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

More documents

Recommendations

Info

This “remanent” secondary stiffness (EJ) zusII is calculated by the summation of (2.34) over all wires in the cable. le. The functions in (2.34), however, have no closed solution for (EJ) (EJ)zusII and the summation must be done numerically (see also Section 2.7). For the summations in the two equations for stiffness (EJ) (EJ)min in acc. with (2.30) and (EJ) (EJ)zusI in acc. with (2.33), 3), a simple equation can be found for each, however: The summation in each case includes the nL n identical wires in a layer of the cable. The corresponding cable cable stiffnesses are simple simple to to calculate from the summation summation of of all all the the layer layer stiffnesses stiffnesses using the equations above, Section 3.5. The following identity is a special case of (2.38): This is valid for ϕi = 2 /nL i = 1,…..,n 1,…..,nL and nL > 2, which is always true for helically twisted cables. This This relationship, relationship, hitherto hitherto known known as as an an empirical empirical rule [EPRI, [EPRI, 1979, p.15], p.15], is proven in Annexure II. II. 2.5. The cable bending moment Based on the known stiffness ffness (EJ) and curvature κ in the cable, the natural equation for the elastic curve can be used to calculate the associated cable bending moment M = (EJ) κ. By using the relationship derived in the previous paragraph: 25
this results in: In this equation, Mmin is is the the wire wire bending bending moment moment of of the the cable, as a result of the the wires wires bending around their own axis and Mzus is is the secondary bending bending moment moment of of the the cable, cable, caused caused by internal internal friction friction between wire layers and dependent on the slippage experienced by the individual wires. The The entire entire internal internal cable cable moment moment M is is therefore the the total of of the wire moment and the secondary secondary moment. moment. These These relationships relationships are are illustrated illustrated in in Fig. Fig. 2.13. 2.13. The two (curvature) Regions I I and II II are are shown shown separately, respectively where e there there is is no no slippage anywhere along along the the wires wires and where the wires have have slipped slipped along along their their entire length. length. These These two conditions conditions of the cable are characterised by the two different bending stiffnesses acc. to (2.36) and (2.37) and are explained in more det detail ail in the next paragraph. Region I Transition Region II Fig. 2.13 Moments - Bending (M-B) B) curve of a single layer cable 26
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 and 16: 6 From early years, overhead transm
Page 17 and 18: 2. Basic principles 2.1. The tensil
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: Depending Depending on on the the s
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
Page 67 and 68: 3.4. Tensile Tensile force in in th
Page 69 and 70: To determine the stiffnesses, momen
Page 71 and 72: Assumption 1: Undisturbed isturbed
Page 73 and 74: Fig. 3.7d M-B B diagram diagram und
Page 75 and 76: Phase 1 The The relative position p
Page 77 and 78: Fig. 4.2c Bending of a cable under
Page 79 and 80: Phase 0 The strain energy W0D = W4D
Page 81 and 82: Fig. 4.3 M-B B diagram for the anal
Page 83 and 84: The The balance balance of of momen
Page 85 and 86:
76 In the next step, for an “arbi
Page 87 and 88:
Input module The cable data input,
Page 89 and 90:
( x )E*I = f ( k ) 80 Stiffness for
Page 91 and 92:
82 The same process is now repeated
Page 93 and 94:
84 Fig. 4.13 Flow chart of the SEIL
Page 95 and 96:
(a) Fig. 5.1 Cable bending: (a) for
Page 97 and 98:
The The sensor sensor is is mounted
Page 99 and 100:
Fig. 5.4 Single cross-section secti
Page 101 and 102:
5.2. The test set-up 92 To better o
Page 103 and 104:
Stiffness EJ [N*m^2] Fig. 5.11 Bend
Page 105 and 106:
This machine can handle tensile for
Page 107 and 108:
5.3. The test cables A four-layer h
Page 109 and 110:
The input values for the SEIL progr
Page 111 and 112:
Triggered by the dx signal, a 150 p
Page 113 and 114:
Sag [m] Fig. 6.1 Measured and calcu
Page 115 and 116:
Sag [m] Fig. 6.4 Measured and calcu
Page 117 and 118:
108 Fig. 6.6 also clearly shows tha
Page 119 and 120:
Fig. 6.9 Hysteresis for Cardinal at
Page 121 and 122:
Figure Figure 6.10 6.10 shows shows
Page 123 and 124:
6.5. Effect of the sample length 11
Page 125 and 126:
116 Force--displacement curve Fig.
Page 127 and 128:
This This is is based based on on e
Page 129 and 130:
Secondary stress [N/mm^2] Secondary
Page 131 and 132:
After After the the wire stresses s
Page 133 and 134:
124 The above is summarised in Fig.
Page 135 and 136:
The The trend trend determined here
Page 137 and 138:
128 Even if the conductor model pos
Page 139 and 140:
8. Prospects 130 In the last chapte
Page 141 and 142:
Annexure I The The tensile stress s
Page 143 and 144:
Considering Considering the the abo
Page 145 and 146:
It follows that: If the angle is do
Page 147 and 148:
The position of the catenary in the
Page 149 and 150:
The The following following matrice
Page 151 and 152:
For single component conductors: Fo
Page 153 and 154:
144 CIGRE: Study Committee 22 - Wor
Page 155 and 156:
146 Papailiou, Müller, Roll: Anwen
Page 157 and 158:
List of symbols Latin symbols 148 a
Page 159 and 160:
ma mi mL 150 Friction summation fac
Page 161 and 162:
Z0 Z1 Za Z c,n Zd Z d,a Zd,i Zd,L Z
Page 163 and 164:
ρ Curvature radius of the cable ax
Page 165 and 166:
156 Fig. 3.3 Effect of the tensile
Page 167 and 168:
158 assumptions; 1: (EJ)(κ); 2: (E
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?