# A Hybrid Vibration Isolator Based on Elastomeric and Electromagnetic Restoring Force
## 2 Description of the Isolation System  
The proposed isolation system consists of a combination of a passive and an active vibration control system.  
The isolator (Figure 2) comprises two plates between which are placed (i) four ball transfer units (BTU), placed at the vertices of the plates (Figure 3), to sustain the vertical load, allowing the plates to have relative horizontal motion with low friction; (ii) two elastomeric pads providing a viscoelastic restoring force; (iii) three coils (C1, C2, C3) forming an electromagnetic actuator providing a force whose magnitude and direction depend on the supply current. Figure 3 shows a three-dimensional scheme of the lower plate with the Oxyz reference frame adopted to define the relative position between the plates. This prototype allows the behavior of the isolator to be studied in the case of relative motion of the plates in the x direction, but it is easy to define a construction scheme that allows the isolator to operate along any direction of the horizontal plane xy.  
Figure 2: Vibration isolator scheme.  
Each BTU support consists of a large load-bearing ball that sits on many smaller balls encapsulated in a semi-spherical cup; the model (Ominitrack 9520) adopted for the isolator prototype has a load capacity of 1880 N. This type of BTU is characterized by the presence of a Belleville spring between the main ball and the external case of the BTU so that, above the vertical load of 1880 N, the main ball retracts into the case. This peculiarity prevents the isolator from working if the mass to be isolated is excessive, as large inertia forces would involve excessive relative horizontal displacements between the isolator plates, damaging the elastomeric pads. The adoption of four BTUs gives the system greater stability against overturning, and although the system is overdetermined, the presence of the spring between the case and the main ball allows each BTU to collaborate in supporting the vertical load unless there are any detachments between the main balls and the rolling surface. Due to the presence of the BTUs, the elastomeric pads are slightly loaded by the weight of the structure, and they can be sized only considering their transversal stiffness and the shear load arising from the horizontal plates' relative motion. The pads adopted for the prototype have a cylindrical shape (\(\phi\)50 \(\times\) 30 mm) and are in silicon rubber; a first approximation of the transversal stiffness is evaluated considering only its elastic shear stiffness, defined as \(k=GA_{t}/h\), where \(G\) is the shear modulus, equal to about 1.75 \(\times\) 10\({}^{5}\) N/m for the silicon rubber; \(A_{t}\) is the transversal circular area; and \(h\) is the height of the pad.  
The electromagnetic actuator comprises three coils equipped with a ferromagnetic core. The C3 coil is attached to the upper plate, and its position coincides with the origin of the \(x\)-axis when the pads are not deformed. Coils C1 and C2 are symmetrically arranged with respect to the yx plane. The variations in the current intensity versus the coil's windings allow the magnetic restoring force magnitude to be adjusted. The main characteristics of the coils are reported in Table 1.