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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.
A Flywheel energy storage system works at 60 000 rpm – 500 000 rpm (1 kHz – 8.3 kHz) range using a passively magnetic levitated flywheel in a vacuum. [8] The choice of the flywheel material is not the most dense, but the one that pulverises the most safely, at surface speeds about 7 times the speed of sound.
Peak torque is reached at higher rpm and is spread over a wider range of rpm. The specifications of these are known factors and can be designed to. Torque is a function of the length of the stroke, the shorter the stroke, the less available torque at lower rpm, but the piston velocity can be taken to much greater speeds, meaning higher engine rpm.
The exact RPM is not always needed, a close approximation will work. For instance, a machinist may want to take the value of π {\displaystyle {\pi }} to be 3 if performing calculations by hand. R P M = C u t t i n g S p e e d × 12 π × D i a m e t e r {\displaystyle RPM={CuttingSpeed\times 12 \over \pi \times Diameter}}
Dunkerley's method [1] [2] 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
The angle domain equations above show that the motion of the piston (connected to rod and crank) is not simple harmonic motion, but is modified by the motion of the rod as it swings with the rotation of the crank.
Analysis shows that there are well-damped critical speed at lower speed range. Another critical speed at mode 4 is observed at 7810 rpm (130 Hz) in dangerous vicinity of nominal shaft speed, but it has 30% damping - enough to safely ignore it. Analytically computed values of eigenfrequencies as a function of the shaft's rotation speed.
The critical speed of a rotating machine occurs when the rotational speed matches its natural frequency. The lowest speed at which the natural frequency is first encountered is called the first critical speed, but as the speed increases, additional critical speeds are seen which are the multiples of the natural frequency.