On the dynamics of ball bearings

This investigation on the dynamic behaviour of ball bearings was motivated by the demand for silent bearings in noise-sensitive applications, especially in the household appliance and automotive industry. The present investigations are intended to provide a clear understanding of the role of the bearing in the application with respect to its design, its quality and the way in which it is mounted in the housings. Ball bearings can be important generators of noise and vibrations in applications. Due to the rotation of the lubricated contacts, the stiffness in the bearing is time dependent and generates parametric excitations. Furthermore , vibrations are generated by geometrical imperfections on the individual bearing components. The imperfections are caused by irregularities during the manufacturing process, and although their amplitudes are on the nanometer scale, they can still produce significant vibrations in the application. An important type of imperfection for noise related problems is waviness. Waviness is to be understood as global sinusoidally shaped imperfections on the outer surface of components. In the present approach, the waviness is treated using a statistical approach. In the approach followed the bearing is considered as an integral part of the application. The time dependent behaviour of the application was studied by means of predictive modelling. The shaft, the housings and the outer ring of the bearing were modelled using the finite element method. To solve the equations of motion of the application by means of time integration, the large finite element models were reduced by component mode synthesis. To account for the flexibility of the outer ring in combination with the rotation of the rolling element set, a new method was developed. By means of a verification study it was shown that this new method is fast and accurate. The stiffness and damping of the elastohydrodynamically lubricated contacts between the balls and the guiding rings were modelled as simplified vi spring-damper models. Their constitutive behaviour was predicted beforehand with the help of transient contact calculations. The three-dimensional ball bearing model developed here was validated successfully with measurements on a standard vibration test spindle. The predicted resonances of the bearing and the vibrations generated by paramet-ric excitations and geometrical imperfections agreed well with the measured ones up to 10 kHz. It was found that in the audible range, most of the vibrations generated by the bearing can be attributed to waviness imperfections on the balls. The damping of the individual …