Residual magnetic flux density (Br), commonly known as remanence, is one of the most critical parameters defining the performance of permanent magnet materials. Residual magnetic flux density testing measures the magnetization retained by a material after an external saturating field is removed, providing essential data for magnet selection, quality control, and design verification. This article explains the technical principles, applicable standards, sample requirements, testing methods, and typical applications of Br measurement for permanent magnet materials.
Technical Overview
Residual magnetic flux density, denoted as Br, is defined as the magnetic flux density remaining in a ferromagnetic material when the externally applied magnetizing field strength H is reduced to zero after the material has been saturated. On the hysteresis loop of a permanent magnet material, Br corresponds to the intersection of the normal magnetization curve with the B axis (at H = 0). Together with coercivity (HcB and HcJ) and the maximum energy product (BHmax), Br constitutes the fundamental set of magnetic properties used to grade and classify permanent magnet materials.
A higher Br value generally indicates that a magnet can produce a stronger magnetic field in a given circuit geometry, directly influencing the torque density of electric motors, the sensitivity of sensors, and the efficiency of magnetic assemblies. Accurate Br measurement is therefore essential for incoming material inspection, production quality control, lot acceptance testing, and failure analysis in industries relying on permanent magnets.
The measurement of Br is governed by internationally recognized standards, including IEC 60404-5 (measurement of magnetic properties of permanent magnet materials in a closed magnetic circuit), ASTM A977/A977M (test method for magnetic properties of high-coercivity permanent magnet materials using hysteresisgraph techniques), and GB/T 3217 for the Chinese market. Accredited third-party laboratories typically perform Br testing with calibrated hysteresisgraphs, permeameters, vibrating sample magnetometers (VSM), or fluxmeter–Helmholtz coil systems, with measurement uncertainties typically within ±1% to ±2% for closed-circuit measurements.
Testing Samples
Sintered Neodymium-Iron-Boron (NdFeB) Magnets
Sintered NdFeB magnets exhibit the highest Br values among commercial permanent magnets, typically ranging from approximately 1.0 T to 1.5 T depending on the grade. Test specimens are usually machined into cylinders or rectangular blocks with dimensions suitable for closed-circuit measurement, and their surfaces are ground to ensure tight contact with the pole pieces of the measuring permeameter.
Sintered Samarium-Cobalt (SmCo) Magnets
SmCo magnets, including both SmCo5 and Sm2Co17 types, offer Br values typically between 0.85 T and 1.15 T combined with excellent thermal stability. These materials are frequently tested for aerospace, defense, and high-temperature applications where flux stability is critical.
Aluminum-Nickel-Cobalt (AlNiCo) Magnets
AlNiCo alloys provide moderate Br values, generally between 0.5 T and 1.3 T, with very low temperature coefficients of remanence. Because of their relatively low coercivity, AlNiCo samples must be handled carefully during testing, and measurement after magnetization must avoid demagnetizing influences.
Hard Ferrite (Ceramic) Magnets
Sintered hard ferrite magnets based on barium or strontium hexaferrite exhibit Br values typically between 0.2 T and 0.45 T. Their low cost makes them high-volume test articles, and lot sampling plans are commonly applied in production inspection.
Bonded and Injection-Molded Magnets
Bonded magnets, which combine magnetic powders (NdFeB or ferrite) with polymer binders, show Br values typically between 0.1 T and 0.7 T depending on the loading fraction. Because isotropic bonded NdFeB can be magnetized into complex multipole patterns, Br verification is often performed on ring or arc-shaped samples using specialized fixtures.
Soft Magnetic Materials (Remanence Verification)
Certain applications, such as relays, electromagnets, and demagnetization-sensitive instruments, require verification that soft magnetic components (e.g., electrical steel, pure iron) retain minimal residual induction after demagnetization. Testing of residual induction in soft magnetic materials is conducted according to IEC 60404-4 and related methods using ring specimens or Epstein frame measurements.
Testing Items
A comprehensive residual magnetic flux density test report typically includes the following measured and derived parameters:
- Residual magnetic flux density Br (mT or T): the primary measured quantity, determined at the zero-field intercept of the hysteresis loop after saturation.
