1. FACULTY OF SCIENCE AND TECHNOLOGY
BEng (Hons) Engineering
May 2016
Designing for Variable Stiffness with Additive
Layer Manufacturing
by
Adam Brann
2. 2
REPORT DECLARATION
This Project Report is submitted in partial fulfilment of the requirements for an Extended
Undergraduate degree at Bournemouth University. I declare that this Project Report is my
own work and that it does not contravene any academic offence as specified in the University’s
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under the Freedom of Information Act.
Signed: A.Brann
Name: Adam Brann
Date: 02/06/2016
Programme: BEng (Hons) Engineering
3. 3
Abstract
Additive Layer Manufacture is a rapidly developing technology. This paper suggests and
demonstrates the potential to design variable stiffness into components using hollow
sections, so as to locally increase their sensitivity to bending a torsion. The project embraces
both analytical and empirical methods, with extensive use of Finite Element Analysis.
Material property experiments on extruded PLA is performed, alongside a detailed carbon
footprint analysis. Results showed FEA results that correlated well with analytic findings, and
FEA studies that demonstrated the principle well, under both bending, and torsion. Elastic
modulus was found to be 2168MPa, though subsequent results suggested error in
measurement. FEA studies and physical test data displayed moderate correlation.
Project requirements are successfully achieved, exploring variable stiffness in components
produced using fused deposition modelling subjected to simple bending, and torsion.
Keywords: Variable stiffness, additive layer manufacturing, fused deposition modelling,
7. 7
Acknowledgements
Firstly, I’d like to express my sincere gratitude to my project supervisor, Dr. Kamran
Tabeshfar. His constant advice, patience and enthusiasm for this project has been
invaluable. I’d also like to thank Mehai Dupac for his assistance with analytical aspects of the
project, and Ben Thomas for providing insight and advice on the sustainability element of this
project.
I could not have done this without the support and love of my parents. Without their love,
support, and constant encouragement this year would not have been possible. Thanks to my
friends, who have made my life at University fantastic. Dan Forbes you have been an
awesome course mate, and an absolute brother to me.
9. 9
9.2 Appendix B ................................................................................................................... 47
9.3 Appendix C ................................................................................................................... 48
9.4 Appendix D ................................................................................................................... 50
9.5 Appendix E ................................................................................................................... 51
9.6 Appendix F ................................................................................................................... 52
9.7 Appendix G................................................................................................................... 53
10. 10
List of Figures
Figure 1. Light-weighted aircraft hinge produced with additive manufacturing...................... 12
Figure 2. Three build orientations (Hague 2014) ................................................................... 14
Figure 3. Beam with tapered cavity........................................................................................ 15
Figure 4. First integration…………………………………………………………………………...17
Figure 5. Second integration……………………………………………………………………….17
Figure 6. Simplified geometry for analytical study. ……………………………………………...18
Figure 7. Model used for FEA study ...................................................................................... 20
Figure 8. FEA Boundary conditions. ...................................................................................... 20
Figure 9. Meshing i................................................................................................................. 21
Figure 10. Edge from which displacement results were gathered ......................................... 21
Figure 11. Warpage on specimen F....................................................................................... 22
Figure 12. 3D print specimen................................................................................................. 22
Figure 13. G-clamp constraining 25mm section of specimen................................................ 23
Figure 14. Flexural testing arrangement. ............................................................................... 23
Figure 15. Loading using hanging weights ............................................................................ 24
Figure 16. Variable stiffness specimen geometry.................................................................. 25
Figure 17. Halved specimen for inspection (top). Poor fusion on bridging layer (bottom)..... 25
Figure 18. Marking of the specimen. Constraining a checking for perpendicularity ............. 26
Figure 19. Different measurement positions .......................................................................... 26
Figure 20. Boundary constraints for variable stiffness FEA study. ........................................ 27
Figure 21. Meshing ii.............................................................................................................. 27
Figure 22. Comparison study boundary constraints .............................................................. 27
Figure 23. Variable stiffness model for torsion study............................................................. 28
Figure 24. Meshing and mesh control.................................................................................... 28
Figure 25. Boundary constraints for variable stiffness component under torque .................. 28
Figure 26. FEA displacement colour plot ............................................................................... 30
Figure 27. Comparison of analytical results........................................................................... 30
Figure 28. Graph illustrating elastic modulus across specimens A-E.................................... 31
Figure 29. FEA Discrete colour plot showing displacement .................................................. 31
Figure 30. Side-by-side comparison of colour plots............................................................... 32
Figure 31. Results comparison across FEA studies .............................................................. 33
Figure 32. Deflection results gathered from deflection experiment ....................................... 34
Figure 33. Comparison of results........................................................................................... 34
Figure 34. Results comparison, using E=1.35GPa for FEA study......................................... 35
Figure 35. Angular displacement comparison........................................................................ 36
Figure 36. Colour plot showing tangential displacement across components....................... 36
11. 11
1.0 Introduction
1.1 Project overview
This project details the research, methodology, and results of testing hollow variable stiffness
components created using fused deposition modelling.
1.2 Aims
This project aims to demonstrate the potential for designing hollow variable stiffness
components created using additive layer manufacturing (ALM)
1.3 Objectives
This project will achieve these aims by:
Performing an analytical study, comparing results gained from using the Euler-
Bernoulli double integration method, and Finite Element Analysis (FEA).
Performing an empirical study, demonstrating the principle using physical testing on
specimens created using fused deposition modelling (FDM), and comparing results
to FEA studies
Discuss discrepancies between FEA, and analytical and empirical results
1.4 Rationale
Most ALM procedures, such as fused deposition modelling (FDM) allow the designer to
create 1 piece components that are hollow, or contain cavities. Designers often create hollow
components to reduce build times, save materials or for light-weighting purposes (Beeck et
al. 2004). However, the potential for using the cavities to alter the mechanical properties of
the component, such as stiffness, is often ignored. By adding a cavity to a component, 2nd
moment of area is reduced, causing the section to become less rigid. This reports aims to
draw attention to the potential to design custom stiffness into components using fused
deposition modelling.
