Bleeding and Shrinkage in Rapid Manufacturing Using a 3D Printer

Transcription

1 Bleeding and Shrinkage in Rapid Manufacturing Using a 3D Printer Prashanthi Dhulipudi Problem Report submitted to the College of Engineering and Mineral Resources At West Virginia University In partial fulfillment of the requirements For the degree of Master of Science in Industrial Engineering Dr. Rashpal Singh Ahluwalia, Chair Dr. Robert Creese, Dr. Xing Bo Liu Department of Industrial and Management Systems Engineering Morgantown, West Virginia 2009 Keywords: Rapid Prototyping, 3D Printing, Bleeding, Shrinkage, Sintering, Orientation, SAS, ANOVA

2 ABSTRACT Investigation of the Accuracy and Shrinkage in Rapid Manufacturing using 3D Printer Technology Prashanthi Dhulipudi Bleeding effect and shrinkage behavior was analyzed in a 420 stainless steel/bronze composite (S4) cuboid printed using 3D printing technology and heat treated through a sintering process. The cuboids were prismatically symmetric with the opposite sides in symmetry. Cuboids of three different volumes were made in sets of three. Each set had constant width and depth and length varying. The positioning of the cuboids in each set was that the first two cuboids were positioned in a similar way along the y-axis, which was perpendicular to the print head. The third cuboid in the set was positioned or oriented along the x-axis parallel to the print head. These cuboids were cured and initial measurements are taken. Bleeding effect was observed from these measurements. The cured cuboids were heat treated by sintering to gain strength and measured again. Shrinkage had been experienced, as the part is not fully dense. The measurements taken for bleed and shrinkage, depending on their independent variables (volume, orientation, and axes), were experimentally designed to a factorial design having three factors at three levels, each with single replication. The analysis from statistical hypothesis was observed to have variations in the independent variable rejecting the null hypothesis. The significant main effect for the bleed was observed to be axes and the significant interaction effect to be between axes and orientation. The specific difference between the treatment means of the significant main effect was observed to be in the y-axis which was along the printing direction. Secondly, it was observed that the significant main effect for the shrinkage model is observed to be volume and axes. The significant interaction was observed to be between axes and orientation. The specific difference in the treatment means was observed to be in the y-axis and the least in the z-axis. The shrinkage was observed to follow the behavior of the bleeding.

3 DEDICATION To my parents, love you. iii

4 ACKNOWLEDGEMENTS A journey is easier when you travel together. This research is the result of two years of work whereby I have been accompanied and supported by many people. It is a pleasant aspect that I have now the opportunity to express my gratitude for all of them. The first person I would like to thank is Dr. Creese, for his hard work and guidance throughout and for believing in my abilities. I have learned so much, and without him this would not have been possible. I would like to express my deep and sincere gratitude to Dr. Rashpal Singh Ahluwalia for serving as the Committee Chair and Dr. Majid Jaraiedi for his support in helping me to statistically analyze the experimental data. I wish to express my warm and sincere thanks to Dr. Xing Bo Liu for his valuable comments and suggestions as a committee member. I would like to express my sincere gratitude and appreciation to the Department of Industrial and Management Systems Engineering, West Virginia University for allowing me this opportunity to pursue M.S degree in the department. I would like to thank Mr. Jim Dalton for his cooperation in the machine shop where in I successfully completed my experiments. I would also like to thank my colleagues in the machine shop for being patient and friendly. I would like to thank all my close friends for making my Master s life joyful and to have become an extended family. I am very grateful to my parents and my little sister for their unconditional love and support in all my efforts, and for being the reason to what I am. iv

5 TABLE OF CONTENTS ABSTRACT...ii DEDICATION... iii ACKNOWLEDGEMENTS... iv TABLE OF CONTENTS... v LIST OF FIGURES... viii LIST OF TABLES... x LIST OF ACRONYMS... xi CHAPTER INTRODUCTION Rapid Prototyping Rapid Manufacturing Three dimensional printing (3DP) Motivation for current work Significance of current work Aim and objectives of current study... 5 CHAPTER LITERATURE REVIEW Accuracy pattern with 3D printing Shrinkage control and its behavior CHAPTER v

6 METHODOLOGY D Printing for concept modeling ProMetal 3D printing Material Selection Design in CAD and fabrication of the designed part Curing Sintering Selection of supporting powder Debinding set up Selecting a sintering profile Infiltration Final Product Defining the axis of the machine Symmetry of the cuboid Measurements Tool maker s microscope Micrometers Experimental Design Bleeding effect on the cuboid Shrinkage in the cuboid CHAPTER RESULTS AND DISCUSSION Numerical validation vi

7 4.2 Statistical analysis for the bleeding on the cuboid Analysis of Variance Tukey s Test Normality test Statistical analysis for the shrinkage on the cuboid Analysis of variance Tukey s Test Normality test Verification of the symmetry of the cuboid CHAPTER CONCLUSION REFERENCES APPENDIX A APPENDIX B vii

8 LIST OF FIGURES Figure 1: Binder drops were printed beyond the structure borders [9]... 9 Figure 2: The feed piston is seen on the left side, the roller on the right [9] Figure 3: Positioning of N = 100 cubes in the entire workspace of the 3D-printer [9] Figure 4: A 3D Printed Part Sintered from a Green part showing Shrinkage [7] Figure 5: A ProMetal 3D printing and thermal process Figure 6: Sintering Behavior [ProMetal Handout] Figure 7: 3D Printing process [14] Figure 8: Microscopic structure of molecules during sintering [14] Figure 9: Debinding/sintering cycle for profile 3 [ProMetal Handout] Figure 10: Cuboids measuring 20x10x10 mm Figure 11: Cuboids measuring 30x10x10mm Figure 12: Cuboids measuring 40x10x10 mm Figure 13: SAS output for Pearson Correlation Coefficients Figure 14: SAS output for ANOVA performed to analyze bleed Figure 15: Box plot for Bleed vs. Volume Figure 16: Box plot of bleed vs. orientation Figure 17: Box plot for bleed vs. axes Figure 18: Line plot for the interaction effect between volume and orientation on the bleed viii

