The purpose of this section is to show how the energy and force equations can be applied to an actuator to determine the armature force. The reluctance actuator shown in Fig. 1.8a will be used for this discussion. The saturable iron regions of the actuator include the armature, which moves in the x direction, two stationary poles, and a coil core. The magnetic flux generally remains in the iron regions; however, it must cross air gap 1 and air gap 2 to reach the armature. Some of the magnetic flux finds alternative air paths which bypass the armature; these flux paths are called leakage flux paths. The air flux path shape and the reluctance equations are derived
FIGURE 1.8 (a) Actuator iron and air flux paths, and (b) equivalent reluctance network.
This completes the solution for the state of the magnetic field in the actuator. The x-direction force on the armature can now be determined by calculating the change in the magnetic coenergy as a function of armature displacement in the x-direction. The magnetic coenergy can be calculated for the entire actuator or for just the working air gaps.
Iron is a ferromagnetic material and by definition it has nonlinear magnetic properties. Therefore, the magnetic coenergy in each of the iron reluctances must be calculated by integrating the area under the B-H curve, as follows. The total magnetic coenergy in the iron is the summation of the iron coenergies.
