Sensors for vibration measurement: Principles of operation and measuring ranges

Ernst Fischer, winter semester 2015/16

Sensors for vibration are sensors that operate according to different mechanical or optical principles to detect vibrations of an observed system.

The measurement of vibrations can be done using various types of sensors. Although there are no direct vibration sensors, vibrations can be measured indirectly, deducing values from classic mechanical or optical quantities. These sensors differ in some features. Among other things they can be divided based on active and passive behaviour, there are sensors that measure relative and others absolute. Other distinctive features are frequency range, signal dynamics and the quality of the measurement data. The following sensors shown here were first structured in a contacting and a non-contacting group and within these in the sub items path, velocity and acceleration measurement. ^[1]

Contact vibration measurement

Path measurement

Potentiometric Transmitter

The potentiometric transmitter is a one-dimensional position sensor. It is based on the potentiometer, an adjustable potential divider. A voltage is applied to a resistive track. A wiper runs along this resistive track and thus divides the resistor in two parts, as shown in figure 1 (resistor R1 and R2). At different positions of the wiper, specific resulting voltages can be measured, due to the change in resistance. The wiper moves because it is attached to the motion of the vibrating object. ^[2] The frequency ranges from 5 Hz to 2 kHz, which corresponds to a possible maximum acceleration of 20 g. Potentiometric transmitters can achieve measuring strokes from 1 mm up to 2 m with an infinite resolution. The operating temperature ranges between double-digit temperatures below zero and 150 °C. ^{[3] [4] [5] [6]}

Linear Variable Differential Transformer

The Linear Variable Differential Transformer (LVDT) is a kind of transformer which is based on induction. It can be used for relative measurement of the displacement. As shown in figure 2, this sensor works along one axis and it is possible to determine the direction of the motion. The LVDT basically consists of three coils and a core. The primary coil is connected to an AC supply for excitation. The two other coils are placed on each side of the primary coil and are arranged series-opposed. In the center of this coil assembly is a core that influences the magnetic flux from the primary to the secondary coils. Depending on the motion of the core, which is attached to the vibrating object, direction and distance can be deduced from the output signal. The carrier frequency range goes from 50 Hz to 25 kHz, which is typically defined as 10 times the frequency of the core motion. Using this setup, measuring displacements of more than ± 50 cm and an accuracy up to 0.1 μm is possible. The temperature range is between -270 °C and 600 °C. ^{[7] [8]}

Speed measurement

Principle of electrodynamics

The principle of electrodynamics is used in a relative speed sensor. It is based on the phenomenon of induction. In order to apply this principle a coil and a light permanent magnet is used. The magnet is fixed to the vibrating object. The magnet either moves contactless or it is guided within the coil. Due to the movement of the magnet a voltage is induced in the coil. This voltage can be measured and it is directly proportional to the speed of the vibrations. The isolation of the wires is the only restriction for the maximum voltage. ^[1] For example there are sensors with a working frequency range between 1 Hz and 2 kHz. ^[9]

Seismometer

Absolute speed can be measured with the Seismometer. The Seismometer consists of a seismic mass and a spring within a housing. Due to the inertia of the mass, there is a relative movement between the seismic mass and the housing, in case of vibrations. A coil, which is fixed to the housing, can be used cause induction. Due to the movement of the mass, a voltage is induced in the coil. This voltage speed can be measured because it is proportional. Often attenuation equalization is installed in such a seismometer in order to avoid resonance peaks. ^{[1] [10]} In today's seismometers the mass is fixed motionless in relation to the housing. Thus there is no voltage amplitude caused by motion of the seismic mass. However the force, that is needed to hold the mass in balance, is measured through voltage. Modern seismometers are able to register frequencies from less than $//<![CDATA[ \begin{array}{l}10^{-3}\end{array} //]]>$ Hz up to 100 Hz. It is possible to detect movements in the range of about 1 nm and several centimetres. ^{[10] [11] [12]} The principle of seismic mass can also be used in path and acceleration measurement. ^[1]