12. 12
2.0 Background
2.1 Additive Layer Manufacturing
ALM (also known as 3D printing, or rapid prototyping) is a fast growing industry, growing in
popularity (Wong & Hernandez 2012). Developed in the 1980’s, ALM involves converting a
CAD file into an STL file. The STL file is then sliced into layers which are then ‘printed’ on top
of each other to build a complete model. This allows for complex models to be produced in
one single process, previously impossible using conventional manufacturing techniques.
Additionally, components produced using additive layer manufacture have exceptionally low
lead times due to the lack of a need for specialist tooling or fixtures.
The term ALM includes a wide range of technologies, such as direct metal laser sintering
(DMLS), fused deposition modelling (FDM) (also known as fused filament fabrication) and
stereolithography (also known as optical fabrication) (Yan and Gu 1996; Materialise 2016),
the most common of which is FDM (Palermo 2013). See appendix A for an overview of these
techniques. Whilst DMLS and STL techniques can create hollow components, they must
allow for support material to be removed from within the component, which usually requires
drilling a hole to allow for support material to be drained, or dissolved (Clinkenbeard et al.
2002; Wu et al. 2009). FDM allows certain geometries to be purely hollow, as the extrusion
head can extrude across open space, between two supports provided the distance in
relatively small (Zegard and Paulino 2015).
ALM has been adopted by the aerospace industry to produce components in complex
shapes with enhanced strength to weight properties (Lyons 2014; Masanet 2015) (see figure
1).
Despite this, additive layer manufacture has yet to be adopted by high volume manufacturing
sectors (Bak 2003). Whilst the potential for additive layer manufacture has been recognised
for its light-weighting capabilities (Meisel et al. 2012; Compton and Lewis 2014), no
significant research was found concerning its potential for creating components with variable
stiffness.
Figure 1. Light-weighted aircraft hinge produced with additive manufacturing (Masanet 2015)
13. 13
2.2 Stiffness
Bending
Stiffness is the resistance of an elastic body to deflection by an applied force (Ashby 2005);
in other words, the stiffness of a beam dictates how a beam will deflect under a load. The
stiffness of a component depends on material properties (E), and its geometry (I); 𝑆 ∝
𝐸𝐼 (Ashby 2005). Stiffness resisting flexure, or bending stiffness, is known as flexural rigidity,
‘EI’ along the plane of bending (Gere and Goodno 2009; Timoshenko 2009).
Euler Bernoulli Beam Theory (thin beam theory)
Arguably the most widely applied beam deflection theory is that of Euler and Bernoulli. The
Euler-Bernoulli equation describes the relationship between the beams deflection and the
applied load;
𝐸𝐼 (
𝑑2
𝑦
𝑑𝑥2
) = 𝑀(𝑥)
Where M is a moment, E is the elastic modulus of the beam, and I is the second moment of
area of the beam. The curve 𝑦(𝑥) describes the deflection at a position 𝑥 along the beam
(Sokolnikoff and Spect. 1956; Gere et al. 1997).
The Euler-Bernoulli beam theory is based on the following assumptions (Rahman 2016):
The beam is thin; a thin beam has a Length/Height aspect ratio of approximately 5 or
more (Ji et al. 2015). It is this assumption which makes the Euler-Bernoulli beam
theory synonymous with ‘Thin beam theory’.
The cross section of the beam remains normal to the axis of bending, no shear
deformation takes place along the longitudinal axis of the beam
Deformations are assumed to be relatively small, and elastic; the model cannot
describe any deformation as a result of plastic yielding.
The cross section of the beam remains constant
Assuming the beams material is homogeneous (E remains constant), a component will owe
any non-uniform stiffness to a change of shape along the axis of bending. To describe
bending in a beam with a non-uniform cross section, an equation must be derived from the
Euler-Bernoulli equation.
Torsion
The principle of variable stiffness also applies to components subjected to torsion. A
components resistance to torsion is also dependant on its cross section. Resistance to
torsion is the sum of the second moment of area in the radial and circumferential directions,
such that 𝐼𝑧𝑧 = 𝐼𝑥𝑥 + 𝐼 𝑦𝑦.
14. 14
2.3 Stiffness in fused deposition modelled components
Variables such as raster orientation and wall thickness are known to effect the mechanical
properties of components produced by FDM (Letcher & Waytashek 2014; Letcher et al.
2015, Stratasys 2016). The FDM process produces components that are anisotropic in
nature – their properties are dependent on the print orientation. Studies by Hague (2014)
detail the effect of print orientation on various mechanical properties, including flexural
strength. The study showed samples exhibited the highest flexural strength when built on the
‘edge’ orientation (see figure 2).
Other variables such as print quality / resolution are known to affect the mechanical
properties of components produced (Letcher et al. 2015). The quality of components can
vary according to the specific machine they are produced on, even across identical models
(Makerbot 2011), due to minute calibration differences that may be present.
Figure 2. Three build orientations (Hague 2014)
15. 15
3.0 Methodology
The methodology for this study falls under two separate brackets; Analytical and empirical.
The analytical section aims to prove the principal, deriving an equation to describe bending
in a hollow non-uniform cross section beam, and verifying the results against an FEA study.
The empirical side demonstrates the principle using finite element analysis, and physical
testing of hollow components created using FDM.
