中文摘要：

采用分形参数研究表面粗糙度对粗糙表面轮廓几何形貌的影响规律。结合表面粗糙度加工参数和随机抽样方法，模拟得到服从正态分布和预设粗糙度的表面轮廓曲线，根据统计得到的模拟轮廓曲线几何形态共性特征．建立基于平均峰角和平均峰高的等腰三角形轮廓曲线分形模型。采用剖面位形法通过轮廓曲线总长及其相应分形标度获得不同轮廓算术平均偏差下的分形维数，通过幂律拟合得到分形维数与表面粗糙度问的函数关系。在同一表面粗糙度下用数学软件回归得到分形标度与平均峰角的数学表达式，同时建立数学表达式中相关参数与分形维数间的函数关系．最终得到表面粗糙度在0．1—1．6μm范围内的粗糙表面轮廓几何形貌特征值（平均峰角和平均峰高）的分形参数（分形维数和分形标度）描述公式。

英文摘要：

The influences of surface roughness on the geometric morphology of rough surfaces＇ profile curve were investigated.The profile curve obeying normal distribution and rameters of surface roughness and Monte Carlo random with preset surface roughness was simulated by the processing pasampling.From the micro-geometric characteristics of the simulated profile curves with different surface roughness, fractal geometry model was constructed with the isosceles triangle as element.The fractal dimensions under different surface roughness were calculated with the profile configuration method, and the power law relationship between the fractal dimension and surface roughness was obtained.According to the calculating data and the mathematical regression, the average peak angle and height of the isosceles triangle element in the fractal geometry model can be descripted by using the fractal dimension and fractal scale.The description formula of the rough surfaces＇ geometric morphology characteristic and fractal parameter were built and used under the surface roughness from 0. 1 μm to 1.6 μm.