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. Under the name of J-damper the concept has been used in Formula 1 racing car suspension systems.
It can be constructed with a flywheel mounted on a rack and pinion. It has a similar effect to increasing the inertia of the sprung object.

Discovery

, a control engineering professor at the University of Cambridge, first introduced inerters in a 2002 paper. Smith 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 and flywheels.
The generated strength satisfies the equation
for a suitable constant b.

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.

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.
Researchers are developing new vibration-control devices based on inerters to build high-rise skyscrapers which can withstand high winds.