International Journal of Advanced Research in Engineering and Technology (IJARET) Volume 9, Issue 6, November-December 018, pp. 10 18, Article ID: IJARET_09_06_013 Available online at http://www.iaeme.com/ijaret/issues.asp?jtype=ijaret&vtype=9&itype=6 ISSN Print: 0976-6480 and ISSN Online: 0976-6499 IAEME Publication NUMERICAL SIMULATION AND EXPERIMENTAL EVALUATION OF BENDING DEFLECTION OF TRANSMISSION LINE CONDUCTOR Shankar. G Associate Professor, Dept of Mechanical of Engineering, MVJ College of Engg, Bangalore, India Dr.N. S Parthasarathy Retired Professor, Dept of Mechanical of Engineering, MVJ College of Engg, Bangalore, India) ABSTRACT Cable bending models are generally proposed with bending stiffness computations in two extreme ranges namely, a monolithic behaviour with maximum bending stiffness and a loose wire assembly, with a minimum bending stiffness. But the bending stiffness of a cable in a realistic situation, varies as per the coefficient of friction present in the wire interfaces. Since enough theoretical models are not available for this situation, it is proposed to adopt a numerical simulation procedure to evaluate the deflection at various locations of an axially loaded cable under cross load influence and to experimentally verify it,to give a first-hand knowledge of the variation of deflection and hence bending stiffness across a cable length. Both the numerical computation and experimental verification are carried out with a single layered ACSR Racoon Conductor, used in overhead transmission lines. Keywords: Bending stiffness, Conductor, Inter wire friction, Cable. Cite this Article: Shankar. G and Dr.N. S Parthasarathy, Numerical Simulation and experimental Evaluation of Bending deflection of Transmission Line Conductor, International Journal of Advanced Research in Engineering and Technology, 9(6), 018, pp 10 18. http://www.iaeme.com/ijaret/issues.asp?jtype=ijaret&vtype=9&itype=6 1. INTRODUCTION Cables made of helically wound wires, known as conductors, find wide application in the overhead electrical power transmission lines. These conductors, while in service are most frequently exposed to wind loads, which induces an additional bending load on the conductors. The conductors exposed to such bending loads over a period of time losses its stiffness and may fail to retain its structural integrity. Many studies related to the prediction of the change in bending stiffness due to the bending loads are carried out but the exact bending http://www.iaeme.com/ijaret/index.asp 10 editor@iaeme.com
Numerical Simulation and experimental Evaluation of Bending deflection of Transmission Line Conductor stiffness reduction can be confirmed only by carrying out experimental tests on such conductors for various load conditions and also at various locations. A few significant research works carried out in this direction include the contribution of McConnell and Zemke (1980), carried out experimental to study the flexural stiffness in ACSR conductors. The bending stiffness computed from the measured deflections along a span, indicated its closeness to the loose wire behaviour of conductors. Goudreau and Cardou (1993) studied the behaviour of an oversized epoxy 1+6 strand under axial load. The equivalent bending stiffness was calculated from the mid span deflection. The gradual change of bending stiffness was not observed with increasing transverse load. Papailiou(1995,1997) proposed a model based on thin rod approximation, in which the individual wire behaviour under tensile and bending loads were studied. The model considered the presence of interlayer friction and slip in the conductor during bending. Jolicoeur (1997) studied the behaviour of multi-layered wire strands under axial and bending loads. Lévesque. F, et al (015) presented experimental data for the deformed shape of two ACSR conductor undergoing vibrations. The study provides data for comparing the numerical model of a vibrating conductor.cheng Z (015) experimentally studied the bending performance of a structural cable. The author reported the limited experimental discussions on bending studies in cables. A series of quasi static bending tests were performed on semi parallel wire cables, stranded ropes and steel strands, to