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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.
Rotational frequency, also known as rotational speed or rate of rotation (symbols ν, lowercase Greek nu, and also n), is the frequency of rotation of an object around an axis. Its SI unit is the reciprocal seconds (s −1 ); other common units of measurement include the hertz (Hz), cycles per second (cps), and revolutions per minute (rpm).
Revolutions per minute (abbreviated rpm, RPM, rev/min, r/min, or r⋅min −1) is a unit of rotational speed (or rotational frequency) for rotating machines. One revolution per minute is equivalent to 1 / 60 hertz .
Cutting speed may be defined as the rate at the workpiece surface, irrespective of the machining operation used. A cutting speed for mild steel of 100 ft/min is the same whether it is the speed of the cutter passing over the workpiece, such as in a turning operation, or the speed of the cutter moving past a workpiece, such as in a milling operation.
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:
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In physics, angular velocity (symbol ω or , the lowercase Greek letter omega), also known as the angular frequency vector, [1] is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction.