Torsional Vibrations in a Crank Shaft

Abstract

In this paper, we analyze the torsion in the crank shaft of a gas compressor with one crank. The effect of damping will not be studied here. The geometry is as drawn in Fig. 1. Two forces are exerted on the shaft. First, it is at one end driven by a motor. We assume that this happens with uniform angular velocity ω, irrespective of the load of the crank. Second, the piston meets with the gas force, which is passed on to the shaft via the connecting rod and the crank. The geometry of the system implies, that the moments of inertia around the shaft of the moving parts may depend on the rotation angle φ of the shaft. The equation of motion for the torsion in this shaft has consequently periodically varying coefficients. A common approach to analyze this torsion is to average these coefficients over a period [1]. The resulting modelling equation can be dealt with in terms of eigenfrequencies, resonances and solutions, which are periodic in time. However, the solutions of the original equation of motion might be non-periodic and even show chaotic behaviour. The purpose of this study is to compare the behaviour of the reduced model with that of the original one in order to check the reliability of the reduction in case of realistic compressor data.