## Exacting Solutions

Basic problems of permanent magnet design revolve around estimating the distribution of magnetic flux in a magnetic circuit, which may include permanent magnets, air gaps, high permeability conduction elements and electrical currents. Exact solutions of magnetic fields require complex analysis of many factors. Although approximate solutions are possible based on certain simplifying assumptions, obtaining an optimum magnet design often involves experience and trade-offs.

### Finite Element Analysis

Magnetic Design has become a critical feature of Bunting-DuBois growth and we seek to work with our customers to realize their ideas. Finite Element Analysis (FEA) modeling programs are used to analyze magnetic problems in order to arrive at more exact solutions, which can then be tested and fine-tuned against a prototype of the magnetic structure. Using FEA models, flux densities, torques, and forces may be calculated. Results can be output in various forms, including plots of vector magnetic potentials, flux density maps, and flux path plots. Bunting-DuBois uses a suite of 2D and 3D transient FEA modeling packages backed-up with in house design software and many years experience, not just in magnetics but also in general engineering. This allows us to undertake a wide range of design contracts in many industries and many applications. The length of design contract ranges from a few hours to many days and we pride ourselves on the cost effectiveness of this service.

### The BH Curve

The basis of magnet design is the BH curve, or hysteresis loop, which characterizes each magnet material. This curve describes the cycling of a magnet in a closed circuit as it is brought to saturation, demagnetized, saturated in the opposite direction, and then demagnetized again under the influence of an external magnetic field.

The second quadrant of the BH curve, commonly referred to as the “Demagnetization Curve”, describes the conditions under which permanent magnets are used in practice. A permanent magnet will have a unique, static operating point if air-gap dimensions are fixed and if any adjacent fields are held constant. Otherwise, the operating point will move about the demagnetization curve, the manner of which must be accounted for in the design of the device.

The most important characteristics of the BH curve are the points at which it intersects the BH axes (Br – the residual induction and Hc – the coercive force) and the point at which the product of BH are at a maximum (BH max – the maximum energy product). Br represents the maximum flux the magnet is able to produce under closed circuit conditions. In actual useful operation permanent magnets can only approach this point. Hc represents the point at which the magnet becomes demagnetized under influence of an externally applied magnetic field. BH max represents the point at which the product of BH, and the energy density of the magnetic field into the air gap surrounding the magnet, is at a maximum. The higher this product, the smaller need be the volume of the magnet. Designs should also account for the variation of the BH curve with temperature.

Measurement of BH curves requires specialist equipment. The most common types are DC Hyteresis graphs (Permeameter) where the magnet is driven around its BH loop in a DC electromagnet with sensing coils to the measure the BH of the magnet. Bunting-DuBois has a temperature controlled permeameter which can BH curves at temperatures from ambient up to 150°C. We use this data to qualify our materials and to supply accurate material data for our design software.