Theoretical Model for the Dynamics of an Unconstrained Cutting Brush of a Street Sweeper

A theoretical model for the free-flight behaviour of an oscillatory cutting brush of a street sweeper is developed. The bristles are modelled as cantilever beams, and the equation of motion for the transverse vibrations is derived based on the theory of vibrations and small deflection beam theory. Two angular velocity functions are studied: a sinusoidal function and a function that provides small shaft accelerations and whose exact shape depends on a parameter b. The model is applied for a range of frequencies of oscillation that contains the first and second natural frequency of the bristle. The effects of the alternating component of the rotational speed, the type of function, and the value of b are also studied. The results are compared with those obtained in a previous work for a flicking brush. The findings suggest that the bending moment and bristle deflection tend to depend fairly linearly on the alternating velocity. In contrast to the bristles of a flicking brush, in the cutting brush resonance tends to occur only near the natural frequencies of the bristle. Additionally, the behaviour of the cutting brush is similar for both functions and for different values of b.