MATHAMATICAL TIME ESTIMATION OF VARIOUS
Synopsis of the project
MATHAMATICAL TIME ESTIMATION OF VARIOUS
PARTS IN 3D PRINTER
to be submitted in partial fulfillment of the requirements for the Project of
MEE2016
NAME
REG.No
MANIK CHAUHAN
15BEM0096
1|Page
BONAFIDE CERTIFICATE
This is to certify that the following students have successfully completed the
project as a part of their CAL J-Project Component for the subject,
RAPID MANUFACTURING AND TECHNOLOGY (MEE2016)
The students worked under the guidance of their Faculty, Prof.
M.Sugavaneswaran and were supported by the School Of Mechanical
(SMEC, VIT University).
Name of the student:
MANIK CHAUHAN (15BEM0096)
(Signature of the Faculty)
2|Page
INDEX
S.No
Title
Page No.
1.
Acknowledgement
4
2.
Introduction
5
3.
Top 5 3D Printing Factors
That Affect Printing Time.
4.
Analysis
8
5.
Parts
9
6.
Calculation
7.
Result
12
8.
Conclusion
13
3|Page
6,7
10,11
ACKNOWLEDGEMENT
A project provides you with deeper understanding of the theoretical
topics that is learnt in the class. On this occasion, I would like to express our
heartfelt gratitude to our faculty, Prof. M.SUGAVANESWARAN for his
relentless guidance and encouragement throughout the completion of this
project.
We would like to thank everyone who abetted us during the course of our
work. Specially the lab-assistant of TT – 014 Lab for providing us all facilities
and guidance wherever required.
Last but not the least, we would like to thank VIT University for providing us
with an opportunity to work on such projects to enhance our practical
knowledge and exemplifying the process of making an Engineer.
Thank you
Manik Chauhan
15BEM0096
4|Page
INTRODUCTION
Time estimation is essential for production scheduling, machine
selection, and cost estimation. Acquisition of the accurate result
requires an understanding of the factors that influence the printing
time.
One of the main objectives of this research is to statistically illustrate
the relation between the geometric attributes and build time of the
parts. Hence, the effect of the most important geometric parameters is
analyzed. The final model that will be developed in this work cannot
be applied to all parts and processes. The scope of this research is
limited to the parts that can fit in a bounding box that is less than 10
inches in all dimensions.
In this project we are going to find the approximate time estimation of
a simple part in 3D Printing mathematically. Afterwards we will
compare our estimated time with the machine estimated time,
While comparing we will also find the error and error percentage.
5|Page
Top 5 3D Printing Factors That Affect Printing
Time
1. Resolution and Layer Thickness :- The biggest factor to
consider is resolution or layer thickness. The 3D printers have
the capability of building from .005 to .013 (layer resolution).
This resolution is represented by the thickness of the tool path.
Printing at .005 is going to produce some very sharp details; it’s
also going to reduce any stepping that might occur when
building curves. The recommendation is to use this resolution
when files have fine details. There is one drawback to printing
in .005, and that is the amount of time needed to complete the
part. It can take up to 3 times longer than a standard .010 build.
2. Model Fill and Density :- Another important factor to think
about is the model fill and density. Parts do not always need to
be built in solid. Sometimes building it solid can have a less
preferred outcome. How? When a part is first extruded it’s at a
molten temperature, the plastic liquefies allowing it to pass
through the tips and lay out as a tool path. When plastic cools,
it contracts. With large solid builds, as it cools, the part may
curl upwards. This might not be the preference for benchmarks
when spe ’s need to e exa t. One possi le solution to this is
building with sparse fill. Sparse will create air gaps in the
interior of the part. You can increase or reduce the distance of
these gaps by the selection of model fill. Solid will create a
stronger part, but sparse will take less time and use less
material.
6|Page
3. Print Orientation :- The next specification to think about is the
part positioning on a build tray. The difference between a
vertical or horizontal positioning before it is sliced is going to
affect the strength and quality of the part. For example, if the
part is in the shape of a dowel or rod, the software is going to
slice along the X-axis. If the rod is horizontal along the X-axis it
will be a fairly strong part but the curves might show some
stepping. If the same part is to be printed vertically the tool
path is still going to be along to X-axis. However, there will be a
nice round edge but a weaker part due to the slice layers
required. This will also affect the time needed to build,
ultimately affecting the costs.
