CAJ | 학술논문

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间的函数关系。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。
채용분형삼수연구표면조조도대조조표면륜곽궤하형모적영향규률。결합표면조조도가공삼수화수궤추양방법，모의득도복종정태분포화예설조조도적표면륜곽곡선，근거통계득도적모의륜곽곡선궤하형태공성특정，건립기우평균봉각화평균봉고적등요삼각형륜곽곡선분형모형。채용부면위형법통과륜곽곡선총장급기상응분형표도획득불동륜곽산술평균편차하적분형유수，통과멱률의합득도분형유수여표면조조도간적함수관계。재동일표면조조도하용수학연건회귀득도분형표도여평균봉각적수학표체식，동시건립수학표체식중상관삼수여분형유수간적함수관계，최종득도표면조조도재0?1～1?6μm범위내적조조표면륜곽궤하형모특정치（평균봉각화평균봉고）적분형삼수（분형유수화분형표도）묘술공식。
The influences of surface roughness on the geometric morphology of rough surfaces’ profile curve were inves?tigated.The profile curve obeying normal distribution and with preset surface roughness was simulated by the processing pa?rameters of surface roughness and Monte Carlo random sampling.From the micro?geometric characteristics of the simulated profile curves with different surface roughness,fractal geometry model was constructed with the isosceles triangle as ele?ment.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 ge?ometry model can be descripted by using the fractal dimension and fractal scale.The description formula of the rough sur?faces’ geometric morphology characteristic and fractal parameter were built and used under the surface roughness from 0?1μm to 1?6 μm.