accuracy and manufacturing speed improvement of the form 25 disposition of master thesis on 2nd...
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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 DrstvenΕ‘ek Signature:
Co-mentor:
Assist. Prof. Dr. TomaΕΎ 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 DrstvenΕ‘ek 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
Β΅m. 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 Formlabsβ 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 partβs 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 β Model Z-edge length ..................................... 60
4.9.2. Second print file: Low volume ratio β Model Z-vector ......................................... 60
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4.9.3. Third print file: High volume ratio β Model Z-edge length. ................................. 60
4.9.4. Fourth print file: High volume ratio β 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 mirrorΒ² ................................................................................................. 18 Figure 5: Build platform with threaded rod ....................................................................................... 19 Figure 6: Build platform and machine axes positionΒ³ ....................................................................... 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 ππ ....................... 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 ππ ....................... 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 ππ ....................... 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 Ξshrinkage 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 [cmΒ³/h] ..................................... 65 Table 52: Influence of VR, TR, and VR*TR on gross printing speed [cmΒ³/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 masterβs 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 Iβd 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.
Iβd 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 DrstvenΕ‘ek 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. TomaΕΎ 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 Iβve 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 masterβs 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 masterβs
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 masterβs 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 βlevelsense boardβ. [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 wonβt
solidify stuck to the silicone layer.
Figure 3: Resin tank with wiper2 Figure 4: galvanometers and mirrorΒ²
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 positionΒ³
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 Β΅m, 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 Formlabsβ 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: βthe newer
the print tray is, the more accurate parts will be producedβ.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 doesnβt 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 Β΅m 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 14Β°.
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 60Β°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
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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).
βVolume ratio is defined as a ratio between partβs volume and partsβ envelope volume. It takes the
partβs 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 partβs relative size compared
to the machineβs workspace. It is defined as a ratio between partβs envelope bottom area and the
area of the machineβs work trayβ (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 Leveneβs 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 Β΅m, 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:
π·ππ π‘ππππ[mm] = β(πππβπππ2β πππβπππ1
)2 + (πππβπππ2β πππβπππ1
)2 + (πππβπππ2β πππβπππ1
)2
Table 1: Vector lengths and sphere diameters.
Position [x;y] VR TR
Dist X [mm]
Dist Y [mm]
Dist Z [mm]
ΓΈ X1 [mm]
ΓΈ X2 [mm]
ΓΈ Y1 [mm]
ΓΈ Y2 [mm]
ΓΈ Z1 [mm]
ΓΈ 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:
πβπππππππ π [%] = (πππππππ πππ π‘ππππ π β ππππ π’πππ πππ π‘ππππ π
πππππππ πππ π‘ππππ π) . 100%
πβπππππππ π [%] = (πππππππ πππ π‘ππππ π β ππππ π’πππ πππ π‘ππππ π
πππππππ πππ π‘ππππ π) . 100%
πβπππππππ π [%] = (πππππππ πππ π‘ππππ π β ππππ π’πππ πππ π‘ππππ π
πππππππ πππ π‘ππππ π) . 100%
The average sphere diameters were determined using following equations:
ΓΈ π ππ£π [mm] =ΓΈ π1 + ΓΈ π2
2
ΓΈ π ππ£π [mm] =ΓΈ π1 + ΓΈ π2
2
ΓΈ π ππ£π [mm] =ΓΈ π1 + ΓΈ π2
2
The value for shrinkage [%] and the average sphere diameter are shown in Table 2.
30
Table 2: Vector shrinkages and average sphere diameters
Position [x;y] VR TR
%shrinkage X
%Shrinkage Y
%shrinkage Z
ΓΈ X avg [mm]
ΓΈ Y avg [mm]
ΓΈ 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
Suggested Orientation
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.
