Abstract
A new dynamical model with five rigid frames (RFs), driven by two counter-rotating exciters, is proposed to explore the synchronization, stability, and motion characteristics of the system in this paper. The motion differential equations and the corresponding responses of the system are given firstly. Using the average method, the average torque balance equations for the two exciters are deduced. According to the relationship between the difference of the dimensionless effective output electromagnetic torques for the two motors and the coupling torques of the system, the theory condition of realizing synchronization is obtained. Based on the Hamilton’s theory, the theory condition of stability of the system is deduced. The stability and motion characteristics of the system for different resonant regions are qualitatively discussed in numeric, including the stable phase difference of the two exciters, relative phase relationships among the five rigid frames, amplitude-frequency characteristics, stability coefficients, and the effective load torque between the two exciters. Simulations are carried out to further quantitatively validate the feasibility of the above theoretical and numerical qualitative results. It is shown that in engineering the reasonable working points of the system should be selected in Region II, only in this way, can the synchronous and stable relative linear motion of the system with the zero stable phase difference in vertical direction be realized, and in this case, the vibrations of the four inner rigid frames (IRFs) in the horizontal direction are compensated with each other, and the energy is also saved due to utilizing the resonant effect. Based on the present work, some new types of vibrating coolers/dryers or vibrating screening machines can be designed.
Highlights
The problems and researches about vibrations in engineering and technology fields generally consist of vibration suppression and vibration utilization. For the former, which are related to the vibration isolations, such as vibration absorbers;[1,2,3] while for the latter, one of the most important representatives is the synchronization of exciters, based on which many new vibrating machines can be invented and widely used in the industrial production process, implement the screening, cooling/drying, conveying, feeding of the materials, and so on, and more and more researchers are inspired to investigate it
The working point of the system should be selected in Region II of Figure 2, and in this case, the greater vibration amplitudes of the relative linear motion with the same phases of the four inner rigid frames (IRFs) in y-direction can be realized, while the vibrations in x-direction of the four IRFs are compensated with each other, and the energy is saved due to the resonant effect
The resonant regions of the system are divided into three regions by the two natural frequencies x0 and x4, in regions of x0 < xm0 < x4 and the first narrow range of super resonant region with respect to x4, the phase difference between two exciters is stabilized in the vicinity of zero, and in this case, the relationship between the four IRFs and the outer rigid frame (ORF) is the relative linear motion with the opposite phases in the vertical direction, while the total system reflects no vibration in the horizontal direction
Summary
The problems and researches about vibrations in engineering and technology fields generally consist of vibration suppression and vibration utilization. In order to improve the isolative effect of the system and make full use of the space, the inclined angles between the springs connected to IRFs and the horizontal line are actively set up Based on this new dynamical model, some new types of vibrating machines, such as vibrating cooling/drying fluidized bed, and vibrating screens, can be designed. A new dynamical model with five RFs and two exciters and the motion differential equations are given firstly, and the synchronization and stability of the system will be investigated in detail by theory. The average kinetic energy (AEp) and average potential energy (AEk) equations over one period are yielded as AEp
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