3.1 Analytical
To demonstrate the principle of variable stiffness, an analytical study was performed. In this
study, an example of a rectangular beam, with a rectangular tapered cavity was used (see
figure 3). However the basic principle will remain the same regardless of the geometry of the
design.
Research into thin-beam theory was performed. 3 different strategies to describe the
deflection as a function of 𝑥 were implemented.
3.11 Primary derivations
1. The first strategy attempted to describe the beam with a tapered cavity (see figure 3).
First ‘I’ was written as a function of 𝑥.
B, D, and b remain constant along the length (figure 3). ‘d’ changes with respect to x.
‘d’ as a function of x may be written as:
𝑑 = 2𝑥 tan(𝜃) + 𝑎
The second moment of area at any point along the cavity may be written as:
𝐼 =
𝐵𝐷3
12
−
𝑏𝑑3
12
Therefore, I as a function of x may be written as:
𝐼𝑥 =
𝐵𝐷3
12
−
𝑏(2𝑥 tan(𝜃) + 𝑎)3
12
The function was then substituted in the Euler-Bernoulli equation:
Figure 3. Beam with tapered cavity. B and D are the external dimensions of section, and b and d are
the dimensions of the cavity. ‘a’ represents the initial width of the taper. X is measured form the start of
the cavity. It is assumed that the section of the beam without a cavity is small enough to be negligible.
Beam is fixed at x=0
17. 17
Integrating once to find the slope as a function of z, and again for displacement. Due to the
complexity of the integration required, integration was performed using a computational
maths engine, WolframAlpha®.
In a discussion with project supervisors, the resulting equation was deemed too complex to
input into an excel spreadsheet. A simplified geometry to analyse was suggested.
Figure 4. First integration. Giving slope as a function of z, where z = x + u
Figure 5. Second Integration. Giving deflection as a function of z, where z = x + u
18. 18
3.12 Secondary derivation
The second strategy was a simplified version of the first, with less realistic geometry, that
makes for a simpler derivation.
First ‘I’ was written as a function of X:
𝐼𝑥 =
𝑏𝑑 𝑥
3
12
𝑑 𝑥 = 2𝑥 tan 𝜃
𝐼𝑥 =
𝑏(2𝑥 tan 𝜃)3
12
Multiplying out, and simplifying this becomes:
𝐼𝑥 =
2
3
𝑏𝑥3
tan3
𝜃
Ix was then substituted into the Euler-Bernoulli equation:
𝑑2
𝑦
𝑑𝑥2
=
𝑀(𝑥)
𝐸𝐼(𝑥)
𝑑2
𝑦
𝑑𝑥2
=
𝐹𝑥
𝐸 (
2
3
𝑏𝑥3 𝑡𝑎𝑛3 𝜃)
Figure 4. Simplified geometry for analytical study. Beam is fixed at x=L. Force is applied to free end
19. 19
Substitution:
2
3
𝐸𝑏 𝑡𝑎𝑛3
𝜃 = 𝐴
𝑑2
𝑦
𝑑𝑥2
=
𝐹𝑥
𝐴𝑥3
𝐴
𝐹
∙
𝑑2
𝑦
𝑑𝑥2
= 𝑥−2
Integrating once for slope:
𝐴
𝐹
∙
𝑑𝑦
𝑑𝑥
= −𝑥−1
+ 𝑐1
Integrating again for deflection:
𝐴
𝐹
∙ 𝑦 = − ln 𝑥 + 𝑐1 𝑥 + 𝑐2
Calculating 𝑐1:
𝑊ℎ𝑒𝑛 𝑥 = 𝐿,
𝑑𝑦
𝑑𝑥
= 0
−𝐿−1
+ 𝑐1 = 0
𝑐1 = 𝐿−1
Calculating 𝑐2:
𝑊ℎ𝑒𝑛 𝑥 = 𝐿, 𝑦 = 0
− ln 𝐿 +
𝐿
𝐿
+ 𝑐2 = 0
𝑐2 = ln 𝐿 − 1
Therefore, deflection y may be written in terms of x like so:
𝑦 =
3𝐹
2𝐵𝐸𝑡𝑎𝑛3 𝜃
∙ (−ln(𝑥) +
𝑥
𝐿
+ ln(𝐿) − 1)
Maximum deflection occurs when X = 0. Therefore maximum deflection may be written as:
𝑦 =
3𝐹
2𝐵𝐸𝑡𝑎𝑛3 𝜃
∙ (−ln(𝑥) +
𝑥
𝐿
+ ln(𝐿) − 1)
20. 20
This equation was entered into an excel spreadsheet. A displacement curve was formed
using excels graph function. Displacement was calculated for a theoretical specimen with
dimensions such that L=150mm, B=150mm, angle of taper = 5°. Young’s’ modulus was
assumed to be 3000 MPa, the Young’s modulus of 3D printed PLA, according to research
performed by Letcher and Waytashek (2014). Loading was set at 1N.
3.13 Finite element analysis
For the next stage of the analytical study, an FEA study was performed.
Above is the model used for the FEA study. Differences from the analytical model include a
5mm section on the free end, and radii on the internal section. Both were added to avoid
yielding stress singularities in the mesh, which make FEA results unreliable (Hutton 2004).
Boundary constraints were added to the model (see figure 6). The fixed face was
Figure 5. Model used for FEA study
Figure 6. FEA Boundary conditions. Fixed geometry constraint on the back face, UDL of 1N applied at
the free end in the –y direction.
21. 21
restricted in all 6 degrees of freedom, and a 1N load was applied at the free end. 1N load
was chosen to keep the displacements small, so they could be described by thin beam
theory.
The component was meshed using a standard 4 point Jacobian mesh. Maximum element
size was set at 1.5mm, minimum was set at 0.075mm. Mesh convergence study was
deemed unnecessary as mesh quality does not have a significant effect on displacement
results (Hutton 2004). The simulation was run, and displacement values were measured
from the nodes along the top left hand edge of the model.
