By Dr Colin Mercer, Technical Director, Prosig
Any vibration signal may be analyzed into amplitude and phase as a function of frequency. The phase represents fifty percent of the information so it is most important to measure phase for vibration monitoring. Most vibrations on a rotating machine are related to the rotational speed so it is clearly important to have a measure of the speed, either directly or as a once per revolution tacho pulse. A question some time arises as to whether a once per revolution tacho reference signal is needed to measure phase. Is it possible to get phase if we only have a speed signal? This note gives some insight into those questions. Actually the question that should be asked is - “Can we measure a meaningful phase, for use in vibration monitoring, if we only have a speed signal as well as the vibration signals?” read »»»
By Dr Colin Mercer, Technical Director, Prosig
Standards DIN 4150-2:1999-06 and DIN 45669-1:1995-06 provide a means of assessing the effect on human beings of vibration caused by vehicle traffic, trains both above and below ground, construction work and occasional impulsive type vibration caused by, say, blasting and the like.
DIN 45669-1 describes the signal processing actions and DIN 4150-2 details how these are used. Provisions are included for day or night levels and for five categories of building:
- Industrial
- Predominantly Commercial
- Mixed Commercial and Residential
- Residential
- Special Areas such as Hospitals
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By Dr Colin Mercer, Technical Director, Prosig
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. read »»»
By Dr Colin Mercer, Technical Director, Prosig
Order cuts are taken from a set of FFTs, each one at a different rpm. The rms level is then found as the Square root of the Sum of the squares of each of the FFT values. Mathematically, if Xks is the modulus (magnitude) of the kth value of the FFT at speed s for k = 1…N-1 then the rms value at that speed is given by
This takes into account the entire energy at that speed both the order and the non order components, including any noise. read »»»
By Dr Colin Mercer, Technical Director, Prosig
Accelerometers are robust, simple to use and readily available transducers. Measuring velocity and displacement directly is not simple. In a laboratory test rig we could use one of the modern potentiometer or LVDT transducers to measure absolute displacement directly as static reference points are available. But on a moving vehicle this is not possible.
More here… OmegaArithmetic.pdf
By Dr Colin Mercer, Technical Director, Prosig
In many cases only significant events, such as bumps or other transients in a signal are of relevance. The objective is to be able to isolate these events in a meaningful manner so that they may be automatically recognised and either removed or extracted for analysis in a structured way.
There are two principle objectives initially: one is to be able to recognise an event and the other is to be able to mark it in some way so that subsequent software is able to operate on the actual event. We must also note that an event has a start and an end; the criterion we use to recognise the start may not necessarily be the same criterion we use to recognise the end. Searches for the start and end points are carried out on a Reference Signal. How the reference signal is formed is discussed in detail later, it includes the original signal, various running statistical measures such as the dynamic RMS, differentiation for slope detection, integration and so on. In many cases the start criterion will be some check on the level achieved by the reference signal. By the time any check level has been detected then it is almost certain that the event started earlier! That is, a pre trigger capability is essential. read »»»
By Dr Colin Mercer, Technical Director, Prosig
The “standard” centre frequencies for 1/3 Octaves are based upon the Preferred Numbers. These date from around 1965. They are not specific to third octaves. The only reference we have is to British Standard BS2045:1965 Preferred Numbers. There are probably equivalent ISO and ANSI versions. read »»»
By Dr Colin Mercer, Technical Director, Prosig
With shafts, gears and the like, the general method of determining the rotational speed is to use some form of tachometer or shaft encoder. These give out a pulse at regular angular intervals. It we have N pulses per rev then obviously we have a pulse every (360/N) degrees. Determining the speed is nominally very simple: just measure the time between successive pulses. If this period is Tk seconds and the angle travelled is (360/ N) degrees then the rotational speed is simply estimated by 360/(N*Tk) degrees/second or 60/(N*Tk) rpm. read »»»
By Dr Colin Mercer, Technical Director, Prosig
A shaft has been instrumented with two shaft encoders, one at each end. Each shaft encoder gives out a once/rev pulse and a 720 pulses/rev signal. Each signal was digitised at 500,000 samples/second. The objective is to measure the twist in the shaft and analyze into orders. The test stand was already equipped with a data acquisition system so a Prosig acquisition system was not required. Instead it was decided that the data captured by the resident system would be imported into the DATS software. The only format available from the customer system was ‘comma separated variables’ or CSV. This is not ideal as it is an ASCII based format and therefore creates very large files. read »»»
By Dr Colin Mercer, Technical Director, Prosig
The following article was written in response to a question from a visitor to the website. The gentleman in question had been reading some of the Prosig signal processing articles and had the following question.
Dear Sir,
It was interesting reading the articles in your mail.I would like
to know the options available in hardware and/or software for measurement/calculation
of phase angle of first harmonic of a vibration signal which is
sinosoidal. The phase angle is the relative phase angle difference
between the signal and the tacho - one into rpm signal.
