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Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10471-10477 10471
www.etasr.com Zisopol et al.: A Theoretical-Experimental Study on the Influence of FDM Parameters on the …
A Theoretical-Experimental Study on the
Influence of FDM Parameters on the
Dimensions of Cylindrical Spur Gears Made of
PLA
Dragos Gabriel Zisopol
Mechanical Engineering Department, Petroleum-Gas University Ploiesti, Romania
zisopol@zisopol.ro
(corresponding author)
Mihail Minescu
Mechanical Engineering Department, Petroleum-Gas University Ploiesti, Romania
mminescu@upg-ploiesti.ro
Dragos Valentin Iacob
Production Department, Marelli Ploiesti Romania, Romania
dragoshicb@gmail.com
Received: 29 January 2023 | Revised: 12 February 2023 | Accepted: 15 February 2023
ABSTRACT
This paper presents the results of a theoretical-experimental study on the influence of FDM parameters
(height of the deposited layer at one pass Hs and percentage of filling Pu) on the dimensions of cylindrical
spur gears made of PLA (shaft diameter d and bore diameter D). In this context, we designed the 3D model
of a cylindrical gear with module m= 1 and z= 60 spur teeth, which we used for FDM 3D printing of 27
PLA parts with different values of coating height deposited at a pitch Hs of 0.10, 0.15, 0.20mm and
different values 50, 75, and 100% of filling percentage Pu. The 324 values obtained from measuring the
diameters d and D of 27 cylindrical spur gears made of PLA and the calculated values of statistical
indicators (arithmetic mean, standard deviation, dispersion) were used to determine the dimensional
accuracy of the analyzed parts. The study results show that the percentage of filling has a greater influence
than the shaft diameter on the dimensional accuracy of cylindrical spur gears made of PLA.
Keywords-3D printing; FDM parameters; experimental test; spur gears
I. INTRODUCTION
Nowadays, production processes are undergoing
transformations in terms of flexibilization according to market
requirements, the main objective being to reduce costs in order
to strengthen market position and maintain sustainable
competitive advantage [12-17]. Additive manufacturing
technologies are a viable solution for many industries such as
automotive, aerospace, and defense due to advantages in
comparison with formative and subtractive manufacturing
technologies, e.g. the manufacturing costs are significantly
reduced, complex geometries are achieved without special base
and fixing elements, simplicity in use, material waste is
negligible, use of bio materials, etc. [1, 6, 11].
Fused deposition modeling is one of the most popular
manufacturing technologies due to its affordability, the wide
range of materials used, and the possibility of customization for
printed parts. However, this technology has certain limitations
such as run time and surface quality. Depending on the field of
use of the manufactured part, the limitations can be adjusted
from the process parameters: the height of the layer deposited
in one step, the filling percentage, the printing speed, etc. [9,
10]. The materials used for FDM are thermoplastics, the most
popular among them being PLA (polylactic acid), ABS
(acrylonitrile butadiene styrene), PET (polyethylene
terephthalate), Nylon, and PC (polycarbonate) [3]. The study of
the influence of 3D printing parameters has attracted the
scientific interest. Authors in [1] showed a comparative study
about dimensional accuracy from errors of FFF printed spur
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gears using PLA and Nylon and authors in [11] showed a
development of a prediction system for 3D printed part
deformation using SLS technology.
The novelty of this work consists in the theoretical-
experimental determination of the influence of FDM
parameters on the dimensions of cylindrical spur gears (shaft
diameter d and bore diameter D) made of PLA. The greater
influence between the two studied parameters Hs and Pu is
found with statistical calculations following the measurements.
II. 3D PRINTING OF CYLINDRICAL SPUR GEARS
The quality of the parts manufactured additively by
thermoplastic extrusion is influenced by the material type and
the 3D printer used, [9, 10]. In this context, PLA filament with
a diameter of 1.75mm (Verbatim brand) and the Creality CR-X
3D printer with a printing volume of 300×300×400mm and XY
positioning accuracy of ±0.10mm were used to manufacture all
cylindrical spur gears. Figure 1 shows the steps taken to
perform the experimental study on the influence of FDM
parameters on the dimensions of cylindrical spur gears Rd made
of PLA.
Fig. 1. Stages of the experimental study on the influence of FDM
parameters on the dimensions of cylindrical spur gears fabricated from PLA.