π£πππ‘ππ οΏ½οΏ½ = π πβπππ ππππ‘ππ π2 β π πβπππ ππππ‘ππ π1
π£πππ‘ππ οΏ½οΏ½ = π πβπππ ππππ‘ππ π2 β π πβπππ ππππ‘ππ π1
π£πππ‘ππ οΏ½οΏ½ = π πβπππ ππππ‘ππ π2 β π πβπππ ππππ‘ππ π1
31
ποΏ½οΏ½ = ππΆππ (ππ₯ . ππ₯ + ππ¦. ππ¦ + ππ§ . ππ§
|π| . |π|) = ππΆππ (
π . π
|π| . |π|)
ποΏ½οΏ½ = ππΆππ (ππ₯ . ππ₯ + ππ¦. ππ¦ + ππ§ . ππ§
|π| . |π|) = ππΆππ (
π . π
|π| . |π|)
ποΏ½οΏ½ = ππΆππ (ππ₯ . ππ₯ + ππ¦. ππ¦ + ππ§ . ππ§
|π| . |π|) = ππΆππ (
π . π
|π| . |π|)
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 ποΏ½οΏ½ [Β°] ποΏ½οΏ½ [Β°] ποΏ½οΏ½ [Β°]
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
Suggested Orientation
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.
π·ππ£πππ‘πππ ππ π [mm] = ππππ π’πππ ππππππ πππ π β πππππππ ππππππ πππ π
π·ππ£πππ‘πππ ππ π [mm] = ππππ π’πππ ππππππ πππ π β πππππππ ππππππ πππ π
π·ππ£πππ‘πππ ππ π [mm] = ππππ π’πππ ππππππ πππ π β πππππππ ππππππ πππ π 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
Suggested Orientation
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
π·ππ£πππ‘πππ ππ π [%] = (π·ππ£πππ‘πππ ππ π
πππππππ πππ π‘ππππ π) . 100%
π·ππ£πππ‘πππ ππ π [%] = (π·ππ£πππ‘πππ ππ π
πππππππ πππ π‘ππππ π) . 100%
π·ππ£πππ‘πππ ππ π [%] = (π·ππ£πππ‘πππ ππ π
πππππππ πππ π‘ππππ π) . 100%
Table 5: Relative wall thickness (WT) and edge thickness (ET) deviations
Position [x;y] VR TR
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
Suggested Orientation
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
Position [x;y] VR TR
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
Suggested Orientation
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 couldnβt 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
Test of between-subject effects
Dependant value: Shrinkage of Y vector
Source Type III sum of Squares df
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).
H0 couldnβt 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 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
Test of between-subject effects
Dependant value: Shrinkage of Z vector
Source Type III sum of Squares df
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.
πβπππππππ π = β0,808 + 1,585 . ππ + 1,77 . ππ β 4,182 . ππ . ππ
Since the parameter VR is not statistically relevant, this equation could be simplified to the
following.
πβπππππππ π = β0,412 + 1,119 . ππ β 1,579 . ππ . ππ
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.
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.
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
Test of between-subject effects
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 = 0,000β¦).
H0 couldnβt be rejected for any of the parameters (Sig > 0,05 for all parameters).
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 results in Table 11 represent the influence of VR, TR and VR*TR on the sphere diameters in
the YZ plane (spheres Y1 and Y2).
Table 11: Influence of VR, TR, and VR*TR on sphere size shrinkage in the YZ plane
Test of between-subject effects
Dependant value: Sphere size in YZ plane
Source Type III sum of Squares df Mean square F Sig.
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 = 0,000β¦).
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.
ππβπππ π ππ§π ππ = 14,747 + 0,278 . ππ + 0,146 . ππ β 0,002 . ππ . ππ
Since the combined effect of the parameters VR and TR is not statistically relevant, this equation
could be simplified to the following.
ππβπππ π ππ§π ππ = 14,747 + 0,277 . ππ + 0,146 . ππ
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.
ππβπππ π βπππππππ ππ [%] = β1,692 + 1,88 . ππ + 0,987 . ππ β 0,058 . ππ . ππ
Or as could be written down in the simplified version without the combined effect of VR.TR:
ππβπππ π βπππππππ ππ [%] = β1,684 + 1,85 . ππ + 0,972 . ππ 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 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 results in Table 12 represent the influence of VR, TR and VR*TR on the sphere diameters in
the XY plane (spheres Z1 and Z2).
