Abstract
The problem of the occurrence of semi-slow speed oscillations of an unbalanced rotor during its passage through the resonance zone has been solved using the method of direct separation of motions. It has been proved that when a stationary regime is established, semi-slow damping oscillations of the rotor speed arise in the region of the Sommerfeld effect, they are the result of the superimposement of free accompanying oscillations with a relatively low frequency on forced fast oscillations. In this respect, the initial amplitudes of such oscillations are quite large, and oscillations damping is relatively slow.
Highlights
Inertial vibration exciters are used to drive a wide variety of vibration machines
The described regularity of the system motion is represented as the presence of the “inner pendulum” and its semi-slow oscillations in the region of the Sommerfeld effect
The maximum amplitudes of the arising semi-slow oscillations of the rotor speed are quite large, and their dampening happens slowly, it can be of a significant danger for vibration machines [11]
Summary
Inertial vibration exciters are used to drive a wide variety of vibration machines. Most of these machines operate in resonance mode. A review of the works in this field is given, for example, in the books [1, 2] These studies draw our attention to the fact of existence of fast, slow and semi-slow motions in the region of the Sommerfeld effect. It is important that semi-slow oscillations are used to facilitate the passage of vibration machines though the resonance zones. Using the direct motion separation method it is shown that the general solution for the fast motion equation describes a transition process towards ascertainment of a stationary motion mode of an unbalanced rotor in the resonance zone of vibration machine, as well as that semi-slow oscillations of the rotor speed are seen as transition process in the region of the Sommerfeld effect
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