The Test Study on Tension-torsion Coupling Effect of ACSR in Overhead Transmission Lines

In order to analyze the relationship between the tensile and torsional characteristics of the Aluminum Conductor Steel Reinforced (ACSR), test research on the coupling effect of tension and torsion in conductors was carried out. A conductor tension-torsion coupling test device was designed, and selected the JL/G1A-630/45-45/7 ACSR as sample which is commonly used in ultra-high voltage AC engineering. The relationship between conductor tension, torque, and tensile strain, torsional strain was measured. And obtain the stiffness coefficients of conductor tension, torsion, and tension-torsion coupling. The testing results show that the tension and torque of the conductor gradually change from non-linear to linear under the action of tension or torsion deformation; The torsional stiffness Kφφ and tension-torsion coupling stiffness Kεφ when the conductor is turned to the right are greater than the corresponding stiffness when it is turned to the left.


Introduction
ACSR is widely used in overhead transmission line conductor.Due to the structural characteristics of helical stranded strand, the conductor will produce torque in the opposite direction of stranded strand under axial tensile action, that is the tension-torsion coupling effect of the conductor [1].The coupling effect of tension and torsion of conductor has an important influence on its torsional characteristics, and then affects the quality of conductor in tension pay-off construction.
The twisted structure of ACSR for transmission lines is similar to that of steel wire ropes.The early research mainly focused on the structure of steel wire ropes.Hruska proposed the mechanical relationship between tension and torsion in the pure tension model of steel wire rope [2], but did not consider the torsional stiffness and twist angle changes of the steel wire itself; McConnell et al. considered the torsion stiffness of the steel wire itself on this basis [3]; Costello et al. considered the bending, torsion stiffness and Poisson effect of the steel wire in the construction of the mechanical model of the steel wire rope based on the Love curve bar theory [4][5][6][7][8], and the test obtained satisfactory results; with the maturity of the finite element theory, a new method is provided for the analysis of the strand structure considering the contact friction between the strands, and certain results are achieved in the calculation of the contact friction and layered stress characteristics of the strands [9][10].The above studies mainly focus on the theoretical analysis and test of the strand with simple structure, and there are few testing studies on the related mechanical properties of the multi-layer twisted steel core aluminium strand which is commonly used in UHV transmission lines.

The Tension-torsion Coupling Effect of Conductor
Considering the coupling effect of tension and torsion, the axial tension F, torque T, and axial tensile strain ε and torsional strain τ of the conductor under axial load are shown in figure 1, and the relationship can be simply described as: In the formula, K εε and K ϕϕ respectively represent the tensile stiffness and torsional stiffness coefficients of the conductor.K εϕ , K ϕε respectively represent the conductor tension-torsion coupling stiffness and torsion-tension coupling stiffness coefficient; ε、τ are the axial tensile strain and torsional strain of the conductor respectively, ，and l0 is the length of the conductor; Δl is the elongation length; Δφ is the angle of twist.Assuming the initial axial tension and torque of the conductor respectively are F1 and T1,then the following conclusion can be obtanied by fixing the torsion angle (τ= 0) and conductor length (ε= 0).
In summary, according to equation ( 2), the tensile stiffness coefficient K εε , torsional-tensile coupling stiffness coefficient K ϕε , tensile-torsional coupling stiffness coefficient K εϕ , and torsional stiffness coefficient K ϕϕ of the conductor can be obtained.

The Equipment of Test
According to the test purpose, a conductor tension-torsion coupling test device was designed and processed, which can apply both the tension and torque for the conductor.The device can also achieve the measurement of conductor in tensile length and torsion angle.The composition of the test device is

Test Sample
The JL/G1A-630/45-45/7 conductor commonly used in ultra-high voltage AC transmission line engineering was selected for the test, with a rated tensile strength RTS of 150.2kN.The main structure and mechanical parameters of the conductor are shown in table 1.The effective length of the test conductor is about 6meters, as shown in figure 4; The two ends of the conductor are connected by an assembled traction device, which can be reused, as shown in figure 5.

Test Process
According to the test conditions, the conductor test is carried out separately according to the fixed torsion angle and fixed tensile length.The main test process is shown in figure 6.

Analyze the Test Results
Process the test data of JL/G1A-630/45-45/7 conductor according to the fixed torsion condition and fixed length condition, and calculate the various stiffness coefficients of the conductor according to equation (2).

Test Results of Fixed Torsion Condition for Conductor
When the JL/G1A-630/45-45/7 conductor is fixed the torsion, the conductor tension is loaded from 5% RTS to 25% RTS, that the curve of conductor tension and the torque with elongation is obtained, as shown in figure 7. The torque and angle direction of the test measurement results are determined by the right-hand rule.

The Test Results of Fixed Conductor Length Working Condition
When the JL/G1A-630/45-45/7 conductor is fixed in length under 5% RTS tension, the tension and torque curves of the conductor with respect to the torsion angle during the process of loading from the current torque value to 100N.m (right-hand rotation) or 60N.m (left-hand rotation) are shown in figures 8 and 9.Among them, the right turn is that the direction of the conductor torsion is consistent with the direction of the outer strand helix.

Conclusion
The relationship between axial tension and torsion characteristics of JL/G1A-630/45-45/7 was measured through tests, and the coupling stiffness coefficient of conductor tension and torsion was obtained.The results indicate that: (1) When the elongation or angle of the conductor is small, the changes in tension and torque exhibit nonlinearity; As the elongation and rotation angle increase, the tension and torque gradually exhibit linear changes with the deformation of the conductor.
(2) According to the calculated stiffness coefficients of the conductor, it can be seen that the tension-torsion coupling stiffness Kεφ and torsion-tension coupling stiffness Kφε of the conductor are not equal, and the torsion stiffness Kφφ and tension-torsion coupling stiffness Kεφ of the conductor when turned to the right are greater than the corresponding stiffness when turned to the left.

Figure 1 .
Figure 1.The schematic diagram of conductor deformation under force.

Figure 9 .
Figure 9.The left rotation test curve of JL/G1A-630/45-45/7 conductor which fixed the length.Based on the above test measurement data, excluding the factors such as initial deformation of the conductor and loose strands, the stiffness coefficient of the test was calculated by selecting the section with linear increase in tension and torque.The average value of multiple sets of test data is shown in table2