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solid mechanics Solid mechanics, also known as mechanics of solids, is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and ...
, in the field of rotordynamics, the critical speed is the theoretical
angular velocity In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an object ...
that excites the
natural frequency Natural frequency, also known as eigenfrequency, is the frequency at which a system tends to oscillate in the absence of any driving force. The motion pattern of a system oscillating at its natural frequency is called the normal mode (if all pa ...
of a rotating object, such as a shaft, propeller, leadscrew, or gear. As the speed of rotation approaches the object's natural frequency, the object begins to resonate, which dramatically increases system
vibration Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin ''vibrationem'' ("shaking, brandishing"). The oscillations may be periodic, such as the motion of a pendulum—or random, su ...
. The resulting resonance occurs regardless of orientation. When the rotational speed is equal to the numerical value of the natural vibration, then that speed is referred to as critical speed.


Critical speed of shafts

All rotating shafts, even in the absence of external load, will deflect during rotation. The unbalanced mass of the rotating object causes deflection that will create resonant vibration at certain speeds, known as the critical speeds. The magnitude of deflection depends upon the following: *Stiffness of the shaft and its support *Total mass of shaft and attached parts *Unbalance of the mass with respect to the axis of rotation *The amount of damping in the system In general, it is necessary to calculate the critical speed of a rotating shaft, such as a fan shaft, in order to avoid issues with noise and vibration.


Critical speed equation

Like vibrating strings and other elastic structures, shafts and beams can vibrate in different mode shapes, with corresponding natural frequencies. The first vibrational mode corresponds to the lowest natural frequency. Higher modes of vibration correspond to higher natural frequencies. Often when considering rotating shafts, only the first natural frequency is needed. There are two main methods used to calculate critical speed—the
Rayleigh–Ritz method The Rayleigh–Ritz method is a direct numerical method of approximating eigenvalues, originated in the context of solving physical boundary value problems and named after Lord Rayleigh and Walther Ritz. The name Rayleigh–Ritz is being debate ...
and
Dunkerley's method Dunkerley's method is used in mechanical engineering to determine the critical speed of a shaft-rotor system. Other methods include the Rayleigh–Ritz method. Whirling of a shaft No shaft can ever be perfectly straight or perfectly balance ...
. Both calculate an approximation of the first natural frequency of vibration, which is assumed to be nearly equal to the critical speed of rotation. The Rayleigh–Ritz method is discussed here. For a shaft that is divided into ''n'' segments, the first natural frequency for a given beam, in ''rad/s'', can be approximated as: :\omega_ \approx \sqrt where ''g'' is the acceleration of gravity, and the w_i are the weights of each segment, and the y_i are the static deflections (under gravitational loading only) of the center of each segment. Generally speaking, if ''n'' is 2 or higher, this method tends to slightly overestimate the first natural frequency, with the estimate becoming better the higher ''n'' is. If ''n'' is only 1, this method tends to underestimate the first natural frequency, but the equation simplifies to: :\omega_ \approx \sqrt where y_ is the max static deflection of the shaft. These speeds are in ''1''/''s'', but can be converted to ''RPM'' by multiplying by \frac . Static deflections for several types of uniform-cross-section beams can be found
here Here is an adverb that means "in, on, or at this place". It may also refer to: Software * Here Technologies, a mapping company * Here WeGo (formerly Here Maps), a mobile app and map website by Here Television * Here TV (formerly "here!"), a ...
. If a beam has multiple types of loading, deflections can be found for each, and then summed. If the shaft diameter changes along its length, deflection calculations become much more difficult. The static deflection expresses the relationship between rigidity of the shaft and inertial forces; it includes all the loads applied to the shaft when placed horizontally.Technical Bulletin

, ''Krueger''. Retrieved on 18 June 2015.
However, the relationship is valid no matter what the orientation of the shaft is. Critical speed depends upon the magnitude and location of the shaft unbalance, the length of the shaft, its diameter, and the kind of bearing support. Many practical applications suggest as good practice that the maximum operating speed should not exceed 75% of the critical speed; however, there are cases that require speeds above the critical speed to work correctly. In such cases, it is important to accelerate the shaft through the first natural frequency quickly so that large deflections don't develop.


See also

*
Damping ratio Damping is an influence within or upon an oscillator, oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. E ...
* Oscillate *
Natural frequency Natural frequency, also known as eigenfrequency, is the frequency at which a system tends to oscillate in the absence of any driving force. The motion pattern of a system oscillating at its natural frequency is called the normal mode (if all pa ...
*
Resonance Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscil ...
* Campbell diagram *
Vibration Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin ''vibrationem'' ("shaking, brandishing"). The oscillations may be periodic, such as the motion of a pendulum—or random, su ...


References

{{reflist Mechanical engineering hu:Kritikus fordulatszám it:Velocità critica flessionale