Practical Solutions Of Machinery And Maintenance Vibration Problems - Understanding Resonance

For practical purposes, the terms "natural frequency," "resonance" and "critical speed" are synonymous. A part passing though its "critical" or "critical speed" may also be said to be "resonant" or "resonating." The vibrations of a precisely balanced part can be magnified by the structure in which it is assembled. Anyone who has driven an automobile knows that it will vibrate more at a certain speed than at others. According to the formula for centrifugal force, vibration should increase steadily with a rise in rpm. What happens instead is that the vibration not only in- creases with r m. but suddenly rises at a much higher rate through the critical speed, and then apparently smooths out as the rpm passes beyond it. To visualize what happens, consider a simple flat spring with a weight mounted at one end. When the spring is deflected by pulling down on the weight and then letting it go, the spring will oscillate, and the spring-and-weight system will vibrate at its natural frequency. If the timing or direction bf the impulses imparted to the spring did not coincide with its natural frequency, the result would be an irregular vibration that would not build up. If, on the other hand, the timing and direction of the impulses did coincide with the spring's natural frequency, the result would be a larger and larger amplitude. If the impulses were continued indefinitely, the amplitude of the spring's vibrations would go on rising [while its frequency stayed the same] until the spring broke or the amplitude of the vibrations reached an equilibrium [because frictional or other forces would tend to damp it]. Resonance magnifies the amplitude of vibrations in a relatively undamped system between 100 to 200 times over that of nonresonant vibrations. Frictional or viscous damping often reduces the magnification [from 10 to 20 times], but even with this reduction the amplitude would still be large enough to cause excessive wear, and sometimes even fractures. For example, a blower might show only 0.001 in. of vibration on the manufacturer's test stand. Installed, the blower could pass into its critical speed [the speed at which the frequency of the vibrations caused by the rotor coincides with the supporting structure's natural frequency], and the 0.001 in. of vibration could be resonated to 0.010 in., or as much as 0.020 in. The cure for such a condition would not be to lower the vibration of the blower by further balancing or better alignment but to separate the two frequencies by at least 20 to 30%.