## Orders v Time – Comparing Overall Levels

By combining a speed signal with a data signal and using the Short Time FFT algorithm (Hopping FFT), it is possible to extract order data directly as a function of time (Orders from Hopping FFT) rather than as a function of speed (Waterfall). This is very useful when analyzing a complete operational cycle which includes run ups, rundowns and periods at operational speeds.

OVERALL LEVEL, DYNAMIC RMS & STANDARD DEVIATION

The overall level, the dynamic rms and the standard deviation are different commonly used names for the same quantity. They all imply that the mean or dc level of the time history has been ignored in the calculation. The overall level is typically used with acoustics and measures the dynamic part of the signal. In acoustics it is usually expressed in dB but with vibration then linear units are preferred. Dynamic Rms is a term used to indicate it only pertains to the vibration content. The standard deviation is a term used by statisticians to again signify using the fluctuating part of the signal.

As part of this process the Prosig DATS software calculates the overall signal level (rms) as a function of time. This is actually available in two forms: one as the overall level computed from frequency data; and secondly as the Dynamic Rms computed by the DATS FFTHOP module from each time slice. A third and independent method of evaluating the variation of the overall level with time is to use the trend module to compute the Standard Deviation.

Figure 1: Using Rectangular/Bartlett window

Figure 2: Using Hanning window

In the example in Figure 1 all three measures give the same results but this is not always the case as shown later.

The example the Hopping FFT sequence in Figure 1 used a Rectangular data window but in Figure 2 we see exactly the same data with the exception that the Hopping FFT sequence used a Hanning window.

Figure 3: Over plotted on original time history

The overall level now differs from the other two measures because it is calculated after the application of the data window. In this case the Hanning data window has emphasized the central section of each time slice, so that it is more “time centered”. This is illustrated in Figure 3 by showing the measures when over plotted on the original time history.

The use of the data window helps to localise the phenomenon.

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#### Dr Colin Mercer

Chief Signal Processing Analyst at Prosig
Dr Colin Mercer was formerly at the Institute of Sound and Vibration Research (ISVR), University of Southampton where he founded the Data Analysis Centre. He then went on to found Prosig in 1977. Colin retired as Chief Signal Processing Analyst at Prosig in December 2016. He is a Chartered Engineer and a Fellow of the British Computer Society.

## 6 thoughts on “Orders v Time – Comparing Overall Levels”

1. Dr ShiPing Yao

Dear Colin,

If I process the displacement time domain data to get velocity and acceleration, what points will I need to pay attention? It seemed I could not get reasonable velocity/acceleration signals by differentiate the time domain signal of displacement by using DATS software from Prosig. Please advise. Thanks.

S. Yao

2. Colin Post author

Hi
There is not usually a problem with differentiating signals in the time domain. What I am often asked about is integration when it is vital to remove any dc offset (eg reduce to zero mean first or use a high pass filter or both!)

In the frequency domain if your displacement signal had a spectrum X(w) then the corresponding velocity spectrum is given by i*w*X(w) where w = 2*PI*f. That is differentiating is like a high pass filter with a frequency response iw. As a result if you have a lot of high frequency noise in your displacement signal then this will dominate the calculated velocity.

I would suggest low pass filtering your displacement signal, but look at the spectrum first. For example suppose you are interested up to 100Hz and have some noise at 1000Hz then this noise will be “magnified” ten times more than the region of interest. Another thing to think about is the sample rate as sometimes this is too high for the region you are really concerned about! No matter what differentiation formula is used it will involve dividing by the time between samples. It we have a very small value due to a high sample rate then that may introduce more error; this is another manifestation of amplifying to higher frequent noise. So sometimes it pays to decimate the signal (doing it properly with the necessary filtering step of course).

3. Dr Colin Mercer

What is an order? This is a fundamental point I did not include! An order is that frequency directly proportional to the rotational speed. So if we have a rotation speed of R rpm then first order is (R/60)Hz, second order is (2R/60)Hz and so on. Suppose we have a single cylinder 4 stroke engine then there is a firing pulse every two revolutions so we would expect excitation to happen every half order. If the engine had four cylinders then we would get two firing pulses every revolution So we expect excitation at every second order, that is at orders 2, 4, 6 and so on.

Colin Mercer

4. Yogeshwar

Hello Colin,

We are analyzing 6 cylinder diesel engine for NVH. We wre getting different orders of vibration. Why 6th order is more critical in this engine??

1. Chris Mason

Hello Yogeshwar

Dr Mercer explains this in his comment above. The main ‘event’ in a petrol or diesel engine is the firing of the cylinders. This is what causes the majority of the noise and vibration. For a 4-stroke 4-cylinder engine there are two firings per revolution. So this means 2nd order will usually dominate, but there will also be significant harmonics at integer multiples of the 2nd order. So the dominant orders for a 4-cylinder engine are 2, 4, 6, 8 etc. Similarly, for a 6-cylinder engine there are 3 firing ‘events’ per revolution so 3rd order will be the primary one and there will be harmonics of 6, 9, 12 etc.

Sometimes, in the case of 4-cylinder engines, 4th or 6th order may dominate over certain rpm ranges. Similarly, in the 6-cylinder case, 6th order may be most significant at certain speeds.

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