Gene Vogel
EASA Pump and Vibration Specialist
There are three fundamental parameters for machinery vibration data: amplitude, frequency and phase. When testing machine vibration, amplitude and frequency are the two primary measurements for acceptance testing and for diagnostics. Both of these parameters have several units in which they can be recorded.
Converting from one unit of measurement to another is not difficult if both amplitude and frequency data are available. In many cases, only amplitude measurements are available, without the needed frequency information, so conversion to other amplitude units is not possible.
Knowing when conversion is possible and how to a apply conversion formulas is important when assessing customer specifications and analyzing diagnostic data.
Various units of measurement are available for both vibration amplitude and frequency. The relationship between the different frequency units is straightforward and easily applied. Most vibration frequency data is in either cycles per minute (CPM) or in cycles per second (Hz).
To convert between the two, you simply multiply or divide by the factor of 60 seconds to a minute. Table 1 illustrates that relationship.
Orders frequency
An additional unit of measure for frequency is Orders. This references a rotating speed of a machine shaft or other fundamental frequency, so that information must be available. A pump with five impeller vanes may have vibration at 5 times rotating speed (5 x rpm). Vibration at twice line frequency (2 x lf) is common on most electric motors. These are examples of frequency in Orders.
While converting frequency units is a simple, intuitive procedure, involving a single step multiplication or division, converting amplitude units is more complex. Common amplitude units are Displacement, Velocity and Acceleration. But each of these could be either U.S. units or metric. And since these are dynamic and not static parameters, each could be peak (pk), peak-to-peak (pk-pk) or root mean square (rms), which are averaging schemes.
Further, the conversion between Displacement, Velocity and Acceleration requires a factor of the actual frequency of the vibration. As mentioned earlier, if the frequency of the vibration is not known, the conversion to other units is not possible. It should be noted that any such conversions will be for a single frequency and cannot be applied to overall vibration levels.
Understanding relationship
An explanation of the relationship between Displacement, Velocity and Acceleration is helpful in understanding why this is true. Using Displacement and Velocity as an example, the Displacement is how far a point on a machine travels as it vibrates back and forth. Velocity is how fast the point is moving as it vibrates.
Imagine that two points on a machine are vibrating the same distance, say 0.005” (5 mils), but at different frequencies, one at 2400 CPM and the other at 4800 CPM. The point vibrating at the higher frequency must move twice as fast to travel the same 0.005” distance twice while the lower frequency point only travels that distance once.
Thus, when converting from Displacement to Velocity, the Displacement value must be multiplied by a factor of the frequency. The relationship between Velocity and Acceleration is similar, and also requires multiplication by a factor of the frequency.
As mentioned previously, certain vibration units are commonly expressed as peak-to-peak (pk-pk), peak (pk) or root-mean-squared (rms) units. The most common use of these is displayed in Table 2. The difference between these averaging methods can be expressed as a simple proportional factor. To convert from pk to pk-pk, simple multiply by 2. To convert from pk to rms, divide by the square root of 2 (√2). For the reverse conversion, simply divide by the factor instead of multiplying. The conversion formulas in the table account for the applicable averaging method.
Conversion between U.S. and metric units is simply a matter of applying the proper proportion. One complication is that U.S. units are a mixture of Mils and inches – a Mil is a thousandth of an inch (0.001”). The conversion to metric units involves the proportion of millimeters (mm) to inches. There are 25.4 mm to an inch. In some cases it is more convenient to use the reciprocal value of 1/25.4 = 0.03937. When combined with the 1000 factor of inches to Mils, that value becomes 39.37. That value may be familiar since there are 39.37 inches to a meter.
For example, vibration from a v-belt is measured at 0.12 in/sec pk @ 1100 CPM. The frequency in CPM is converted to Hz by dividing by 60: 1100/60 = 18.33 Hz. To convert this velocity amplitude of 0.12 in/sec to metric displacement units of mm pk-pk: 0.12 x 8.0851 = 0.9702, then divide by the frequency in Hz: 0.9702/18.33 = 0.529 mm pk-pk.
Another example: A bearing fault frequency is measured at 6.77 mm/sec rms @ 189 Hz. The frequency units are already in Hz so no conversion is needed there. To convert the velocity amplitude of 6.77 mm/sec rms to acceleration units of g rms: 6.77 x 189 = 1279.53, then divide by the conversion factor: 1279.53/1560.3 = 0.820 g rms.
Use calculator or spreadsheet
The conversion values are presented here as simple factors to be multiplied or divided. The conversion can be accomplished with any simple calculator or with a spreadsheet. There are also a variety of online conversion utilities that can be accessed via the Internet. Some of vibration instrument vendors provide downloadable programs or slide rule type tools for converting units.
In any case, it is important to remember that when changing units, as from Displacement to Velocity, or Velocity to Acceleration, the frequency of the vibration must be known. Thus overall vibration amplitude measurements cannot be converted to different units.
The amplitude and frequency of a vibration are most often determined from a vibration spectrum. Almost any vibration instrument that will display a spectrum will allow the amplitude units to be set to any of those displayed in the table.
So another method for converting units is to simply display the spectrum with the desired amplitude units. For practice, try comparing the same spectrum displayed in two different units. Apply the formulas in the table provided and see if the values match the spectrum. Good Luck!
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