Build Orientation Analysis in fused deposition modeling

Build orientation analysis in FDM
Mechanical Engineering, Sipna COET, Amravati Page 1
INTRODUCTION
In the recent times, many manufacturing organizations are widely using
digital prototyping in different areas for product development. After the Machine
Component is digitally prototyped, and tested for the actual application, under
virtual conditions; and then in the manufacturing of the real prototype or product,
lot of alternative solutions and approaches will be involved. In order to prototype,
3D Printing technique is being used in the present world. This method is also called
as Additive Manufacturing process or Rapid prototyping. In this process, addition
of material is used in order to build the machine component or the component,
which is under manufacturing. There is no metal cutting and associated chips
production in 3D Printing process. In this method, the required complex shaped
components are modeled using CAD software and stored in .stl file format, which
in turn is loaded into the 3D Printing machine. The required components are
fabricated automatically with materials like ABS plastics. [ 8 ]
In the process of adopting 3D Printing Technology, Fused Deposition Modeling
(FDM) is one of the important processes that are used at present by many Industries.
In this process, one important consideration is to minimize the quantity of support
material of the product, which has a large influence on the product as far as many
considerations such as reduction of time in the design phase, reducing the cost of
manufacturing (post-processing), improvement in the accuracy and surface finish
with which the product is being fabricated.[8]

1. FUSED DEPOSITION MODELING
Figure 1 Fused deposition modeling [5]
It is one of the more popular methods for generative manufacturing. In this process,
three-dimensional object are produced by depositing a molten thermoplastic material
layer by layer. Stratasys Inc. is commercially manufacturing machines for FDM. A
solid filament of thermoplastic material with 1.25 mm diameter is fed into an x-y
controlled extrusion head. The material is melted by a resistance heater at a temperature
of 180°F (1°F above its melting temperature). As the head is moved along the required
trajectory using computer control, the thermoplastic material is deposited by extruding
it through a nozzle by a precision volumetric pump. As the extruded material, deposited
as a fine layer, comes out with a temperature just above the melting point, it resolidifies
within 0.1 second by natural cooling. To ensure proper adhesion of the deposited fused
material to the previously deposited layer, the object temperature is maintained just
below the solidification temperature. After one layer is deposited, the platform,
supporting the object, is lowered by one layer thickness.
To maintain stability in the process, the rate of flow of the extruded molten filament
is controlled to match,

( i ) the travelling speed of the depositing head (which can go upto 380 mm/sec),
(ii) the desired thickness of the layer (that varies from 0.025 mm to 1.25 mm), and
(iii) the width of the deposited line (which varies from 0.23 mm to 6.25 mm).
The repeatability and positional accuracy of this process are claimed to be
about+0.025 mm with an overall tolerance of 0.125 mm over a cube with 305 mm sides.
The FDM process is still not very suitable for parts with very small features. The
typically-used materials for the process include investment casting wax, wax filled
adhesive material, and tough nylon-like material. Polymer type thermoplastics can also
be used. [ 5 ]
Advantages:
1. Strength and temperature capability of build materials.
2. Safe laser free operation.
3. Easy Post Processing.
4. Quick and cheap generation of models.
5. Easy and convenient date building.
6. No worry of possible exposure to toxic chemicals, lasers, or liquid polymer bath.
7. No wastage of material during or after producing the model.
8. No requirement of clean-up.
9. Quick change of materials.
Disadvantages:
1. Process is slower than laser based systems.
2. Build Speed is low.
3. Thin vertical column prove difficult to build with FDM.
4. Physical contact with extrusion can sometimes topple or at least shift thin vertical
columns and walls.
5. Restricted accuracy due to the size of the material used: wire of 1.27 mm diameter.

Applications:
1. Investment Casting.
2. Medical Applications
3. Flexible Components.
4. Conceptual modeling.
5. Fit, form and functional applications and models for further manufacturing procedures.
6. Investment casting and injection molding.
2. LAMINATED OBJECT MANUFACTURING
Figure 2 : Laminated Object Manufacturing
(Source: https://www.azom.com/article.aspx?ArticleID=1650)
Lamination implies a laying down of layers that are bonded adhesively to one another.
Several variations of laminated-object manufacturing (LOM) are available. The
simplest and least expensive versions of LOM involve using control software and vinyl
cutters to produce the prototype. Vinyl cutters are simple CNC machines that cut shapes
from vinyl or paper sheets. Each sheet then has a number of layers and registration
holes, which allow proper alignment and placement onto a build fixture. Figure
illustrates the manufacture of a prototype by laminated-object manufacturing with

manual assembly. Such LOM systems are highly economical and are popular in schools
and universities because of the hands-on demonstration of additive manufacturing and
production of parts by layers.
LOM systems can be elaborate, the more advanced systems use layers of paper
or plastic with a heat activated glue on one side to produce parts. The desired shapes are
burned into the sheet with a laser, and the parts are built layer by layer (Fig. 2 ). On
some systems, the excess material must be removed manually once the part is
completed. Removal is simplified by programming the laser to burn perforations in
crisscrossed patterns. The resulting grid lines make the part appear as if it had been
constructed from gridded paper with squares printed on it, similar to graph paper.[ 5 ]
System Parameters:
There are various controlling parameters such as laser power, heater
speed, material advance margin, and support wall thickness and heater
compression.
1.Laser Power:
It is the percentage of total laser output wattage. For e.g. LOM 1015 is operated
at a laser power of about 9% of maximum 25W laser or approximately 2.25W. This
value will be different for various materials or machines but essentially it is set to cut
through only one sheet of build material.
2.Heater Speed:
It is the rate at which hot roller passes across the top of the part. The rate is
given in inches/second. It is usually 6”/sec for `initial pass and 3”/sec for returning pass
of heater. The heater speed effects the lamination of the sheet so it must be set low
enough to get a good bond between layers.
3.Material Advance Margin:
It is the distance the paper is advanced in addition to length of the part.

