## 3 Internal Contact Pressure Model Validation
### Validation for Twist Model
Figure 14c,d shows the distribution patterns of pressure at different contact points, with contact points \(\langle 1\rangle\) and \(\langle 2\rangle\) manifesting patterns of monotonically increasing and decreasing pressure, respectively. This behavior is contingent upon the angle between the direction of twisting force and the direction of contact transmission. Due to the twisting forces provided by the upper-layer wires being directed towards the central wire, in the left half-region, contact point \(\langle 1\rangle\) can accommodate a higher proportion of transmission, while contact point \(\langle 2\rangle\) experiences fewer transmissions. Conversely, in the right half-region, this scenario is reversed, thereby presenting a distinctly opposite distribution pattern between the two contact points. Theoretically, the PIC model is also applicable to the calculation of contact pressure between steel wire strands. To validate the efficacy of the theory, the computed results are compared with the contact stress between equally sized steel wire strands [38; 39]. Employing an identical configuration of eight layers of wires, a helix angle of 12\({}^{\circ}\), and a wire diameter of 6.5 mm, the comparison is established. As Figure 15 shows, owing to the distinct arrangement of parallel wires and steel strands, the contact pressure in the inner layers (1-4 layers) is significantly influenced by the arrangement. Consequently, the model exhibits substantial deviations from the HDS and MHDS (modified HDS) models. However, in the outer layers (5-8 layers), the errors caused by the arrangement decrease, leading to a more consistent trend between this model and the HDS and MHDS models. The closer one is to the outer layer of the cables, the smaller the contact pressure, a discrepancy primarily determined by the helix angle \(\alpha_{(i,j)}\) of the wires and the distance \(r\) from the central wire. Generally speaking, wires closer to the outer layer exhibit a smaller  
Figure 15: Comparison of PIC theoretical model with HDS and MHDS model: (**a**) comparison of HDS and PIC for layers 1–4; (**b**) comparison of MHDS and PIC for layers 1–4; (**c**) comparison of HDS and PIC for layers 5–8; (**d**) comparison of MHDS and PIC for layers 5–8. The solid line 1–8 is the curve of PIC model, and the dashed line (1)–(8) is the curve of steel wire rope model. helix angle and a greater distance from the central axis. According to Formula (1), the calculated contact torsional force is consequently greater, leading to a proportional increase in contact force. Without considering the nonlinear factors, the growth of the contact pressure with strain is linear. Moreover, wires closer to the inner layers experience a higher growth rate. This is because the torsional direction of the wires is directed towards the central wire. The torsional force from the outer layer wires superposes layer by layer onto the contact pressure of the inner layer wires, resulting in greater contact pressure closer to the inner layers, reaching a peak at the central wire. Although the contact pressure of the central wire increases with the addition of wire layers, this growth is not unlimited. For wires in the same layer, the closer to the inner layers, the fewer the contact points, and consequently, there are fewer paths for the transmission of contact pressure. Therefore, the difference in contact pressure between adjacent layers gradually diminishes.