Using the Solidworks 2022 software, the 3D model of a
cylindrical spur gear with module m=1 and z=60 was designed
using the ToolBox function and was converted from SLD to
STL format, [6, 7, 20]. The 3D model was the basis for the 2D
drawing shown in Figure 2 of [6]. Using the STL format file,
corresponding to the spur gear with spur teeth shown in Figure
2, and the Creality Slicer of the Creality CR-X 3D printer, we
inserted the printing parameters shown in Table I and generated
the G-Code file [6, 7]. The FDM 3D printing parameters of
PLA spur gears (Rd) with module m= 1 and z= 60 spur teeth,
shown in Table I, fall into two categories, constant parameters
and variable parameters, [5-8]. We transferred the G-Code file
to the Creality CR-X printer and fabricated 27 cylindrical gears
Rd from PLA with modulus m= 1 and z= 60 spur teeth. Figure
3 shows the cylindrical toothed wheel Rd made of PLA with
m= 1 and z= 60 in Creality Slicer, generated by using the
height of the deposited layer at one pass Hs=0.10mm, filling
percentage Pu= 50%, printing speed Vp=80mm/min, and filling
pattern type line oriented at 45° [8].
TABLE I. PARAMETERS OF 3D FDM PRINTING OF Rd SPUR
GEARS WITH m=1 AND z=60
Constant
parameters
Variable parameters
Coding of
the gear set
Material
Part
orientation
X, Y
Temperature
of the
extruder,
Te= 210°C
Table
temperature,
Tb= 60°C
Printing
speed,
Vp= 80mm/s
Filling
pattern
- Lines 45°
Height of the
deposited layer
Hs
Filling
Percentage
Pu
Rdi PLA
(mm) (%) (i = 1… 9) (parts)
0.10
100 Rd1 3
75 Rd2 3
50 Rd3 3
0.15
100 Rd4 3
75 Rd5 3
50 Rd6 3
0.20
100 Rd7 3
75 Rd8 3
50 Rd9 3
The mass of the cylindrical gear with modulus m=1 and
spur teeth z=60, shown in Figure 2, is 14g (equivalent to
4.957m of PLA filament) and its running time is 2 hours and 53
minutes. The G-Code file of the cylindrical gear shown in
Figure 2 contains 108500 control lines [8].
Fig. 2. Rd PLA cylindrical gear with m=1 and z=60 spur teeth (Hs=0.10
mm, Pu=50%, Vp=80mm/min, 45° oriented line fill pattern) in Creality Slicer.
III. DETERMINATION OF THE INFLUENCE OF FDM
PARAMETERS ON THE DIMENSIONS OF SPUR GEARS
MADE OF PLA
A. Working Methodology
For the experimental study we used 324 values obtained by
measuring with a digital caliper the diameter of the shaft
(d=62±0.1mm) and the diameter of the bore (D=20.2±0.1mm)
of 27 cylindrical gears made of PLA, with m=1 and z=60,
additively manufactured by thermoplastic extrusion (using the
parameters in Table I). Each part was measured as shown in
Figure 3. The 324 values are used to determine the arithmetic
mean (1), standard deviation (2), and dispersion (3),
corresponding to each set of cylindrical gears Rdi in PLA with
m=1 and z=60 [1, 18, 19]:
�̅ � ������...��
(1)
Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10471-10477 10473
www.etasr.com Zisopol et al.: A Theoretical-Experimental Study on the Influence of FDM Parameters on the …
� � �∑��� ��̅��
(2)
�� � �
∑��� − �̅�� (3)
A set of cylindrical gears Rdi made of PLA, with m=1 and
z=60, contains 3 parts characterized by the same 3D printing
parameters (see Table I). Two sets of measurements were
performed for each part, resulting in 12 values - 6 values for
shaft diameter d and 6 values for bore diameter D, as shown in
Figure 3.
Fig. 3. Measuring points of the diameters of cylindrical gears Rd made of
PLA with modulus m=1 and spur teeth z=60.
B. Results
The 324 values resulting from the measurement of the
diameters of the 27 cylindrical gears Rd made of PLA,
additively manufactured by thermoplastic extrusion, are
graphically represented in Figures 4-21. Tables II-XIX show
the results obtained from the calculation of statistical indicators
arithmetic mean, standard deviation, and dispersion. The
variation of the values of the arithmetic means �̅ of the shaft
diameter d for each set of Rdi gears (i= 1...9) is shown in Figure
23. The variation of the values of the arithmetic means �̅ of the
bore diameter D for each set of gears Rdi (i= 1...9) is shown in
Figure 22.
Fig. 4. Values of shaft diameter d for gear set Rd1.(Hs = 0.10mm, Pu=
100%).
TABLE II. VALUES OF THE STATISTICAL INDICATORS
FOR THE SET OF SPUR WHEELS RD1
Variable
parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.10mm,
Pu=100%
mm mm mm
61.95 0.086 0.007
Fig. 5. Values of shaft diameter d for gear set Rd2. (Hs= 0.10mm, Pu=
75%).
