Bending of helically twisted cables under variable ... - Pfisterer

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1.4. Limitations 7 Although the original problem definition stems from cable vibrations and therefore constitutes dynamic stressing of the cable, the stress is considered “quasi static” in this project. This approach proved successful in earlier studies [Poffenberger and Swart, 1965, EPRI, 1979, CEA, 1986]. In this sense, this project thus does not cover the problem of fatigue in overhead conductors. This is quite a complex process and a quantitative solution does not appear within reach at present. Based on the new insights gained here into the “internal” cable mechanisms dependent on bending stiffness as a function of friction, cable curvature and tensile force on the cable, including the displacement behaviour of the wires in the cable construction, this project nevertheless hopes to provide a foundation for solving conductor fatigue problems. And finally, this project does not intend to deal with problems of clamping and force application through the cable suspension and clamps. This would substantially complicate an already complex task and render a closed overall solution impossible. The results of this project should, however, contribute significantly to clarification of this topic as well. 1.5. Project structure To achieve the abovementioned objectives, this project was structured as follows: The model for single-layer cables is developed in Chapter 2, taking into account the results of earlier work and the variable bending stiffness of the cable, as a function of the curvature, internal friction and tensile force. The developed fundamentals are extended to multi-layer helically twisted cables and the (non-linear) Moment-Bending characteristic is introduced in Chapter 3. This forms the basis for the finite element model for the calculation of the bending of tensioned cables in Chapter 4. Chapter 5 deals with the newly developed measuring method (“cable scanner”), for experimental verification. Chapter 6 provides a comparison between measurement and calculation and a sensitivity analysis of the effect various parameters have on the interpretation of the results. In Chapter 7, the findings of this project are transferred to the important practical field of vibrations of conductors and possible influences are discussed on the dimensioning of such conductors.
2. Basic principles 2.1. The tensile stress 8 This Section deals with the tensile stress on the cable. This is the basic stress on the cables investigated in this project. In all the tests, the first stress to be applied to the cable under no load is a tensile force. This tensioning has a significant effect on the bending stress, i.e. the resultant stresses in the cable. The book by Feyrer (1990) deals with this topic in detail and only the essential aspects are therefore repeated here. The special conditions pertaining to stressed reinforced conductors (especially ACSR overhead conductors) were discussed in detail especially by Ziebs (1970). In this case also, the full derivation of the formulae is dispensed with here. Fig. 2.1 Geometry of a wire belonging to layer L of a helically twisted cable Fig. 2.1 shows a wire in an arbitrary layer L of a helically twisted cable defined by its cross-sectional centre, also showing the full lay length ℓL of the unwound wire.
Page 1 and 2: Bending of helically twisted cables
Page 3 and 4: For my father
Page 5 and 6: Zusammenfassung Die Seilbiegung ste
Page 7 and 8: And another special word of thanks
Page 9 and 10: 5. Measurements....................
Page 11 and 12: 2 Their acquisition value is estima
Page 13 and 14: 4 This device measures the deflecti
Page 15: 6 From early years, overhead transm
Page 19 and 20: Figure 2.3 explains these relations
Page 21 and 22: Fig. 2.4 Determining the radial pre
Page 23 and 24: It It appears appears suitable suit
Page 25 and 26: Fig. 2.7 Geometry of the cable cros
Page 27 and 28: Fig. 2.9 Curves Curves for the seco
Page 29 and 30: 2.4. The bending stiffness As menti
Page 31 and 32: Fig. 2.12 Distribution of the cable
Page 33 and 34: Depending Depending on on the the s
Page 35 and 36: this results in: In this equation,
Page 37 and 38: We may derive the mean transition c
Page 39 and 40: The moment moment below the transit
Page 41 and 42: Fig. Fig. 2.15 2.15 finally shows s
Page 43 and 44: During During bending in in Region
Page 45 and 46: Fig. 2.18 Hysteresis in the M-B B d
Page 47 and 48: with: and: with: The tensile stress
Page 49 and 50: The The situation situation is is d
Page 51 and 52: As As the curvature curvature incre
Page 53 and 54: This shows that, based on the propo
Page 55 and 56: A wire of the outer layer therefore
Page 57 and 58: The Zn,a values values are are the
Page 59 and 60: According According to to the law o
Page 61 and 62: First First approximation: Continuo
Page 63 and 64: This means that the outer layer is
Page 65 and 66: By applying the Zi just just achiev
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3.4. Tensile Tensile force in in th
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To determine the stiffnesses, momen
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Assumption 1: Undisturbed isturbed
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Fig. 3.7d M-B B diagram diagram und
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Phase 1 The The relative position p
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Fig. 4.2c Bending of a cable under
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Phase 0 The strain energy W0D = W4D
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Fig. 4.3 M-B B diagram for the anal
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The The balance balance of of momen
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76 In the next step, for an “arbi
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Input module The cable data input,
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( x )E*I = f ( k ) 80 Stiffness for
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82 The same process is now repeated
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84 Fig. 4.13 Flow chart of the SEIL
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(a) Fig. 5.1 Cable bending: (a) for
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The The sensor sensor is is mounted
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Fig. 5.4 Single cross-section secti
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5.2. The test set-up 92 To better o
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Stiffness EJ [N*m^2] Fig. 5.11 Bend
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This machine can handle tensile for
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5.3. The test cables A four-layer h
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The input values for the SEIL progr
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Triggered by the dx signal, a 150 p
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Sag [m] Fig. 6.1 Measured and calcu
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Sag [m] Fig. 6.4 Measured and calcu
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108 Fig. 6.6 also clearly shows tha
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Fig. 6.9 Hysteresis for Cardinal at
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Figure Figure 6.10 6.10 shows shows
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6.5. Effect of the sample length 11
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116 Force--displacement curve Fig.
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This This is is based based on on e
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Secondary stress [N/mm^2] Secondary
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After After the the wire stresses s
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124 The above is summarised in Fig.
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The The trend trend determined here
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128 Even if the conductor model pos
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8. Prospects 130 In the last chapte
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Annexure I The The tensile stress s
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Considering Considering the the abo
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It follows that: If the angle is do
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The position of the catenary in the
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The The following following matrice
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For single component conductors: Fo
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144 CIGRE: Study Committee 22 - Wor
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146 Papailiou, Müller, Roll: Anwen
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List of symbols Latin symbols 148 a
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ma mi mL 150 Friction summation fac
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Z0 Z1 Za Z c,n Zd Z d,a Zd,i Zd,L Z
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ρ Curvature radius of the cable ax
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156 Fig. 3.3 Effect of the tensile
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158 assumptions; 1: (EJ)(κ); 2: (E
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Bending of helically twisted cables under variable ... - Pfisterer

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