4.Support Wall Thickness:
It controls the outer support box walls throughout a part. The support
wall thickness is generally set 0.25” in the X and Y direction, although this
value can be changed by operator.
5.Compression:
It is used to set the pressure that the heater roller exerts on the layer. It is
measured in inches which are basically the distance the roller is lifted from its initial
track by the top surface of part. Values for compression will vary for different machines
and materials, but are typically 0.015”-0.025”.
3. STEREOLITHOGRAPHY
a b c
Figure 3 : Stereolthography [ 3 ]
A common rapid-prototyping process-one that actually was developed prior to fused-
deposition modeling is stereolithography (STL). This process is based on the principle
of curing (hardening) a liquid photopolymer into a specific shape. A vat, containing a
mechanism whereby a platform can be lowered and raised is filled with a photocurable
liquid-acrylate polymer. The liquid is a mixture of acrylic monomers, oligomers
(polymer intermediates), and a photo initiator (a compound that undergoes a reaction
upon absorbing light).

At its highest position of the platform (a in figure), a shallow layer of liquid
exists above the platform. A laser generating an ultraviolet (UV) beam is focused upon
a selected surface area of the photopolymer and then moved around in the x-y plane.
The beam cures that portion of the photopolymer (say, a ring- x ; shaped portion) and
thereby produces a solid body. V The platform is then lowered sufficiently to cover the
cured polymer with another layer of liquid polymer, and the sequence is repeated. The
process is repeated until level b in Fig.3 is reached. Thus far, we have generated a
cylindrical part with a constant wall thickness. Note that the platform is now lowered by
a vertical distance ab.
At level b, the x-y movements of the beam define a wider geometry, so we
now have a flange-shaped portion that is being produced over the previously formed
part. After the proper thickness of the liquid has been cured, the process is repeated,
producing another cylindrical section between levels b and c. Note that the surrounding
liquid polymer is still fluid (because it has not been exposed to the ultraviolet beam) and
that the part has been produced from the bottom up in individual “slices.” The unused
portion of the liquid polymer can be used again to make another part or another
prototype. Note also that, like FDM, stereolithography can utilize a weaker support
material. In stereolithography, this support takes the form of perforated structures. After
its completion, the part is removed from the platform, blotted, and cleaned
ultrasonically and with an alcohol bath. Then the support structure is removed, and the
part is subjected to a final curing cycle in an oven. The smallest tolerance that can be
achieved in stereolithography depends on the sharpness of the focus of the laser;
typically, it is around 0.0125 mm. Oblique surfaces also can be of very high quality.[ 3 ]
Advantages:
1) Parts have best surface quality
2) High Accuracy
3) High speed.

Disadvantages:
1) It requires Post Processing. i.e. Post Curing.
2) Careful handling of raw materials required.
3) High cost of Photo Curable Resin.
Applications:
1) Investment Casting.
2) Wind Tunnel Modeling.
3) Tooling.
4) Injection Mould Tools.
4. SELECTIVE LASER SINTERING
Figure 4 : Selective Laser Sintering
Selective laser sintering (SLS) is a process based on the sintering of nonmetallic or less
commonly, metallic powders selectively into an individual object. The basic elements in

this process are shown in Fig.4.The bottom of the processing chamber is equipped with
two cylinders:
I. A powder-feed cylinder, which is raised incrementally to supply powder to the
part-build cylinder through a roller mechanism.
2. A part-build cylinder, which is lowered incrementally as the part is being
formed.
First, a thin layer of powder is deposited in the part-build cylinder. Then a
laser beam guided by a process-control computer using instructions generated by the
three-dimensional CAD program of the desired part is focused on that layer, tracing and
sintering a particular cross section into a solid mass. The powder in other area remains
loose, yet it supports the sintered portion. Another layer of powder is then deposited;
this cycle is repeated again and again until the entire three-dimensional part has been
produced. The loose particles are shaken off, and the part is recovered. The part does
not require further curing-unless it is a ceramic, which has to be fired to develop
strength.
A variety of materials can be used in this process, including polymers (such as
ABS, PVC, nylon, polyester, polystyrene, and epoxy), wax, metals, and ceramics with
appropriate binders. It is most common to use polymers because of the smaller, less
expensive, and less complicated lasers required for sintering. With ceramics and metals,
it is common to sinter only a polymer binder that has been blended with the ceramic or
metal powders. if desired, the part can be carefully sintered in a furnace and infiltrated
with another metal.[ 3 ]
Purpose of Selective Laser Sintering:
1. To provide a prototyping tool.
2. To decrease the time and cost of design to product cycle.
3. It can use wide variety of materials to accommodate multiple application throughout the
manufacturing process.
Advantages:
1. Wide range of build materials.
2. High throughput capabilities.
3. Self-supporting build envelop.

4. Parts are completed faster.
5. Damage is less.
6. Less wastage of material.
Disadvantages:
1. Initial cost of system is high.
2. High operational and maintenance cost.
3. Peripheral and facility requirement.
Applications:
1. As conceptual models.
2. Functional prototypes.
3. As Pattern masters.
5. THREE DIMENSIONAL PRINTING
Figure 5 : Three dimensional printing [ 3 ]
In the three dimensional printing (3DP) process, a print head deposits an inorganic
binder material onto a layer of polymer, ceramic, or metallic powder. A piston,
supporting the powder bed, is lowered incrementally, and with each step a layer a
deposited and then fused by the binder.