TABLE III. VALUES OF STATISTICAL INDICATORS FOR
THE SET OF SPUR GEARS RD2
Variable
Parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.10mm,
Pu=75%
mm mm mm
61.95 0.093 0.009
Fig. 6. Values of shaft diameter d for gear set Rd3. (Hs= 0.10mm, Pu=
50%).
TABLE IV. VALUES OF STATISTICAL INDICATORS FOR
THE SET OF SPUR GEARS RD3
Variable
parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.10mm,
Pu=50%
mm mm mm
61.99 0.111 0.012
Fig. 7. Values of shaft diameter d for spur gear set Rd4. (Hs= 0.15mm, Pu=
100%).
TABLE V. VALUES OF STATISTICAL INDICATORS FOR
THE SET OF SPUR GEARS RD4
Variable
parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.15mm,
Pu=100%
mm mm mm
61.98 0.070 0.005
Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10471-10477 10474
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Fig. 8. Values of shaft diameter d for spur gear set Rd5. (Hs= 0.15mm,
Pu= 75%).
TABLE VI. VALUES OF STATISTICAL INDICATORS FOR
THE SET OF SPUR GEARS RD5
Variable
parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.15mm,
Pu=75%
mm mm mm
62 0.047 0.002
Fig. 9. Values of shaft diameter d for spur gear set Rd6. (Hs= 0.15mm,
Pu= 50%).
TABLE VII. VALUES OF STATISTICAL INDICATORS FOR
THE SET OF SPUR GEARS RD6
Variable
parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.15mm,
Pu=50%
mm mm mm
61.99 0.063 0.004
Fig. 10. Values of shaft diameter d for spur gear set Rd7. (Hs= 0.20mm, Pu=
100%).
TABLE VIII. VALUES OF STATISTICAL INDICATORS FOR
THE SET OF SPUR GEARS RD7
Variable
parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.20mm,
Pu=100%
mm mm mm
61.96 0.062 0.004
Fig. 11. Values of shaft diameter d for spur gear dințate Rd8. (Hs= 0.20mm,
Pu= 75%).
TABLE IX. VALUES OF STATISTICAL INDICATORS FOR
THE SET OF SPUR GEARS RD8
Variable
parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.20mm,
Pu=75%
mm mm mm
62.02 0.113 0.013
Fig. 12. Values of shaft diameter d for spur gear set Rd9. Hs= 0.20mm, Pu=
50%).
TABLE X. VALUES OF STATISTICAL INDICATORS FOR
THE SET OF SPUR GEARS RD9
Variable
parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.20mm,
Pu=50%
mm mm mm
61.95 0.061 0.004
Fig. 13. Values of bore diameter D for spur gear set Rd1. (Hs= 0.10mm, Pu=
100%).
TABLE XI. VALUES OF STATISTICAL INDICATORS FOR
THE SET OF SPUR GEARS RD1
Variable
parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.10 mm,
Pu=100%
mm mm mm
20.29 0.058 0.003
Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10471-10477 10475
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Fig. 14. Values of bore diameter D for spur gear set Rd2. (Hs= 0.10mm, Pu=
75%).
TABLE XII. VALUES OF STATISTICAL INDICATORS FOR
THE SET OF SPUR GEARS RD2
Variable
parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.10mm,
Pu=75%
mm mm mm
20.32 0.077 0.066
Fig. 15. Values of bore diameter D for spur gear set Rd3. (Hs= 0.10mm, Pu=
50%).
TABLE XIII. VALUES OF STATISTICAL INDICATORS FOR
THE SET OF SPUR GEARS RD3
Variable
parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.10mm,
Pu=50%
mm mm mm
20.25 0.117 0.014
Fig. 16. Values of bore diameter D for spur gear set Rd4. (Hs= 0.15mm, Pu=
100%).
TABLE XIV. VALUES OF STATISTICAL INDICATORS FOR
THE SET OF SPUR GEARS RD4
Variable
parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.15mm,
Pu=100%
mm mm mm
20.28 0.091 0.008
Fig. 17. Values of bore diameter D for spur gear set Rd5. (Hs= 0.15mm, Pu=
75%).
TABLE XV. VALUES OF STATISTICAL INDICATORS FOR
THE SET OF SPUR GEARS RD5
Variable
parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.15mm,
Pu=75%
mm mm mm
20.31 0.088 0.008
Fig. 18. Values of bore diameter D for spur gear Rd6. (Hs= 0.15mm, Pu=
50%).
TABLE XVI. VALUES OF STATISTICAL INDICATORS FOR
THE SET OF SPUR GEARS RD6
Variable
parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.15mm,
Pu=50%
mm mm mm
20.29 0.068 0.005
Fig. 19. Values of bore diameter D for spur gear set Rd7. (Hs= 0.20mm, Pu=
100%).