9 Figure 19: Line plot for the interaction effect between orientation and axis on the bleed Figure 20: line plot for the interaction effect between volume and axis on the bleed Figure 21: Tukey s test for the variable axis for the bleed Figure 22: Plot of the residuals versus their expected values when the normal distribution is normal Figure 23: SAS output for ANOVA performed to analyze shrinkage Figure 24: Boxplot for shrinkage vs volume Figure 25: Boxplot for shrinkage vs orientation Figure 26: Boxplot for shrinkage vs axis Figure 27: Line plot for the interaction effect between volume and orientation on the shrinkage Figure 28: Line plot for the interaction effect between orientation and axis on the shrinkage Figure 29: Line plot for the interaction effect between volume and axis on the shrinkage Figure 30: SAS output for the tukey's test on the variable axis for shrinkage Figure 31: Plot of residuals versus their expected values when the distribution is normal ix

10 LIST OF TABLES Table 1: Results of measurement of N = 100 cubes over entire workspace [9] Table 2: Results of measurement of N = 15 cubes over reduced are of the workspace [9] Table 3: Mechanical Properties of ProMetal Materials [ProMetal Handout] Table 4: Measurements on the faces of the cuboid (mm) x

11 LIST OF ACRONYMS CAD Computer Aided Design SL - Stereolithography SLS - Selective Laser Sintering FLM - Fused Layer Modeling 3DP - 3D Printing LLM - Layer Laminate Manufacturing BPM - Ballistic Particle Modeling DLS - Direct Laser Sintering LOM - Laminated Object Manufacturing RP Rapid Prototyping RM Rapid Manufacturing RPBPS - Rapid Pattern Based Powder Sintering XPA - Xeroderma Pigmentosum group A PVD - ProMetal Vibration Depowdering xi

12 CHAPTER 1 INTRODUCTION 1.1 Rapid Prototyping Rapid prototyping/tooling and manufacturing have experienced tremendous growth and attracted great attention in national and international manufacturing industry. Rapid prototyping includes a class of technologies that can build a physical model from 3D modeling data (CAD), which can be used to create a tangible prototype (rapid prototyping), make tooling (rapid tooling), and produce parts (rapid manufacturing). There are six classes of prototyping that represent the most important model-making processes. They are 1) Stereolithography (SL), 2) Selective laser sintering (SLS), 3) Fused layer modeling (FLM), 4) 3D printing (3DP), 5) Layer laminate manufacturing (LLM) and 6) Ballistic particle modeling (BPM). Although these techniques have revolutionized manufacturing processes, there is a dimensional and density variation in the product during the process of its fabrication due to bleeding and during its formation due to shrinkage. Among the six classes of prototyping, this study is based on the 3D printing. 1.2 Rapid Manufacturing Rapid manufacturing is the direct production of finished goods from additive fabrications. The technique uses a free-form process to deliver finished parts directly from digital data, which eliminates tooling. It is a fabrication technique where solid 1

13 objects are manufactured in a sequential manner. It may involve custom parts, replacement parts, and short run production or series production. The difference between rapid manufacturing and prototyping is that rapid prototyping is used only in the part s development process, whereas rapid manufacturing is used until the finished product is produced. A sample or prototype is often required as part of the design cycle to allow demonstration, evaluation, or testing of the proposed part before production. The fast creation of the prototype is called rapid prototyping, and the fast production of the finished part is called rapid manufacturing. 1.3 Three dimensional printing (3DP) The term 3D printing has evolved to include both rapid prototyping and rapid manufacturing. Used for making prototypes as well as final products, 3DP is a solid, free fabrication technique using an additive fabrication method, building the part one layer at a time. Each layer is of 0.01 mm thick for this study, so a 10 mm thickness is divided to 100 layers. Although building materials like liquid, powder, or sheet material can be used in this experiment, powder metallurgy is studied. Green preforms made by 3DP consist of less than 60 % volume of metal powder and about 10 % volume of binder, with the remaining being pore space [13]. The green preform is fragile and must undergo thermal processing to achieve desirable mechanical properties and density. The parts produced in this technique have green properties similar to those produced by metal injection molding [7]. 2

14 1.4 Motivation for current work In a wide variety of applications, such as conceptual modeling, medical applications, design aids, anatomical modeling, to mention a few, the question of accuracy is largely irrelevant. In important applications such as fit and function or pattern making for a number of moldings and forming processes, the accuracy is of prime importance. It appears that not as much is published on this topic for a number of commercial RP and RM systems using 3DP principle than is true for the older, high-end systems such as SLA and SLS [2]. Similarly, modeling, compensation, and analysis of shrinkage has been made during the sintering for both conventional methods, such as injection molded powder,compact metal compact, and unconventional methods such as DLS and SLA [12]. However, there is less discussion on the shrinkage behavior during the sintering process for 3D printing. With a thorough literature survey in the area of accuracy and shrinkage using powder metal in rapid prototyping, it was found that both numerical and experimental data was lacking specifically in the area of 3D printing and its sintering process. This study was motivated by the future works of the metal parts generation by 3D printing [7], where the investigation of the parameters related to part dimensional accuracy has to be analyzed. Here the concept of accuracy includes the dimensional offset from the original design. Thus it is necessary to study the accuracy pattern and shrinkage (dimensional change after the thermal process) behavior of the metal powder in 3D printing and its sintering process. The accuracy pattern implies the bleeding issues on the 3

15 cuboids. Due to the nature of the 3D printing, bleeding is observed on the outer surface of the part. Bleeding is the deviation of the dimensions from the actual designed part to the original printed part. 1.5 Significance of current work In an experimental study of rapid manufacturing of complex parts of stainless steel and titanium [1], it was observed that, except for the ProMetal benchmark model built by 3DP technique, all models require supports for building, and these support structures were very difficult to remove. This conclusion from the experiment brought about an incentive to work on this technique, which seemed to be simple even for the complex parts. Accuracy and shrinkage effects had been studied numerous times with different types of rapid prototyping methods. But relatively few studies had been performed to study the effects of the bleeding and shrinkage dependency on the direction and position oriented in 3D printing. These studies are needed as 3DP is used more and more for rapid prototyping with great potential toward rapid manufacturing. Designers need to know the direction and orientation causing the deviation to include the compensation in the design. This study investigated the performance of cuboids with different dimensions in length, with width and height remaining constant. It has also taken advantage of prior experimental and numerical work done on printer calibration and contour accuracy manufacturing with 3D-print technology [9]. Since the effort made in the study to find 4

