NdFeB Magnet Air Gap Flux Density: Design Targets, Grade Selection, and Measurement

Introduction

Grade datasheets report remanence (Br) under closed-circuit, zero-gap conditions. The number that actually drives torque, back-EMF, and winding design is air gap flux density - the flux density the magnet delivers once a real air gap, stator iron, and leakage paths are in the circuit. The gap between the datasheet Br and the in-service air gap flux density is governed by the permeance coefficient (Pc) of the magnetic circuit, and it is where most preliminary motor sizing goes wrong. This guide sets out how to translate an air gap flux density target into a grade decision, how temperature shifts that target, and how to verify the result in production.

1. What Air Gap Flux Density Actually Controls in Motor Design

Air gap flux density - the magnetic field in the physical gap between rotor magnet and stator iron - is the single most load-bearing number in a permanent magnet motor. It determines torque constant, back-EMF, core loss, and how much copper current you need to hit a given torque target. Get it wrong by 15% and your winding design is off, your thermal model is off, and your efficiency map looks nothing like the prototype.

Br (remanence) from the magnet datasheet is not the same thing as air gap flux density. Br is a material property measured under closed-circuit, zero-gap conditions. The moment you open a physical air gap, flux density drops - and how much it drops depends on magnet geometry, air gap length, leakage paths, and the stator iron's saturation behavior. Treating Br as a proxy for air gap flux density is the most common mistake in preliminary motor sizing, and it consistently produces optimistic torque estimates.

2. The Permeance Coefficient and Why It Drives Grade Selection

The operating point of a magnet in a circuit is defined by the permeance coefficient Pc - the ratio of magnet length to the effective gap it drives flux across. For most radial-flux BLDC rotors with concentrated windings, Pc falls between 3 and 8 in no-load conditions. Under load, the stator field demagnetizes the magnet, pushing the operating point lower. The load line intersection with the B-H curve gives the actual flux density the magnet delivers.

At Pc = 5 with no leakage, a grade N45 magnet (Br ≈ 1.33 T) delivers roughly 1.1–1.15 T in the magnet itself. After accounting for the fringing and leakage losses typical in real laminated stators, air gap flux density lands around 0.85–0.95 T. For a small BLDC motor targeting 0.9 T in the gap, N45 is a reasonable match. Upgrading to N52 (Br ≈ 1.45 T) gains you about 0.06–0.08 T in the gap - real but modest. In a compact motor where the magnet volume is already constrained, that difference matters.

3. Matching Grade to Gap Target: A Practical Decision Table

The table below maps common design targets to NdFeB grades, assuming Pc ≈ 4–6 and a typical laminated stator. These are starting points, not substitutes for FEA.

If your air gap flux density target is 0.70–0.80 T: N35 or N38 covers it. This range is common in cost-sensitive fans, pumps, and small appliance motors where magnet cost is a dominant constraint. Using N45 here wastes money and creates a risk of over-magnetizing your stator iron into saturation.

For 0.80–0.90 T: N42 or N45 is the standard choice. Most mid-range industrial BLDC and PMSM motors land here. N42H adds thermal headroom to 120°C without changing the room-temperature flux significantly.

For 0.90–1.00 T: N48 or N50. You're into high-performance servo territory. Magnet thickness typically increases to sustain a higher operating point. At this level, assembly tolerances on the air gap become critical - a 0.05 mm variation in gap length produces about 1.5–2% variation in flux density.

Above 1.00 T: N52 in small, thermally benign applications only. N52 is borderline for most industrial use - its Hcj is lower than N45H, so resistance to demagnetization under overcurrent or elevated temperature is worse. Using N52 in a motor that sees 80°C windings and field-weakening operation is a field-failure waiting to happen. HIMAGNET regularly advises customers to size down from N52 to N48H or N45SH in applications where peak temperature and peak current overlap.