Results were exported to a .csv file, and then imported into a spreadsheet to compare
against analytical results.
Figure 8. Edge from which displacement results were gathered
Figure 7. Meshing i
22. 22
3.2 Empirical
3.21 Testing for Elastic Modulus
The elastic modulus of the batch of PLA was ascertained using a cantilever bending test.
The pre-test quality control was performed in accordance with ISO 178 (British Standards
Institution 2010) (see appendix B). 6 specimens were printed on a Makerbot replicator, using
Makerbot PLA filament; measuring 15 X 7.5 X 150mm. Specimens were printed with 25%
infill, linear infill pattern, 2 shells, and with a layer height of 0.2mm. PLA was extruded at
212°C. Specimens were printed in ‘edge’ orientation (see figure 2).
Specimens were lettered A-F using a marker pen to avoid confusion. The parts were visually
inspected against a flat surface for warpage and twisting. Specimen F was rejected due to
excessive warping (see figure 9).
The middle third of each specimen was measured at 5 points equidistant points (see figure
10), using a digital Vernier calliper, to the nearest .01mm, as per ISO 178. Prior to
measurement, flash and ‘bulge’ were removed using a Stanley knife.
Figure 10. 3D print specimen. Part will be fixed on the 25mm shaded section. Measurement were
taken in the middle 3rd of the bending section, shown by the 5 adjacent lines.
Figure 9. Warpage on specimen F.
23. 23
Specimens A-F were tested using a cantilever flexure test. Specimens were clamped to a
heavy workbench using a G-clamp, across a 25mm section. A metal shim was used to
distribute the clamping load. Specimens were made square to the workbench using an
engineer’s square.
Deflections were measured using a finger clock, mounted on a clock arm. The clock arm
base was clamped to the workbench to restrict any potential movement. Deflection was
measured from the underside of the specimen.
Figure 11. G-clamp constraining 25mm section of
specimen
Figure 12. Flexural testing arrangement.
24. 24
Loading was applied using a 50g hanging weight, in the centre of the tip of the specimen.
The load chosen to produce small deflections, as the finger clock had a measuring range of
0-0.56mm. The weight was carefully lowered onto the specimen by hand.
Deflections were recorded to the nearest 0.01mm, and entered into a spreadsheet.
Limitations for the cantilever test
Whilst the cantilever flexure test was desirable for its simplicity, certain limitations in this
testing method have been recognised. Specifically this form of testing does not allow for
controlling of strain rate. The rate at which loading is applied to polymers is known to affect
its perceived mechanical performance (Sepe 2011). It is likely that test specimens will
appear slightly stiffer using the cantilever test than the Instron, as the loading is applied
instantly, rather than gradually.
Figure 13. Loading using hanging weights
25. 25
3.22 Variable stiffness testing
3.221 Testing FDM components
Variable stiffness was demonstrated using semi-hollow specimens. 5 specimens were made.
All print variables were kept consistent to those at which the flexural test specimens were
printed (see 3.21). The printer and batch of PLA were also kept the same. The literature was
consulted, and it was found that the Makerbot could achieve the required bridge without
altering any existing print settings, and without the presence of extra cooling devices. The
printer and batch of PLA were also kept the same. The quality of bridging and the internal
section were inspected on a randomly selected specimen.
Inspection revealed good overall print quality, but weak fusion between the 2 shells on the
bridging layer. It is possible that these layers were forced apart during the process of sawing
the specimen open. It was decided to accept the specimens, and apply the load with the
bridge layer facing upwards, so it would bear tensile stresses rather than compressive
stresses that could potential buckle the thin layers.
Remaining components were checked for twisting and warping, and the outer dimensions
were measured with a digital Vernier and recorded. 1 Specimen was discarded due to
extreme warping.
Figure 14. Variable stiffness specimen geometry. Change for new geometry.
Figure 15. Halved specimen for inspection (top). Poor fusion on bridging layer (bottom).
26. 26
5mm increments were marked on the components to aid with measurement (Figure 16). A
25mm section of the specimen were fixed to the work station using a g-clamp and a metal
grip. The components angle in relation to the edge of the work bench was checked using an
engineer’s square (figure 16).
A 2.5 kg load was applied to the free end using hanging weights. The load was temporarily
removed in between measurements. Displacements were measured using a Mercier
analogue dial indicator on a magnetic stand (Figure 17). Displacements were initially
measured from the centre of the specimen (Figure 17 Left). This yielded poor results. It was
posited that the dial indicators spindle was depressing the roof of the cavity. The
experiments were repeated, this time measuring deflections from the side of the component
(Figure 17 Right), which yielded less erratic results.
Results were recorded from the 3 remaining specimens. An average was taken from all
displacement values, and presented in a scatter graph.
Figure 16. Marking of the specimen (left). Constraining a checking for perpendicularity (right)
Figure 17. Different measurement positions
27. 27
3.222 Finite element analysis
FEA was performed on the variable stiffness components under single point bending.
Meshing and boundary constraints were kept consistent with the primary analytical FEA
study.
A 4 point Jacobian, non-curvature based mesh was used. Element size was controlled at
1.5mm, with a 0.075mm tolerance.
Nodal values were probed along the length of the components edge, and exported into
a .csv file. Results from variable stiffness specimens were in turn compared with defection
results measured from a specimen without cavities.
Figure 19. Meshing ii. Displacement values were probed from the edge marked in red.
Figure 18. Boundary constraints for variable stiffness FEA study. Fixed in 6 degrees of freedom at one
end, vertical load of 25N applied.