Multi jet modeling and poly Jet processes are sometimes referred to as three
dimensional printing technologies, because they operate similarly to inkjet printers, but
incorporate a third (thickness) direction. In fact, 3DP has been used interchangeably
with rapid prototyping or digital manufacturing to include all rapid prototyping
operations; however, 3DP is most commonly associated with printing a binder onto
powder. Three dimensional printing allows considerable flexibility in the materials and
binders used. Commonly used powder materials as blends of polymers and fibers,
foundry sand, and metals. The effect is a three dimensional analog to printing
photographs, using three ink colors (red, cyan, and blue) on an ink jet printer.
The parts produced through the 3DP process are somewhat porous, and thus
may lack strength. [ 3 ]

FUSED DEPOSITION MODELING
Figure 6: Fused Deposition modeling
In order to create a complex physical object from a digital set of instructions, many
mechanical systems must work together to get the job done correctly. In addition to
these mechanical systems, software used to control the nozzle temperature, motor
speeds & direction, and methods in which the printer lays out the material are equally
important to create a highly accurate model.
The nozzle in a 3D printer has one of the most important jobs of all the
mechanical systems. It is the last mechanical device that is used to build up a 3D object
and it’s design and functionality is extremely important when it comes to the accuracy
and build quality of the printer. The biggest contributor to the performance of the nozzle
is its orifice size. Typically, the nozzle size used on many 3D printers is 0.4mm. This
size is small enough to produce high quality parts while maintaining reasonable build
times. Printers such as the Makerbot Replicator use this size nozzle. Depending on the
over-all goal of the part being printed however, these nozzles can be changed to larger
diameters in order to increase the speed of the print job. While doing so will decrease
the horizontal accuracy, parts that will be used as rough drafts or that will be post
processed with fillers or paints will still perform as in-tended. It is important to never
set the layer height higher than the nozzle size. This will dramatically decrease the bond

strength between the layers and overall build quality. For example, if a 3D printer is
using a 0.6 mm nozzle, then the maximum layer height should not exceed 0.5 mm.
While the nozzle is used to direct molten plastics in a precise manner, it’s other
job is to convert the solid coil of plastic material into the molten state by utilizing a
heating element within the extruder assembly. This heating element can be a vitreous
enamel resistor, a nichrome wire, or a cartridge heater. In addition to the heating
element, there is usually a thermistor (temperature sensor) integrated into the extruder
assembly to control the required temperature for the specific material being used. For
example, one of the most common materials used in FDM is PLA (polylactic acid)
which has a melting temperature of around 160 degrees Celsius. In contrast, another
very popular material used is nylon. This material requires extrusion between 240 and
270 degrees Celsius. It is very important to use the correct extrusion temperature in
order to minimize the risk of the nozzle jamming and also maximize the bond between
bead layers. The design of the extruder is very important to not only the printing
accuracy, but also to the overall performance and maintenance of the printer. While the
bottom end of the extruder must be able to heat the material to a desired temperature
within a few degrees, the upper end must remain as cool as possible in order to avoid
jamming. This is due to the feed mechanism located above the extruder, which requires
the filament material to be in a completely solid state in order to function properly. One
way to decrease heat transfer from the heating element to the feed mechanism and in
turn decreasing the chance of jamming, is to use fans to cool the top end of the extruder.
Depending on the type of model being printed, and the type of material being used, a
heated bed may be important to maintain the structure’s shape while it cools. Since
plastics shrink as they cool, a quick temperature drop could cause the corners of a part
to curl up off of the printer bed. To minimize this risk, some printers incorporate an
electronically heated bed that keeps the temperature steady. This allows the model to
cool at a more even rate and improve its overall dimensional accuracy.
There are many factors that contribute to the build quality of a 3D printed part.
The extruder assembly which includes the extruder, heating element, & nozzle
contribute greatly to the overall build quality.[ 1 ]

VARIOUS PROCESS PARAMETERS OF FDM PROCESS
Figure 7 : Various Process Parameter of FDM Process
1:Layer thickness
Layer thickness refers to the distance traveled in the z-direction between successive layers, and
has a direct impact on the build time and the surface quality of sloped surfaces. Each of the
three different nozzle tip sizes on the FDM 2000 (T10, T12, and T16) has an associated range
of recommended layer thickness. The layers in an FDM model are determined by the extrusion-
die diameter, which typically ranges from 0.050 to 0.12 mm. This thickness represents the best
achievable in the vertical direction. In the x-y plane, dimensional accuracy can be as fine as
0.025 mm as long as a filament can be extruded into the feature. The thickness of the layer
increases, the roughness increases. Layer thickness is the thickness of layer deposited by nozzle
tip and the value of layer thickness depends on the material and tip size.
This is the vertical height change from one layer to the next. While a smaller layer
height yields a higher resolution part, the build time is much longer. On the other
hand, large layer heights take much less time to produce but also decrease the surface

quality. As mentioned before, the layer height must not exceed the nozzle diameter.
This will lead to little or no bond between the layers. [ 1 ]
Figure 8 : Effect of Layer Thickness on Surface Finish
2.Build Orientation:
Part-build orientation is the only variable examined which is defined within the CAD stage of
the FDM process. Build orientation is varied by rotating the .STL file with respect to the
machine coordinate system. The important aspects of the orientation include the z-height of the
part and the angle each part surface or facet creates with the x-y plane or machine table. The z-
height can vary between the limits of the minimum layer feasible (0.178mm) and the maximum
height of the FDM2000 work envelope (25.4cm). The experimentation focused on orientations
requiring minimal or no support material.[ 6 ]
Part build orientation or orientation refers to the inclination of the part in the build platform
with respect to X, Y, and Z axis, where X and Y-axis are considered parallel to build platform
and Z- axis is along the direction of part build.
Tangent
Vertical
Normalθ
θ=Build orientation
t=Slice thickness
Figure 9: Build orientation [ 4 , 7 ]

