Abstract
A computationally efficient load distribution model for deep groove ball bearings that accounts for local geometrical imperfections is developed. The generalized 5-DOF model is capable of accounting for different race supporting conditions. The model formulated consists of rigid bodies that are actual ball bearing components, and, hypothesized contact elements which mathematically represent contact. The resulting governing equation is composed of the compatibility conditions and equilibrium equations both of which relate the properties of rigid bodies to the contact elements. The initial separations, rigid body approach and elastic approach are components of the compatibility condition. The race and ball equilibrium are components of the equilibrium equations. A modified simplex style algorithm is implemented to capture contact non-linearity along with an iterative scheme that captures geometric non-linearity in the form of instantaneous contact elements. Common errors and manufacturing tolerances are then discussed with a parametric equation. An example analysis compares the base load distribution to an existing load distribution model. The load distribution with modifications to race diameter, race groove curvature, and, ± 5 μm random ball diameter variation is carried out. The load distribution and contact pressures developed for the three cases are compared with the base solution. This comparison highlights the use of and need for such a model.
