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Lucrarea 2.1 - TRANSFORMATORUL DIFERENŢIAL LINIAR VARIABIL

(Echipament TQ)

Obiectiv: măsurarea deplasărilor folosind transformatorul diferenţial liniar variabil (LVDT)

Pe parcursul experimentului veţi:

• observa modul de ataşare a unui LVDT la un sistem care se deplasează liniar • studia caracteristicile unui LVDT • trasa graficul de calibrare a unui LVDT şi veţi face aprecieri asupra liniarităţii, repetabilităţii,

acurateţei şi sensibilităţii unui LVDT

Partea (a): caracteristicile unui LVDT

Experimentul ilustrează modul în care tensiunile de la bornele înfăşurărilor secundare ale transformatorului sunt influenţate de deplasarea miezului confecţionat din oţel moale. Pentru aceasta, folosind un osciloscop dublu canal, se vizualizează şi se măsoară (dublul amplitudinii, Vpk+pk şi frecvenţa) formele de undă ale tensiunilor din circuit.

Folosind conectorii, realizaţi montajul experimental.

Poziţionaţi ansamblul liniar la jumătatea cursei. Vizualizaţi formele de undă ale tensiunilor de la bornele înfăşurării primare şi una din înfăşurările secunadre şi măsuraţi defazajul dintre ele. Schimbaţi între ele conexiunile sondei osciloscopului la bornele înfăşurării secundare şi măsuraţi noul defazaj. Comparaţi cele două defazaje.

Atenţie: în timpul măsurătorilor una dintre cele două borne ale înfăşurării secundare trebuie să fie conectată la 0V.

Deplasaţi ansamblul liniar spre dreapta, până la capătul cursei.

Deplasaţi apoi ansamblul liniar spre stânga (până la capătul cursei), cu pasul de 1 mm (o rotatie completă a discului gradat), măsurând şi notând tensiunile vârf-vârf (pk-pk) la bornele celor două înfăşurări secundare.

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Repetaţi măsurătorile precedente conectând în serie cele două înfăşurări secundare astfel încât tensiunile lor să se însumeze în fază. Sonda osciloscopului se conectează la extremităţile libere din secundar, una dintre cele două extremităţi fiind conectată la 0V. Observaţi ce se întâmplă cu tensiunea din secundar.

Partea (b): caracteristicile diferenţiale ale LVDT

In această parte se va pune în evidenţă modul de lucru în montaj diferenţial al LVDT pentru măsurarea deplasărilor.

Folosind conectorii, realizaţi montajul experimental, conectând cele două înfăşurări secundare astfel încât tensiunile lor să se însumeze în antifază.

Deplasaţi ansamblul liniar spre dreapta, până la capătul cursei.

Cu ajutorul osciloscopului măsuraţi tensiunea din secundar pentru o deplasare completă spre stânga a ansamblului liniar. Reprezentaţi grafic tensiunea din secundar în funcţie de deplasare.

Partea (c): măsurarea deplasării cu LVDT

Conectaţi acum extremitatea liberă a secundarului (realizat în montjaj diferenţial) la borna de intrare a detectorului sensibil la fază.

Referinta

Deplasare [mm]

V1pk-pk [V]

V2pk-pk [V]

0 1 2 3 4 5 6 7 8 9

Deplasare [mm]

Vspk-pk [V]

0 1 2 3 4 5 6 7 8 9

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Folosind conectorii realizaţi montajul experimental.

Deplasaţi ansamblul liniar spre dreapta, până la capătul cursei.

Folosind semnalul de referinţă de la borna 0o, măsuraţi tensiunile de la ieşirea detectorului sensibil la fază pentru o deplasare completă (cu pasul de 1 mm) a ansamblului liniar.

Repetaţi măsurătorile pentru cazul în care semnalul de referinţă este luat de la borna 180o.

Reprezentaţi grafic tensiunea din secundar în funcţie de deplasare pentru cele două cazuri.

Din reprezentările grafice determinaţi sensibilitatea sistemului şi evaluaţi liniaritatea lui.

Deplasare [mm]

Vpk-pk, 0° [V]

Vpk-pk, 180° [V]

0 1 2 3 4 5 6 7 8 9

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Anexa

(Acest material este reprodus pentru studenti dupa manualul de utilizare a SIS - TQ Education and Training Ltd.)

