Practical Solutions to Machinery and Maintenance Vibration Problems
Chapter 2, Mechanical Resonance
Section 1 Understanding Resonance
For practical purposes, the terms "natural frequency," "resonance" and "critical speed," though not actually synonymous, will be used to mentally describe the same concept. A part passing through its "critical" or "critical speed" may also be said to be "resonant" or "resonating." However, the expression "critical speed" or "critical" is more accurately used when it is the rotor itself that is resonant. When a non-rotating part, such as a span of pipe, beam or column is resonant, it technically should not be referred to as a "critical speed" or "critical." More technically-oriented vibration analysts and instructors keep this in mind, but as vibration knowledge has become more and more practical and practiced by less technical people, those in industry becomes less careful in using the technically correct expressions. Therefore, it is very common today to mix the terms and use the words "critical speed" to mean "resonant frequency" or "resonance frequency," even when referring to a non-rotating part. The mixing of terminology is now so common that the expressions used in this book will do the same.
There could be many sources for vibration. If any source creates a vibration frequency that is equal to or nearly equal to a part's resonant frequency, that part will resonate. For example, the vibrations of even a fairly well-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, centrifugal force varies as the square of rpm. The vibration amplitude not only increases with rpm, but it suddenly rises at a much higher rate when passing through the responding part's resonance or critical speed and then smooths out as the rpm passes beyond. This results from vibration at a frequency from any source, such as misalignment, unbalance, gearmesh, electrical hum, etc., that matches the natural frequency or resonant frequency of either a part or total spring system.
To visualize what happens, consider a simple flat spring with a weight mounted at one end (similar to a diving board). When the spring is deflected by pulling down on the weight and then letting it go, the spring oscillates and the spring-and-weight system vibrates at its natural frequency.
If only a single impulse is given, the amplitude of the vibration usually progressively decreases with time, due to friction and other energy losses. If for continuous periodic impulses, the timing or direction of the impulses did not coincide with its natural frequency, the result would be an out-of-tune vibration that does 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 tuned vibration and a progressively larger and larger amplitude with each added cycle. The amplitude finally reaches a maximum (due to friction or viscous damping forces).
Resonance magnifies the amplitude of vibrations in relatively undampened systems anywhere from 5 to 10 and sometimes 20 times over that of non-resonant vibrations. Damping often reduces the magnification, but even with this reduction, the amplitude is still large enough to cause excessive wear and sometimes even fracture. Refer to the chapter on "Plotting The Mode Shape From Point-to-Point Amplitude Readings (To Determine Whether Or Not A Part Is Resonant). Typically, systems have either more damping or are only partially resonant, with the resulting magnification for example, being only 2 to 5 times what it would have been if completely non-resonant.
This textbook contains only part of the information in our Practical Vibration Analysis seminar.