Experimental Testing and Analysis of Inerter Devices

This paper presents a first in-depth experimental study of mechanical devices that are designed to approximate the dynamics of the ideal inerter, which is a two-terminal mechanical element analogous to the ungrounded capacitor. The focus of the paper is experimental testing and identification of stand-alone inerter devices as well as the study of practical issues involved in their feedback control using standard hydraulic damper test rigs. Two contrasting inerter embodiments are studied, one in which a flywheel is driven by a rack-and-pinion mechanism and the other employing a ballscrew. Due to the fact that the ideal inerter is a dynamic element whose admittance function is 90 deg out of phase with that of the ideal damper, particular attention is needed to ensure closed-loop stability in testing using standard hydraulic damper test rigs. As expected, instability is observed in default configurations, and it is seen to manifest itself in a nonlinear manner with backlash playing a significant role. By using a basic model of the hydraulic rig and a model of an ideal inerter with backlash, the nature of the instability is reproduced and explained in a qualitative way. To achieve closed-loop stability without the need to redesign the controller as a function of the load, a methodology is proposed involving the design of a mechanical buffer network to be connected in series with the inerter device. It is demonstrated that this approach removes the instability problem for a wide range of inertance loads. Finally, the dynamic characteristics of the inerter devices are identified. It is verified experimentally that the admittance of the devices approaches the ideal inerter admittance over a useful frequency range and that friction in the devices is a major source of deviation from the ideal inerter behavior.