Abstract
As a continuous work of the previous literatures, a special dynamical model with one cylindrical roller driven by a single exciter and one outer ring, is taken for example to explore the vibratory synchronization transmission (VST) of the system considering sliding dry friction in this paper. The motion differential equations of the system, are given firstly. Using the average method, the theory condition of implementing VST is obtained. The VST characteristics are qualitatively discussed in numerical, which are further quantitatively verified by simulations. It is shown that, the vibration amplitudes of the roller in the horizontal and vertical directions are basically identical, and less affected by the friction coefficient, but the stable phase difference between the exciter and the outer ring is affected too much by it. Based on the present work, some new types of vibrating equipments, such as vibrating crushers/mills, can be designed.
Highlights
There are many vibration or synchronization problems in engineering or real-time system fields, such as the chaotic vibration, bifurcation, stabilization and synchronization control for fractional discrete-time systems, digital chaos and local synchronization for a universal analog-digital hybrid mechanism, and vibration for the gear system, etc. [1]–[3]
When the above conditions are satisfied, under the effect of the sliding dry friction between the cylindrical roller and the outer ring, the outer ring centroid can be driven by the rotating roller to move around the stationary centroid O of the system, and the outer ring can be regarded as an ‘exciter’ rotating around O, which means this ‘exciter’ can follow the cylindrical roller to realize a circular motion with a certain frictional force
According to Eq (17), it can be known that when the eccentric radius s of the outer ring rotating surround the mass center does not exceed 1 +2 fR times than its motion amplitude A under the condition of the dry friction, the outer ring can be regarded as an exciter rotating around the center of the system
Summary
There are many vibration or synchronization problems in engineering or real-time system fields, such as the chaotic vibration, bifurcation, stabilization and synchronization control for fractional discrete-time systems, digital chaos and local synchronization for a universal analog-digital hybrid mechanism, and vibration for the gear system, etc. [1]–[3]. Considering the effects of damping of the system, Wen et al [8], [9] developed the synchronization theory of exciters, studied the synchronization problems for n (n ≥ 1) times frequency, and based on which invented many new vibrating. The present work aims at revealing deeply the coupling mechanism of implementing VST of the system by theory and numeric methods, based on the [4] and [5]. This can be considered as another attempt to develop the theory of VST and expand its application field, base on which a new engineering application approach of VST can be expanded.
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