2. Build time
Build time is important as it directly affects the cost of the part and is dependent on the part
deposition orientation as the sum of areas of all slices is different in different orientations. The
accurate estimation of build time for FDM processed parts require slicing of the part,
calculation of the area of the slices, generation of roads for laying the extruded material from a
nozzle, acceleration and deceleration of the nozzle tip while laying the material, and other non-
productive times like lowering the platform after deposition of a layer. Therefore, accurate
estimation of build time is tedious and time consuming.
3.Raster Orientation
The direction of the beads of material (roads) relative to the loading of the part.Raster angle
refers to the angle of the raster pattern with respect to the X axis on the bottom part layer.
Specifying the raster angle is very important in parts that have small curves. The typical
allowed raster angles are from 0° to 90°. Raster width is the width of the material bead used
for raster. Larger value of raster width will build a part with a stronger interior. Smaller value
will require less production time and material. The value of raster width varies based on
nozzle tip size. Vertical to Z axis is Axial and Perpendicular to Z axis is Tranverse.
Figure10: Raster orientation [ 2 ]
4. Model Build Temperature:
The temperature of the heating element for the model material .This controls how molten the
material is as it is extruded from the nozzle. Model temperature is the liquefier chamber
temperature. This is the temperature at which the model material is melted. The variation in
model temperature would affect the fluidity of the material as it is being laid. This factor was
selected to see if it influences the surface roughness. The levels considered were 250
o
C,
270
o
C and 280
o
C. At higher temperatures it was expected that the material would be in a

more fluid state, thus it would lead to more bulging of the material as it is being laid down.
This would result in rounding off of the stair-steps thus leading to better surface finish.
5.The interior fill strategy
The general path plan used in filling the inner portion of each layer. The user is offered three
possible interior fill types, as represented in order of decreasing material usage:
 solid;
 part fast;
 cross hatch. and
 Low density
If prototype function does not require a densely solid object, the user may want to decrease the
amount of material used and the total build time by selecting part fast (medium material usage)
or cross hatch (minimum material usage). [ 6 ]
6.Structure of Support Material
It is common for more advanced software to allow the user to modify how the support material
is utilized. Usually, this task is handled by the software automatically. There are certain cases
where this may be beneficial. For example, if a user finds that a printed object is warped after it
is completed, then adding additional supports to the object during the print process can help
prevent this. Another example would mostly be used as a last resort. If the user finds that the
bed of the printer is not level, then the Raft option could be used. [ 1 ]
7.Speed :
The maximum speed of the machine is governed by the firm-ware installed on the motor
controllers. However, it can be beneficial to adjust the speed in order to decrease the build time
(fast), or increase the build quality (slow). The speed settings can be split in three categories;
the perimeter, infill, and travel speed. The perimeter speed is the speed at which the print head
moves while printing the perimeter of the model. The infill speed is the speed at which the print
head moves during the infill operation. And lastly, the travel speed is the speed at which the
print head moves from one location to another while not printing. For example, if there are

multiple parts being printed at once, then the travel speed will be the speed of the print head
when it is traveling to the other part to be printed. Typical speeds for the perimeter and infill
are 50mm/sec and 70mm/sec, respectively. [ 1 ]
8.Perimeters :
This is the number of times the printer will draw the outer surface of a layer before proceeding
on to the infill. Usually, there are 2 layers printed before the infill is done. The user may select
to add more layers in order to increase the strength of the outer surface. This will however,
increase the build time. Perimeter to raster air gap refers to gap between the inner most contour
and the edge of the raster fill inside of the contour. [ 1 ]
9.Air Gap:
This is the space between the beads of FDM material. The default is zero, meaning that the
beads just touch. It can be modified to leave a positive gap, which means that the beads of
material do not touch. This results in a loosely packed structure that builds rapidly. It can also
be modified to leave a negative gap, meaning that two beads partially occupy the same space.
This results in a dense structure which requires a longer build time. Air gap refers to the gap
between adjacent raster tool paths on the same layer.
Air gap between roads
Z
Figure11: the air gap between roads [ 2 ]

DESIGN OF EXPERIMENT
1. Problem Statement:
To analyze the effect of layer thickness (L.T), Orientation about X axis (θx),
Orientation about Y axis (θy) on the change in volume of model material (M.M) and
support material (S.M) required for a selected interior fill pattern as well as to
investigate the effect of the afore said factors on the time required to build the model.
Silencer of a two wheeler is considered as a sample component to conduct the
experimentation.
A solid CAD model of silencer was modeled using CATIA V5. The stl file of the
above model was imported to CatalystEx 4.4 software for conducting simulation runs.
Observations about volume of model and support material required and time taken for
fabrication were recorded by simulating the fabrication of the sample model as per
different settings of independent parameters obtained from DOE.
Figure 12 : CAD model of Silencer

The Silencer component is designed using CATIA V 5, as shown in Fig.12 . The
CAD model of the Silencer component is converted into .stl file format. It is loaded into
CatalystEx 4.4 software of printing (FDM) machine.
A sample position of the component at 90 degrees is shown in Fig. 13.
Figure 13: CAD model of the Silencer in 90°
2. Design Of Experiment:
As the Catalyst Ex 4.4 software provides control over limited process
parameters, following factors were selected as independent variables:
1. Orientation about X axis (θx)
2. Orientation about Y axis (θy)
3. Layer Thickness (LT)
Range of variables :
1. θx:- 0 to 180°
2. θ y:- 0 to 180°
3. L.T:- 0.007 to 0.01

