**By R. Belmans**

**The overall term coupled problems considers** the coupled fields and in addition includes the coupling of methods as well. The link between different methods, hybrid methods, to solve a field problem, for example using the combination of finite element and boundary element method, is understood as a coupled problem.

**Fig. 6.2. Material mesh of end-ring and bar-ends and coil meshes of the stator end-winding of an induction machine.**

**Or the classical analytical** machine theory delivers models that can be combined with a numerical technique in order to form an overall coupled model of higher accuracy. For example the computation of end-winding effects, using a three-dimensional FEM model, to extract the parameters for an equivalent circuit model, can be seen as an approach of coupled models as well (Fig. 6.2). With respect to computational efforts, for example for dynamic simulations of motor models or observer models for the machine control, the coupling of those methods is advantageous to obtain an accurate but simple overall model of the machine.

Observing problems in the transient modelling of relative motion of machine parts such as in a rotating motor, a possible solution of this modelling problem can be a coupling of geometries by element types with special properties. Overlapping shape functions can be used to join different meshes of a FEM model and this can be understood as a coupled problem.

**A further example of this type of problem**, the coupling of measurements with a numerical model, can be given. The basic idea in this type of problem is to measure inaccessible parameters and to use them as input for the numerical field computation. Such parameters are mainly non-linearly dependent on the field quantities and their interdependency from them is unknown. For example material data obtained by measurements are approximated by interpolating polynoms and can be used in this numerical format for the field computations. Look-up tables with measured data samples are possible as well.