Regards.
etc.
read »»»
By Dr Colin Mercer, Technical Director, Prosig
One would expect that averaging waterfalls and then extracting orders would give the same result as extracting orders from individual waterfalls and then averaging them. This is not the case. read »»»
By Dr Colin Mercer, Technical Director, Prosig
When working with audio signals a common requirement is to be able to equalise, cut or boost various frequency bands. A large number of hardware devices on the market provide this capability. The key aspect is that such filters are able to control bandwidth, centre frequency and gain separately. There are broadly two classes of filter used, a “shelving” filter and an “equalising “filter (also known as a “peak” filter). A shelving filter is akin to low pass and high pass filters. An equalising filter is like a bandpass or band reject filter. read »»»
By Dr Colin Mercer, Technical Director, Prosig
When we have a very noisy signal with a large number of spikes and signal bursts then if all else fails try Median Filtering. This is a technique often used in cleaning up pictures. The operation is almost childishly simple in concept but we will save the details until we have examined an example. read »»»
By Dr Colin Mercer, Technical Director, Prosig
Fourier analysis takes a signal and represents it either as a series of cosines (real part) and sines (imaginary part) or as a cosine with phase (modulus and phase form). As an illustration we will look at Fourier analysing the sum of the two sine waves read »»»
By Dr Colin Mercer, Technical Director, Prosig
What are RC Filtering and Exponential Averaging and how do they differ? The answer to the second part of the question is that they are the same process! If one comes from an electronics background then RC Filtering (or RC Smoothing) is the usual expression. On the other hand an approach based on time series statistics has the name Exponential Averaging, or to use the full name Exponential Weighted Moving Average. This is also variously known as EWMA or EMA. read »»»
By Dr Colin Mercer, Technical Director, Prosig
Sometimes data has spikes which are clearly artefacts of the processing or are due to some other external source. One is used to seeing these on time series but in some cases there are unrepresentative “spikes” in the frequency analysed data. An example spectrum is shown below. read »»»
By Dr Colin Mercer, Technical Director, Prosig
The measurement of the twist angle between two points along a shaft or through a gear train may be derived from a pair of tacho signals, one at each end of the shaft. Typically the tacho signals would be derived from gear teeth giving a known number of pulses/revolution. For example one end of a shaft could have a gear wheel with say 60 teeth giving 60 pulses/revolutions when measured with say an inductive or eddy current probe. read »»»
By Dr Colin Mercer, Technical Director, Prosig
The most common form of digitising data is to use a regular time based method. That is data is sampled at a constant rate specified as a number of samples/second. The Nyquist frequency, fN, is defined such that fN = SampleRate/2. As discussed elsewhere Shannons Sampling Theorem tells us that if the signal we are sampling is band limited so that all the information is at frequencies less than fN then we are alias free and have a valid digitised signal. Furthermore the theorem assures us that we have all the available information on the signal. read »»»
By Dr Colin Mercer, Technical Director, Prosig
Accurate measurement of a signal depends on the dynamic range and the overall level of the data acquisition system. The overall level setting may be thought of as determining the largest signal that can be measured. This clearly depends on the present gain setting. That is the overall level is related to the gain. Clearly if the overall level is too small (gain too high) then the signal will be clipped and we will have poor quality data. The dynamic range then tells us that for the given overall level what is the smallest signal we can measure accurately whilst simultaneously measuring the large signal.
In a very simple sense suppose we have an artificial signal which consists of a sinewave at a large amplitude A for the first half and that this is followed by a sinewave with a small amplitude a for the second half. We will set the gain (the overall level) to allow the best measurement of the A sinewave. The dynamic range tells us how small a may be so we can also measure that without changing settings.
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By Dr Colin Mercer, Technical Director, Prosig
It is sometimes necessary to pass a signal through a high pass filter to eliminate low frequency signals. These may arise for instance from whole body vibrations when perhaps our interest is in higher frequency components from a substructure such as an engine or gearbox mounting. The vibration levels are speed sensitive and the usual scheme is to record a once per revolution ‘tacho’ signal with the vibration data. The tacho signal, which ideally is a nice regular pulse train, is processed to find rotational speed and hence to select which part of the vibration signal is to be frequency analysed. The most common form of analysis is a waterfall type such as shown below. read »»»
By Dr Colin Mercer, Technical Director, Prosig
In many real-world applications it is impossible to avoid “spikes” or “dropouts” in data that we record. Many people assume that these only cause problems with their data if they become obvious. This is not always the case. Consider the following two time histories. read »»»
By Dr Colin Mercer, Technical Director, Prosig
Not all systems vary linearly. One very well known case is, of course, thermocouples. International standard curves are available for these so they present little difficulty. The issue discussed here is determining a calibration curve and if appropriate reducing to a polynomial. read »»»
By Dr Colin Mercer, Technical Director, Prosig
Some devices, particularly digital tape recorders, apply A-weighting to all their data in order to achieve acceptable data compression. This is fine unless you want to analyse the unweighted data or apply a different weighting factor. Using DATS it is a simple task to instruct the WEIGHT module to either simply unweight the data or remove one weighting factor and apply another. read »»»
By Dr Colin Mercer, Technical Director, Prosig
To illustrate the use of the cross correlation function, a source location example is shown below. For this it is assumed there is a noise source at some unknown position between 2 microphones. A cross correlation technique and a transfer function like approach were used to determine the location. read »»»
By Dr Colin Mercer, Technical Director, Prosig
Sometimes we have digitised data at a much higher rate than we need. How can we reduce the sampling rate? If I wanted to say halve the sample rate can I just throw away every other data point?
The answer is NO, except in pathological conditions where you know that there is no frequency content above the new Nyquist frequency. read »»»