Table 1 : Levels considered
Levels
Parameter 1 2 3 4 5 6 7 8 9
θx 0 22.5 45 67.5 90 112.5 130 157.5 180
θy 0 22.5 45 67.5 90 112.5 130 157.5 180
LT 0.007 0.01
Considering two fators with 9 Levels each and 1 factor with 2 levels as
mentioned above , a full factorial design of experiment was carried out in Minitab
software. The DOE with 162 experimental runs obtained from Minitab software is as
follows:
Table 2 : D.O.E
Independent Variables Independent Variables
Sr. no. θx θy LT Sr. no. θx θy LT
1 90 0 0.007 25 45 135 0.01
2 22.5 90 0.01 26 90 135 0.01
3 112.5 157.5 0.01 27 22.5 0 0.007
4 157.5 67.5 0.01 28 180 112.5 0.007
5 157.5 157.5 0.007 29 135 0 0.007
6 157.5 180 0.007 30 0 112.5 0.01
7 45 90 0.01 31 135 67.5 0.01
8 157.5 180 0.01 32 135 180 0.007
9 22.5 135 0.007 33 67.5 180 0.01
10 112.5 22.5 0.007 34 22.5 67.5 0.007
11 45 180 0.007 35 90 135 0.007
12 67.5 90 0.01 36 135 90 0.007
13 135 157.5 0.007 37 180 0 0.007
14 0 45 0.007 38 180 67.5 0.007
15 135 45 0.007 39 90 22.5 0.007
16 157.5 45 0.01 40 0 135 0.01
17 67.5 45 0.01 41 135 45 0.01
18 112.5 45 0.007 42 45 135 0.007
19 22.5 22.5 0.01 43 157.5 45 0.007
20 22.5 157.5 0.01 44 180 45 0.01
21 180 180 0.01 45 135 22.5 0.01
22 157.5 157.5 0.01 46 90 67.5 0.007
23 157.5 112.5 0.007 47 112.5 135 0.01
24 67.5 112.5 0.01 48 135 180 0.01

49 90 45 0.007 87 157.5 22.5 0.01
50 0 22.5 0.01 88 0 22.5 0.007
51 67.5 22.5 0.01 89 0 180 0.007
52 180 0 0.01 90 0 67.5 0.01
53 0 45 0.01 91 0 157.5 0.007
54 67.5 67.5 0.01 92 67.5 0 0.007
55 180 67.5 0.01 93 67.5 0 0.01
56 135 157.5 0.01 94 0 0 0.01
57 0 180 0.01 95 90 157.5 0.01
58 180 135 0.007 96 45 157.5 0.01
59 22.5 180 0.01 97 112.5 157.5 0.007
60 67.5 90 0.007 98 180 45 0.007
61 67.5 22.5 0.007 99 45 67.5 0.01
62 180 157.5 0.007 100 180 22.5 0.01
63 112.5 0 0.007 101 135 22.5 0.007
64 90 0 0.01 102 45 67.5 0.007
65 67.5 180 0.007 103 67.5 135 0.01
66 0 67.5 0.007 104 67.5 112.5 0.007
67 22.5 112.5 0.007 105 157.5 135 0.007
68 22.5 135 0.01 106 45 45 0.007
69 22.5 180 0.007 107 180 180 0.007
70 180 90 0.01 108 157.5 22.5 0.007
71 22.5 90 0.007 109 67.5 157.5 0.007
72 90 157.5 0.007 110 0 90 0.01
73 22.5 22.5 0.007 111 90 67.5 0.01
74 157.5 67.5 0.007 112 67.5 45 0.007
75 90 90 0.01 113 22.5 157.5 0.007
76 0 0 0.007 114 67.5 67.5 0.007
77 112.5 0 0.01 115 22.5 0 0.01
78 157.5 0 0.01 116 45 45 0.01
79 112.5 135 0.007 117 45 90 0.007
80 22.5 67.5 0.01 118 135 135 0.007
81 135 67.5 0.007 119 22.5 112.5 0.01
82 90 45 0.01 120 112.5 45 0.01
83 90 112.5 0.01 121 90 90 0.007
84 90 180 0.01 122 45 22.5 0.007
85 45 157.5 0.007 123 90 112.5 0.007
86 180 112.5 0.01 124 45 180 0.01

125 180 22.5 0.007 144 157.5 90 0.01
126 135 0 0.01 145 112.5 180 0.01
127 22.5 45 0.01 146 45 112.5 0.007
128 112.5 67.5 0.01 147 90 22.5 0.01
129 0 112.5 0.007 148 157.5 0 0.007
130 67.5 157.5 0.01 149 135 112.5 0.007
131 180 157.5 0.01 150 135 112.5 0.01
132 67.5 135 0.007 151 112.5 90 0.007
133 22.5 45 0.007 152 112.5 90 0.01
134 112.5 180 0.007 153 45 0 0.01
135 0 157.5 0.01 154 112.5 112.5 0.01
136 112.5 22.5 0.01 155 135 90 0.01
137 45 0 0.007 156 135 135 0.01
138 45 22.5 0.01 157 180 135 0.01
139 112.5 112.5 0.007 158 0 90 0.007
140 45 112.5 0.01 159 112.5 67.5 0.007
141 180 90 0.007 160 157.5 90 0.007
142 0 135 0.007 161 90 180 0.007
143 157.5 112.5 0.01 162 157.5 135 0.01
Where,
i. θx : Build orientation about X-axis in degree.
ii. θy : Build orientation about Y-axis in degree.
iii. L.T.: Layer thickness in inches.
iv. S.M. : Support material in Cubic inches.
v. M.M. : Model material in Cubic inches.
vi. T : Build time in Hours.