4. Temperature Effects on Air Gap Flux Density

NdFeB remanence decreases with temperature at approximately −0.11 to −0.12%/°C for standard grades. Over a 100°C operating range - say, 20°C cold start to 120°C steady-state rotor magnet temperature - Br drops by roughly 11–12%. That means a motor designed for 0.90 T at 20°C is producing closer to 0.79–0.80 T at operating temperature. If your torque constant calculation was based on the cold value, your motor will run ~11% short of torque at steady state.

The correct approach is to specify the air gap flux density at the maximum expected magnet temperature, then back-calculate the room-temperature grade needed. For a target of 0.88 T at 100°C magnet temperature, you need a grade delivering approximately 0.98–1.00 T at 20°C under the same operating point - which points to N48 or N50, not N45. This is a systematic error in many motor datasheets that specify "N45" without qualifying the measurement temperature.

Switching to an H or SH suffix grade does not increase room-temperature flux - it increases coercivity (Hcj) to resist demagnetization at elevated temperature. If your operating temperature is below 100°C and you're not field-weakening, the Hcj of standard N45 is adequate and there's no magnetic reason to pay the premium for N45H.

5. Measuring Air Gap Flux Density in Production

Flux density in the air gap can be measured directly with a Hall probe on an assembled rotor, or inferred from a flux measurement on individual magnets plus a circuit model. Both approaches have tradeoffs.

Direct Hall probe measurement in the gap is accurate for the specific assembly measured but requires the motor to be at least partially assembled. It catches assembly variations - incorrect magnet thickness, rotor skew, glue line variation - that part-level measurement misses. For high-volume production, 100% in-gap measurement is impractical; sample-based inspection with tight incoming magnet Br control is the standard approach.

For incoming magnet inspection, a flux measurement on a calibrated fixture (measuring total flux or peak surface field) is more repeatable than a Hall probe reading, because it averages over the magnet face. The fixture must be calibrated against magnets with known Br, and the correlation to in-motor air gap flux density must be established empirically for each motor geometry. Correlation factors of 0.75–0.85 between fixture surface field and in-motor air gap density are typical for segmented arc magnets in BLDC rotors.

6. Grade Selection Checklist Before You Specify

Before locking a grade on a drawing, verify these five points. Each one has caused production problems when skipped.

First: what is the maximum magnet surface temperature in worst-case duty, not just at ambient? Use thermal simulation or measurement - not an estimate based on winding temperature alone, because the gap between winding and magnet temperature is motor-design-specific and can be 20–40°C in high-slot-fill designs.

Second: what is the minimum Pc in the circuit under maximum demagnetizing current? This is the load-line intersection that determines whether the magnet operates above or below its knee. If the operating point under field weakening drops below the knee for your chosen grade, irreversible demagnetization occurs and the motor's characteristics shift permanently.

Third: is the air gap length controlled tightly enough that a reasonable Cpk on gap tolerance won't create more than ±3% variation in flux density? If not, tighten the tolerance before upgrading the magnet grade.

Fourth: does the stator iron have adequate Bsat margin at the target air gap flux density? Going from 0.85 T to 0.95 T in the gap can saturate a poorly designed tooth, eliminating much of the torque gain and adding iron loss.

Fifth: is the cost premium of N48 or N50 justified by the torque density gain, or can the same torque be achieved with N45 and slightly larger magnets? In production quantities above 10,000 units, the grade-cost difference often exceeds the tooling cost of a slightly larger rotor pocket. HIMAGNET's engineering team can run a comparison on your geometry - contact us with your motor OD, stack length, and torque target.

How HIMAGNET Supports Air Gap Flux Density Specification

HIMAGNET provides magnet performance data, including full demagnetization curves at multiple temperatures (20°C, 60°C, 100°C, 120°C, 150°C depending on grade), so customers can run load-line and operating-point analysis without starting from a blank datasheet. For custom motor programs, our engineering team reviews circuit geometry - magnet length, air gap, and stator configuration - to confirm the grade selection meets the target air gap flux density at the specified operating temperature before the design is locked.

If you have a target air gap flux density, operating temperature, and motor geometry, contact HIMAGNET with your specifications for a grade selection review.