Inerter (mechanical networks)

In the study of mechanical networks in control theory, an inerter is a two-terminal device in which the forces applied at the terminals are equal, opposite, and proportional to relative acceleration between the nodes. The generated strength satisfies the equation

$F=b({\dot {v}}_{2}-{\dot {v}}_{1})$,

for a suitable constant b.

Malcolm C. Smith first introduced inerters in a 2002 paper; a similar device was demonstrated in 1998 by a Polish engineer Lucianus Lagiewka and used in automobile bumper application but the principle and design are the same: kinetic energy absorbing system that can be used as a bumper or as vibration absorber - the device was a public knowledge since 1998. Smith is a control engineering professor at the University of Cambridge. He extended the analogy between electrical and mechanical networks. He observed that the analogy was incomplete, since it was missing a mechanical device playing the same role as an electrical capacitor. It was found that it is possible to construct such a device using gears.

Applications

Shortly after its discovery, the inerter principle was used under the name of J-damper in the suspension systems of Formula 1 racing cars. When tuned to the natural oscillation frequencies of the tires, the inerter reduced the mechanical load on the suspension. McLaren Mercedes began using a J-damper in early 2005, and Renault shortly thereafter.

J-dampers were at the center of the 2007 Formula One espionage controversy which arose when Phil Mackereth left McLaren for Renault.

Construction

A linear inerter can be constructed by meshing a flywheel with a rack gear. The pivot of the flywheel forms one terminal of the device, and the rack gear forms the other.

A rotational inerter can be constructed by meshing a flywheel with the ring gear of a differential. The side gears of the differential form the two terminals.

References

• The Inerter Concept and Its Applications, lecture notes.
• J-dampers in Formula 1