. 0.013399 0.006857 0.006857 0.006857 0.006857 0.006857 0.006206 0.006206 0.006206 0.006206 0.006206 0.008398 0.008398 0.008398 0.008398 0.008398 0.008398 0.008398 0.008398 0.008398 0.008398 R-sq= 98.0% T 60.170 5.805 -5.203 0.396 1.288 2.087 -9.012 -13.339 -12.384 -9.997 -8.088 -1.194 -0.452 -3.053 1.903 4.383 -0.701 1.449 0.223 1.145 0.948 P 0.000 0.000 0.000 0.700 0.224 0.061 0.000 0.000 0.000 0.000 0.000 0.258 0.660 0.011 0.084 0.001 0.498 0.175 0.827 0.276 0.363 R-sq (adj) = 94.4% With the above analysis we found while considering all the response simultaneously only factor (A), and (B), and interaction term A*A, B*B, C*C, D*D, E*E, A*D, B*C. The coefficient of determination (R2) which indicates the percentage of total variation in the response explained by the terms in the model is 98%. 74 With the above analysis we found the following regression equation:Os =0.806193+0.039803A – 0.035677B -0.055893(A*A) – 0.082735(B*B) – 0.076808(C*C) 0.062007 (D*D) - 0.050166(E*E) – 0.025638(A*D)+0.036812(B*C) . Table 6.7 ANOVA analysis for grey relational grade Source Regression Linear Square Interaction Residual Lack of fit Pure error Total DF 20 5 5 10 11 6 5 31 Tensile strength MS 0.030792 0.015107 0.099341 0.004360 0.001128 0.001625 0.000533 SS 0.615837 0.075534 0.496706 0.043597 0.012413 0.009750 0.002663 0.628250 F 27.29 13.39 88.03 3.86 p 0.000 0.000 0.000 0.018 3.05 0.121 6.3 Response Optimization of GRG and optimal parameter setting: With the help of response optimizer we have found the optimal parameter setting for all three responses: response Goal Maximum Lower 0.35714 Predicted GRG Responses desirability Target 1 Upper 1 Weight 1 = 0.80619 = 0.80619 For the above predicted response the optimal parameter setting is Parameter Layer thickness Sample orientation Raster angle Raster width Air gap value 0.190 30 30 0.4464 0.004 75 Units (mm) (degree) (degree) (mm) (mm) Importance 1 Table 6.8 Comparison of parameter setting individual and simultaneous optimization ( Uncoded Value) Parameter Individual optimization Tensile Flexural Impact strength strength strength 0.254 0.190 0.190 A (mm) 0 30 30 B (degree) 0 30 30 C (degree) 0.4064 0.4464 0.4464 D (mm) 0 0.004993 0.005367 E (mm) 76 Simultaneous optimization 0.190 30 30 0.4464 0.004 CHAPTER 7 ______________________________________________________________________________ RESULT, CONCLUSION AND FUTURE SCOPE 7. Results, conclusions and future scope 7.1 Results and discussions: The tensile strength data of ABS sample with different level of process parameter are shown in table (2). The ultimate strength were the highest (17.76 MPa) for the layer thickness 0.222 mm, sample orientation 15o , raster angle 15o , raster width 0.4264 mm, and air gap 0.002 mm combination set and the lower strength (11.04 MPa) for layer thickness 0.158 mm, sample orientation 45o, raster angle 15o , raster width 0.4264 mm, and air gap 0.002 mm, the lower strength in the solid model could have been caused by residual stress from the volumetric shrinkage , weak interlayer bonding, or interlayer porosity. Examination of the fracture surfaces revealed fracture paths that were controlled by either weak interlayer bonding or interlayer porosity. Weak interlayer bonding probably was a result of residual stresses caused by volumetric shrinkage of the polymer layers during solidification from the melt. Weak interlayer bonding could also be caused by the low molecular diffusion and low cross-linking between the polymer layers during deposition from the melt. In addition, the interlayer porosity reduced the load-bearing area across the layers and hence provided an easy fracture path. The percent elongation of the tensile specimens was <2%, and the ABS material failed in a semi-brittle manner. Because the ABS elongation was so low. The 3-point bending test data of ABS sample shown in table (2).the flexural strength are greater than the tensile strengths because the modulus of rupture measure the maximum strength at the outer fiber of the beam. This is expected because during bending, the sample is subjected to both compressive and tensile load in this test flexural strength is highest (42.3 MPa) for the layer thickness 0.190 mm, sample orientation 30o , raster angle 30o, raster width 0.4464 mm, and air gap were 0.004 mm. and min. flexural strength (19.20 MPa) for layer thickness 0.222 mm, 77 sample orientation 45o, raster angle 15o , raster width 0.4664 mm, and air gap 0.002 mm. again as in the tensile testing, this low flexural strength is due to rapid prototyping sample having weak interlayer bonding or interlayer porosity. During impact testing, the material is subjected to quick, intense blow by a hammer pendulum. The impact test measures the energy absorption