16 the printer calibration and contour accuracy were not fully investigated experimentally to identify the deviation that occurred in a particular orientation, an experimental approach was used to investigate the accuracy dependency on the orientation in which the part is fabricated as well as the axis in that orientation. The shrinkage behavior of direct laser sintering metallic powder [12] and the shrinkage control on the Rapid Pattern Based Powder Sintering (RPBPS) technique [11] had been studied where the shrinkage behavior and the shrinkage occurrence was considered. As these two techniques also fall under solid free fabrication, this study took advantage of the conclusions to experiment and determine the results in 3D printing. Thus this study is significant as it fills the gap between the other types of rapid prototyping and 3D printing on the shrinkage behavior during the sintering process. 1.6 Aim and objectives of current study The cuboids that are printed out by the 3D printer were observed to have a bleeding effect. This effect was caused due to the binder jets printing from the print head on the metal powder through capillary action. These cuboids also experienced shrinkage in this process after the sintering, as these parts were not 100 % dense. Bleeding was measured on the three faces of the cuboid in millimeters after printing and before sintering. Similarly, shrinkage was measured after sintering. The objective of this research is to build an experimental design to analyze the dependent and independent variables. A statistical hypothesis is to be studied for the variations in the independent variables. 5

17 The following effects are studied: 1. The significant main effects and interaction effects of the independent variables affecting the dependent variables, bleeding, and shrinkage. 2. The significant treatment level of the main effects affecting the model. 3. The trend followed for each independent variable with the dependent variables, bleeding and shrinkage. 6

18 CHAPTER 2 LITERATURE REVIEW In this chapter, a brief background of accuracy of the prototyping and shrinkage of the sintering process are presented. The chapter is divided into two sections. The first section focuses on a new method for accurate part manufacturing using a 3D printer and to establish reliable calibration (scaling) constants to minimize the bias in all three axes. The second section focuses on the related shrinkage control in the RPBPS technique and the study on shrinkage behavior of direct laser sintering metallic powder. 2.1 Accuracy pattern with 3D printing Metal parts generated by 3D printing were studied in various applications, and the bleeding occurrence due to binders was observed. An experiment was conducted to show the use of the 3DP process to produce injection molding tooling and end-use parts [7]. The powder used in this experiment was a 316L spherical stainless steel powder. To give the powder surface enough cohesive strength to resist deformation during printing, several methods were tried. First, in order to bind the layers together via capillary tension, the entire powder layer surface was sprayed with water from an ultrasonic sprayer prior to printing. The presence of moisture in the top layer powder greatly enhanced transport of the binder material in the powder bed even though the desired 7

19 cohesive strength was obtained. Therefore, a complete loss of edge definition in each printed layer was produced due to binder bleeding [9]. Numerous studies have been done on achievable accuracy in 3D printing technology. It is well known from the literature that the accuracy of the 3D printer is affected by different factors [9], such as nominal dimensions, work piece orientation within the 3D printer, and post-treatment procedures. Different gauges were developed for the comparison of different rapid prototyping systems [15, 16]. The position dependency accuracy inside the build position area did not account for these prototypes, however [9]. The suitability of 3D printers for manufacturing parts with accuracy requirements was examined, and in particular, the calibration of the printer. The bleeding factor was used for the orientation dependent printer. Using the standard parameter settings, contours were inaccurate [9], making the printed part too thick (Figure 1). The orientation in the building area determines the degree to which the part becomes thick. Preliminary tests were conducted, and it was observed that the size of the printed parts did not correspond accurately to the design data records. It also suggests that the errors were direction dependent [9]. 8

20 Figure 1: Binder drops were printed beyond the structure borders [9]. The printer model, Spectrum Z510 (Z corporation) was used for the experiments; the material used was plaster powder ZP130 measured with a caliper gauge. Two experiments were conducted. The first experiment had cubes of 10mm length printed over the entire building area. The purpose was to show the deviation of the printed edge lengths from the defined edge lengths. The building area and the coordinate system of the building are shown in Figure 2. The preliminary tests were verified by placing the testing cubes over the entire printable area in order to determine whether the location and orientation of the parts in the workspace affected the printed results. Along the Y- axis, about 100 cubes were lined up in 10 rows as shown in Figure 3. 9

21 Figure 2: The feed piston is seen on the left side, the roller on the right [9]. Figure 3: Positioning of N = 100 cubes in the entire workspace of the 3D-printer [9]. 10

22 A direction dependency was observed from the values determined in experiment one from the defined geometry. A high standard deviation was observed in the Z- direction in relation to all three directions in space as shown in Table 1. In [15,16] the second experiment, 15 cubes of 10mm dimension were printed out in the center of the workspace and measured. This step was conducted to verify the assumption that the deviation of the edge lengths of the cubes was smaller on a reduced scale. A higher standard deviation was observed in the Y-direction in relation to all the three directions as shown in Table 2. Note: X-direction represents the printer, x-axis and Y-axis represents printer, y- axis and Z-axis represent the depth of the cube. Table 1: Results of measurement of N = 100 cubes over entire workspace [9]. X (mm) Y (mm) Z (mm) m bar S Table 2: Results of measurement of N = 15 cubes over reduced are of the workspace [9]. X (mm) Y (mm) Z (mm) m bar S

23 Thus for the cubes printed and measured over the entire workspace of the printer, the deviation is more on the X-axis in the direction of the rollers or parallel to the printer head. For the cubes printed and measured over a reduced area of the workspace of the printer, the deviation was more on the Y-axis in the direction of the printer or perpendicular to the printer head. This conclusion was the basis of assumption for the current study. 2.2 Shrinkage control and its behavior A comparison of rapid prototyping technologies was studied where different technologies such as Stereolithography, Selective Laser Sintering, Laminated Object Manufacturing (LOM), 3D Printing, and Fused Deposition Modeling are compared on their strengths and weaknesses [1]. This study also gave data for common process parameters such as layer thickness, system accuracy and speed operation. It was concluded that the information obtained from the 3D printing shows a higher shrinkage with its end products to the rest of the technologies. After the printing process was done to produce an injection-molding tool, the entire powder bed was placed in an oven and fired at 100 o C for an hour to completely cure the acrylic binder used. The green part was then removed and loosened by thermal decomposition in an inert gas. During thermal decomposition, the binder polymer chains were broken and the binder evolved into a gaseous product. Here, the debinding was done in an argon atmosphere tube furnace where parts were heated to 400 o C to burn out 12

24 the acrylic binder followed by firing at 1000 o C to give the skeleton sufficient strength. Therefore, on completion of debinding, the process parts showed a dimensional change of +/-0.2% along x and y-axes and up to +2% in the z- axis [7]. The x-axis along the printed line, the y-axis across the printed line, and the z-axis was across the printed layers. These tool inserts gained sufficient strength to be handled after debinding was sintered to higher density. To obtain parts with final densities between 65% and 92% theoretically, various firing schedules were used. The part had been sintered to 78% of theoretical density in this case, resulting in obvious shrinkage. A photograph of a green and sintered part is shown below in Figure 4. Based on this experiment, shrinkage in the current study was considered after the sintering process. Figure 4: A 3D Printed Part Sintered from a Green part showing Shrinkage [7]. 13