Figure 20. Comparison study boundary constraints
28. 28
3.223 Finite element analysis – Torsion
A finite element analysis study was performed on a hollow variable stiffness geometry under
torsion, and compared with a solid section under the same loading parameters.
The model was meshed using a 4 point Jacobian mesh. Global mesh size was set to 3mm.
A split line was made drawn along the length of the component, and the mesh was controlled
locally to 2mm, to allow for parametric readings to be probed from it (see figure 21).
The model was fixed at one end (X=0). A 1N torque was applied across the cylindrical face
(see figure 22).
Studies were simulated. As Solidworks does not have a function for measuring displacement
in terms of rotation, displacement was measured against a polar coordinate system, which
allowed tangential displacement to be measured. Results were exported into a .csv file.
Figure 21. Variable stiffness model for torsion study. 25mm cavity located in the centre of the span
X=0
Figure 23. Boundary constraints for variable stiffness component under torque
Figure 22. Meshing and mesh control (blue line)
29. 29
Angle displaced was calculated using the equation 𝑆 = 𝑟𝜃, where S = tangential
displacement, r = radius, 𝜃 = angle subtended. Results were compared against a model that
was solid all the way through. Boundary constraints and meshing were kept the same
through both studies.
3.23 Further FEA
Further studies were performed to explore and demonstrate the effect of different cavity
geometry on the deflection of the component. Mesh settings were kept consistent from the
set-up detailed in 3.222. Geometry and results may be found in appendix G.
30. 30
4.0 Results
4.1 Analytical Results
The integration phase yielded a general equation to describe deflection in a beam with an
open, constant tapered cavity:
𝑦 =
3𝐹
2𝐵𝐸𝑡𝑎𝑛3 𝜃
∙ (−ln(𝑥) +
𝑥
𝐿
+ ln(𝐿) − 1)
Displacement reading were taken from 192 nodes along the components edge (see figure
10). FEA colour plot showed realistic deformation.
Displacement (y) between X=0 and X=150 were plotted across intervals of 0.777202 mm
(this interval was defined by the parametric spacing of the nodes from Solidworks results).
Hand calculation results were compared with results from the FEA analysis (see figure 25).
See appendix C for raw data tables.
Maximum deflection varies by 14.415% between the two studies. This is likely due to the fact
that Solidworks considers the weight of the component, whereas hand calculation does not.
Further analysis showed the variance between the results could be corrected with an
additional 0.25N load (see appendix D). The deflection shape also varies significantly
between the two studies. The deflection described by the derived formula owes it
asymptotical shape to the fact that as X approaches L, ‘I’, the resistance to bending
approaches 0.
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
X
6.217616
12.435232
18.652848
24.870464
31.08808
37.305696
43.523312
49.740928
55.958544
62.17616
68.393776
74.611392
80.829008
87.046624
93.26424
99.481856
105.699472
111.917088
118.134704
124.35232
130.569936
136.787552
143.005168
149.222784
Deflection(mm)
Distance from fixed end (mm)
Hand calcs.
SWKs FEA
Figure 25. Comparison of analytical results, showing expected deflection and FEA deflection in
response to a 1N end load.
Figure 24. FEA displacement colour plot
31. 31
4.2 Empirical Results
4.21 Testing for Elastic Modulus
Cantilever tests investigated the elastic modulus of the PLA with custom print settings (see
3.21). Quality control checks found specimens A-E conformed to ISO 178 guidelines. See
appendix E for further data.
The arithmetic mean average was taken across all test pieces in accordance with ISO 178.
Mean average was 2168.1 MPA, with a standard deviation of 74.76 MPA, and a confidence
interval of ±65.5 at 95% confidence level. Statistical interpretation was performed in
accordance with ISO 2602 (British Standards Institution 1980).
4.22 Variable stiffness testing
4.221 Variable stiffness testing - FEA
Displacement results were measured from 269 nodes along the length of the model.
A B C D E1950
2000
2050
2100
2150
2200
2250
2300
ElasticModulus(MPa)
Elastic Modulus Testing
Specimen A
Specimen B
Specimen C
Specimen D
Specimen E
Figure 26. Graph illustrating elastic modulus across specimens A-E
Average = 2168 MPA
+5%
-5%
Figure 27. FEA Discrete colour plot showing displacement
33. 33
Deflection results were exported from the model, and presented in a graph (see figure 29).
As expected, deflection remains identical between the two specimens until approximately
X=45, where the tapered cavity section begins. The rate of divergence between the
deflections increases in between X=120-200.
Figure 29. Results comparison across FEA studies
-1.2
-1.1
-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170
Deflection(mm)
X (mm)
FEA Study: Specimen Bending Comparison
Uniform cross section
Variable stiffness
Tapered cavity
section
Full cavity
section
34. 34
4.222 Physical testing of variable stiffness specimens
Results gathered from the cantilever test were fairly consistent, but produced results that
were unexpected. Results from physical testing were significantly larger than results yielded
from FEA (see figure 31), in terms of percentage difference.
Figure 30. Deflection results gathered from deflection experiment
Figure 31. Comparison of results
-2.4
-2.3
-2.2
-2.1
-2.0
-1.9
-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
-1.0
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170
Deflection(mm)
X (mm)
Variable stiffness deflection experiment
B
C
D
Average
Tapered cavity
section
Full cavity
section
-2.3
-2.2
-2.1
-2
-1.9
-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170
Deflection(mm)
X (mm)
Results Comparison
FEA model
FDM component
Tapered cavity
section
Full cavity
section
35. 35
Results were re-plotted using an Elastic modulus value approximated from the literature
-2.3
-2.2
-2.1
-2
-1.9
-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0 10 20 30 40 50 60 70 80 90 100110120130140150160170
Deflection(mm)
X (mm)
Results Comparison: Corrected elastic modulus
FEA results
FDM Component
Figure 32. Results comparison, using E=1.35GPa for FEA study
36. 36
4.223 Variable stiffness under torsion
Tangential displacement was measured from 200 nodes along both models. Results were
recorded and compiled in a graph (see figure 33).
