Gear Fatigue 02

   
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Gear Fatigue:
Press together an assembly and examine fatigue stresses at the root of anti-backlash gear teeth where failure occurs.

Special features:
3D model setup with bricks, trusses, contacts, static and kinetic friction, prescribed displacements, large deflections, and reaction forces.

Output:
Displacements, strains, stress components.

Comments:
This was a very sophisticated analysis. Click on the first thumbnail above. Shown is the pinion assembly for an anti-backlash gear system. The ball bearing fits into the pinion gear with a light press. The drive, in turn, is now pressed into the bearing. The drive has an elliptical circumference, which makes the bearing shape go elliptical. The distorted bearing now distorts the pinion gear. The gear teeth on the major axis of the now elliptical pinion gear wedges into the corresponding gaps between the teeth of the mating gear (not shown). This wedging fit prevents backlash.

Assume that the pinion gear is fixed: when the drive revolves at a high speed the major axis of the ellipse revolves at the same speed. As you can imagine, the cycling stresses are very high due to the repeated elliptical distortion. Since the numbers of teeth on the fixed gear (not shown) and the pinion are unequal, the pinion turns at a slower rate than the drive, which together function like a speed reducing planetary gear system. Because the alternating stresses are so high, the gear teeth and root designs must be optimized.

FEA is the means of best determining what the optimized shape should be. The analytical sequence involved pressing the pinion onto the bearing and then thermally expanding a shrunk-down drive within the bearing's inner race until it attained its net shape where the stresses due to various design geometries could be evaluated.

Clicking on the following thumbnails will show the structure animated with various outputs. The first shows the model displacing during the assembly sequence. Notice the model was created in 1/4 symmetry (solve times generally go as the square of the finite element count so reducing the model by a quarter means the model will solve in 1/16th the time - this model solved in just under 3 hours). The different colored bands of the pinion and drive are areas of mesh refinement to reduce model size and speed solve times. The truss elements can be seen that simulate the behavior of the balls in the bearing that keep the bearing races from collapsing and transfer the elliptical interior shape to an exterior ellipse acting directly on the pinion. Note expansion along the major ellipse axis and contraction of the bearing/gear on the minor axis. The next animation shows Von Mises stress in the assembly. Note the change in the legend scale, some portions will plastically deform. The model was rerun with plasticity turned ON (not shown here). This is an example of what can be done with Autodesk Simulation. Space does not permit a thoroughly rigorous demonstration. The next animation shows Maximum Principal stresses (legend scale is fixed).

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