understand the cable bending response. Zang (016) studied the stiffness of a single layered conductor with friction, the author found that the numerical results predicted were consistent with the experimental observation reported in the literature. Khan (018) studied the bending behaviour of axially preloaded multi-layered spiral strands. The theoretical prediction related to contact forces, deformation and bending stiffness were compared with the available experimental data in the literature. In view of the limited experimental studies for predicting the bending response in a transmission line conductor, the present work proposes a numerical simulation and experimental evaluation of the bending stiffness in a conductor as a function of strand bending curvature. The numerical computations are made for an ACSR Racoon conductor of 1+6 wire configuration and are evaluated with elaborate experimental tests under varying axial loads and cross loads.. EXTREME VALUES OF STRAND BENDING STIFFNESS Most of the studies related to the bending stiffness, predict only the extreme bounds of upper and lower bending stiffness. The existence of lower bending stiffness is realised in the complete absence of friction among the wires and all the wires behave as though they are loosely packed and its value is given by, ( EI) min m π = Eid 64 i = 1 4 i where Ei is the modulus of elasticity, di is the diameter of the strand, mis the total number of wires in a conductor. The upper bound on bending stiffness can be obtained by assuming as though the wires were welded together, with infinite friction among the wires and depicting a solid body behaviour, and is given by m π d EI = E d a max + 4 i= 1 16 ( ) 4 i i i i where ai is the perpendicular distance from the neutral axis to the center of wire crosssectional area. () (1) http://www.iaeme.com/ijaret/index.asp 11 editor@iaeme.com
Shankar. G and Dr.N. S Parthasarathy 3. NUMERICAL SIMULATION OF THE BENDING PHENOMENON WITH A TRANSVERSE LOAD The numerical simulation of the bending phenomenon is considered as a function of strand bending curvature. Figure 1 shows a stranded cable subjected to an axial pull (P) and an additional transverse load (Q) applied at the mid span of the test length. The equilibrium equations of the cable can be written as below, by considering the moments at various sections, as denoted by the limiting ranges y EI Py = M V x and Figure.1 Schematic arrangement of cable loading 1 1 x (3) y EI Py = M V x + Q(x L ) 1 1 x (4) where EI is the bending stiffness of the cable, M1and V1 are the moment and force at the left end and L is the span. Equations (3) and (4) have the solution regions of (0 < x < L ) and (L < x < L) respectively. The expressions for the end reaction V 1 and moment M1can be derived as Q V1 = (5) Q 1 cosh λ = λ (6) M1 b sinh b = ( P / EI) 1/ where (7) λ = ( ) 1/ and PL 4EI (8) If λ >>1, the term within the bracket becomes approximately equal to one and hence the Equation (6) becomes M 1 Q = b (9) http://www.iaeme.com/ijaret/index.asp 1 editor@iaeme.com
Numerical Simulation and experimental Evaluation of Bending deflection of Transmission Line Conductor Substituting V1 and M1in Equation (3), the deflection at a point x along the span can be obtained as 3 QL 1 cosh λ y( x) = 3 ( 1 cosh bx) + ( bx sinh bx) 16EIλ sinh λ (10) NUMERICAL RESULTS The numerical computation of deflections(y) at various locations(x) along the span are carried out as a function of cross loads(q),as per Equation(10),for an assumed axial load(p).for each location,the deflection calculations are carried out as per the loose wire behaviour, with minimum stiffness of EI as per Equation (1) and as per the monolithic behaviour with maximum stiffness EI as per Equation().The Conductor sample(acsr Racoon)adopted for this numerical study is as per the specifications in Table 1. Table 1: Geometric and material properties of Racoon conductor Parameter Value Core diameter, D, mm 4.09 c Wire diameter, D, mm 4.09 w Helix angle of the wire, α, Degree 75.604 Elasticity modulus of the core, E c, GPa 07 Elasticity modulus of the helical wire, E w, GPa 79 Poisson s ratio of the core, γ c 0.3 Poisson s ratio of the helical wire, γ w 0.33 Number of wires, m 6 Coefficient of friction, µ 0.3 Cable length, L,mm 3,000 Breaking load, N 6,940 The computations are done with an axial load P of 700kg(6860N) and with cross loads Q, varying from 98N to 980N, as shown in Column of Table. The deflections obtained with the extreme values of stiffness are tabulated for four different locations of 500mm, 750mm, 1000mm and 1500mm, for each cross load in Column 3 and 4 of Table. 