Aeolian Vibration Chuck Rawlins

Transcription

1 Aeolian Vibration Chuck Rawlins Single conductors with dampers Bundled conductors Ground wires Insulators Davit arms Aircraft warning devices Etc., etc., etc. Aeolian Vibration of Damped Single Conductors.. Waves, Dampers & Damping Efficiency 3. How the Technology Works 4. What to Do Prandtl & Tietjens 934. V f = St ( St.) D V (mph) f (Hz) = 3.6 D(inches) V = to 5 mph Drake f 6 to 44 Hz Fujarra et al (998) 3 Koopman Koopman

2 Pw Pc PD = P - P - W C P = D P W P C Pick a wind velocity e. g. mph. Pick a conductor, e. g. Drake mph f = 3.6 = 9.4 Hz.8 inches 7 8 components Vibration loops Power Balance Components V = mph P w λ = f H / m Power λ Amplitude 5% RS λ to 8 feet 9 Self damping components Power Balance Components V = mph λ = f H / m P c P w λ Power Amplitude

3 components Power Balance Components V = mph Power Balance Components V = mph P c P w P w Power Power P w - P c P w - P c Amplitude Amplitude 3 4 Effect of span Power Balance Components V = mph Power Balance Components V = mph Power P( p w w- P c pc) L Power 5 6 ( p p ) L w c Amplitude Amplitude 5 6 Fatigue curve Protectable span Power Balance Components V = mph σ a Y π m σ a = de a a fy EI N Power 5 6 Amplitude ( p p ) L w c 7 8 3

4 Maximum safe span Protectable span - feet 3. Waves, Dampers & Damping Efficiency Wind velocity - mph

5 PA = Zω A P= Zω A B ( ) PB = Zω B A Frictionless roller ω = π f y = A+ B B Characteristic Impedance Z = H m ZR Fixed rails Dashpot 5 6 P Damping efficiency = P P= Zω A B ( ) A A B = A + B y = A+ B B Y = ( A+ B) Ymin = ( A B) Y Ymin P = Z ω y y Z 7 8 F Damper resistance & reactance X R Fixed rails Dashpot Resistance - Ns/m Damper Resistance 6 Y D =.5 mm Frequency - Hz

6 Damper Reactance R, X D D Reactance - Ns/m Y D = mm Frequency - Hz π xd XS = Zcot λ X = X + X T D S θ = R / Z χ = X T / Z D A B θ = tanh tanh + θ + χ P Y D PD / P = Y θ 3 3 PD/P Damping efficiency measured in the laboratory PD = Pw Pc P P P P P w c = P = Z ω y Y P/P ( pw pc) L (P w -PP c )/P.5 Y /D.5.5 Y /D 5 f 5 f

7 Y - inches Predicted Amplitudes P/P Power Balance at 3.8 Hz Frequency - Hz 37. Damper Wind - self damping Y 38 Power Balance at 4. Hz How the Technology Works P/P.6.4. Damper Wind - self damping (a) A Look Under the Hood (b) Road Test Y 39 4 Wind power Conductor fatigue characteristics 4 Courtesy Alcoa Laboratories 4 7

8 Tunnel throat Brika & Laneville Pw/f 3 D 4 Specific Wind Power - Sine Loops Rawlins 98 Brika & Laneville 995 Polimi 3 Diana et al δ r Reduced Decrement - Sine Loops Pw Pc = P P P Rawlins (98) Brika & Laneville (995) Polimi (3) Diana et al (5) Pw V ρld = St δr P H m m / 5... y /D y /D 46 Measuring self-damping Wind power Conductor fatigue characteristics Alcoa Massena Memorial University of Newfoundland

9 Self damping of Drake at 5% RS PC/P per feet Hz PC/P per feet.6.4. Self Damping of Hawk at 5%RS (4 Labs) Frequency = 4 to 45 Hz Y (in) Munaswamy & Haldar (997) Y inches 5.3 Multilayer ACSR in Suspension or Clamps Bell-mouthed No armor rods fy m/s.. Courtesy GREMCA, University of Laval 5.. megacycles 5 F = ma

10 mass & stiffness θ = tanh tanh + θ + χ P Pw = PD + Pc Shaker test σ σ, end D = n i σ i > Shaker test Shaker test Lab span test Lab span test Field recordings 59 6

11 Shaker test Lab span test 3. How the Technology Works (b) Road Test! Field recordings Inspection of line 6 6 F = ma The Source T, m, EI ZD Z D / Z Shaker test CIGRE Study Committee B - Working Group Task Force Vibration Principles / G. Diana P c x D PD / P Lab span test Assessments of the Technology P w L σ. megacycles Pw = PD + Pc Y, Yb σ σ, end D = n i σ i > Field recordings Inspection of line Modeling of Aeolian Vibrations of Single Conductors - Assessment of the Technology, Electra No. 8 (998) Modeling of Aeolian Vibrations of a Single Conductor Plus Damper: Assessment of Technology, Electra No. 3 (5) IREQ s Varennes Test Line The Course The Course IREQ Varennes Test Line near Montreal Photo courtesy of IREQ 65 66

