Accuracy and manufacturing speed improvement of the Form 25 Disposition of Master Thesis on 2nd level study programme Accuracy and manufacturing speed improvement of the Form 2 stereo-lithographic

Disposition of Master Thesis on 2nd level study programme

Accuracy and manufacturing speed improvement of the Form 2

stereo-lithographic apparatus.

Student: Benjamin BEIRLAEN

Study programme: Applied engineering technologies

Field of Study: Electromechanics

Mentor:

Assoc. Prof. Dr. Igor Drstvenšek Signature:

Co-mentor:

Assist. Prof. Dr. Tomaž Brajlih

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Disposition of Master Thesis on 2nd level study programme

Accuracy and manufacturing speed improvement of the Form 2

stereo-lithographic apparatus.

Student: Benjamin BEIRLAEN

Study programme: Applied engineering technologies

Field of Study: Electromechanics

Mentor:

Assoc. Prof. Dr. Igor Drstvenšek Signature:

Co-mentor:

Assist. Prof. Dr. Thomaz Brajlih

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Accuracy and manufacturing speed improvement of the Form 2 stereo-lithographic apparatus. Definition and description of the research subject problem

The dimensional and geometrical accuracy of the parts produced via desktop stereolithographic

(SLA) manufacturing is not consistent, and might be influenced by the parts complexity of shapes.

Objectives and hypothesis of the master dissertation

To begin with, the total operating process of the Form 2 was examined and discussed.

Further, the hypothesis of this dissertation is that there is a relation between the part complexity and

the geometrical and dimensional accuracy. The goal is to find and describe this relation, allowing to

compensate for the expected deviations by using corrections in the shrinkage compensation of the

different axes. Further, an evaluation was made regarding the print orientation suggested by the

PreForm software. The relationship between part complexity and dimensional accuracy was put to

the test. In this master dissertation, the correctness of the estimated print time was tested.

A relationship between the print speed and part complexity was found.

Assumptions and research limitations

In this dissertation, research is presented regarding the Form 2 printer from Formlabs, using the V4

white resin from Formlabs. Parts in this dissertation were all printed using a layer thickness of 100

µm. It can be assumed that the findings in these dissertation also apply to similar desktop SLA

printers as well as other similar types of resin.

The Form 2 software itself already compensates the shrinkage, the exact compensation is unique for

each resin. However, the results do not always bring satisfaction.

To gain the most useful result of the experiment, this shrinkage compensation should be put to 0.

It is however not possible to put this shrinkage compensation to 0, since the software is encrypted,

breaking into it would be against Formlabs’ policies. Without turning off this shrinkage

compensation, the results of the dissertation can still be useful, when superposed on top of the

already present shrinkage-compensation method. This dissertation provides in general a method for

establishing a model to improve the dimensional accuracy.

This superposition is off course only valid until the moment that Formlabs changes their shrinkage

compensation software, and only for the specific V4 white resin.

The assumption is made that the position of the part on the print platform has no significant

influence on the part’s dimensional and geometrical accuracy.

The experiment is limited in size. Therefore only the influences of volume ratio and tray ratio were

investigated.

Planned research methods

Analogue to the method used in (Brajlih et al, 2010), this method was used to define the geometric

complexity of a part, as well as the presented 2k factorial experiment with adaptable test parts. Test

parts were made and analysed using an Atos v6.0.2-6 three dimensional optical scanner. The data

was then analysed.

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There are many different causes for inaccuracy, for example the wear of the silicone layer in the

resin tray or uncleanliness of the optical surfaces. To reduce those influences, the research in this

dissertation is done using a new resin tank, a clean machine, and for every test part the same post-

curing process was used.

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Index

Summary of contents ..................................................................................................................... 15

List of resources provided. ............................................................................................................ 15

Word of thanks ................................................................................................................................ 15

1. Introduction .................................................................................................................................. 17

1.1. State of the art .................................................................................................................. 17

2. Operating principles of the Form 2 .......................................................................................... 17

2.1. Resin tank with wiper ....................................................................................................... 18

2.2. Scanner System ............................................................................................................... 19

2.3. Build platform .................................................................................................................... 19

3. Causes of dimensional and geometrical inaccuracy. ........................................................... 19

3.1. Non-uniform shrinkage .................................................................................................... 19

3.2. Non-uniformity of the laser beam .................................................................................. 19

3.3. Wear of the Polydimethylsiloxane (PDMS) .................................................................. 20

3.4. Suction forces during peel operation ............................................................................ 20

4. Experiment .................................................................................................................................. 20

4.1. Materials and equipment ................................................................................................. 20

4.2. Test part definition and used parameters ..................................................................... 21

4.3. Evaluation using ANOVA ................................................................................................ 21

4.4. The 2k factorial design test ............................................................................................. 22

4.5. Printer test part setup ...................................................................................................... 22

4.6. Evaluation of the measurement results ........................................................................ 28

4.7. Evaluation of the shrinkages using ANOVA ................................................................ 34

4.7.1. Linear shrinkage in function of VR and TR ........................................................... 34

4.7.2. Sphere size in function of VR and TR ................................................................... 37

4.7.3. Perpendicularity of the planes ................................................................................ 40

4.7.4. Wall- and edge thickness in function of VR and TR ............................................ 41

4.7.5. Total length of the part edges. ................................................................................ 45

4.8. Evaluation of the part orientation suggested by the PreForm software. ................. 47

4.8.1. Linear shrinkage in function of part orientation .................................................... 47

4.8.2. Sphere size in function of VR and TR ................................................................... 48

4.8.3. Perpendicularity of the planes ................................................................................... 49

4.8.4. Wall- and edge thickness ........................................................................................... 53

4.8.5. Total length of the part edges. ................................................................................ 57

4.9. Validating the linear compensation model. ..................................................................... 58

4.9.1. First print file: Low volume ratio – Model Z-edge length ..................................... 60

4.9.2. Second print file: Low volume ratio – Model Z-vector ......................................... 60

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4.9.3. Third print file: High volume ratio – Model Z-edge length. ................................. 60

4.9.4. Fourth print file: High volume ratio – Model Z-vector .......................................... 61

4.9.5. Measurement results of the printed validation part ............................................. 61

4.9.6. Discussion on shrinkage compensation models .................................................. 63

4.10. Evaluating the estimated printing time ...................................................................... 64

4.11. Influence of VR and TR on printing speed ............................................................... 64

4.11.1. Influence of VR and TR on the net printing speed ........................................... 65

4.11.2. Influence of VR and TR on the gross printing speed ...................................... 66

General Conclusion ........................................................................................................................ 69

References ....................................................................................................................................... 70

Addendum A: Influence of the positioning of the part ............................................................... 71

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List of Figures

Figure 1: Form 2 ..................................................................................................................... 17

Figure 2: Resin cartridge (left) and resin tank sensor (right) ............................................................ 18 Figure 3: Resin tank with wiper2 ....................................................................................................... 18 Figure 4: galvanometers and mirror² ................................................................................................. 18 Figure 5: Build platform with threaded rod ....................................................................................... 19 Figure 6: Build platform and machine axes position³ ....................................................................... 19

Figure 7: Build tray with PDMS layer............................................................................................... 20 Figure 8: UV cure chamber ............................................................................................................... 21 Figure 9: Part print positions on build platform. ............................................................................... 22 Figure 10: Different TR and VR print files. ...................................................................................... 23

Figure 11: Suggested orientation - part print positions ..................................................................... 24 Figure 12: Print-file for validating the suggested orientation ........................................................... 24 Figure 13: Part prepared for scanning - with reference points .......................................................... 25

Figure 14: Scanning setup ................................................................................................................. 26 Figure 15: Atos Software ................................................................................................................... 27 Figure 16: GOM inspect software - best fitting spheres .................................................................... 27 Figure 17: Measuring dimensions ..................................................................................................... 28

Figure 18: Shrinkage of Z vector in function of VR and TR ............................................................ 37 Figure 19: Sphere shrinkage in YZ plane (spheres Y1 and Y2) in function of VR and TR ............. 39

Figure 20: Shrinkage of wall thickness in Z direction in function of VR and TR ............................ 44 Figure 21: Shrinkage of Edge Length in Z direction in function of VR and TR .............................. 47 Figure 22: Comparrison of the XY angle between different orientations ......................................... 50

Figure 23: Comparison of the YZ angle between different orientations ........................................... 51

Figure 24: Comparison of the ZX angle between different orientations ........................................... 52 Figure 25: Comparison of the angles in different orientations .......................................................... 53 Figure 26: Effect of support locations on the wall thickness in Y direction ..................................... 55

Figure 27: Validation part file, low VR (left) and high VR (right) ................................................... 58 Figure 28: Suggested orientation of the regression validation print file ........................................... 59

Figure 29: Validating part, GOM inspect with primitives................................................................. 59

Figure 30: Warpage causing shorter Z vector while causing longer Z edge length .......................... 63 Figure 31: Net printing speed in function of VR and TR .................................................................. 65

Figure 32: Gross printing speed in function of VR and TR .............................................................. 67 Figure 33: Net printing speed in function of Tray Ratio, with VR = 0,25 ........................................ 67 Figure 34: Net printing speed in function of Tray Ratio, with VR = 0,70 ........................................ 68

Figure 35: Gross printing speed in function of Tray Ratio, with VR = 0,25 ..................................... 68 Figure 36: Gross printing speed in function of Tray Ratio, with VR = 0,70 ..................................... 68

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List of Tables

Table 1: Vector lengths and sphere diameters. .................................................................................. 28

Table 2: Vector shrinkages and average sphere diameters ................................................................ 30 Table 3: Angles between the vectors ................................................................................................. 31 Table 4: Absolute wall thickness (WT) and edge thickness (ET) deviations .................................... 32 Table 5: Relative wall thickness (WT) and edge thickness (ET) deviations ..................................... 33 Table 6: Relative and absolute edge length (EL) deviations ............................................................. 34

Table 7: Influence of VR, TR, and VR*TR on X-vector shrinkage .................................................. 35 Table 8: Influence of VR, TR, and VR*TR on Y-vector shrinkage .................................................. 35 Table 9: Influence of VR, TR, and VR*TR on Z-vector shrinkage .................................................. 36 Table 10: Influence of VR, TR, and VR*TR on sphere size shrinkage in the XZ plane .................. 37

Table 11: Influence of VR, TR, and VR*TR on sphere size shrinkage in the YZ plane .................. 38 Table 12: Influence of VR, TR, and VR*TR on sphere size shrinkage in the XY plane .................. 39 Table 13: Influence of VR, TR, and VR*TR on the angle between X and Y vectors ...................... 40

Table 14: Influence of VR, TR, and VR*TR on the angle between Y and Z vectors ....................... 40 Table 15: Influence of VR, TR, and VR*TR on the angle between Z and X vectors ....................... 41 Table 16: Influence of VR, TR, and VR*TR on relative wall thickness shrinkage in X direction ... 42 Table 17: Influence of VR, TR, and VR*TR on absolute wall thickness shrinkage in X direction.. 42

Table 18: Influence of VR, TR, and VR*TR on absolute wall thickness shrinkage in Y direction.. 43 Table 19: Influence of VR, TR, and VR*TR on relative wall thickness shrinkage in Z direction ... 43

Table 20: Influence of VR, TR, and VR*TR on absolute wall thickness shrinkage in Z direction .. 43 Table 21: Influence of VR, TR, and VR*TR on relative edge length shrinkage in X direction ....... 45 Table 22: Influence of VR, TR, and VR*TR on relative edge length shrinkage in Y direction ....... 45

Table 23: Influence of VR, TR, and VR*TR on relative edge length shrinkage in Z direction........ 46

Table 24: influence of part orientation on sphere size shrinkage in the XZ plane ............................ 48 Table 25: influence of part orientation on sphere size shrinkage in the YZ plane ............................ 48 Table 26: influence of part orientation on sphere size shrinkage in the XY plane............................ 49

Table 27: influence of part orientation on the angle between the X and Y vectors .......................... 49

Table 28: Main statistical parameters regarding influence of part orientation on 𝑋𝑌 ....................... 50 Table 29: influence of part orientation on the angle between the Y and Z vectors ........................... 50

Table 30: Main statistical parameters regarding influence of part orientation on 𝑌𝑍 ....................... 51 Table 31: influence of part orientation on the angle between the Z and X vectors ........................... 51

Table 32: Main statistical parameters regarding influence of part orientation on 𝑍𝑋 ....................... 52 Table 33: influence of part orientation on the angles between the vectors ....................................... 52 Table 34: Main statistical parameters regarding influence of part orientation on all part angles. .... 53

Table 35: influence of part orientation on wall thickness shrinkage in Y direction .......................... 54 Table 36: Main statistical parameters regarding influence of part orientation on wall thickness

shrinkage in Y direction .................................................................................................................... 54 Table 37: influence of part orientation on relative wall thickness shrinkage in Z direction ............. 55 Table 38: influence of part orientation on absolute wall thickness shrinkage in Z direction ............ 55

Table 39: influence of part orientation on relative edge width shrinkage in Y direction .................. 56 Table 40: influence of part orientation on relative edge width shrinkage in Z direction .................. 56 Table 41: influence of part orientation on relative edge length shrinkage in X direction ................. 57 Table 42: influence of part orientation on relative edge length shrinkage in Y direction ................. 57 Table 43: influence of part orientation on relative edge length shrinkage in Z direction ................. 58

Table 44: Measurement results of validating part ............................................................................. 61 Table 45: Descriptive information of shrinkage in Z direction of model based on edge length Z

shrinkage ............................................................................................................................................ 62

Table 46: ANOVA analysis of shrinkage in Z direction of the model based on edge length Z

shrinkage ............................................................................................................................................ 62

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Table 47: Descriptive information of shrinkage in Z direction of model based on Z vector shrinkage

........................................................................................................................................................... 62

Table 48: ANOVA analysis of shrinkage in Z direction of the model based on Z vector shrinkage 62 Table 49: Correlation Coefficients between Δshrinkage Z and the angular accuracy ...................... 63 Table 50: Estimated and measured printing times ............................................................................ 64 Table 51: Influence of VR, TR, and VR*TR on net printing speed [cm³/h] ..................................... 65 Table 52: Influence of VR, TR, and VR*TR on gross printing speed [cm³/h] ................................. 66

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Summary of contents

The first main part of the dissertation project contains a description of the Form 2 operating

principles. The second part consists of the experiments and their results. In the end of this

dissertation project, a general conclusion is written down.

