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 and flywheels.

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

^ Smith, M. C. (2002). "Synthesis of mechanical networks: The inerter". IEEE Transactions on Automatic Control. 47 (10): 1648–1662. doi:10.1109/TAC.2002.803532.
^ Chen, M.; Papageorgiou, C.; Scheibe, F.; Wang, F. C.; Smith, M. (2009). "The missing mechanical circuit element". IEEE Circuits and Systems Magazine. 9: 10–26. doi:10.1109/MCAS.2008.931738.

External links

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

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[1] Smith, M. C. (2002). "Synthesis of mechanical networks: The inerter". IEEE Transactions on Automatic Control. 47 (10): 1648–1662. 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: 10–26. doi:10.1109/MCAS.2008.931738.

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