Gene Vogel
EASA Pump & Vibration Specialist
As we communicate internationally, language barriers persist. In the technical fields, the metric-imperial units clash is slowly diminishing. (It’s been said the U.S. is going to the metric system an inch at a time.) In the vibration analysis field, metric and imperial units for vibration amplitude both remain prolific. Many vibration analysts are “bilingual” in that respect and are comfortable using either system. But for more casual users who may only encounter vibration data in regard to meeting specs, unfamiliar vibration amplitude units can be a challenge.
Complicating the situation is the fact that even within one of the systems (metric or imperial), conversion between different vibration amplitude parameters is often not understood. Common vibration amplitude parameters are displacement, velocity and acceleration, and the conversion between them requires applying a factor for the frequency of the vibration. Frequency itself has three different units: cycles per minute (CPM), cycles per second (Hz) and multiples of rotating speed (Orders). Throw in the issue of Peak to Peak (Pk-Pk), Peak (pk) and root-mean-squared (rms), and applying vibration amplitude specifications can be challenging even before one encounters a metric-imperial units situation. (For an easy solution skip to the end of this article.)
The key to the metric-imperial conversion is that the relationship is defined exactly by “1 inch = 25.4 mm.” That is not an approximation; it is exact. So, the proper application of the 25.4 factor will always work. The question usually becomes, “Do I multiply or divide?” A memory cue is that for equivalent values, there are always more mm’s than there are inches. So, when going to mm’s, multiply, and when going to inches, divide.
Example:
0.15 in/sec pk converted to metric is 0.15 x 25.4 = 3.81 mm/sec pk
3 mm/sec pk converted to imperial is 3 ÷ 25.4 = 0.12 in/sec pk
The values 0.15 in/sec pk and 0.12 in/sec pk are both referenced in the NEMA MG1 standard on which clause 4.5.6 Vibration Tests in the EASA AR100 standard is based, so those are good equivalent values to remember.
Similarly, the conversion from pk to rms is governed by an exact factor. That factor is the irrational value √2, which can be approximated as 1.414. (Some may be familiar with the reciprocal value 1/√2 approximated as 0.707.) The memory cue here is that pk values are always greater than equivalent rms values. So, when converting to pk, the result must be greater; when converting to rms, the result must be less. Of course, pk to pk-pk is simply a factor of 2.
Those two rules are all that’s needed to convert units within a single vibration amplitude parameter (displacement, velocity, acceleration). However, when converting between any of those three parameters, a frequency factor must be applied. The frequency factor is based on the actual frequency of the vibration in units of Hz. If the frequency is known in CPM, that CPM value must be divided by 60 (60 seconds in a minute). Frequency in Orders is divided by the reference RPMx60. If the frequency of the vibration is not known, the conversion cannot be made. It is not possible to convert an overall vibration value from one parameter to another. The conversions are thus:
− velocity = displacement x Hz x k
− acceleration = velocity x Hz x k
− Therefore: acceleration = displacement x Hz x Hz x k
Where k is a factor for converting between mils, inches, micrometers, mm and g’s as appropriate. Determining k for conversion to or from acceleration in g’s requires the proper application of the gravity constant 9.81 mm/sec2.
Inverse conversions divide by Hz rather than multiply by Hz, and of course, there are many permutations of k depending on the metric-imperial units.
The proper application of the metric-imperial factor (25.4), the pk to rms factor of √2 and pk to pk-pk factor 2, the proper application of the frequency factor Hz and the factor k will yield the desired converted value of any commonly used vibration unit. There are a few uncommonly used vibration amplitude units such as acceleration in m/sec2 rms and logarithmic units VdB and AdB, but these are very rare.
Fortunately, EASA provides a solution for accurately converting vibration amplitude units. Log into the EASA website (easa.com), and navigate to Resources > Online Calculators > Vibration Unit Converter (go.easa.com/vuc). Enter the amplitude value and select the units from the drop down menus for the Input and Output. Only if converting between vibration amplitude parameters (displacement, velocity, acceleration), must the frequency of the vibration be entered. The accurate converted value will be displayed in the Output field.
AVAILABLE IN SPANISH
EASA Technical Manual
More information on this topic can be found in EASA's Technical Manual- Section 10: Mechanical
- Section 11: Formulas & Conversion Factors
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