List of resources provided.

For this master’s dissertation, a number of resources were provided by the University of Maribor,

faculty of mechanical engineering, additive manufacturing laboratory.

The laboratory provided free use of the Form 2 apparatus, equipped with a post curing box.

Two litres of V4 white resin from Formlabs were also provided by the faculty, as well as a new

print tray.

An Atos v6.0.2-6 three-dimensional optical scanner [see Figure 14] was also provided by the

laboratory.

Word of thanks

In this section I would like to show my thanks to all the people who helped me realise this project.

In general I’d like to thank the University of Maribor, for allowing me to do this project here, and

providing equipment and materials for this dissertation at their costs.

I’d also like to thank the University of Ghent, for allowing me to study in Maribor for my final

semester.

My thanks goes also to the Erasmus+ program, for giving me the amazing experience of studying

abroad for a semester.

Special thanks goes to Izr. Prof. Dr. Igor Drstvenšek who was my mentor for this project and

provided me with adequate advice and gave me the freedom that I needed for this project.

Special thanks also goes to Doc. Dr. Tomaž Brajlih who was my co-mentor for this project, for

providing me with a good strategy of experiment, for giving good advice and spending quite a lot of

time scanning the printed parts.

On the list of special thanks is also Prof. Ludwig Cardon, for bringing me in contact with the

University of Maribor, for encouraging and allowing me to go on Erasmus+ exchange. For

answering my questions and helping me to figure out the paperwork.

In this section I would also like to thank my parents, for giving me freedom in my decisions and for

supporting the decisions that I’ve made.

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1. Introduction

1.1. State of the art

The work done by (Brajlih et al, 2010) provides a technique to examine the accuracy of a printed

part in an objective way. This method also defines some parameters such as Volume Ratio (VR)

and Tray Ratio (TR), which prove to be helpful in describing the geometric complexity of a part.

This paper proved to be a very useful reference, as in this master’s dissertation, the goal is to

describe the relationships between geometric complexity and dimensional accuracy and print time.

For the evaluation of microscale dimensional accuracy, (Yankov, E., Nikolova, P., 2017) provides a

method using a printed grid of micro cubes. This work provides an alternative way of evaluating the

dimensional accuracy. Even though it works on a different scale than is the focus in this master’s

dissertation, it provides insight in how additive manufacturing accuracy can be evaluated.

A general method to improve accuracy in rapid prototyping is provided by (Brajlih et al, 2006).

This method makes use of genetic programming. Even though this paper describes a whole different

approach on improving the accuracy in rapid prototyping, it provides some insights which are also

useful for this master’s dissertation. The parts can be scaled according to one particular axis, which

provides better results in that axis.

In the publication of (Cajal et al., 2013) another method is presented to improve dimensional and

geometrical accuracy in rapid manufacturing technologies. This work presents another optimization

process, which requires a relatively large number of measurement points. This optimization is based

on describing a kinematic model for the additive manufacturing apparatus.

2. Operating principles of the Form 2

The operating principle of the Form 2 stereo-lithographic apparatus

[see Figure 1] differs from the traditional SLA process. The main

difference is that the parts are printed upside down, hanging on a

build platform. As with all additive manufacture technologies, the

part is produced in layers.

In the operating principle of the Form 2, each new layer is added on

the bottom of a resin tank.

The part is than raised out of the tank, which allows the resin to

redistribute over the bottom surface of the resin tank. The part is

lowered again, and the process is repeated.

The main advantage of this production method is that a lot less

photopolymer resin needs to be present in order to produce a part.

A laser scans the surface of each new layer, solidifying the layer.

Each layer is only partly solidified, and the light from the laser is

able to penetrate through the layer, resulting in the solidification of

the former layer together with the new layer. Figure 1: Form 2 1

1 Figure 1 is property of Formlabs

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2.1. Resin tank with wiper

The resin is added to the apparatus with a resin cartridge. Each cartridge contains a microchip

containing data about the resin type and amount of resin that is left inside. The resin in the resin

tank is checked with a sensor called the ‘levelsense board’. [See Figure 2]

Figure 2: Resin cartridge (left) and resin tank sensor (right) 2

The resin is automatically added inside the resin tank. After the solidification of each layer, the part

is lifted out of the resin, and the resin wiper [see Figure 3] wipes the surface of the resin tank clean.

This wiping action has multiple purposes. It removes solidified resin which might be stuck on the

bottom silicone layer. Also it oxygenates this silicone layer, assuring that the next layer won’t

solidify stuck to the silicone layer.

Figure 3: Resin tank with wiper2 Figure 4: galvanometers and mirror²

The resin tank is heated which ensures that the resin inside the tank has the desired viscosity,

preventing resin droplets splashing out of the tray. The heating temperature depends on the used

resin type. It is also possible to print in open mode, allowing the use of resins from other

companies. In this open mode the heating system and the wiper action are turned off for safety

reasons.

2 Figure 2 - 4 are property of Formlabs

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2.2. Scanner System

The scanner system consists of a 405 nm violet diode LASER source with a maximum power

output of 250 mW. The laser beam is directed by 2 galvanometers and a large mirror surface. [See

Figure 4]

Each galvanometer regulates the position in one axis, X or Y.

A galvanometer has the same working principle of an analogue ampere meter, which means that the

position of the laser is current-controlled.

2.3. Build platform

The build platform is the platform on which the part is printed. It moves in the Z-direction of the

machine. The Z-position is regulated by the rotational position of a threaded rod [see Figure 5].

Figure 5: Build platform with threaded rod3 Figure 6: Build platform and machine axes position³

The build platform can be detached from the machine using a Cam handle. When the print is

completed, the part has to be detached form the platform.

The coordinate system of the Form 2 is not specified by Formlabs. In the interest of clear

description of the print part positions, the coordinate system that is used in this dissertation is

defined and shown in Figure 6.

3. Causes of dimensional and geometrical inaccuracy.

3.1. Non-uniform shrinkage

When the liquid resin solidifies, shrinkage occurs. The amount of shrinkage is not the same in every

direction. Its behaviour is rather complex and depends on the complexity of a part and other

variables.

In this dissertation, the focus is to reduce the influence of this shrinkage on the dimensional

accuracy as much as possible.

3.2. Non-uniformity of the laser beam

The laser beam has a non-uniform distribution of light intensity. While this is necessary to have a

good solidified connection between consecutive layers, it also leads to the edges being only partly

solidified. After the post-curing process, these edges are also fully solidified. Since the laser spot

size is only 140 µm, the effects on the accuracy are rather small.

3 Figure 5 and 6 are property of Formlabs

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3.3. Wear of the Polydimethylsiloxane (PDMS)

The bottom part of the resin tank is covered with a layer of polydimethylsiloxane (PDMS) [see

Figure 7]. The wavelength of the laser light has very little effect on this material. However, because

every layer is printed on top of this layer, wear of the PDMS layer occurs, as well as cloudiness.

The cloudiness of the PDMS layer causes the laser light to diffuse, making it less accurate. Wear of

the PDMS makes the PDMS stickier, sometimes resulting in print failure. According to the

experience of users on the Formlabs’ forum, it is advised to frequently print on different locations

of the build platform. There are some theories that assume that the pigment from the resin slowly

diffuses inside the pores of the PDMS layer. All different theories agree on one thing: ‘the newer

the print tray is, the more accurate parts will be produced’.4

Figure 7: Build tray with PDMS layer5

3.4. Suction forces during peel operation

Another cause of inaccuracy is the suction forces that occur during the peel operation. Those effects

can be reduced by using a reasonable part orientation and design. After the printing of each layer,

the tray moves sideways and the part is lifted upwards. This movement creates some shear force

and tensile force. Print orientation should be chosen in such a way that between consecutive layers,

the surface area doesn’t suddenly increase too much. Also entrapped chambers should be avoided,

since the part will be pressed against the PDMS layer, creating a considerable suction force. The

effects of a bad part orientation can be warpage or print failure. When part orientation is chosen in a

good way, the effects on the accuracy are rather small.

4. Experiment

4.1. Materials and equipment

This experiment was performed on the Form 2 SLA 3D printer by Formlabs.

The used photopolymer resin is the white resin V4 from Formlabs.

A layer thickness resolution of 100 µm is used in this experiment.

CAD models were mainly made in solidworks 2017 software, and exported to STL file format.

Some CAD models were also made using the Siemens NX11 software.

The STL files were made using a tolerance of 0.005 mm with a maximum angle deviation of 14°.

The slicing and placing of supports was done using the PreForm software from Formlabs.

To prevent influence by a cloudy tray-bottom, a new tray was used for this experiment.

Prior to being measured, all the test parts were post-cured in a UV cure box, at a monitored

temperature of 60°C, for 60 minutes [see Figure 8].

4 Forum topics discussing PDMS.

https://forum.formlabs.com/t/pdms-life-expectancy/17345

https://forum.formlabs.com/t/cause-of-pdms-clouding/10393

https://forum.formlabs.com/t/component-diffusion-into-pdms/1049 5 Figure 7 is property of Formlabs

https://forum.formlabs.com/t/pdms-life-expectancy/17345

https://forum.formlabs.com/t/cause-of-pdms-clouding/10393

https://forum.formlabs.com/t/component-diffusion-into-pdms/1049

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Figure 8: UV cure chamber

For measuring and analysing the produced parts, an Atos v6.0.2-6 three-dimensional optical scanner

from GOM was used.

Analysing the scanned images was done using the Atos viewer software, in combination with the

GOM inspect 2017 software from GOM.

4.2. Test part definition and used parameters

The used test parts and experimentation method are based on (Brajlih et al., 2010). As described,

three steps have to be completed. At first the numerical description for the complexity of a part is

described by the two parameters volume ratio (VR) and tray ratio (TR).

“Volume ratio is defined as a ratio between part’s volume and parts’ envelope volume. It takes the

part’s complexity into account presuming that parts with many thin walls are more geometrically

complex that parts with thick walls. Tray ratio is used to describe the part’s relative size compared

to the machine’s workspace. It is defined as a ratio between part’s envelope bottom area and the

area of the machine’s work tray” (Brajlih et al., 2010).

4.3. Evaluation using ANOVA

In the second step the initial test parts were measured and statistically analysed in order to test the

hypothesis. At the end of the experiment, parts that were printed after the optimization of print

parameters were also scanned and analysed to validate if there was any improvement.

Also analysis were made about the suggested orientation by PreForm, as well as for the printing

speed of the Form 2.

In this statistical analysis, first the Levene’s test of homogeneity of variances was executed.

This test is designed to check whether or not the normalised variances of different groups of normal

distributed data have the same variance. In this dissertation, a 95% certainty was applied. Meaning

that unless we were 95% sure that they were not the same, these variances are assumed to be the

same.

Within this dissertation, when these variances were not the same, further analysis of this data was

considered too inaccurate to be useful.

The second part of the statistical analysis is the actual ANOVA analysis. This analysis checks the

difference in variances within groups, with the variances between groups. If the difference in

variance between the groups is significantly bigger than the variance within groups, the conclusion

can be made that there are significant differences in both groups. Also here, the groups have to be

different with 95% certainty, before we consider this to be true.

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4.4. The 2k factorial design test

After the data from the test parts was collected, the results were examined using a 2k factorial design

strategy, as explained in (Brajlih et al., 2010). The 2k factorial design strategy requires every part to

be printed in all combinations of high and low values for each parameter. Since in this experiment

only the influence of 2 parameters (VR and TR) is investigated, 4 different print files [see Figure

10] should be sufficient.

The factorial design test provides a polynomial function, which can be used to reduce the

dimensional and geometrical errors. At the end of the experiments, more test parts were printed

using this polynomial functions as a correction, in order to validate the functions.

4.5. Printer test part setup

In order to be able to identify every printed part, a unique code was printed onto each part. The code

contains the information about the used TR and VR, as well as which position it was printed on the

build platform. The positions are defined as shown in Figure 9.

Figure 9: Part print positions on build platform.

At first four print files have been printed in which the VR and TR variate. As can also be seen in

Figure 10. For each print file, the Preform software provides an estimated printing time. The

correctness of this printing time estimations have also been validated.

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Figure 10: Different TR and VR print files.

In addition to the original experiment, an analysis was also made to see whether the part orientation

suggested by the PreForm software has a positive effect on the dimensional accuracy of the parts.

Since the projected area of these part orientations are larger, only four parts could be printed at once

[see Figure 12]. This resulted in the need to redefine the position coordinates on the platform. The

position coordinates for the suggested orientations can be seen in Figure 11.

