# Viscoelastic Dampers for Rotors: Modeling and Validation at Component and System Level
## 2 Viscoelastic Model Identification  
### Machine for Testing Operations  
In rotordynamics, the adoption of elastomeric dampers interposed between the bearings and the non-rotating part of the machine is a common practice [8; 9]. Two different layouts of the suspension can be adopted, as illustrated in Figure 1. The first (a) exploits a viscoelastic ring (5) press-fitted directly between the stator (1) and the external part of the ball bearing (4), while in the second one (b), the viscoelastic material (5) is molded between two metallic supports (2), the external is screwed on the stator while the internal is press-fitted on the ball bearing. In the first configuration, the friction between the rubber and the bearing modifies the axial preload of the bearing in an uncontrolled way, and hence the radial stiffness of the suspension. In the second configuration, this problem is not present since no relative displacement between the viscoelastic element (5) and its metallic supports (2) occurs. The preload of the bearing can be provided in a predictable way by installing the two metallic supports of the rubber with a small misalignment along the axial direction of the suspension. The configuration installed in the machine that is considered in this paper exploits the layout (b). Although the presented solution appears simple and reliable, the viscoelastic nature of elastomers imposes to perform experimental identification of the damper to predict its behavior at design stage at varying operation frequencies and applied static loads. To this end, a dedicated machine (Figure 2) has been designed and realized to simulate the forces acting on rotors in working conditions, providing profiles simulating the synchronous excitation due to the unbalance. Figure 1: Layout of the suspension. (**a**) Viscoelastic element (square-ring) press-fitted directly between the stator and the ball bearing. (**b**) Viscoelastic element molded between two annular elements. The internal element is press-fitted on the rotor, while the external one is screwed on the stator. (1) Stator of the machine. (2) Damper metallic supports. (3) Shaft. (4) Ball bearing. (5) Viscoelastic section. Figure 2: (**a**) Picture of the machine. (**b**) View from top. (1) Actuators. (2) Displacement sensors. (3) Damper support. (4) Body of the machine. A couple of orthogonal linear voice coils allow to provide a rotating force vector simply driving the actuators in order to generate two sinusoidal forces with the same amplitude and the same frequency, but with a phase-lag of 90 degrees between them. In principle, this layout permits to also perform a linear characterization if one-directional measures are requested. In addition to being used in the design phase to characterize elastomer mechanical parameters at the component level, the rig, whose maximum excitation frequency is 1.5 kHz equivalent to a spin speed of 90,000 rpm, can be exploited to perform tests concerning the reliability and durability of the supports in working conditions. The machine is designed to be installed on a seismic mass ((10) in Figure 3). The main steel structure is composed of an external body (9) on which the static parts of the actuators (3) are installed. The mobile part of the voice coils (1) is connected to the external support of the damper (11) with a screw (4), and is supported by a collet (2) to guarantee a good alignment of the actuation direction. The internal support of the damper (12) is screwed in the main body. Two eddy current displacement sensors (14) are adopted to detect the relative movement between the internal and the external part of the damper in order to evaluate its traction and compression. The two actuators, whose current-force coefficient is 37 N/A, can exert a maximum force of 200 N with an excitation frequency ranging from 0 to 1500 Hz. They are supplied with a DC (Direct Current) voltage of 30 V at a maximum current of 5 A.