Dynamics of a freely rotating cutting brush subjected to variable speed

Cutting and flicking brushes of street sweeping vehicles sweep the debris that lies in the road gutter. As most of the debris is found in the gutter, it is of interest to understand and improve the behaviour of these brushes. This article investigates the dynamics of a novel oscillatory cutting brush in free rotation, by means of an analytical model derived by the authors. Two oscillatory functions are dealt with: a sinusoidal function and a function developed by the authors. The latter function, called Vanegas Useche–Abdel Wahab–Parker (VAP), depends on a smoothness parameter, b, which controls the smoothness of the angular speed function and the maximum brush accelerations. The parameters that affect brush behaviour are identified. The effects of the type of function, frequency of oscillation, smoothness parameter, ratio between the alternating and mean angular speed, bristle length, mount angle and mount radius are studied. The model indicates that bristle deflections and stresses are proportional to the square of the mean angular speed, provided that the ratio between the alternating and mean angular speed is constant, and depend linearly on the mount radius. The results indicate that, for the cases studied, the first mode dominates bristle vibrations, and that there tends to be resonance when the frequency is close to the first natural frequency of the bristles. Notably, bristle dynamics exhibits a peculiar behaviour, a condition similar to resonance at odd fractions of the natural frequencies for the VAP function. The intensity of this phenomenon could be controlled by adjusting the value of b or changing the frequency of oscillation. It is noted that the results of this work are also applicable to a small-deflection cantilever beam, when this is subjected to a function that is the square of a triangle, sinusoidal, or VAP wave. As the VAP function can achieve a resonant behaviour not only at the natural frequency of the bristle but also at odd fractions of at least the first four natural frequencies, small frequencies may be needed to produce a high-frequency mode resonant characteristic.