异性分形表面合成方法及表面特性研究  

Study of Synthesis and Properties of Anisotropic Fractal Surfaces

作　　者：张玲[1] 郑国磊[1] 杨荣荣[1] ZHANG Ling;ZHENG Guolei;YANG Rongrong(School of Mechanical Engineering and Automation,Beihang University,Beijing 100191)

机构地区：[1]北京航空航天大学机械工程及自动化学院

出　　处：《机械工程学报》2019年第21期118-126,共9页Journal of Mechanical Engineering

摘　　要：针对异性分形表面的建模,提出了一种以二维离散傅里叶变换为基础,以名义维数Dx,Dy为驱动参数的表面合成方法--合成维数法。通过对比名义维数与采用轮廓功率谱公式和数值分析法得到的表面计算维数的关系,验证了该方法的有效性。探讨了名义维数对x,y方向轮廓能量分布以及对表面及轮廓粗糙度的影响。一方面在轮廓功率谱分析的基础上定义了轮廓累计功率比,用于描述表面轮廓的能量分布特性,不仅促进了对名义维数和轮廓能量关系的定性理解,更能定量地解释不同维数值影响下频率和轮廓能量分布的关系。另一方面以能量分析为切入点,建立了名义维数与表面及轮廓粗糙度参数间的联系,并且依据能量守恒定律,证明并揭示了轮廓粗糙度Rqx,Rqy之间以及二者与面粗糙度Sq的关系。同时得出结论,Dx或Dy值越小,低频部分能量占比越高,反之亦然,但是x,y方向轮廓总功率始终相等,并随Dx,Dy增大而增大;Dx,Dy只影响Sq,Rqx,Rqy的绝对数值,二者的增大会引起粗糙度值增加,但并不影响Rqx,Rqy的相对关系。For modeling of anisotropic fractal surfaces, a novel synthesis method named by synthetic dimension method is proposed, which is based on discrete Fourier transform and aroused by the nominal dimension Dx, Dy. By contrasting nominal dimension with computed dimension values that are obtained by the derived power spectrum formula of surface’s profiles and the concomitant numerical calculation, the method proves to be useful. Further, relationships between nominal dimensions with power distribution and roughness of the generated fractal surface and surface profiles in x, y direction are discussed. On the one hand, through analyzing of surface’s profile power spectrum, profile’s cumulative power ratio is introduced to describe power distribution, by which the qualitative understanding of effects of nominal dimensions on profile’s power can be promoted, and the relation between profile’s frequency with power distribution under the impact of the dimensions is also explained quantitatively. On the other hand, taking energy analysis as an entrance, connections of nominal dimensions with surface and profile roughness are established. Meanwhile, according to the conservation of energy principle, relationships of the profile roughness Rqx, Rqy and the surface roughness Sq are revealed. The results show that smaller Dx or Dy induces a higher low-frequency energy ratio in corresponding direction, and vice versa, however, the total profile’s powers in x and y direction always equal, and increase with Dx and Dy. In addition, Dx, Dy only affect the absolute roughness values of Sq, Rqx and Rqy by causing roughness increase with them, not the relative relation of Rqx and Rqy.

关 键 词：分形表面 离散傅里叶变换 合成维数法 名义维数 轮廓能量分布 粗糙度 

分 类 号：TH161[机械工程—机械制造及自动化]