## 2 Hybrid Vibration Isolation System
### Electromagnetic Actuator  
As the active actuator of the hybrid vibration isolation system, the electromagnetic actuator is mainly composed of a copper coil wound in the stator core along the axial direction, with the mover embedded with a permanent magnet and C-type stator core. Figure 4: Curve of the lateral stiffness and thickness of the adhesive layer. Figure 3: Partial sectional view of the hybrid vibration isolation system. Permanent magnets are embedded axially in the upper and lower ends of the mover core, as shown in Figure 5 below. Their N poles are radially outward. The working principle of the electromagnetic actuator is shown in Figure 6. When an alternating current is applied to the coil, an alternating magnetic field is induced in the C-shaped area according to the electromagnetic induction principle. This turns the stator core into an electromagnet with alternating N and S poles at both ends. The two poles of the stator core are attracted or repelled by the permanent magnets embedded at both ends of the mover, which output alternating axial electromagnetic force between the mover and the stator. In addition, in order to reduce the eddy current loss, the mover yoke and the stator yoke are provided with radial slots, with a structure shown in Figure 7, to reduce the eddy current loss generated when the actuator is excited by a high-frequency current, as well as to improve the magnitude and linearity of the output force. The relationship between the electromagnetic force and structural parameters was further studied. Using COMSOL Multiphysics, a two-dimensional electromagnetic simulation was carried out on the electromagnetic actuator. Arbitrary screenshots were selected to draw the structure, add materials (the mover and stator cores were made of DWSi3  
Figure 5: Three-dimensional sectional view of the electromagnetic actuator. Figure 6: Schematic diagram of the electromagnetic actuator. silicon steel, which is a soft magnetic material, and the permanent magnet was made of N50 Ru-Fe-B, which has strong remanence), select the magnetic field interface to set the boundary conditions (the strength of the remanence and direction of the permanent magnet, the number of coil turns, the diameter of the coil, etc. ), divide the grids and set the frequency-domain study. The magnetic induction intensity nephograms, output curves under different frequency domains and different current inputs were obtained, as shown in the following Figures 8 and 9. As can be seen from Figure 8, the skin effect becomes increasingly obvious with the increase in the current frequency under the same current amplitude. In the meantime, the magnetic flux in the stator yoke increased and approached magnetic saturation along with the increase in the current. As can be seen from the lines in Figure 9, at a constant frequency, although the electromagnetic force generated per unit current gradually decreased due to the magnetic saturation limitation of the magnetic conductive material as the current increased, the current was basically in direct proportion to the output of the actuator under the condition of a nonhigh current. When the current is constant, because of the eddy current loss, the electromagnetic force output will decrease with the increase in frequency. But as the mover yoke and the stator yoke are provided with radial slots, this can effectively reduce the eddy current losses. In summary, this meets the design requirements. After the basic geometric parameters and material parameters were determined using the two-dimensional electromagnetic simulation, the structure was modeled and simulated with three-dimensional electromagnetic-mechanical multifield coupling using JMAG 17.1 software. After the modeling was completed, the material parameters and boundary conditions were also set (the materials of the permanent magnet were radially magnetized, the materials of the stator and the mover were added and the coils were set), and then the permanent magnet, mover ring, stator core, air gap and air domain were meshed.