Parametric instability of an axially moving belt subjected to multi-frequency excitations: experiment and analytical validation

Abstract

In belt drive applications, the tension fluctuation caused by transverse vibration has important consequences on belt and bearing lifetime. Additionally, pulley oscillations induce tension fluctuations that are a source of parametric instabilities that create transverse vibration. This paper focuses on an experimental investigation of an industrial axially moving belt subjected to multi-frequency parametric excitation. The experimental results validate a corresponding theoretical analysis previously developed. First, a stationary parametrically excited beam is considered. A simply supported, Euler-Bernoulli beam is subjected to mono-frequency sinusoidal tension fluctuation via a shaker and torque arm assembly on one pulley of a two pulley drive. The transverse vibration from parametric instability is measured for varying amplitude and frequency of tension fluctuation and compared with theoretical predictions. In industrial applications, excitation sources are not at a single frequency as in the previous case, especially in an automotive engine. Engine firing and driven accessories cause multi-frequency speed and tension fluctuation. A specific test bench was built to reproduce this kind of excitation. The set-up is composed of four pulleys linked together by an automotive multi-ribbed belt.The driving shaft is driven by an electric motor, and the driven shaft is linked to a hydraulic pump. The internal design of the pump creates torque fluctuation when it rotates, which induces tension fluctuation in the belt drive. Angular positions are measured by optical encoders mounted on the pulleys, belt tension by a piezo-electric sensor on a pulley support, and lateral vibration by a laser displacement sensor. Data acquisition is based on the principle of angular sampling and is applied here for the first time on non-discrete geometry. This technique is particularly useful for rotating system with variable speed, as the samples always have the same size and the angular resolution remains the same. A speed sweep is performed on this test bench. Results demonstrate that when a second source of excitation exists at a lower frequency than the major one causing the instability, the entire instability region shifts to lower frequency,instead of occurring at twice a natural frequency. While this phenomenon is not classical, the experimental observations confirm the theoretical results. This experiment also demonstrates unexpected sources of excitation from changing belt characteristics (longitudinal stiffness and friction coefficient) along the belt length. These variation can also excite parametric instability.