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

Abstract

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.

Modeling of Contact Forces for Brushing Tools

“…In theory, dynamic oscillatory behavior and subsequent striking filament motions lead to an increase of the process forces and thereby to an increase of the material removal rate [16][17][18][19]. Although dynamic behavior can be both confirmed and controlled based on technological investigations, a positive influence on productivity remains to be confirmed.…”

“…Except for the tier, the contact normal impulse pn qualitatively resembles the contact time tc (Figure 4b) indicating that the contact normal force Fn affects the contact normal impulse pn considerably less than the contact time tc, Equation (3). In theory, dynamic oscillatory behavior and subsequent striking filament motions lead to an increase of the process forces and thereby to an increase of the material removal rate [16][17][18][19]. Although dynamic behavior can be both confirmed and controlled based on technological investigations, a positive influence on productivity remains to be confirmed.…”

Image-Based Tool Characterization and DEM Simulation of Abrasive Brushing Processes

“…In contrast, Sommerfeld et al [4,[19][20][21] devised another dynamic method based on multi-body systems (MBS), which were derived from Lagrange mechanics and allowed for the free oscillation and interaction of several filaments. Vanegas Useche et al [22][23][24][25][26][27][28][29] also investigated the large deflection elastic theory, discretization approaches, and later the finite element method (FEM) to simulate the elastic deformation of filament clusters in oscillatory street sweeping brushes. However, the computational complexity and precision of FEM systems allow only for small numbers of filaments, whereas industrial brushing tools have filament counts ranging in the tens of thousands.…”

Modelling rotary sweeping brushes and analyzing brush characteristic using finite element method

“…Except some modelling studies for painting and writing brushes [3,4], most investigations on brush techniques were associated with industrial brush polishing and brush sealing applications. Many researchers [5][6][7][8][9][10][11][12] have developed mathematical models to calculate the deformation and the dynamic characteristics of brush bristles, by which means brush stiffness as well contact profile, could be deduced. Classic large deformation mechanics have been used to calculate the bristle deformation due to surface constraint [5,13].…”