This article is concerned with the modeling of an electromechanical component using an equivalent circuit generated from magnetostatic simulations in CST EM STUDIO® (CST EMS). CST DESIGN STUDIO™ (CST DS) is then used to simulate the coupled electric circuit and mechanical dynamics.
This approach is highly efficient since the circuit analysis takes just a few seconds, allowing optimization to be performed on the system level. A full 3D transient analysis is costly in terms of time, especially when the complexity of the system increases. For this system, CST DS is sufficient. For more complex systems, specialist tools may be applied in the same manner. Synopsys® Saber offers look-up tables which can be used to import the CST EMS data.
The method has been applied to the simulation of a simple solenoid system with a mass, spring and hard stop. ...
Figure 1 shows an animation of the field lines as a function of the solenoid plunger displacement. The forces and the flux linkage are stored as a function of coil current and plunger position (co-energy and inductance are also available). The solenoid was simulated with the CST EMS 2D axisymmetric magnetostatic solver. Although the geometry is constructed in 3D, the user can determine whether the model is simulated in 2D or 3D - material data, excitation and boundary conditions are consistent between the models. Non-linear BH materials are used in the solenoid.
A simple Look-Up Table (LUT) approach has been applied to allow the flux linkage and force data, obtained from parametric magnetostatic analysis, to be used in the circuit simulation. Analogies  based on voltage = position and current = force allow the modeling of mechanical components and effects. Standard spice components can be used to model mechanical hard-stops (switches), gravity by current sources etc.
Typical results are shown in figure 3. The analogy taken in this simulation leads to the position being described by the voltage. The current in the coil shows the characteristic dip typical in solenoid and actuator devices.
Further time-dependent data is also available such as force, velocity, inductance etc.
For such dynamic simulations, a combination of CST DS and CST EMS may be applied under the assumption that eddy currents may be neglected. In that case, this approach may be still modified to estimate the effect of the eddy currents on the performance of the device. The technique may also be extended to model other effects (in MEMS for example).
This method is not new but still offers the advantage of efficiently solving such problems without recourse to lengthy transient simulations.
 H. Tilmans, "Equivalent circuit representation of electromechanical transducers I Lumped-parameter systems",J. Micromech. Microeng. 6 (1996) 157–176.