Inerter (mechanical networks)

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In the study of

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. The analogy makes mass the analogy of capacitance, but the capacitor representing a mass always has one terminal connected to ground potential. In a real electrical network, capacitors can be connected between any two arbitrary potentials, they are not limited to ground. Noticing this, Smith set about finding a mechanical device that was a true analog of a capacitor. He found that he could construct such a device using gears and flywheels, one of several possible methods.

The constitutive equation is,

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

where the constant b is the

and has units of mass.

Construction

A linear inerter can be constructed by meshing a

. 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

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.[3]^[4]

See also

• Dashpot

References

External links

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