time interval selection for RMS of vibration

Question

What is the general practice for selecting time interval for RMS calculation for vibration data (mm/s)

Should it be linked to the the frequency of the motor or the sampling rate?

Thanks!

Answer 1

• Your sampling frequency $f_{samp}$ should be at least 2 - Times higher the highest expected relevant frequency $f_{max}$ because of the Nyquist - Shannon Theorem. However you minimize error by using a higher sampling frequency (Rule of thumb $f_{samp} = 5 f_{max}$)
• If you want to get the RMS of smaller frequency bands (for example by performing a FFT), your measuring time $t_M$ should be long enough to get a high enough frequency resolution $\Delta f $ (difference between two interesting frequency bands, formula see next point).
• Also if you are not aiming for a fft, you should measure long enough to measure at least one full cycle of the expected minimal frequency of interest $f_{min}$ ($f_{min} = \Delta f = 1/t_M$)
• Longer measurements provide kind of a averaging.

Example:

• You want to measure a fan with 9 blades rotating with 10 Hz.
• In one measurement, you want to have at least 12 revolutions.
• You definitly want to measure the 90 Hz blade pass frequency.

• You also want to measure 5 harmonics -> 450 Hz

• To make sure you get the 450 Hz you need to sample with at least 900 Hz, $f_{samp} = 2250 Hz$ would be better though.

• To measure one cycle you have to measure at least 0.1 s. If you want to measure over 12 revolutions you need to measure at least $t_M = 1.2 s$

--> You end up with:

• $f_{samp} = 2250 Hz$ -> $f_{max} = 1225 Hz$
• $T_{m} = 1.2 s$ -> $f_{min} = \Delta f = 0.83 Hz$