Table 12: Influence of VR, TR, and VR*TR on sphere size shrinkage in the XY plane
Test of between-subject effects
Dependant value: Sphere size in XY plane
Source Type III sum of Squares df Mean square F Sig.
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
Using this results, we observed that the model is definitely significant (Sig = 0,000β¦).
H0 couldnβt 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 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.
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.
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
Test of between-subject effects
Dependant value: π΄ππππ ποΏ½οΏ½
Source Type III sum of Squares df
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
Using this results, we observed that the model is definitely significant (Sig = 0,000β¦).
H0 couldnβt 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
perpendicularity between the vectors X and Y.
4.7.3.2. Angle between Y and Z vectors
The results in Table 14 represent the influence of VR, TR and VR*TR on the measured angle
between the Y and Z vectors. Table 14: Influence of VR, TR, and VR*TR on the angle between Y and Z vectors
Test of between-subject effects
Dependant value: π΄ππππ ποΏ½οΏ½
Source Type III sum of Squares df
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
Using this results, we observed that the model is definitely significant (Sig = 0,000β¦).
H0 couldnβt be rejected for any of the parameters (Sig > 0,05 for all parameters).
41
Meaning that we cannot say that there is a significant influence of the parameters on the
perpendicularity between the vectors Y and Z.
4.7.3.3. Angle between Z and X vector
The results in Table 15 represent the influence of VR, TR and VR*TR on the measured angle
between the Z and X vectors.
Table 15: Influence of VR, TR, and VR*TR on the angle between Z and X vectors
Test of between-subject effects
Dependant value: π΄ππππ ποΏ½οΏ½
Source Type III sum of Squares df
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
Using this results, we observed that the model is definitely significant (Sig = 0,000β¦).
H0 couldnβt 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
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.
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.
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
Test of between-subject effects
Dependant value: Wall thickness in X [%]
Source Type III sum of Squares df
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
Test of between-subject effects
Dependant value: Wall thickness in X [mm]
Source Type III sum of Squares df Mean square F Sig.
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. (Leveneβs 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
Test of between-subject effects
Dependant value: Wall thickness in Y [mm]
Source Type III sum of Squares df Mean square F Sig.
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
Test of between-subject effects
Dependant value: Wall thickness in Z [%]
Source Type III sum of Squares df Mean square F Sig.
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
Test of between-subject effects
Dependant value: Wall thickness in Z [mm]
Source Type III sum of Squares df Mean square F Sig.
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 = 0,000β¦).
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 0,000β¦
A positive number of shrinkage corresponds with an increase in dimension.
ππππ π‘βππππππ π π βπππππππ ππ π [%] = 44,816 β 113,81 . ππ β 33,011 . ππ + 102,755 . ππ . ππ
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.
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.
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
Test of between-subject effects
Dependant value: Edge Length in X [%]
Source Type III sum of Squares df
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).
H0 couldnβt 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
of the edge length in X-direction.
4.7.5.2. Edge length in Y direction
The results in Table 22 represent the influence of VR, TR and VR*TR on the edge length shrinkage
measured in the Y direction [%].
Table 22: Influence of VR, TR, and VR*TR on relative edge length shrinkage in Y direction
Test of between-subject effects
Dependant value: Edge Length in Y [%]
Source Type III sum of Squares df
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).
H0 couldnβt 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
of the edge length in Y-direction.
4.7.5.3. Edge length in Z direction
The results in Table 23 represent the influence of VR, TR and VR*TR on the edge length shrinkage
measured in the Z direction [%].
Table 23: Influence of VR, TR, and VR*TR on relative edge length shrinkage in Z direction
Test of between-subject effects
Dependant value: Edge Length in Z [%]
Source Type III sum of Squares df
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 = 0,000β¦).