or the toughness of the material. The V-notched specimen evaluates the materials resistance to crack propagation. In this test we found ultimate impact strength (15.50 joule) for the parametric combination of layer thickness 0.190 mm, sample orientation 30o, raster angle at 30o, raster width 0.4464 mm, and air gap 0.004 mm. and min. impact strength (10.4 joule) for the parametric combination of layer thickness 0.222 mm, sample orientation 15o, raster angle 45o, raster width 0.4664 mm, and air gap 0.002 mm. in FDM, heating and rapid cooling cycles of the material result in non-uniform temperature gradients. This cause stresses to build up leading to distortion, dimensional inaccuracy and inner layer cracking or de-lamination. The reasons attributed to non uniform heating and cooling cycles are explained as follows: (1) In FDM, heat is dissipated by conduction and forced convection and the reduction in temperature caused by these processes forces the material to quickly solidify onto the surrounding filaments. Bonding between the filaments is caused by local re-melting of previously solidified material and diffusion. This results in uneven heating and cooling of material and develops non uniform temperature gradients. As a result, uniform stress will not be developed in the deposited material and it may not regain its original dimension completely. (2) Speed at which nozzle is depositing the material may alter the heating and cooling cycle and results in different degree of thermal gradient and thus also affects the part accuracy. 78 At lower slice thickness, nozzle deposition speed is slower as compared to higher slice thickness. Also during deposition, nozzle stops depositing material in random manner (in between depositing a layer and after completely depositing a layer) and return to service location for tip cleaning. While depositing the material at the turns near the boundary of part, nozzle speed has to be decreased and then increase to uniform speed . If deposition path length is small, this will result in non uniform stress to build up especially near the part boundary. (3) The pattern used to deposit a material in a layer has a significant effect on the resulting stresses and deformation. Higher stresses will be found along the long axis of deposition line. Therefore, short raster length is preferred along the long axis of part to reduce the stresses. (4) Stress accumulation also increase with layer thickness and road width. But the thick layer also means fewer layers, which may reduce the number of heating and cooling cycles. Also, a smaller road width will input less heat into the system within the specified period of time but requires more loops to fill a certain area. More loops means more time required for deposition of single layer and more non uniform nozzle speed. This will keep the deposited material above its desired temperature for regaining its original shape and in the mean time new material will be deposited and contraction of previously deposited material will be constrained Hence, with the response surface analysis we have seen that tensile strength, flexural strength, and impact strength, are higher at different parametric combination, optimization of all three responses is impossible. So grey Taguchi method is used to convert these multiple response into a single response, and with the help of response optimizer we found out the optimal parameter setting to maximize all three responses. 79 7.2 Conclusion: Effect of five process parameters layer thickness, sample orientation, raster angle, raster width and air gap are studied on three responses viz., tensile strength, flexural strength and impact strength of test specimen. Experiments were conducted using centre composite design (CCD). Empirical relations between each response and process parameters were determined and their validity is proved using analysis of variance (ANOVA) and the normal probability plot of residues. Response surface plots of respective strength shows that parameter effect are dependent on each other and their optimal setting depends upon the level selected for other parameters. The main reason attributed for weak strength is the distortion within the layer or between the layers. To get the optimal level concept of simultaneous optimization of three responses desirability function is used for maximizing the all the responses and found out the optimal parameter setting. 7.3 Future scope: The response surface methodology is a robust process for optimization of the single response as well as multiple responses. In present work, optimization of three FDM responses is considered are tensile, flexural, and impact strength. 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