4. EXPERIMENTAL TESTS The experimental test setup and measurements were carried out at the vibration laboratory of Central Power Research Institute, Bangalore. A single layered bimetallic conductor used for overhead electrical power transmission was subjected to an axial pretension and a transverse load was applied at the mid span of the conductor specimen fixed between the two end clamps and the mechanical response of the conductor in terms of deflection was measured. 4.1. Experimental setup The experimental setup consisted of a 40-meter span test rig of with end fixtures to support the cable specimen and to exert a pulling force up to 100kN.A double acting hydraulic actuator of 100kN capacity was used to impart the tensile load in the strand. To measure the response of the strand specimen, a load cell type force transducer of 5Ton capacity was used in the axial direction and another load cell of Ton capacity was used in the transverse http://www.iaeme.com/ijaret/index.asp 13 editor@iaeme.com
Shankar. G and Dr.N. S Parthasarathy direction to which a turn buckle arrangement useful for loading the conductor in the transverse direction was connected. Dial gauge setups were used to measure the transverse deflections at various locations along the span of the conductor. Figure shows the general experimental setup and the hydraulic actuator for imparting the axial load is shown in Figure 3.Figure 4and Figure 5 show the end fixture and load cell arrangement for imparting transverse load. Fig : Experimental test setup Fig 3: Double acting hydraulic actuator of 100kN capacity Figure 4 End fixture arrangement Figure 5 Load cell arrangement 4.. Test procedure A bimetallic single layer conductor as shown in Table 1was used to find the bending response. The conductor was initially pre tensioned axially to maintain it in a taut condition and varying cross loads were applied at the mid span of the cable. The conductor spanchosen for testing is around three meter in length. An axial load of 700kg(6860N) was applied and clamped, then the cross loads were applied from49n up to 980 N in increments and the deflections of the cable at 500mm,750mm,1000 and 1500mm were measured using the dial gauge setup fixed vertically at those locations. The maximum axial load applied was restricted to 30% of the breaking load of the ACSR Racoon conductor as per BIS specifications. http://www.iaeme.com/ijaret/index.asp 14 editor@iaeme.com
Numerical Simulation and experimental Evaluation of Bending deflection of Transmission Line Conductor 5. EXPERIMENTAL MEASUREMENTS The experiment as described above is carried out with a pre tensile load of 6860 N applied to the conductor. Transverse loads are applied varying from 98N to 980N.The deflections obtained location wise for various transverse loads, are tabulated in the 5 th column of Table. Table Comparison of deflection at various locations for 6860N axial load. Reference from fixed end, in mm 500 Transverse load Q in N Theoretically predicted deflection for minimum stiffness in mm y theomin Theoretically predicted deflection for maximum stiffness in mm y theomax Experimental observed deflection in mm y 98 3.308.896 4 147 4.961 4.343 6 196 6.615 5.791 9 45 8.69 7.39 11 94 9.93 8.687 1 343 11.58 10.13 15 39 13.3 11.58 17 441 14.88 13.03 19 490 16.54 14.48 0 588 19.85 17.37 4 686 3.15 0.7 6 784 6.46 3.17 30 88 9.77 6.06 3 980 33.08 8.96 34 exp 750 98 5.093 4.678 4 147 7.64 7.017 7 196 10.19 9.356 11 45 1.73 11.69 14 94 15.8 14.03 17 343 17.83 16.37 0 39 0.37 18.71 441.9 1.05 5 490 5.47 3.39 9 588 30.56 8.07 3 686 35.65 3.74 36 784 40.75 37.4 40 88 45.84 4.1 44 980 50.93 46.78 46 1000 98 6.879 6.46 5 147 10.3 9.69 9 196 13.76 1.9 14 http://www.iaeme.com/ijaret/index.asp 15 editor@iaeme.com
