目的 为了研究高机动车辆变速铜基复合材料摩擦副的磨损状态和规律,优选低磨损率摩擦副、揭示磨损规律,需要建立反映表面磨损机理的解析磨损模型,为不同表面形貌及物理特性摩擦材料磨损率提供预判手段,进而提高摩擦副磨损性能研发效率。方法 研究通过采集不同尺度条件铜基复合材料摩擦表面拓扑参数和材质特征,采用计盒维数法计算分形维数D,关联分型维数与尺度系数,生成摩擦表面分形形貌,建立铜基摩擦副分形磨损计算模型。研究包括分形参数和摩擦副真实接触面积、摩擦磨损机理、磨损量与磨损体积的相关性及敏感因素。结果 铜基复合材料摩擦表面的分形维数D,主要分布在1.36~1.48之间,平均值为1.43。当D值处于1.4~1.6 区间时,磨损率最低且稳定性最佳。此外,表面粗糙度参数增大导致磨损加剧,而材料常数（硬度与弹性模量之比）增大则有助于降低磨损。结论 采用磨合等工艺手段将铜基复合材料摩擦表面的分形维数D值控制在1.4~1.6的稳定区间,可有效改善高机动换挡条件下的磨损率稳定性并降低磨损水平。通过优化面压分布等改进措施,在面压载荷加大时进一步趋近于D值1.5附近对应的最低磨损率区间。

Wear, the progressive loss of material from contacting surfaces, poses a significant challenge for the durability of high-power density transmission systems in high-mobility vehicles. This study aims to develop a predictive wear model for copper-based sintered composite friction materials, which are critical components in such systems, operating under fluctuating contact pressures during gear shifting. The core innovation of this research lies in the application of the fractal theory to quantitatively link surface topography to wear rate. The investigation begins with a detailed characterization of the copper-based composite's surface topology. Through comparative analysis, laser profilometry is selected as the preferred method for acquiring high-fidelity 3D surface data, as it provides the precision and minimal distortion required for accurate fractal analysis. The digitized surface profiles (Figs.1-4) exhibit self-affine characteristics, confirming the applicability of a fractal approach. The fractal dimension (D), a key parameter describing surface complexity, is calculated from an extensive dataset of over 600 sample areas. The results show that D values for these surfaces range from 1.36 to 1.48, with a mean value of 1.43 (Fig.5). Leveraging this topological foundation, a theoretical wear model is formulated. The model is grounded in Archard's adhesive wear principle but extends it by integrating a contact mechanics analysis that differentiates between elastic and plastic deformation regimes. Crucially, the actual contact area, which is central to wear calculation, is expressed as a function of fractal parameters. This leads to the derivation of a comprehensive dimensionless wear rate equation: V*=f(A_r*, D, G*, Φ). In this equation, V* represents the dimensionless wear rate, A_r* is the dimensionless real contact area, D is the fractal dimension, G* is the dimensionless fractal roughness parameter, and Φ is a material constant (H/(2E)), combining material hardness (H) and elastic modulus (E). A systematic parametric study is conducted to elucidate the influence of D, G*, and Φ on the predicted wear rate V* (Figs. 6-9). A fundamental finding is that V* invariably increases with the dimensionless real contact area A_r*. Among all parameters, the fractal dimension D is identified as the most influential. The relationship between D and wear stability is non-monotonic. At low D values (e.g., 1.2-1.3), the wear rate is high and highly sensitive to changes. Importantly, the current operational range for the manufactured composites (D=1.36-1.48) resides within a more favorable, stable wear regime. Within this range, the wear rate shows less sensitivity to variations and trends towards a minimum value observed in the vicinity of D=1.5 (Fig. 7). This indicates that current manufacturing and run-in processes are producing surfaces with inherently good wear stability. The study further suggests that proactively optimizing surfaces to achieve a D value closer to the ideal value of 1.5, specifically within the 1.4-1.6 range, would further enhance performance. Additionally, the model predicts that a higher surface roughness (G*) exacerbates wear, whereas a higher material constant Φ (implying greater hardness relative to elasticity) mitigates it (Fig.8 and Fig.9). To validate the model under realistic conditions, a novel experimental technique employing a blind-hole embedded sensor is developed to measure dynamic contact pressure distributions across the friction surface (Fig.10). The measurements reveal substantial pressure fluctuations during operation, with values ranging from 0.4 MPa to 7.1 MPa (Fig.11, Tab.1). This empirically determined pressure range provides a critical input for applying the wear model to real-world scenarios. In conclusion, this research successfully establishes a feasible and practical fractal-based model for predicting the wear of copper-based composites under the demanding conditions of high-mobility vehicle gear shifting. The analysis confirms that the surface topography of current-generation components, characterized by a fractal dimension around 1.43, already promotes relatively stable wear. The findings provide a clear strategic direction: targeted optimization of surface topography to achieve a D value near 1.5, coupled with control of surface roughness and material properties, holds the key to achieving superior wear resistance and long-term reliability for these critical transmission components.