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Differential displacement and strain analysis of transmission line cables

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Abstract

This paper presents a strain analysis in transmission line cables caused by mechanical vibrations induced mainly by the wind action that can cause the fatigue rupture of the cable. The tests were performed on a test bench that consists of two spans of 9 and 12 m, respectively, and it was built using elements of transmission lines (suspension clamps, insulators, anchoring towers, etc.). The vibrations were generated by an electrodynamics shaker. Strains were measured by means of micro-electric strain gauges set in 04 wires of the cross-section of the cable at the vicinity of the suspension clamp, which presents severe levels of dynamic stresses. The cable bending amplitude was measured with two laser transducers. The bending amplitude was converted in strain with the Poffenberger-Swart equation. The comparison between the measured strain and that predicted theoretically showed RMS errors of 31 and 48 % for axial load levels of 20 and 30 % UTS, respectively.

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Abbreviations

a :

Horizontal distance of L1 laser transducer to the clamps’s centre of rotation, m

A :

Standarized distance of 89 mm from the last point of contact between the cable and the clamp

b :

Constant of integration

d :

Wire diameter, m

E :

Young modulus, N/m2

EI:

Bending stiffness, N m2

f :

Frequency, Hz

I :

Area moment of inertia, m4

j :

Stiffness parameter, m

k :

Bending curvature, 1/m

L :

Loop length, m

m :

Mass per unit length, kg/m

M :

Bending moment, N.m

M 0 :

Couple, N.m

n :

Sample size

n L :

Number of loops

S :

Span length, m

T :

Traction load, N

V t :

Travel wave velocity, m/s

V T :

Accurate travelling wave velocity, m/s

x :

Horizontal axis

y :

Deflection, m

y a :

Bending amplitude (peak to peak), m

y′′ :

Second derivatives of y, 1/m

w :

Ransverse load, N/m

Δβ :

Rotation angle, rad

Δ L1 :

Displacement measured with L1 laser transducer

Δ L2 :

Displacement measured with L2 laser transducer

ε:

Strain amplitude (zero to peak), m/m

λ:

Dimensionless parameter of Poffenberger-Swart equation

θ :

Rotation angle, rad

ϕ :

Dimensionless parameter of Poffenberger-Swart equation

a :

Relative to distance

L:

Relative to loop

t :

Relative to the travel wave velocity

T :

Relative to the accurate travelling wave velocity

0:

Relative to the maximum amplitude (w) or to a couple (M)

max:

Relative to maximum

min:

Relative to minimum

slip:

Relative to maximum friction stress which act on each wire

stick:

Relative to the situation when all wires stick together as a solid body

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Acknowledgments

The authors would like to thank CNPq—“Conselho Nacional de Desenvolvimento Científico e Tecnológico”, of the Brazilian Ministry for Science and Technology and ELETRONORTE—“Centrais Elétricas do Norte do Brasil” for the financial support provided.

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Authors and Affiliations

  1. Civil Engineering College, Federal University of Pará, Belém, Pará, 66075-110, Brazil

    Adriana Lima Rolim, Luis A. C. M. Veloso & Remo Magalhães de Souza

  2. Mechanical Engineering College, Federal University of Pará, Belém, Pará, 66075-110, Brazil

    Jouberson L. da R. Moreira

  3. Department of Mechanical Engineering, University of Brasília, Brasília, Distrito Federal, 70910-900, Brazil

    José Alexander Araújo

Authors
  1. Adriana Lima Rolim
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  2. Jouberson L. da R. Moreira
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  3. Luis A. C. M. Veloso
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  4. Remo Magalhães de Souza
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  5. José Alexander Araújo
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Correspondence to Adriana Lima Rolim.

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Technical Editor: Paulo Varoto.

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Rolim, A.L., Moreira, J.L.R., Veloso, L.A.C.M. et al. Differential displacement and strain analysis of transmission line cables. J Braz. Soc. Mech. Sci. Eng. 35, 327–336 (2013). https://doi.org/10.1007/s40430-013-0026-x

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  • DOI: https://doi.org/10.1007/s40430-013-0026-x

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