Worst-case core flux comes from voltage, frequency and effective-area bounds that can occur together. Build those permitted combinations explicitly to identify the contribution that controls magnetic margin.
For sinusoidal excitation at fixed turns, B/B₀ = (V/V₀)(f₀/f)(A₀/A) [1]. Keep the denominator effects explicit; adding tolerance percentages is only an approximation.
Separate contributions before evaluating the joint case
The following example uses fictional bounds: voltage +3%, frequency −2%, effective area −1.5%, and nominal peak flux 1.60 T. It assumes these extremes are permitted simultaneously. They are not recommended operating allowances.
| Illustrative case | Flux multiplier | Peak flux |
|---|---|---|
| Voltage only | 1.0300 | 1.648 T |
| Frequency only | 1/0.98 = 1.0204 | 1.633 T |
| Area only | 1/0.985 = 1.0152 | 1.624 T |
| All three bounds together | 1.03/(0.98 × 0.985) = 1.0670 | 1.707 T |
Adding 3%, 2% and 1.5% would give 6.5%, whereas the joint ratio gives about 6.70%. That difference may matter when the candidate lies close to its constraint. More seriously, the entire corner case may be invalid if the supply specification couples voltage and frequency or a control system prevents that combination.
Use the permitted excitation envelope
List normal, exceptional and transient duties separately, including their durations and tap positions. Use the actual voltage across the energized winding and the turns active at that position. A nameplate line voltage entered as a phase-winding voltage creates a larger error than careful tolerance propagation can repair.
For a distorted voltage, calculate flux from the relevant voltage-time integral and initial conditions. The sinusoidal ratio is not a substitute for DC offset, transient energization or asymmetric excitation. Nor does a permitted average flux establish acceptable local joint flux.
Make the area bound physical
Use one consistent area account: sum net steel dimensions, or apply the relevant stacking factor to measured gross packet geometry. Do not apply the factor again to an area already corrected for non-steel space. Keep packet count, gauge, compression and measurement definitions consistent.
Use a bounded worst-case calculation when the specification requires every permitted corner to pass. Use a probability model only when its joint distributions and decision purpose are established. Uncertainty in a measured input is different from a permissible production range.
Use catalogue nominal gauge 0.23 mm [2], assumed to represent net steel thickness in this ledger. A 1,000-sheet schedule sums to 230.0 mm; missing ten sheets removes 2.3 mm and leaves 227.7 mm, or 0.99 of nominal area at unchanged width. With the stated voltage/frequency bounds, B = 1.60 × 1.03/(0.98 × 0.99) = 1.699 T. The separate 1.5% total-area bound gives 1.707 T. Establish whether missing-sheet effects are already included in that total before adding another deduction. Compare permitted joint corners with the actual excitation requirements and material-data coverage.
Sheet counting, gauge verification, packet placement and compression establish effective area. Preserve these records alongside the joint schedule; a gross envelope measurement alone does not establish the net magnetic section.
The contribution table then shows where design margin is being spent. If effective-area variation dominates the limiting case, purchasing more nominal margin may be less useful than stabilizing the packet build. If the voltage/frequency duty dominates, tighter steel dimensions alone cannot close the gap. The chosen remedy should act on the contribution that actually controls the constraint.
References
- U.S. Department of Energy, DOE-HDBK-1011/4-92, Electrical Science, Volume 4, 1992.
- Nippon Steel Corporation, Grain-Oriented Electrical Steel Sheets, catalogue D004je, April 2020, specification and typical-property tables.