25 While conducting a study to compensate for the shrinkage in metal skeletons by 3D printing [4], it was quoted that in general there is no uniform shrinkage and there is an amount of error associated with the sintered part. The growth of the necks between the powder particles during the sintering step causes shrinkage [4]. The tools made by this process were successfully finished for injection mold parts in large quantity. Dimensional control was approximated to +/- 0.2% of the part dimension and was the primary issue in this technique. The subsequent magnitude of the shrinkage was 1.5%, and the uncertainty is 0.2% in the current practice [4]. Nevertheless, the uncertainty in the value of shrinkage was directly interchangeable to the loss of dimensional control of the parts. Thus, there is a need to improve the dimensional control of metal parts produced by 3D printing before and after sintering. A number of studies, both experimental and numerical, had been performed on shrinkage control and behavior related to their respective prototyping. A rapid patternbased powder sintering technique (RPBPS) was proposed for the analysis of related shrinkage control [11]. Experimental and numerical studies were carried out to study the shrinkage behavior of direct laser sintering metallic powder (DLS) [12]. These studies concluded that the major shrinkage occurred during the thermal process (sintering and infiltration), and the shrinkage behavior was anisotropic, respectively. In a DLS technology, shrinkage and beam offset became the main sources of dimensional changes. Therefore, the mechanism of shrinkage was investigated during DLS. It was concluded that the shrinkage of metallic powder in DLS was anisotropic, which leads the current study to verify the direction of the shrinkage occurrence. It was also seen that the in- 14

26 plane shrinkage was caused by sintering shrinkage, thermal shrinkage, and thermal expansion. Therefore, a proposed hypothetical model for the explanation of in-plane expansion supports that the dimensions could be controlled to high precision if the shrinkage in the in-plane can be controlled. From the above study, shrinkage as the main source of dimensional change and the sintering shrinkage causing the in-plane shrinkage are focused to verify the ProMetal 3D printing technique. 15

27 CHAPTER 3 METHODOLOGY This chapter describes the underlying principles of the ProMetal solid free-form fabrication technology and provides step by step process information for successful part production. Thermal processing impacts each step of part production, including design, printing, handling, sintering, and infiltration. Each step is discussed in detail in the following sections. A block diagram representing the process is shown below in Figure 5. Figure 5: A ProMetal 3D printing and thermal process 16

28 3.1 3D Printing for concept modeling In this section an overview of the ProMetal 3D printing process used and the material selection for the printing (in this study) will be discussed ProMetal 3D printing As discussed earlier, the ProMetal 3D printing resulted in a green preform part, mold, or component that consisted of approximately 60 % volume of the metal powder selected, about 10 % volume binder to hold the powder together; and the remaining 30 % consisted of pores. Therefore, the fragile parts had to undergo thermal processing to achieve desirable mechanical properties and density. The thermal process consisted of curing, debinding, sintering, and infiltration. Green strength was improved dramatically while the binder was dried and cured during the curing process. In the debinding and sintering cycle, the polymer binder was burned out, and the metal powder sintered together to form the skeleton that would be infiltrated to full density in the infiltration cycle. During infiltration, the pore spaces are subsequently filled with an infiltrating metal whose melting point is less than that of the skeleton metal. Green preforms occasionally fail in sintering cycles resulting in bends, warping, or collapse of the preform structure. There are few reasons attributed to it. One is the impact of gravitational force. Gravitational force is not homogenous and may cause stress concentration in preforms with geometrical complexity. Therefore, in this experiment ceramic powder was distributed around the perform, and support tabs were 17

29 included in the design to support it during sintering. The support tabs can later be removed by machining. Infiltration cycles may also cause failure. As infiltration process was not studied in this experiment, not much of the literature is found in this report, but it can be a topic for future study. Temperature gradients inside the furnace and preform may also cause shrinkage gradients. In order to avoid cracked performs, heating and cooling rates of the thermal process should be monitored and regulated to maintain a safe gradient level. In this study a sintering cycle was followed, which is discussed in the following section Material Selection Most conventional manufacturing processes have limitations in the type of parts they can produce. Multiple materials are possible in this process [10]. There were three ProMetal materials that could be used on this 3D printer. They are S3, S4, and S4H. S3 is a 316 stainless steel/bronze composite, which has a high corrosion resistance. S4 is a 420 stainless steel/bronze composit designed for components requiring higher strength. S4H is also a 420 stainless steel/bronze composite, but the 420 stainless steel powder used to make S4H has a bimodal particle size distribution. Material selection for a preform part, mold, or component is dependent on the end user application and the customer s preference. The powder currently used for 3D printing was S4, 420 stainless steel powder, which had a packing density of 57% to 58% of the full density. Particle density was particularly important in the 3D printing process. A higher packing density was desired 18

30 generally when selecting a powder. An increase in packing density could be achieved by using bimodal powder mixtures. Higher sintered strength could be achieved by adding fine powder, because fine powder has higher sinterability. The size of the shrinkage void depends on the interstitial space between solid particles of the preform skeleton, as the shrinkage from liquid to solid is 4-5%. Reducing the interstitial space in the skeleton can reduce the occurrence of shrinkage voids. A great capillary force is found in small interstitial spaces from the preforms made from bimodal powder. Hence, bimodal preforms of bimodal powder are likely to be infiltrated. For solid, free-form fabrication technologies incorporating powder metallurgy process, low shrinkage materials and process have been researched to improve geometric accuracy as the dimensional variation increases with the increase of sintering shrinkage. The small particles in bimodal powder significantly impact the sintering response compared to that of a large particle skeletal structure when sintering at lower temperatures. However, at critical temperatures, the small particles will have negligible effects. This sintering behavior is schematically shown in Figure 6. Temperature sensitivity to the shrinkage of bimodal powder differs from single modal powder. Assuming an inherent temperature error ( T), the resulting shrinkage errors are dependent on the local slopes of the shrinkage curves. It is evident that less dimensional scatter occurs with bimodal powder ( L 2 ) than with single modal powder ( L 1 ). 19