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Figure 11: Suggested orientation - part print positions

Figure 12: Print-file for validating the suggested orientation

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After the printing of the test samples, they were prepared for measuring in the optical scanner

system. In order to get a good result from the scanner, a number of reference points were fixed on

the part. To avoid incorrect measurements due to reflection of light, the parts were sprayed with a

thin layer of Titanium dioxide spray. This layer adds a thickness of only a few µm, but improves the

measurement accuracy, resulting in general in a better measurement [see Figure 13].

Figure 13: Part prepared for scanning - with reference points

After the parts were scanned from 4 different points of view, they were processed using the Atos

v6.0.2-6 software [see Figure 14] and exported to STL file format [see Figure 15].

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Figure 14: Scanning setup

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Figure 15: Atos Software

The STL files where then analysed using the GOM inspect 2017 software. In the sphere cut-outs, a

best fitting primitive was applied.

The coordinates of the spheres, as well as the diameter of each sphere were logged for further

processing [see Figure 16].

Figure 16: GOM inspect software - best fitting spheres

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The parts were later also physically measured using a micro meter. The parts were measured on 9

different locations, and every measurement was repeated twice to reduce the influence of human

measuring mistakes. The parts edge and wall thickness, as well as the edge length were measured in

every direction.

These dimensions are defined as shown in Figure 17.

Figure 17: Measuring dimensions

4.6. Evaluation of the measurement results

The data regarding the vector lengths and sphere diameters is shown in Table 1.

To obtain the distance between two sphere centres, the following formula was used:

𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒[mm] = √(𝑋𝑆𝑝ℎ𝑒𝑟𝑒2− 𝑋𝑆𝑝ℎ𝑒𝑟𝑒1

)2 + (𝑌𝑆𝑝ℎ𝑒𝑟𝑒2− 𝑌𝑆𝑝ℎ𝑒𝑟𝑒1

)2 + (𝑍𝑆𝑝ℎ𝑒𝑟𝑒2− 𝑍𝑆𝑝ℎ𝑒𝑟𝑒1

)2

Table 1: Vector lengths and sphere diameters.

Position [x;y] VR TR

Dist X [mm]

Dist Y [mm]

Dist Z [mm]

ø X1 [mm]

ø X2 [mm]

ø Y1 [mm]

ø Y2 [mm]

ø Z1 [mm]

ø Z2 [mm]

1;1 0,10 0,23 15,00 14,95 14,93 15,03 14,98 14,81 14,87 15,09 15,07

2;2 0,10 0,23 15,00 14,96 14,93 15,03 14,98 14,81 14,86 15,09 15,07

3;3 0,10 0,23 14,91 14,87 14,99 14,84 14,82 14,76 14,74 15,03 14,98

1;1 0,10 0,68 14,90 15,10 15,07 15,08 15,03 14,87 14,98 15,07 15,16

2;2 0,10 0,68 14,79 14,94 15,05 14,69 14,76 14,82 14,90 14,99 15,02

3;3 0,10 0,68 14,89 14,96 15,07 14,91 14,89 14,79 14,78 15,10 15,14

1;3 0,10 0,68 14,94 14,99 15,04 14,89 14,94 14,85 14,90 15,01 15,04

3;1 0,10 0,68 14,77 15,04 14,97 14,90 14,95 14,90 14,96 14,96 15,01

1;1 0,40 0,23 15,05 14,99 14,97 14,94 14,98 14,93 14,92 15,04 15,08

2;2 0,40 0,23 14,88 14,89 14,97 14,64 14,74 14,93 14,85 14,90 14,92

3;3 0,40 0,23 14,96 14,90 14,99 14,80 14,86 14,90 14,82 14,94 14,96

29

1;1 0,40 0,68 15,04 15,02 14,98 14,98 15,00 15,00 15,00 15,07 15,00

2;2 0,40 0,68 14,90 14,89 14,97 14,65 14,77 14,95 14,95 14,93 14,97

3;3 0,40 0,68 14,99 14,89 15,00 14,78 14,84 14,93 14,88 15,05 15,08

1;3 0,40 0,68 15,00 14,94 14,97 14,81 14,86 14,93 14,90 15,00 15,05

3;1 0,40 0,68 14,88 15,00 15,01 14,79 14,95 15,02 15,02 14,94 14,95

Suggested Orientation

1;1 0,19 0,52 15,00 14,95 14,96 14,81 14,88 14,85 14,84 14,99 14,97

2;1 0,19 0,52 14,87 14,96 15,02 14,80 14,80 14,97 14,92 14,97 14,96

1;2 0,19 0,52 14,99 14,92 15,02 14,76 14,77 14,96 14,86 15,06 15,00

2;2 0,19 0,52 15,05 14,90 14,98 14,80 14,87 14,86 14,80 15,07 14,95 1;1 0,05 0,47 14,93 14,88 14,93 15,10 15,03 15,11 15,01 14,97 14,88

2;1 0,05 0,47 14,95 14,85 14,89 15,14 15,07 14,93 14,79 14,94 14,79

1;2 0,05 0,47 14,89 14,89 14,96 15,11 15,04 15,11 15,03 15,08 14,93

2;2 0,05 0,47 14,97 14,81 14,92 15,10 15,06 14,98 14,89 15,08 14,95

Using the distances between the sphere centres, the relative shrinkages in % were determined using

the following equation:

𝑆ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑋 [%] = (𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑋 − 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑋

𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑋) . 100%

𝑆ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑌 [%] = (𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑌 − 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑌

𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑌) . 100%

𝑆ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑍 [%] = (𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑍 − 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑍

𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑍) . 100%

The average sphere diameters were determined using following equations:

ø 𝑋 𝑎𝑣𝑔 [mm] =ø 𝑋1 + ø 𝑋2

2

ø 𝑌 𝑎𝑣𝑔 [mm] =ø 𝑌1 + ø 𝑌2

2

ø 𝑍 𝑎𝑣𝑔 [mm] =ø 𝑍1 + ø 𝑍2

2

The value for shrinkage [%] and the average sphere diameter are shown in Table 2.

30

Table 2: Vector shrinkages and average sphere diameters


%shrinkage X

%Shrinkage Y

%shrinkage Z

ø X avg [mm]

ø Y avg [mm]

ø Z avg [mm]

1;1 0,10 0,23 0,018 -0,306 -0,463 15,005 14,840 15,080

2;2 0,10 0,23 0,031 -0,254 -0,463 15,005 14,835 15,080

3;3 0,10 0,23 -0,584 -0,845 -0,098 14,830 14,750 15,005

1;1 0,10 0,68 -0,659 0,648 0,494 15,055 14,925 15,115

2;2 0,10 0,68 -1,391 -0,390 0,344 14,725 14,860 15,005

3;3 0,10 0,68 -0,758 -0,292 0,471 14,900 14,785 15,120

1;3 0,10 0,68 -0,385 -0,092 0,254 14,915 14,875 15,025

3;1 0,10 0,68 -1,508 0,297 -0,183 14,925 14,930 14,985

1;1 0,40 0,23 0,322 -0,077 -0,191 14,960 14,925 15,060

2;2 0,40 0,23 -0,801 -0,732 -0,208 14,690 14,890 14,910

3;3 0,40 0,23 -0,266 -0,668 -0,058 14,830 14,860 14,950

1;1 0,40 0,68 0,240 0,148 -0,109 14,990 15,000 15,035

2;2 0,40 0,68 -0,662 -0,739 -0,203 14,710 14,950 14,950

3;3 0,40 0,68 -0,086 -0,722 -0,029 14,810 14,905 15,065

1;3 0,40 0,68 0,013 -0,406 -0,233 14,835 14,915 15,025

3;1 0,40 0,68 -0,785 0,016 0,035 14,870 15,020 14,945


1;1 0,19 0,52 -0,033 -0,327 -0,257 14,845 14,845 14,980

2;1 0,19 0,52 -0,845 -0,266 0,165 14,800 14,945 14,965

1;2 0,19 0,52 -0,064 -0,531 0,142 14,765 14,910 15,030

2;2 0,19 0,52 0,323 -0,666 -0,158 14,835 14,830 15,010

1;1 0,05 0,47 -0,476 -0,812 -0,436 15,065 15,060 14,925

2;1 0,05 0,47 -0,358 -1,022 -0,762 15,105 14,860 14,865

1;2 0,05 0,47 -0,742 -0,739 -0,245 15,075 15,070 15,005

2;2 0,05 0,47 -0,221 -1,255 -0,503 15,080 14,935 15,015

The angles between the two planes were determined using the following formulas.

𝑣𝑒𝑐𝑡𝑜𝑟 �� = 𝑠𝑝ℎ𝑒𝑟𝑒 𝑐𝑒𝑛𝑡𝑟𝑒 𝑋2 − 𝑠𝑝ℎ𝑒𝑟𝑒 𝑐𝑒𝑛𝑡𝑟𝑒 𝑋1

𝑣𝑒𝑐𝑡𝑜𝑟 �� = 𝑠𝑝ℎ𝑒𝑟𝑒 𝑐𝑒𝑛𝑡𝑟𝑒 𝑌2 − 𝑠𝑝ℎ𝑒𝑟𝑒 𝑐𝑒𝑛𝑡𝑟𝑒 𝑌1

𝑣𝑒𝑐𝑡𝑜𝑟 �� = 𝑠𝑝ℎ𝑒𝑟𝑒 𝑐𝑒𝑛𝑡𝑟𝑒 𝑍2 − 𝑠𝑝ℎ𝑒𝑟𝑒 𝑐𝑒𝑛𝑡𝑟𝑒 𝑍1

31

𝑋�� = 𝑎𝐶𝑜𝑠 (𝑋𝑥 . 𝑌𝑥 + 𝑋𝑦. 𝑌𝑦 + 𝑋𝑧 . 𝑌𝑧

|𝑋| . |𝑌|) = 𝑎𝐶𝑜𝑠 (

𝑋 . 𝑌

|𝑋| . |𝑌|)

𝑌�� = 𝑎𝐶𝑜𝑠 (𝑌𝑥 . 𝑍𝑥 + 𝑌𝑦. 𝑍𝑦 + 𝑌𝑧 . 𝑍𝑧

|𝑌| . |𝑍|) = 𝑎𝐶𝑜𝑠 (

𝑌 . 𝑍

|𝑌| . |𝑍|)

𝑍�� = 𝑎𝐶𝑜𝑠 (𝑍𝑥 . 𝑋𝑥 + 𝑍𝑦. 𝑋𝑦 + 𝑍𝑧 . 𝑋𝑧

|𝑍| . |𝑋|) = 𝑎𝐶𝑜𝑠 (

𝑍 . 𝑋

|𝑍| . |𝑋|)

With |X|, |Y|, |Z| = the length of the vectors which were

already calculated in Table 1.

The resulting angles between the vectors of the printed part are shown in Table 3.

Table 3: Angles between the vectors

Angle between Vectors

Position [x;y] VR TR 𝑋�� [°] 𝑌�� [°] 𝑍�� [°]

1;1 0,10 0,23 90,159 89,792 89,608

2;2 0,10 0,23 90,144 89,806 89,650

3;3 0,10 0,23 90,345 89,738 90,009

1;1 0,10 0,68 90,152 89,974 89,490

2;2 0,10 0,68 90,063 90,006 89,500

3;3 0,10 0,68 90,667 89,802 89,879

1;3 0,10 0,68 90,263 89,766 89,290

3;1 0,10 0,68 90,248 90,056 89,745

1;1 0,40 0,23 89,891 89,824 89,349

2;2 0,40 0,23 90,165 89,874 89,496

3;3 0,40 0,23 90,257 89,780 89,761

1;1 0,40 0,68 90,033 90,097 89,667

2;2 0,40 0,68 90,014 89,991 89,671

3;3 0,40 0,68 90,189 89,841 89,840

1;3 0,40 0,68 90,011 89,765 89,531

3;1 0,40 0,68 89,836 90,275 89,690


1;1 0,19 0,52 89,663 90,142 89,346

2;1 0,19 0,52 89,867 90,261 89,850

1;2 0,19 0,52 89,812 90,107 89,846

2;2 0,19 0,52 89,833 89,991 89,629

1;1 0,05 0,47 89,930 90,061 90,178

2;1 0,05 0,47 89,801 90,394 90,080

1;2 0,05 0,47 90,175 90,550 89,875

2;2 0,05 0,47 89,982 90,333 90,204

32

Furthermore, the wall thickness, edge thickness and edge length were measured using a micro

meter.

For the processing of the wall thickness measurements obtained by the micro meter, both the values

in mm as in % were used. This is because the effect on the deviations are not only caused by

shrinkage, but also by the remains of support structure, and since the dimensions for wall thickness

are not the same for variating VR, the results of the statistical analysis are also not the same.

The measurements of wall thickness and edge thickness were subtracted with their nominal value,

and the deviation in mm is shown in Table 4. Table 5 shows the same deviations in a relative

measurement. Table 6 shows the measurement deviations for edge length, both in absolute as in

relative values.

𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑊𝑇 𝑋 [mm] = 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛 𝑋 − 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛 𝑋

𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑊𝑇 𝑌 [mm] = 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛 𝑌 − 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛 𝑌

𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑊𝑇 𝑍 [mm] = 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛 𝑍 − 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛 𝑍 Table 4: Absolute wall thickness (WT) and edge thickness (ET) deviations

Position [x;y] VR TR Deviation WT X [mm]

Deviation WT Y [mm]

Deviation WT Z [mm]

Deviation ET X [mm]

Deviation ET Y [mm]

Deviation ET Z [mm]

1;1 0,1 0,23 -0,01 -0,02 0,32 -0,07 -0,07 -0,140

2;2 0,1 0,23 0,02 -0,01 0,42 0,04 -0,27 -0,080

3;3 0,1 0,23 0,03 0,01 0,38 -0,07 -0,05 -0,040

1;1 0,1 0,68 0,01 -0,02 0,27 0,03 -0,28 -0,075

2;2 0,1 0,68 0,01 0,00 0,24 0,04 0,03 -0,105

3;3 0,1 0,68 0,00 0,00 0,25 -0,04 -0,05 -0,110

1;3 0,1 0,68 0,00 0,00 0,20 0,00 -0,12 -0,130

3;1 0,1 0,68 0,00 -0,03 0,23 0,03 -0,15 -0,135

1;1 0,4 0,23 0,07 0,04 0,09 -0,05 0,04 -0,080

2;2 0,4 0,23 0,13 0,04 0,12 0,03 0,05 -0,145

3;3 0,4 0,23 0,09 0,00 0,00 -0,07 0,03 0,155

1;1 0,4 0,68 0,03 0,07 0,40 0,01 0,02 0,000

2;2 0,4 0,68 0,09 0,03 -0,03 0,02 0,03 -0,160

3;3 0,4 0,68 0,09 0,03 0,36 -0,04 0,02 -0,020

1;3 0,4 0,68 0,04 0,05 0,40 0,01 0,01 -0,005

3;1 0,4 0,68 0,20 0,06 0,33 -0,02 0,04 -0,005


1;1 0,19 0,52 0,29 0,14 0,25 -0,04 0,06 0,04

2;1 0,19 0,52 0,22 0,08 0,40 0,03 0,03 -0,30

1;2 0,19 0,52 0,30 0,12 0,33 -0,03 0,06 -0,09

2;2 0,19 0,52 -0,09 0,05 0,17 -0,04 0,07 0,08

1;1 0,05 0,47 -0,01 0,01 0,00 -0,15 -0,05 -0,17

2;1 0,05 0,47 -0,03 0,05 0,04 -0,17 -0,11 0,02

1;2 0,05 0,47 -0,01 0,04 0,04 -0,14 0,02 -0,06

2;2 0,05 0,47 0,02 0,05 0,01 -0,18 0,06 -0,04

33

𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑊𝑇 𝑋 [%] = (𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑊𝑇 𝑋

𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑋) . 100%

𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑊𝑇 𝑌 [%] = (𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑊𝑇 𝑌

𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑌) . 100%

𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑊𝑇 𝑍 [%] = (𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑊𝑇 𝑍

𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑍) . 100%

Table 5: Relative wall thickness (WT) and edge thickness (ET) deviations


Deviation WT X [%]

Deviation WT Y [%]

Deviation WT Z [%]

Deviation ET X [%]

Deviation ET Y [%]

Deviation ET Z [%]

1;1 0,10 0,23 17,43 -0,76 -1,15 3,20 -0,70 -0,75

2;2 0,10 0,23 17,43 1,53 -0,38 4,15 0,45 -2,65

3;3 0,10 0,23 17,43 2,67 0,76 3,75 -0,75 -0,55

1;1 0,10 0,68 52,28 1,15 -1,53 2,70 0,30 -2,80

2;2 0,10 0,68 52,28 1,15 0,00 2,35 0,45 0,25

3;3 0,10 0,68 52,28 0,00 0,00 2,45 -0,40 -0,50

1;3 0,10 0,68 52,28 0,38 0,38 1,95 0,00 -1,20

3;1 0,10 0,68 52,28 0,00 -1,91 2,25 0,30 -1,45

1;1 0,40 0,23 3,81 1,08 0,67 0,90 -0,55 0,35

2;2 0,40 0,23 3,81 2,17 0,58 1,20 0,30 0,55

3;3 0,40 0,23 3,81 1,50 -0,08 -0,05 -0,70 0,30

1;1 0,40 0,68 11,42 0,50 1,17 3,95 0,10 0,20

2;2 0,40 0,68 11,42 1,42 0,50 -0,25 0,15 0,30

3;3 0,40 0,68 11,42 1,58 0,50 3,60 -0,40 0,15

1;3 0,40 0,68 11,42 0,67 0,83 3,95 0,10 0,10

3;1 0,40 0,68 11,42 3,25 1,00 3,25 -0,20 0,35


1;1 0,19 0,52 21,76 10,31 19,08 -0,35 0,65 0,45

2;1 0,19 0,52 16,79 6,11 30,53 0,25 0,25 -2,95

1;2 0,19 0,52 22,90 9,16 25,19 -0,25 0,65 -0,90

2;2 0,19 0,52 -7,25 3,82 12,98 -0,35 0,75 0,80

1;1 0,05 0,47 -0,38 1,15 0,38 -1,45 -0,55 -1,70

2;1 0,05 0,47 -2,29 3,82 3,05 -1,70 -1,10 0,15

1;2 0,05 0,47 -0,76 3,44 3,44 -1,40 0,15 -0,65

2;2 0,05 0,47 1,91 3,82 0,76 -1,75 0,60 -0,40

34

Table 6: Relative and absolute edge length (EL) deviations


Deviation EL X [mm]

Deviation EL Y [mm]

Deviation EL Z [mm]

Deviation EL X [%]

Deviation EL Y [%]

Deviation EL Z [%]

1;1 0,10 0,23 0,10 0,14 0,15 0,26 0,35 0,37

2;2 0,10 0,23 -0,16 -0,11 0,23 -0,41 -0,27 0,59

3;3 0,10 0,23 0,03 0,08 0,10 0,09 0,19 0,26

1;1 0,10 0,68 0,15 0,13 0,00 0,36 0,34 0,00

2;2 0,10 0,68 -0,03 -0,04 0,12 -0,09 -0,10 0,29

3;3 0,10 0,68 0,20 0,12 0,10 0,51 0,29 0,25

1;3 0,10 0,68 0,06 0,06 0,02 0,15 0,16 0,06

3;1 0,10 0,68 -0,10 0,08 0,01 -0,25 0,20 0,01

1;1 0,40 0,23 0,12 0,09 -0,01 0,30 0,23 -0,02

2;2 0,40 0,23 -0,16 -0,16 -0,06 -0,40 -0,39 -0,15

3;3 0,40 0,23 0,10 -0,12 -0,02 0,26 -0,29 -0,05

1;1 0,40 0,68 0,17 0,15 0,02 0,44 0,36 0,04

2;2 0,40 0,68 -0,07 -0,03 0,05 -0,18 -0,09 0,14

3;3 0,40 0,68 0,09 -0,06 0,02 0,21 -0,15 0,06

1;3 0,40 0,68 -0,03 0,01 -0,02 -0,08 0,02 -0,05

3;1 0,40 0,68 -0,10 0,10 0,01 -0,25 0,26 0,02


1;1 0,19 0,52 0,07 -0,05 -0,21 0,18 -0,12 -0,53

2;1 0,19 0,52 -0,02 -0,02 -0,10 -0,06 -0,05 -0,25

1;2 0,19 0,52 0,09 -0,05 -0,02 0,21 -0,14 -0,06

2;2 0,19 0,52 0,06 -0,19 -0,09 0,16 -0,46 -0,21

1;1 0,05 0,47 -0,08 -0,01 0,34 -0,19 -0,02 0,85

2;1 0,05 0,47 0,06 0,13 0,23 0,16 0,31 0,56

1;2 0,05 0,47 -0,01 -0,09 0,27 -0,02 -0,24 0,68

2;2 0,05 0,47 0,18 -0,17 0,23 0,45 -0,44 0,57

4.7. Evaluation of the shrinkages using ANOVA

4.7.1. Linear shrinkage in function of VR and TR

To determine whether or not VR and TR have a significant influence on the shrinkage between the

sphere centres in X, Y and Z direction, ANOVA was used.

The null hypothesis H0 is that there is no influence of the parameters on these shrinkages.

To reject H0 , a 95% confidence interval was used, meaning that in order to reject H0 , the sigma

value should be smaller than 0,05.

35

4.7.1.1. Shrinkage in X direction

The results in Table 7 represent the influence of VR, TR and VR*TR on the shrinkage in X

direction [%].

Table 7: Influence of VR, TR, and VR*TR on X-vector shrinkage

Test of between-subject effects

Dependant value: Shrinkage of X vector

Source Type III sum of Squares df

Mean square F Sig.

Model 5,028 4 1,257 5,766 0,008

VR 0,354 1 0,354 1,622 0,227

TR 0,555 1 0,555 2,547 0,137

VR * TR 0,533 1 0,533 2,446 0,144

Error 2,616 12 0,218

Total 7,644 16

Using this results, we observed that the model is significant (Sig = 0,008).

H0 couldn’t be rejected for any of the parameters (Sig > 0,05 for all parameters).

Meaning that we cannot say that there is a significant influence of the parameters on the shrinkage

in X direction.

4.7.1.2. Shrinkage in Y direction

The results in Table 8 represent the influence of VR, TR and VR*TR on the shrinkage in Y

direction [%].

Table 8: Influence of VR, TR, and VR*TR on Y-vector shrinkage


Dependant value: Shrinkage of Y vector


Mean square F Sig.

Model 1,971 4 0,493 3,116 0,056

VR 0,149 1 0,149 0,943 0,351

TR 0,401 1 0,401 2,538 0,137

VR * TR 0,115 1 0,115 0,730 0,410

Error 1,897 12 0,158

Total 3,886 16

Using this results, we observed that the model is just barely insignificant (Sig = 0,056).



in Y direction.

36

4.7.1.3. Shrinkage in Z direction

The results in Table 9 represent the influence of VR, TR and VR*TR on the shrinkage in Z

direction [%].

Table 9: Influence of VR, TR, and VR*TR on Z-vector shrinkage


Dependant value: Shrinkage of Z vector


Mean square F Sig.

Model 0,858 4 0,215 5,658 0,009

VR 0,036 1 0,036 0,938 0,352

TR 0,411 1 0,411 10,832 0,006

VR * TR 0,308 1 0,308 8,113 0,015

Error 0,455 12 0,038

Total 1,313 16

Using this results, we observed that the model is significant (Sig =0,009).

H0 was rejected for TR (sig = 0,006) and for the combined effect of VR and TR (sig = 0,015).

Meaning that we can say with great confidence that there is an effect of these parameters on the

shrinkage in Z direction.

To approximate the effects of the parameters on the shrinkage in Z, a linear regression model was

used, and the following formula was found, with a significance of 0,005.

𝑆ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑍 = −0,808 + 1,585 . 𝑉𝑅 + 1,77 . 𝑇𝑅 − 4,182 . 𝑉𝑅. 𝑇𝑅

Since the parameter VR is not statistically relevant, this equation could be simplified to the

following.

𝑆ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑍 = −0,412 + 1,119 . 𝑇𝑅 − 1,579 . 𝑉𝑅. 𝑇𝑅

In this master dissertation, the decision has been made to use the linear regression model containing

all factors. A visual representation of the influence of VR and TR has been made in Matlab and is

shown in Figure 18.

37

Figure 18: Shrinkage of Z vector in function of VR and TR

4.7.2. Sphere size in function of VR and TR

To determine whether or not VR and TR have a significant influence on the sphere diameters in the

different planes, ANOVA was used.

The null hypothesis H0 is that there is no influence of the parameters on the sphere diameters.



4.7.2.1. Sphere size in XZ plane

The results in Table 10 represent the influence of VR, TR and VR*TR on the sphere diameters in

the XZ plane (spheres X1 and X2).

Table 10: Influence of VR, TR, and VR*TR on sphere size shrinkage in the XZ plane


Dependant value: Sphere size in XZ plane

Source Type III sum of Squares df Mean square F Sig.

Model 3543,413 4 885,853 66549,920 0,000

VR 0,037 1 0,037 2,752 0,123

TR 0,002 1 0,002 0,130 0,724

VR * TR 0,005 1 0,005 0,403 0,537

Error 0,160 12 0,013

Total 3543,573 16

38

Using this results, we observed that the model is definitely significant (Sig = 0,000…).


Meaning that we were unable to say that there is a significant influence of the parameters on the

sphere size in the XZ plane.

4.7.2.2. Sphere size in YZ plane


the YZ plane (spheres Y1 and Y2).

Table 11: Influence of VR, TR, and VR*TR on sphere size shrinkage in the YZ plane


Dependant value: Sphere size in YZ plane


Model 3548,182 4 887,046 338854,428 0,000

VR 0,026 1 0,026 9,908 0,008

TR 0,017 1 0,017 6,335 0,027

VR * TR 1,042 E-7 1 1,042 E-7 0,000 0,995

Error 0,031 12 0,003

Total 3548,214 16

Using this results, we see that the model is definitely significant (Sig = 0,000…).

H0 was rejected for the parameters VR and TR, but not for the combined effect of those two.

Meaning that we can say, with great confidence that there is an effect of these parameters on the

sphere size in the YZ plane.

To approximate the effects of the parameters on the sphere size in YZ plane, a linear regression

model was used, and the following formula was found, with a significance of 0,012.

𝑆𝑝ℎ𝑒𝑟𝑒 𝑠𝑖𝑧𝑒 𝑌𝑍 = 14,747 + 0,278 . 𝑉𝑅 + 0,146 . 𝑇𝑅 − 0,002 . 𝑉𝑅. 𝑇𝑅

Since the combined effect of the parameters VR and TR is not statistically relevant, this equation

could be simplified to the following.

