Design and modelling of a fluid inerter

This article was downloaded by: [Beihang University]

On: 13 March 2014, At: 23:20

Publisher: Taylor & Francis

Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

International Journal of Control

Publication details, including instructions for authors and subscription information:

/loi/tcon20

Design and modelling of a fluid inerter

S. J. Swift a , M. C. Smith a , A. R. Glover b , C. Papageorgiou a , B. Gartner c & N. E.

Houghton a

a Department of Engineering , University of Cambridge , Cambridge , CB2 1PZ , UK

b McLaren Automotive , Chertsey Road, Woking, Surrey , GU21 4YH , UK

c Penske Racing Shocks , 150 Franklin Street, Box 1056, Reading , PA , 19603 , USA

Accepted author version posted online: 18 Sep 2013.Published online: 14 Nov 2013.

PLEASE SCROLL DOWN FOR ARTICLE

International Journal of Control ,2013

V ol.86,No.11,2035–2051,/10.1080/00207179.2013.842263

Design and modelling of a fluid inerter

S.J.Swift a ,M.C.Smith a ,∗,A.R.Glover b ,C.Papageorgiou a ,B.Gartner c and N.E.Houghton a

a

Department of Engineering,University of Cambridge,Cambridge,CB21PZ,UK;b McLaren Automotive,Chertsey Road,W oking,

Surrey,GU214YH,UK;c Penske Racing Shocks,150Franklin Street,Box 1056,Reading,P A 19603,USA

(Received 6January 2013;accepted 4September 2013)

Mechanical spring-damper network performance can often be improved by the inclusion of a third passive component called the inerter.This ideally has the characteristic that the force at the terminals is directly proportional to the relative acceleration between them.The fluid inerter presented here has advantages over mechanical ball screw devices in terms of simplicity of design.Furthermore,it can be readily adapted to implement various passive network layouts.Variable orifices and valves can be included to provide series or parallel damping.Test data from prototypes with helical tubes have been compared with models to investigate parasitic damping effects of the fluid.Keywords:design;modelling;control;mechanical device;inerter

1.Introduction

In Smith (2002),an ideal mechanical modelling element called the inerter was introduced with the property that the applied force at the terminals is directly proportional to the relative acceleration between them.Embodiments using a rack,pinion and gears,ball screw or gear pump driving a flywheel were described in Smith (2001).Such devices have been successfully used in Formula 1race cars where they have been given the name ‘J-damper’(Chen,Papageorgiou,Scheibe,Wang,&Smith,2009).It was also shown in Smith (2002)that general passive mechan-ical impedances can be realised using mechanical circuits comprising springs,dampers and inerters only.This re-port describes a new inerter implementation (Gartner &Smith,2010;Glover,Smith,Houghton,&Long,2009)which uses the mass of a fluid flowing through a heli-cal channel to provide the inertance.Durability and sim-plicity are the main advantages of this new implementa-tion,with additional benefits from the straightforward ad-dition of flow restrictions to incorporate series or parallel damping effects into the device.This paper presents the mechanical design of the new implementation and some variants and investigates their modelling and experimental behaviour.

A schematic diagram of the new implementation is shown in Figure 1.The cylinder body and the piston rod are the two device terminals,their relative motion driving fluid through the helical channel.The channel fluid velocity is scaled up from the piston velocity by the ratio of the areas of the channel and the piston.Thus,the device inertance can be increased by reducing the area of the channel or

∗

Corresponding author.Email:mcs@

increasing the area of the piston,both of which increase the fluid velocity for a given rate of strut movement.

Prototypes have been constructed with tightly wound helical channels inside the piston head and alternatively outside the piston cylinder.This first type results in a slim design which is relatively long due to the length of the pis-ton head,the latter style has a shorter and wider shape with a larger helix diameter.These have been used in experiments with low and medium viscosity automotive oils to deter-mine frequency response,parasitic damping and inertance.The parasitic damping is due to viscous effects in the fluid which act to resist the flow through the channel.This be-haviour appears to be well modelled by a damper in parallel with the inertance where the damping force is proportional to a power of the piston velocity which is a little less than 2.Increasing the helix diameter reduces the parasitic damping due to channel curvature,and hence this paper will focus upon designs using an external-helical channel.2.Fluid inerter modelling

Consider a piston and cylinder driving fluid through a he-lical tube surrounding the cylinder,as shown in Figure 1.Let A 1be the annular area of the main cylinder,namely the working area of the piston face.Let A 2be the channel cross-sectional area, be the channel length and ρbe the fluid density.Let F be the equal and opposite force applied to the terminals and x be the relative displacement between them.An ideal inerter is described by the following equation:

F =b ¨x,

(1)

C 2013Taylor &Francis

D o w n l o a d e d b y [B e i h a n g U n i v e r s i t y ] a t 23:20 13 M a r c h 2014