###### Abstract  
Fretting wear of the stay cable is an important factor affecting the service life of the cable. To accurately calculate the extent of fretting wear, it is necessary to calculate the internal contact pressure in the cable. Although there are many theories and experiments on the contact behavior between wires, there are still no theoretical formulations for calculating the distribution of contact pressure in stay cables. In this paper, by studying the transfer effect of contact pressure in the cable, the PIC (parallel wire cable internal point contact pressure) model for calculating the contact pressure in the parallel wire cable is proposed, considering the effects of wire twisting, sheath compression, and cable bending on the contact pressure. A finite element model corresponding to the contact mode between steel wires is established, and the effectiveness of the PIC model is verified through numerical simulation analysis and a comparison of the existing contact models. The results indicate that contact pressure caused by wire twisting (CWT) is superimposed layer by layer inwards, with the contact pressure increasing closer to the inner layers, and its magnitude is mainly related to the axial tension and twist angle. Simultaneously, on the same layer, contact points along the diagonal experience the greatest contact pressure. Contact pressure caused by sheath compression (CSC) is assumed to conform to the Boussinesq distribution, with the outer layers exhibiting greater contact pressure compared to the inner layers. Contact pressure caused by cable bending (CCB) conforms to the two-dimensional closely arranged contact force transmission model, has a clear layering phenomenon, and the contact pressure within the same layer does not change significantly. The magnitude of the contact pressure is exponentially related to the curvature of the cable and proportional to the tension of the cable, which explains the reason why the slip occurs later for the cables with high tensile forces. Among these three types of contact pressure, CWT is the greatest, followed by CCB, while CSC is the smallest. The theoretical analysis results show that factors such as wire radius, tension, torsion angle, and wire position have an impact on contact pressure. Contact pressure is transmitted along force chains within the cable, following the superposition law between layers. It is uncertain whether slip occurs in the neutral axis or in the outermost layer because of the different distributions of tangential force and interlayer frictional resistance between the layers of wires. Fretting wear simulations of two wires demonstrate that contact pressure has a significant influence on wear patterns, and the \"averaging\" of contact pressure is a major reason for achieving uniform interface wear. While the contact width increases proportionally with the contact pressure, excessive contact pressure can complicate the problem by changing the contact mode from gross slip to partial slip. This study provides a theoretical method for calculating contact pressures at any contact point within the cables in engineering practice.  
contact pressure; parallel wire cable; fretting wear; theoretical method; finite element analysis +
Footnote †: journal: Applied Sciences