4. Support Material :- The support style selected is also
important to the cost and time. Choices for Fused Deposition
Modelling (FDM) 3D printers include basic, break-away, SMART,
and surround, can have an impact on how much support
material is used for the build. If you are a Poly Jet 3D printer
user, the new Objet Eden VS offers the option of soluble
support or the traditional support that can be removed with
the water water jet.
5. Other Dimensional Factors :- Surface area, Volume, Density,
Weight etc. are also some factors which affects the time
estimation for 3d printing.
Greater the value of these factor , greater will be the time taken
to finish the product. So these factor should also be kept in
mind.
7|Page
ANALYSIS
The mathematical formula to calculate the time estimation of a 3D
printer is given by.
Print Time=0.005390527+(0.064608959*SA)+(0.102169623*V)(0.011981463*XY)- (0.001236407*ZSA)
Attributes
X
Basic Geometry, length
Y
Basic Geometry, width
Z
Basic Geometry, height
V
Basic Geometry, volume
SA
Surface Area
ZSA
Product of the part height and surface area
XY
Projected area of part to the working plane
In order to calculate the time estimation and for comparison we took 4
parts with a particular simple shape (mainly cube and cuboid).
We used the formula to calculate estimated time mathematically and
then comparing it with actual value so as to find error and error
percentage.
8|Page
PARTS
Figure 1: 6x6x6 (inches)
Figure 3: 5x5x4 (inches)
9|Page
Figure 2: 6x9x6 (inches)
Figure 4: 7x7x6 (inches)
CALCULATION
Input: (5X5X4)
Experimental time taken(Total time– Support structure and heating
time):
19 : 28 – 1 : 30 = 17hours 58minutes
Now,
Print Time=0.005390527+(0.064608959*SA)+(0.102169623*V)(0.011981463*XY) - (0.001236407*ZSA)
So print time is : 17.72 hour = 17 hour 43 min
Input: (6X6X6)
Experimental time taken(Total time– Support structure and heating
time):
36 : 08 – 1 : 30 = 34hours 38minutes
Now,
Print Time=0.005390527+(0.064608959*SA)+(0.102169623*V)(0.011981463*XY) - (0.001236407*ZSA)
So print time is : 34.037 hour = 34 hour 3 min
10 | P a g e
Input: (7X7X6)
Experimental time taken(Total time– support structure time):
48 : 51 – 1 : 30 = 47hours 21minutes
Now,
Print Time=0.005390527+(0.064608959*SA)+(0.102169623*V)(0.011981463*XY) - (0.001236407*ZSA)
So print time is : 44.76 hour = 44 hour 46 min
Input: (6X9X6)
Experimental time taken(Total time– Support structure and heating
time):
53 : 29 – 1:30 = 51hours 59minutes
Now,
Print Time=0.005390527+(0.064608959*SA)+(0.102169623*V)(0.011981463*XY) - (0.001236407*ZSA)
So print time is : 49.04 hour = 49 hour 3 min
11 | P a g e
RESULT
After all the mathematical calculation we get the following result:
S.NO
PARTS
1
5x5x4
1659.595
17hr 43min
17hr 58min
0.24
1.33%
2
6x6x6
3580.505
34hr 03min
34hr 38min
0.596
1.72%
3
7x7x6
4871.414
44hr 46min
47hr 21min
2.59
5.46%
4
6x9x6
5370.595
49hr 03min
51hr 59min
2.94
5.65%
12 | P a g e
MATERIAL ESTIMATED
USED(cm^3)
TIME
ACTUAL
TIME
DIFFERENCE ERROR
(hour)
%
CONCLUSION
From this experiment and research I got to know about mathematical
formula to calculate time estimation.
There is still no accurate formula to calculate time estimation
accurately.
But by this formula we can easily calculate approximate value for
simple 3D printing. But we can get approximate time to calculate the
print time of the given simple part. Complex structure time estimation
is tough to calculate.
From the given result we can calculate parts of less volume more
accurately than the parts with greater volume as can be
concluded with the % error increase. So greater the volume,
greater will be the error and lesser be the accuracy (for this
formula).
And also when the dimensions exceed 10 inches this formula can’t
be used as it shows inaccurate value with greater error.
This time estimation is very useful as it gives us the time before hand
and through this we can further estimate the price of that particular
part.