Angular displacement remains the same from X=0-87.5mm. From X=87.5-112.5mm the
variable stiffness component displays a localised sensitivity to torsion, before normalising
beyond X=112.5. This is further illustrated by the colour plot (see figure 34).
0
0.000005
0.00001
0.000015
0.00002
0.000025
0
11
22
33
44
55
66
77
88
99
110
121
132
143
154
165
176
187
198
Displacement(rad)
X (mm)
Angular Displacement Comparison
Uniform cross section
Variable Stiffness
Figure 33. Angular displacement comparison.
Figure 34. Colour plot showing tangential displacement across solid component (top) and component with cavity
(bottom). Black lines mark the beginning and end of the cavity section.
37. 37
5.0 Professional Issues
5.1 Sustainability
This project promotes the capabilities of ALM. As well as its ability to produce complex
components, ALM has various advantages relevant to sustainable manufacturing.
Sustainable manufacturing is defined as “The creation of manufactured products that use
processes that minimize negative environmental impacts, conserve energy and natural
resources, and are economically sound” (DOC 2014; Mani et al 2014). Table 1 includes the
key advantages additive layer manufacture holds that are relevant to sustainable
manufacturing.
Carbon footprint analysis: FDM
Power consumption varies across the various processes, so for the purposes of this carbon
footprint analysis, only FDM modelling will be considered. One of the most popular filaments
FDM machines use is PLA. PLA is a biodegradable thermoplastic derived from organic
starch (Ryan 2011).
In the primary production process, 3.43-3.79 kg of CO2 is emitted to produce 1kg of PLA
(Granta Design 2015). The power consumption of a desktop FDM machine varies with speed
and resolution, and typically varies between 100-200 watts (walls et al 2014). For this study,
the Makerbot replicator will be considered, which consumes 100 watts (Starno 2011). It
takes approximately 9.3 minutes to print 1 gram of PLA (using a Makerbot replicator) (Starno
2011). Therefore the energy consumption per gram of PLA printed may be calculated using:
𝑝𝑜𝑤𝑒𝑟 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 ×
𝑡𝑖𝑚𝑒
𝑤𝑒𝑖𝑔ℎ𝑡 (𝑔)
= 𝑒𝑛𝑒𝑟𝑔𝑦 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 𝑝𝑒𝑟 𝑔𝑟𝑎𝑚 𝑜𝑓 𝑃𝐿𝐴
0.1 ×
9.3
60
= 0.0155 kWh/g
= 15.5 kWh/kg
Based on data from 2015, the UK grid produces approximately 0.5 kg of CO2 for every kWh it
provides (National Energy Foundation 2015; UK Gov 2015). The carbon footprint of a PLA
component produced using ALM may then be calculated:
𝐶𝑎𝑟𝑏𝑜𝑛 𝐹𝑜𝑜𝑡𝑝𝑟𝑖𝑛𝑡 = (15.5
kWh
kg
× 0.5
kg
kWh
) + Primary Production
= (7.75 + 3.61)
𝑘𝑔 𝐶𝑂2
𝑘𝑔 𝑃𝐿𝐴
= 11.36
𝑘𝑔 𝐶𝑂2
𝑘𝑔 𝑃𝐿𝐴
Less waste because of the nature of the additive process, unlike parts produced
by subtractive methods
No specialized tooling or fixtures required for AM
Reduced need for energy intensive and wasteful manufacturing processes such
as casting or machining which requires coolant
Reduces the need for large amounts of raw material within the supply chain and
transportation
Ability to create on-demand spare parts, reducing or eliminating inventory
Parts can be made lighter at no extra cost, and little/no expense to functionality,
thus lowering the carbon footprint in the transportation process
Table 1. Key additive layer manufacturing advantages relevant to sustainable manufacturing (Adapted
from Sreenivasan et al 2010, and Mani et al 2014)
38. 38
To put this figure in perspective, it may be compared to the carbon footprint of injection
moulding. Injection moulding is an additive manufacturing technique, and thus shares many
of the same advantages as additive layer manufacturing, but still requires specialist tooling,
and affords designers less flexibility in terms of the geometry it can produce.
Carbon footprint analysis: Injection moulding*
𝐶𝑎𝑟𝑏𝑜𝑛 𝑓𝑜𝑜𝑡𝑝𝑟𝑖𝑛𝑡 = 𝑝𝑟𝑖𝑚𝑎𝑟𝑦 𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑖𝑛𝑔 𝑓𝑜𝑜𝑡𝑝𝑟𝑖𝑛𝑡 + 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑖𝑛𝑔 𝑓𝑜𝑜𝑡𝑝𝑟𝑖𝑛𝑡
𝐶𝑎𝑟𝑏𝑜𝑛 𝑓𝑜𝑜𝑡𝑝𝑟𝑖𝑛𝑡 = 3.61 + 1.21
= 4.62 𝑘𝑔/𝑘𝑔
*using data from Granta Design 2015
FDM shows a higher carbon footprint than injection moulding. However these figures don’t
consider production and transport of bespoke tooling that injection moulding requires.
Injection moulds are typically machined out of aluminium or steel.
