Eddy Current Displacement Sensor
Theory: eddy currents oppose the coil's field
Overview
How does an eddy-current sensor measure shaft runout without touching the metal?
High-frequency current in the coil at the sensor tip produces an alternating field. Nearby metal carries eddy currents that oppose the changing field, and their field couples back into the coil. The closer the metal, the stronger the opposition and the lower the coil's inductance; reading that change electronically gives distance. At high frequency eddy currents flow only near the surface, so the metal acts like a mirror and can be modelled as an image coil carrying opposite current on the far side.
Skin depth
ρ is resistivity and μ_r relative permeability. Eddy currents flow in a layer about one skin depth thick; targets about three skin depths thick respond like thick plates.
Inductance by the image method
The coil is a 5 mm flat coil of 20 turns spread over radii 1.0–2.5 mm (wire radius 0.04 mm). Each turn is a circular loop; an image coil with opposite current sits at distance 2g beyond a target at gap g. The target is a perfect conductor (very small skin depth). Free-space inductance L₀ is 1.47 μH.
From rotating-machinery monitoring
Non-contact eddy-current displacement sensors came into wide use from the 1960s for monitoring shaft vibration in steam turbines and compressors. Shafts in fluid-film bearings move slightly within the bearing clearance, and non-contact sensors suited measuring that motion directly. Measuring shaft position within the clearance from two directions to trace an orbit is now fundamental to condition monitoring of rotating machinery.
Worked examples
Example 1: skin depth by material and frequency
| Material | 100 kHz | 1 MHz | Thickness needed at 1 MHz (3δ) |
|---|---|---|---|
| Aluminium | 0.259 mm | 0.082 mm | 0.25 mm |
| Copper | 0.206 mm | 0.065 mm | 0.20 mm |
| SUS304 | 1.350 mm | 0.427 mm | 1.28 mm |
| Carbon steel (μr 100) | 0.066 mm | 0.021 mm | 0.06 mm |
Example 2: gap, inductance and sensitivity (5 mm flat coil)
| Gap | Gap/diameter | L/L₀ | Sensitivity (μH/mm) | vs sensitivity at 0.1 mm |
|---|---|---|---|---|
| 0.1 mm | 0.02 | 0.165 | 2.52 | 100% |
| 0.25 mm | 0.05 | 0.378 | 1.73 | 69% |
| 0.5 mm | 0.10 | 0.602 | 1.00 | 40% |
| 1.0 mm | 0.20 | 0.819 | 0.39 | 15% |
| 1.5 mm | 0.30 | 0.908 | 0.17 | 7% |
| 2.0 mm | 0.40 | 0.948 | 0.08 | 3% |
| 3.0 mm | 0.60 | 0.980 | 0.03 | 1% |
Beyond 0.3 diameters the sensitivity drops below 10%.
A coil's field weakens sharply over distances comparable to its size. The image coil sits at twice the gap, so beyond a few tenths of a diameter the opposing effect barely reaches. Extending range therefore requires a larger coil, which needs a larger target and loses lateral resolution. The inductance–gap curve is also nonlinear, so raw output isn't linear; real sensors linearise electronically and calibrate on a specific target material. Changing material alters skin depth and permeability and hence the response, so recalibration is required.
Sensor design and analysis workflow
- Choose coil diameter (several times the range) from the required range.
- Choose frequency so target thickness exceeds about three skin depths.
- Compute impedance versus gap with axisymmetric electromagnetic analysis.
- Check effects of target size (about 3 diameters or more) and curvature.
- Evaluate temperature-dependent resistivity and nearby metal.
“Runout read larger than it was”
On a compressor, eddy-current runout readings were clearly larger than dial-gauge measurements. The sensor viewed the steel shaft surface directly, where microstructure and residual stress were uneven, so permeability and conductivity varied around the circumference. The sensor couldn't distinguish this from distance changes and reported it as apparent runout — a phenomenon called electrical runout. Grinding the target surface to even out the material condition reduced the apparent runout.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Reusing another material's calibration | Wrong distance | Calibrate per material |
| Target too thin | Sensitivity changes | At least 3δ thick |
| Target too small | Output drops | 3 diameters or more |
| Ignoring nearby metal | Mounting shifts output | Analyse as mounted |
| Electrical runout | Apparent runout | Treat the target surface |
I'd like to learn related topics.
Related pages include LVDT sensors, Hall-effect sensors, magnetoresistive sensors, search coils and Rogowski coils.
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