FFT spectrum tips

It is almost a given today to analyze vibration using data in frequency domain or as a spectrum. Engineers rely so much on the spectrum analysis that it is easy to forget that there are accuracy trade offs that are built into the process of obtaining the spectrum. Windowing is one of them. It is built in almost all vibration analyzers and

FFT is based on the Fourier theorem, which assumes that we deal with an infinitely long time function. Since we don't have infinite time, we just take a snapshot of time data and make the algorithm think that this piece of data repeats infinitely. Since repeating the time data sample causes abrupt changes at the ends of the sample, the process causes a truncation error that is also called spectral leakage. A standard technique to deal with this problem is to use a Window filter. A variety of functions can be used, which brings the values at the beginning and the end of a time data sample to zero or close to zero. This solves the spectral leakage problem, however all window functions reduce the amount of useful data used in the FFT calculation and distort the spectrum, often causing the peaks in a spectrum appear wider and lower. If a vibration analyzer has a choice of window functions it is important to compare spectra processed with the same window function all the time.

If the same analyzer is used for vibration measurement and for modal analysis, the window functions have to be different. For example, for vibration measurements Hann (also called Hanning) window is often used, while for modal analysis a rectangular window (no window function) may be preferred. It is important that the window functions are set correctly each time the analyzer is used for a new task.

Vibration Analyzer Settings Discussion

I just read this article by Jason Tranter about vibration measurement errors. The topic is very close to what we have been talking about. It is interesting and the advice is very good, however tips like these are rarely followed because so much of this is just arbitrary. The author is not explaining why his recommendations make sense. For example, the requirement to select "Fmax of 70 times the running speed of the shaft". Why? Why not 50 or 100? By the way, in the example that follows the author uses Fmax at 100 times the speed (1800 RPM is 30Hz and he is using Fmax 3000 Hz).

Another arbitrary requirement is that the shaft "should turn at least 50 times during your measurement". Again, why? There must be a reason to it and a vibration analyst will be able to apply this rule more efficiently if he or she knows why the rule exists. And, while we are at it, why not give a simple formula that would help to calculate the number of shaft revolutions during the measurement? The author skips this part. I would use this formula:

revolutions = (lines/Fmax)*((1-overlap/100%)*(averages-1)+1)*RPM/60

Following the example from the article, where lines=3200, Fmax=3000, overlap=67%, averages=5, and RPM=1800, this formula yields 74.24 revolutions. Well, the 75 revolutions sited in the article is close enough.

In vibration analysis, as in many other areas, there is no single answer to how the techniques should be applied. It is true that vibration analyzers today have all these capabilities but using them by following a set of arbitrary recommendations may not work in all situations. It is important to understand the objectives of the measurement and know the machine being tested and its operating characteristics.

There are trade offs in using settings that are not dictated by the task at hand. For example, if unnecessarily long samples are taken, there is a chance that a fluctuation in rotating speed will smear the spectrum peaks at forcing frequencies. If the analysis bandwidth (Fmax) is set too high, there may not be enough resolution to analyze the frequencies of interest. If the resolution is set too high, it might lead to a longer measurement and large file size.

Instrumentation - Dynamic Resoluiton

When sensor signals are being converted to data the capabilities of ADC (analog to digital converter) should be considered. The dynamic resolution of an ADC is related to a number of steps the original signal is approximated with. If the ADC has 10 bit resolution, that means that the full input range will be digitized using 2^10 (two to the power of ten) or 1024 steps. For many applications it is too crude, especially if the signal is not amplified. Typically, for vibration measurements ADCs with 16 or even 24 bits of resolution are used. For industrial vibration monitoring a 16 bit ADC is quite enough. A sensor with the sensitivity of 100 mV/g and the signal range of -10/+10V will have the smallest step of 3mg at 16 bit ADC. Dynamic resolution is sometimes listed in dB in device specifications.

If more dynamic resolution is needed, the signal can be amplified, or an ADC with higher resolution can be used. There are trade-offs with either method. An analog amplifier can introduce noise while a higher resolution ADC results in a more expensive device. There is a signal processing technique that can boost dynamic resolution through oversampling.

Instrumentation: Data Acquisition: Sampling Rate

When a dynamic process such as vibration has to be studied it is important to perform measurements correctly. The data acquisition process converts an analog signal obtained from a sensor into a discrete function. This is done by sampling the signal at equal intervals. The speed at which the sampling takes place is called sampling rate. Why do it? Because the resulting data is very convenient to transmit, process and store.

The faster the sampling rate, the closer the digital function is to the original signal. So, what sampling rate is really needed? It depends on the highest frequency of interest. Technically, the sampling rate has to be at least twice the highest frequency of interest. The ratio used in the industry is 2.56, which is called Nyquist factor. This means that if the highest frequency we would like to study is 1000 Hz, the sampling rate has to be at least 2560 samples per second.

