A differential transformer-based force sensor utilizing a magnetic fluid core


A force sensor utilizing a transformer concept with a ferrofluid core was developed. A ferrofluid reservoir was machined out of Teflon and the open top of the reservoir was sealed with a thin silicone membrane. Forces applied to the silicone membrane caused the membrane to deflect, resulting in the displacement of the ferrofluid in the reservoir through an external tube. The ferrofluid in the tube acted as the core of voltage transformer. The ferrofluid core was excited by an alternating current across a wire coil wound around the tube. A secondary coil was wound around the top portion of the tube which was vertically oriented. As the ferrofluid level in the tube rose in response to applied forces, the secondary coil became engaged by the magnetized ferrofluid, resulting in a voltage induced in the secondary coil that varied with the level of the ferrofluid. The sensor was characterized by the relationship between the forces applied to the membrane and the output voltage readings across the secondary coil in loading and unloading cycles. This relationship was found to be nonlinear and following a negative second-degree polynomial relationship. The sensor was tested at three primary frequencies of 60, 100 and 120 kHz. It was found that 13% of the 5 V A/C exciting voltage applied across the primary coil at 60 kHz was induced into the secondary coil when it was fully engaged by the magnetized ferrofluid. It was determined that the sensor generates the highest sensitivity of 68.3 mV/N over the effective range of 0.1–2.5 N at 60 kHz. The sensor was analyzed for error and the characteristic error was found to be comparable to existing inductive sensors. Sources of most significant of error were identified and proposals for improvements to future designs of this sensor type are provided.

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\( \varvec{\epsilon} \) :

Electromotive force (V)

\( \varvec{\epsilon}_{1} \) :

Electromotive force across the primary coil (V)

\( \varvec{\epsilon}_{2} \) :

Electromotive force across the secondary coil (V)

\( \varvec{N}_{1} \) :

Number of wire turns in the primary coil

\( \varvec{N}_{2} \) :

Number of wire turns in the secondary coil that are affected by the magnetic flux transferred by the ferrofluid core

\( \varvec{\varPhi}_{\varvec{B}} \) :

Magnetic flux (Wb)

\( \varvec{P} \) :

Force applied at the center of the membrane (N)

\( \varvec{h} \) :

Linear vertical distance from the base of the secondary coil/end of the primary coil to the level of the ferrofluid (mm)

\( \varvec{w} \) :

Deflection of the silicon membrane (mm)

\( \varvec{\gamma} \) :

Constant representing the geometric and material property constants of the silicon membrane

\( \varvec{R} \) :

Radius of the fixed edge of the silicon membrane (mm)

\( \varvec{r} \) :

Internal radius of the tube through which the ferrofluid is displaced (mm)

\( \varvec{\rho}_{\varvec{c}} \) :

Vertical linear coil density (turns/mm)


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We thank Trevor Michelson for his assistance in 3D printing the parts and initiating the test setup.


This research was supported by Alfred State Applied Learning Program.

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Correspondence to Reza Rashidi.

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Martin, J., Rashidi, R. A differential transformer-based force sensor utilizing a magnetic fluid core. Microsyst Technol 27, 115–126 (2021). https://doi.org/10.1007/s00542-020-04923-5

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