In most studies finite element fretting models have been used to analyze two-dimensional contacts.  However, as processing power becomes less expensive, we can expect that three-dimensional models will become the norm.  The finite element method has already been used for three dimensional fretting wear analysis with Abaqus.

One reason for using three dimensional analysis is that many “real world” components and interactions are too complex to be closely approximated in two dimensions.  One such application is the spline-coupling which appears in the gas turbines used to power airplanes.  These couplings experience varying torques, axial loads, and bending moments during each flight.  A schematic of the coupling is shown in the following figure.  Expand the image for a better view.

The authors give a list of six tools which are required in order to perform this analysis:

1. A detailed geometrical model of the coupling; (ii) knowledge of how the coefficient of friction changes with distance slid;
2. (iii) a solver to calculate the contact pressure, traction and sub- surface stresses, and slip distributions at preset increments during the application of each loading cycle;
3. (iv) a mesh of sufficient detail to permit adequate resolution of the parameters listed in (iii);
4. (v) an algorithm to calculate the wear, and its direction, at each contact node after a prescribed number of simulated loading cycles;
5. (vi) a routine to re-mesh the contact elements according to the computed contact node wear values and directions.

A great deal of complexity has been included in modeling the spline coupling.  For example see the loading cycle which was matched to the operational conditions.  Here a major cycle was considered to be a flight while minor fluctuations were the change in loading during a flight.  

Interestingly, a non-linear wear rate was observed.  At the beginning of the test the wear rate was very high and it decreased to a roughly constant value by 4,000 cycles.  This took place at many  locations across the spline-coupling.  

Two different approximate geometries were modeled in this study: an cyclic-symmetric model with one tooth and a full model with all 18 teeth.  However, the simplified model did not work well because it could only model axially symmetric torque and axial loads.

• Ding, J., McColl, I., Leen, S., 2007, “The application of fretting wear modelling to a spline coupling,” Wear, Vol. 262, pp. 1205-1216.