3D Printing and Additive Manufacturing Capability Modelling
Vaughan Michell
University of Reading, Whiteknights, Reading, U.K.
Keywords: 3D Printing, Capability, Affordance, Capability-Affordance Model, Additive Manufacturing.
Abstract: The use of 3D, or additive manufacturing, is becoming more widespread and is seen as a new industrial
revolution due to the advantages of a material deposition approach compared to material removal. However,
little work has been done to identify and formalise the capabilities of this new technology. This paper formally
analyses the generic 3D printing process of additive manufacturing and compares it with the traditional
subtractive manufacturing process using the capability affordance model to determine its unique capabilities.
The CAM model defines a capability as a mechanism and space-time path. Results show that whilst the
mechanisms differ in terms of force and heat drivers, it is the space time path topology that is key to
manufacturing capability differences. We apply a topological analysis to identify the unique affordance path
of 3D printing which clearly demonstrates its superiority in complex and integrated part manufacture. Finally
we outline the differences in the key capability affordance factors for manufacturing in the two methods. This
paper builds on earlier work concerning the capability affordance model as a knowledge model to analyse and
understand capabilities and the unique advantages and possibilities of 3D printing.
Rapid prototyping (RP) is an additive manufacturing
technology based on the addition of materials layer
by layer instead of traditional cutting and removal of
material in subtractive manufacturing (SM) (Berman,
2012). RP was developed to provide a general
fabrication machine enabling construction of
complex 3 dimensional (3D) shapes and to use
designs directly from CAD (Choi and Samavedam,
2002). The term rapid prototyping – RP is often used
to describe the rapid fabrication of parts and
prototypes layer by layer (Berman, 2012). The term
additive manufacturing (AM) is used to generally
denote technology where fabrication of parts and
products occur by adding or depositing material.
Three dimensional printing (3DP) is really a
versatile consumer adaptation of rapid prototyping
technologies evolved from additive manufacturing by
adding a 3rd vertical z dimension to the general
architecture of a typical x-y inkjet or laser printer.
This greatly reduces the cost of the RP/AM machine
by several orders of magnitude, making it affordable
to companies and end users alike. Instead of ink, 3D
printing deposits material, usually hot plastics or their
derivatives. The print head thus becomes a means to
deposit the material as a fluid deposition of 3d
cylinders or ‘slugs’ of material in successive layers
(Berman, 2012). Pham and Guilt (Pham and Guilt,
2012) identified up to eight different technology
approaches to additive manufacturing. For
comparison purposes this paper focuses on a
frequently used 3DP technology where a heater melts
a suitable material and temperature sensors ensure the
correct flow viscosity. To enable a continuous feed of
material a series of rollers is used to drive the plastic
filament at the correct rate to be melted.
1.1 3D Printing Fabrication
3D printers enable CAD models to be converted to a
series of layers that can be printed one layer at a time.
This layer based model is typically in the form of a
stereo lithography or STL file. The STL file records
the surface shape/section of each layer, The internal
structure is reduced to a series of diagonal webs to
reduce both the volume and density of the
construction and the time taken to print it compared
to a solid layer. STL files can be generated from
traditional CAD packages by electronically slicing
the design.
The key to 3DP business success is reducing costs
and complexity of part creation whilst integrating
with consumer software (Pham and Guilt, 2012). For
this reason printing plastics have focused on
Michell V.
3D Printing and Additive Manufacturing Capability Modelling.
DOI: 10.5220/0006222400730083
In Proceedings of the Sixth International Symposium on Business Modeling and Software Design (BMSD 2016), pages 73-83
ISBN: 978-989-758-190-8
2016 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
thermoplastics PLA and ABS (Bassett et al., 2015).
However thermoplastics have their own
limitations of strength and robustness as PLA suffers
from degradation. The 3D object is built by
depositing material from the minimum of a point
‘blob’ to an x-y plane of material. Moving the bed on
which the material is deposited along the
perpendicular z axis away from the print head enables
the model to grow vertically. Additional control of the
deposition process is usually achieved by heating the
build bed or enclosing the build volume with a case
to optimise the conditions for solidification without
Another fabrication benefit is the ability of a 3D
laser scanner to digitise the spatial position of points
on the surface of a scanned object The CAD
compatibility enables a 3D model to be built from
data capture of the surface of any scanned object. This
enables scanned object models to then be quickly
scaled and printed out on a 3D printer subject to the
size limitations of the deposition mechanism used and
the build bed in a form or ‘scanning to production’ of
a finished part.