Shankar. G and Dr.N. S Parthasarathy Reference from fixed end, in mm Transverse load Q in N Theoretically predicted deflection for minimum stiffness in mm y theomin Theoretically predicted deflection for maximum stiffness in mm y theomax Experimental observed deflection in mm y 45 17. 16.15 18 94 0.64 19.38 1 343 4.08.61 5 39 7.5 5.8 9 441 30.96 9.07 3 490 34.4 3.3 36 588 41.7 38.76 4 686 48.15 45. 46 784 55.03 51.68 5 88 61.91 58.14 56 980 68.79 64.6 61 exp 1500 98 10.19 9.356 6 147 15.8 14.03 10 196 0.37 18.71 18 45 5.47 3.39 3 94 30.56 8.07 8 343 35.65 3.74 33 39 40.75 37.4 37 441 45.84 4.1 41 490 50.93 46.78 46 588 61.1 56.13 53 686 71.31 65.49 60 784 81.49 74.85 67 88 91.68 84. 7 980 101.9 93.56 75 Figure 6 shows the variation of cable deflection values at 1000mm, as a function of cross loads, as per the extreme limits of stiffnesses. The experimentally measured deflections at this location for various cross loads are also indicated in the figure. http://www.iaeme.com/ijaret/index.asp 16 editor@iaeme.com
Numerical Simulation and experimental Evaluation of Bending deflection of Transmission Line Conductor 70 60 Deflection y in mm 50 40 30 0 10 0 0 00 400 600 800 1000 Cross load Q in N Deflection at minimum stiffness Deflection at maximum stiffness Experimental deflection Figure 6 Deflection at a single location (1000mm) for varying transverse loads Figure 7 shows a plot of cable deflection values for a cross load of 980 N, as a function of cable axial locations, as per the extreme limits of stiffness, along with the corresponding measured deflection results. 10 100 Deflection in mm 80 60 40 0 0 0 00 400 600 800 1000 100 1400 1600 Location in mm Theoritical minimum deflection Theoritical deflection maximum Experimental deflection Figure 7: Deflection at various locations for a single transverse load of 980 N. 5. RESULTS AND DISCUSSTIONS The numerical values of deflection obtained at each location, with minimum and maximum stiffness assumptions are compared with the experimentally measured deflections, for each cross load in Table. From the above results it is observed that the measured deflection values are closer to loose wire behaviour, than that of the monolithic one. http://www.iaeme.com/ijaret/index.asp 17 editor@iaeme.com
Shankar. G and Dr.N. S Parthasarathy 6. CONCLUSIONS A numerical solution procedure to calculate the vertical deflections at various positions of an axially loaded cable, under a cross load arrangement has been demonstrated. The deflections obtained with two extreme behaviour conditions, namely monolithic and loose wire assembly, are compared with the experimental deflections obtained with an ACSR, single layer, Racoon Conductor. The experimental results are found to lie closer to the loose wire assumption. It is hoped that this study of variation of bending stiffness will enable cable designers to predict the strand deflections at any locations accurately. REFERENCES [1] Chen Z, Yu Y, Wang X, Wu X, Liu H. Experimental research on bending performance of structural cable. Constr Build Mater. 015;96:79-88. [] Goudreau, S.and Cardou,A. Flexural testing of anepoxyoversized strands modelunder traction, Experimental Mechanics, Vol. 33, pp.300-307,1993. [3] Jolicoeur C. Comparative study of two semicontinuous models for wire strand analysis. J Eng Mech. 1997;13(8):79-8. [4] Khan SW, Gencturk B, Shahzada K, Ullah A. Bending behavior of axially preloaded multilayered spiral strands. J Eng Mech. 018;144(1). [5] Lévesque F, Goudreau S, Langlois S, Légeron F. Experimental Study of Dynamic Bending Stiffness of ACSR Overhead Conductors. IEEE Trans Power Delivery. 015;30(5):5-9. [6] Zhang D, Ostoja-Starzewski M. Finite element solutions to the bending stiffness of a single-layered helically wound cable with internal friction. J Appl Mech Trans ASME. 016;83(3). [7] McConnell,K.G.andZemke,W.P. Measurement of flexural stiffness of multistranded electrical conductors while under tension, Experimental Mechanics,Vol.0(6),pp.198-04,1980. [8] Papailiou, K.O. (1995), Wire rope bending, taking into account bending stiffness variation due to internal friction, imposed axial traction and curvature, Ph.D. Thesis, ETH Zürich. [9] Papailiou, K.O. On the Bending Stiffness of Transmission Line Conductors, IEEE Transactionson Power Delivery, Vol.1, pp.1576 1588,1997. http://www.iaeme.com/ijaret/index.asp 18 editor@iaeme.com