Dr. Foerster Codebreaker Series: Understanding the Fill-Factor Offset

For this codebreaking session, refer to Figure 1.

Figure 1

• Fill Factor (η): Defined as η= , it expresses the ratio of the test-object diameter (d) to the coil diameter (D).

• Vector OB: Represents the constant offset 1−η contributed by the empty-coil (air-ring) region.

• Vector BA: Represents the scaled contribution ημeff from the material itself.

For η = 1 (full fill), OB = 0 and the locus in Figure 1 directly coincides with the μeff curve. For η = 0.5, the entire trajectory is shifted along the real axis by 0.5 and scaled by 0.5, illustrating both amplitude reduction and phase alteration.

How μeff Traces Reveal Test Frequency Effects

As the test frequency f varies relative to the limit frequency fg (where μeff starts to drop significantly), the point A in Figure 1 moves along the curve:

• Low f/fg (<1): μeff is close to unity; A lies near the top of the curve (minimal eddy-current shielding, deeper penetration).

• High f/fg (>1): μeff falls and acquires an imaginary component; A spirals inward, indicating surface-dominated currents and increased phase lag.

Comparing the η=1 and η=0.5 traces shows that partial fill not only reduces magnitude but also compresses the phase excursion, affecting defect-sizing accuracy unless compensated.

Key Lessons from Figure 1

1. Maximize η Wherever Possible:

   Full coil coupling (η≈1) yields the largest signal swing and broadest phase sensitivity, making small defects easier to detect.

2. Interpret Signal Offsets:

   A static real-axis shift (OB) indicates fill-factor effects rather than material changes—recognizing this prevents misclassifying geometric variations as defects.

3. Frequency-Selective Testing:

   By choosing f/fg appropriately (e.g., high f/fg for surface cracks, low f/fg for subsurface), the μeff trajectory emphasizes the defect signature while minimizing unwanted geometry or conductivity responses.

   
   

Applying These Insights Today

• Digital Probe Calibration: Modern ECT instruments can auto-calculate the fill-factor offset and apply software corrections so that the on-screen signal corresponds directly to μeff rather than P.

• Finite Element Modeling (FEM): Replacing old mercury models, FEM lets engineers simulate various η scenarios, predicting exactly how P will move in the complex plane for a given coil/test object setup .

• Custom Coil Design: For small-diameter tubes, designing coils with reduced D or specialized secondary-winding geometries helps recover η closer to unity without mechanical contact, improving signal-to-noise.

• Differential Arrangements: By using paired probes or bridge circuits that share the same fill-factor offset, common-mode shifts (OB) are canceled, isolating the η μeff component that carries defect information .

Practical Recommendations

1. Inventory Your Coils: Check the outside diameters for each probe and calculate η. Tag coils with η values so that operators select the optimal coil for each job.

2. Verify appropriate test frequency for each material (for optimal detection AND phase spread): Use formula or slide rule.

3. Phase-Rotation Tuning: Adjust instrument phase so that the fill-factor offset lies on one axis, allowing defect signals (perpendicular components) to be read on the orthogonal axis with minimal interference (think F90).

   
   

By mastering the interpretation of Figure 1’s fill-factor effects, ECT practitioners can fine-tune both coil selection and test frequencies to maximize defect sensitivity while suppressing geometry-induced noise. Share your own experiences with coil fill factors in the comments below, and subscribe for more practical tips on advanced eddy current testing techniques!