Acceleration measurement

Piezoelectric sensor

The piezoelectric sensor works on the basis of the seismic principle and the piezoelectric effect. Here quartz crystal and piezo ceramic replace the spring used in a Seismometer. The piezo material is fixed to the vibrating object on the one side and to the seismic mass on the other. Vibrations forces lead to strain and compression on the piezo material. The piezoelectric effect describes the occurrence of an electric charge due to the change in length of the polarised materials. This charge is proportional to the acting force and can be tapped. Since the force is a product of mass and acceleration it can be easily computed. The piezo materials are very rigid, therefore damping might be necessary. This can be achieved by adding stoppers or immersing the parts in oil. ^{[1] [13] [14] [15]} The weight of piezoelectric sensors varies from less than 1 g up to several grams. The linear frequency range of piezoelectric sensors varies from below 0.1 Hz up to $//<![CDATA[ \begin{array}{l}10^4\end{array} //]]>$ Hz. Thus, piezoelectric sensors allow measurements of accelerations under 1 g and up to several thousand g. ^{[14] [16] [17]}

Piezo-resistive sensor

The piezo-resistive sensor uses four semiconductor strain gauges. These strain gauges are mounted on the vibrating object along with a seismic mass, using a bridge-circuit. Vibrations lead to a deformation of the strain gauges. During a motion in one direction two strain gauges are stretched and the other two are compressed, which results in voltage changes. An advantage compared to the piezoelectric effect is the possibility of also measuring constant accelerations. ^{[1] [14] [18]} It is possible to measure accelerations up to 1000 g. ^[19] Piezoelectric sensors are more appropriate for high frequencies while semiconductor sensors are preferred at low frequencies. ^[18]

Resistive sensor

The functional principle of the resistive sensor is the same as the one of the piezo-resistive sensor. The only difference is that the strain gauges are not built of materials that have a piezo effect. This leads to similar properties. But the measurable signal is lower. ^[1]

Inductive sensor

The inductive sensor for acceleration measurement is based on the fact that the reaction force of the seismic mass can be converted into a path. Now the covered distance can be calculated through measuring the induced voltage and thus the magnitude and direction of the vibration can be ascertained. However this path-dependent measurement requires the sensor to be a lot bigger than comparable acceleration sensors.^[1]

Non-contact vibration measurement

Path measurement

Capacitive Principle

The capacitive principle can be applied to non-contact vibration measurement, if the vibrating object or a relevant part of it is useable as a plate of a capacitor. In order to do measurements, a second plate is needed. Now the whole setup works like any common capacitor. The variation of the distance of the two plates is proportional to the capacity. An AC supply is connected to the capacitor. Depending on the distance between the plates, a specific amplitude can be recognized by the sensor which can be used for further processing. The measuring stroke reaches from several μm to mm with a resolution of some nm. The band of frequencies lies between 0 and 6 kHz. However this non-contact method is not feasible for application in high quantities and must be adapted to the individual case. ^{[1] [2]}

Eddy current sensor

In eddy current sensors, the displacement measurement of vibrations is limited to metallic objects or at least objects with a metallic surface. The sensor consists of a coil which is connected to an AC supply. This configuration develops an electromagnetic field that in turn causes eddy currents within the metallic object. These eddy currents interfere with the electromagnetic field and result in a measureable dissipation. ^{[1] [2] [20]} Possible path measurements are between 0.5 and 80 mm. Here the resolution lies somewhere between nm and μm. The band of frequency ranges between 1 Hz and 100 kHz. ^{[2] [21] [20]}

Hall sensor

The Hall sensor uses the Hall-effect for the non-contact path measurement. To that end a small permanent magnet has to be fixed on the measured object. As soon as vibrations occur, an electric signal can be detected through measuring the effect of the Lorentz force. The output signal is proportional to the covered path. However the non-linear characteristic curve and the high sensibility to environmental impacts results in a limited usability. ^{[1] [13]}