Carbon footprint analysis: Tooling*
𝐶𝑎𝑟𝑏𝑜𝑛 𝑓𝑜𝑜𝑡𝑝𝑟𝑖𝑛𝑡 = 𝑝𝑟𝑖𝑚𝑎𝑟𝑦 𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑖𝑛𝑔 + 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑖𝑛𝑔 + 𝑡𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡
Primary processing Aluminium: 12.1 kg/kg
Primary Processing Steel: 2.6 kg/kg
Material processing aluminium: 0.35 kg/kg removed
Material processing steel: 0.35 kg/kg removed
Transport fuel: 8.91kg of CO2 per gallon consumed
*Data from Granta Design 2015; Carbon fund 2016
As the size of the mould, and detracted material will vary substantial depending on the
application, it is impossible to calculate a specific value for carbon footprint. However it is
clear to see that when considered for one-off production, or small batches, these carbon
footprints make a significant impact on the carbon footprint of the injection moulding process.
As the batch size is increased (i.e. 100+ parts) the footprint becomes negligible on a per-part
basis.
It may be concluded that ALM is a good carbon efficient option when producing one-off, or
small batch components. Its ability to produce components locally to demands, without the
need of a specialist facility is also desirable. However, for high volume production, injection
moulding outperforms ALM from a sustainability point of view.
As the UK grid starts to rely on sustainable energy sources more, the appeal of additive
manufacture will not lie in its power efficiency, but in its ability to produce parts with minimal
waste material. Additive manufacturing of any kind should be encouraged from an
environmental and sustainable perspective.
5.2 Standards
The physical testing of material properties of 3D printed PLA used ISO 178 as a guideline for
quality control, and ISO 2602 was adhered to for statistical interpretation. The testing stage
itself did not adhere to ISO 178 on account of the method used – ISO 178 requires 3 point
bending, at a controlled strain rate.
5.3 Intellectual Property
Due to the nature of the project, copyrighting/trademarking is deemed irrelevant.
39. 39
6.0 Critical Evaluation
Task and deliverables within this project have been accomplished, whilst largely conforming
to the initial product design specification (Appendix F). The project plan was altered as the
project developed, to overcome unforeseen complications with the analytical stage of the
project, and access to the Instron 3 point bending machine. The project can be considered a
success as it effectively demonstrated the principle, and potential, of designing for non-
uniform stiffness using ALM. Whilst results gathered from physical testing didn’t align
perfectly with FEA results, limitations and explanations for this have been discussed, and the
principle was illustrated well using FEA and analytical methods.
The analytical stage of this project became a large part of the project, due to the complexity
of the primary derivation. Various professors and specialists were consulted during this
stage. In hindsight, although it vastly improved my knowledge and proficiency of calculus,
this stage should have been simplified sooner. Results yielded from the analytical stage
were ok. Initially analytical and FEA results varied by 14.15%. It was shown that by adding
an extra .25N load to the analytical results to account for the beams weight, variance
between the total deflections was removed. The value of .25N was purely an approximation,
and further investigation should have been performed to verify this assumption. As well as
the beams weight, it is acknowledge that the geometries being analysed were in fact slightly
different, as the analytical idealisation would have been impossible to create on Solidworks,
due to zero thickness geometry. The extra moment produced by the load bearing section on
the Solidworks model could have caused the initial variance between the two sets of results.
Initially physical testing results conflicted with FEA results. It is likely the variance between
FEA results and actual results is due to erroneous calculation of young’s modulus. Whilst
print settings and material batch were kept constant, it is also possible that some
uncontrollable variables, such as ambient temperature and humidity may have affected the
stiffness of the material across the two batches. In addition to this, the testing did not adhere
to the equipment requirements of ISO 178, opting to using a cantilever test instead of a three
point bending test. The method of testing also didn’t allow the strain rate to be controlled,
which is a factor that can effect total deflection in polymers, and is cited as a requirement for
ISO 178. Another possibility is measurement error whilst recording the results. Whilst
percentage difference between the two data sets is relatively high, average absolute
variance is only 0.2991mm. Correcting the elastic modulus reduces the variance between
the two data sets to approximately 15% (see figure 34). The remaining 15% error could
possibly be caused by insufficient constraint on the FDM specimens – this would also
explain steep deflection close to X=0 recorded in the results.
Whilst material property tests produced fairly consistent results, confidence levels could have
been increased by utilising the Instron, and full conformance to ISO 178 could have been
achieved. Further elastic modulus testing could have been performed on a material sample
with known properties, and results compared to rule out human/systematic error. Using
approximations of the elastic modulus from the literature to correct results reduced variance
between physical results and FEA results. It is worth noting that E=135GPa only for a few
specific brands of PLA filament, and it is likely that the PLA extruded from the Makerbot is in
fact stiffer than this.
Anisotropic qualities of the material were considered during testing. Material was tested in
the direction which best allowed for the bridging on the variable stiffness specimens. Further
material testing on the materials secondary direction could have been performed for a more
comprehensive analysis, but were considered out of the scope of this project.
The inclusion of components subjected to torsion into the FEA studies opened up a further
area of research. Whilst these studies lacked the analytical background and physical testing
that the simple bending studies had, the studies still provided an interesting demonstration
into the capabilities of 3D printed components.
40. 40
This project could have been managed better. The project was slow to start, defining the
project itself was especially difficult. The scope was developed with the help of my project
supervisor. The analytical side of the project was well spaced throughout the year, despite
drawing out longer than expected. Dedicating attention to the project proved difficult through
second semester, as workload from various other university modules dramatically increased.
Meetings with supervisors throughout the year helped keep the project up to date, alongside
presenting completed work to my peers, and gaining feedback. More time should have been
dedicated towards physical testing in the workshop in the less busy periods of the year.
Overall I am pleased with the quality of work that was achieved.
7.0 Conclusions
An analytical study was performed, demonstrating the theoretical principle of variable
stiffness in hollow components. An equation describing deflection in terms of 𝑥 for a
simplified ALM component was derived from Euler-Bernoulli beam theory. The equation was
used to describe a deflection curve. Results were compared against FEA results, the results
varied by an average of 14.5%. Introducing a .25N load to the analytical study to simulate
the UDL exerted by the beams weight reduced the variance between the results. Moderating
factors and limitations were discussed.
