Non-linear vibration of power transmission belts

Non-linear vibration of a prototypical power transmission belt system, which is excited by pulleys having slight eccentricity, is investigated through experimental and analytical methods. Laboratory measurements demonstrate the role of non-linearity in setting the belt's response, particularly in the near-resonance region, and at high running speeds. The belt is coated with a retroreflective medium so as to improve displacement and velocity measurements made through non-contact laser interferometry. A frequency crossing diagram relates the belt's speed-dependent excitation and natural frequencies, and is shown to be useful for identifying those speeds at which resonance is expected. Distinctive jump and hysteresis phenomena in the near-resonant response are observed experimentally, and are also studied with a model that includes non-linear stretching of the belt. In that regard, a modal perturbation solution is developed in the context of the asymptotic method of Krylov, Bogoliubov, and Mitropolsky for a general, continuous, non-autonomous, gyroscopic system with weakly non-linear stiffness. The solution is subsequently specialized to the belt vibration problem at hand. Near- and exact-resonant response amplitudes are predicted by the perturbation method, and they are compared with those obtained by laboratory tests and by direct numerical simulation of the non-linear model. (C) 1997 Academic Press Limited.