𝑆𝑝ℎ𝑒𝑟𝑒 𝑠𝑖𝑧𝑒 𝑌𝑍 = 14,747 + 0,277 . 𝑉𝑅 + 0,146 . 𝑇𝑅

This formulas were reformed to make a more general formula for the shrinkage of sphere diameter

in %. A positive shrinkage corresponds with an increase in diameter.

𝑆𝑝ℎ𝑒𝑟𝑒 𝑠ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑌𝑍 [%] = −1,692 + 1,88 . 𝑉𝑅 + 0,987 . 𝑇𝑅 − 0,058 . 𝑉𝑅 . 𝑇𝑅

Or as could be written down in the simplified version without the combined effect of VR.TR:

𝑆𝑝ℎ𝑒𝑟𝑒 𝑠ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑌𝑍 [%] = −1,684 + 1,85 . 𝑉𝑅 + 0,972 . 𝑇𝑅 In this master dissertation, the decision has been made to use the linear regression model containing


shown in Figure 19.

39

Figure 19: Sphere shrinkage in YZ plane (spheres Y1 and Y2) in function of VR and TR

4.7.2.3. Sphere size in XY plane


the XY plane (spheres Z1 and Z2).

Table 12: Influence of VR, TR, and VR*TR on sphere size shrinkage in the XY plane


Dependant value: Sphere size in XY plane


Model 3610,674 4 902,668 249950,497 0,000

VR 0,015 1 0,015 4,231 0,062

TR 0,001 1 0,001 0,171 0,687

VR * TR 0,001 1 0,001 0,330 0,576

Error 0,043 12 0,004

Total 3610,717 16



Meaning that we cannot say that there is a significant influence of the parameters on the sphere size

in the XY plane.

40

4.7.3. Perpendicularity of the planes

To determine whether or not VR and TR have a significant influence on the perpendicularity of the

different planes, ANOVA was used.

The null hypothesis H0 is that there is no influence of the parameters on the perpendicularity.



4.7.3.1. Angle between X and Y vectors

The results in Table 13 represent the influence of VR, TR and VR*TR on the measured angle

between the X and Y vectors.

Table 13: Influence of VR, TR, and VR*TR on the angle between X and Y vectors


Dependant value: 𝐴𝑛𝑔𝑙𝑒 𝑋��


Mean square F Sig.

Model 130039,024 4 32509,756 1039692,313 0,000

VR 0,131 1 0,131 4,180 0,063

TR 0,001 1 0,001 0,019 0,894

VR * TR 0,021 1 0,021 0,678 0,426

Error 0,375 12 0,031

Total 130039,399 16



Meaning that we cannot say that there is a significant influence of the parameters on the

perpendicularity between the vectors X and Y.

4.7.3.2. Angle between Y and Z vectors


between the Y and Z vectors. Table 14: Influence of VR, TR, and VR*TR on the angle between Y and Z vectors


Dependant value: 𝐴𝑛𝑔𝑙𝑒 𝑌��


Mean square F Sig.

Model 129310,038 4 32327,509 1624631,313 0,000

VR 0,014 1 0,014 0,681 0,425

TR 0,090 1 0,090 4,540 0,054

VR * TR 0,001 1 0,001 0,032 0,862

Error 0,239 12 0,020

Total 129310,276 16



41


perpendicularity between the vectors Y and Z.

4.7.3.3. Angle between Z and X vector


between the Z and X vectors.

Table 15: Influence of VR, TR, and VR*TR on the angle between Z and X vectors


Dependant value: 𝐴𝑛𝑔𝑙𝑒 𝑍��


Mean square F Sig.

Model 128553,360 4 32138,340 861202,045 0,000

VR 0,014 1 0,014 0,368 0,555

TR 0,001 1 0,001 0,023 0,883

VR * TR 0,095 1 0,095 2,558 0,136

Error 0,448 12 0,037

Total 128553,808 16




perpendicularity between the vectors Z and X.

4.7.4. Wall- and edge thickness in function of VR and TR

To determine whether or not VR and TR have a significant influence on the shrinkage of the walls

and edges of the part, ANOVA was used.

The wall thickness variates together with the volume ratio.

Therefor the analysis of the wall thickness shrinkage was done both on the relative shrinkages [%]

as well as on the absolute shrinkages [mm].

The null hypothesis H0 is that there is no influence of the parameters on the shrinkage of wall

thickness.



42

4.7.4.1. Wall thickness in X direction

The results in Table 16 represent the influence of VR, TR and VR*TR on the wall thickness

shrinkage measured in the X direction [%]. The results in Table 17 represent the same data but in an

absolute measurement [mm].

Table 16: Influence of VR, TR, and VR*TR on relative wall thickness shrinkage in X direction


Dependant value: Wall thickness in X [%]


Mean square F Sig.

Model 23,883 4 5,971 5,586 0,009

VR 1,804 1 1,804 1,688 0,218

TR 0,474 1 0,474 0,443 0,518

VR * TR 0,244 1 0,244 0,229 0,641

Error 12,826 12 1,059

Total 36,709 16

Table 17: Influence of VR, TR, and VR*TR on absolute wall thickness shrinkage in X direction


Dependant value: Wall thickness in X [mm]


Model 0,068 4 0,017 9,845 0,001

VR 0,025 1 0,025 14,332 0,003

TR 0,000 1 0,000 0,107 0,749

VR * TR 3,750 E-6 1 3,750 E-6 0,002 0,963

Error 0,021 12 0,002

Total 0,088 16

Using this results, we observed that both models are significant (Sig < 0,05).

H0 was rejected for the parameter VR, and this only in the test of the absolute measurements.

However, using this results, it was quite difficult to determine the exact relationship between VR

and the wall thickness in X direction, as the results would be too inaccurate.

4.7.4.2. Wall thickness in Y direction

The results in Table 18 represent the influence of VR, TR and VR*TR on the absolute value of the

measured wall thickness shrinkage in the Y direction [mm].

The results of the relative shrinkages could not be used, since the homogeneity of the data could not

be validated. (Levene’s test of equality of error variances returned a Sigma value of 0,014)

43

Table 18: Influence of VR, TR, and VR*TR on absolute wall thickness shrinkage in Y direction


Dependant value: Wall thickness in Y [mm]


Model 0,014 4 0,003 11,436 0,000

VR 0,006 1 0,006 21,697 0,001

TR 0,000 1 0,000 1,270 0,282

VR * TR 0,001 1 0,001 2,732 0,124

Error 0,004 12 0,000

Total 0,017 16

Using this results, we observed that the model is significant (Sig < 0,05).

H0 was rejected only for the parameter VR, and this again only in the test of the absolute

measurements.

However, using this results, it is quite difficult to determine the exact relationship between VR and

the wall thickness in Y direction, as the results would be too inaccurate.

4.7.4.3. Wall thickness in Z direction

The results in Table 19 represent the influence of VR, TR and VR*TR on the wall thickness

shrinkage measured in the Z direction [%]. The results in Table 20 represent the same data but in an

absolute measurement [mm].

Table 19: Influence of VR, TR, and VR*TR on relative wall thickness shrinkage in Z direction


Dependant value: Wall thickness in Z [%]


Model 4109,383 4 1027,346 150,656 0,000

VR 1510,160 1 1510,160 221,459 0,000

TR 41,919 1 41,919 6,147 0,029

VR * TR 185,733 1 185,733 27,237 0,000

Error 81,830 12 6,819

Total 4191,213 16

Table 20: Influence of VR, TR, and VR*TR on absolute wall thickness shrinkage in Z direction


Dependant value: Wall thickness in Z [mm]


Model 1,119 4 0,280 23,396 0,000

VR 0,057 1 0,057 4,732 0,050

TR 0,007 1 0,007 0,575 0,463

VR * TR 0,120 1 0,120 10,030 0,008

Error 0,143 12 0,012

Total 1,262 16

44

Using this results, we observed that both models are significant (Sig = 0,000…).

According to the relative shrinkages, H0 was rejected for all parameters.

According to the absolute shrinkages, H0 was rejected for VR*TR and for VR.

To make an approximation of the effects, a linear regression is applied for the results of the relative

shrinkage [%]. The statistical significance of this regression is 0,000…

A positive number of shrinkage corresponds with an increase in dimension.

𝑊𝑎𝑙𝑙 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑠ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑖𝑛 𝑍 [%] = 44,816 − 113,81 . 𝑉𝑅 − 33,011 . 𝑇𝑅 + 102,755 . 𝑉𝑅. 𝑇𝑅

This formula should be used merely as an indication, since the actual dimensions will be influenced

by how well the support structures are removed. A visual representation was made in Matlab and is

shown below in Figure 20.

Figure 20: Shrinkage of wall thickness in Z direction in function of VR and TR

4.7.4.4. Edge width

The shrinkages of the edge widths were evaluated for each direction.

However, after processing the data, the Levene's test for homogeneity of variance made clear that

the data is statistically not usable.

No statistical conclusions could be made about the edge width shrinkage.

45

4.7.5. Total length of the part edges.

To determine whether or not VR and TR have a significant influence on the shrinkage of the part

edges in the different directions, ANOVA was used.

The null hypothesis H0 is that there is no influence of the parameters on these shrinkages.



4.7.5.1. Edge length in X direction

The results in Table 21 represent the influence of VR, TR and VR*TR on the edge length shrinkage

measured in the X direction [%].

Table 21: Influence of VR, TR, and VR*TR on relative edge length shrinkage in X direction


Dependant value: Edge Length in X [%]


Mean square F Sig.

Model 0,109 4 0,027 0,256 0,900

VR 0,001 1 0,001 0,009 0,925

TR 0,017 1 0,017 0,158 0,698

VR * TR 0,031 1 0,031 0,293 0,598

Error 1,279 12 0,107

Total 1,388 16

Using this results, we observed that the model is actually not significant (Sig = 0,900).



of the edge length in X-direction.

4.7.5.2. Edge length in Y direction


measured in the Y direction [%].

Table 22: Influence of VR, TR, and VR*TR on relative edge length shrinkage in Y direction


Dependant value: Edge Length in Y [%]


Mean square F Sig.

Model 0,282 4 0,071 1,145 0,382

VR 0,104 1 0,104 1,684 0,219

TR 0,098 1 0,098 1,584 0,232

VR * TR 0,019 1 0,019 0,309 0,588

Error 0,739 12 0,062

Total 1,021 16

46

Using this results, we observed that the model is actually not significant (Sig = 0,382).



of the edge length in Y-direction.

4.7.5.3. Edge length in Z direction


measured in the Z direction [%].

Table 23: Influence of VR, TR, and VR*TR on relative edge length shrinkage in Z direction


Dependant value: Edge Length in Z [%]


Mean square F Sig.

Model 0,601 4 0,150 11,581 0,000

VR 0,298 1 0,298 22,925 0,000

TR 0,027 1 0,027 2,047 0,178

VR * TR 0,153 1 0,153 11,752 0,005

Error 0,156 12 0,013

Total 0,757 16

Using this results, we observed that this model is significant (Sig = 0,000…).

H0 was rejected for VR, as well as for the combination of VR*TR.

(Sig < 0,05 for those parameters).

Meaning that we can find a relationship between the parameters and the shrinkage of the edge

length in Z-direction.

In order to approximate the effects of the parameters on the shrinkage of the edge length in Z

direction, a linear regression model was used, which resulted in the following equation:

𝑆ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑜𝑓 𝐸𝑑𝑔𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑍 [%] = 0,78 − 2,283. 𝑉𝑅 − 0,92 . 𝑇𝑅 + 2,944 . 𝑉𝑅 . 𝑇𝑅

Since the effect of the parameter TR is not statistically relevant, this equation could be simplified to

the following form.

𝑆ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑜𝑓 𝐸𝑑𝑔𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑍 [%] = 0,307 − 0,893. 𝑉𝑅 + 0,237 . 𝑉𝑅 . 𝑇𝑅

In this master dissertation, the decision has been made to use the linear regression model containing


shown in Figure 21.

47

Figure 21: Shrinkage of Edge Length in Z direction in function of VR and TR

4.8. Evaluation of the part orientation suggested by the PreForm software.

4.8.1. Linear shrinkage in function of part orientation

To determine whether or not part orientation has a significant influence on the shrinkage between

the sphere centres in X-, Y- and Z direction, ANOVA was used.

The null hypothesis H0 is that there is no influence of the part orientation on these shrinkages.



4.8.1.1. Shrinkage in X direction

The results of the statistical analysis showed that the homogeneity of the variance of the collected

data could not be ensured (Levene’s test; sigma = 0,001…). Making further analysis of this data

pointless.

Meaning that we cannot say that there is a significant influence of this part orientation on the

shrinkage in X-direction.

4.8.1.2. Shrinkage in Y direction

The results of the statistical analysis, showed that the homogeneity of the variance of the collected


pointless.


shrinkage in Y-direction.

48

4.8.1.3. Shrinkage in Z direction



pointless.


shrinkage in Z-direction.

4.8.2. Sphere size in function of VR and TR

To determine whether or not part orientation has a significant influence on the sphere diameters in

the different planes, ANOVA was used.

The null hypothesis H0 is that there is no influence of this part orientation on the sphere diameters.



4.8.2.1. Sphere size in XZ plane

The results in Table 24 represent the influence of part orientation on the sphere diameters in the XZ

plane (sphere X1 and X2).

Table 24: influence of part orientation on sphere size shrinkage in the XZ plane

ANOVA

Sum of Squares df Mean square F Sig.