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:
πβπππππππ ππ πΈπππ πππππ‘β π [%] = 0,78 β 2,283. ππ β 0,92 . ππ + 2,944 . ππ . ππ
Since the effect of the parameter TR is not statistically relevant, this equation could be simplified to
the following form.
πβπππππππ ππ πΈπππ πππππ‘β π [%] = 0,307 β 0,893. ππ + 0,237 . ππ . ππ
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 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.
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.
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 (Leveneβs test; sigma = 0,001β¦). 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
data could not be ensured (Leveneβs test; sigma = 0,004β¦). 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 Y-direction.
48
4.8.1.3. Shrinkage in Z direction
The results of the statistical analysis, showed that the homogeneity of the variance of the collected
data could not be ensured (Leveneβs test; sigma = 0,007β¦). 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 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.
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.
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 couldnβt 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
Sum of Squares df Mean square F Sig.
Sphere size in YZ plane
Between Groups 0,389 1 0,389 1,429 0,245
Within Groups 5,984 22 0,272
Total 6,373 23
H0 couldnβt 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 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
Sum of Squares df Mean square F Sig.
Sphere size in XY plane
Between Groups 0,539 1 0,539 3,301 0,083
Within Groups 3,583 22 0,163
Total 4,121 23
H0 couldnβt 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 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.
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.
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
Sum of Squares df Mean square F Sig.
π¨ππππ πΏοΏ½οΏ½ Between Groups 0,387 1 0,387 11,733 0,002
Within Groups 0,726 22 0,033
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 βarmsβ of the boxplot show the minimum
and maximum measured values.
50
Table 28: Main statistical parameters regarding influence of part orientation on ποΏ½οΏ½
π΄ππππ ποΏ½οΏ½ 95% Confidence interval
N Mean [Β°] Std. Deviation [Β°]
Std. Error [Β°]
Lower Bound [Β°]
Upper Bound [Β°]
Minimum [Β°]
Maximum [Β°]
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 ποΏ½οΏ½ is closer to 90Β°, 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 results in Table 29 represent the influence of part orientation on the measured angle between
the Y and Z vectors.
Table 29: influence of part orientation on the angle between the Y and Z vectors
ANOVA
Sum of Squares df Mean square F Sig.
π¨ππππ ποΏ½οΏ½
Between Groups 0,583 1 0,583 21,537 0,000
Within Groups 0,595 22 0,027
Total 1,178 23
H0 was rejected for this part orientation (Sig = 0,000β¦).
Meaning that we can say that there is a significant influence of this part orientation on the
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 βarmsβ of the boxplot show the
minimum and maximum measured values.
51
Table 30: Main statistical parameters regarding influence of part orientation on ποΏ½οΏ½
π¨ππππ ποΏ½οΏ½ 95% Confidence interval
N Mean [Β°]
Std. Deviation [Β°]
Std. Error [Β°]
Lower Bound [Β°]
Upper Bound [Β°]
Minimum [Β°]
Maximum [Β°]
Normal orientation 16 89,8992 0,15183 0,03796 89,8183 89,9801 89,74 90,28
Suggested orientation 8 90,2298 0,18878 0,06675 90,0719 90,3876 89,99 90,55
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 ποΏ½οΏ½ is further away from 90Β°, 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 results in Table 31 represent the influence of part orientation on the measured angle between
the Z and X vectors. Table 31: influence of part orientation on the angle between the Z and X vectors
ANOVA
Sum of Squares df Mean square F Sig.
π¨ππππ ποΏ½οΏ½
Between Groups 0,307 1 0,307 5,979 0,023
Within Groups 1,130 22 0,051
Total 1,437 23
H0 was rejected for this part orientation (Sig = 0,023).
Meaning that we can say that there is a significant influence of this part orientation on the
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 βarmsβ of the boxplot show the minimum
and maximum measured values.
