# Order analysis, need help

Hi fellow electronics enthusiasts. I'm currently working on vibration detection machine used to detect unbalance from a rotating shaft, rotating from 300-2500 Hz. I have both the tacho signal ( 1 PPR ) and the vibration from transducer.

Now I'm really confused. After the transducer there is sweep filter that uses the tacho signal as center frequency so at 1 kHz the output sine wave is 1 kHz.

How do i extract useful data from this signal ?

I've read for the past week on the internet about order analysis and different methods but im so confused about how to implement it, how fast should the ADC sample rate be for the order tracking?

Should I do Fourier transform over the sine wave?

How to transfer the signal to angular domain?

Everything is just confusing. A little help on order analysis, or how to extract information from rotating shaft would be very appreciated!

• You need to determine the amplitude of the sinewave, and also its phase relative to the tachometer reference signal. The easiest way to do this is to sample it at 4x the tachometer frequency and do some simple math on the numbers. I have no idea what you mean by "order analysis" or "order tracking". – Dave Tweed Feb 22 '16 at 13:40
• Hello @DaveTweed thank you for your reseponse. Order analysis is just like frequency analysis but done in the angular domain. Instead of using time, the revolotuions are used as reference. But Im still confused whether or not I should perform fourier analysis over the simple sine wave so I can get amplitude for that particular frequency en.wikipedia.org/wiki/Order_tracking_(signal_processing) Heres a reference, maybe you will understand it better than I did. – Dan Kr Feb 22 '16 at 16:47
• Is it possible to subtract the filtered signal from your original signal and get the imbalance signal remaining? – Andy aka Feb 22 '16 at 18:24
• I don't have time to write a full answer right now. In my previous comment, I was alluding to the fact that if you sample the waveform synchronously with the tachometer signal, deriving amplitude and phase information is relatively straightforward, at least for a simple sine wave. The Wikipedia article is talking about the math required when the sampling is asynchronous. It is also more general, capable of dealing with waveforms more complex than a sine wave. – Dave Tweed Feb 23 '16 at 12:32
• Thank you @DaveTweed . Do I need to make FFT over the samples i acquire ? And about the tacho signal, do i need to interpolate the values between each pulse so they equal the vibration values which are sampled 4x? Also what do you mean by simple math on the sine wave can you give me some papers or example I can research. Thank you in advance! – Dan Kr Feb 24 '16 at 12:45

We can identify the problem at hand better by some analysis. There is a difference between

• Vibration detection
• Vibration measurement

Measuring can solve the problem of detection. But mere detection cannot solve measurement! We can define these two approaches like this-

• Detection can be about a single anomaly of pulse or a set of frequencies, above the ideal (inherent) noise of a balanced shaft rotor.

• Measurement is about so many other things. RMS amplitude, THD- total harmonic distortion, mean, mode, std/variance, Median frequency. Or PSD- power spectral density of balanced shaft vs. unbalanced shaft.

Assuming you have either a dedicated electronics setup to measure these (Like an analog section, ADCs, pulse counters, timers and a micro controller) or a NI hardware with LabVIEW etc., the following approach may work.

(Not touching the angular domain mathematics here. Your 1PPR tacho may not give angular position)

In your test setup /script, split the measurement setup into these parts-

Up-ramp rotation speed from 18000rmp (300Hz pulse) to 150,000rmp (2500Hz pulse). With an unbalanced shaft, the relation between input RPM command and Tachometer will not be aligned. There will be non linearity, drift and jitters. One would first measure this relationship.

The main parameter is Jitter. This is the amount of deviation from the ideal position. You should determine the distribution of this jitter next. If this falls into random distribution, find what kind. (Gaussian etc.). Also determine if there is a drift. This will be difference of slope between ideal Input-RMP against Output Tachometer graph, and what is measured. Also examine if there is a non-linearity and if that is repeatable.

Repeat the same step with down-ramp from 150,000rpm(2500Hz) to 18,000rmp(300Hz).

Also during the ramp, acquire the noise signal from the vibration transducer. Ideally few tens multiple higher bandwidth than the max rpm.

These two together may give some insights into the non-linear model.

Once you know the RMS jitter value, you may compensate it for the "Time window" of the vibration transducer to do an FFT, or any other spectral measurements.