31 Figure 6: Sintering Behavior [ProMetal Handout] Mechanical Properties of ProMetal Materials are shown in Table 3. Because the S4H material has a relatively high fraction of stainless steel, the strength of S4H is greater than that of S4 material. Table 3: Mechanical Properties of ProMetal Materials [ProMetal Handout] Mechanical S3 S4 S4H Properties Hardness 60 HRB 30 HRC 35 HRC Ultimate Strength 59 KSI 99 KSI 111 KSI Yield Strength 34 KSI 66 KSI 82 KSI Modulus 21.5 MPSI 21.4 MPSI 21.4 MPSI Elongation 8.00% 2.30% 3.80% 20

32 3.2 Design in CAD and fabrication of the designed part A print file with an stl format is created prior to printing. A green preform is created when the ProMetal machine and controls distribute powder and binder. The print file defines this process. The print file defines the orientation of the printed preform in the print bed as well as the location of support tabs or stilts. In this study, cuboids of different dimensions were created with support tabs in AUTOCAD Challenges such as high stress concentration; long print and processing times; and preform bending, warping, and even collapse can result from poor component designs. During infiltration, bronze penetration routes can be hindered due to inappropriate support tabs, resulting in increased machining and materials. To avoid the challenges, mold or component designs must be reviewed prior to creation of the print file. The ability of printed parts to undergo thermal process successfully should be considered. The areas of high stress concentration in the component design should be checked for minimization. Efficient orientation should be checked for the component in the print bed to optimize print, sintering, and infiltration times. Positioning of support tabs should be determined to reduce possible bends, warps, or collapse during sintering. Generally the vertical or Z-axis is minimized when considering how to orient the preform in the print bed to reduce material waste and time in printing. However, the orientation of the preform during sintering and infiltration may not follow these guidelines. 21

33 3D Printing The 3D printing process is very similar to an ink-jet printer. A binder or polymer glue is used instead of ink to print into a powder layer following a computer pattern, which is obtained by applying a slicing algorithm to the computer model. As discussed earlier, the 3D printing process is an additive process, which allows it to create objects with complicated internal features that cannot be manufactured by other means. Figure 7: 3D Printing process [14] Challenges faced during printing include cracking in the green state, which is due to low green strength, which is caused by uneven distribution of the binder during printing where green strength is compromised. Analyzing and optimizing print parameters, such as layer thickness, can significantly improve the preform green 22

34 strength. Layer thickness and print speed are the most important attributes of the print process for the ProMetal machine. 3.3 Curing Curing hardens the newly printed preform. Curing is conducted in the powder bed where temperatures are increased to 300 o F-350 o F. Curing time depends upon the size of the printed preform. Challenges faced include the inadequate curing time that will allow the preform to soften, reducing the probability of a successful sinter cycle. In this study, the stainless steel powder is printed with XPA binder that has to be cured in the powder bed at 150 o C. The firing time depends on the size of the printed preform. Firing preform time is 4 hours for large preforms and 3 hours for small preforms. A large preform is one with a dimension sum (length + width + height) greater than 25 inches or a weight over 10 pounds. An adequate firing time is ensured so that the preform being cured is hardened. As the size of the part being prototyped in this study is very small with the largest dimension being less than 2 inches, the average curing time was 2 hours. Preform removal from Print bed After curing, the preforms are removed from the powder bed. The removed preforms are measured for their dimensions to determine the bleeding effects using a tool maker s microscope. The following are the guidelines for the conventional way of removing the preform [ProMetal Handout]. 23

35 1. The build box is moved to the powder recovery station, and the piston is raised to reveal the preform. The loose powder is then cleaned with soft brushes. 2. ProMetal Vibration Depowdering (PVD) is used to remove unbound powder from inside internal cavities and conformal channels. The cured preform is held on a specially designed fixture attached at the foot of the random orbital sander. 3. The unbound powder removed from internal cavities is verified by comparing the weight of the preform with the calculated preform weight. An insignificant weight variation between the depowdered preform and calculated preform signifies that minimal powder remains inside internal cavities and conformal channels. Calculation of Green Part Weight for 420 Series Materials Part weight for S4 (kg) = Part volume (mm 3 ) kg/mm 3 Part weight for S4H (kg) = Part volume (mm 3 ) kg/mm 3 The challenges faced are that the green preforms are extremely fragile and need to be handled with care to avoid breaking when being moved and depowdering. The PVD system has been developed to remove unbounded powder from internal cavities and conformal channels. The challenge faced in this system is that the cured perform binder forms bonds to hold particles together, while the unbounded particles are interlocked mechanically inside internal cavities and conformal channels. So, when the vibration source is applied to the preform, particles start to oscillate around their original 24

36 position. The energy of the individual particle s oscillatory motion is determined by frequency and amplitude of the vibration source. The vibration source has to be high enough to unlock the unbounded particles to depowder a preform but not so high that the particles of the binding forces and breaks the preform. However, in this study the preform is cured and then removed from the print bed following the first step of the guidelines, but the PVD system has not been used, as there are no internal cavities in the design of the part in this study. The cured preform is dusted to remove the unbounded powder with a soft brush. Measuring it just after curing with a tool maker s microscope checks the dimensional difference or the variation of the preform from the print file. 3.4 Sintering Sintering is one of the thermal processes and involves three major steps which are categorized as follows: 25

37 Figure 8: Microscopic structure of molecules during sintering [14] i. Selection of supporting powder ii. iii. Debinding set up Selecting sintering profile Selection of supporting powder The supporting powder used is the ceramic powder to support the preform during the debinding/sintering process. There are several criteria for the selection of supporting ceramic powder. The following are the guidelines: 1. The sintering temperature should not affect the supporting ceramic powder. 2. The fractional packing density of the supporting ceramic powder should be close to the skeleton fractional density. 3. The internal and external cavities must be easily filled and evacuated for which the supporting ceramic powder should have high flow ability. 4. The supporting powder should have good thermal conductivity. 5. In the case of S3 preform, the supporting powder is alumina powder (36 grit). The challenges faced are that the supporting powder cannot fill all the external undercut cavities and overhangs efficiently. The packing density of supporting powders 26

38 may be lower than the packed stainless steel powder. Ceramic powder leaves a space in between the support powder and supported preform as it will sinter and shrink itself. As a result, it may result in a distorted preform or collapse under its own height. The difference of the coefficient of expansion between stainless steel preform and ceramic powder will cause preform cracking and distortion. Therefore, the above guidelines must be followed Debinding set up Debinding is a process where the binder has to be removed before sintering without disrupting the particles that make up the preform. It is the process by which the binder decomposes. At 500 o C temperature complete debinding is achieved. Once the binder is heated, the green preform softens and is unable to withstand the shear stress from gravity or thermal gradients. Therefore, the green preform must be prepared for debinding by placing it in crucible and surrounding it with ceramic powder. After debinding, the preform is free of the binder and should be subjected to a minimum amount of handling. A continuous debinding/sintering process that takes place in one furnace cycle should be annexed whenever possible. The challenge would be to avoid failure in removing the binder prior to sintering to prevent preform cracking and contamination. Hence the following guidelines need to be followed to avoid damaging the preform. 27