Now, how much data do we have to collect to have enough to calculate a spectrum? This depends on the spectrum resolution we are trying to achieve. At 800 lines per spectrum we will need 800*2.56=2048 samples. Here, again we multiply by the same Nyquist factor. Time needed to collect the samples we need is found by dividing the number of samples by the sampling rate: 2048/2560=0.8 seconds. It is easy to see that at lower frequencies and higher spectrum resolution it might take quite a while to collect the data. That is why it is sometimes takes so long to acquire a data set.

Instrumentation - Data Acquisition

Sensor signals have to be converted to data (digitized) before they can be processed and stored. This process is called data acquisition. For vibration data the best solution is to acquire a dynamic signal, the function of acceleration over time. This function can later be processed with several algorithms to yield valuable machine condition and diagnostic data. The data acquisition process assigns a number to every level of acceleration at equal time intervals. It takes place in a data acquisition device that contains a micro processor, an ADC (analog to digital converter), necessary filters, and other components. In addition, the data acquisition device has to have means for sending the data out for further processing and storage.

There are many decisions that have to be made about the data acquisition. Here are some of the questions that are typically asked about data acquisition:

How much data has to be collected?

What is the required sampling rate?

What is the proper ADC resolution?

How the signal has to be filtered?

From the practical standpoint these selections must be made behind the scene in software and not by the user. However, many data acquisition systems assume technically savvy users who know how to use these parameters. A more user friendly system should ask a different set of questions:

What is required frequency resolution?

What is required analysis bandwidth?

What is required dynamic resolution?

Answers to these questions help set up proper data acquisition parameters and they borderline with our next topic - Data Processing and Storage.

Low Power Sensors

One important point was not covered by my previous post. As almost any sensor needs power to operate, it is becoming more important how much power each sensor uses. It could be surprising since we are talking of very low amounts of power in any case. Why would we care about this? Because power wiring of machine monitoring systems adds costs in installation and in some locations simply cannot be done.

As wireless data communications are becoming a standard, the last remaining tether is the power connection. In the field of remote machine monitoring we don't deal with a mobile application because heavy equipment does not normally travel around the plant. Even with that, there is a need for fully autonomous monitoring solutions that will not need an external power hookup. These systems will have to harvest energy from the environment or the machines they monitor.

Suddenly, the power consumption by the sensors has become important. Here again we can find that MEMS sensors require significantly lower power to operate in comparison with traditional analog sensors. The MEMS technology will be evolving to produce sensors with more features and lower power requirements in the future, but even today their benefits are obvious.

Instrumentation -- Sensors

Since we are talking specifically about machine condition monitoring, our primary interest will be in vibration sensors. Over many years the standard vibration sensor has been an accelerometer. The sensing technology in a standard accelerometer is pretty much the same today as it was thirty years ago.

In spite of its wide use the standard accelerometer is not an ideal vibration sensor. It requires a charge amplifier that is usually built into the sensor body and an analog signal conditioner, which adds to the cost. Low frequency applications are challenging because the sensor is not sensitive to static acceleration while the dynamic acceleration is very low at low frequencies. These sensors require regular recalibration in condition monitoring applications. However the main issue with traditional accelerometers is cost. An accurate, temperature stable accelerometer with a wide frequency range can cost a few hundred dollars.

The good news is that soon this is going to change. New technology is already here and is waiting to be widely adopted. I am talking about MEMS accelerometers. The MEMS technology has been widely used for sensors and MEMS accelerometers are commonly used in electronic devices as motion sensors. Industrial applications could not benefit from the MEMS technology until last year when Analog Devices has released the ADXL001 accelerometer. Designed specifically for industrial applications, this accelerometer features a wide frequency range, high temperature stability, excellent low frequency characteristics, and does not need recalibration.

Sounds like a perfect vibration sensor? Well, not so fast. There is a gap between the sensor's microchip form factor and the industry's requirement for robustness. This sensor needs an appropriate packaging, in which the sensor will be sealed from the environment and have means to be mounted to a machine. InCheck Technologies is working on a version that a user will be able to permanently mount into a small hole in a bearing housing. The package will also include a temperature sensor microchip, forming a dual sensor.

Speaking about temperature sensors, MEMS sensors can compete with traditional thermocouples and RTD's in the -40°C to +125°C temperature range. Unlike RTD's MEMS temperature sensors produce linear output and unlike thermocouples they do not require external electronics.

Did I mention the main advantage of the MEMS sensors? Yes, they are pretty inexpensive. The ADXL001 is still a little pricey, but it already beats the traditional technology hands down. And since the MEMS output is compatible with standard ADC input, no addition analog electronic components are necessary. With machine monitoring applications the low cost will be the key to wide adoption. The future apparently is with the MEMS technology.