Week 8 Worm Gear Challenge

Transient Structural Analysis of Worm and Ring Gear Assembly

Objective:
To carry out a Transient structural analysis on a Worm and Ring Gear Assembly and determine the Total Deformation, Equivalent Stress andEquivalent Elastic Strain developed in the system.

Geometry:
The geometry consists of an assembly of a worm gear of 7 teeth, 5.05mm inner dia and 14.816mm tooth dia and a ring gear of 48mm inner dia and 50 teeth.

To accomodate the assembly in the student version, the ring gear is split in half by defining a plane along the Z-axis. The lower half of the ring gear is then deleted.

Material Definition:
Both, the worm gear and the ring gear are assigned Structural Steel as the working material, the properties of which are as follows:

Contact Definition:
A frictionless contact is defined between the mating teeth of the worm gear and the ring gear.

The interface treatment is set to "Add Offset, No Ramping" to ensure that a contact gap exists initially.

Joint Definition:
Tow Body-Ground revolute joints are defined-one for the worm gear and the other one for the ring gear- to constrain the motion of the gearsto their respective Z-axes only.

Mesh Definition:
The assembly is meshed with an element size of 3.5mm, 2mm keeping in mind the node/element limit imposed by the licence. The elementSmoothening Quality is set to "Medium".

Analysis Settings:
The simulation is run in 36 steps for the transient analysis, with an initial time step, minimum time step and maximum time step of 0.2s,0.2sand 0.5s respectively. The time step is carried over from the second step on wards.

Non-linear controls are left to their default. Results for Nodal forces, Stress, Strain and General Miscellaneous are requested to be written to the results filethrough the Output controls.

Joint Rotation Definition:
The Body-Ground revolute joint of the worm gear is provided with a rotation of 2850 degress is total, in increments of 80 degrees over the 36 steps.

The rotation of such large magnitude is provided to simulate the worm gear displacing almost to the end of the half ring gear.

Results

The simulation is run and the results are plotted.

1) Total Deformation:
The maximum total deformation observed is 26.48mm on the edge of the tooth face of the ring gear. This basically shows the totaldisplacement of a point in assembly from its initial position.

2) Equivalent Stress:
A maximum of 1002.01MPa of Von-Mises stress is experienced by the model (on the ring gear) during the run.The green, blue and red lines in the graph indicate the maximum, average and minimum equivalent stress respectively

3) Equivalent Elastic Strain:
A maximum elastic strain of 1.0201E-02 is experienced on the ring gear during the run.The green, blue and red lines in the graph indicate the maximum, average and minimum equivalent elastic strain respectively.

Inference:
From the analysis results the following can be deduced:
The maximum and minimum deformations are basically measurements of displacement of a point on the model with respect to its initial position. In this case, the maximum deformation is observed on the ring gear teeth face edge which has displaced 19mm from its initial position. The minimum deformation of 0.6970mm is observed on the inner surface edge of the worm gear that stops rotating a little short of its diameter, at the end of the simulation.

The maximum Von-Mises Stress is computed at the flank region of the ring gear where the gear tooth intersects with the dedendum circle radius. Due to the constant mating of the teeth of the two gears and the sharp geometry of the region, the stress in this region is the highest.

The maximum equivalent Elastic Strain is also observed at the flank of the ring gear teeth, which intersects with the dedendum circle. The sharp geometry in this region induces highly concentrated stress and consequently elastic strain.

The stresses in the geometry exceed the yield strength of the assigned material, but no plastic deformations can be observed. This is due to the fact that, being a linear static analysis, the solver interpolates all the results within the linear elastic region of the stress-strain curve and no plastic deformation is
visible.