3DP has proliferated among manufacturing
companies, designers, end users and hobbyists as it
meets attributes of successful innovation as it is
cheaper than subtractive manufacturing, compatible
with CAD/CAM, less complex, easy to try out and
produces rapid end results. (Pham and Guilt, 2012).
Figure 1: Creation flow using 3D printing.
Any new product idea can be quickly rendered in
CAD and then fabricated after STL conversion on a
3D printer or scanned and then printed. This greatly
reduces the complexity of the design and creation
process as seen in Figure 1.
1.2 Paper Motivation and Layout
3DP is widely reported as a game changer that will
alter the world in terms of product supply,
manufacturing and retail (D'aveni, 2013). Whilst
there are limitations due to low speed of fabrication
and robustness of the materials used these are rapidly
being overcome (Nair, 2014).This is aided by the
rapid and wide use of AM/3DP among industry,
designers and hobbyists and consequent reduction in
unit costs driven by innovation. It prompts two
research questions; a) What are the perceived
business and technical advantages of 3D printing b)
How can we compare and model the capability of 3D
printing with traditional subtractive manufacturing?
To answer these questions our paper sections cover:
The background to 3D printing and its structure
Advantages of 3DP from a business and technical
Subtractive manufacturing and limitations
Capability and affordance modelling
• Mechanism Modelling
Path Topology Modelling methods
Discussion of findings/conclusion.
2.1 Business Advantages of 3DP
The benefits of 3D printing lead to major business
advantages, where a business advantage is defined as
superiority in delivering a strategic business benefit.
3DP/AM offers the benefit of a single general
production tool compared to a myriad of machine
tools required in subtractive manufacturing. 3DP/AM
develops this advantage due to its 3 axis and point
deposition versatility enabling the creation of
complex parts all on one machine. This removes the
need for sequential machining processes and jigging
and tooling (Choi and Samavedam, 2002) necessary
to hold parts firm against the cutting force implicit in
subtractive manufacturing.
3DP/AM also provides the opportunity for
integrated design to manufacture via as the software
format of 3DP has evolved from, and was deliberated
designed to integrate with CAD models (Choi and
Samavedam, 2002).
3DP has a unique benefit of rapid mass
customisation from creator to end user. The designer
and/or the end user is able to rapidly design parts in
well-established CAD formats. High quality and fast
Inventor Designer
Sixth International Symposium on Business Modeling and Software Design
fabrication can also be cheaply outsourced by sending
it to company to print anywhere in the world.
This greatly simplifies and reduces the cost of the
traditional mass customisation models that require
complex processes and equipment, for example used
by companies like Dell (Berman, 2012). This enables
any customer to create a new product, design or adjust
their product off line and send it directly to a
manufacturer in a ‘democratisation of the design
process’ (Hoy, 2013).
With 3DP/ the number of devices required to
enable design to production is reduced to one low cost
unit, reducing the learning curve and start-up costs,
hence encouraging adoption. (Nair, 2014).
2.2 Technical Advantages of 3DP
We define a technical advantage as an advantage in
the process, or mechanism of use, of a technology.
One of the critical advantages of AM over traditional
material removal and moulding methods is the ability
to develop unique shapes. This property is a function
of the topology of the printing device due to its point
deposition of material so that objects can be built in
single 3D points and layers at a time (Rosen, 2007).
The creation of a part from a single point enables
almost any shape to be built (Rosen, 2007) subject to
the need for support at overhangs and specific angles
and fine topographies on certain 3DP process types.
This differs from SM processes that require extensive
force application to remove material via traditional
lathe and milling machinery. AM deposition is
relatively force free apart from the weight of
deposited material that can distort the design when
setting. Depending on the resolution of the print head
and materials used, this enables extremely fine, small
and optimally engineered parts to be produced
without the force problems caused by material
removal. The point disposition ability at any location
within a build volume, coupled with digital design,
also enables parts to be made ‘within a part’ as there
is no necessity for cutter insertion and removal space
as in traditional manufacturing. For example the
creation of ball type bearings inside a complete ball
race can be executed in a single AM operation
(Conner et al., 2014). The point deposition ability of
AM enables sub-assemblies and products to be built
as complete volumes and surfaces, significantly
reducing the need for assembly and reducing costs.
For example a complete nylon ball bearing assembly
can be produced in one operation as one part vs 18
separate parts assembled using traditional
manufacturing due to SM machining limitations
(Conner et al., 2014).
The 3DP point deposition ability further enables
parts to be created as a fine mesh or space frame,
greatly reducing weight, in contrast to machining
from solid. This enables maximisation of strength per
unit volume (Pham and Guilt, 2012).The ability to
deposit in points and layers also supports integrated
materials structure variations within a part and the
creation of cellular materials to support energy,
thermal and acoustic design variations (Rosen, 2007).
