On the connection between precession and the nature of stress changes at forced oscillations of the shaft-line
Abstract
The influence of the type of precession of the shafting section on the nature and frequency of stress changes during their monitoring is shown. As a result of measurements of the rotors necks oscillations and other control points in the shaft, the nature of the precession of the rotor can be determined.
In any textbook on the dynamics of rotors [1], it is indicated that in the case of a direct synchronous precession of the rotor, it rotates curved, and the stresses do not depend on time, but depend on the size of the deflection. In real life, direct synchronous precession is rare.
As already shown in [2], a shaft or even a single rotor can have several sections of forward and reverse precession, and on the boundaries between these sections the elliptical trajectories degenerate into segments, and the oscillations of the cross section of the rotor have the same phase for the vertical and horizontal directions. If the phase of horizontal motion is greater than the phase of vertical motion, then we have a direct precession. If the phase of vertical motion is greater, then we have a reverse precession.
Thus, the appearance of zones of direct and reverse precessions is determined at each frequency of rotation by the forms of forced oscillations in each plane and their kinematic addition [3]. As a result, if the section of the shaft runs with a straight elliptical precession, then this motion can be considered as the sum of two: motion with a direct synchronous precession at which the stresses are constant in time and the motion with deviations twice in one turnover in the direction of the major axis.
The frequency of the change in the stresses for such deviations is equal to twice the rotational frequency. The phase of the change in stress is determined by the ratio and slope of the axes of the ellipse. With direct synchronous precession, the stresses with a doubled frequency degenerate.
With reverse precession, we have another picture. The main part of the motion with reverse precession has a doubled frequency of stresses variation with respect to the rotation frequency. And an additional movement, it can be shown that it comes with direct precession, gives a constant component of the stresses. Thus, under forced oscillations of the shafting, the stresses are either constant or change with a double frequency. A stresses from its own weight and shifts of shaft supports change with a frequency equal to the rotation speed. These conclusions are important for assessing the vibrational reliability and service life of the shafting and half-coupler bolts in the process of stress monitoring [5,6].
In any textbook on the dynamics of rotors [1], it is indicated that in the case of a direct synchronous precession of the rotor, it rotates curved, and the stresses do not depend on time, but depend on the size of the deflection. In real life, direct synchronous precession is rare.
As already shown in [2], a shaft or even a single rotor can have several sections of forward and reverse precession, and on the boundaries between these sections the elliptical trajectories degenerate into segments, and the oscillations of the cross section of the rotor have the same phase for the vertical and horizontal directions. If the phase of horizontal motion is greater than the phase of vertical motion, then we have a direct precession. If the phase of vertical motion is greater, then we have a reverse precession.
Thus, the appearance of zones of direct and reverse precessions is determined at each frequency of rotation by the forms of forced oscillations in each plane and their kinematic addition [3]. As a result, if the section of the shaft runs with a straight elliptical precession, then this motion can be considered as the sum of two: motion with a direct synchronous precession at which the stresses are constant in time and the motion with deviations twice in one turnover in the direction of the major axis.
The frequency of the change in the stresses for such deviations is equal to twice the rotational frequency. The phase of the change in stress is determined by the ratio and slope of the axes of the ellipse. With direct synchronous precession, the stresses with a doubled frequency degenerate.
With reverse precession, we have another picture. The main part of the motion with reverse precession has a doubled frequency of stresses variation with respect to the rotation frequency. And an additional movement, it can be shown that it comes with direct precession, gives a constant component of the stresses. Thus, under forced oscillations of the shafting, the stresses are either constant or change with a double frequency. A stresses from its own weight and shifts of shaft supports change with a frequency equal to the rotation speed. These conclusions are important for assessing the vibrational reliability and service life of the shafting and half-coupler bolts in the process of stress monitoring [5,6].
