Shakedown limits for an oscillating, elastic rolling contact with Coulomb friction

• We examine a three dimensional elastic rolling contact with Coulomb friction.
• Slight oscillatory rolling leads to frictional shakedown or ratcheting.
• We derive the analytical shakedown limits and the shakedown displacement.
• Shakedown leads to a significant reduction of the tangential load capacity.

We examine experimentally and theoretically the effect of frictional shakedown of a three-dimensional elastic rolling contact. Small oscillations of the local normal forces lead to incremental sliding processes within the area of contact. Consequently, this causes a macroscopic slip motion of the two contacting bodies. If the oscillation amplitude is sufficiently small, the frictional slip ceases after the first few loading periods and a safe shakedown occurs. Otherwise the slip motion is continued and the contact fails.Using the method of dimensionality reduction, we derive analytical shakedown limits on the parameter plane tangential loading-oscillation amplitude and compare them to results of numerical simulations with Kalker’s program CONTACT. Both models show very good agreement with experimental data and allow an accurate prediction of the shakedown displacement and the maximum tangential load capacity in the shakedown state.