- Normal coercivity HcB (kA/m): the field strength at which the magnetic flux density B in the material falls to zero.
- Intrinsic coercivity HcJ (kA/m): the reverse field at which the intrinsic magnetization is fully cancelled, a key indicator of thermal and demagnetization stability.
- Maximum energy product BHmax (kJ/m³): the peak value of the B·H product on the demagnetization curve, representing the energy available in a magnetic circuit.
- Complete demagnetization curve (second-quadrant B–H and J–H curves): provided for design engineers performing finite-element simulation and circuit optimization.
- Recoil permeability μrec: the effective slope of the recoil line, relevant for dynamic operating conditions.
- Temperature coefficients of Br (α) and HcJ (β): determined by measuring Br and HcJ at elevated temperatures, typically 80 °C, 100 °C, 120 °C, 150 °C, or 180 °C.
- Magnetic flux or magnetic moment: measured open-circuit using a fluxmeter with a search coil or Helmholtz coil for acceptance testing of finished magnet components.
- Surface flux density mapping: performed with a calibrated Hall probe to verify flux distribution and pole geometry on finished parts.
Testing Methods
Closed-Circuit Hysteresisgraph Method (IEC 60404-5, ASTM A977)
The reference method for Br determination uses an electromagnet-based hysteresisgraph with a B-coil and H-coil (or H-sensing devices such as Hall sensors or a surrounding magnetizing coil). The specimen, machined to a standardized geometry with a length-to-diameter ratio appropriate for uniform magnetization, is placed between the pole pieces of an electromagnet to form a closed magnetic circuit. The specimen is first saturated with a pulsed or continuous field, after which the field is cycled to trace the complete hysteresis loop. Br is extracted at H = 0 from the second quadrant of the measured loop. This method provides the highest accuracy for Br, with typical uncertainties below ±1%, and is applicable to materials with intrinsic coercivity up to approximately 2000 kA/m when suitable magnetizing field sources are available.
Vibrating Sample Magnetometer (VSM) Method
The VSM method measures the magnetic moment of a small specimen (typically a few millimeters in size) vibrating in a detection coil set within a controlled applied field. The measured moment is converted to magnetization and, subsequently, to flux density using the specimen volume. VSM measurements offer high sensitivity and are suitable for research, grade verification of high-coercivity materials, and temperature-dependent studies. Because the measurement is performed in an open-circuit configuration, corrections for the self-demagnetizing field must be applied, and the specimen geometry must be accurately determined to minimize volume-related uncertainty.
Fluxmeter with Helmholtz Coil (Open-Circuit Method)
For production acceptance testing of finished magnets, a fluxmeter connected to a Helmholtz coil measures the total magnetic moment of a fully magnetized sample. The sample is withdrawn from or rotated within the coil, and the integrated induced voltage yields the magnetic flux. When the sample geometry and material permeability are known, the moment measurement can be related to Br. This method is fast, non-destructive, and well suited to statistical lot inspection, although it does not provide the full demagnetization curve.
Pulsed Field Magnetometer (PFM) Method
High-coercivity grades of NdFeB and SmCo may require magnetizing fields exceeding 4000 kA/m, beyond the capability of conventional electromagnets. Pulsed field magnetometers apply capacitor-driven pulsed fields of up to several megamperes per meter and record the dynamic hysteresis loop with calibrated inductive sensors. Eddy-current effects in electrically conductive specimens must be corrected for, and IEC TR 62976 addresses the qualification of pulsed field magnetometers for permanent magnet testing.
Surface Field Mapping with Hall Probe
For finished components and magnetic assemblies, a calibrated Hall effect probe measures the flux density at defined points or scans the surface to generate a field map. While not a direct Br measurement, this method verifies that the assembled product delivers the expected field, accounting for circuit geometry, magnetization pattern, and any demagnetizing effects from assembly.
Sample Preparation and Measurement Conditions
Reliable Br measurement requires that the specimen be fully saturated before measurement; an insufficient magnetizing field will yield an artificially low apparent Br. Specimen surfaces must be flat and parallel to minimize air gaps in closed-circuit measurements. Tests are normally performed at a reference temperature of 23 °C ± 5 °C, and the ambient temperature must be recorded since Br decreases with temperature at a rate of roughly −0.11%/°C to −0.13%/°C for NdFeB materials. Demagnetized handling, clean pole faces, and calibrated reference magnets are essential elements of a valid measurement chain.
