Amy.Sissala
12/13/2012

Table of Figures ............................................................................................................................................. 1
Table of Tables .............................................................................................................................................. 1
Introduction and Purpose ............................................................................................................................. 2
Approach ....................................................................................................................................................... 2
Results ........................................................................................................................................................... 4
Rectangular Teeth ..................................................................................................................................... 4
Steel-Steel Gears ................................................................................................................................... 4
Steel-PLA Gears ..................................................................................................................................... 5
PLA-PLA Gears ....................................................................................................................................... 6
Triangular Teeth ........................................................................................................................................ 7
Steel-PLA Gears ..................................................................................................................................... 7
PLA-PLA Gears ....................................................................................................................................... 8
Conclusion ..................................................................................................................................................... 9
References .................................................................................................................................................. 11
Figure 1: Cross Sectional View of Rectangular Gear Teeth Model ............................................................... 3
Figure 2: Cross Sectional View of Triangular Gear Teeth Model .................................................................. 4
Figure 3: Maximum Von Mises Stress of Steel-Steel Rectangular Gear Teeth ............................................. 5
Figure 4: Maximum Von Mises Stress of Steel-PLA Rectangular Gear Teeth ............................................... 6
Figure 5: Maximum Von Mises Stress PLA-PLA Rectangular Gear Teeth ..................................................... 7
Figure 6: Maximum von Mises Stress Steel-PLA Triangular Teeth ............................................................... 8
Figure 7: Maximum Von Mises Stress PLA-PLA Triangular Gear Tooth ........................................................ 9
Table 1: Material Properties of A36 Steel (ASTM A36 Steel, 2012) .............................................................. 3
Table 2: Material Properties of PLA (Aji P. Mathew, 2004) .......................................................................... 3
Table 3: Rectangular Gear Teeth Results .................................................................................................... 10
Table 4: Triangular Gear Teeth Results ....................................................................................................... 10
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Polylactic acid (PLA) is a biomaterial plastic with a low melting point. The material has been around since the 1930s but has recently become a major material used in the three-dimensional (3D) printing industry. (Lunt, 1998) Three dimensional printers work by either an additive or subtractive process. That is, they either add the material onto itself or cut the shape from a solid piece. PLA is popular with additive 3D printers because of its low melting point and modest strength.
Advances in the technology have recently shrunk 3D printers to a size of a desktop printer.
People have come up with a multitude of uses for these printers from printing original designs to repairing or enhancing existing products. By using 3D printers to repair or replace parts they will have to interact and function with the original design. This paper looks at how 3D printed objects would interact, specifically the teeth stresses, with a common object found in a manufacturing setting, gears.
High stresses often occur in gears, especially the teeth. In manufacturing, these appendages are liable to break and thus halt production. One solution for getting high stakes operations up and running again in situations where replacement parts, due to uncommon design, deadlines, or location, might be hard to come by is utilizing the 3D printing technology. With a computer and a 3D printer any number of different parts and designs can be printing only in the amount needed. Realistically PLA does not have the strength of steel but in an emergency it can serve as a temporary fix until the proper piece arrives.
The finite element analysis computer software COMSOL was used to model, analyze and study the stresses that develop between gear teeth. The problem was simplified in order to reduce processing time to looking at just one tooth from two interacting gears. In the triangular gear tooth model some of the surrounding material of the gear is also included for further study. Also, in order to reduce the processing time only two dimensional models were used.
The other material examined in these gears besides PLA is A36 steel. A36 is a common variation of steel. In COMSOL the plasticity of both materials is used in the analysis in order to better predict the
deformation of gear teeth. The material properties values for steel are in Table 1 and for PLA are in
Table 2 below.
2

