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

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Preamble I completed this thesis in the course of my professional engagement at the Sefag AG company in Malters/Lu. For this reason, I am grateful to Mr. K.H. Pfisterer, the main Sefag shareholder, for having enabled me to carry out these demanding studies. There are two sides to working on a thesis whilst professionally employed: On the one hand, one embarks on this from a certain age, which should be accompanied by some maturity and therefore the necessary discernment of the essential. The assertiveness required in professional life for the pursuance of goals certainly also helps to further the task at hand. In many cases one also has a better perspective on the practical problems, again helping with the execution of the work. Also the stress accompanying such work, performed mainly in spare time, is significant - both personally and for the family in particular. Only the anticipation of achieving the target you set yourself and the expectation, or rather the hope, of making a personal contribution to an interesting and user-oriented engineering problem constantly encourage you to “stick with it”. This was exactly my experience over the years in which I was engaged with this project. And for this reason I wish to once again thank all those who helped me with the completion of the work behind this thesis, now that it is finished. Special thanks first of all to my “PhD supervisor”, Prof. Dr. Meyer-Piening, for his willingness to support this work, for making the infrastructure of the Institute for Light Construction and Cableway Technology (ILS/ETH) available, especially for carrying out the experiments, but particularly for his always constructive criticism and valuable comment – helping me find my way out of many a dead end. I am very grateful also to Dr. V. Esslinger of the EMPA and Prof. Dr. G. Oplatka of the ILS, who were always available for discussions, made valuable suggestions and in this sense were always at my side in this work, also acting as co-supervisors. A special word of thanks goes to my friend Prof. Dr. M. Leider. Not only was I able to benefit from his earlier work, constituting a milestone on this topic, but he was also constantly available in word and deed, making many valuable contributions.
And another special word of thanks to my “fatherly” friend and erstwhile boss Dr. W. Bückner and my CIGRE colleague for many years, Prof. Dr. R. Helms of the BAM [Federal Institute for Materials Research and Testing], Berlin, who introduced me to this topic as a young engineer and fostered my interest in working on it. Let me also include my old acquaintance Jim Poffenberger in this list who, through his well-known equation, animated me to study the bending stiffness of conductors in depth. Also deserving my praise are the staff of the ILS and EMPA [Swiss Federal Laboratories for Materials Testing and Research], Dübendorf, Division for Fatigue and Service Strength, who were in charge of the test rig and the measurements and were always ready to support me in the course of the work, especially Messrs. Kopanakis, Roth, Siebenthaler, Vaczlavic, Bollier, Müller and Schuler of the ILS as well as Sauter, Beisswanger and Heiniger of the EMPA. My thanks also to Dr. Klaffke of the BAM for carrying out the friction measurements so competently. Mr. Frank Schmidberger, who wrote the software programs for this project and also assisted me in many aspects, both in thinking and in helping, more than deserves my gratitude. Last but not least, allow me to express my sincere thanks to my dear wife Margarita at this point. Not only has she always encouraged me to persevere even though family life often bore the brunt but, as a graphic artist and publisher, she personally handled the entire graphic content – also in the course of her other professional obligations – and coordinated the pressure of work, shouldering it as well. Thanks, darling. All in all, the author would also like to strongly recommend a “lifetime job” such as this even to the “older generation”, into which group the author is by now obliged to count himself – not by dint of being the “perennial student”, but because of a yearning for never-ending learning. It enlivens the spirit, creates intensive contacts to many interesting people and, given a bit of luck as I appear to have had, yields results that can be directly applied to practical engineering challenges. Malters, October 1994
Page 1 and 2: Bending of helically twisted cables
Page 3 and 4: For my father
Page 5: Zusammenfassung Die Seilbiegung ste
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 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
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The Zn,a values values are are the
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According According to to the law o
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First First approximation: Continuo
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This means that the outer layer is
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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
Page 167 and 168:
158 assumptions; 1: (EJ)(κ); 2: (E
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Bending of helically twisted cables under variable ... - Pfisterer

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