This enables ‘designed property gradients’ where the
density of the product can be designed to vary to suit
design needs (Rosen, 2007). 3DP further enables the
creation of generic ‘graded’ ‘cellular materials’ such
as lattices, honeycombs etc to suit design needs for
density and other physical property variations (Rosen,
A potential revolutionary advantage of the
material deposition technique is that it enables the
embedding of different material types or even whole
components as the part is fabricated. This facilitates
variation in composition of the object material
properties and additional elements such as areas of
electrical conductivity or embedded components to
suit design needs (Doubrovski et al., 2011).
3.1 Limitations of SM
This section explores the traditional subtractive
manufacturing process of material removal using a
range of different machine tools based on different
cutter topologies.
The capability of traditional machine tools are
limited by the cutter path which is determined by the
cutter shape and mechanics. For example a lathe has
two degrees of freedom about an axial symmetry,
resulting in a capability for producing axially
symmetric parts. A milling cutter has three degrees of
freedom about x, y, z axes to produce a diverse range
of convex and concave parts. In contrast a drill has
effectively only one degree of vertical freedom to
create a hole of varying depth.
In traditional SM the lack of a universal cutting
machine and limitations of cutter path and finite
cutter size means the order in which a complex part is
manufactured must be considered to avoid unwanted
tool interactions (Matthews, 2007). This order of
processing (OOP) limitation adds complexity by
imposing machining precedence constraints and
conditions on the direction of tool application or
3D Printing and Additive Manufacturing Capability Modelling
approachability, limiting what is feasible to fabricate
(Gupta et al., 1997).
One complication is accessibility (AC), where the
arrangement of certain shapes drives the order of
machining, otherwise there would be no cutter access.
Gupta et al., (Gupta et al., 1997) defined feature
accessibility as a condition where the volume of space
required for accessibility Av has not been lost by a
volume already removed from the workpiece.
For example, if the accessible volume of a piece
of material X intersects with the removal volume of
Y, the cutter must approach a through the volume
occupied by Y and hence Y must be machined before
X (Matthews, 2007).
Also if X and Y have different approach
directions, and machining X provides a surface to act
as datum for measurement or tolerance, then X must
be machined first. This is a Datum Dependency (DD)
limitation of SM (Matthews, 2007).
Another concern is approachability (AP): if X is
machined before Y then Y will not be able to
approached or accessed to create the shape (Gupta et
al., 1997). For example eg a hole may need to be
machined first to provide access to cut a slot.
3.2 Cutter Path Limitations (Cpl)
At the fine scale level for SM we must also consider
limitations due to cutter size and geometry.
Whilst convex parts can be relatively easily
machined with SM, concave parts eg edges and
pockets or blind holes to be cut into the part are
limited by the need to ensure cutter access.
Gupta et al (Gupta et al, 1997) defined three types
of limitations for cutter path access:
CPL1: The curvature of the tool must be less than
the curvature of a concave edge – otherwise the
tool cannot follow and cut the edge (dcur);
CPL2: Where two closed edges form a narrow
passage to be cut by the tool the diameter of the
passage must be less than the tool (dpas) to enable
the cutting of the passage by the tool;
CPL3: Concave corners formed by the cutter path
must be larger than the tool (dcor) to enable cutter
CPL4: as the tool size increases the cutting
trajectory (ie the minimum amount of arc that you
can cut with this size cutter decreases ie is a limit
on dtra) beyond which you will cut a bigger arc
than specified;
CPL5: The max diameter of tool also must be less
than the smallest diameter feature (min dmax).
This results in Gupta’s set of cutter path trajectory
limitations for the maximum cutter diameter:
du = min (dcur, dpas, dcor, dtra, dmax) (1)
Some topologies eg producing a part within a part
(PP) using subtractive manufacturing are almost
impossible with SM as it requires a tool to enter the
interior of a billet of material and then the operation
of that tool via a cutter path wholly within the billet.
The geometry of the cutting tool with respect to
the part is also subject to two further cutter geometry
(CG) limitations. The tool cutting edge angle
with respect to the cutter motion ά and the inclination
of the tool cutting edge with respect to the part, ie the
rake angle β must be within ranges to avoid skimming
or gouging the material and adversely affecting
surface quality (Blackenfelt, 2001).
3.3 SM Conceptual Model
Based on the above discussion we can now develop
an outline conceptual model for subtractive
manufacturing. Consider the following: where Ps is a
part to be created by the subtractive manufacturing
process, B = material billet from which the part is
machined, and Fi is the i’th machined feature (eg
hole, passage, curved surface etc) where i = 1,…n .
