# CST – Computer Simulation Technology

## CST EM STUDIO and SIMULINK for the Dynamic Simulation of a Two-state Linear Actuator for an Automated Gear Box

This article shows a common approach to the simulation of electromechanical problems. A parametric set of 3D magnetostatic simulations are carried out using CST EM STUDIO® (CST EMS) on a linear actuator in order to obtain its electromagnetic characteristics for use in SIMULINK® where both the electrical and dynamic performance can be obtained i.e. coupling with mechanical system: spring, damping, etc. and coupling with external circuit with a rectangular voltage waveform.

This weakly-coupled approach has the advantage that the electromagnetic simulation time is short and the speed of circuit simulation lends itself well to system parameterization and optimization. Furthermore, strongly-coupled field simulator approaches require much longer simulation times meaning that parametric analysis is not efficiently and rapidly carried out....

Several formulations are available depending on the state variables required [1] - energy/co-energy, flux linkage etc versus current and position. In this example, look-up tables of flux linkage and force against current and position are used for the dynamic analysis. The energy/co-energy approach is also possible in CST EMS.

CST EMS and SIMULINK® Models obtained with the permission and courtesy of Professor Aldo Canova, Politechnico Torino.

Figure 1: CST EMS Model of the two-state actuator

Figure 1 shows the geometry of the linear actuator for an automated gear box which consists of a stator, a moving cursor and two excitation coils.

Figure 2: Magnetic flux density for coil 1 excitation only

Shown in figure 2 is the magnetic flux density for the case with just one coil excited. This represents one of the states of the excitation as defined in figure 5 below.

Figure 3: Coupled electro-mechanical system

In addition to the EM model of the actuator, the electrical supply (coils) and mechanical (load) parts of the complete system are shown in figure 3. Two equations are solved, two electrical and one mechanical. These components of the system can be arbitrarily defined.

Figure 4: SIMULINK® model of the actuator system

CST EMS results are transferred to the SIMULINK® via look-up tables, shown in Figure 4, which contain the flux-linkage and force as a function of coil current and position.

Figure 5: Spring characteristic and coil voltage excitations

Figure 5 shows the piecewise non-linear characteristic used to simulate the spring (force versus displacement) and the excitation signals for the coils (voltage versus time).

Figure 6: Coil currents versus time obtained from the SIMULINK® model

Figure 6 shows the parameters for the external system, the electrical coil excitations and the piecewise approximation used for the spring.

Figure 7: SIMULINK® results of the force, position and speed versus time

The position of the cursor as a function of time resulting from the dynamic analysis is shown figure 7. The time for the cursor to switch from the central position to the upper and lower (final) position is 50 ms.

This article has served to demonstrate the possibility to perform a dynamic system analysis of an electromechanical device with the aid of a 3D EM simulation to characterise the electromagnetic behaviour in terms of flux linkages and forces. In many cases, a weakly-coupled approach is satisfactory provided that the eddy curents can be neglected. Even in this instance, techniques exist where the effect of eddy currents can be accounted for in the system model.

References

[1] E. Melgoza, D. Rodger, "Comparison of table Models of Electromagnetic Actuators", IEEE Trans. Magnetics, Vol. 38, No. 2, March 2002.