Wire twisting stiffness modelling with application in wire race ball bearings. Derivation of analytical formula and Finite Element validation

Since Erich Franke produced the first wire race bearings in 1934, they have not been used profusely until these last years in applications such as computerized tomography, X-ray machines, wheels with direct drive... where low weight and inertia constraints are important. Accounting for the structural behaviour of the bearing, there exist a key phenomenon not present in other kind of more known bearings, which is the wire twisting under load; this wire twisting steers the force transmission among the bearing rings and the rolling elements. In this sense, for design and selection purposes, if a complete structural model of the bearing is to be done in an efficient way to assess bearing stiffness and load distribution over the rolling elements, the twisting stiffness of the wire has to be modelled properly. This work develops a simple analytical expression of that stiffness to be used in structural models, derived from an evidence-based deformation assumption at differential level for the section of the wire.