STATISTICAL ANALYSIS & MODELING
Regression analysis is a set of statistical processes for estimating the relationships
among variables. It includes many techniques for modeling and analyzing several variables,
when the focus is on the relationship between a dependent variable and one or
more independent variables. More specifically, regression analysis helps one understand how
the typical value of the dependent variable changes when any one of the independent variables
is varied, while the other independent variables are held fixed.
Most commonly, regression analysis estimates the conditional expectation of the
dependent variable given the independent variables – that is, the average value of the dependent
variable when the independent variables are fixed. Less commonly, the focus is on a quantile,
or other location parameter of the conditional distribution of the dependent variable given the
independent variables. In all cases, a function of the independent variables called the regression
function is to be estimated.
1. Hypothesis:
We start analyzing the data by considering that no relationship exist between the dependent and
independent variables i.e., we propose a Null Hypothesis at the initial stage. The regression
analysis along with ANNOVA is carried out to accept or reject the hypothesis.
2. Analyzing effect of θx on
Table 3 : Data set for analyzing the effect of θx
Independent Variables Dependent Variables
θx θy LT MM SM T
0 0 0.01 2.53 1.75 8.34
22.5 0 0.01 2.47 2.11 10
45 0 0.01 2.38 1.97 11.05
67.5 0 0.01 2.34 1.27 9.58
90 0 0.01 2.34 1.18 9.12
112.5 0 0.01 2.34 1.06 9.15
135 0 0.01 2.35 2.17 11.27
157.5 0 0.01 2.39 2.39 10.12
180 0 0.01 2.39 2.33 8.56

i. Support Material ( S.M. )
Regression Analysis: θx Vs. SM
Regression Statistics
Multiple R 0.330915
R Square 0.109505
Adjusted R
Square
-0.03891
Standard Error 0.558676
Observations 8
ANOVA
Df SS MS F
Significance
F
Regression 1 0.230288 0.230288 0.737822 0.423343
Residual 6 1.872712 0.312119
Total 7 2.103
Coefficients
Standard
Error
t Stat P-value
Intercept 1.476786 0.435317 3.39244 0.014632 0.411604
θx 0.003291 0.003831 0.858966 0.423343 -0.00608
Residual Plots for SM:
Graph 1 : θx Vs. SM
 (P≥0.05) Null hypothesis can’t be rejected.

ii. Model Material ( M.M )
Regression Analysis: θx Vs. MM
Multiple R 0.592142
R Square 0.350632
Adjusted R
Square
0.257865
Observations 9
ANOVA
Df SS MS F
Significance
F
Regression 1 0.012327 0.012327 3.779714 0.092965
Residual 7 0.022829 0.003261
Total 8 0.035156
Coefficients
Standard
Error
t Stat P-value
Intercept 2.449556 0.0351 69.78719 3.26E-11
θx -0.00064 0.000328 -1.94415 0.092965
Residual Plots for MM
Graph 2 : θx Vs.MM
 (P≥0.05) Null hypothesis can not be rejected.

iii. Time
Regression Analysis: θx Vs. T
Multiple R 0.295739
R Square 0.087462
Adjusted R
Square
-0.06463
Observations 8
ANOVA
Df SS MS F
Significance
F
Regression 1 0.552005 0.552005 0.575067 0.476973
Residual 6 5.759382 0.959897
Total 7 6.311388
Coefficients
Standard
Error
t Stat P-value Lower 95%
Intercept 10.37214 0.76341 13.5866 9.87E-06 8.504146
0 -0.0051 0.006719 -0.75833 0.476973 -0.02154
Residual Plots for T:
Graph 3 : θx Vs. T

Analyzing effect of θy on
Table 4 : Data set for analyzing the effect of θy.
Independent Variables Dependent Variables
θx θy LT MM SM T
0 22.5 0.01 2.55 1.78 8.29
0 45 0.01 2.53 1.99 8.38
0 67.5 0.01 2.46 1.83 7.48
0 90 0.01 2.39 1.95 6.57
0 112.5 0.01 2.44 2.65 8.21
0 135 0.01 2.55 2.91 9.25
0 157.5 0.01 2.55 2.55 9.11
0 180 0.01 2.54 2.34 9.02
0 0 0.01 2.53 1.75 8.34
iv. Support material ( S. M )
Regression Analysis : θy Vs.SM
Multiple R 0.780276
R Square 0.608831
Adjusted R Square 0.552949
Observations 9
ANOVA
Df SS MS F
Significance
F
Regression 1 0.895482 0.895482 10.89506 0.013107
Residual 7 0.575341 0.082192
Total 8 1.470822
Coefficients
Standard
Error t Stat P-value
Intercept 1.705778 0.17621 9.680344 2.65E-05
θy 0.00543 0.001645 3.300767 0.013107

Residual Plots for SM
Graph 4 : θy Vs.SM
Regression Equation
SM = 1.706 + 0.00543 θy
 (P ≤0.05) Null hypothesis can be rejected.
v. Model Material (M.M)
Regression Analysis :θy Vs.MM
Multiple R 0.046273
R Square 0.002141
Adjusted R Square -0.14041
Observations 9
ANOVA
Df SS MS F
Significance
F
Regression 1 6E-05 6E-05 0.01502 0.905902
Residual 7 0.027962 0.003995
Total 8 0.028022