Linear variable differential transformer (LVDT) Linear variable differential transformers (usually referred to in their abbreviated form of LVDT), are probably the most commonly used sensors for accurately measuring displacements up to about 300 mm.

Typically a transformer consists of two closely coupled coils wound around a soft iron former. These are known as the primary coil and the secondary coils. When an a.c. voltage is applied to the primary coil, an a.c. voltage is induced in the secondary coil. This is because of electromagnetic induction.

When an alternating current (a.c.) flows through the primary coil it produces an alternating magnetic flux. Because of Faraday's Law of Electromagnetic Induction, an e.m.f. is induced in the secondary coil. The size of the e.m.f. induced in the secondary coil depends on the amount of the current flowing in the primary coil and the ratio of primary and secondary turns. Hence the voltage across the secondary coil depends on the ratio of turns in the windings.

Faraday's Law of Electromagnetic Induction states that when a conductor moves through a magnetic field an electromotive force (e.m.f.) is induced across it proportional to the rate of cutting flux. The linear variable differential transformer is a precision instrument designed and used for measuring displacement. The linear variable differential transformer is aptly named since its operating principles can be readily obtained by considering its name word by word, in reverse order.

• Firstly, it is a transformer, obeying all of the principles of electromagnetic induction appropriate to this type of device. It has one primary winding and two secondary windings connected to provide the difference in their respective voltage levels at the output. This is the differential.

• It is variable because the magnetic coupling between the primary and each of the two secondary coils can be varied to affect the magnitude of the induced e.m.f.s.

• Finally, the design of the whole assembly is such that the variation in the coupling between the primary and the secondary coils is linear.

The above figure shows the relative position of the three windings of an LVDT wound on a hollow former. They lie along a single axis, the primary winding in the centre and the two secondary windings on either side. A soft iron core is positioned in the centre of the windings which is free to move in either direction within the coils.

Initially assume that the soft iron core is centrally positioned within the primary winding. When energised by an a.c. signal, usually at a frequency of 5 kHz or above, the current flowing produces a magnetic flux in the soft iron core. This flux links with both of the secondary windings equally and these have identical e.m.f.s induced across them. This is shown here:

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The secondary voltages, Vs1 and Vs2 are in phase with each other and have the same amplitude.

If the two secondary windings are now connected as shown to the right then the two signals will cancel.

However, should the soft iron core be moved in either direction the flux linkage to one secondary winding will increase while the flux linkage to the other secondary winding will reduce. Similarly, should the core be moved in the opposite direction the effect will be reversed. The graph below shows the relative amplitude of the combined outputs from the secondary windings against displacement in either direction.

Note that with no displacement the secondary voltage is zero. This voltage increases with displacement in either direction. Eventually the linkage is wholly with one secondary winding and not the other and so the output voltage is at a maximum and unable to increase further (saturated). This limits the effective working range of the LVDT. For displacements in one direction only, positive or negative, a measure of the secondary voltage amplitude alone would give an indication of displacement.

Where displacement is expected to be in either direction then further signal conditioning is required. This can be achieved by comparing the secondary output voltage with a reference, usually the primary supply. Whichever of the two individual secondary voltages is largest controls the phase of the combined secondary output, either in-phase or antiphase (assuming no inductive effects in the windings causing their own phase shifts). A phase sensitive detector may be used to compare the secondary output voltage with the reference. This produces a signal proportional to the amplitude of the secondary with a polarity governed by whether it is in phase or anti-phase with the reference. To take advantage of this effect to measure displacement only requires the LVDT soft iron core to be connected to the object.

Some commercially available LVDTs can be supplied from a d.c. source, and provide a d.c output. They are based on the same principles as a.c. LVDTs but have built in signal conditioning. The d.c. is converted to a.c. before being input to the LVDT, and the output is then converted back from a.c. to d.c. This gives a d.c. output dependant on the position of the soft iron core.

The LVDT is extremely sensitive and provides resolution down to about 0.05 mm. They have operating ranges from about ±0.1 mm to ±300 mm. Accuracy is ±0.5 % of full-scale reading. Because there is no contact between the magnetic core and the coils, there is very little friction and wear. If necessary they can be constructed to withstand shock and vibration. Consequently LVDTs are in wide use in various applications. These range from use in machine tools, to robotics and digital positioning systems.

LVDTs often form part of systems which measure force, pressure and acceleration