Experiments were performed in order to ascertain the elastic modulus of the Makerbot batch
of PLA. It was found that PLA printed on a custom setting exhibited an elastic modulus of
2162MPa. Quality control of the specimens conformed to the process detailed in ISO 178.
Statistical interpretation of the results conformed to ISO 2602.
A cantilever test measuring deflection was performed on a semi-hollow FDM component.
Using the elastic modulus value ascertained in the material testing stage, and identical
boundary constraints an FEA study was performed. The results were compared. Using the
calculated figure of E=2162MPa yielded poor results. An approximated value from the
literature was used, producing results with an average variance of 15% from the FEA study.
Results suggested that further elastic modulus testing needed to be performed.
An FEA study was performed to demonstrate the principle of variable stiffness in a
component under torsion. Similar to FEA studies for bending, the study compared results
from a solid section to that of a semi-hollow section. Results showed a localised sensitivity to
torsion, before normalising after the cavity section.
Carbon footprint analysis was performed on additive manufacturing techniques, FDM and
injection moulding. It was found FDM produces a smaller carbon footprint when used for
one-off production, or localised small batch work. Injection moulding was found to be better
suited to high volume production. The carbon footprint for producing a PLA component using
FDM was calculated to be 11.36kgCO2/kg PLA.
Results have produced viable conclusions and demonstrated a useful principle for future
designers.
7.1 Further Work
First and foremost, further experimentation of the materials properties must be performed, in
order to validate and explain the results yielded from these studies. Elastic modulus should
be measured using a 3 point bending test, as described in ISO 178, for more reliable results.
The ability to control strain rate should produce more reliable results. Physical testing on
components under torsion should be performed in order to verify FEA results.
In addition to this, potential applications should be considered for the principle of variable
stiffness in components produced by ALM. This paper would suggest research into
potentially applying this principle to active aerodynamics in Formula One. ALM allows critical
41. 41
cross sections and outer geometries to remain the same, whilst a) saving weight, and b)
allowing aerodynamic sections to deform into more drag efficient shapes upon certain
loading (i.e. at certain speeds).
42. 42
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45. 45
9.0 Appendices
9.1 Appendix A
Fused Deposition Modelling
Fused deposition modelling produces a component by extruding a coil of molten metal wire
or plastic filament onto a CNC bed. The extruded material instantly solidifies after extrusion,
forming the model/component.
Direct metal laser sintering
DSLS produces a component by selectively melting powdered metal. The part is built up
layer by layer, essentially welding the layers together (see figure ii). DMLS offers less
flexibility in terms of material range than FDM, as the material must be in powdered form
(Khaing et al. 2001).
Stereolithography
Figure i. FDM Process. 1. Nozzle extruding molten materials.
2. Deposited material (Modelled part) 3. Machine bed. (Anon
2016)
Figure ii. DMLS Process. (Additively 2016)
46. 46
Stereolithography creates components by selectively curing photosensitive resin with an
ultraviolet laser. For each layer that is solidified, the build platform sinks down to allow a
fresh layer to be added on top, similar to the DMLS process.
Figure iii. Stereolithography process (Solidsmack 2016)
47. 47
9.2 Appendix B
ISO 178
Included are all relevant stipulation from ISO 178 that were used during testing the flexural
properties of 3D printed PLA.
Specimen geometry and quality control
The specimen will have a rectangular cross section, with no rounded edges
Thickness within the central 3rd of the length must not deviate within 2% of its mean
value, measuring to the nearest 0.01mm
Width within the central 3rd of the length must not deviate from its mean value by
more than 3%, measuring to the nearest 0.1mm
Cross sectional aspect ratio must conform to certain predefined measurements, see
figure iv.
Specimens will be free of twist and have mutually perpendicular surfaces. This is to
be checked visually against a flat surface, or using micrometre callipers.
At least 5 specimens are to be tested
Anisotropic materials
Anisotropic material: in the case of materials having properties that depend on
direction, flexural stress will be applied in a manner that would be experienced in the
end use application.
If using the Instron:
Speed of 1mm/minute
Span length of 120mm
Record stress at strain values 0.0005 and 0.00025
Tested until 5% max strain occurs
Figure iv. Cross section requirements for flexural testing (ISO 178)
51. 51
9.5 Appendix E
The following results were recorded during testing for elastic modulus
52. 52
9.6 Appendix F
1.0 Product design Specification
1.1 Performance
1.1.1 Test pieces must be able to be suitably constrained in a cantilever bending test
1.2 Shape
1.2.1 Test pieces must have an L/H aspect ratio of above 5 in order to conform to Euler-
Bernoulli thin beam model
1.2.2 There must be a suitable surface for fixture, to allow for clamping.
1.2.3 It must be made obvious where the cavity starts and finishes, to allow for accurate
fixture. End to cavity distance will remain uniform throughout all test parts
1.3 Manufacture
1.3.1 All Parts to be built using the same machine.
1.3.2 Parts to be built simultaneously on same machine where possible
1.3.3 Hollow geometry is to be created using ‘bridging’ method
1.3.4 Parts to be built in ‘edge’ orientation
1.3.5 Parts to be measured post production, and checked for warpage.
Height, width and length dimensions to be recorded. Parts to be weighed and weight
recorded for density estimation
1.4 Materials
1.4.1 Material used will be Makerbot PLA filament
1.4.2 Material will be sourced from the same roll of filament
1.5 Quantity
1.5.1 At least 5 of each specimen will be made, in accordance with ISO 178
1.5.2 3 Different geometries to be compared including a solid control specimen
