Week 1 Spur Gear Challenge

Week 1 Spur Gear Challenge

Objective : Objective of this challenge is Comparing the results which is Equivalent stress, Total deformation and Stress intensityobtained by using three different materials for spur gears.

spur gear :The most common type of gear is the spur gear. These gears have straight teeth and must be mounted on parallel shafts for their teeth to mesh with those of other gears.spur gears used to generate power and also to increase speed.

Stress intesity : stress intesity used to find possible location for fracture.it depent on stress intensity factor.
stress intensity factor,

The stress intensity factor, K, is used in fracture mechanics to predict the stress state (stress intensity) near the tip of a crack or notch caused by a remote load or residual stresses. in general case stress intensity factor is written by following formula,

k=α σ√(πa)

where,

σ= far field stress
a= crack length

Materials :

• Case 1:

                   Using Cast Iron(ductile) as a material

• Case 2:

                   Using Cast Steel as material

• Case 3:

                   Using Cast Bronze as material.

Objective 1:-
For all the 3 cases the below boundary conditions and meshes are the same. Only the material was changed in each case to check which material was better suited for this spur gear assembly.

Figure 1- Rotational and frictional contact boundary condition for the spur gear.
The connection between both the gears has been set to frictional for all the gear teeth. Augmented Lagrange has been chosen
to resist the penetration of the contacts.

Figure 2- default mesh

The above picture shows the default mesh size of 3.155mm provided according to the geometry in the Ansys. The number of
nodes and elements in the above spur gear assembly are 8142 and 1140. Since Ansys student’s version provides analysis with
fewer elements, the mesh quality is poor.

 

Figure 3 - fine mesh

Figure 4 – Assignment of the revolute joint for spur gears. Left gear applied with 20 degrees’ step rotation and right gear applied
with a moment of 10Nm for all the steps.

For both the gears have revolute joint along the z-axis constraint has been applied so that both the gear will rotate along the zaxis.
Left gear will rotate in the clockwise and right gear will rotate along the anti-clockwise direction. Left gear has been applied
the rotational constraint of 30 degrees per step, and right gear has been applied with a moment of 10Nm to resist the rotation
of the left gear.

 

Case 1 - Cast iron

 

Figure 4- Deformation contour for cast iron

The maximum deformation of 30 mm is seen at the tooth land and this is due to the contact between the two gears. The
maximum deformation is indicated by red contour in the above picture. The minimum deformation is seen at the inner
diameter (root diameter) of the gear where no contact of two parts are there.

Figure 5- Von-Mises stress contour for cast iron

In the above picture, the von-Mises stress is maximum at the point of contact between the two gears. It is 458.42 MPa which is
more than the yield strength of cast iron which is 276 MPa. For the safe level of designing the von-Mises stress should be lower
than the yield strength so that the part does not fail during its operation at harsh environments. And at the other regions of the
gear where there is no contact and very less negligible stress levels are observed.

Figure 6:- Equivalent strain contour for cast iron

In the above picture, the equivalent strain contours for the spur gear simulated with cast iron are shown and the maximum
equivalent elastic strain is 0.28%. Maximum equivalent elastic strain is observed at the point of contact between two gears.

 

Case 2:- Cast Steel

Figure 7 - Deformation contour for cast steel

The maximum deformation of 30 mm is seen at the tooth land and this is due to the contact between the two gears. The
maximum deformation is indicated by red contour in the above picture. The minimum deformation is seen at the inner
diameter (root diameter) of the gear where no contact of two parts are there.

 

Figure 8:- Von-Mises stress contour for cast steel

In the above picture, the von-Mises stress is maximum at the point of contact between the two gears. The yield strength of cast
steel is 354.65MPa, which is less than the von-Mises stress from the above simulation results. Therefore, the above spur gear will
be safe during operation when compared to the spur gear made up from cast iron. And at the other regions of the gear where
there is no contact and very less negligible stress levels are observed.

Figure 9:- Equivalent strain contour for cast steel

In the above picture, the equivalent strain contours for the spur gear simulated with cast steel are shown and the maximum
equivalent elastic strain is 0.14%. Maximum equivalent elastic strain is observed at the point of contact between two gears.

Case 3: Cast Bronze

Figure 10:- Deformation contour for cast bronze
The maximum deformation of 30 mm is seen at the tooth land and this is due to the contact between the two gears. The
maximum deformation is indicated by red contour in the above picture. The minimum deformation is seen at the inner
diameter (root diameter) of the gear where no contact of two parts are there.

Figure 11:- Von-Mises stress contour for cast bronze
In the above picture, the von-Mises stress is maximum at the point of contact between the two gears. It is 315.69 MPa which is
more than the yield strength of cast bronze which is 144 MPa. For a safe level of designing the von-Mises stress should be lower
than the yield strength so that the part does not fail during its operation at harsh environments. And at the other regions of the
gear where there is no contact and very less negligible stress levels are observed.

Figure 12:- Equivalent strain contour for cast bronze
In the above picture, the equivalent strain contours for the spur gear simulated with cast bronze are shown and the maximum
equivalent elastic strain is 0.4%. Maximum equivalent elastic strain is observed at the point of contact between two gears.

 

Sr.No.	Time  (Sec)	Cast Iron	Cast Steel	Bronze Cast
		Total displacement(mm)
		Average displacement(mm)	Average displacement(mm)	Average displacement(mm)
1	1	6.1622	6.0953	6.1046
2	2	11.888	11.77	11.775
3	3	16.807	16.643	16.647
4	4	20.579	20.38	20.383
5	5	22.949	22.729	22.732
6	6	23.755	23.529	23.529

 

Figure 13:- Average displacement vs time step for three materials.

 

 

 

Sr.No.	Time  (Sec)	Cast Iron	Cast Steel	Bronze Cast
		Von Mises Stress  (MPa)
		Average Von Mises Stress  (MPa)	Average Von Mises Stress  (MPa)	Average Von Mises Stress  (MPa)
1	1	8.7623	10.298	9.0217
2	2	9.1748	10.95	9.6219
3	3	9.3157	9.3909	9.4373
4	4	9.0686	11.037	9.7305
5	5	8.7431	10.295	8.8723
6	6	8.3594	9.0178	8.8409

Figure 14:- Maximum von-mises stress vs time step for all three materials.

 

 

Conclusion: -

Displacement: - No change in all three materials.

Von-mises stress: - Maximum stress has been plotted and from the three materials cast steel is better as the von-mises stress is
less than the yield strength of cast steel. For cast iron and cast bronze, the von-mises stress is very high than the yield strength
of the materials and they will fail under real-world applications.

Equivalent elastic strain: - Average Equivalent elastic strain has been plotted for the three materials. From the graphs, it is clear
that very high equivalent elastic strain for cast bronze when compared to cast iron and cast steel. And the material with less
equivalent elastic strain is cast steel.
From the above contours and graphs, we could conclude that the cast steel is recommended when compared to the other two
materials.