This article demonstrates the workflow for the electromagnetic simulation of an industrial circuit breaker using CST EM STUDIO® (CST EMS). The circuit breaker simulation consists of calculating the current flow as a source for the magnetic field. The force resulting from the magnetic field is then calculated using the Maxwell Stress Tensor technique. Accurate force is assured by the application of automatic mesh adaption and higher order finite element basis functions. Non-linearity of materials is also taken into account. The Magnetostatic solver has been used to solve the problem. Furthermore, complex CAD models, already available in the design process, can be easily imported as well as modified for use in parametric analyses. In this case, a CATIA model was used.
Figure 1 shows a view of the imported CATIA (part or product files) model of the circuit breaker. No modifcations are required besides the removal of superfluous components (e.g. plastic). The model may be modified for either parametric analysis of air-gap position or geometrical parameters such as chamfers, coil widths etc.
The circuit consists of a bus bar conductor which twists around a magnetic plunger. Once the current exceeds a design value, the force on the plunger is large enough to trip the connected electric circuit. Springs and additional components not relevant to the electromagnetic calculation of the field and the force calculation are not included in this model.
Figure 2 shows the mesh and a contour plot of DC current flow in the conductor bar. The automatically pre-computed current is used as a source for the magnetostatic field computation.
Mesh adaption has been applied with some initial manual local mesh refinement.
DC current flow vectors in the conducting bus bar are shown in Figure 3.
The magnetic flux density from the magnetostatic simulation is shown in Figure 4. The complex 3D field path demonstrates the advantage of simulation for such a device. From this field distribution, the magnetic force on the armature and other components may be caclulated. The method of weighted Maxwell Stress Tensor (MST) is applied in CST EMS. As a check of the accuracy of the force, force monitors show the convergence of force with each mesh adaption pass. Other quantities such as (co-)energy, flux linkage and inductance (apparent and incremental) are automatically calculated.
The above procedure can be repeated to obtain data such as pull-out forces. Geometries, even imported ones, may be parameterized. In this model, a parameter has been defined representing the position of the armature relative to the stationary core component. The force is then extracted at each position to obtain the pull-out characteristic as shown in Figure 5.
The results of such simulations may be used to optimize the circuit on the magnetic level or on the system dynamics level. For more information about how the results can be incorporated in an electromechanical system please refer to  where a state-space model of a solenoid was generated for use in CST DESIGN STUDIO™ (CST DS).
3D EM Simulation can be efficiently applied to the simulation of electromechanical devices and provide useful information about the electromechanical behavior of a complex device which is difficult to analyze analytically and, consequently, to optimize. Data may be extracted for dynamic studies. The approach of characterizing a device on parametric magnetostatic analyses has advantages such as efficiency and the ability to rapidly generate a library of models which can be simply imported into a circuit simulator for dynamic studies.