Probabilistic Life Assessment of Spherical Roller Bearings with Angular Misalignment

Angular misalignment of spherical roller bearings in wind turbine main shafts is a known cause of premature failure. Manufacturing and assembly tolerances introduce unavoidable variability in this misalignment—a source of uncertainty typically neglected in deterministic life models, thereby creating a gap between installation quality and system reliability. A probabilistic framework combining a Hertzian contact model, the Ioannides–Harris fatigue theory, and Monte Carlo simulation is developed to predict the fatigue life of double-row spherical roller bearings under uncertain misalignment. The sensitivity of eight geometric parameters, selected based on manufacturing tolerances, is quantified using Sobol indices for global sensitivity analysis, allowing their relative importance to be ranked. Application to a 950-series wind turbine main bearing under nominal and extreme loads shows that even with centered installation a non-negligible failure probability persists under nominal conditions. The strongly asymmetric bearing response requires asymmetrical installation tolerances to ensure high reliability. Global sensitivity analysis identifies the misalignment angle as the dominant source of uncertainty, followed by the roller contour radius. Under extreme loads, the bearing is under-dimensioned relative to the 20-year design life required for wind turbine main bearings, leading to a fatigue failure probability that approaches unity regardless of installation quality. The interaction between misalignment and radial clearance becomes pronounced under extreme overloads. Overall, the proposed framework provides a quantitative basis for reliability-based tolerance specification and emphasizes the necessity of considering the full load spectrum—including assembly variability—in bearing design.