Then the part is the billet minus the union of all the
Ps = B – Fi
But each of the i in number features are topological
elements that in SM are created by the intersection of
the swept volume of the j in number cutter operations
Sc required to machine the features with the billet
volume B such that:
Ps = B – (B
sum ( (j= 1-n) Scj)
But as we have seen the swept volume is limited by
cutter approach geometry, size and access limitations
and the prohibited volumes discussed earlier. Hence
a generic model for traditional machine tool material
removal manufacturing is:
Ps = B – (B
sum ( (j= 1-n) Scj ) - CPV
Subject to the constraints that the j cutter paths are
processed in the appropriate order and within
processing constraints (AC, DD, AP, CG ) and cutter
path limitations (CPL). Where Sc is the swept volume
of cutter, CPV are the cutter prohibited volumes, such
as a part within a part etc. We will reuse this equation
later, but we now focus on how we can identify and
measure capability.
Sixth International Symposium on Business Modeling and Software Design
4.1 Overview
Capability is a function of an action process, and the
nature of the interaction between two or more objects
or resources (Michell, 2011). Capabilities can be
modelled by understanding the way possible actions
or affordances can or cannot occur. Gibson (Gibson,
1979) defined affordance as the ‘property that the
environment or physical system offered the animal to
enable a possible useful transformation for the benefit
of the animal’. Affordances refer to descriptions of
(verb-noun) object abilities such as a road is
‘walkonable’ or the ‘cup affords drinking’ (Gibson,
1979) indicating that the structure/disposition of a
road or cup– enables it to be walked on or drunk from.
Affordances focus on the possibilities of how the
object could be used by the animal or person.
Affordances require a driving agent, an animal or
natural process for them to occur. Turvey’s
affordance model related animal properties Z and
properties of other entities X in an environment and
showed that affordance depended on the state or
properties of the animal/object and their
‘dispositions’ (Turvey, 1992). Using the concept of
affordance we developed a model of capability – the
capability affordance model (CAM) (Michell, 2012).
The model decomposed the affordance-effectivity
disposition into (i) a causal energy mechanism eg
force, temperature or electrical difference that
enables, the capability to occur. This energy flow is
transferred or dissipated through a (ii) space-time
affordance path that varies with the characteristics of
the animal and objects used in the interaction
(Michell and Roubtsova, 2014).
As affordances require animal or natural changes
to occur to make them realisable we define the
affordance mechanism as the cause and effect
transformation at the interface between two or more
interacting resources and its properties that enable the
transformation (Michell 2013). Mechanism thus
refers to the behaviour and properties of the energy
transfer that drives the transformation. For example a
potential difference enabling an electric motor to
rotate, or human energy is transferred to enable the
capability of a manual device like a syringe to ‘afford’
injection. Affordance mechanisms AM can be
typically modelled as force, heat or other energy
equations. However, for comparison purposes it is not
necessary to include the detailed mathematics, only to
understand their differences. The affordance path AP
is the set of possible space-time movement and
geometric configuration conditions that must exist to
enable the affordance mechanisms to act and execute
the capability (Michell, 2012). In the syringe injection
case the affordance mechanism is the force from the
doctor’s hands holding and pressing the plunger of a
syringe to give a patient an injection. This force is
transmitted along (a linear in this case) affordance
path from the plunger into the drug fluid which is
driven out into the patient (Michell and Roubtsova,
2014). The affordance transmission path for any
capable action forms an affordance chain from the
originating source of energy through the operating
parts of the device.
We can identify the energy mechanism and the
(affordance) path of the energy by observing the
chain of actions to make the man-machine capability
work (Michell and Roubtsova, 2014). At the point of
executing the capability to inject for example the
affordance chain, eg for injection will be a force
transfer from hand to syringe, to drug fluid pressure,
to patient. (See Michell and Roubtsova, 2014 for
details).A specific man- machine combination will
however have specific values and measures of
specific factors such as force, velocity and energy,
path topology and device volume and geometry
limits. These must be within a certain range for the
capability to occur. These capability affordance
factors (CAF) such as the range of angles the syringe
can be held at, or the minimum force to grip a syringe
or maximum force possible before breaking it will
characterise the capability and enables us to model
and compare capabilities (Michell and Roubtsova,
2014). To study and compare the capabilities of
additive vs subtractive manufacturing we therefore
need to identify the a) energy transfer mechanisms of
the two sets of machines and b) their resulting
transmission or affordance path and c) the critical
affordance factors and range of values that make it
5.1 SM Mechanism Affordance Chain
The mechanism represents the difference in energy
that causes an action to occur. In subtractive
manufacturing the affordance mechanism is typically
the application of force greater than the material
strength to cut or remove the material to the desired
shape of the final part. This process is typically
achieved via electrical energy used to rotate electric
motors to drive a rotary cutter and to s move the cutter
or part in a specific intersecting 3D space-time path.
