Cables

Question 1

What are the main problems related to the conductors wind induced motion?

Answer 1

1) Aeolian Vibrations
2) Wake induced oscillations or subspans oscillations
3) Galloping

Question 2

What are aeolian vibrations?

Answer 2

Aeolian vibrations or vortex induced oscillations are due to vortex shedding from the conductors and can produce fatigue failures of the conductors themselves.

Question 3

What are subspan oscillations?

Answer 3

Subspan oscillations occur on conductor bundles. When the wind blows on the bundle, some sub-conductor may be in the wake of another, so sub conductors can be excited by the wake effect.

Question 4

What is galloping?

Answer 4

Galloping is a kind of instability due to the unstable shape assumed by the conductors when they are covered with ice. This phenomenon can cause failures of the conductor fitting and of the tower components.

Question 5

When does vortex shedding occur?

Answer 5

Vortex sheddding occurs in bluff bodies, or in any case, when there is flow or boundary layer separation. The BL produces vorticity and as a consequence, oscillating vortices arise behind the object.

The vortex shedding from the body exerts a periodic force on the body itself and if the associated frequency is close to that of the body natural frequencies, the body starts to oscillate.

Vortex shedding frequency: Fs = St V/D, where D is the Strouhal number.

Τhe amplitude is limited and the maximum is equaal to the cylinder diameter.

Question 6

Why are there alternating forces?

Answer 6

In the case of a static cylinder and the incoming flow velocity, almost three quarter of the cilinder is subjected to a negative pressure, the negative pressure peak position moving from one side to the other as the vortices are formed. This fluctuating pressure results into mean and alternating loads.

Question 7

What is the lock-in and synchronization range?

Answer 7

When the flow velocity satisfies the equation V=Vc, the vortex shedding frequency becomes equal to the cylinder natural frequency and the cylinder starts to vibrate.

The vibration amplitude increased and reaches a steady value. The amplitude value depends on the damping.

The damping can be identified via the Scurton number, defined as.

Sc = 2pi hm/ρD^2

The flow speed range defined by 0.9<V/Vs<1.5 the vortex shedding frequency becomes equal to the vibration frequency. In other words, vortex shedding locked to the cylinder natural freqeuncy in all the wind speed range called synchronization range. Synchronization occurs when the lift force frequency locks to the cylinders natural frequency. No synchronziation ofccurs when the force frequency is the strouhal frequency for a fixed cylinder.

Question 8

What depends on the Scruton number?

Answer 8

1) The damping of the system
2) The syncrhonization range of the system

Question 9

Why is it important to control aeolian vibrations?

Answer 9

Aeolian excitation induces conductor vibrations, which produce an alternate bending strain close to the point of connection between conductor and tower (suspension clamp or dead end).

Fatigue in stranded cables is caused by the combined effect of the alternate bending strain and the fretting among the single wires of the conductor. Fretting causes the generation of micro-cracks, depending on the strain level, may cause the failure of a single wire and/or the conductor. Fretting reduced the fatigue limit of a stranded cable.

Question 10

Ηow is the wind energy input measured?

Answer 10

The wind energy input is measured through wind tunnel tests on rigid or flexible cylinders as a function of frequency and amplitude of vibration.

Question 11

How is the energy dissipated by the cable measured?

Answer 11

The energy dissipated by the cable is measured through tests on a laboratory span as a function of tensile load, frequency and amplitude of vibration. If dampers are included, the same measurement can happen.

Question 12

What are the methods for cable self-damping tests?

Answer 12

1) Decay Method
2) Power Method
3) Inverse Standing Wave Ratio (ISWR)

Question 13

Explain the structural model of the conductor.

Answer 13

It is modelled as a 2D string. THe natural frequencies fn are given by:

fn = 1/λn sqrt(T/mL) = n/2L sqrt(T/ml). Τhe modes are sinusoidal functions.

Question 14

Explain the Decay Method, the Power Method and the Inverse Standing Wave Ratio (ISWR) for the measurement of self damping h.