I also got to know about various factors affecting the time and price
for 3D printing process
13 | P a g e
MATHAMATICAL TIME ESTIMATION OF VARIOUS
PARTS IN 3D PRINTER
to be submitted in partial fulfillment of the requirements for the Project of
MEE2016
NAME
REG.No
MANIK CHAUHAN
15BEM0096
1|Page
BONAFIDE CERTIFICATE
This is to certify that the following students have successfully completed the
project as a part of their CAL J-Project Component for the subject,
RAPID MANUFACTURING AND TECHNOLOGY (MEE2016)
The students worked under the guidance of their Faculty, Prof.
M.Sugavaneswaran and were supported by the School Of Mechanical
(SMEC, VIT University).
Name of the student:
MANIK CHAUHAN (15BEM0096)
(Signature of the Faculty)
2|Page
INDEX
S.No
Title
Page No.
1.
Acknowledgement
4
2.
Introduction
5
3.
Top 5 3D Printing Factors
That Affect Printing Time.
4.
Analysis
8
5.
Parts
9
6.
Calculation
7.
Result
12
8.
Conclusion
13
3|Page
6,7
10,11
ACKNOWLEDGEMENT
A project provides you with deeper understanding of the theoretical
topics that is learnt in the class. On this occasion, I would like to express our
heartfelt gratitude to our faculty, Prof. M.SUGAVANESWARAN for his
relentless guidance and encouragement throughout the completion of this
project.
We would like to thank everyone who abetted us during the course of our
work. Specially the lab-assistant of TT – 014 Lab for providing us all facilities
and guidance wherever required.
Last but not the least, we would like to thank VIT University for providing us
with an opportunity to work on such projects to enhance our practical
knowledge and exemplifying the process of making an Engineer.
Thank you
Manik Chauhan
15BEM0096
4|Page
INTRODUCTION
Time estimation is essential for production scheduling, machine
selection, and cost estimation. Acquisition of the accurate result
requires an understanding of the factors that influence the printing
time.
One of the main objectives of this research is to statistically illustrate
the relation between the geometric attributes and build time of the
parts. Hence, the effect of the most important geometric parameters is
analyzed. The final model that will be developed in this work cannot
be applied to all parts and processes. The scope of this research is
limited to the parts that can fit in a bounding box that is less than 10
inches in all dimensions.
In this project we are going to find the approximate time estimation of
a simple part in 3D Printing mathematically. Afterwards we will
compare our estimated time with the machine estimated time,
While comparing we will also find the error and error percentage.
5|Page
Top 5 3D Printing Factors That Affect Printing
Time
1. Resolution and Layer Thickness :- The biggest factor to
consider is resolution or layer thickness. The 3D printers have
the capability of building from .005 to .013 (layer resolution).
This resolution is represented by the thickness of the tool path.
Printing at .005 is going to produce some very sharp details; it’s
also going to reduce any stepping that might occur when
building curves. The recommendation is to use this resolution
when files have fine details. There is one drawback to printing
in .005, and that is the amount of time needed to complete the
part. It can take up to 3 times longer than a standard .010 build.
2. Model Fill and Density :- Another important factor to think
about is the model fill and density. Parts do not always need to
be built in solid. Sometimes building it solid can have a less
preferred outcome. How? When a part is first extruded it’s at a
molten temperature, the plastic liquefies allowing it to pass
through the tips and lay out as a tool path. When plastic cools,
it contracts. With large solid builds, as it cools, the part may
curl upwards. This might not be the preference for benchmarks
when spe ’s need to e exa t. One possi le solution to this is
building with sparse fill. Sparse will create air gaps in the
interior of the part. You can increase or reduce the distance of
these gaps by the selection of model fill. Solid will create a
stronger part, but sparse will take less time and use less
material.
6|Page
3. Print Orientation :- The next specification to think about is the
part positioning on a build tray. The difference between a
vertical or horizontal positioning before it is sliced is going to
affect the strength and quality of the part. For example, if the
part is in the shape of a dowel or rod, the software is going to
slice along the X-axis. If the rod is horizontal along the X-axis it
will be a fairly strong part but the curves might show some
stepping. If the same part is to be printed vertically the tool
path is still going to be along to X-axis. However, there will be a
nice round edge but a weaker part due to the slice layers
required. This will also affect the time needed to build,
ultimately affecting the costs.
