In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating object, such as a shaft, propeller, leadscrew, or gear.
The magnitude of deflection depends upon the following: 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.
The first vibrational mode corresponds to the lowest natural frequency.
Both calculate an approximation of the first natural frequency of vibration, which is assumed to be nearly equal to the critical speed of rotation.
For a shaft that is divided into n segments, the first natural frequency for a given beam, in rad/s, can be approximated as: where g is the acceleration of gravity, and the
If a beam has multiple types of loading, deflections can be found for each, and then summed.
A system's critical speeds depend upon the magnitude, location, and relative phase of shaft unbalance, the shaft's geometry and mechanical properties, and the stiffness and mass properties of the support structure.
In such cases, it is important to accelerate the shaft through the first natural frequency quickly so that large deflections don't develop.