A Dynamic Modeling Approach for Spindle Bearing System Supported by Both Angular Contact Ball Bearing and Floating Displacement Bearing

Abstract

This paper presents a new dynamic modeling approach for spindle bearing system supported by both angular contact ball bearing (ACBB) and floating displacement bearing (FDB). First, a dynamic model of FDB is developed based on the discrete element method with each bearing component having six degrees-of-freedom (DOFs). Based on the developed FDB dynamic model and Gupta ACBB dynamic model, a fully coupled dynamic model of the spindle bearing system combined both ACBBs, and FDB is developed. In the proposed spindle bearing system model, the spindle shaft is modeled using finite element (FE) method based on the Timoshenko beam theory with the consideration of centrifugal force and gyroscopic moment. The coupling restriction between the dynamic bearing models and the FE spindle shaft model are the restoring forces and moments that are transmitted to the shaft by the bearings and the dynamic vibration response shared by both the bearing inner races and the corresponding nodes of the shaft where bearings are installed. A Fortran language-based program has been developed for the spindle bearing system with the dynamic bearing models solved using the Runge–Kutta–Fehlberg integration method and FE shaft model solved by Newmark-β method. Based on the developed model, the effect of the FDB radial clearance, system preload, and spindle rotating speed on the system dynamics, and the effect of the FDB radial clearance on the system unbalanced response have been investigated.