39 1. Ceramic powder is to be poured in the bottom of the crucible, leveling it to at least on inch in thickness. 2. The component is to be laid on the ceramic bed. 3. The external cavities that face down to the bottom of the crucible are to be filled. 4. The preforms are to be covered with ceramic powder and void spaces are to be checked, especially at the sides of the preforms. 5. Lastly, the sintering profile is to be selected for the appropriate size of the part Selecting a sintering profile Sintering commonly refers to the process involved in the heat treatment of powder preforms at elevated temperatures, usually T>0.5T m. In a sintering-infiltration process, sintering is conducted at a temperature where the particles bond to each other to attain desired properties with dimensional change of the preform minimized. The challenges faced are that the temperature gradients cannot be avoided inside the furnace and preform. It is to be noted that the porous preform and ceramic powder used to support the preform are not good conductors; therefore, the sintering time and ramp depend on the furnace load and preform size. Hence, large preforms require longer sintering time and slower ramp rates. 28

40 Debinding and sintering are carried out in one furnace cycle under an industrial forming gas atmosphere, where debinding is performed in the initial heating stage of the cycle. With the increase in temperature, the binder is removed and metallurgical bonds are formed between the metal particles. After debinding, the furnace temperature is increased to sintering temperature. The following are the sintering profiles for the materials selected for ProMetal 3D printing. Profile 1 (S3): Sintering at 1235 o C for 90 min with ramp 5 o C/min Profile 2 (S3): Sintering at 1235 o C for 180 min with ramp 2 o C/min Profile 3(S4): Sintering at 1140 o C for 90 min with ramp 5 o C/min Profile 4(S4): Sintering at 1140 o C for 180 min with ramp 2 o C/min Profile 4 is used in the current study. The sintering is conducted at 1140 o C at a ramp of 2 o C with a total time of 9.5 hours for the whole process in an atmosphere of argon and hydrogen (Ar+H 2 ) % of each. This setting cannot be manually controlled once it is set. 29

41 Figure 9: Debinding/sintering cycle for profile 3 [ProMetal Handout] 3.5 Infiltration Infiltration is a final step of the thermal process in ProMetal 3D printing. Infiltration refers to a process in which a liquid penetrates through a previously sintered or unsintered porous skeleton via capillary action. A porous skeleton filled with liquid after a prolonged process is similar to liquid phase sintering. There are two kinds of infiltration methods: one-step and two-step infiltration. The basic method is two-step infiltration, which consists of an independent full-furnace cycle to pre-sinter the preform followed by a second full for infiltration. The molten infiltrant is drawn into the interconnected pores of the skeleton through capillary action and fills the entire pore volume. In a one-step infiltration, both sintering and infiltration are done in a single step. Large parts require long processes in a two-step infiltration and may take one to two days. One-step infiltration consists of one full furnace cycle combining sintering and infiltration, saving at least one heating and cooling cycle. One-half of the cost and 30

42 manpower for set up of the thermal process is reduced by the one-step process. Hence, production can be increased with no addition of equipment or manpower. For the current study, the furnace available has both one-step and two-step infiltration methods. The infiltrant material used for S4H-stainless steel sintered porous skeleton is bronze. The profile that can be used is 1140 o C for 150 min with ramp 2 o C/min. Even though no experimental analysis has been made on the infiltration process in this study, shrinkage and density behavior after infiltration can be studied. 3.6 Final Product A final product is obtained after the designed part in CAD is fabricated and processed through curing, sintering, and infiltration. The final product is free from the extra supports and stilts for infiltration. A category of products produced in this way could be used as molds in injection molding [7]. 3.7 Defining the axis of the machine The main component of the machine to which the orientation of the cuboids is described is the print head. The print head is located in the x-direction of the machine and moves along the y-direction of the machine to print the binder jets on the metal powder. The cuboids 1 and 2 are located in the y-direction, which is perpendicular to the 31

43 print head and is named as orientation 1 and 2, respectively. The cuboid 3 is positioned in the x-direction and is parallel to the print head. Figure 10: ProMetal 3D printer. 3.8 Symmetry of the cuboid The cuboid on which the current study is based is assumed to have symmetrical opposite sides. The cuboids are compared to a dice having six faces. To verify this assumption, an experiment was conducted. The following describes the steps of the experiment. 1. A set of three cuboids are designed with dimensions mm length, breath, and height, respectively, in AUTOCAD The designed parts are fabricated in 3D printing with two oriented perpendicular to the printer head and one parallel to the printer head just as in the above verification process. 32

44 3. The printed preforms are cured at 150 o C for about 2 hours so that the green preform gains strength and can be handled. 4. The cured parts are measured for dimension along the four sides of each face and verified with their respective opposite side in a tool maker s microscope. Therefore, the assumption of opposite sides of cuboids being symmetrical was verified with this experiment. 3.9 Measurements Mainly two devices measure the dimensions of the cuboids, and they are the tool maker s microscope and the micrometers in inches and metric. The following gives a description about the role of these devices used to measure the parts in this experimental study Tool maker s microscope A tool maker s microscope is used for measuring fabricated parts before sintering to determine bleeding percentage. This microscope is able to view and measure linear distances, thread angles, thread pitch, tool edges, and more. Though their main application is measuring and viewing tool edges and wear surface in the tooling industry, in this study the microscope is mainly used for measuring linear distances of the cuboids on the three faces (assuming that the faces on the opposite side are equal, having 33

45 prismatic symmetry). Hypothesis testing was conducted to check the validity of the assumption. A precise measurement of distances and circles are allowed through their x-y stage micrometer. The crosshair reticle in the eyepiece gives a precise point of reference as the microscope s stage is moved, and the stage micrometer is used to provide a readout of distance travelled. Precise measurement of lengths, diameters and distances is important for many applications in industry. Common tools and equipment used are the measuring microscope and vernier calipers. English and metric systems are the two major measurement standards. A manual or a digital vernier caliper is able to give basic measurements. The reason it is not used in the current study is because the preforms are not strong enough to be handled and measured in the vernier caliper, just after curing. The precise measurement is 1/10000th of an inch in the English measuring system, while the metric unit of measurement generally is in microns (1 millionth of a meter) Micrometers The sintered parts are measured for their dimensional difference caused by shrinkage. These measurements are made with the micrometers in both the metric and inch systems, depending on the size of the sintered parts. A metric micrometer was used to measure a sintered part whose largest dimension was 20 mm or less. The metric micrometer that was available and used has 2 millimeter threads and thus one complete move through a distance of 0.5 mm. It is graduated with 1 millimeter divisions and

