Study of Synthesis and Properties of Anisotropic Fractal Surfaces

doi:10.3901/JME.2019.21.118

Abstract

Abstract: 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 D_x,D_y. 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 R_qx,R_qy and the surface roughness S_q are revealed. The results show that smaller D_x or D_y 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 D_x and D_y. In addition, D_x, D_y only affect the absolute roughness values of S_q,R_qx and R_qy by causing roughness increase with them, not the relative relation of R_qx and R_qy.

Key words: fractal surface, discrete Fourier transform, synthetic dimension method, nominal dimension, profile's power distribution, roughness

CLC Number:

TH161

ZHANG Ling, ZHENG Guolei, YANG Rongrong. Study of Synthesis and Properties of Anisotropic Fractal Surfaces[J]. Journal of Mechanical Engineering, 2019, 55(21): 118-126.

References

[1] 梁志强,黄迪青,周天丰,等. 螺旋伞齿轮磨削表面形貌仿真与试验研究[J]. 机械工程学报,2019,55(3):204-211. LIANG Zhiqiang,HUANG Diqing,ZHOU Tianfeng,et al. Simulation and experimental research on grinding surface topography of spiral bevel gear[J]. Journal of Mechanical Engineering,2019,55(3):204-211.
[2] 秦红玲,郭建义,徐翔,等. 滑动轴承表面形貌的分形模拟及对摩擦学性能的影响[J]. 润滑与密封,2018,43(2):47-52. QIN Hongling,GUO Jianyi,XU Xiang,et al. On fractal modeling and tribological properties of surface morphology for sliding bearing[J]. Lubrication Engineering,2018,43(2):47-52.
[3] HU Songtao,HUANG Weifeng,BRUNETIERE N,et al. Stratified effect of continuous bi-Gaussian rough surface on lubrication and asperity contact[J]. Tribology International,2016,104:328-341.
[4] THOMAS A P,THOMAS T R. Engineering surface as fractals,fractal aspects of materials[M]. Pittsburgh:Materials Research Society,1986.
[5] 周超,高诚辉. 基于离散傅里叶变换的分形粗糙表面轮廓合成与研究[J]. 机械工程学报,2011,47(17):99-103. ZHOU Chao,GAO Chenghui. Study of synthesized fractal surface's profiles based on discrete Fourier transform[J]. Journal of Mechanical Engineering,2011,47(17):99-103.
[6] 陈辉,胡元中,王慧,等. 粗糙表面分形特征的模拟及其表征[J]. 机械工程学报,2006,42(9):219-223. CHEN Hui,HU Yuanzhong,WANG Hui,et al. Simulation and characterization of fractal rough surfaces[J].Chinese Journal of Mechanical Engineering,2006,42(9):219-223.
[7] 淦犇,黄宜坚. 铣削加工表面轮廓的几何分形特征[J].华侨大学学报,2010,31(4):371-377. GAN Ben,HUANG Yijian. Geometry fractal characteristics of milled surface profiles[J]. Journal of Huaqiao University,2010,31(4):371-377.
[8] THOMAS T R,ROSEN B G,AMINI N. Fractal characterization of the anisotropy of rough surfaces[J]. Wear,1999,232(1):41-50.
[9] LI Chengui,DONG Shen,ZHANG Guoxiong. Evaluation of the anisotropy of machined 3D surface topography[J]. Wear,2000,237(2):211-216.
[10] WU Jiunnjong. Analyses and simulation of anisotropic fractal surfaces[J]. Chaos Solitons & Fractals,2002,13(9):1791-1806.
[11] 黄祥,王清辉,李伟晨,等. 各向异性表面生成算法及其应用[J]. 华南理工大学学报,2013,41(7):1-6. HUANG Xiang,WANG Qinghui,LI Weichen,et al. Generation algorithm of anisotropic surface and its application[J]. Journal of South China University of Techonology,2013,41(7):1-6.
[12] 赵歆波,PETROU M,张定华,等. 基于频谱合成的自然地形生成方法[J]. 机械科学与技术,2004,23(3):263-265. ZHAO Xinbo,PETROU M,ZHANG Dinghua,et al. A method for generating natural terrain based on spectral synthesis[J]. Mechanical Science and Technology for Aerospace Engineering,2004,23(3):263-265.
[13] 周超,黄健萌,高诚辉. 各向异性分形表面建模研究[J]. 中国机械工程,2015,26(8):1019-1023. ZHOU Chao,HUANG Jianmeng,GAO Chenghui. Modeling of anisotropic fractal surface[J]. Journal of China Mechanical Engineering,2015,26(8):1019-1023.
[14] PEITGEN H O,SAUPE D. The science of fractal images[M]. Berlin:Springer-Verlag,1988.
[15] REED I S,LEE P K,TRUONG T K. Spectral representation of fractional Brownian motion in n dimensions and its properties[J]. IEEE Transactions on Information Theory,1995,41(5):1439-1451.
[16] KULESZA S,BRAMOWICA M. A comparative study of correlation methods for determination of fractal parameters in surface characterization[J]. Applied Surface Science,2014,293(8):196-201.
[17] 王余松,张学良,温淑花,等. 分形粗糙表面特征长度尺度参数小波识别法[J]. 机械工程学报,2018,54(5):185-192. WANG Yusong,ZHANG Xueliang,WEN Shuhua,et al. Wavelet method identifying the characteristic length scale parameter of fractal rough surface[J]. Journal of Mechanical Engineering,2018,54(5):185-192.
[18] 中华人民共和国国家质量监督检验检疫总局,中国国家标准化管理委员会. GB/T 33523.2-2017产品几何技术规范(GPS)表面结构区域法-第2部分:术语、定义及表面结构参数[S]. 北京:中国标准出版社,2017. General Administration of Quality Supervision,Inspection and Quarantine of the People's Republic of China,Standardization Administration of the People's Republic of China. GB/T 33523.2-2017 Geometrical product specifications (GPS)-Surface texture:Areal-Part 2:Terms,definitions and surface texture parameters[S]. Beijing:China Press Standards,2017.
[19] OPPENHEIM A V,SCHAFER R W. Discrete-time signal processing[M]. 3rd ed. Englewood Cliffs:Prentice Hall,2009.