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Design Notes

Units and conversions of magnetic properties

• H, or coercive force is the magnetic field strength applied to the magnet as a magnetizing or demagnetizing field.  This is measured in Oersteds or kilo-Oersteds in cgs units, and in Amperes per meter or, more commonly, kilo-Amperes per meter in SI units.
• One Oersted is 4π kilo-Amperes per meter.
• To convert from Oer. to KA/m divide by 4π.
• B, or flux density, is the magnetic induction in the magnet, induced by the applied magnetizing or demagnetizing field.  It can be defined as the number of flux lines per unit area.  This is measured in Gauss or kilo-Gauss in cgs units, and in Tesla or milli-Tesla in SI units.
• One Tesla is 10,000 Gauss.
• To convert from KGauss to T, divide by 10.
• To convert from Gauss to mT, divide by 10.
• BHmax., or maximum energy product is the operating point on the normal demagnetization curve where the product of B and H is maximized, representing the optimum (most efficient) energy operating point.  This is measured in MGOe  or Mega Gauss Oersted in cgs units, and in KJoules/m3 in SI units.
• One MGOe is 100/4π  KJ/m3
• To convert from MGOe to KJ/m3, multiply by 100 and divide by 4π

Further units and conversions of magnetic properties
• Permeability, μ, is the relationship between B and H.  In cgs units, the permeability of a vacuum is 1 Gauss per Oersted.  In SI units, the permeability of a vacuum is 4π T per A/m
• Permeability is expressed as μ=B/H, or commonly as B= μH.
Recoil permeability, μr defines the slope of the demagnetization BH curve followed when an applied reverse field is removed.  The material properties will “recoil” to a new  reduced level along a slope defined by the recoil permeability.
• Magnetic flux, Φ , is the total number of lines, defined as B across the full area.
• More accurately, the mathematical relationship: Φ =  ∫ B ∙ dA
• In cgs units, flux is in Maxwells which is Gauss x cm2.  In SI units, flux is in Webers or Volt seconds
• One Weber or one volt second is 100,000,000 (108) Maxwells.
• Magnetic moment
• In cgs units, in a vacuum, B=H.  In SI units, B= 4πH.
• For this reason, cgs units are often considered easier for magnet design activity.
• The permeability and load lines are slopes which are more easily used in cgs with no 4π conversion .
• For use in motors or other circuits, SI units are often more appropriate, consistent with the the common design equations for these applications.

Explanation of BH, demagnetization, curves
• How to read a BH, or demagnetization curve
• The important part of the hysteresis curve is the second quadrant or demagnetization portion of the curve.  This is where virtually every permanent magnet operates in the application.
• Magnetization of the magnet occurs in the first quadrant.  Third and fourth quadrants are mirror images of the first and second quadrants respectively and only useful forlooking at full reversal effects with re-magnetized/reversed parts.
• There are typically two curves, a normal curve and intrinsic curve.
• The normal curve tells us what’s happening to the world due to the magnet.
• The intrinsic curve tells us what’s happening inside the magnet.
• The normal curve is B vs H and the intrinsic curve is J vs H, where J=B-H.
• The B vs. H curve is used to determining the amount of flux density contributed to the circuit.
• The J vs. H, or B-H vs. H, or intrinsic curve is used for determining the resistance to demagnetization.
• The operating point (Bd and Hd) is determined by the intersection of the demagnetization curve and the load line (Pc load line for the B or normal curve, Pcj or dynamic load line for the J or intrinsic curve).  Bd is the flux density provided to the circuit.
• Pc is calculated from the dimensions of the magnet and relationship with the magnetic circuit defined as a slope of B/H and is always negative.  The “minus” is often dropped in discussion of load lines, but it is there.
• Pcj=Pc-1 with Pc always a negative number.  This can be derived from the relationship between B and J (J=B-H).
• When analyzing the effects of an applied reverse field, Pcj is shifted to the left by the magnitude of the applied field.
• When the intersection of Pcj and the intrinsic curve starts to go over the knee, we have significant permanent losses of flux density and consequent performance degradation.

Properties learned from BH, demagnetization, curves
• Br is the intersection of the demagnetization curves and the B or vertical axis.  (Both curves intersect at the same point.)
• At Br the magnet is producing the highest flux density it can with no field applied, in a fully closed circuit.
• Hc or Hcb, or normal coercivity, is the intersection of the normal, BH curve, with the H or horizontal axis.
• If a demagnetization field is applied to Hcb, the normal curve will read zero flux density, but if the reversal is removed it will recoil to something less than Br, recoiling parallel to the normal curve at Br.
• Hcj or Hci, or intrinsic coercivity, is the intersection of the intrinsic, J curve (B-H vs H curve), with the H or horizontal axis.
• If a demagnetization field is applied to Hcj, the magnet is completely demagnetized and will remain at zero if the reversal is removed.
• At Hcj, the normal curve is in the third quadrant so actually the normal curve recoils as above, recoiling to zero B.
• Energy product or BHmax is the product of B and H at the point of the normal curve where this product maximizes.
• This property is considered a figure of merit, indicating the amount of energy the material is capable of providing in an optimized circuit.

Temperature effects on BH, demagnetization, curves
• In all permanent magnet materials, flux density has a negative relationship with temperature.
• The relationship is defined as Alpha, expressed as % per degree C and is dependent on the material.
• For Nd2Fe14B materials, Alpha is close to -0.10 % / degree C, (0.08% to 0.11%) with higher Hcj materials having somewhat better Alpha than the lower Hcj materials.
• In Nd2Fe14B materials, coercivity also has a negative relationship with temperature.
• The relationship is defined as Beta, expressed as % per degree C and is also dependent on the material.
• Beta ranges from -0.37 % to -0.65 %, with highest Hcj materials having significantly better Beta than the lower Hcj materials.
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