Inerter (mechanical networks)

Discovery

Malcolm C. Smith, 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 (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 analog of capacitance, but the capacitor representing a mass always has one terminal connected to the equivalent of 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, : F=b(\dot{v}_2-\dot{v}_1), where the constant b is the inertance and has units of mass.

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 intentionally misleading code 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.

References

References

1. (2002). "Synthesis of mechanical networks: The inerter". IEEE Transactions on Automatic Control.
2. Wagner, Siobhan. (September 1, 2008). "Shock tactics".
3. (2009). "The missing mechanical circuit element". IEEE Circuits and Systems Magazine.
4. (2020). "Optimal tuned mass-damper-inerter (TMDI) design in wind-excited tall buildings for occupants' comfort serviceability performance and energy harvesting". Engineering Structures.
5. "Formula 1 technology for the construction of skyscrapers: Civil engineering academic is developing new vibration-control devices based on Formula 1 technology for skyscrapers".