Rolling bearing vibrations: the effects of varying compliance, manufacturing tolerances and wear

In this study some common types of Rolling Bearing vibrations are analysed in depth both theoretically and experimentally. The study is restricted to vibrations in the radial direction of bearings having pure radial load and a positive radial clearance. The general vibrational behaviour of such bearings has been investigated with respect to the effects of varying compliance, manufacturing tolerances and the interaction between the bearing and the machine structure into which it is fitted. The equations of motion for a rotor supported by a bearing in which the stiffness varies with cage position has been set up and examples of solutions,obtained by digital simulation. is given. A method to calculate amplitudes and frequencies of vibration components due to out of roundness of the inner ring and varying roller diameters has been developed. The results from these investigations have been combined with a theory for bearing/machine frame interaction using mechanical impedance technique, thereby facilitating prediction of the vibrational behaviour of the whole set up. Finally. the effects of bearing fatigue and wear have been studied with particular emphasis on the use of vibration analysis for condition monitoring purposes. A number of monitoring methods have been tried and their effectiveness discussed. The experimental investigation was carried out using two purpose built rigs. For the purpose of analysis of the experimental measurements a digital mini computer was adapted for signal processing and a suite of programs was written. The program package performs several of the commonly used signal analysis processes and :include all necessary input and output functions.

Finite element analysis of the statics of and vibrations in axisymmetric shells

The finite element process is now used almost routinely as a tool of engineering analysis. From early days, a significant effort has been devoted to developing simple, cost effective elements which adequately fulfill accuracy requirements. In this thesis we describe the development and application of one of the simplest elements available for the statics and dynamics of axisymmetric shells . A semi analytic truncated cone stiffness element has been formulated and implemented in a computer code: it has two nodes with five degrees of freedom at each node, circumferential variations in displacement field are described in terms of trigonometric series, transverse shear is accommodated by means of a penalty function and rotary inertia is allowed for. The element has been tested in a variety of applications in the statics and dynamics of axisymmetric shells subjected to a variety of boundary conditions. Good results have been obtained for thin and thick shell cases .