Week 1 Spur Gear Challenge

ANSYS MODEL SETUP (common for all the gear materials):
1). Mesh Settings:
Element Type: Hexahedrals
Adaptive Sizing: Off
Element Size: 1mm
Smoothing: Medium
Error Limits: Aggressive, Mechanical
Number of Nodes: 16474
Number of elements: 4900

2). Analysis Settings:
The rotation of each spur gear is divided into 6 steps lasting 1 second each and all the steps are divided into time stamps at which the solver runs a static simulation and gives us the result. The net simulation is derived as a transient like simulation but is actually a series of static simulations. The simulation is run at the end of each step (i.e. we get static results at 1,2,3,4,5 seconds each) and the initial time step for each step is 0.2 seconds, which means we also get results at 0.2,1.2,2.2,3.2,4.2,5.2 seconds. Within the steps, the time steps range between 0.05 seconds to 0.5 seconds.

To achieve static equilibrium and carry out static simulation at each time instant, the configuration of the gears is defined at the end and beginning of each step. Both the gears are jointed to the ground body with the help of revolute bodies for rotation about their own axis. A frictional contact is defined between the tooth faces of the teeth in contact for both the gears with the behaviour being set to symmetric, augmented lagrange being used to reduce chatter and the interface treatment being set to ‘Adjust to Touch’. The right gear is kept as the driver gear, with a constant torque being introduced to its revolute joint. Since the torque is constant (=10 Nm), at each step, the moment joint load value of 10Nm is mentioned. The left gear is kept as the driven gear, with its rotational motion due to the driving right gear being defined at the beginning and end of each step.

Based on the number of time stamps (or substeps) within each step, the configuration of the system is interpolated for each time stamp so that individual static analysis for each time stamp can be carried out.

To account for geometric non-linearity in the gears, large deflections are kept on.

REQUESTED OUTPUTS:
1). Von-Mises (equivalent stress): as the name suggests, it is the equivalent non-directional value of stress generated in the gear material. More specifically, it is the distortion/shear strain energy density in the gear.
2). Stress intensity: In terms of fracture mechanics, stress intensity is a measure of the stress fields and distribution around a developed crack and is a fundamental parameter which is used to study crack propagation leading up to failure. In this context, it refers to the localized stress distribution in the gear tooth which are in contact with each other. Intuitively, the gear tooth which come in contact will be the ones experiencing the most stress and thus, all the stress will be concentrated near this region. Stress intensity is a measure of that concentrated stress around the tooth contact.
3). Total deformation: It outputs the total deformation (in all directions) that each node in the mesh experiences.

For each of the requested outputs, the minimum, average and maximum values are computed at each time stamp and for simplicity in comparison, only the maximum values of the outputs will be considered.

	Cast iron (Ductile)	Cast Steel	Cast Bronze
Max. VM Stress (MPa), Timestamp (s)	393.62 (3.2 s)	393.61 (3.2 s)	394.79 (3.2 s)
Max. Stress Intensity (MPa), Timestamp (s)	420.61 (3.2 s)	420.61 (3.2 s)	424.61 (3.2 s)

Maximum total deformation in all the cases will be the same (10mm)

Comparison of maximum Von Mises stresses at each time stamp (from 0.2 seconds to 6 seconds):

Comparison of maximum stress intensity at each time stamp (from 0.2 seconds to 6 seconds):

As seen above, the maximum vonMises stress and the stress intensity follow almost the same kind of distribution except the stress intensity is a little higher than the von mises stress.

LOCATIONS FOR POSSIBLE FRACTURE:
The locations where there are highest stress concentrations will be susceptible for fracture. For all the cases, the tooth face end experiences the highest stress intensity (and thus VonMises Stress) at each time stamp and thus is the location for possible failure.

CHOOSING MATERIAL FOR DESIGN:
Since all the materials face almost equal amount of stress, based on the available data, design choices can be made in terms of the strength and the stiffness of the materials, both of which are quite low for cast bronze and thus won’t be preferable to use. Cast steel and cast iron (ductile) both have similar strength and stiffness properties, with cast steel having slightly higher stiffness and ultimate tensile strength and thus based on the available material data, should be selected for the gears. Based on the application of the gears, weight and cost efficiency may also be important deciding factors which can change the choice of the material.

ANIMATIONS:
CAST IRON (DUCTILE):

https://drive.google.com/file/d/19VqZe1VRBm9tr-yVlY39ASmSuI8unyJq/view?usp=sharing
https://drive.google.com/file/d/1p-t7DeZa_nWa4QdiE1r8lbW2HDD8Mtw2/view?usp=sharing

CAST STEEL:

https://drive.google.com/file/d/1eqyXL9Zdx9N6GEJI7ZFYffOSm9JA0MoT/view?usp=sharing
https://drive.google.com/file/d/1__7Q46fEHK2GSrF5yvvpJ0H4DPW-Jc97/view?usp=sharing

CAST BRONZE:

https://drive.google.com/file/d/1d3wQ8ORhx87vSOfAj_W_nBOhHPwXVDdB/view?usp=sharing
https://drive.google.com/file/d/1lRdjcstAAR0syQcKhHyFhWvSBkX-vUaS/view?usp=sharing