4. Support Material :- The support style selected is also
important to the cost and time. Choices for Fused Deposition
Modelling (FDM) 3D printers include basic, break-away, SMART,
and surround, can have an impact on how much support
material is used for the build. If you are a Poly Jet 3D printer
user, the new Objet Eden VS offers the option of soluble
support or the traditional support that can be removed with
the water water jet.
5. Other Dimensional Factors :- Surface area, Volume, Density,
Weight etc. are also some factors which affects the time
estimation for 3d printing.
Greater the value of these factor , greater will be the time taken
to finish the product. So these factor should also be kept in
mind.
7|Page
ANALYSIS
The mathematical formula to calculate the time estimation of a 3D
printer is given by.
Print Time=0.005390527+(0.064608959*SA)+(0.102169623*V)(0.011981463*XY)- (0.001236407*ZSA)
Attributes
X
Basic Geometry, length
Y
Basic Geometry, width
Z
Basic Geometry, height
V
Basic Geometry, volume
SA
Surface Area
ZSA
Product of the part height and surface area
XY
Projected area of part to the working plane
In order to calculate the time estimation and for comparison we took 4
parts with a particular simple shape (mainly cube and cuboid).
We used the formula to calculate estimated time mathematically and
then comparing it with actual value so as to find error and error
percentage.
8|Page
PARTS
Figure 1: 6x6x6 (inches)
Figure 3: 5x5x4 (inches)
9|Page
Figure 2: 6x9x6 (inches)
Figure 4: 7x7x6 (inches)
CALCULATION
Input: (5X5X4)
Experimental time taken(Total time– Support structure and heating
time):
19 : 28 – 1 : 30 = 17hours 58minutes
Now,
Print Time=0.005390527+(0.064608959*SA)+(0.102169623*V)(0.011981463*XY) - (0.001236407*ZSA)
So print time is : 17.72 hour = 17 hour 43 min
Input: (6X6X6)
Experimental time taken(Total time– Support structure and heating
time):
36 : 08 – 1 : 30 = 34hours 38minutes
Now,
Print Time=0.005390527+(0.064608959*SA)+(0.102169623*V)(0.011981463*XY) - (0.001236407*ZSA)
So print time is : 34.037 hour = 34 hour 3 min
10 | P a g e
Input: (7X7X6)
Experimental time taken(Total time– support structure time):
48 : 51 – 1 : 30 = 47hours 21minutes
Now,
Print Time=0.005390527+(0.064608959*SA)+(0.102169623*V)(0.011981463*XY) - (0.001236407*ZSA)
So print time is : 44.76 hour = 44 hour 46 min
Input: (6X9X6)
Experimental time taken(Total time– Support structure and heating
time):
53 : 29 – 1:30 = 51hours 59minutes
Now,
Print Time=0.005390527+(0.064608959*SA)+(0.102169623*V)(0.011981463*XY) - (0.001236407*ZSA)
So print time is : 49.04 hour = 49 hour 3 min
11 | P a g e
RESULT
After all the mathematical calculation we get the following result:
S.NO
PARTS
1
5x5x4
1659.595
17hr 43min
17hr 58min
0.24
1.33%
2
6x6x6
3580.505
34hr 03min
34hr 38min
0.596
1.72%
3
7x7x6
4871.414
44hr 46min
47hr 21min
2.59
5.46%
4
6x9x6
5370.595
49hr 03min
51hr 59min
2.94
5.65%
12 | P a g e
MATERIAL ESTIMATED
USED(cm^3)
TIME
ACTUAL
TIME
DIFFERENCE ERROR
(hour)
%
CONCLUSION
From this experiment and research I got to know about mathematical
formula to calculate time estimation.
There is still no accurate formula to calculate time estimation
accurately.
But by this formula we can easily calculate approximate value for
simple 3D printing. But we can get approximate time to calculate the
print time of the given simple part. Complex structure time estimation
is tough to calculate.
From the given result we can calculate parts of less volume more
accurately than the parts with greater volume as can be
concluded with the % error increase. So greater the volume,
greater will be the error and lesser be the accuracy (for this
formula).
And also when the dimensions exceed 10 inches this formula can’t
be used as it shows inaccurate value with greater error.
This time estimation is very useful as it gives us the time before hand
and through this we can further estimate the price of that particular
part.
I also got to know about various factors affecting the time and price
for 3D printing process
13 | P a g e