For example a lathe has a motor to rotate the billet
3D Printing and Additive Manufacturing Capability Modelling
about an axis, whilst the cutter is stationary and
moved at right angles to the work. In contrast in a
milling machine the cutter is rotated via an electric
motor and the billet is clamped to table that can move
in x, y and z directions with three degrees of freedom.
Figure 2: Example SM Mechanisms.
In subtractive manufacturing, unlike 3DP, there is
no universal tool solution. A part, if complex, is
produced with a series of machining actions on
different machining centres, such as a lathe, mill, drill
etc. Hence the affordance path comprises a series of
cutting actions on separate machines, separated by
moving the part between machine set up operations,
where the billet is locked into the correct position and
orientation for cutting. Each cutting operation
comprises a relative simple mechanism or short
affordance chain representing the application of a
cutting force along a space time path in relation to a
constrained billet as dictated by the machine and
cutter geometry as in Figure 2.
5.2 Mechanism Driven CAF for
Subtractive Manufacturing
Due to the forces involved in machining hard
materials fixture constraints to hold the part being
machined against the cutting forces may be required
to be designed, positioned and applied, hence
increasing the complexity and cost of setting up the
additive manufacturing operation (Matthews, 2007).
There are upper and lower bounds in the forces
required to remove unwanted material from a lump of
metal or billet. For example there must be sufficient
average torque Tm to cut the part but less than the
maximum machine torque to damage material. A
related factor is the tool spindle speed w, which again
must be greater than a minimum value to ensure a
smooth surface finish, but less than the critical value
to cause burning or melting of the tool or part. In
addition as tools are liable to be bent with high forces,
the average cutting force Fm must be sufficient to cut
smoothly with minimum tool deflection and less than
the force required to cause part damage or failure such
to limit the average cutter deflection dc will limit the
capability of the tool to produce a quality part. Further
the cutting force Fm must be less than the critical
value necessary to cause significant tool wear
(Blackenfelt, 2001).
The force required to cut a material and the
material properties will dictate potential distortion
especially in features of the manufactured product
that have thin walls (Matthews, 2007). Further there
is a limit to feature production of very fine parts. For
example very thin cylinders or point features are not
able to be machined due to these force limitations.
Similarly the creation of a mesh from a solid billet
would be extremely difficult, time consuming and
very costly.
5.3 Mechanism for Additive
Additive manufacturing deposition mechanisms can
vary widely from heated molten plastic to laser
sintering (Norton, 2001). For capability comparison
we will focus on the most typical mechanism used in
the cheaper 3D printers – based on heated plastic
deposition. In a typical 3D printer of this form there
are 4 component mechanisms that form an affordance
chain of interacting actions (Figure 3).
Firstly a material feed process is usually via
electrically driven rollers applying a rotary
constraining force to a fibre of the plastic working
material which is dragged into an electrically driven
heating element. This heats the plastic to a pliable
temperature φ and viscosity within a range that
enables the melted plastic to flow through the nozzle
in a continuous stream according to the feed
The plastic flows through the nozzle at a steady
velocity Vp driven by the force Ff imparted to the
plastic filament by the rotation of the pinch rollers.
For deposition path planning & control, the heater
and nozzle are typically fixed to a framework of
motor driven slides (similar to a 2D inkjet printer) that
enables the precise positioning of a point or a
line/area of the deposited material dictated by the
optimised STL model of the structure driven by the
CAD design model. The material deposited internal
to the shape – the ‘infill’ is not solid but an STL lattice
structure that can be 80% or more less than the full
CAD solid model (Bassett et al., 2015).
Finally full x, y, z coverage of a three degree of
freedom build space is achieved by lowering the x-y
plane or build table in the z direction as successive
layers are added. This table is often heated, or the
build volume enclosed, to minimise warping of the
Mechanism:CuttingforceFl perpendiculartorotation
Mechanism:CuttingforceFm indirectionofbedtravel(x,y,z)
Velo cityVl,
Vel ocit yVm,
Tur nfeatureof
Sixth International Symposium on Business Modeling and Software Design
part which would otherwise occur with rapid cooling
back to room temperature.
Figure 3: 3D Printer Key Components and Mechanism.
