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Research Papers

Experimental Testing and Analysis of Inerter Devices

[+] Author and Article Information
Christos Papageorgiou

 Red Bull Technology Ltd., Building 1, Bradbourne Drive, Tilbrook, Milton Keynes MK7 8BJ, UKchristos.papageorgiou@redbulltechnology.com

Neil E. Houghton

Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UKneh27@eng.cam.ac.uk

Malcolm C. Smith

Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UKmcs@eng.cam.ac.uk

J. Dyn. Sys., Meas., Control 131(1), 011001 (Dec 04, 2008) (11 pages) doi:10.1115/1.3023120 History: Received November 21, 2005; Revised August 07, 2008; Published December 04, 2008

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.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 2

Schematic of the rack-and-pinion inerter

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Figure 3

Schematic of the ballscrew inerter

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Figure 4

Simple closed-loop system for the hydraulic test rig

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Figure 5

The effect of an increasing load mass on T0(s) (left) and on sP(s) (right) with controller K1

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Figure 18

Comparison of force signals recorded with and without the buffer under a sinusoidal excitation in the displacement of 4 Hz, 11 Hz, and 20 Hz

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Figure 19

The admittance of the ballscrew inerter (left) and the load (right) with different flywheels

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Figure 20

The admittance of the rack-and-pinion inerter with different flywheels

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Figure 21

Comparison of the friction effect in the two inerter devices

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Figure 22

Diagram of the closed-loop system for the hydraulic test rig

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Figure 23

The effect of the increasing load mass on the return-ratio transfer function

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Figure 24

The effect of the increasing load mass on the closed-loop transfer function T0(s)

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Figure 1

Rack-and-pinion inerter (left) and ballscrew inerter (right) partially disassembled

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Figure 14

The explanation of the spiking characteristic on the inerter force in terms of the backlash angle

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Figure 15

Qualitative comparison of theoretical and experimental forces through the rack-and-pinion inerter at f=3 Hz

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Figure 16

Mechanical buffer network for testing inerter devices (left) and its implementation (right)

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Figure 17

Theoretical comparison of the load admittance Y(s) with the inerter admittance

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Figure 6

The spiking characteristic is observed in the force measurement under closed-loop testing

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Figure 7

The effect of the controller gain on the spiking characteristic

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Figure 8

Nonlinear instability when testing the ballscrew inerter

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Figure 9

Schematic of the backlash model

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Figure 10

The inerter with the backlash model

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Figure 11

Comparison of the experimental and theoretical forces through the rack-and-pinion inerter under a step excitation in the displacement of 0.4 mm

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Figure 12

Open-loop simulation of the inerter model with backlash

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Figure 13

Qualitative comparison of theoretical and experimental forces through the rack-and-pinion inerter at f=0.5 Hz

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