What is defined as the speed at which resonance occurs in rotational machinery?

The term that defines the speed at which resonance occurs in rotational machinery is critical speed. Critical speed is a specific rate of rotation where the natural frequency of a rotating system coincides with the frequency of external excitations. When the operational speed of the machinery approaches critical speed, vibrations can increase significantly, potentially leading to mechanical failure or damaging resonance effects.

Understanding critical speed is vital in vibration analysis and machinery design because it helps to ensure that operational speeds are maintained below this threshold or to design systems that avoid excitation at this frequency. In many applications, engineers design machinery to operate well below critical speeds or use damping techniques to mitigate the effects of resonance at or near critical speeds.

Other terms such as operating speed, linear speed, and setup speed do not specifically refer to the condition of resonance. Operating speed simply refers to the speed at which a machine is intended to function, while linear speed involves motion along a path rather than rotational dynamics. Setup speed is not a standard term in the context of resonance, and hence does not apply to the concept of critical speed in rotational machinery.