52
Table 32: Main statistical parameters regarding influence of part orientation on ποΏ½οΏ½
π΄ππππ ποΏ½οΏ½ 95% Confidence interval
N Mean [Β°]
Std. Deviation [Β°]
Std. Error [Β°]
Lower Bound [Β°]
Upper Bound [Β°]
Minimum [Β°]
Maximum [Β°]
Normal orientation 16 89,6358 0,19075 0,04769 89,5342 89,7375 89,29 90,01
Suggested orientation 8 89,8758 0,28888 0,10213 89,6343 90,1173 89,35 90,20
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 ποΏ½οΏ½ is closer to 90Β°, 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
Sum of Squares df Mean square F Sig.
Angle Between Groups 0,161 1 0,161 2,152 0,147
Within Groups 5,241 70 0,075
Total 5,402 71
H0 couldnβt 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
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 βarmsβ 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 [Β°]
Std. Deviation [Β°]
Std. Error [Β°]
Lower Bound [Β°]
Upper Bound [Β°]
Minimum [Β°]
Maximum [Β°]
Normal orientation 48 89,8958 0,27643 0,03990 89,8155 89,9760 89,29 90,67
Suggested orientation 24 89,9961 0,26778 0,05466 89,8830 90,1092 89,35 90,55
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
90Β°. 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 Β±0,2Β° with a certainty of 95%.
Another way to put it is that the machine has an absolute angle accuracy of about Β±0,6Β°.
This suggested orientation likely has a positive effect on the angle, but this can only be said with
85% certainty (Sigma β 0,15).
4.8.4. Wall- and edge thickness
To determine whether or not the accuracy of the partβs 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 widthβs, 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.
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.
54
4.8.4.1. Wall thickness in X direction
The results of the statistical analysis, showed that the homogeneity of the variance of the collected
data could not be ensured (Leveneβs test; sigma = 0,000β¦). 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 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. (Leveneβs test of equality of error variances returned a Sigma value of 0,000β¦)
Table 35: influence of part orientation on wall thickness shrinkage in Y direction
ANOVA
Sum of Squares df Mean square F Sig.
Wall Thickness in Y direction
Between Groups 0,014 1 0,014 12,902 0,002
Within Groups 0,024 22 0,001
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
Suggested orientation 8 0,0681 0,04079 0,01442 0,0340 0,1022 0,02 0,14
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
Sum of Squares df Mean square F Sig.
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
Sum of Squares df Mean square F Sig.
Wall Thickness in Z direction [mm]
Between Groups 0,043 1 0,043 2,036 0,168
Within Groups 0,463 22 0,021
Total 0,506 23
56
According to the relative and absolute shrinkages, H0 couldnβt be rejected.
Meaning that we cannot say that there is a significant influence of this part orientation on the
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 = 0,001β¦).
Meaning that we cannot say that there is a significant influence of this part orientation on the
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 widthβs shrinkage
measured in the Y direction [%].
Table 39: influence of part orientation on relative edge width shrinkage in Y direction
ANOVA
Sum of Squares df Mean square F Sig.
Edge Width shrinkage in Y
Between Groups 2,146 1 2,146 2,346 0,140
Within Groups 20,126 22 0,915
Total 22,272 23
According to the relative shrinkages, H0 couldnβt be rejected ( Sig > 0,005).
Meaning that we cannot say that there is a significant influence of this part orientation on the
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 widthβs shrinkage
measured in the Z direction [%].
Table 40: influence of part orientation on relative edge width shrinkage in Z direction
ANOVA
Sum of Squares df Mean square F Sig.
Edge Width Shrinkage in Z
Between Groups 0,003 1 0,003 0,003 0,958
Within Groups 20,145 22 0,916
Total 20,147 23
According to the relative shrinkages, H0 couldnβt be rejected (Sig > 0,005).
Meaning that we cannot say that there is a significant influence of this part orientation on the
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.
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.
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
Sum of Squares df Mean square F Sig.
Edge Length Shrinkage in X
Between Groups 0,015 1 0,015 0,200 0,659
Within Groups 1,605 22 0,073
Total 1,620 23
H0 couldnβt 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
shrinkage of the edge length in X-direction.