5.4 Mechanism Driven CAF for
Additive Manufacturing
A capability affordance factors that limit and define
whether the affordance and capability will occur for
3DP are based on the heat transfer and feed rate
variables for the melted material deposition
mechanism a sample of which is discussed below, but
a wider range can be seen in (Choi and Samavedam,
Firstly the material melting temperature θ must be
within a range that enables flow, but not burning of
the PLA/ABS material. For example 175 < θpla < 200
degrees, 225 < θabs < 230 degrees (Basset et al,
2015). Secondly the build bed must be heated within
a given temperature range to avoid warping as the part
cools. For example 20 < γpla < 70 degrees, and for
ABS 105 < γ < 105 degrees (Basset et al., 2015). The
material filament feed rate Vf must be within a range
consistent with smooth deposition to avoid gaps or
bunching, or unwanted spreading of the material.
The material viscosity μ at this temperature must
be sufficiently liquid to flow, but not too low to result
in puddling and spreading. The x,y,z velocity of the
nozzle travel Vn-xyz must also be in proportion to the
material viscosity and flow rate and be above a
minimum where material bunching will occur and
less than a maximum that would cause gaps in the
deposition. The deposition layer height hd is
important for part surface finish and fineness and is
dependent on nozzle diameter, but must be above a
minimum value that would unacceptably increase the
time to produce the part (Basset et al., 2015). The
infill structure density р must also be within a range
of values that enables sufficiently rapid printing, but
not too sparse to cause problems with structural
Various combinations of these factors will affect
the capability and mathematical models have been
built to establish the range of control parameters and
the physics and heat transfer involved (Ganeriwala
and Zohdi, 2014). For example the plastic feed rate
must be related to the x, y, z velocity for a given
material viscosity to avoid gaps or lumps in the
deposited plastic. Feed rate and viscosity will affect
the layer thickness, which in turn will affect surface
accuracy as a series of stacked layers or ‘stair step
effect. (Choi and Samavedam, 2002). The mechanism
driven factors for AM and 3DP can be seen in Figure
To compare 3DP capability with traditional
manufacturing we need to develop a conceptual
model of the affordance path that takes into account
the path geometry and the mechanism of the different
methods. Both manufacturing methods involve the
forming/sculpting of three dimensional solids, one by
removing material from a solid block or billet of
material by force and the other by deposition. Much
research has been conducted into traditional
manufacturing focusing on cutter path geometries
(Feng and Cusiak, 1995) and the study of tool
vibration effects (Blackenfelt, 2001). Other work has
focused on identifying the optimum sequence and
type of machining (Gupta et al, 1997) or machining
process simulation (Blackenfelt, 2001) and the
problem of modelling machining features (Tapie et
al., 2012). However using a mathematical geometric
approach to modelling these methods is unduly
complex and unnecessary for our comparison
An alternative method that is appropriate to
accommodate the massive variation in machine tools
and machined or 3dp manufactured objects is to
model the situation from a topological set theory
perspective. Consideration of the problem suggests
that for subtractive manufacturing we need to model
the intersection of a polygonal volume with a cutter
path with different degrees of freedom. The additive
manufacturing (3DP) model can be considered as the
intersection of a bound build volume space with a
three degree of freedom deposition path.
Topological modelling defines spatial
relationships for geometries that are preserved under
rotation and scaling transformations (Egenhofer et al.,
1994). Such modelling can be used to define
topological relationships between two spatial objects
(Borrmann et al., 2006). Based on the fact that
boundaries and interiors have been identified as the
crucial descriptions of polygonal intersections
(Wagner, 1988), Egenhofer developed a point set
model of topological spatial relations between
Tab le&zaxis
Veloc it yV, Force
3D Printing and Additive Manufacturing Capability Modelling
regions or areas (Egenhofer and Franzosa, 1991). The
point set approach considered a set of points x and a
set of points y with neighbouring and overlapping
topologies defined by the set theory. Egenhofer
defined the results of the intersections of the
boundaries and interiors of two shapes in terms of
non-empty ¬ Ø and empty sets Ø , resulting in nine
feasible topological relations.
6.1 Three Dimensional Modelling
The 2D model was formally extended by
specification of the interior, boundary and exterior
point sets of spatial object by Egenhofer et al, who
described the topological relations between two
volumetric cells A and B. He considered A and B as
arbitrary objects composed of sets of points
(Egenhofer, 1994). These comprised three ‘object
parts’; interior designated by , boundary designated
by δ and exterior designated by and the two point
sets;{A, δA, A} and {B, δB, B}.
The combinations of intersections between
interior, boundary and exterior point sets result in the
nine intersection model (9-IM).
Figure 4: The 9-IM Topological Intersection Model.
Borrmann et al’s work describes a generic
intersection matrix for intersections of point, line,
area and 3d body (Borrmann et al., 2006). This gives
a number of intersection volumes that include; non-
touching (disjoint), equal volumes, a volume
containing and touching a volume and a volume
totally within a volume (Borrmann and Rank, 2009).
Whilst their work focused on modelling intersections
of architectural buildings, as these are simply
intersecting polygons, the same approach can be
adapted to manufacturing of polygonal parts. This is
equivalent of the intersection of the billet and the
cutter path. For our purposes we only consider the
body intersection which we can use to model the 3D
billet, cutter path or deposition path.
Using the same principle, the ‘equal volumes’
topology can be used to describe the 3D printer
situation, where the material deposition volume of a
3D printer is equal to the full 3D build space
available. This represents a ‘total topological
relationship’ (Billen and Kurata, 2008), where any
point, line, area or the full work volume can be
reached with the three degrees of freedom of
deposition of the 3D printer
Earlier in equation 3 we defined Ps as a part
produced by subtractive manufacturing. As
topological relations are indicated by the presence or
absence of intersections in the 9-IM model, we can
rewrite the model for AM and SM and apply the set
theoretic approach to show which relationship holds.
For an additive manufacturing process the
completed part Pa should be exactly the same as the
part produced by subtractive manufacturing Ps. For
Pa the topological path model is a function of the
swept deposition volume Pd and the available build
volume limits V. The finished part depends on the
volume of deposited material defined by the set of
points Pd in relation to the overall volume available
to build in V.
Ps = Pa = V
Hence using the same 9-IM matrix M (V, Pd) we can
represents the possible topology for the 3D printer
AM approach. Where A in the original 9M matrix
represents the deposition path volume Pd from the
deposition of melted plastic points in layers. B
represents the available free space V to build in.
6.2 Capability Path Comparison
Using the above topologies the resulting
manufactured part is described by the range of non-
empty sets formed by the intersection of the four
feasible relations in the 9-IM model and defines the
gross path capability of each manufacturing approach
as seen in figure 6. This clearly shows the versatility
of the additive 3DP solution in its ability to deposit
material in any part of the build volume. Additive
manufacturing enables non empty sets for a part
within a part represented by the ‘contains’ relation
where an unused volume is completely contained by
the build volume and by extension a separate part
could also be present if deposition was stopped and
restarted. It also holds for the touch relation where the
internal void produced by AM touches an external
boundary. In contrast for subtractive manufacturing
all these options are empty sets and prohibited, apart
from the intersection topology, which has limitations
based on the capability affordance factors of
accessibility and operation sequence discussed
However, despite its greater path flexibility 3DP
has additional path conditions. The material
deposition as a slug of melted plastic will vary with
the curvature of the ‘tool’ or print head and thus build
bounda rya
interiorb bounda rya
bounda ryb bounda rya
bounda rybexteriora
Bᵒ δA
δB δA
Bᵒ A
Sixth International Symposium on Business Modeling and Software Design
orientation of the part will also affect final part quality
(Nelaturi and Shapiro, 2015). In addition the cooling
of the melted material in certain geometries may
result in drooping and warping and hence certain
features and overhangs may require additional build
support structure to be added during construction to
prevent this. In contrast the path driven capability
affordance factors for subtractive manufacturing as
discussed earlier are far more numerous, complex and
onerous. See figures 5 and 7 for both sets of factors.
7.1 Summary
We have analysed the perceived business and
technical advantages of 3D printing and shown how
these are derived by the mechanism and path
limitations of the AM and SM approaches. We have
compared the capability of 3D printing with
traditional subtractive manufacturing using a
capability affordance comparison method and a
topological model. The model demonstrated that the
mechanism of subtractive manufacturing is largely
based on force application and that this leads to the
requirements for extensive jigs and fixtures to hold
the part in place. This compared to the heat transfer
mechanism aided by a small filament force of 3D
printing. The 3DP mechanism in contrast relies on
gravity and the precise location of a point of material
to constrain the finished part. However, the 3DP heat
transfer mechanism produces a greater number of
more difficult to control factors such as flow rate,
viscosity etc as seen in Figure 5.
In contrast the topological model comparison
emphasises how traditional subtractive
manufacturing methods are limited by the path
geometry of the cutters used and the need for cutter
access This is emphasised by the fact that a 3D printer
with three degrees of freedom of point material
deposition has a ‘total topological relationship’,
compared with the ‘partial topological relationship’
of subtractive machining methods. SM is further
limited by the need, especially for complex parts, to
carefully consider the order of subtractive operations,
demonstrated by the larger range of geometric critical
affordance factors than 3DP seen in Figure 7.
