Piezo Accelerometer Tutorial
Synthesis of Properties
Piezoelectric accelerometers are popular
It has been shown that piezoelectric accelerometers are very often the best choice for measuring absolute vibrations in industry but also in the laboratory. There are different designs for almost any application and thus a wide variety of models. Compared to other types of sensors, piezoelectric accelerometers have important advantages:
With piezoelectric measuring elements, sensors with an extremely large dynamic range can be realised, because on the one hand they are very robust and on the other hand they generate an almost noise-free signal.
There are piezoelectric accelerometers that can accurately measure 1 μg (=0.000001 g), while others can withstand 100'000g. A single sensor can perfectly reproduce vibration amplitudes in the range of 1 to 1'000'000 (120dB) with an excellent linearity of typically less than 1% over the entire dynamic range.
Dynamic Range, Linearity
In addition, there are piezoelectric accelerometers which have extreme frequency ranges. Frequencies of the order of 50 mHz to 50 kHz can be measured with less than 5% deviation
There are piezoelectric accelerometers that operate from 4K (-269°C) to 1020K (747°C) operating temperature. This temperature range of over 1000K is covered by one single piezo material !
Reliability / Robustness
Piezoelectric accelerometers are very compact and very robust. They have no moving parts and therefore no wear, resulting in an exceptional reliability.
Mean Time Between Failure
The common measure of reliability is expressed in a number called MTBF, Mean Time Between Failure. MTBF is literally the average time that elapses between one failure and the next failure. So it is the average time during which something works until it fails and has to be repaired again. For non-repairable products, it is called Mean Time To Failure (MTTF). A defective accelerometer is often not repaired because the cost is not economically viable. In practice, however, the term MTBF is usually used instead of MTTF.
Calculating the MTBF is a science in itself. It requires empirical values for the failure of the individual parts, or more precisely for the failure of the function of the part. For example, a connecting wire can have the function of signal transmission, but this also includes the corresponding solder joint or other connection. For each function, a failure probability or failure rate λ must be determined. This indicates how many failures of the function must be expected in a period of time, e.g. in 1'000'000 hours. It is assumed that the probability of failure is constant over time. To find the failure rate of the entire accelerometer, the λ values of all functions are combined according to a failure logic.
If the individual functions are connected in series, which means one component failure = complete system failure, then the λ-values can be simply added. For the function of the entire unit then applies:
MTBF = 1 / λtotal
If there are partly redundant functions, such as two parallel contact wires etc, then the calculation becomes much more complicated.
Long Term Stability
Last but not least, the stability of the function over a longer period of time is one of the important characteristics of piezoelectric accelerometers.
There are piezoelectric materials which are tremendously stable over time. This is particularly the case for single crystals. When used within specified limits a single crystal sensor will not alter measurably its sensitivity even after years or decades of service.
Piezoceramic based accelerometers show sometimes a certain fluctuation of the sensitivity over longer periods or after an excursion of temperature or load. However the sensitivity will normally stay within 1 or 2 percent of the initial calibration.
Of course the materials must be used within the given limits throughout the life and shall not be overstressed mechanically, electrically or temperature-wise.
Also the resonance of an accelerometer remains extremely constant over time. This means that the frequency response will not alter.
If a resonance on a used sensor has changed with respect to the initial value, it is a sign that the sensor has been overstressed.
Of course there are also characteristics which are less desirable.
More on this you will find in the chapter "Disturbing Factors".
Trade-off between Sensitivity-Frequency-Temperature
The three main axes determining the sensor are sensitivity, temperature capability and frequency response (resonance). There is a strong dependence between these three chracteristics axes.
In order to show this we recall the calculation of the sensitivity of a compression element.
With the mass m, the piezoelectric constant d and the number of piezo disks n, we obtain:
S = m · d · n
and for the resonant frequency:
Fres² ~ k / m with k ~ 1/n
We find a typical trade off situation betweeen these three main chracteristics. If we favour one axis, the two other will suffer.
To obtain a high sensitivity we need a big mass m and (or) a large coefficient d.
S ↑ ↔ m ↑ ,d ↑
With increasing temperature capability the piezoelectric constant d is decreasing drastically.
Tmax ↑ ↔ d ↓
To obtain a high resonance we need to reduce the mass m and reduce the number of disks n.
Fres ↑ ↔ m ↓
Trade off between sensitivity, temperature capability and frequency response