Dynamics of an unconstrained oscillatory flicking brush for road sweeping

This article studies the dynamics of a freely rotating flicking brush by means of a mathematical model. The bristles are treated as cantilever prismatic beams subjected to small deflections. A solution of the equation of motion for their forced transverse vibration is obtained through the normal-mode method. A novel oscillatory motion is superimposed onto the rotary motion of the brush. Two functions of oscillation are investigated: a sinusoidal angular velocity and a novel function, named after the authors ‘VAP’ (Vanegas Useche, Abdel Wahab, Parker), developed to provide small shaft accelerations. The VAP function may be a square wave, a triangle wave, or a smooth wave between them, depending on the value of a smoothness parameter, b. The results indicate that the maximum bending moment, stress, and deflection are independent of the mean angular velocity, are proportional to its alternating component, and increase linearly with the mount radius and the sine of the mount angle. In addition, the behaviour of the brush is strongly affected by the frequency of oscillation, the type of function, the value of b, and bristle wear, amongst other parameters. For the sinusoidal and VAP function, resonance occurs at the bristle natural frequencies. Moreover, the VAP function tends to produce a condition similar to resonance also at odd fractions of the natural frequencies. This phenomenon may be accentuated or reduced, by adjusting the value of b, and be expedited or impeded, by the selection of the frequency. The results of this work may also be applied to the case of a small-deflection cantilever beam, when the transverse external force is a sinusoidal, square, or triangle wave or when it is given by the new VAP function. Finally, the VAP wave may enable to excite a condition similar to resonance not only at the natural frequencies of the beam, but also at odd fractions of them. Small frequencies may be required to achieve a resonant behaviour of a high-frequency mode; this behaviour can be controlled by means of the smoothness parameter.