Answer 14

1) Decay Method
It is based on the free response on the system. Using the logarithmic decrement method h = δ/2pi, where δ = ln(Xi/Xi+1).

It is quick and easy but there is a disconnection of the exciting force.

2) Power Method

The energy input from the shaker is measured for a defined set of cable vibration frequencies and amplitudes: THis equals the energy dissipated by the overall system (conductor, terminations) when a stadionary condition is reached.

The assumption is that the Energy Input is equal to the Energy dissipation.

damping h is measured as a function of Ediss divided by Ekin-max

3) Inverse Standing Wave Ratio (ISWR)

It is based on the measurement of nodal and antinodal amplitudes along the test span. Considering two sections A, B of the span, the energy dissipated by the conductor is equal to the Flux of Energy(A) - Flux of Energy(B).

The ISWR at node i is equal to Si = αi/uv = amplitude at node i/ amplitude at the antinode

Then the damping is equal to h = Sa - Sb/πnv (nv is the number of antinodes between node A and node B)

The estimated damping is only the conductor self damping, but the measurement at the node is needed (ai = 1/1000uv) and the method is based on an electrical analogy model.

Question 15

What is the non-dimensional damping function of.

Answer 15

It is function of u/d and the frequency. Increasing f, the damping increases.

Question 16

How can the aeolian vibrations be controlled?

Answer 16

They can be controlled by adding damping to the cable, in the form of dampers and spacer-dampers.

Question 17

What are the kind of dampers?

Answer 17

1) Stockbridge dampers (type of tuned mass damper (TMD)), which consists of a clamp, a messenger cable and weights.

Question 18

What is the hysteresis mechanism in steady state response?

Answer 18

Increasing the wind speed and then reducing it, the system doesnt follow the same amplitude path.

Question 19

What are the methods for calculating the wind energy input?

Answer 19

The wind energy input is measured through wind tunnel tests on rigid or flexible cylinders as a function of frequency and amplitude of vibration.

1) Method 1

By measuring the Build Up energy and the Decay Energy. The Wind energy is equal to Ewind = Ebuild-up + Edeecay. Decay tests are made in still air and build up tests are made in the airflow. ΔΕΚi of the build up is measured by measuring the displacement amplitude of two nodes, and the Edecay is measured by using the average of the previously defined nodes.

2) Method 2
By measuring the pressure along the cylinder section

Ei = S FL vi dt

Wind Power Input curved are measured for different reduced velocities. The value of the Reduced velocity corresponds to the ratio of V/Vs devided by the strouhal number (V*/St = V/Vs). The largest curve corresponds to the envelop and is the one we need. (the one that inputs largest energy).

Question 20

What are the EBP limitations?

Answer 20

The wind velocity variation in space and time is such that more vibration modes can be simultaneously excited.

The presence of more than one vibration mode causes the disappearance of the vibration nodes, and the phenomenon can become unsteady and very complex. Therefore, it is difficult to calculate the maximum energy input from the wind as measured in wind tunnels on rigid or flexible cylinders allowed to vibrate under a harmonic function. The first is a conservative choice, while the second is less due to the presence of mroe modes of vibration.

Question 21

How to alleviate VIV problems?

Answer 21

1) Change structural natural frequency
2) Increase structural damping
3) Aerodynamic modification

Question 22

How to use TMD?

Answer 22

1) TMD without damping on 1Dof vibrating system

Two different natural frequencies occur on the system, ω1 and ω2. If we choose k2/m2 = ω1, then the two natural freqs are the same. The design parameter is μ = m2/m1.

An undamped TMD can protect the system if the external force is monoharmonic (with circular frequency ω0) and has a width band succifiently narrow so as to not influence the two resonance zones of the couples system.

2) If the external force F1 acts in a wide frequency band, a damp TMD is requiredfor the system. The design parameters are μ = m2/m1 and h = r2/2m2ω2.

Τhe amplitudes of vibration are greatly reduced.