4.8.5.2. Edge length in Y direction
The results in Table 42 represent the influence of this part orientation on the edge length shrinkage
measured in the Y direction [%].
Table 42: influence of part orientation on relative edge length shrinkage in Y direction
ANOVA
Sum of Squares df Mean square F Sig.
Edge Length Shrinkage in Y
Between Groups 0,246 1 0,246 3,949 0,059
Within Groups 1,327 22 0,062
Total 1,618 23
H0 couldnβt be rejected for this part orientation (Sig > 0,05).
Meaning that we cannot say that there is a significant influence of the parameters on the shrinkage
of the edge length in Y-direction.
58
4.8.5.3. Edge length in Z direction
The results in Table 43 represent the influence of this part orientation on the edge length shrinkage
measured in the Z direction [%].
Table 43: influence of part orientation on relative edge length shrinkage in Z direction
ANOVA
Sum of Squares df Mean square F Sig.
Edge Length Shrinkage in Z
Between Groups 0,041 1 0,041 0,369 0,550
Within Groups 2,436 22 0,111
Total 2,477 23
H0 couldnβt be rejected for this part orientation (Sig > 0,05).
Meaning that we couldnβt 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 β Model Z-edge length
In the first and third print file, the dimensions are scaled along the printerβs 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.
ππ = ππππ‘ ππππ’ππ
πΈππ£πππππ ππππ’ππ= 0,097
ππ = πππππππ‘ππ ππππ‘ ππππ . #ππππ‘π
π‘ππ‘ππ ππ’πππ ππππ= 0,180
πβπππππππ πΈπΏ π [%] = 0,78 β 2,283. ππ β 0,92 . ππ + 2,944 . ππ . ππ = 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 β Model Z-vector
In the second and fourth print file, the dimensions are scaled along the printerβs Z-axis, using the
shrinkage compensation model based on the data obtained from the measurements of Z vectors.
πβπππππππ π π£πππ‘ππ [%] = β0,808 + 1,585 . ππ + 1,77 . ππ β 4,182 . ππ . ππ = β0,409%
To compensate this expected shrinkage, the part was scaled along the printer-Z-axis using a factor
1,00409.
4.9.3. Third print file: High volume ratio β 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
ππ = ππππ‘ ππππ’ππ
πΈππ£πππππ ππππ’ππ= 0,270
ππ = πππππππ‘ππ ππππ‘ ππππ . #ππππ‘π
π‘ππ‘ππ ππ’πππ ππππ= 0,227
πβπππππππ πΈπΏ π [%] = 0,78 β 2,283. ππ β 0,92 . ππ + 2,944 . ππ . ππ = 0,135%
To compensate this expected shrinkage, the part was scaled along the printer-Z-axis using a factor
0,99865.
61
4.9.4. Fourth print file: High volume ratio β Model Z-vector
πβπππππππ π π£πππ‘ππ [%] = β0,808 + 1,585 . ππ + 1,77 . ππ β 4,182 . ππ . ππ = β0,234%
To compensate this expected shrinkage, the part was scaled along the printer-Z-axis using a factor
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 couldnβt be done in an
accurate way, since there were support structure remains which couldnβt 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
Sum of Squares df Mean square F Sig.
shrinkage in Z Between Groups 0,049 1 0,049 1,146 0,299
Within Groups 0,775 18 0,043
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
Sum of Squares df Mean square F Sig.
shrinkage in Z Between Groups 0,049 1 0,233 5,959 0,025
Within Groups 0,703 18 0,039
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 Ξshrinkage is defined as following:
βπ βπππππππ π [%] = π βπππππππ πΈπππ πΏππππ‘β π [%] β π βπππππππ π£πππ‘ππ π[%]
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 (Ξshrinkage). This experiment is conducted on the parts produced by the first 4 print files.
The Pearson Correlation coefficiΓ«nt 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 Ξshrinkage.
