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

Malcolm C. Smith, a control engineering professor at the University of Cambridge, first introduced inerters in a 2002 paper.^[1] Smith extended the analogy between electrical and mechanical networks (the mobility analogy). 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.

The generated strength satisfies the equation

$F=b(\dot{v}_2-\dot{v}_1)$,

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.^[2]

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

References

1. Smith, M. C. (2002). "Synthesis of mechanical networks: The inerter". IEEE Transactions on Automatic Control 47 (10): 1648. doi:10.1109/TAC.2002.803532.
2. Chen, M.; Papageorgiou, C.; Scheibe, F.; Wang, F. C.; Smith, M. (2009). "The missing mechanical circuit element". IEEE Circuits and Systems Magazine 9: 10. doi:10.1109/MCAS.2008.931738.

External links

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