This research project was motivated by the possibility of using
fracture mechanics to assist in optimizing gear design. The primary goal
is to develop a state-of-the-art capability for modeling three-dimensional
crack propagation in gears using boundary element method, finite element
method, and fracture mechanics. It is being conducted by a grant between
Cornell University and the NASA-Glenn Research Center (formerly known as
Lewis Research Center).
A common application of spiral-bevel gears is in helicopter transmissions.
Due to the cyclical loading on a gear's tooth, fatigue crack propagation
is likely to occur. The trajectory of the crack growth determines the failure
mode of the gear. Two modes of failure are common. The first mode, loss
of a gear tooth, is usually not catastrophic. The second failure mode,
crack propagation into the rim, could lead to the loss of aircraft and
life.
A desirable design objective of these gears is to minimize their weight.
One way to accomplish this is to reduce the material in the gear's rim.
However, Lewicki and Ballarini [1997] showed that as the rim thickness
of a spur gear is reduced, there is an increased risk of failure of the
gear's rim (Figure 1). Therefore, it is essential to be able to predict fatigue crack
trajectories to evaluate the safety of a proposed gear design.
Figure 1: Experimental and predicted crack growth trajectories
in a spur gear. FRANC2D was used for the predictions. The loadings on
the tooth in the simulations were highest point of single tooth contact
and centrifigal forces produced by the rotation of the gear.
Crack growth in spiral-bevel gears is fully three-dimensional. The cracks are arbitrarily curved surfaces with arbitrarily shaped fronts. The simulation system developed will be fully three-dimensional and allow crack trajectories and shapes that are completely arbitrary. The research will use the FRANC3D simulation system as a framework.
Figures 2 and 3 are images of a spiral-bevel pinion boundary element model built with OSM/FRANC3D and analyzed using BES. Three teeth of the pinion are explicitly modeled. A crack has been inserted into the tooth root of the middle tooth. The contours show the calculated primary stress.
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| Figure 2: Spiral bevel pinion model built with OSM/FRANC3D | Figure 3: Close up of three teeth in pinion model |
The light purple region on the tooth is the location of the applied
traction. The deep purple line between the yellow zones in the tooth
root is the location of the crack.
Some finite element simulations have also been performed with the spiral bevel gear. Click here to watch a simulation of a crack growing in the gear: Gear Simulations
References:
Lewicki, D.G. and Ballarini, R., "Effect of Rim Thickness on Gear Crack
Propagation Path," Journal of Mechanical Design, 119, 88-95
1997.
Lewicki, David G. and Ballarini, Roberto, "Rim Thickness Effects on Gear Crack Propagation Life," International Journal of Fracture, 87, 59-86, 1997.
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