By R. Belmans Introduction An original design and the step by step optimization of physical technical devices is in practice often a trial and error process. During the design and construction of a device several expensive prototypes have to be built to monitor and check the mathematical approximations and the physical reality. This procedure is [...]

# Numerical Modelling and Design of Electrical Machines and Devices

## Finite element based CAD systems (Electrical Machine)

By R. Belmans Computer aided design in magnetics For designing and constructing electromagnetic devices an accurate knowledge of the field quantities inside the magnetic circuit is necessary. In many cases the air gap is of particular importance (e.g. motors, switches, relays, contactors, actuators). Here the conversion from elcctrical to mechanical energy and vice versa takes [...]

## Design strategies (Electrical Machine)

By R. Belmans The development and design of electromagnetic devices reflects a complex process. Originating from an initial idea, the construction runs through different phases. This procedure is terminated when a final concept is selected and considered to be designed, subject to various targets and constraints. As a whole, the task of the design engineer [...]

## Quasi stationary fields (Electrical Machine)

By R. Belmans Electromagnetic fields The notation and basic laws of the electric and magnetic fields are explained in this section. It is not intended to present the complete electromagnetic field theory. Only a limited set is given, necessary to understand the types of physical problems treated in this topic, enabling the modelling of technical [...]

## Boundary value problem (Electrical Machine)

By R. Belmans Many scientific engineering or physical problems lead to boundary value problems. The describing differential equations have to be solved in a volume satisfying particular conditions on its boundary T (Fig. 3.2). Therefore, the definition of a boundary value problem is necessary and evident. The proper definition of a numerical model is important [...]

## Field equations in partial differential form (Electrical Machine)

By R. Belmans Every electromagnetic phenomenon can be attributed to the seven basic equations, the four Maxwell equations of the electro-dynamic and those equations of the materials. The latter can be • isotropic or an-isotropic • linear or non-linear • homogenous or non-homogenous. The Maxwell equations are linked by interface conditions. Together with the material [...]

## Magnetic vector potential (Electrical Machine)

By R. Belmans Potentials and formulations The Maxwell equations represent the physical properties of the fields. To solve them, mainly the differential form of the equations and mathematical functions, the potentials, satisfying the Maxwell equations, are used. The proper choice of a potential depends on the type of field problem. In this section, the various [...]

## Electric vector potential for conducting current (Electrical Machine)

By R. Belmans For the calculation of eddy current problems the electric vector potential is often employed. The current density fulfils the zero divergence condition. Therefore, and analogous to A, an electric vector potential T can be defined:

## Electro-static scalar potential (Electrical Machine)

By R. Belmans By using the vector identityi can be rewritten: The negative sign is arbitrary and applied to have a close similarity to the definition of the magnetic scalar potential. Employing E to eq.(iv), (3.29) yields: This is an equation of the Poisson type.

## Magnetic scalar potential (Electrical Machine)

By R. Belmans By analogy to the electric field, the magnetic field strength is calculated as the gradient of a scalar potential. It must be distinguished between current-carrying and current-free regions. Current-free regions The magneto-static problem without conducting currents can be formulated in terms of the magnetic scalar potential With the vector identityand Ampere’s law, [...]