Applications
Residual magnetic flux density testing supports a wide range of industries and product categories:
- Traction and auxiliary motors for electric and hybrid vehicles, where Br directly determines torque output and efficiency.
- Wind turbine generators, in which large volumes of NdFeB magnets must meet lot-by-lot Br specifications for consistent output power.
- Industrial servo motors, stepper motors, and brushless DC motors for automation and robotics.
- Acoustic transducers, including loudspeakers, headphones, and microphones, where Br influences sensitivity and frequency response.
- Magnetic sensors, encoders, and Hall-effect devices requiring precisely controlled magnet strength.
- Magnetic assemblies, holding systems, magnetic couplings, and magnetic separators.
- Medical devices, including magnetic components for hearing aids, implantable devices, and MRI-related hardware.
- Aerospace and defense systems, where temperature coefficients of Br and long-term flux stability must be validated through elevated-temperature testing.
- Consumer electronics, such as magnetic closures, wireless charging alignment magnets, and actuator magnets.
- Quality disputes, lot rejection analysis, and failure investigations, where independent verification by accredited third-party laboratories provides authoritative measurement results.
FAQ
What is the difference between Br and surface flux density?
Br is an intrinsic material property measured inside a magnet under closed-circuit conditions at H = 0, whereas surface flux density is the external field measured at a specific distance from a magnetized part. Surface field depends on the magnet geometry, magnetization pattern, and operating point on the demagnetization curve, and it is always lower than Br for an isolated magnet due to the self-demagnetizing field.
Why does the measured Br value sometimes fall below the nominal grade value?
Common causes include incomplete saturation of the specimen, an unfavorable length-to-diameter ratio that increases the demagnetizing factor, air gaps between the specimen and pole pieces, temperature above the reference condition, or actual material non-conformity. Accredited third-party laboratories apply saturation verification and geometry corrections to distinguish measurement artifacts from genuine material deficiencies.
Which standards govern residual magnetic flux density testing?
The principal standards are IEC 60404-5 for closed-circuit measurement of permanent magnet materials, ASTM A977/A977M for high-coercivity materials using hysteresisgraph techniques, IEC TR 62976 for pulsed field magnetometers, and GB/T 3217 as the corresponding Chinese national standard. Soft magnetic residual induction is covered by IEC 60404-4 and related Epstein and ring-method standards.
Can finished magnets and assemblies be tested without cutting samples?
Yes. Open-circuit flux measurement with a Helmholtz coil and fluxmeter, together with Hall probe surface mapping, allows non-destructive testing of finished components and complete assemblies. These methods verify magnetic output at the product level and are widely used for outgoing inspection and statistical process control.
How is temperature dependence of Br evaluated?
Specimens are measured at the reference temperature and again at specified elevated temperatures using a temperature-controlled environment integrated with the hysteresisgraph or VSM. The temperature coefficient α(Br) is calculated as the relative change in Br per kelvin, and the irreversible flux loss at each temperature is also reported. This data is essential for selecting magnet grades for high-temperature operating environments.
What measurement uncertainty can be expected?
Closed-circuit hysteresisgraph measurements of Br on well-prepared specimens typically achieve expanded uncertainties of approximately ±1% to ±2% (k = 2). Open-circuit moment measurements and VSM results may exhibit slightly larger uncertainties depending on geometry determination, coil calibration, and demagnetization corrections. Laboratories accredited to ISO/IEC 17025 provide calibrated, traceable results with documented uncertainty budgets.
How should samples be submitted for Br testing?
Samples should be machined to standard closed-circuit geometries (such as 10 mm × 10 mm × 10 mm blocks or 10 mm diameter cylinders with appropriate length), with ground and parallel end faces. Samples may be submitted in the demagnetized or magnetized state; the laboratory will saturate the specimen prior to measurement. Detailed submission requirements, including sample quantity, dimensions, material grade, and requested test temperatures, should be confirmed with the testing laboratory in advance.