A DYNAMIC ANALYSIS OF TAPERED ROLLER BEARING UNDER FULLY FLOODED CONDITIONS .1. THEORETICAL FORMULATION

A vector method is used to solve the quasi-dynamic equilibrium in a ta pered roller bearing. Besides the complex external loads the quasidyna mic analysis includes both centrifugal forces and roller gyroscopic mo ment. The primary solutions obtained in this way are used in successio n to carry out a complete dynamic analysis based on the integration pr ocess of the differential equations written for both rollers and cage. The numerical equalities proposed by Houpert (Trans. ASME J. Tribol., 106 ( 1984) 375-385) are used to establish the lubrication regimes fo r both the roller-raceway contact and the rib-roller end contact. The sliding traction forces developed in the concentrated contacts are det ermined by assuming a nonlinear, viscoelastic lubricant. The shear str esses for both the unidirectional flow (line contact) and for the bidi rectional flow (rib-roller end contact) are computed. The roughness ef fect of the contact surfaces, as well as the thermal EHD effects, are included. The results obtained in the dynamic analysis are presented i n Part 2 of the paper and are compared with published data for analogo us working conditions.