12 The Drivers F = ma Dampers A, B, C Diana et al (University of Milan) H-J Krispin (RIBE) Leblond & Hardy (IREQ) Rawlins (Alcoa Fujikura) Sauter & Hagedorn (University of Darmstadt) P w σ T, m, EI P c. megacycles L x D ZD PD Z D / Z / P Pw = PD + Pc Y, Yb σ σ, end D = n i σ i > Shaker test Lab span test Field recordings Inspection of line Damper D Benchmark Comparison - 5% Turbulence Rawlins Results Results Free-Loop Single Amplitude (mm) 4 3 Measured in test line Damper A Damper B Damper C 3 4 Frequency (Hz) Amplitude -Peak [mm] 4. Measured 3.5 Damper C (.5EJ 5% turb.) 3. Damper B (.5EJ 5% turb.) Damper A (.5EJ 5% turb.) Frequency [Hz] 69 Electra Fig. 5 7 Results Results Measured Damper C 5% turb. (Diana) Damper C 5% turb. (Rawlins) Measured Damper A 5% turb. (Diana) Damper A 5% turb. (Rawlins) Damper A 5% turb. (Krispin) Amplitude [mm].5..5 Amp. [mm].5..5 Damper A 5% turb. (S&H) Damper A 5% turb. (Leblond&Hardy) Frequency [Hz] Frequency [Hz] Electra Fig. 7 7 Electra Fig. 8 7

13 RMS (Error % (A-M)/M) Rawlins - C T5% Diana - C T5%.5*EJ Hardy - A con EJ Rawlins - A T% Rawlins - C T% Diana - B T5%.5*EJ Rawlins - A T5% Hardy - A fune Rawlins - A T5% Krispin - A T5% EJmin Diana - A T5%.5*EJ Krispin - A T5%.5*EJ Rawlins - B T5% S&H - A T5% Krispin - A T% EJmin Rawlins - B T% Krispin - A T%.5*EJ Diana - A T5%.5*EJ Diana - A T5%.5*EJ Rawlins - C T5% Rawlins - B T5% S&H - C T% S&H - B T% Best Runs Diana - B T5%.5*EJ Diana - C T5%.5*EJ Diana - B T5%.5*EJ Diana - C T5%.5*EJ S&H - A T5% Differences between teams:. s.. Self damping models. 3. Secondary effects, e.g. stiffness. 4. Modeling damper/conductor in different ways. A B Electra Fig Differences between teams:. s.. Self damping models. 3. Secondary effects, e.g. stiffness. 4. Modeling damper/conductor in different ways. Differences with field data:. All of the above.. Modeling damper/conductor interaction. Benchmark Results The different teams differed widely in their predictions of vibration amplitudes. Some differences were due to different data bases on wind power and self-damping. None of the predictions agreed well with field measurements. This is mainly due to problems in the modeling of the interaction of the damper with the conductor Conclusion This branch of the technology is not accurate enough to use in specifying vibration protection. Damper Accelerometers T, m, EI Z D Shaker test ZD / Z P w x D P c L PD / P Pw = PD + Pc Y, Yb DEAM System A B P= Zω A B ( ) Leblond & Hardy

14 Conclusion Calculated from measured reflection coefficient Measured Max. antinode amplitude, (mm) This branch may be accurate enough to use in specifying vibration protection.. T, m, EI P c x D ZD PD Z D / Z / P Shaker test Damper Lab span test P w Pw = PD + Pc Frequency, (Hz) L Y, Yb Leblond & Hardy Why did I spend all this time presenting the technology, when I knew it wasn t very useful to the designer? 4. What to Do?. OK, if that isn t useful, what is?. OK, if that isn t useful, what is? 8 8 Resources:. Your own experience. If it worked before (or didn t), it will do the same again.. Experience of others. If it worked for them... KLs based on ruling span Alcoa Field Experience Case Collection - ACSR with Armor Rods No damage Conductor fatigue Excessive wear Tension (%RS) at average annual minimum temperature 84 4

15 3 Pw V ρld = St δr P H m m / Pw P LD = St V ρ δr H m D K = RS w T % = H RS LD/m 5 5 Alcoa Field Experience Case Collection - ACSR with Armor Rods No damage Conductor fatigue Excessive wear "Conductor Vibration - A Study of Field Experience," C. B. Rawlins, K. R. Greathouse & R. E. Larson, AIEE Conférence Paper CP H/m - meters 86 Safe Design Tension with Respect to Aeolian Vibrations CIGRE B WG TF4 - Claude Hardy, Convenor Recommended Safe Tensions for Single Conductor Lines Part : Single Unprotected Conductors Electra No. 86, October 999 Part : Damped Single Conductors Electra No. 98, October Part 3: Bundled Conductors Electra No., June 5 Overhead Conductor Safe Design Tension with Respect to Aeolian Vibrations, CIGRE Technical Brochure No. 73, June 5 87 CIGRE Brochure 73, Fig Field cases Terrain # Resources: L D / m, (m /kg) 5 Terrain # Terrain #3 Terrain #4 Safe Design Zone Special Application Zone. Your own experience. If it worked before (or didn t), it will do the same again.. Experience of others. If it worked for them H/w, (m) Figure 4 : Ranking parameters of twin horizontal bundled lines in North America fitted with non-damping spacers and end-span Stockbridge dampers in relation to estimated safe boundaries. 3. Your friendly. Electra No., June

16 Why???!! All suppliers have some system for making recommendations. They have the most comprehensive knowledge of their system s performance. They are well motivated to avoid repetition of any unsatisfactory performance. They are in the best position to maintain the system to achieve that. 9 9 Protection recommendations will not agree.. Suppliers have different technical approaches.. Their damper designs are different. 3. Their exposures to field experience have differed.. Why did I spend all that time presenting the technology, when I knew it wasn t very useful? The End