# time interval selection for RMS of vibration

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!

• Sampling frequency should be at least 2* frequency you are interested in because of harmonics... – Solar Mike Jan 22 '19 at 7:16

• 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:

• $$f_{samp} = 2250 Hz$$ -> $$f_{max} = 1225 Hz$$
• $$T_{m} = 1.2 s$$ -> $$f_{min} = \Delta f = 0.83 Hz$$
• Does taking fsamp to be 5 instead of 2 introduce unnecessary noise into the signal? – zae Apr 11 '19 at 1:49
• You will get higher frequencies in your signal as well, when sampling with a factor of 5. They will be harmonics and/or noise. You could also add a Lowpass Filter with a cutoff around the factor 2. – gmc Apr 11 '19 at 7:30