A winding that meets one corner of a core window may be encountering a narrow opening. It may also be encountering an opening with the correct nominal width that has sheared sideways. Those conditions require different corrections.
Measure corresponding corners and edges at a common height and in a common coordinate plane. Mixing the front upper corner with the rear lower corner introduces three-dimensional twist into what is supposed to be a planar squareness check.
Separate size from shear
Represent an idealized window as a parallelogram. Let its bottom edge be the vector a = (w, 0), and its side edge be b = (s, h), all in millimetres. Here w is the horizontal width, h the vertical rise, and s the horizontal shift of the upper edge.
The diagonals are a + b and a − b. Their squared lengths differ by 4ws. Therefore s = (d₁² − d₂²)/(4w), with the sign determined by which diagonal is labeled first. This is a geometric estimate of racking under the parallelogram assumption, not a universal formula for an irregular window.
For example, a positive s means the upper edge has moved sideways relative to the lower edge. Increasing w will not remove that shear. It may make the opening larger while preserving the corner interference.
| Measured pattern | Likely geometric interpretation | Additional check |
|---|---|---|
| Both widths low, corresponding sides parallel | Opening too narrow | Confirm the required winding envelope |
| Upper edge shifted, opposite sides parallel | Parallelogram racking | Compare diagonal-derived shift with corner coordinates |
| Widths differ with height | Taper or nonparallel sides | Map the edge positions through height |
| Front and rear maps differ | Twist or local surface displacement | Measure the three-dimensional opening |
Why equal diagonals are insufficient
An isosceles trapezoid can have equal diagonals while its sides are not perpendicular to its bases. A window with local inward bow can also retain nearly equal corner-to-corner distances. Diagonals provide a useful cross-check; they do not replace edge geometry.
Fit the intended winding envelope into the measured opening using the allowed assembly pose. A rectangular winding cannot necessarily follow a sheared parallelogram even when its nominal width and height appear adequate. Insulation thickness, temporary assembly supports and insertion movement can further restrict the usable space.
Before adjusting clamps or restacking, compare the shape under the specified measurement condition. Changing support pressure can change corner coordinates, so a free stack and a clamped stack should not be treated as the same geometry. Record the state alongside the measurements.
If the corner coordinates and diagonal calculation disagree beyond their uncertainties, inspect the measurement definition first. The diagonals may have been taken between different edge peaks, or the window may simply be too irregular for the parallelogram approximation. Use its measured boundary for the fit decision instead of forcing the opening into a convenient four-number description.
Keep stock-width variation separate from window shear
The catalogue width tolerance for 300 mm wide, 0.23 mm stock is 0/−0.3 mm [1]. Assume an ideal planar frame with 1,100 mm outside width, two opposed 300 mm limbs, 800 mm window height and upper-edge shift s = 2.00 mm. Ignoring other build terms, window width ranges from 500.0 to 500.6 mm. At w = 500 mm, the diagonals are √(502² + 800²) = 944.460 mm and √(498² + 800²) = 942.340 mm. Their squared difference divided by 4w recovers 2.00 mm. An assumed 1.00 mm permitted shear is exceeded, even though width remains 500 mm. Verify corner correspondence and uncertainty [2], then correct the racking mechanism; the 0.6 mm width range from stock tolerance cannot remove the shear.
Manufacturing controls. Joint alignment, packet seating, yoke squareness, supports and clamp sequence control window shear. Record front and rear maps separately so twist cannot masquerade as planar racking.
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.