46 millimeter subdivisions on the frame. The least count on the scale is 0.01 mm as the thimble is graduated with 50 divisions further. An inch system micrometer was used when the sintered part was more than 25 mm on its largest dimension. The spindle of an inch-system micrometer has 40 threads per inch, so that one turn moves the spindle axially inch, equal to the distance between two graduations on the frame. The least count of the scale is inch as the thimble has 25 graduations and allows a inch to be further divided by 25 graduations Experimental Design This section deals with experimental and design parameters considered for the bleeding and shrinkage effect on the cuboids produced by 3D printing technology on a PROMETAL 3D printer. An experiment is a trial or special observation, made for testing different assumptions by trial and error under specified conditions constructed and controlled by the examiner. During the experiment one or more conditions called independent variables are allowed to change in an organized manner, and the effects of these changes on associated conditions, called dependent variables, are measured, recorded, validated, and analyzed for arriving at a conclusion. Every experiment involves a sequence of activities: 1. Hypothesis 2. Experiment 35

47 3. Analysis 4. Interpretation 5. Conclusion The concept of Analysis of Variance (ANOVA) has been applied to this design experiment to analyze the parameters in the process. ANOVA is a technique that can be used for testing the hypothesis under the assumption that the populations are normally distributed. In this experiment, models built for analyzing the bleeding and shrinkage effect on the cuboids follow a generalized linear model. The analysis was done by using SAS (Statistical Analysis System). In the analysis type I error (α) = 0.05 was used. The following are the assumptions for this experiment: 1. The errors are normally distributed with mean zero. 2. The error variance does not change for different levels of a factor or according to the levels of the predicted response. 3. Each error is independent of all other errors Bleeding effect on the cuboid Cuboids made of S4 stainless steel are considered for this experimental analysis. The bleeding in the cuboids with different dimensions, orientation, and axes were obtained after the cuboids were printed and cured. The governing equation for the bleeding is, 36

48 Bleeding = O A Where, O = Original set dimension on an individual axis (i.e.: x or y or z axis) A = Average measurement before sintering in an individual axis (i.e.: x or y or z axis). The independent variables considered for this experiment are categorical variables and they are volume, orientation, and axes Shrinkage in the cuboid Shrinkage in the cuboids with different dimensions, orientation and axis is obtained after the cuboids are heat treated by sintering at 1140 o C. The governing equation for the shrinkage is Shrinkage (in x-axis) = A- B where, A = Average measurement before sintering in an individual axis (e.g.: x, y and z axis) B = Average measurement after sintering in an individual axis (e.g.: x, y and z axis) Similar to the analyses for the bleeding, the independent variables chosen for the shrinkage are the same. 37

49 CHAPTER 4 RESULTS AND DISCUSSION 4.1 Numerical validation This chapter presents the results and discusses the bleeding and shrinkage effect on the cuboids as a function of volume, orientation, and axis. These parameters are tested for their significant effect on the model. The analysis made on these printed parts compare the effect of the bleeding with orientation that is perpendicular and parallel to the printer and with the volumes of the cuboids printed before sintering as a green preform. It also compares the shrinkage behavior with the same variables as above, after sintering. Tables and graphs are represented in the following subsections to compare and analyze. Discussions are followed after each analysis. Figures 10, 11, and 12 represent different volume cuboids arranged in three sets with three in each and positioned in three ways. Figure 11: Cuboids measuring 20x10x10 mm 3 38

50 Figure 12: Cuboids measuring 30x10x10mm 3 Figure 13: Cuboids measuring 40x10x10 mm Statistical analysis for the bleeding on the cuboid This analysis was performed using SAS software on the linear data obtained by manual measurement of the S4 stainless steel cuboid before sintering. This analysis follows a factorial design of three factors with three levels and one replication which is 3 3 x1 = 27 runs. 39

51 Analysis of Variance with Tukey s test, test for correlation variance, and normality tests were performed. Correlation Analysis Pearson s Correlation Coefficient is determined in order to find the correlation, if any, between the independent factors. The resulted output obtained by SAS is shown in Figure 13. Figure 14: SAS output for Pearson Correlation Coefficients The p- values between the three independent variables (0.8263, , and ) are greater than the statistically significant α-value (0.05). Therefore, there is no correlation between the three independent variables Analysis of Variance The independent variables for this model are volume, orientation, and axis. The dependent variable is the bleed. The hypothesis in this test is, 40

52 Ho: The model is not affected by the independent variables Hα: The model is affected by the independent variables If the p-value is lower than the probability of rejecting the null hypothesis when the null hypothesis is true (α or type I error) then Ho is rejected. In this test from Figure 14, the p-value is , which is greater than the desired α value (0.05). Therefore, the null hypothesis is rejected. The R-square value explains about 90.38% of variability in the model and F-value (4.17) at p-value (0.0226) less than the α-value (0.05) indicates that the model is significant. The Coefficient of Variance (C.V) explains the unexplained variability in the data as % of the mean of the response variable. Furthermore, among the main effects F-value for the variable, axis is observed to be highest (12.66), which is significant at p-value (0.0033) < α-value (0.05), indicating that axis is significant in effecting the model. It is also observed that there is a significant interaction between axis and orientation with F-value (8.86) significant at p-value (0.0049) < α-value (0.05). 41

53 Figure 15: SAS output for ANOVA performed to analyze bleed. Figure 16: Box plot for Bleed and bleed % vs. Volume 42

54 From Figure 15 above, it is observed that the mean of the bleed increases with increase in volume and has a positive effect. The variation in the bleed due to volume is not as high as the variation due to axis, which is demonstrated in the graph below. From Figure 16, bleed remains the same for the first two orientations as expected,because they were positioned in a similar way. It is also observed that bleed is higher on the 1 st and 2 nd orientation when compared to the 3 rd orientation. Figure 17: Box plot of bleed and bleed % vs. orientation As the axes are the main effect influencing the bleed in the model, a further investigation of axes is done. From Figure 17, it is observed that the most variation in the bleed is due to the y-axis rather than the other two axes and the least in the z-axis. 43

