Self excited vibration is very common in nature and life. For example, the tree tops are whistling in the wind, the viola is playing melodious serenades, the tap water pipe is suddenly surging, and the old wall clock on the wall is continuously ticking in the dead of night. These are all kinds of self-excited vibrations. When using, milling, planing, grinding and other machine tools for processing, if they are not well done, the self-excited vibration of the tool will bite wavy lines on the surface of the workpiece, seriously affecting the smoothness of processing and the life of the machine tool. Therefore, self-excited vibration is a quite common phenomenon. [2]
Self excited vibration is maintained by the excitation generated by the system itself nonlinear vibration 。 In addition to vibration elements, self-excited vibration system also has non oscillatory energy, regulation and feedback links. Therefore, it can also produce a stable periodic vibration without external excitation. The alternating force to maintain self-excited vibration is generated by the motion itself and controlled by the feedback and adjustment links. Once the motion itself stops, its alternating force disappears and the self-excited vibration stops. Self excited vibration is another kind of vibration in engineering besides free vibration and forced vibration. Self excited vibration relies on energy sources outside the system to supplement energy, but the difference from forced vibration is that the energy source of self excited vibration is constant. [3]
Self-excited vibration and Forced vibration It is also the most common vibration in nature and engineering, but its generation mechanism is much more complex and often associated with nonlinear systems. Common self-excited vibration includes: reciprocating motion of piston of internal combustion engine or steam engine; Machine tool vibration caused by cutting workpiece; The vibration of the pendulum wheel in the mechanical clock; Flutter of aircraft wings caused by airflow; The vibration of the strings when playing the violin and the vibration of the reeds when playing the accordion. [4]
The occurrence of self-excited vibration requires two conditions: first, the instability of the system near the equilibrium point; Second, the external disturbance that forces the working point of the system to deviate slightly from the equilibrium point. It can be seen that self-excited vibration does not need external excitation. In fact, it should be said that self-excited vibration is a kind of "disturbed vibration", because it always originates from an accidental external disturbance. Just because the size of this disturbance is independent of the form, and the real world is always full of all kinds of disturbances, the second condition above is always met. In this way, as long as the first condition is formed, that is, as long as the instability of the system itself near the equilibrium point is formed, there is no need to wait at all, and an accidental disturbance will break through immediately, causing a sharp rise in vibration. Because of this, the focus and method of studying self-excited vibration is different from that of studying free vibration and forced vibration: there is no need to study the size and form of the accidental disturbance that causes vibration, and there is no need to explore the relationship between this disturbance and the vibration it excites. Instead, it is necessary to focus on the mechanism and law that forms the instability of the system itself. [5]
① Self excited vibration is an undamped vibration, and the vibration process itself can cause some force Periodic change Through this force change, the vibration system can periodically obtain energy supplement from the energy without alternating characteristics, so as to maintain vibration. The external vibration source may play a role in the initial excitation of vibration, but it is not the internal cause of vibration. ② The frequency of self-excited vibration is equal to or close to the natural frequency of the vibration system, that is, it is determined by the parameters of the vibration system itself.
③ The generation and amplitude of self-excited vibration depend on the comparison of energy obtained and consumed by the vibration system in each vibration cycle. If the energy obtained is greater than the energy consumed, the amplitude will continue to change until the two energies are equal; If the energy obtained is less than the energy consumed, self-excited vibration will not occur. [6]
Based on practical experience, the methods to avoid self-excited vibration can be summarized as follows:
(1) External resistance is introduced to increase the unstable speed, for example Squeeze film damper ； (2) Increase the critical speed of the rotor system above the maximum operating speed, such as improving the rotor rigidity or Support stiffness ； (3) Eliminate specific causes of instability.
Next, we will summarize the elimination methods of various self-excited vibration.
For the instability caused by friction between parts on the rotor. First, check whether there are axial friction marks between some parts of the rotor or coupling. If there is friction trace, the way to eliminate this instability is to eliminate and reduce friction. In case of loose sleeve tooth connection, lubricating oil can be introduced. In addition, the rotor structure or support rigidity can be changed, so that when the subsynchronous precession occurs, there is no local axial sliding of the parts, so there is no friction.
Self excited vibration instability caused by sliding bearing, labyrinth or annular sealing device, with precession ratio of 0.15~0.48. If it is sliding bearing , available tilting bearing 。 If it is a sealing device, an imported anti rotation piece can be added on the stationary part, or the honeycomb sealing structure can be used instead, or the inner circular surface of the stationary part of the sealing device can be rough, or the brush like outer ring can be used. The precession ratio of self-excited vibration caused by liquid accumulation in the rotor is 0.5~1.0, and more often 0.7~0.9. Small holes can be opened at appropriate parts of the rotor to discharge liquid to avoid such self-excited vibration.
Self excited vibration and Centrifugal impeller For self-excited vibration caused by, propeller, etc., the precession ratio depends on the size of fluid force, and is independent of speed. Try to eliminate or reduce the eccentric rotation of the impeller as much as possible, which can be achieved by strengthening the stiffness of the impeller or setting a support with greater stiffness near the impeller. The self-excited vibration instability caused by dry friction is different from the instability caused by the above reasons in the form of swing or reverse precession. Circumferential friction traces can be detected when such instability occurs. This instability can be eliminated by eliminating the possibility of dry friction according to the specific situation. [3]
