Practical Solutions to Machinery and Maintenance Vibration Problems
Chapter 2, Mechanical Resonance
Section 7, Resonant Vibration at Multiples of RPM
A high resonant frequency is sometimes reached even when operating rpm is low, due to the impulses created by a rotor's teeth or vanes. For example, a machine tool spindle with a resonant frequency of 4,900 cycles/min and turning at only 600 rpm can vibrate excessively due to its rotor's eight cutting teeth, creating impulses of 4,800 cycles/min, bringing it close to resonance of a relatively rigid part such as the machine tool's frame.
Vanepass vibration in a pump (rpm x number of vanes) or bladepass vibration in a blower (rpm x number of blades) is usually of such low amplitude that it causes no trouble and therefore is not noticed. However, when the rpm of the rotor, multiplied by the number of vanes, approaches a resonant frequency, the vibration rises well beyond an acceptable limit. Resonances can be excited in the pipe, base, valve, etc.
However, a pump's excessive amplitude at vanepass frequency may not actually be caused by resonance. Instead, it could be caused by a rate of flow that is too low. Excessive vanepass vibration amplitude often occurs when the flow rate is lower than approximately 40 percent of the best efficiency flow. This percentage can vary. For higher speeds or high pressure pumps, vanepass vibration can occur at lower percentages of reduced flow. (See section, "Flow-Related Problems in a Centrifugal Pump.")
Experience indicates that when vibration at rpm x number of blades or teeth becomes excessive, there is a strong possibility that a resonant condition has magnified the vibration. In such instances, tune the vibration instrument to the vibration frequency, and then probe various parts to determine which one is resonant. As such vibrations tend to have a relatively high frequency, they are most apt to resonate at much higher frequencies than their own first resonance frequency. As a result, the mode shape would include several nodes and antinodes. (See section "Plotting the Mode Shape From Point-to-Point Amplitude Readings [To Determine Whether or Not a Part is Resonant]).")
For rotary pumps, vanepass frequency vibration resonances are often found in the bending or torsional resonance of the pump shaft itself, often causing a "fatigue break" at one of the nodes. The various spans of pipe, elbows and even the valve parts are also subject to resonance. Possible cures are to change rpm (usually not practical), change the number of vanes, or to find the resonant part and detune it. Most often the easiest solution is to work with the pump manufacturer to obtain an impeller with a different number of vanes. The replacement impeller should have a vanepass frequency at least 20 to 25 percent away from the resonant frequency.
Similar solutions are used for gear teeth vibration. Not only can the shaft be resonant in bending or torsion, but the gearplate or a section of the gearbox housing can be a fault. Gearmesh frequency vibration can also be caused by an excessively large shaft centerline vibration orbit at lower frequencies, such as that caused by unbalance or shaft/coupling misalignment (see section "Gear Vibration [Of Already Built Machinery].")
A relatively common situation is what happened in a wood cooling tower having four, 20 foot diameter fans, each with three blades. The fans operated at 300 rpm. Regardless of which fan was operating, the tower vibrated excessively. The vibration frequency was measured as 3 x rpm. By using a stroboscope, it was discovered that the tip of each fan blade would rise about three inches when it passed over a horizontal driveshaft located about one foot below. Every time a blade passed over the shaft, it lost a part of its load. This action imparted a vibration impulse to the cooling tower equal to 3 x rpm of the rotor. Without a resonance to this frequency, the amplitude of the impulses would be acceptable, but as the resonance frequency of the tower was approximately 900 cycles/min, these impulses were greatly magnified.
Tightening all of the tower's joints and installing additional wood braces raised the resonance frequency of the tower above 900 cycles/min, thus eliminating the excessive vibration. However, it became necessary to retighten the joints once a year. Other possible solutions would be to either change the rpm or the number of blades.
Another case involved a roof exhaust fan that had relatively flexible blades. Although there were several hundred such fans in operation throughout the country, this was the only fan that had ever vibrated excessively. It was finally determined that the vibration frequency of number of blades x rpm corresponded to the times/min that the blades passed over a tie rod, and that frequency corresponded to the natural frequency of a supporting "I" beam. Changing the number and spacing of the tie rods was the easiest way to change the source frequency so that it no longer would resonate the "I" beam.
Increasing or decreasing the rotor's rpm will have a large detuning effect by adjusting the source frequency away from the resonance frequency. For every rpm change, there is even greater change in the frequency of number of blades or vanes x rpm. (The same applies for resonance at gearmesh frequency.) However, as it is usually not easy to change rotor speed, the resonant part may still have to be detuned or the vibration reduced at its source.
The preceding situations describe resonances to frequencies at exact multiples of rpm. These frequencies are synchronous with rpm. There are also several source frequencies that are not synchronous with rpm, such as those that originate from electrical hum, bearing defect frequencies and cavitation. Any of these non-synchronous frequencies could also be resonated when they are close to or matching a part's resonance frequency.
This textbook contains only part of the information in our Practical Vibration Analysis seminar.