A kinematic hysteresis model for an overhead transmission lines anti-galloping damper

Аuthors

Danilin A. N.^1*, Kuznetsova E. L.^2**, Kurdumov N. N.^2***, Shalashilin A. D.¹

1. Institute of Applied Mechanics of Russian Academy of Science, IAM RAS, 32a, Leninskii av., Moscow, В-334, GSP-1, 119991, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: andanilin@yandex.ru
**e-mail: vida_ku@mail.ru
***e-mail: nick.n.kurdyumov@gmail.com

Abstract

Torsional Damper and Detuner (TDD) is a mechanism for detuning and attenuation of low- frequency oscillations of OHL conductors galloping. The oscillation energy is dissipated in the damping unit (DU), which represents a structure of two disks interconnected by the joint revolution axis and an ensemble of viscous-elastic elements, which react in relative rotation of disks. One of disks is a leader and is connected to the phase conductors via a rigid frame. Another disk is a follower and is connected to the balancing lever of pendulum type.

A mathematic model of TDD functionality is developed for selection of geometric, mass and viscous- elastic parameters enabling the effective operation of the device in the frequency range 0.1-0.4 Hz. This model takes into account the hysteretic type of power dissipation appropriate to the type of DU under consideration.

The process of hysteretic deformation of viscous-elastic elements due to their displacement inside DU is of extreme complexity and cannot be subject to a rigorous mathematic description. That is why the approximate methods are traditionally employed making use of experimental data. One of approaches consists in substitution of hysteresis by viscous-elastic deformation using the tension-compression diagrams of the

elastoplastic samples and a logarithmic decrement of vibrations. Another possible approach consists in assignment a-priori of a diagram of deformation after a model of Drucker-Prager. According to this model, the hysteresis diagram is represented by a parallelogram inclined by a certain angle around its center. However, the use of such models may cause serious errors in selection of TDD structural parameters, since they do not take into account the shape and «size» of path along the deformation diagram which defines the stiffness of a damping unit and its transfer function.

In this work a cinematic model of hysteresis is suggested which relates upon the hysteresis diagram. According to it, the torque and relative angle of torsion are related one to another via a special differential equation of the first order, its coefficients being defined after experimental values for the limit hysteretic cycle. In this case one succeeds to describe, in a single equation, an infinite set of similar cycles; each of them is uniquely defined by a position of a starting point on a deformation diagram inside a limit cycle. Similarity of these curves is defined by their asymptotic approximation to the limit cycle curve. Such a model results in a natural definition of hysteretic cycle «orbital» under external harmonic action on DU.

Keywords:

mathematical modeling, kinematic model, galloping conductors, hysteresis, damping devices, dampers low-frequency oscillations

References

1. Bekmetev R.M., Zhakaev A.Sh., Shirinskikh N.V. Plyaska provodov vozdushnykh linii elektroperedachi (Dance ofoverhead power lines), Alma-Ata, Nauka Kazakhskoi SSR, 1979, 151р.
2. Glazunov A.A. Osnovy mekhanicheskoi chasti vozdushnykh linii elektroperedachi (Foundations ofthe mechanical part ofoverhead power lines), Moscow, Gosenergoizdat, 1956, vol.1, 192p.
3. Lilien Jean-Louis State of the art ofconductor galloping. Cigre: Task force B2.11.06, June 2007, 140p.
4. Lilien Jean-Louise, Vinogradov A.A. Patent WO2005117228, 08.12.2005.
   
5. Danilin A.N., Zakharov A.P. Mekhanika kompozit-sionnykh materialov i konstruktsii, 2008, vol.14, no4, pp. 604-622.
   
6. Danilin A.N., Shalashilin V.I. A method to identify hysteres is by an example of an antigalloping device, International Applied Mechanics, 2010, vol.46, no.5. pp. 588-595.
   
7. Danilin A.N., Kozlov K.S. Trudy IX vserossiiskoi nauchnoi konferentsiiim. Yu.I. Neimarka «Nelineinye kolebaniya mekhanicheskikh sistem», 24-29 September 2012, Nizhnii Novgorod, pp. 320-329.
   
8. Danilin A.N., Yanovsky Yu.G., Semenov N.A., Shalashilin A.D. Kinematic model of the rheological behavior of non-Newtonian fluids in conditions ofnonstationary cyclic loadin, Composites: Mechanics, Computations, Applications. An International Journal, 2012, vol.3, no.4, pp. 1-15.