Optical sensor

Optical sensors use lasers to detect changes in distance. In addition to a laser, beam splitters, a reflector, a Bragg cell and a photo detector are necessary to carry out measurements. These devices are needed to obtain two beams, a measuring beam and a reference beam. The measuring beam is focused on the vibrating object. Its reflection merges with the reference beam and starts to interfere. The generated interference pattern can be decoded by the photo detector. The range of an optical sensor lies within few millimetres with a resolution in the region of nanometres. ^{[1] [22]}

Speed measurement

Laser-Doppler vibrometer

The Laser-Doppler vibrometer (LDV) uses the Doppler frequency shift for non-contact speed measurement. In principle, it consists of a laser, beam splitters, a reflector, a Bragg cell and a photo detector. The coherent laser light is split into a measuring beam and the reference beam by means of polarisation. The measuring beam is projected onto the vibrating object and is reflected on its surface. The reference beam is used to be send through a Bragg cell for a frequency shift. This frequency shift allows the detection of motion direction later. The interference of both beams leads to a frequency modulated signal. Various demodulation methods are able to translate the signal into path or speed information. ^{[1] [22]} Commercial LDVs have a frequency range between 0 Hz and 30 MHz and can follow vibration speeds from 100 nm/s up to 20 m/s. ^[22]

Acceleration measurement

So far there is no way known to gain acceleration data directly. It is possible to receive this data by derivation from the speed measurement. However measurement noise has a great effect on the quality of the derived data. Thus it is not always possible or useful to do so. ^[1]

Table of Sensors

Literature

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10. Wielandt, E.: Seismographen. In: Wechselwirkungen. Universität Stuttgart. Stuttgart, 1996. Checked on 16.01.2016.
11. Stolzenberger-Ramirez, A.: Breitband-Seismometer. Facultad de Ciencias Agrarias de Universidad Nacional de Jujuy. Jujuy, Argentina. Checked on 16.01.2016.
12. Bönnemann, C.; Stammler, K.: Seismologische Verfahren. Bundesanstalt für Geowissenschaften und Rohstoffe. 2010. Checked on 16.01.2016.
13. Buchner, S.: Beschleunigungssensoren. Seminararbeit. Institut für integrierte Naturwissenschaften der Universität Koblenz-Landau. Koblenz, 2009. Checked on 16.01.2016.
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15. Weber, M.: Piezoelektrische Beschleunigungsaufnehmer. Theorie und Anwendung. 6. Auflage. Metra Mess- und Frequenztechnik in Radebeul e.K. (Hg.). Radebeul, 2012. Checked on 16.01.2016.
16. Weber, M.: Hauptkatalog Vibration Measurement. Metra Mess- und Frequenztechnik in Radebeul e.K. (Hg.). Radebeul, 2015. Checked on 16.01.2016.
17. AS - 079. Beschleunigungs-Sensor. Brüel & Kjær Vibro GmbH. Darmstadt, 2010. Checked on 21.01.2016.
18. Schmidt, W. D.: Sensorschaltungstechnik (Elektronik 8). 3. Auflage. Vogel Buchverlag. 2007. ISBN-10: 3834331112. ISBN-13: 978-3834331113.
19. TYP: FA 1102. Beschleunigungsaufnehmer. FGP Sensors & Instrumentation. Berkshire, United Kingdom, 2013. Checked on 16.01.2016.
20. Wirbelstromsensor. Serie TX. WayCon Positionsmesstechnik GmbH. Taufkirchen, 2015. Checked on 16.01.2016.
21. Betriebsanleitung. Wegsensor System Serie ds821. Wegmessbereich 2 mm. Brüel & Kjær Vibro GmbH. Darmstadt, 2013. Checked on 16.01.2016.
22. Hoffmann, J.: Handbuch der Messtechnik: mit 93 Tabellen. Ausgabe: 3., neu bearbeitete Auflage. Carl Hanser Verlag. München, 2007. ISBN: 978-3-446-40750-3