Young’s Modulus
Density
2x10 11 Pa
7800 kg/m 3
Poisson’s Ratio
Initial Yield Stress
0.3
250x10 6 Pa
Isotropic Tangent Modulus 1x10 9 Pa
Table 1: Material Properties of A36 Steel (ASTM A36 Steel, 2012)
Young’s Modulus
Density
3.6x10
9 Pa
1260 kg/m 3
Poisson’s Ratio
Initial Yield Stress
0.024
49.6x10
6
Isotropic Tangent Modulus 1x10 6 Pa
Pa
Table 2: Material Properties of PLA (Aji P. Mathew, 2004)
Two different shapes of teeth were looked at: rectangular and triangular. These are two typical
gear designs. The models of the two shapes are below in Figure 1 and Figure 2. The problem was
simplified to just one tooth from the two interacting gears. In the triangular gear tooth model some of the surrounding material of the gear is also included for further study. There were three combinations modeled: two steel gears, one steel and one PLA gear, and two PLA gears. In order to compare the stresses between the teeth in all the models the von Mises stress was calculated and compared.
Figure 1: Cross Sectional View of Rectangular Gear Teeth Model
Y
X
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Y
X
Figure 2: Cross Sectional View of Triangular Gear Teeth Model
The tooth on the right was held on the bottom in both the x and y directions. The tooth on the left was then moved 3E-6 m in the positive x direction. This represents the top gear, or tooth on the left, rotating and thus pushing the gear on the bottom, or right hand tooth.
This analysis looks at several different combinations of steel gear teeth and PLA gear teeth. To begin with two steel, rectangular gear teeth were studied to use as a comparison point. Then one steel tooth was modeled pushing against a PLA gear tooth. This represents if one gear tooth broke and was replaced by on that was made from a 3D printer. Finally two PLA gear teeth were analyzed. This symbolizes a whole gear system that is made from a 3D printer.
Rectangular shaped gear teeth is one common shape for gears found in manufacturing. By first looking at the stresses and displacements of two steel gear teeth the same results from PLA gear teeth can be compared. This will be able to express if PLA is a better or worse material for gear teeth to be made from and how reasonable the concept of using 3D printed parts is in manufacturing.
Steel-Steel Gears
The first model analyzed was two steel, rectangular shaped gear teeth. The left hand gear tooth is displaced in the x direction in order to exert a force on the right hand gear tooth. The maximum von
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Mises stress, as shown in Figure 3, is 2.4693x10
6 N/m 2 or Pa. The stresses are concentrated at where the edges of each tooth contact the next tooth.
Y
X
Figure 3: Maximum Von Mises Stress of Steel-Steel Rectangular Gear Teeth
Steel-PLA Gears
The next model looked at is one steel, rectangular gear tooth pushing on one PLA gear tooth.
The maximum von Mises Stress is 2.269x10
6 Pa. This result is close to the model with two steel gear teeth. Yet the deflected shape of this model is very different. The PLA gear tooth experiences a greater deformation at the edge of the steel tooth. This is logical as A36 is stronger than PLA and has a Young’s modulus larger by a factor of 1000.
5

Y
X
Figure 4: Maximum Von Mises Stress of Steel-PLA Rectangular Gear Teeth
PLA-PLA Gears
The last rectangular gear teeth studied is one of two PLA teeth. Figure 5 shows the maximum
von Mises stress and the deflected shape. Two PLA gear teeth have a much lower von Mises stress,
5.6229x10
4 Pa. The deflected shape looks very similar to the model of two steel gear teeth because now they are both made out of similar material.
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Y
X
Figure 5: Maximum Von Mises Stress PLA-PLA Rectangular Gear Teeth
Another common shape for gear teeth is triangular. Two different material combinations were analyzed: one steel and one PLA gear tooth and two PLA gear teeth.
Steel-PLA Gears
Figure 6 shows the maximum von Mises stress of one steel, triangular gear tooth moved 3x10
6 m towards a PLA, triangular gear tooth. The maximum stress is 6.6432x10
9 Pa. This is almost twice as much as the same rectangular teeth. The deflected shape shows a trough is created in front of the PLA gear tooth as it is pushed in the positive x direction.
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Y
X
Figure 6: Maximum von Mises Stress Steel-PLA Triangular Teeth
PLA-PLA Gears
Figure 7 shows the deflected shape and maximum von Mises stress of two PLA, triangular gear
teeth being pushed together. The maximum stress is 4.3623x10
9 Pa. This is lower than the steel and PLA gear teeth, similar to what happened with the rectangular gear teeth.
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Y
X
Figure 7: Maximum Von Mises Stress PLA-PLA Triangular Gear Tooth
Polylactic acid, also known as PLA for short, is a biomaterial plastic with a low melting point. The material has been around since the 1930s but has recently become a major material used in the threedimensional printing industry. Recently advances in the technology have shrunk 3D printers to a size of a desktop printer. People have come up with a multitude of uses for the printer from printing original gadgets to repairing or enhancing existing products. This paper looks at how 3D printed gears would interact, specifically the teeth stresses, with steel gears.
The yield stress of A36 steel is 250x10 6 Pa and PLA is 49.6x10
6 Pa. By looking at the maximum
stresses seen in all five scenarios in Table 3 and Table 4 it is seen that rectangular gear teeth made out
of PLA would not fail. Yet triangular shaped PLA gear teeth see stresses about 1000 times larger than its yield stress and would not survive. It seems that rectangular gear teeth made from 3D printers of PLA could replace those made of steel. This offers not only a lighter solution but one that can rapidly be produced. Further study should be done on larger forces that are produced from gear rotation.
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Steel-Steel Gear Teeth
PLA-Steel Gear Teeth
PLA-PLA Gear Teeth
Maximum Von Mises Stress (Pa)
2.4693x10
6
2.269x10
5
5.6229x10
Table 3: Rectangular Gear Teeth Results
4
PLA-Steel Gear Teeth
PLA-PLA Gear Teeth
Maximum Von Mises Stress (Pa)
6.6432x10
9
4.3623x10
Table 4: Triangular Gear Teeth Results
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ASTM A36 Steel. (2012). Retrieved December 13, 2012, from Matweb: http://matweb.com/search/DataSheet.aspx?MatGUID=afc003f4fb40465fa3df05129f0e88e6&ck ck=1
Aji P. Mathew, K. O. (2004). Mechancial Properties of Biodegradable Composites from Poly Lactic Acid
(PLA and Microcrystalline Cellulose (MCC). Wiley Interscience, 2014-2025.
Lunt, J. (1998). Large-Scale Production, Properties and Commerical Applications of Polylactic Acid
Polymers. Polymer Degradation and Stability, 145-152.
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