## 6 Effect of the Friction Coefficient  
Because the friction coefficient is affected by the metal type, chemical composition, surface state, deformation temperature, and contact pressure, the friction coefficient between aluminum strands is not easy to determine. This paper mainly studied the bending deformation of a conductor, and the contact between each strand of a conductor is extremely complex during the process of the bending deformation. Coulomb's law was introduced to study this problem. The tangential contact of each strand in the aluminum strand follows this law. The Coulomb friction model was used in Abaqus.  
[PERSON] et al. [25] proposed a conductor model that can withstand both the tension and bending loads, and considered the interlayer friction and slip during the process of wire bending. It was found that the bending analysis of the conductor was extremely sensitive to the selection of the friction coefficients between two adjacent layers of the conductors. The range of friction coefficients between cables was found to be between 0.55 and 0.9. [PERSON] et al. [26] measured the fretting fatigue strength of A1-4 Mg-0.7 Mn in contact with aluminum and copper. It was found that the friction coefficient of A1-4 Mg-0.7 Mn in contact with aluminum and copper was extremely low, but with an increase in the number of fatigue cycles, the friction coefficient increased to approximately 1.0 and remained unchanged at this value. Clearly, a conductor bending analysis is extremely sensitive to the choice of friction coefficient between two adjacent conductors. In the process of long-term service, the friction coefficient between strands of a conductor will change due to the wear between strands. In order to accurately evaluate the change of the friction coefficient in the service process of the mid-phase jumper, this section discusses the influence of the friction coefficient on the stress of the mid-phase jumper when other conditions remain unchanged. Thus, the friction coefficients between the steel-cored aluminum strands were set to 0.3, 0.5, and 0.7. At this time, the equivalent Young's modulus of the whole finite element model was 6.78, 6.68, and 7.67 GPa, respectively, and the other conditions remained unchanged. The influence of the friction coefficient is discussed next.  
As shown in Figure 14, between level-1 and level-3 wind loads, the wind load was small, and thus \(\sigma_{\rm a}\) and \(Y_{\rm b}\) were extremely small; therefore, the friction coefficient had little effect on the corresponding \(\sigma_{\rm a}\) and \(Y_{\rm b}\). Between level-4 and level-7 wind loads, when the friction coefficient was 0.115 to 0.50, \(\sigma_{\rm a}\) and \(Y_{\rm b}\) first decreased and then increased with an increase of the friction coefficient under the same wind load; when the friction coefficient was 0.50 to 0.70, \(\sigma_{\rm a}\) and \(Y_{\rm b}\) decreased again with an increase of the friction coefficient under the same wind load. Therefore, the friction coefficient had a great effect on the corresponding \(\sigma_{\rm a}\) and \(Y_{\rm b}\) between level-4 and level-7 wind loads. The difference in \(\sigma_{\rm a}\) between the outermost layer and the third layer reached the maximum under a level-7 wind load when the friction coefficient took the above four parameters, and the maximum difference did not exceed 20 MPa. In conclusion, the friction coefficient influenced the bending of the mid-phase jumper, but the effect was not great.  
Figure 13: Comparison of the simulated stress and test stress under different wind loads.