Sphere size in XZ plane

Between Groups 1,092 1 1,092 1,614 0,217

Within Groups 14,883 22 0,677

Total 15,975 23

H0 couldn’t be rejected for this part orientation (Sig > 0,05).

Meaning that we cannot say that there is a significant influence of this part orientation on the sphere

size in the XZ plane.

4.8.2.1. Sphere size in YZ plane

The results in Table 25 represent the influence of part orientation on the sphere diameters in the YZ

plane (sphere Y1 and Y2).

Table 25: influence of part orientation on sphere size shrinkage in the YZ plane

ANOVA


Sphere size in YZ plane

Between Groups 0,389 1 0,389 1,429 0,245


Total 6,373 23



size in the YZ plane.

49

4.8.2.2. Sphere size in XY plane

The results in Table 25 represent the influence of part orientation on the sphere diameters in the XY

plane (sphere Z1 and Z2).

Table 26: influence of part orientation on sphere size shrinkage in the XY plane

ANOVA


Sphere size in XY plane

Between Groups 0,539 1 0,539 3,301 0,083


Total 4,121 23



size in the XY plane.

4.8.3. Perpendicularity of the planes

To determine whether or not part orientation has a significant influence on the perpendicularity of

the different planes, ANOVA was used.

The null hypothesis H0 is that there is no influence of the parameters on the perpendicularity.



4.8.3.1. Angle between X and Y vectors

The results in Table 27 represent the influence of part orientation on the measured angle between

the X and Y vectors.

Table 27: influence of part orientation on the angle between the X and Y vectors

ANOVA


𝑨𝒏𝒈𝒍𝒆 𝑿�� Between Groups 0,387 1 0,387 11,733 0,002


Total 1,113 23

H0 was rejected for this part orientation (Sig = 0,002).

Meaning that we can say that there is a significant influence of this part orientation on the

perpendicularity between the vectors X and Y. In Table 28 the mean values and standard deviations

are listed. Figure 22 shows a boxplot. The blue area of the boxplot represents the 95% confidence

intervals for the angle between the X and Y vector. The ‘arms’ of the boxplot show the minimum

and maximum measured values.

50

Table 28: Main statistical parameters regarding influence of part orientation on 𝑋��

𝐴𝑛𝑔𝑙𝑒 𝑋�� 95% Confidence interval

N Mean [°] Std. Deviation [°]

Std. Error [°]

Lower Bound [°]

Upper Bound [°]

Minimum [°]

Maximum [°]

Normal orientation 16 90,1522 0,19423 0,04856 90,0487 90,2557 89,84 90,67

Suggested orientation 8 89,8828 0,15128 0,05348 89,7563 90,0093 89,66 90,18

Total 24 90,0624 0,22001 0,04491 89,9695 90,1553 89,66 90,67

Figure 22: Comparrison of the XY angle between different orientations

When printing in this suggested orientation, the mean value for 𝑋�� is closer to 90°, while the

standard deviation is smaller. Since the differences were statistically significant, we can say that the

suggested orientation provides a better perpendicularity between the X and Y vectors.

4.8.3.2. Angle between Y and Z vectors


the Y and Z vectors.

Table 29: influence of part orientation on the angle between the Y and Z vectors

ANOVA


𝑨𝒏𝒈𝒍𝒆 𝒀��

Between Groups 0,583 1 0,583 21,537 0,000


Total 1,178 23

H0 was rejected for this part orientation (Sig = 0,000…).


perpendicularity between the vectors Y and Z. In the Table 30 the mean values and standard

deviations are listed. Figure 23 shows a boxplot. The blue area of the boxplot represents the 95%

confidence intervals for the angle between the Y and Z vector. The ‘arms’ of the boxplot show the

minimum and maximum measured values.

51

Table 30: Main statistical parameters regarding influence of part orientation on 𝑌��

𝑨𝒏𝒈𝒍𝒆 𝑌�� 95% Confidence interval

N Mean [°]

Std. Deviation [°]

Std. Error [°]

Lower Bound [°]

Upper Bound [°]

Minimum [°]

Maximum [°]



Total 24 90,0094 0,22631 0,04620 89,9138 90,1050 89,74 90,55

Figure 23: Comparison of the YZ angle between different orientations

When printing in this suggested orientation, the mean value for 𝑌�� is further away from 90°, while

the standard deviation is bigger. Since the differences were statistically significant, we can say that

this suggested orientation provides a worse perpendicularity between the X and Y vectors.

4.8.3.3. Angle between Z and X vector


the Z and X vectors. Table 31: influence of part orientation on the angle between the Z and X vectors

ANOVA


𝑨𝒏𝒈𝒍𝒆 𝒁��

Between Groups 0,307 1 0,307 5,979 0,023


Total 1,437 23

H0 was rejected for this part orientation (Sig = 0,023).


perpendicularity between the vectors Z and X. In Table 32 the mean values and standard deviations

are listed. Figure 24 shows a boxplot. The blue area of the boxplot represents the 95% confidence

intervals for the angle between the Z and X vector. The ‘arms’ of the boxplot show the minimum

and maximum measured values.

52

Table 32: Main statistical parameters regarding influence of part orientation on 𝑍��

𝐴𝑛𝑔𝑙𝑒 𝑍�� 95% Confidence interval

N Mean [°]

Std. Deviation [°]

Std. Error [°]

Lower Bound [°]

Upper Bound [°]

Minimum [°]

Maximum [°]



Total 24 89,7158 0,24996 0,05102 89,6102 89,8213 89,29 90,20

Figure 24: Comparison of the ZX angle between different orientations

When printing in this suggested orientation, the mean value for 𝑍�� is closer to 90°, while the

standard deviation is a bit bigger. Since the differences were statistically significant, we can say that

the suggested orientation provides a better perpendicularity between the Z and X vectors.

4.8.3.4. General conclusion on perpendicularity

As seen in previous results, there is a significant difference between the respective angles XY, YZ,

and ZX. However, while examining the boxplots, we could conclude that the different angles are

not necessarily more accurate.

Since in the suggested orientations, the parts coordinate system is not parallel to the machine

coordinate system, we found it to be a good idea to compare the angles as one group.

In essence, each measured angle in the standard orientation was compared with each measured

angle in the suggested orientation.

The results in Table 33 represent the influence of this part orientation on the measured angles.

Table 33: influence of part orientation on the angles between the vectors

ANOVA


Angle Between Groups 0,161 1 0,161 2,152 0,147


Total 5,402 71



53

perpendicularity between the vectors in general. In the Table 34 the mean values and standard

deviations are listed. Figure 25 shows a boxplot. The blue area of the boxplot represents the 95%

confidence intervals for the angles. The ‘arms’ of the boxplot show the minimum and maximum

measured values.

Table 34: Main statistical parameters regarding influence of part orientation on all part angles.

Angle 95% Confidence interval

N Mean [°]

Std. Deviation [°]

Std. Error [°]

Lower Bound [°]

Upper Bound [°]

Minimum [°]

Maximum [°]



Total 72 89,9292 0,27583 0,03251 89,8644 89,9940 89,29 90,67

Figure 25: Comparison of the angles in different orientations

Figure 25 shows that the average angle, using the suggested orientation is very close to the desired

90°. The 95% certainty interval around it is quite narrow. The conclusion can be made, that the

printed angles in this suggested orientation have an accuracy of ±0,2° with a certainty of 95%.

Another way to put it is that the machine has an absolute angle accuracy of about ±0,6°.

This suggested orientation likely has a positive effect on the angle, but this can only be said with

85% certainty (Sigma ≈ 0,15).

4.8.4. Wall- and edge thickness

To determine whether or not the accuracy of the part’s wall- and edge thickness is different using

the suggested part orientations, ANOVA was used.

The wall thickness variates together with the volume ratio.

Therefor it was decided that the analysis of the measurements of the wall thickness will be done

both on the relative shrinkages [%] as well as on the absolute shrinkages [mm].

For the edge width’s, only the relative shrinkages will be analysed.

The null hypothesis H0 is that there is no influence of this part orientation on the shrinkage of wall

thickness.



54

4.8.4.1. Wall thickness in X direction



pointless.


shrinkage of the wall thickness in X-direction.

4.8.4.2. Wall thickness in Y direction

The results in Table 35 represent the influence of part orientation on the absolute value of the

measured wall thickness shrinkage in the Y direction [mm].

The results of the relative shrinkages could not be used, since the homogeneity of the data could not

be validated. (Levene’s test of equality of error variances returned a Sigma value of 0,000…)

Table 35: influence of part orientation on wall thickness shrinkage in Y direction

ANOVA


Wall Thickness in Y direction

Between Groups 0,014 1 0,014 12,902 0,002


Total 0,039 23

H0 was rejected for this part orientation, only in the test of the absolute measurements.

Meaning that we can say with 95% certainty that there is a significant influence of this part

orientation on the shrinkage of the wall thickness in Y-direction.

To further investigate the influence, a closer look is taken at the mean value of the original part

orientation, as well as the mean value for the suggested part orientation [see Table 36].

Table 36: Main statistical parameters regarding influence of part orientation on wall thickness shrinkage in Y direction

Wall thickness shrinkage in Y 95% Confidence interval

N Mean [mm]

Std. Deviation [mm]

Std. Error [mm]

Lower Bound [mm]

Upper Bound [mm]

Minimum [mm]

Maximum [mm]

Normal orientation 16 0,0163 0,02924 0,00731 0,007 0,0318 -0,03 0,07


Total 24 0,0335 0,04109 0,00839 0,0162 0,0509 -0,03 0,14

After examining these results, it can be noted that the mean deviation for the wall thickness in Y

direction is a lot bigger in the parts which were printed using the suggested orientation. Which

means that in this case, the wall thickness in Y direction is actually less accurate when using the

suggested orientation. This effect is most likely caused by remains of support structure, as can be

seen in Figure 26.

55

Figure 26: Effect of support locations on the wall thickness in Y direction

In an actual print order, the part orientation should be chosen in such a way that the support

structures are connected to the least crucial surfaces of the part, while still paying attention that the

part is sufficiently supported.

The PreForm software actually provides a number of suggested part orientations, allowing most

parts to be automatically oriented in such a way.

4.8.4.3. Wall thickness in Z direction

The results in Table 37 represent the influence of this part orientation on the wall thickness

shrinkage measured in the Z direction [%]. The results in the Table 38 represent the same data but

in an absolute measurement [mm].

Table 37: influence of part orientation on relative wall thickness shrinkage in Z direction

ANOVA


Wall Thickness in Z direction [%]

Between Groups 2,427 1 2,427 0,020 0,888

Within Groups 2633,504 22 119,705

Total 2635,931 23

Table 38: influence of part orientation on absolute wall thickness shrinkage in Z direction

ANOVA


Wall Thickness in Z direction [mm]

Between Groups 0,043 1 0,043 2,036 0,168


Total 0,506 23

56

According to the relative and absolute shrinkages, H0 couldn’t be rejected.


shrinkage of the wall thickness in Z-direction.

4.8.4.4. Edge width in X direction

The shrinkages of the edge widths were evaluated for the X-direction.

However, after processing the data, the Levene's test for homogeneity of variance made clear that

the data is statistically not usable (sigma = 0,001…).


shrinkage of the edge width in X-direction.

4.8.4.5. Edge width in Y direction

The results in Table 39 represent the influence of this part orientation on the edge width’s shrinkage


Table 39: influence of part orientation on relative edge width shrinkage in Y direction

ANOVA


Edge Width shrinkage in Y

Between Groups 2,146 1 2,146 2,346 0,140


Total 22,272 23

According to the relative shrinkages, H0 couldn’t be rejected ( Sig > 0,005).


shrinkage of the edge width in Y-direction.

4.8.4.6. Edge width in Z direction

The results in Table 40 represent the influence of this part orientation on the edge width’s shrinkage


Table 40: influence of part orientation on relative edge width shrinkage in Z direction

ANOVA


Edge Width Shrinkage in Z

Between Groups 0,003 1 0,003 0,003 0,958


Total 20,147 23

According to the relative shrinkages, H0 couldn’t be rejected (Sig > 0,005).


shrinkage of the edge width in Z-direction.

57

4.8.5. Total length of the part edges.

To determine whether or not this part orientation has a significant influence on the shrinkage of the

part edges in the different directions, ANOVA was used.

The null hypothesis H0 is that there is no influence of this part orientation on these shrinkages.



4.8.5.1. Edge length in X direction

The results in Table 41 represent the influence of this part orientation on the edge length shrinkage

measured in the X direction [%].

Table 41: influence of part orientation on relative edge length shrinkage in X direction

ANOVA


Edge Length Shrinkage in X

Between Groups 0,015 1 0,015 0,200 0,659


Total 1,620 23



shrinkage of the edge length in X-direction.

4.8.5.2. Edge length in Y direction



Table 42: influence of part orientation on relative edge length shrinkage in Y direction

ANOVA


Edge Length Shrinkage in Y

Between Groups 0,246 1 0,246 3,949 0,059


Total 1,618 23



of the edge length in Y-direction.

58

4.8.5.3. Edge length in Z direction



Table 43: influence of part orientation on relative edge length shrinkage in Z direction

ANOVA


Edge Length Shrinkage in Z

Between Groups 0,041 1 0,041 0,369 0,550


Total 2,477 23


Meaning that we couldn’t find a relationship between this part orientation and the shrinkage of the

edge length in Z-direction.

