Abstract
We study synchronization of two eccentric rotors (ERs) with common rotational axis in the vibration system of the far-resonant spatial motion. We deduce the dimensionless coupling equation of two ERs with applying the average method of small parameters. We convert the synchronization problem into the existence and stability of solving the zero solutions for the dimensionless coupling equations. By introducing the synchronization torque and the difference between the residual torques of two motors, we obtain the synchronization condition that two ERs achieve the synchronized motion. We derive the stability condition of the synchronized motion, which satisfies Routh-Hurwitz criterion. We discuss numerically the choosing motion feature of the vibration system, which indicates that the vibration system has two steady motion modes. The synchronization torque forces the phase difference to approachπwhen the structural parameters of the vibration system satisfy the condition of the spatial cone motion, and the synchronization torque drives the phase difference to approach zero when those satisfy the condition of the spatial circle motion. Finally, through the comparison and analysis of experimental data, the structural parameters of the vibration system satisfying the above two conditions can guarantee the synchronization stability for two ERs.
Highlights
In vibration utilization engineering, synchronization of eccentric rotors (ERs) is a special phenomenon of the nonlinear vibration system, which is used to design the vibration conveyer, the vibration screen, the vibration centrifuge, and so forth [1]
Synchronization of two ERs with the common rotational axis in the vibrating system of the farresonant spatial motion is investigated with applying the average method of small parameters. We addressed that this type of vibration system has the choosing motion feature, and the theory approach is verified to be useful and feasible by experiments
Some simplified forms of theoretical analysis for the synchronization problem have been given in previous section
Summary
Synchronization of ERs ( called exciter) is a special phenomenon of the nonlinear vibration system, which is used to design the vibration conveyer, the vibration screen, the vibration centrifuge, and so forth [1]. The vibration mill is a kind of grinding equipment with high efficiency and energy saving, which has been widely used in many fields, such as metallurgy, chemical, mining, medical, ceramics, cement. For the large-scale vibration mill, its longer barrel is not driven by only one motor. There are many questions about the design of this vibration mill excited by multiple ERs, for example, two motors drive separately two ERs running in synchronization state to replace forced synchronization. Applying the synchronization theory to design the large-scale vibration mill can simplify structure of the vibration mill, decrease production cost of that, and enhance work efficiency of that
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