Table 49: Correlation Coefficients between Ξshrinkage Z and the angular accuracy
Correlations
ΞShrinkage Z π΄ππππ ποΏ½οΏ½ π΄ππππ ποΏ½οΏ½ π΄ππππ ποΏ½οΏ½
ΞShrinkage 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 [cmΒ³]
Part Volume [cmΒ³] PRINTING TIMES
PRINTING SPEED [cmΒ³/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
Validation print file 2 27,71 13,82 3h12 3h31 7,87 3,93
Validation print file 3 67,39 50,44 5h02 5h06 13,21 9,89
Validation print file 4 67,19 50,62 5h01 5h11 12,94 9,75
*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.
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.
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 [cmΒ³/h]
Test of between-subject effects
Dependant value: Net Printing speed
Source Type III sum of Squares df Mean square F Sig.
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 = 0,000β¦).
H0 was rejected for VR, as well as TR and for the combination of VR*TR.
(Sig < 0,05 for those parameters).
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:
πππ‘ πππππ‘πππ π ππππ [cm3
h] = 0,57 + 27,20 . ππ + 6,64 . ππ + 0,13 . ππ . ππ
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].
πππ‘ πππππ‘πππ π ππππ [cm3
h] = 7,37 + 6,67 . ππ π€ππ‘β ππ = 0,25
πππ‘ πππππ‘πππ π ππππ [cm3
h] = 19,61 + 6,73 . ππ π€ππ‘β ππ = 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 [cmΒ³/h]
Test of between-subject effects
Dependant value: Gross Printing speed
Source Type III sum of Squares df Mean square F Sig.
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 = 0,000β¦).
H0 was rejected for VR, as well as TR and for the combination of VR*TR.
(Sig < 0,05 for those parameters).
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:
πΊπππ π πππππ‘πππ π ππππ [cm3
h] = 4,42 + 23,00 . ππ + 11,60 . ππ β 9,854 . ππ . ππ
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].
πΊπππ π πππππ‘πππ π ππππ [cm3
h] = 10,17 + 9,14 . ππ π€ππ‘β ππ = 0,25
πΊπππ π πππππ‘πππ π ππππ [cm3
h] = 20,52 + 4,70 . ππ π€ππ‘β ππ = 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
werenβt 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 werenβt able to discard the already
present shrinkage corrections, we werenβt 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, itβs 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 machineβs 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 β 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). βComparison of the Accuracy of 3D Printed Prototypes Using the Stereolithography (SLA) Method with Digital CAD Modelsβ. 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].
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
Sum of Squares df Mean square F Sig.
Angle ποΏ½οΏ½ Between Groups 0,347 2 0,173 11,328 0,001
Within Groups 0,199 13 0,015
Total 0,546 15 Sphere XY plane Between Groups 0,078 2 0,039 4,195 0,039
Within Groups 0,121 13 0,009
Total 0,199 15 Edge length Y direction [%] Between Groups 0,501 2 0,251 7,374 0,007
Within Groups 0,442 13 0,034
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]:
ποΏ½οΏ½ = 89,387 + 0,003. π with a significance of 0,000β¦
πβπππππππ π πβπππ ππ ππ πππππ [%] = β0,316 β 0,007. π with a significance of 0,126.
Addendum A
73
πβπππππππ ππππ πππππ‘β π [%] = 0,190 β 0,002. πwith 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
Within Groups 1,137 13 0,087
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
πβπππππππ π£πππ‘ππ ππ π ππππππ‘πππ [%] = 0,193 β 0,006. π 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
Within Groups 1,603 13 0,123
Total 2,772 15
Edge Length X [%] Between Groups 0,633 2 0,317 5,889 0,015
Within Groups 0,699 13 0,054
Total 1,333 15
Addendum A
75
πβπππππππ ππππ π€πππ‘β ππ π ππππππ‘πππ [%] = 0,166 β 0,002. π β 0,002. π significance of 0,548.
πβπππππππ ππππ πππππ‘β ππ π ππππππ‘πππ [%] = 0,113 β 0,002. π + 0,001. π significance of 0,283.