55 Figure 18: Box plot for bleed and bleed % vs. axes Figure 19: Line plot for the interaction effect between volume and orientation on the bleed and bleed %. 44

56 From Figure 18, it is observed that there is no interaction effect between the volume and orientation on the bleed as the lines are not intersecting and are parallel. Figure 20: Line plot for the interaction effect between orientation and axis on the bleed and bleed %. From Figure 19 above, it can be observed that there is a strong interaction effect between orientation and axis on the bleed. The significant interaction is indicated by the lack of parallelism of the lines. From Figure 20, it is observed that there is no interaction effect between volume and axis on the bleed, as the lines do not intersect and should be noted that the lines are less parallel when compared to the interaction between volume and orientation. 45

57 Figure 21: Line plot for the interaction effect between axes and volume on the bleed and bleed% Tukey s Test When ANOVA indicates that one or the entire main effects mean differs, it is usually of interest to make a comparison between the individual main effects mean to discover the specific differences. In this experiment, Tukey s test was used on the bleed data with respect to axis, as axis was the significant main effect. When any of the interactions is significant, the analysis includes differences between cell means and interaction effects as well as main effects. It is observed from Figure 21 that the mean bleed for the y-axis is significantly higher and is marked as (A), and the mean bleed for the x and z-axes is marked as B. The means with the same letter are not supposed to be significantly different. 46

58 Figure 22: Tukey s test for the variable axis for the bleed Normality test To test the normality of the model, the Kolomogorov Smirnov test is applied on the residuals. The hypothesis in this test is Ho: Data follows a normal distribution Ha: Data do not follow a normal distribution If the p-value of the test is greater than the desired α, then Ho is accepted. In this test from the figure below, the p-value (0.150) is greater than Hence the normality assumptions are met. 47

59 Figure 23: Plot of the residuals versus their expected values when the normal distribution is normal. 4.3 Statistical analysis for the shrinkage on the cuboid The analysis for the shrinkage was also performed in a similar way as the bleed using SAS software on the linear data obtained by manual measurement of the S4 stainless steel cuboid before sintering. Analysis of Variance with Tukey s test, the test for correlation variance, and the normality test were performed. This analysis follows a factorial design of three factors with three levels and one replication which is 3 3 x1 = 27 runs. The data for these 27 runs are shown in appendix B. Correlation Analysis will be the same for the independent variables for the shrinkage analysis as well. As the coefficients 48

60 of correlation were greater than the α-value, it was concluded that there was no correlation Analysis of variance The independent variables for this model are volume, orientation, and axis. The dependent variable is the shrinkage. The hypothesis in this test is, Ho: The model is not affected by the independent variables Hα: The model is affected by the independent variables If the p-value is lower than the probability of rejecting the null hypothesis when the null hypothesis is true (α or type I error), then Ho is rejected. In this test from the figure (), the p-value is , which is greater than the desired α value (0.05). Therefore, the null hypothesis is rejected. The R-square value explains about 89.08% of variability in the model and F-value (3.63) at p-value (0.0342) less than the α-value (0.05) indicates that the model is significant. The Coefficient of Variance (C.V) explains the unexplained variability in the data as % of the mean of the response variable. From Figure 21 above, it can be further inferred that F-values for the variables, axis, and volume are observed to be higher (8.87 and 5.20), which is significant at p-value ( and ) < α-value (0.05), indicating that axis and volume are significant in affecting the model. It is also observed that there is a significant interaction between axis and orientation with F-value (7.73) significant at p-value (0.0075) < α-value (0.05). 49

61 Figure 24: SAS output for ANOVA performed to analyze shrinkage. From Figure 23, it is observed that the shrinkage increases with the increase in volume. The variation in the shrinkage due to volume is not as high as the variation due to axis, which is demonstrated in the graph below. From Figure 24, shrinkage remains the same for the first two orientations as expected, because they were positioned in a similar way. It was also observed that bleed has outliers in the 1 st and 2 nd orientation, which are at the same level. Orientation does not show any significant variation as expected because of a very high p-value (0.9349). 50

62 Figure 25: Boxplot for shrinkage and shrinkage % vs volume. Figure 26: Boxplot for shrinkage and shrinkage % vs orientation. 51

63 From Figure 25, it was observed that the variable, axes, has the maximum variation when compared to the other two independent variables, which was expected because the p-value was as low as It was also observed that there seems to be more shrinkage on the y-axis and the least in z-axis. Figure 27: Boxplot for shrinkage and shrinkage % vs axis. From Figure 26, there seems to be some interaction effect between volume and orientation on the shrinkage, as the variable volume is a significant main effect on the shrinkage. Since orientation has the least variance, the interaction effect between volume and orientation on the shrinkage is not significant enough to affect the shrinkage. From Figure 27, it was observed that there was significant interaction effect between axes and orientation on shrinkage. Even though orientation has no significant variance, the interaction effect between orientation and axes is observed to be 52

64 significant, as the axes has the maximum variance that it balanced out the no-effect of orientation. The significant interaction is indicated by the lack of parallelism of the lines. Figure 28: Line plot for the interaction effect between volume and orientation on the shrinkage and shrinkage %. Figure 29: Line plot for the interaction effect between orientation and axis on the shrinkage and shrinkage %. 53

65 Figure 30: Line plot for the interaction effect between axes and volume on the shrinkage and shrinkage %. From Figure 28 above, it was observed that there is no interaction effect between volume and axis on the shrinkage, as the lines do not intersect Tukey s Test In this experiment, Tukey s test was used on the shrinkage data with respect to axis, as axis was the significant main effect. When any of the interaction is significant, the analysis includes differences between cell means and interaction effects as well as main effects. It is observed from Figure 29 that the mean shrinkage for the y-axis is significantly higher and is marked as (A) for any dimensioned volume cube, i.e., 4000, 3000, or 2000 mm 3. The mean shrinkage for the z-axis has the least significant effect for any dimensioned volume cube. The means with the same letter are supposed to be not significantly different. 54

66 Figure 31: SAS output for the Tukey's test on the variable axis for shrinkage Normality test To test the normality of the model, Kolomogorov Smirnov test is applied on the residuals. The hypothesis in this test is, Ho: Data follows a normal distribution Ha: Data do not follow a normal distribution If the p-value of the test is greater than the desired α, then Ho is accepted. In this test from the figure below, the p-value (0.150) is greater than Hence the normality assumptions are met. 55