Dynamics of belt-pulley-shaft systems

Abstract

An analytical model of a pair of pulleys mounted on compliant spinning parallel shafts is developed. These form parts of a belt drive system and are connected by a single belt span, which is modeled as a combination of longitudinal and torsional springs. The pulleys are modeled as rigid cylindrical disks and slippage at the belt-pulley interfaces is ignored. The shafts are modeled as continuous beams having torsional flexibilities as well. The rotation speed is high such that the gyroscopic effect is non-negligible. Natural frequency sensitivity to rotation speed (Campbell diagram) and response due to a sinusoidal excitation force on a shaft is obtained. Modal analysis after reducing the discretized system to a first-order form is used for the response calculation. The study shows that the gyroscopic effect is present even for short lengths of the shafts. Splitting of the natural frequencies as well as the mode shapes is observed at low rotation speeds and critical speeds are observed at high rotation speeds. For coupled frequencies, the response of the system is found to be approximated by modal superposition of a smaller number of modes. The peak responses are explained using the Campbell diagram along with the modal energy plots.