Inerter (mechanical networks)
File:Inerter vibration isolation experiment.webm 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. 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,
- [math]\displaystyle{ F=b(\dot{v}_2-\dot{v}_1) }[/math],
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 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.
Researchers are developing new vibration-control devices based on inerters to build high-rise skyscrapers which can withstand high winds.[3][4]
See also
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. http://ntur.lib.ntu.edu.tw/bitstream/246246/223082/1/906.pdf.
- ↑ Petrini, Francesco; Giaralis, Agathoklis; Wang, Zixiao (2020). "Optimal tuned mass-damper-inerter (TMDI) design in wind-excited tall buildings for occupants' comfort serviceability performance and energy harvesting" (in en). Engineering Structures 204: 109904. doi:10.1016/j.engstruct.2019.109904. Bibcode: 2020EngSt.20409904P. https://openaccess.city.ac.uk/id/eprint/23199/1/Petrini_Giaralis_Wang_ES_2019_Authors%27%20version.pdf.
- ↑ "Formula 1 technology for the construction of skyscrapers: Civil engineering academic is developing new vibration-control devices based on Formula 1 technology for skyscrapers" (in en). https://www.sciencedaily.com/releases/2019/12/191209131952.htm.
External links
- The Inerter Concept and Its Applications, lecture notes
- J-dampers in Formula 1
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