A Uniform Analytical Approach for Ball and Roller Bearings Calculations

A novel analytical approach is proposed, uniform for ball and roller bearings, which takes into account 5 relative race displacements (3 translations: dx, dy, and dz, and 2 tilting angles: dθy and dθz) to provide simple analytical relationships for calculating directly the resulting 3 bearing loads: Fx, Fy, and Fz as well as the 2 tilting moments: My and Mz. A full coupling between all these displacements and forces is considered. The maximum rolling element load Qmax, the load distribution Q(Ψ) and the 3-D rolling element load distribution dQ(Ψ, x′) at each roller-race contact slice are also given analytically. It will therefore be possible for bearing users, willing to study for themselves a complete statically indeterminate systems including shafts, housing and bearings, to do such calculations using accurate nonlinear bearing forces-displacements relationships suggested in this paper and to predict easily bearing and other system components performances. This approach can also be implemented in any nonlinear Finite Element Analysis (F.E.A.) package for describing a bearing element connecting the shaft to the housing for example. It completes, therefore, the F.E.A. library of elements.