Uncertainty analysis for rolling contact fatigue failure probability of silicon nitride ball bearings

Uncertainty analysis and parametric studies are presented for estimating the fatigue failure probability of surface cracks in silicon nitride ball bearings subjected to rolling contact fatigue. Uncertainty quantification of input parameters are presented first based on experimental data, inspection capability, and geometric reasoning. Surrogate models for equivalent stress intensity factors are then used for uncertainty propagation, which are built upon high fidelity finite element modeling with half-penny-shaped surface cracks. Instead of black-box type surrogate modeling, physical observations are employed to decompose the high dimensional surrogate model into multiple one-dimensional models. The cross-validation technique is used to find the best surrogate that has the smallest prediction variance. The probability of failure is estimated using Monte Carlo simulation and surrogate models. The parametric studies show that reducing the maximum crack size (by limiting inspection threshold) and increasing the fatigue threshold (by improving fracture toughness of a material) are the most effective ways of reducing the probability of failure. For example, decreasing the maximum crack size by 4.4% and increasing the lowest fracture threshold by 2.8% results in the reduction of probability of failure by 40%. Ball survivability increases with decreasing ball diameter, for a given peak Hertzian stress. In order to apply the current study to hybrid ball bearing design, the survivability results are generalized through non-dimensionalization.