Vibrations of Elliptically Shaped Bearings in Strain Wave Gearings

Abstract

The bearing of a strain wave gearing and the covering thin-walled cup, i.e., the so-called flexspline, are elliptically deformed. This leads to a characteristic excitation of vibration. In this paper, a model for describing the vibration of elliptically deformed bearings is presented. First, the flexspline stiffness is calculated using an a priori finite element (FE) analysis that is validated with measured data. Second, the deformation of the bearing and the flexspline is calculated by superimposing single loads. A numerical study shows that vibrations are mainly caused by the rotation of the ellipse. Furthermore, two types of impulses, i.e., negative impulses and positive impulses, lead to vibration excitation. The negative impulses are caused by the balls passing the angular position of the contact force maxima, while the positive impulses are caused by the balls impacting the surfaces of the races due to the radial tolerance of the bearing. Both negative and positive impulses coincide with characteristic frequencies of the nondeformed bearing. If the surfaces of the bearing are considered to be rough, the characteristic frequencies are not affected. Therefore, characteristic frequencies of nondeformed bearings can be utilized to describe vibrations of elliptically shaped bearings as well.