NON LINEAR DYNAMICS OF HIGH SPEED ROLLER BEARING

Abstract

Rolling element bearings are one of the key components in rotating machinery, and their good condition is vital for the machine performance. Any bearing in operation will invariably fail at some point, with risk of machine breakdown as a result. Allowing a machine to break down before repairing is expensive as production time is lost and the bearing defect may propagate to other machine components which will also need to be replaced. The stiffness, rotational accuracy and vibration characteristics of a high-speed shaft are partly controlled by the ball bearings that support it. In the rotor bearing assembly supported by perfect ball bearings, the vibration spectrum is dominated by the vibrations at the natural frequency and the Varying compliance frequency. The vibrations at this later frequency are called parametric vibrations. For better design of bearing and to reduce the total breakdown of the machine it is very necessary to study the non linear behaviour of the bearing. Main non linearity in the bearing is stiffness and damping actually, each contact between two parts can be replaced by spring and damper. The stiffness at the contact can be finding out by the lIertzian contact stress theory. So, based on that, the mathematical modelling can be done. With the help of solution of mathematical modelling 'l'ime displacement response plot, Orbit plot, FF'l' plot, Poincare Map and Bifurcation diagram can be prepared which gives the idea about the presence of chaos in dynamic system. Chaos is unstable behaviour of the system but it is bounded. But, it tends to the system in the breakdown stage if it will run long time in that situation. So, it is necessary to identify the chaos and the reason for the chaos. The quantitative amount of chaos can be found out by Lyapunov Exponent, Co relation dimension and Fractals. In the present study, the effect of speed (1000 to 10,000RPM) for the bearing (SKI7 6205) having internal radial clearance of 14 micron has been analyzed for balanced and unbalanced rotor. The coupled non linear differential equations have been solved by the Fourth-Order Runge —Kutta numerical method and the response plots like Time displacement response plot, Orbit plot, FFT plot, Poincare map and Bifurcation diagram have been plotted. Based on this plot dynamic behavior of the system at different speed has been identified. Also, the speed at which chaos is happened that is also identified. The numerical result has been verified with experiment results and both of them are in good agreement. The chaos can * be controlled by applying optimize preload.