Biological setal arrays exhibit a complex multi-layer arrangement, allowing for friction behavior regulation through cooperative deformation of the setae. To reveal the friction regulatory mechanism of multi-layer setal arrays under cooperative deformation, this study established friction analytical models and validated the theoretical results through biomimetic experiments. First, for sliding on a smooth surface, under applied displacement, the continuous large deflection deformation of multi-length setae results in faster friction reduction and better multi-stage load-bearing capacity. Then, for sliding on a rough surface, the cooperative deformation of multi-length setae arranged in different directions can reduce fluctuations in the apparent friction and support force curves of the array after force superposition. Compared with single-layer arrays, multi-layer setal arrays demonstrate superior friction regulation. By adjusting the setal length ratio, number of layers, and distance, both the friction and load-bearing performance can be further optimized. This study offers insights for designing biomimetic surfaces with controllable friction.

To investigate the effects of the contact geometry, interfacial friction, and substrate recovery on the behavior of polymer scratching using a conical tip, an analytical model is proposed. The normal stress acting on the contact surface between the tip and the substrate is described as a function of the included angle $\theta$, representing the angle between two planes across the axis of the conical tip, and the attack angle $\beta$, representing the angle between the conical surface and the substrate material surface. The effects of the rear contact geometry on the scratch friction between the tip and substrate, represented by recovery angle $\phi$, owing to the instantaneous elastic recovery of the polymer substrate, are also introduced. Validated by the experimental and numerical results from the literature, the proposed analytical model can describe well the scratch coefficient of friction (SCOF), which is defined as the ratio of the tangential force to the normal force. Meaningful guidance is provided to understand the scratch friction behavior.