A novel finite element-based method for the determination of actual contact angles in angular contact ball bearings <i>SAGE Publications</i>

The contact angle inherently governs the axial-radial load distribution in ball bearings. In many applications, such as Fault Characteristic Frequency calculation and fatigue life ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ) prediction, this angle is often simplified as a constant initial value, a practice that compromises accuracy. To address this limitation, this paper introduces a Finite Element Analysis (FEA)-based method to determine actual contact angles and investigates their impact on fatigue life prediction. The proposed approach first identifies the major-axis endpoints of the contact ellipse from the FEA-derived contact stress distribution and approximates the contact center as the midpoint. The actual contact angles are then computed through vector operations involving the bearing center, ball center, and contact center. The proposed method is validated against Hertzian contact theory under various simulation conditions, demonstrating strong agreement. Furthermore, the influence of actual contact angles on bearing fatigue life is investigated, showing that incorporating actual contact angles significantly enhances the accuracy of fatigue life estimation.