4.9. Validating the linear compensation model.

To validate the linear compensation model, a part was designed and scaled in the Z direction

according to the shrinkage compensation model as a function of VR and TR. The part was designed

in a parametrical way, allowing for easy adjustment of dimensions. This part was designed as a part

that could be printed in a real workspace environment, in contrast to the previous test part, which

was designed with a focus on a laboratory environment. In the first print file, the part was printed

twice with a low volume ratio. In the second print file, the part was printed twice with a high

volume ratio [see Figure 27]. In a first attempt, the parts were printed in a normal orientation, with

the planes perpendicular and parallel to the build platform. This attempt failed however, since the

part walls were very warped. This first attempt, did give us the conclusion that the regression model

for the wall thickness compensation is actually not valid. Since it is quite difficult to separately

scale wall thickness and total part dimensions, the decision was made to just focus on a uniform

scaling for all dimensions within the Z-direction. To avoid the problem of warpage, the part files

have then been printed using a suggested orientation [see Figure 28]. The shrinkage compensations

have been applied to the Z-axis of the printer, which is not the Z axis of the part file.

Figure 27: Validation part file, low VR (left) and high VR (right)

59

Figure 28: Suggested orientation of the regression validation print file

To estimate the shrinkage of the part in Z direction, both the regression model of the shrinkage of

the Z-vector, as well as the shrinkage of the Z edge length were used as an indicator. These are both

function of VR and TR. In an ideal situation, the models would give the same results of shrinkage

for both these indicators. This is however not the case. The decision was made to print in total four

files. For each regression model, two different print files were made, one with a low and one with a

high VR.

After the printing of the test samples, they were prepared for measuring in the optical scanner

system. The part was scanned from a number of different points of view, they were processed using

the Atos v6.0.2-6 software and exported to STL file format.

The STL files where then analysed using the GOM inspect 2017 software. On the planes and

cylinder shape, a best fitting primitive was added [see Figure 29].

Figure 29: Validating part, GOM inspect with primitives

60

4.9.1. First print file: Low volume ratio – Model Z-edge length

In the first and third print file, the dimensions are scaled along the printer’s Z-axis, using the

shrinkage compensation model based on the data obtained from the measurements of Z-edge length.

The nominal dimensions of the low volume ratio validation part are listed below:

Edge Length X-direction = 40 mm

Edge Length Y-direction = 40 mm

Edge Length Z-direction = 25 mm

Wall Thickness = Edge Thickness = 1 mm in all directions.

𝑉𝑅 = 𝑃𝑎𝑟𝑡 𝑉𝑜𝑙𝑢𝑚𝑒

𝐸𝑛𝑣𝑒𝑙𝑜𝑝𝑒 𝑉𝑜𝑙𝑢𝑚𝑒= 0,097

𝑇𝑅 = 𝑃𝑟𝑜𝑗𝑒𝑐𝑡𝑒𝑑 𝑝𝑎𝑟𝑡 𝑎𝑟𝑒𝑎 . #𝑝𝑎𝑟𝑡𝑠

𝑡𝑜𝑡𝑎𝑙 𝑏𝑢𝑖𝑙𝑑 𝑎𝑟𝑒𝑎= 0,180

𝑆ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝐸𝐿 𝑍 [%] = 0,78 − 2,283. 𝑉𝑅 − 0,92 . 𝑇𝑅 + 2,944 . 𝑉𝑅 . 𝑇𝑅 = 0,444%

To compensate this expected shrinkage, the part was scaled along the printer-Z-axis using a factor

0,99556.

4.9.2. Second print file: Low volume ratio – Model Z-vector

In the second and fourth print file, the dimensions are scaled along the printer’s Z-axis, using the

shrinkage compensation model based on the data obtained from the measurements of Z vectors.

𝑆ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑍 𝑣𝑒𝑐𝑡𝑜𝑟 [%] = −0,808 + 1,585 . 𝑉𝑅 + 1,77 . 𝑇𝑅 − 4,182 . 𝑉𝑅. 𝑇𝑅 = −0,409%


1,00409.

4.9.3. Third print file: High volume ratio – Model Z-edge length.

The nominal dimensions of the high volume ratio validation part are listed below:

Edge Length X-direction = 45 mm

Edge Length Y-direction = 45 mm

Edge Length Z-direction = 25 mm

Wall Thickness = Edge Thickness = 5 mm in all directions

𝑉𝑅 = 𝑃𝑎𝑟𝑡 𝑉𝑜𝑙𝑢𝑚𝑒

𝐸𝑛𝑣𝑒𝑙𝑜𝑝𝑒 𝑉𝑜𝑙𝑢𝑚𝑒= 0,270

𝑇𝑅 = 𝑃𝑟𝑜𝑗𝑒𝑐𝑡𝑒𝑑 𝑝𝑎𝑟𝑡 𝑎𝑟𝑒𝑎 . #𝑝𝑎𝑟𝑡𝑠

𝑡𝑜𝑡𝑎𝑙 𝑏𝑢𝑖𝑙𝑑 𝑎𝑟𝑒𝑎= 0,227

𝑆ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝐸𝐿 𝑍 [%] = 0,78 − 2,283. 𝑉𝑅 − 0,92 . 𝑇𝑅 + 2,944 . 𝑉𝑅 . 𝑇𝑅 = 0,135%


0,99865.

61

4.9.4. Fourth print file: High volume ratio – Model Z-vector

𝑆ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑍 𝑣𝑒𝑐𝑡𝑜𝑟 [%] = −0,808 + 1,585 . 𝑉𝑅 + 1,77 . 𝑇𝑅 − 4,182 . 𝑉𝑅. 𝑇𝑅 = −0,234%


1,00234.

4.9.5. Measurement results of the printed validation part

Table 44 shows the results obtained from the scanning of the parts. Also for informative reasons,

the wall thickness in Z direction, as well as the diameters of the small holes were measured using a

micro meter. It must be noted that the measurements of the wall thickness couldn’t be done in an

accurate way, since there were support structure remains which couldn’t be removed in a proper

way. The Shrinkage of the hole diameters shows a trend where a higher VR tends to cause more

shrinkage effects.

Table 44: Measurement results of validating part

Measurement results

Print VR EL X [mm] EL Y [mm]

Depth Z [mm] WT Z [mm]

Small Hole Diameter [mm]

Big hole Diameter [mm]

1.1 0,097 40,720 40,370 24,118 1,38 5,48 38,64

1.2 0,097 40,449 40,551 24,041 1,34 5,50 38,69

2.1 0,097 40,419 40,620 24,179 1,29 5,45 38,61

2.2 0,097 40,381 40,514 24,079 1,32 5,46 38,61

3.1 0,270 45,531 45,450 19,976 5,24 5,46 38,53

3.2 0,270 45,259 45,358 20,082 5,27 5,48 38,56

4.1 0,270 45,649 45,546 20,042 5,22 5,44 38,56

4.2 0,270 45,310 45,349 20,056 5,25 5,46 38,51

Calculated shrinkage averages

Shrinkage EL X [%]

Shrinkage EL Y [%]

Shrinkage Depth Z [%]

Shrinkage WT Z [%]

Shrinkage small hole diameter [%]

Shrinkage big hole diameter [%]

1 0,097 1,461 1,151 0,331 36,00 -0,182 0,168

2 0,097 1,000 1,418 0,523 30,50 -0,818 0,026

3 0,270 0,878 0,898 0,145 5,05 -0,591 -0,142

4 0,270 1,063 0,994 0,245 4,70 -1,000 -0,168

Table 45 shows the results of the parts printed using the compensation model based on Z-edge

length shrinkage. Using this data we observed that on average the deviation of the parts is actually

bigger than the shrinkages obtained in the original test parts [see Figure 13]. However, Table 46

shows that this conclusion is not statistically significant, since the experiment size was limited.

More testing must be done to acquire a solid conclusion about this model.

62

Table 45: Descriptive information of shrinkage in Z direction of model based on edge length Z shrinkage

shrinkage in Z 95% Confidence interval

N Mean [mm]

Std. Deviation [mm]

Std. Error [mm]

Lower Bound [mm]

Upper Bound [mm]

Minimum [mm]

Maximum [mm]

Normal print 16 0,1141 0,19126 0,04782 0,0121 0,2160 -0,15 0,59

Corrected print Edge Length model 4 0,2383 0,27493 0,13746 -0,1992 0,6757 0,12 0,49

Total 20 0,1389 0,20835 0,04659 0,0414 0,2364 -0,15 0,59

Table 46: ANOVA analysis of shrinkage in Z direction of the model based on edge length Z shrinkage

ANOVA


shrinkage in Z Between Groups 0,049 1 0,049 1,146 0,299


Total 0,825 19

Table 47 shows the results of the parts printed using the compensation model based on Z vector

shrinkage. Using this data, we see that on average, the deviation of the parts is quite a lot bigger

than the shrinkages obtained in the original test parts [see Figure 13]. Table 48 shows that this

conclusion is statistically significant.

Table 47: Descriptive information of shrinkage in Z direction of model based on Z vector shrinkage

shrinkage in Z 95% Confidence interval

N Mean [mm]

Std. Deviation [mm]

Std. Error [mm]

Lower Bound [mm]

Upper Bound [mm]

Minimum [mm]

Maximum [mm]

Normal print 16 0,1141 0,19126 0,04782 0,0121 0,2160 -0,15 0,59

Corrected print Z-vector length model 4 0,3838 0,22682 0,11341 0,0228 0,7447 0,21 0,72

Total 20 0,1680 0,22193 0,04962 0,0641 0,2719 -0,15 0,72

Table 48: ANOVA analysis of shrinkage in Z direction of the model based on Z vector shrinkage

ANOVA


shrinkage in Z Between Groups 0,049 1 0,233 5,959 0,025


Total 0,936 19

Since the shrinkage compensation based on vector length is done in the opposite direction of the

shrinkage compensation based on Z-edge length shrinkage, and this shrinkage correction makes the

results with certainty less accurate, this information leads us to believe that the model on Z-edge

length shrinkage will make more accurate parts. Once again, more testing must be done to prove

this conclusion.

63

4.9.6. Discussion on shrinkage compensation models

The models for the Z direction shrinkage, show different results. The results from the Z edge length

measurements suggest that the part tends to be larger than in the CAD file.

The results from the Z vectors suggest that the Z vector tends to be shorter than in the CAD file.

This can be caused by the remains of support structure, which can still be present in the XY bottom

plane. The presence of support structure, is a good argument to use the vector lengths to calculate

shrinkage effects, since they are based on a scan of a surface without support structures.

However, it might be good to open a discussion on another possible effect causing this strange

effect. Figure 30 shows this possibility, where in black the CAD model is shown, and in red the

warped part is sketched.

Figure 30: Warpage causing shorter Z vector while causing longer Z edge length

A new variable Δshrinkage is defined as following:

∆𝑠ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑍 [%] = 𝑠ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝐸𝑑𝑔𝑒 𝐿𝑒𝑛𝑔𝑡ℎ 𝑍 [%] − 𝑠ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑣𝑒𝑐𝑡𝑜𝑟 𝑍[%]

To investigate this effects, the correlation coefficients were calculated in order to see if there is a

relationship between the geometrical accuracy (angular accuracy) and the difference in shrinkage

results (Δshrinkage). This experiment is conducted on the parts produced by the first 4 print files.

The Pearson Correlation coefficiënt is equal to 1 or -1 for perfect correlations. A significance of

95% (<0,05) has to be achieved in order to accept the correlation. In Table 49 the results of the

statistical analysis can be seen. The conclusion was made that there is no significant correlation

between angular accuracy and Δshrinkage.

Table 49: Correlation Coefficients between Δshrinkage Z and the angular accuracy

Correlations

ΔShrinkage Z 𝐴𝑛𝑔𝑙𝑒 𝑋�� 𝐴𝑛𝑔𝑙𝑒 𝑌�� 𝐴𝑛𝑔𝑙𝑒 𝑍��

ΔShrinkage Z Pearson Correlation 1 -0,155 -0,232 0,185

Sig. (2-tailed) 0,566 0,388 0,493

Sum of Squares and Cross-products 2,137 -0,171 -0,199 0,199

Covariance 0,142 -0,011 -0,013 0,013

N 16 16 16 16

64

4.10. Evaluating the estimated printing time

For each print job that was done during this project, the print time was estimated by the PreForm

software. The actual print times were logged, and compared with the estimated times, and the

results can be seen in Table 50. The printing speed was calculated. The gross printing speed

represents the printing speed of all printed material (= part + supports volume). The net printing

speed represents only the speed of the useful printed material ( = part volume).

Table 50: Estimated and measured printing times

Part + support Volume [cm³]

Part Volume [cm³] PRINTING TIMES

PRINTING SPEED [cm³/h]

Estimated Measured Gross Net

Low TR, Low VR 37,45 19,20 3h35 3h57 9,48 4,86

High TR, Low VR 112,12 57,59 8h34 8h31 13,16 6,76

Low TR, High VR 91,91 76,83 6h17 6h14 14,71 12,30

High TR, High VR 273,89 230,50 15h12 14h45 18,56 15,62

Suggested Orientation, Low VR

61,21

25,60 5h39 8h14*

7,43

3,11

Suggested Orientation, High VR

138,72

102,45 9h11 9h00

15,43

11,39

Validation print file 1 28,00 13,70 3h13 3h23 8,27 4,05




*print was paused for an unknown time due to empty resin cartridge, data was not used.

Sometimes the actual print time is a bit longer than the estimated, but sometimes it can even be

shorter than expected. No print time deviations higher than 27 minutes have been recorded during

this dissertation project. Altogether, it can be said that the print time estimation is quite good.