Coefficients
Standard
Intercept 2.500444 0.038847 64.36684 5.74E-11
θy 4.44E-05 0.000363 0.122557 0.905902
Residual Plots for MM
Graph 5 : θy Vs MM
 (P ≥0.05) Null hypothesis can not be rejected.
vi. Time
Regression Analysis : θy Vs. T
Multiple R 0.411568
R Square 0.169388
Adjusted R Square 0.050729
Observations 9
ANOVA
Df SS MS F
Significance
F
Regression 1 0.975375 0.975375 1.427523 0.271076
Residual 7 4.782847 0.683264
Total 8 5.758222

Coefficients
Standard
Intercept 7.784444 0.508057 15.32199 1.22E-06
θy 0.005667 0.004743 1.19479 0.271076
Residual Plots for T
Graph 6 : θy Vs. T
Analyzing effect of θx * θy on
Table 5 : Data set for analyzing the effect of interaction θx* θy.
Independent Variables
Dependent
Variables
Independent Variables
Dependent
Variables
θx θy LT MM SM T θx θy LT MM SM T
22.5 90 0.01 2.69 1.93 6.54 90 113 0.01 2.47 2.78 9.5
112.5 157.5 0.01 2.34 2.21 11.23 90 180 0.01 2.33 1.49 9.4
157.5 67.5 0.01 2.4 2.6 8.55 180 113 0.01 2.4 1.91 7.6
45 90 0.01 2.66 1.94 6.45 157.5 22.5 0.01 2.39 2.58 10
157.5 180 0.01 2.39 2.42 10.33 0 67.5 0.01 2.46 1.82 7.1
67.5 90 0.01 2.69 1.96 7 67.5 0 0.01 2.34 1.27 9.6
157.5 45 0.01 2.4 2.78 10.05 0 0 0.01 2.53 1.75 8.3

67.5 45 0.01 2.39 2.29 11.27 90 158 0.01 2.34 2.12 11
22.5 22.5 0.01 2.4 2.07 9.4 45 158 0.01 2.39 2.17 11
22.5 157.5 0.01 2.46 2.31 9.56 45 67.5 0.01 2.51 1.93 8.4
180 180 0.01 2.39 1.75 8.32 180 22.5 0.01 2.39 2.55 9.1
157.5 157.5 0.01 2.39 2.55 10.4 67.5 135 0.01 2.39 2.56 11
67.5 112.5 0.01 2.53 2.71 9.38 0 90 0.01 2.39 1.95 6.6
45 135 0.01 2.4 2.88 11.11 90 67.5 0.01 2.46 2.14 9.2
90 135 0.01 2.38 2.74 12.46 22.5 0 0.01 2.47 2.11 10
0 112.5 0.01 2.44 2.65 8.21 45 45 0.01 2.39 2.12 10
135 67.5 0.01 2.39 2.43 9.12 22.5 113 0.01 2.58 2.51 8.3
67.5 180 0.01 2.34 1.72 10.37 112.5 45 0.01 2.38 2.55 12
0 135 0.01 2.55 2.91 8.49 45 180 0.01 2.38 1.95 11
135 45 0.01 2.39 2.72 11.26 135 0 0.01 2.35 2.17 11
180 45 0.01 2.4 2.88 9.21 22.5 45 0.01 2.56 2.12 9.3
135 22.5 0.01 2.37 2.32 11.17 112.5 67.5 0.01 2.4 2.19 9.2
112.5 135 0.01 2.38 2.71 12.46 67.5 158 0.01 2.37 1.98 11
135 180 0.01 2.35 2.46 12.38 180 158 0.01 2.39 1.81 8.3
0 22.5 0.01 2.55 1.78 8.29 0 158 0.01 2.55 2.55 9.1
67.5 22.5 0.01 2.38 1.43 10.01 112.5 22.5 0.01 2.34 1.12 9.2
180 0 0.01 2.39 2.33 8.56 45 22.5 0.01 2.39 2.03 11
0 45 0.01 2.53 1.99 8.38 45 113 0.01 2.56 2.49 9.1
67.5 67.5 0.01 2.57 2.03 9.07 157.5 113 0.01 2.4 2.38 8.4
180 67.5 0.01 2.4 2.62 8.2 157.5 90 0.01 2.38 1.97 7
135 157.5 0.01 2.37 2.88 12.37 112.5 180 0.01 2.31 1.8 10
0 180 0.01 2.54 2.34 9.02 90 22.5 0.01 2.34 1.16 9.4
22.5 180 0.01 2.45 2.18 9.59 135 113 0.01 2.39 2.74 9.4
90 0 0.01 2.34 1.18 9.12 112.5 90 0.01 2.39 1.96 7.1
22.5 135 0.01 2.52 2.79 10.04 45 0 0.01 2.38 1.97 11
180 90 0.01 2.39 1.96 6.57 112.5 113 0.01 2.4 2.81 9.5
90 90 0.01 2.39 1.96 7.04 135 90 0.01 2.34 1.97 6.5
112.5 0 0.01 2.32 1.06 9.15 135 135 0.01 2.38 2.93 12
157.5 0 0.01 2.39 2.39 10.12 180 135 0.01 2.4 1.96 8.3
22.5 67.5 0.01 2.55 1.94 8.09 157.5 135 0.01 2.4 2.8 10
90 45 0.01 2.38 2.45 12.19

vii. Support material (SM)
Regression Analysis: θx* θy Vs. S.M.
Multiple R 0.317839
R Square 0.1552
Adjusted R
Square 0.077971
Observations 81
ANOVA
Df SS MS F
Significance
F
Regression 2 1.652712 0.826356 4.382573 0.015712
Residual 78 14.70729 0.188555
Total 80 16.36
Coefficients
Standard
Intercept 1.902198 0.116196 16.37062 5.97E-27
θx*θy -0.000031 0.000010 -3.22 0.002
Regression Equation
For LT :0.010
SM = 1.669 + 0.00388 θx + 0.00484 θy - 0.000031 θx*θy
For LT :0.007
SM = 1.596 + 0.00388 θx + 0.00484 θy - 0.000031 θx*θy

