Papers by Keyword: Nonsmooth

Abstract: For the non-harmonic vibration conveyor, a single-degree-of-freedom dynamics model is built for the horizontal motion of bulk materials, in which the dry friction force is piecewise nonsmooth. The effect on conveying velocity is studied for six vibration parameters in the excitation force with two harmonic components. The conveying velocity increases with the increase of frequency and amplitude, but the optimum frequency ratio is 2, and the optimum amplitude ratio approaches 1/3. The initial phase has no effect on conveying velocity, and the effect of phase difference is periodic, i.e. the forward conveying is best on phase difference π/2, and the backward conveying is best on phase difference -π/2.

Abstract: This paper is concerned with the modelling of gear rattle in Roots blower vacuum pumps. Analysis of experimental data reveals that the source of the noise and vibration problem is the backlash nonlinearity due to gear teeth losing and re-establishing contact.We develop non- smooth ordinary differential equation models for the dynamics of the pump. The models include a time-dependent forcing term which arises from the imperfect, eccentric mounting of the gears. We use a combination of explicit construction, asymptotic methods and numerical techniques to classify complicated dynamic behaviour in realistic parametric regimes. We first present a linear analysis of motions where the gears do not lose contact, and develop upper bounds on eccentricity for quiet operation. We then develop a nonlinear analysis of ‘backlash oscillations’, where the gears lose and re-establish contact, corresponding to noisy pump operation. It is found that noisy solutions can coexist with silent ones, explaining why geared systems can rattle intermittently. We then consider several possible design solutions, and show their implications for pump design in terms of the existence and stability of silent and noisy solutions. Finally, we present conclusions and possibilities for future work.