Question 23

What is the effect of spacers in subspan oscillations?

Answer 23

Spacers are very important, as subspan oscillations are due to the coupling of the vertical mode of the conductors and the full span torsional mode of the conductors+spacers with the horizontal mode of vibration/

Question 24

Explain the excitation mechanism of subspan oscillations.

Answer 24

When the leeward conductor moves inside and outside of the wake generated by the windward conductors, it is subjected to aerodynamic forces that can modify their mechanical behaviour.

The wind-ward conductor produces wake. Some part of the leeward conductor is in the wake and some not and the aerodynamics coefficients vary.

Outside the wake the Cd, Cl values are constant (0 for CL) , but inside the wake they vary.

The horizontal mode generally presents only one anti-node per each subspan. f = 1/λ sqrt(T/m). When the torsional antinodes are located in the center of the subspan, coupling can occur. The frequencies must be close (similar to flutter).

Question 25

What are the critical parametrs of subspan oscillations?

Answer 25

1) Frequency is the paramound parameter
2) Tension. Decreasing the tensile load decreased dissipation and increases wind energy input and the subspan oscillations become worse.
3) Subspan Length. Increasing the subspan length, the frequency decreases and the situation becomes worse.
4) s/d ratio the subspan becomes worse
5) Wind velocity and statistical distribution of the wind velocity.

Question 26

What are the computational methodologies for subspan oscillations based on?

Answer 26

They are based on the quasi steady theory.

V* = V/fL, where L is equal to the bundle separation. The reynolds number value is close to the range of 2 10^4 - 1 10^5.

Question 27

What are important factors for subspan oscillations?

Answer 27

1) Experimental evidence prove that providing the span with different subspan lengths is an useful measure to control the subspan oscillation amplitudes.
2) wind angle of attack wrt to the bundle is very important.

Question 28

What happens when wind speed increases?

Answer 28

Contrary to flutter, increasing the wind speed the problem dissaperars, because the bundle rotates and the leeward cable is no longer in the wake of the windward.

Question 29

Explain the FEM approach

Answer 29

FEM analysis can be for the reproduction of the bundle dynamics and for the application of the aerodynamic forces to each finite element using the QST.

The FEM doesnt succeed adequately.

Question 30

What is the energy approach in subspan oscillations?

Answer 30

Two independent modal coordinates q0 for the horizontal mode and qv for the vertical mode are defined. Harmonic laws are imposed. The maximum instability index is found for a phase between the two mode equal to π/2.

q0 = Sam * e^iωt
qv = Sam* e^i(ωτ +- π/2)
Lumped system of 8 DOF.

The windward conductors are only subjected to the drag force, while the leeward conducters experiences both lift and drag depending the position. The aerodynamic coefficients are measured through static wind tests in wind tunnels.

Once the aerodynamic forces are known it is possible to compute in each section of the bundle the energy introduced by the forces in one complete elliptical cycle. This is a function of the imposed horizontal and vertical orbit amplitudes. The steady state amplitudes of oscillation are defined through the balance between the energy introduced by the aerodynamic foces and the energy dissipated by the bundle, equipped with spacer-dampers.

Question 31

Discuss the Re number for testing subspan oscilaltions

Answer 31

First of all the Re number experiences by windward and leeward cylinders are different.

In a smooth cylinder, the leeward cylinder experienced great aerodynamic coefficient CD changes with Re number. On rough cylinders, the dependance is removed.

Question 32

Discuss the energy in subspan oscillation experiments.

Answer 32

The windward conductor has negative energy and is damping the system.
The leeward conductor produces positive energy, and produces the instability.

Energy depends on frequency and oscillations are more dangerous at low freq. Also roughness increases the energy dissipated making the system more stable.

Question 33

Explain galloping.

Answer 33

Ice on the conductors change its shape into a circular section and is similar to a wing like section. Negative slope of Cl, Cm coefficients cause instabilities similar to 1DOF,2DOF of bridges.