Linear Variable Differential Transformers

The Linear Variable Differential Transformers (LVDTs) are a type of contact-less position sensors that is not well known in the amateur realm. This is mainly due to the fact that the signal conditioning and driving electronics are relatively difficult to design and that the sensor itself requires some mechanical skills to build. They are however extremely sensitives in small displacements and good performances can already be obtained with simple setups. Here, I present a test LVDT that I assembled in about a couple of hours and show that its resolution is already better than 50 µm.

The operating principle of a LVDT sensor is shown in Figure 1. A ferromagnetic core guided by a plastic shaft enters an assembly of three coils of identical wiring. The center coil, called the primary coil, is fed with AC current to generate an alternating magnetic field. The two outer coils, called the secondary coils, will each produce a voltage that is proportional to their magnetic coupling with the primary coil. The magnetic coupling is enhanced by the ferromagnetic core and so the voltage across the secondary coils vary as the shaft move into the assembly. By wiring the two secondary coils in opposition (as shown in Figure 1), it is possible to cancel the differential voltage ∆V when the coupling is equivalent in the two secondary coils. This is the neutral position and it corresponds to the ferromagnetic head being at the centre of the assembly. As soon as we depart from the neutral position, one of the two coils produce more voltage than the other and we get ∆V≠0.

The test LVDT that I built is shown in Figure 2. It is relatively small and was made from Delrin plastic. I have machined deep grooves into a Delrin cylinder and drilled a hole at the centre using a lathe. I have then made the coils using a few turns of 0.5 mm copper wire. On the right handside of the picture, you can see the mobile shaft which is also a Delrin cylinder but with a small iron core at the end that has roughly 1.5× the size of a single coil. I used Thorlabs parts to hold everything in place for the test.

I used my Protec 9205 sweep function generator to generate the primary voltage and I adjusted the frequency by monitoring the voltage at the secondary coils. Because of the very low number of turns used in the test setup, the resonant frequency was found to be 1.37 MHz. Below that, the RL equivalent circuit forms a high-pass filter which decrease the energy transferred into the secondary coils. Above 1.37 MHz, the capacitances start to decrease the signal again.

To create a controlled displacement, I have used a linear stage coupled to a dial indicator as shown in Figure 3. When moving the translation stage back and forth, the ferromagnetic core moves inside the LVDT assembly and varies the coupling between the primary and the two secondary coils. When moving, the translation stage also pushes on the dial indicator such that I can have a precise estimate of the distance travelled.

The translation stage was then moved on 10 mm by 0.1 mm increments with an accuracy of ±0.005 mm (dial indicator reading accuracy). The experimental data are shown in Figure 4 with a quadratic fit in the range 5.5 – 9.8 mm where we are clearly departing off the neutral position.

Ideally, the response of a LVDT should be linear. Here, satisfactory modelling (R²=0.9991) could be obtained with a quadratic curve. The error was evaluated by computing the signal error between the experimental data points and the fit and converting the signal error into a position error through the following relation

The error repartition histogram is shown in Figure 5. The standard deviation was estimated to be 35 µm and 90% of the model deviations were below 60 µm.

The results obtained are very promising for a first test. Also, when looking at the signal deviations, it was found that the signal standard deviation was about 2 mV RMS which is close to the resolution of the oscilloscope that I used to take the measurements. So, it is possible, but not verified, that the LVDT itself was better than 35 µm but that the signal conditioning circuit was the limiting part. The only way to assess that would be to build a custom circuit with a better sensitivity. This is however not easily done at these frequencies and was therefore not attempted here.

On the literature side, sensitivities between 0.002% and 0.05% of the travel range are reported. With a travel range of 5 mm, sensitivities down to the micrometre level can therefore be achieved in theory. The next step would then be to make a second LVDT with larger coils and dedicated electronics to see what resolution can be achieved at the amateur level. This is truly exciting!