4.11. Influence of VR and TR on printing speed

To determine whether or not VR and TR have a significant influence on the printing speed,

ANOVA was used.

The null hypothesis H0 is that there is no influence of the parameters on the printing speed.



The data from Table 50 was used for this, with exclusion of the print time which took 8hours and 14

minutes, due to the unforeseen interruption of the printing process.

The analysis was done both for the net printing speed

Table 51] as well as for the gross printing speed [Influence of VR and TR on the gross printing speed Table 52], the gross printing speed includes also the printed volume of the support structure.

The support structure that was used was generated automatically by the PreForm software.

65

4.11.1.Influence of VR and TR on the net printing speed

Table 51: Influence of VR, TR, and VR*TR on net printing speed [cm³/h]


Dependant value: Net Printing speed


Model 819,029 7 117,004 13765,188 0,000

VR 66,422 1 7814,412 7814,412 0,000

TR 6,812 1 6,812 801,424 0,001

VR * TR 0,504 1 0,504 59,306 0,016

Error 0,017 2 0,009

Total 819,046 9 Using this results, we observed that this model is significant (Sig = 0,000…).

H0 was rejected for VR, as well as TR and for the combination of VR*TR.


Meaning that a relationship between the parameters and the net printing speed can be found.

In order to approximate the effects of the parameters on the net printing speed, a linear regression

model was used, which resulted in the following equation:

𝑁𝑒𝑡 𝑝𝑟𝑖𝑛𝑡𝑖𝑛𝑔 𝑠𝑝𝑒𝑒𝑑 [cm3

h] = 0,57 + 27,20 . 𝑉𝑅 + 6,64 . 𝑇𝑅 + 0,13 . 𝑉𝑅 . 𝑇𝑅

Significance of 0,001

Figure 31: Net printing speed in function of VR and TR

66

To show more insight in the influence of TR on the printing speed, the relationship is shown in a 2-

dimensional form, with a constant VR of 0,25 [see Figure 33] and a constant VR of 0,70 [see Figure

34].


h] = 7,37 + 6,67 . 𝑇𝑅 𝑤𝑖𝑡ℎ 𝑉𝑅 = 0,25


h] = 19,61 + 6,73 . 𝑇𝑅 𝑤𝑖𝑡ℎ 𝑉𝑅 = 0,70

4.11.2.Influence of VR and TR on the gross printing speed

Table 52: Influence of VR, TR, and VR*TR on gross printing speed [cm³/h]


Dependant value: Gross Printing speed


Model 1534,160 7 219,166 3764,116 0,000

VR 28,249 1 28,249 485,173 0,002

TR 14,175 1 14,175 243,456 0,004

VR * TR 0,007 1 0,007 0,124 0,758

Error 0,116 2 0,058

Total 1534,276 9

Using this results, we observed that this model is significant (Sig = 0,000…).

H0 was rejected for VR, as well as TR and for the combination of VR*TR.


Meaning that a relationship between the parameters and the gross printing speed can be found.

In order to approximate the effects of the parameters on the gross printing speed, a linear regression

model was used, which resulted in the following equation:

𝐺𝑟𝑜𝑠𝑠 𝑝𝑟𝑖𝑛𝑡𝑖𝑛𝑔 𝑠𝑝𝑒𝑒𝑑 [cm3

h] = 4,42 + 23,00 . 𝑉𝑅 + 11,60 . 𝑇𝑅 − 9,854 . 𝑉𝑅 . 𝑇𝑅

Significance of 0,001

67

Figure 32: Gross printing speed in function of VR and TR

To show more insight in the influence of TR on the printing speed, the diagram is shown in a 2

dimensional form, with a constant VR of 0,25 [see Figure 35 ] and a constant VR of 0,70 [see

Figure 36].


h] = 10,17 + 9,14 . 𝑇𝑅 𝑤𝑖𝑡ℎ 𝑉𝑅 = 0,25


h] = 20,52 + 4,70 . 𝑇𝑅 𝑤𝑖𝑡ℎ 𝑉𝑅 = 0,70

Figure 33: Net printing speed in function of Tray Ratio, with VR = 0,25

68

Figure 34: Net printing speed in function of Tray Ratio, with VR = 0,70

Figure 35: Gross printing speed in function of Tray Ratio, with VR = 0,25

Figure 36: Gross printing speed in function of Tray Ratio, with VR = 0,70

69

General Conclusion

The experiment proved that the complexity of parts plays an important role in determining

shrinkage and accuracy, as well as machine speed. In this dissertation, it was shown with high

certainty, that the parameters of VR and TR have a significant influence on the shrinkage effects in

the Z direction. Also, the parameters appear to have an effect on the shrinkage of spheres in the YZ

plane (spheres Y1 and Y2).

No real conclusions could be made about the influence in the X and Y directions because we

weren’t able to discard the present shrinkage compensation.

Overall it can be concluded that the behaviour of the shrinkages is rather complex.

We approached the problem of accuracy which was too low for our expectations and found how to

improve this accuracy. We can assume that if we could include our model into the compensation

software of the machine, the accuracy would become better.

Due to limitations in experiment size, as well as the fact that we weren’t able to discard the already

present shrinkage corrections, we weren’t able to really use and evaluate the model in a proper way.

We assumed that the positioning of the parts will have no significant influence on the dimensional

accuracy. However, we found that there is a minor influence of part position on the shrinkage

behaviour in X and Y directions, as well as on the angle between Z and X vectors, as can be seen in

addendum A.

The models that were made for the specific corrections of wall thickness in Z direction, were not

reliable due to the presence of support structure remains. In practice, it’s also not really functional

to apply a variating scale, which would have to depend on whether a part of a body is considered a

wall or a part edge.

In the evaluation of the angular accuracy, it was found that the machine’s angular accuracy is very

high, with an even slightly better accuracy when using the suggested orientations.

The effects of warpage were difficult to quantify and include in the data. It was however quite clear

in the validation part, that using the suggested orientations, the warpage of parts was a lot smaller.

The printing speed was evaluated and a relationship between VR and TR and the print speed has

been described. The speed evaluation was done both with and without taking the support structure

into account, allowing the results to be compared to other additive manufacturing techniques which

use or do not use support structures.

70

References

Brajlih, T., Valentan, B., Balic, J., and Drstvensek, I. (2010). Speed and accuracy evaluation of additive manufacturing machines. Rapid Prototyping Journal,[online], Volume 17 (1), pp. 64-75. Available at: https://www.researchgate.net/publication/235313830_ Speed_and_accuracy_evaluation_of_additive_manufacturing_machines [Accessed 15 March 2018]

Brajlih, T., Drstvensek, I., Valentan, B., Balic, J. (2006). Improving the accuracy of rapid prototyping procedures by genetic programming. In: 5th International DAAAM Baltic Conference. [online] Tallinn: International OCSCO World Pres, pp. 101-106. Available at: https://www.researchgate.net/publication/41720000_Optimizing_scale_ factors_of_the_PolyJet_rapid_prototyping_procedure_by_genetic_programming [Accessed 13 March 2018] Brajlih, T., Valentan, B., Balic, J., and Drstvensek, I. (2010). Possibilities of Using Three-Dimensional Optical Scanning in Complex Geometrical Inspection. Strojniski Vestnik, [online] Volume 57 (11), pp. 826-833. Available at: http://www.sv-jme.eu/article/possibilities-of-using- three-dimensional-optical-scanning-in-complex-geometrical-inspection/ [Accessed 13 March 2018] Cajal, C., Santolaria, J., Velazquez, S., Aquado, J. Albajez. (2013). Vollumetric error compensation technique for 3D printers. In: The Manufacturing Engineering Society International Conference, MESIC. [online] Zaragoza: Procedia Engineering, pp 642-649. Available at: https://www.sciencedirect.com/science/article/pii/S1877705813014896 [Accessed 19 March 2018] Diverse members of the formlabs forum (2018). General threads on Form 2 printing experiences, Consulted during March, April and May 2018, via https://forum.formlabs.com/ Formlabs (2015). Form 2 Tech Specs. [online] Form 2 Tech Specs. Available at: https://formlabs.com/3d-printers/tech-specs/ [Accessed 20 March 2018]. [Figure 1 – 7 ] Formlabs. (2018), Form 2 3D Glossary Available at: https://support.formlabs.com/hc/en-us/articles/115000307950# [Accessed 26 March 2018] Pelovitz J., Formlabs. (2018). Supports, Orientation, and Lasers - Understanding SLA 3D Printing. [online] Supports, Orientation, and Lasers - Understanding SLA 3D Printing. Available at: https://formlabs.com/understanding-sla-3d-printing/ [Accessed 21 march 2018] Yankov, E., Nikolova, P. (2017). “Comparison of the Accuracy of 3D Printed Prototypes Using the Stereolithography (SLA) Method with Digital CAD Models”. In:

Matec Web Conf. [online] EDP Science, pp 1-6.

Available at: https://www.matec-conferences.org/articles/matecconf/abs/ 2017/51/matecconf_mtem2017_02014/matecconf_mtem2017_02014.html [Accessed 7 March 2018]. Zguris Z., Formlabs. (2018). How Mechanical Properties of Stereolithography 3D Prints are Affected By UV Curing. [pdf] Formlabs, pp 1-11. Available at: https://formlabs.com/media/upload/How-Mechanical-Properties-of-SLA-3D-Prints-Are-Affected-by-UV-Curing.pdf [Accessed 7 March 2018].

https://www.sciencedirect.com/science/article/pii/S1877705813014896

https://forum.formlabs.com/

https://formlabs.com/3d-printers/tech-specs/

https://support.formlabs.com/hc/en-us/articles/115000307950

https://formlabs.com/understanding-sla-3d-printing/

https://formlabs.com/media/upload/How-Mechanical-Properties-of-SLA-3D-Prints-Are-Affected-by-UV-Curing.pdf

https://formlabs.com/media/upload/How-Mechanical-Properties-of-SLA-3D-Prints-Are-Affected-by-UV-Curing.pdf

Addendum A

71

Addendum A: Influence of the positioning of the part

The influence of the positioning of parts was only examined for the first 4 print files.

Some influences of the positioning of the part were found. However, since the projects limitations

and the fact that these influences were rather small, it was discarded these influences.

For informational reasons, the results of these influences are shown in this addendum.

Each part of the first print files was printed on a specific location on the build platform. The

locations on the build platform can be seen in Figure 9.

In this chapter, the goal was to determine if these positions have any influence on the shrinkages.

The influence was checked on: - The shrinkage of the vectors between the sphere centres

- The perpendicularity between those vectors

- The sphere diameter (shrinkages)

- The wall thickness shrinkage of the parts

- The edge width shrinkages of the parts

- The edge length shrinkages of the parts

It should be noted that the measurements for edge width and wall thickness are the least accurate

due to remaining support structures, thus the results of these measurements should be viewed only

as an indication.

The data was compared separately for the position on the platform in X and Y direction.

For the location of the X and Y coordinates, the middle point of the top view was chosen.

The shrinkages which have a relationship with only the position in X are shown in the table below.

ANOVA


Angle 𝒁�� Between Groups 0,347 2 0,173 11,328 0,001


Total 0,546 15 Sphere XY plane Between Groups 0,078 2 0,039 4,195 0,039


Total 0,199 15 Edge length Y direction [%] Between Groups 0,501 2 0,251 7,374 0,007


Total 0,943 15

Addendum A

72

In order to approximate the effects of the X-position on the shrinkages, a linear regression model

was used, resulting in the following equations, with X = the position of the middle point of the part

on the X-axis [mm]:

𝑍�� = 89,387 + 0,003. 𝑋 with a significance of 0,000…

𝑆ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑠𝑝ℎ𝑒𝑟𝑒 𝑖𝑛 𝑋𝑌 𝑝𝑙𝑎𝑛𝑒 [%] = −0,316 − 0,007. 𝑋 with a significance of 0,126.

Addendum A

73

𝑆ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑒𝑑𝑔𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑌 [%] = 0,190 − 0,002. 𝑋with a significance of 0,283.

The shrinkage which has a relationship with the position in Y are shown in the table below.

ANOVA

Sum of Squares df

Mean square F Sig.

Shrinkage Y vector Between Groups 1,514 2 0,757 8,651 0,004


Total 2,651 15

In order to approximate the effects of the Y-position on the shrinkages, a linear regression model

was used, resulting in the following equations, with Y = the middle point of the part on the Y-axis

[mm]:

Addendum A

74

𝑆ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑣𝑒𝑐𝑡𝑜𝑟 𝑖𝑛 𝑌 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 [%] = 0,193 − 0,006. 𝑌 with a significance of 0,005.

The shrinkage which has a relationship with both the position in X and Y is shown in the table

below.

ANOVA

Sum of Squares df

Mean square F Sig.

Edge width X [%] Between Groups ,1170 2 0,585 4,744 0,028


Total 2,772 15

Edge Length X [%] Between Groups 0,633 2 0,317 5,889 0,015


Total 1,333 15

Addendum A

75

𝑆ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑒𝑑𝑔𝑒 𝑤𝑖𝑑𝑡ℎ 𝑖𝑛 𝑋 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 [%] = 0,166 − 0,002. 𝑋 − 0,002. 𝑌 significance of 0,548.

𝑆ℎ𝑟𝑖𝑛𝑘𝑎𝑔𝑒 𝑒𝑑𝑔𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑖𝑛 𝑋 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 [%] = 0,113 − 0,002. 𝑋 + 0,001. 𝑌 significance of 0,283.

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