Residual Plots for SM
Graph 7 : θx* θy Vs. SM
 (P ≤0.05) Null hypothesis can be Rejected .
viii. Model Material ( M.M )
Regression Analysis: θx* θy Vs. M.M
Multiple R 0.544899
R Square 0.296915
Adjusted R
Square 0.278887
Observations 81
ANOVA
Df SS MS F
Significance
F
Regression 2 0.169957 0.084979 16.46982 1.08E-06
Residual 78 0.402453 0.00516
Total 80 0.57241

Coefficients
Standard
Intercept 2.495383 0.019221 129.8241 6.72E-93
θx*θy -0.00000 0.000002 -0.16 0.871
Residual plot for MM
Graph 8 : θx* θy Vs. MM
ix. Time
Regression Analysis: θx* θy Vs. T
Multiple R 0.155434
R Square 0.02416
Adjusted R
Square -0.00086
Observations 81

ANOVA
Df SS MS F
Significance
F
Regression 2 4.755231 2.377616 0.965556 0.385275
Residual 78 192.0697 2.462431
Total 80 196.8249
Coefficients
Standard
Intercept 8.955062 0.419907 21.32628 2.78E-34
θx* θy -0.000021 0.000044 -0.47 0.638
Residual plot for T
Graph 9: Interaction θx* θy Vs. Time (T)

RESULT & DISCUSSION
The CAD model of silencer was simulated in Catalyst software in different
orientations as obtained from DOE. The observations were recorded regarding the
volume of model and support material required and the machine time required for
fabrication process. Regression analysis was carried out on the recorded data to
analyze the effect of independent variables θx, θy, and LT on MM,SM, and T.
Initially, Null hypothesis was proposed and regression analysis was carried
out to accept or reject the hypothesis. A p-value helps to determine the significant
relationship between the variables. The p-value is a number between o to 1 and
interpreted in the following ways:
 A small p-value (typically ≤ 0.05 ) indicates significant relation between the
dependent and independent variables and thus the null hypothesis can be rejected.
 A large p-value (typically ≥ 0.05) indicates no significant relation between the
dependent and independent variables and thus the null hypothesis can not be
rejected.
P value for θy Vs. SM & the interaction θx* θy Vs. SM are found to be significant &
hence the null hypothesis can be rejected for these two cases.
The regression equations for the above cases are as mentioned below:
Regression Equation
SM = 1.706 + 0.00543 θy
Graph 10 : θy Vs. SM
200150100500
3.0
2.8
2.6
2.4
2.2
2.0
1.8
1.6
θy
SM
Plot of θy Vs SM
SM = 1.706 + 0.00543 θy

Regression Equation
For LT :0.010
SM = 1.669 + 0.00388 θx + 0.00484 θy - 0.000031 θx*θy
For LT :0.007
SM = 1.596 + 0.00388 θx + 0.00484 θy - 0.000031 θx*θy
Graph 11 : : Interaction θx*θy Vs Support Material (SM)
For all other combination presented above, the P value is insignificant & hence the null
hypothesis can not be rejected.
Thus it can be concluded that the volume of support material required is highly
dependent of θy and the interaction θx* θy.
200150100500
3.0
2.5
2.0
1.5
1.0
θy
SM
Plot of θX*θy Vs SM
I
0
I
50
I
100
I
150
I
200
θx

REFERENCES
1. International Journal of Scientific & Engineering Research, Volume 7, Issue 5, May-
2016 ISSN 2229-5518 Fused Deposition Modeling (FDM) Mechanism BY
FawazAlabdullah.
2. SENSITIVITY OF RP SURFACE FINISH TO PROCESS PARAMETER
VARIATION Bharath Vasudevarao1
, Dharma Prakash Natarajan2
, Mark Henderson3
,
Ph.D. Partnership for Research in Stereo Modeling and Department of Industrial
Engineering Arizona State University.
3. Manufacturing Engineering And Technology by Serope Kalpakjain and Steven R.
Schmid.
4. Pandey, P. M., N. V. Reddy and S. G. Dhande, ”Slicing procedures in layered
manufacturing: a review,” Rapid Prototyping Journal, Volume 9, Number 5, 2003, pp.
274-288.
5. Manufacturing Science by Amitabha Ghosh And Asok Kumar Malik.
6. Computer aided decision support for fused deposition modeling by C.W. Ziemian and
P.M.Crawn III.
7. Optimal part deposition orientation in FDM by using a multicriteria generic algorithm
P. M. Pandey a , K. Thrimurthulu b & N. Venkata Reddy a Department of Mechanical
Engineering, Indian Institute of Technology, Kanpur, India.
8. M Sumalatha1, V V S Kesava Rao, Experimental Evaluation of the best Orientation of
Taper Plug to Minimize Support Material Required in 3D printing (FDM).
9. Cany mendonsa, KV Naveen, Influence of FDM process parameter on build Time
Using ANOVA Approach.
10. Rajan Narang,Deepak Chhabra. Analysis of Process Parameters of Fused Deposition
Modeling ( FDM ) Technique.

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