However, whilst additive manufacturing has a far
greater capability to produce complex and intricate
parts, the machine parameters involved with the
deposition approach can be more difficult to get right
to ensure a quality part compared with tried and
trusted subtractive force driven mechanisms where
much more is known about the kinematics and
thermodynamics involved ensuring consistent quality
part production.
7.2 Conclusion
A have explored the key business and technology
benefits of 3DP additive manufacturing compared
with traditional subtractive manufacturing. We
applied the capability affordance model (CAM)
defining capability as an energy mechanism operating
through a space time path. We have shown via
topology analysis that the key capability difference
and advantage for 3DP is in its superior space time
affordance path due to the three degrees of freedom
to build from a point to enable construction of
complex single part objects and meshes, parts within
parts and very fine constructions. This is superior to
the limited topology available to additive
manufacturing due to the need for cutter access and
geometry limitations. However the force focused
mechanism of additive manufacturing does enable
more consistent surface quality and durability
compared to the heat flow focused mechanism of 3DP
with its more complex capability affordance factors
that lead to this variation. However, the low cost, ease
of use and design friendly format of 3DP enables
significant benefits to small and medium
manufacturers in producing innovative product
capabilities over traditional methods.
3D Printing and Additive Manufacturing Capability Modelling
Figure 5: Affordance Mechanism Comparison.
Figure 6: Comparison of Capability Paths.
Figure 7: Affordance Path Driven Capability Affordance Factors.
Subtra ctiveMa nufacturing(SM)CapabilityAffordanceFactors 3DPAdditiveMa nufacturing(AM)CapabilityAfforda n ceFactors
SCM1 sufficienttocutmaterial<AveragemachineTorqueTm<torqueto
ACM1 175 <plamaterialdepositiontemperatureθpla<20 0degrees
SCM2 speedtoproduceroughsurface<toolspindlespeedw
<tool/p art
ACM2 BuildbedtemperatureForexample20<γPLA<70degrees,105
SCM3 sufficienttocut<averagetoolforceFm<forcerequiredforsurface
ACM3 velocityforgapstooccur<materialfilamentfeedra teve locityVf<
SCM4 sufficienttocut<Fm<distortionforceforthinwallsections ACM4 mini mumflowvalue<materialviscosityμ<viscosityforpuddling
SCM5 sufficienttocut<Fm<forcerequiredtocausesignificanttoolwear ACM5 minimumforspeedrequi rements<depositionlayerheighthd<
ACM7 densityforstructuralissues<infillstructuredensityр<densityfor
ACM8 materialspecif icheatcapacity<criticalval ue forfailure
(burni ng/partdamage)
a b
a b
¬Ø Ø Ø
Ø ¬Ø Ø
Ø Ø ¬Ø
¯ ¯ ¯
Ø Ø ¬Ø
Ø Ø ¬Ø
¯ ¯ ¯
¯ ¯ ¯
¯ ¯ ¯
¯ ¯ ¯
Ø ¬Ø ¬Ø
Ø Ø ¬Ø
Subtractivemfg Additivemfg
no lackoffeasiblecutterpat h to
accessallpoint sonabillet
(limitedbycutte rsizeand
geometryandkinem atics)
yes abilitytodeposi t
mate ri alanywhereinthe
workspac e
no lackoffeasiblecutterpat h
yes abilitytodeposi t
mate ri altocompletely
envelopepart ofthe
yes feasiblecutterpathsto
inters e ction(limited
yes abilitytodeposi t
mate ri alinpartofthe
workspac e
no lackoffeasiblecutterpat h
singlepointonthebounda ry
yes abilitytodeposi t
mate ri altocompletely
envelopetheworks p ace
SubtractiveManufacturing(SM)CapabilityAffordanceFactors 3DPAdditiveManufacturing(AM)CapabilityAffordanceFactors
SCP1 OrderofProcessingenablesallmanufacturingfeaturestobeexist(OOP) ACP1 partorien tati on <criticalpathorientationgeometry
SCP2 Accessibilityiswithinaccessconstraints‐(AC) ACP2 geometrytosupportrequirementsforoverhangingparts
SCP3 DatumDe pendency‐(DD)conditionsare
SCP4 Approachabil ity(AP)conditionsaremet
SCP5 CPL1:Thecurvaturedcurofthetool<mincurvatureofconcaveedges
SCP6 CPL2:tool thediameterofthepassagedpas<tooldiame ter
SCP7 CPL3:Concavecornerdiameter(dcor)formedbythecutterpath>tool
SCP8 CPL4:
SCP9 CPL5:Themaxdiameteroftooldmax<smallestdiameterfeature(min
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