# Viscoelastic Dampers for Rotors: Modeling and Validation at Component and System Level
## 1 Introduction  
Vibrations in mechanical structures are typically caused by structural issues like effects of the material fatigue damage and wear, and are the cause of loss of performance and reliability. In rotordynamics, these negative consequences are emphasized and strongly influence and constrain most of the design phases. Vibrations in rotating machines can be induced by the unavoidable presence of unbalance giving rise to synchronous vibrations in the vicinity of critical speeds. This phenomenon is strictly dependent on the quality of balancing, spin speed, and the presence of damping. It imposes implementing vibration control techniques that can be chosen among a wide range of technologies, according to the application requirements. In aerospace, the adoption of squeeze film dampers (SFD) is common practice. They are very effective in reducing the response for the moderate range of residual unbalance expected from the rotor balancing process and are self-sufficient and robust in the event ofhigh unbalance levels [1]. However, their performance is affected by vibration frequency, engine oil temperature, supply pressure, and thermal growth of the bearing housing. In the oil and gas industry, and in aerospace, solutions based on active/semi-active hydraulic systems, electrorheological [1; 2], and magnetorheological [2] solutions have been proposed for the adaptation of the damping force to the operating conditions. However, these devices cannot avoid drawbacks related to the aging of the fluid and to the tuning that is required for compensating the temperature and frequency effects. Among other technologies, magnetic bearings and dampers witnessed a steady growth in applications, like vacuum pumps, compressors for air conditioning, turbo-compressors in oil and gas industry, turbines for energy recovery, and storage, such as kinetic energy storage systems (KESS) and compressed air energy storage (CAES) [3; 4; 5; 6]. They allow for contactless operation and lack the need of lubrication and oil supply systems. Although attractive, this technology still presents shortcomings related to size and costs. Viscoelastic dampers represent an effective and low-cost solution in high speed applications like turbo-molecular pumps and machine tool spindles or in industrial sectors like automotive, where the construction of engine mounts, torsional dampers and shock absorbers is based on the adoption of these components. Nevertheless, although compact and efficient, the frequency and temperature dependency of the material parameters makes the rotordynamic behavior of the machines equipped with viscoelastic supports hard to predict at design stage [7]. Currently, the design of elastomeric dampers is mainly based on a trial-and-error approach, but a more rigorous method is often required to know exactly the behavior of the supports in operating conditions and to achieve design refinement and performance optimization in terms of vibrations amplitude, unbalance response reduction, and critical speeds tuning. The objective of this paper is to propose a methodology to identify the behavior of viscoelastic dampers and to predict the rotordynamic behavior of shafts supported by them. The technique is based on a preliminary experimental characterization at the component level of the supports by means of a dedicated test rig allowing the replication of the unbalance synchronous excitation by means of two orthogonal actuators. The transfer functions measured between the force of the actuator and the traction or compression generated on the elastomer permits to obtain the behavior of the supports along the whole spin speed range in the form of complex stiffness. Afterwards, the parameters of the reference model adopted to represent the dampers are identified, according to the experimental results by means of a Genetic Algorithm (GA).