A least-squares diameter answers a statistical question: which circle follows the measured points most closely? Coil insertion asks a different question: can every part of the core pass through the available bore? A thin protruding sheet may have little influence on the fitted diameter and still stop the assembly.
Use the winding’s physical constraints to choose the measurement. If the coil is free to shift sideways at each section, a minimum enclosing circle can describe a section’s smallest possible circular envelope. If guides hold the winding on one axis, that freedom disappears. The required envelope must be measured around the actual insertion axis.
Three diameters, three meanings
| Reported quantity | What it represents | Important blind spot |
|---|---|---|
| Least-squares diameter | Average agreement with a fitted circle | Local peaks can lie outside it |
| Minimum enclosing diameter | Smallest circle containing a measured section | Its center may shift between heights |
| Diameter about the insertion axis | Twice the greatest measured radius from the constrained axis | Depends on reliable axis transfer |
Assumptions for this fit example: the core fitted diameter is 200.0 mm. One sheet projects to a radius of 101.0 mm from the intended axis. A rigid 201.0 mm bore has only a 100.5 mm radius. The average fit therefore looks acceptable while that sheet interferes by 0.5 mm radially. These dimensions demonstrate the geometry; they are not recommended production allowances.
Moving the fitted circle sideways might reduce the enclosing diameter. That correction is useful only if the winding can make the same movement. A fixture, insulating cylinder or another limb may prevent it.
Inspect the swept volume
Measure sections along the entire distance traveled by the bore. Keep the same datum axis for all sections, and preserve angular positions so that a protrusion can be located for correction. A series of independently centered circles can hide a bent limb because each fit follows its local center.
For an ideal cylindrical bore translated along a fixed straight axis, let r(z,θ) be the core radius in millimetres at height z and angle θ. Its geometric requirement is Rrequired = max r(z,θ). The available bore radius must exceed this value by the assembly allowance defined for that product. Measurement uncertainty and bore variation must be considered before making the fit decision.
Real stepped windings may have a changing internal profile. In that case, compare the core and bore at every insertion position, including temporary overlap with a shoulder. Checking only their final assembled positions can miss a restriction encountered halfway down.
Before reworking a core, locate the limiting point and confirm it with an independent measurement. A scanner reflection, a loose lamination or an incorrect axis registration can each create an apparent peak. Correct the cause that the assembly would actually meet. Replacing the maximum envelope with a more attractive average diameter leaves the interference in place.
Apply a single-sheet projection to the fixed-axis envelope
Use nominal 0.23 mm 23ZH90 thickness [1] for an assumed outward displacement of one sheet. Other assumptions: fitted section radius 100.00 mm, center offset 0.40 mm, bore radius 100.75 mm and required radial assembly allowance 0.20 mm. Limiting radius is 100.00 + 0.40 + 0.23 = 100.63 mm, leaving 0.12 mm. Without that projection the clearance would be 0.35 mm. The average diameter passes a size comparison but the full envelope misses the assumed allowance by 0.08 mm. Confirm the local peak and axis uncertainty [2] before rework; catalogue thickness is a displacement scale, not a projection specification.
Manufacturing controls. Cut widths, packet count, compression, protruding sheets and limb-axis straightness control the insertion envelope. A final check must retain the highest relevant point through the entire allowed coil trajectory.
References
- Nippon Steel Corporation, Grain-Oriented Electrical Steel Sheets, catalogue D004je_03_202004, 2020, Specifications; Size and Form Tolerances.
- JCGM, JCGM 100:2008, Evaluation of measurement data — Guide to the expression of uncertainty in measurement, 2008.