TABLE XVII. VALUES OF STATISTICAL INDICATORS FOR
THE SET OF SPUR GEARS RD7
Variable
parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.20mm,
Pu=100%
mm mm mm
20.07 0.152 0.023
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Fig. 20. Values of bore diameter D for spur gear set Rd8. (Hs= 0.20mm, Pu=
75%).
TABLE XVIII. VALUES OF STATISTICAL INDICATORS FOR
THE SET OF SPUR GEARS RD8
Variable
parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.20mm,
Pu=75%
mm mm mm
20.13 0.120 0.014
Fig. 21. Values of bore diameter D for spur gear set Rd9. (Hs= 0.20mm, Pu=
50%).
TABLE XIX. VALUES OF STATISTICAL INDICATORS FOR THE
SET OF SPUR GEARS RD9
Variable
parameters
Mean
��
Standard
Deviation �
Dispersion
��
Hs= 0.20mm,
Pu=50%
mm mm mm
20.13 0.130 0.017
Using the values of the arithmetic means �̅ of the shaft
diameter d and of the bore diameter D (see Tables II-XIX) for
each set of gears Rdi (i=1...9), the graphs in Figure 22 and 23
were constructed, respectively.
Fig. 22. Variation of the arithmetic mean values �̅ of the shaft diameter d
for each set of gears Rdi (i=1...9).
Fig. 23. Variation of the arithmetic mean values �̅ of the bore diameter for
each set of gears Rdi (i= 1...9).
C. Disscusion
The study was carried out using the 162 values resulting
from the measurement with the digital caliper of the shaft
diameter d=62±0.1mm (see Figure 3) and the 162 values
resulting from the measurement with the same instrument of
the bore diameter D= 20.2±0.1 mm (see Figure 3) of the 27
cylindrical spur gears made of PLA, with modulus m= 1 and
spur teeth z= 60, additively manufactured by thermoplastic
extrusion (using the parameters in Table I), certify the
significant influence on their dimensions of the height of the
layer deposited at one pass Hs and the percentage of filling Pu.
In this context, analyzing the graphs in Figures 4-23 and the
result summary in Tables II-XIX the following results are
issued:
1) For Shaft Diameter d= 62±0.1mm
The best values were obtained by measuring the set of spur
gears Rd5 (Hs= 0.15mm, Pu= 75%), the calculated mean
being �̅= 62mm and dispersion ��= 0.002 (see Figure 9 and
Table VI).
The largest deviations were obtained in the measurement of
the spur gear set Rd2 (Hs= 0.10mm, Pu= 75%), the
calculated mean average being �̅= 61.95mm, and dispersion
��= 0.0087 (see Figure 5 and Table III);
100% of the values obtained in the measurement of the spur
gear set Rdi (i= 1...9) are within the tolerance of ±0.10mm,
the best values being obtained for 3D printing with the
height of the deposited layer at a pitch Hs= 0.15mm (see
Figure 22).
2) For Bore Diameter D= 20.2±0.1mm:
The best values were obtained in the measurement of the
spur gear set Rd3 (Hs= 0.10mm, Pu= 50%), the calculated
mean being �̅ = 20.25mm, and dispersion � � = 0.014 (see
Figure 15 and Table XIII).
The largest deviations were obtained in the measurement of
the spur gear set Rd7 (Hs= 0.20mm, Pu = 100%), the
calculated average being �̅ = 20.07mm, and dispersion ��=
0.023 (see Figure 19 and Table XVII).
Only 66.6% of the values obtained in the measurement of
the spur gear set Rdi (i= 1...9) fall within the tolerance of
±0.10mm, very close to the upper and lower limits (see
Figure 23).
Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10471-10477 10477
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IV. CONCLUSIONS
The current paper presents the results of a theoretical-
experimental study on the influence of FDM parameters
(height of the deposited layer at one pass Hs and percentage of
filling Pu) on the dimensions (shaft diameter d and bore
diameter D) of cylindrical spur gears made of PLA. Cylindrical
spur gears were printed on Creality CR-X 3D printer using
PLA filament - Verbatim brand.
Regarding the shaft diameter d, all values obtained in the
measurement of FDM 3D printed spur gears are within the
required tolerance of ±0.10 mm.
Regarding the bore diameter D, one third of the measued
values were outside the tolerance limits. The difference
between the extreme values of the arithmetic mean is 0.25mm.
The theoretical-experimental study demonstrates that of the
two FDM parameters analyzed, the Pu filling percentage has a
greater influence on the dimensional accuracy of spur gears
made of PLA.
The results of the study are useful for optimizing FDM
parameters for additive manufacturing of PLA spur gears by
thermoplastic extrusion within specified dimensional
tolerances. The study can be extrapolated to other types of
materials used in additive manufacturing technologies.
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