db2 wavelet decomposition of simulated profiles generated by W-M function with known G is executed. From the decomposition results, it is found that the wavelet decomposition parameters have obvious regularity. Based on this, a new approach to identify the characteristic length scale parameter G of a rough surface profile is proposed. The characteristic length scale parameters of the rough surface profile generated by W-M function and fractional brownian motions as well as actual machined surface profile are calculated using the proposed approach. The results are compared with the calculation results of other four kinds of methods such as the power spectral density method. But the calculation results are not of the same order of magnitude from the different methods. For simulated profiles generated by W-M function, the results from the wavelet method presented are the closest to the theoretical value. By contrast the values of the other methods differ by orders of magnitude from the theoretical value, and the errors are shown to increase with the decrease of fractal dimensions. The power spectral density method has the largest error with the calculation exceeding the theoretical value dramatically, and the error of the equations method follows, then structure function method follows. The calculating error of the equation in the literature[6] is smaller. For the simulated profiles generated by fractional brownian motions, the wavelet method and the equation in the literature[6] and structure function method give the similar calculation results as the wavelet method in this paper. For the actual profile, the wavelet method and the equation from the literature[6] give similar results. In general, the wavelet method is similar to the equation from the literature[6] and the validity of the wavelet method is proved.
WANG Yusong
,
ZHANG Xueliang
,
WEN Shuhua
,
FAN Shirong
. Wavelet Method Identifying the Characteristic Length Scale Parameter of Fractal Rough Surface[J]. Journal of Mechanical Engineering, 2018
, 54(5)
: 185
-192
.
DOI: 10.3901/JME.2018.05.185
[1] SAYLES R S,THOMAS T R. Surface topography as a nonstationary random process[J]. Nature,1978,271(2):431-434.
[2] MAJUMDAR A,BHUSHAN B. Fractal model of elastic-plastic contact between rough surfaces[J]. Journal of Tribology,1991,113(1):1-11.
[3] MAJUMDAR A,BHUSHAN B. Role of fractal geometry in roughness characterization and contact mechanics of surfaces[J]. Journal of Tribology,1990,112(2):205-216.
[4] MAJUMDAR A,TIEN C L. Fractal characterization and simulation of rough surfaces[J]. Wear,1990,136(2):313-327.
[5] 张学良. 机械结合面动态特性及应用[M]. 北京:中国科学技术出版社,2002. ZHANG Xueliang. Dynamic characteristics and its applications of machine joint surfaces[M]. Beijing:Press of Science and Technology of China,2002.
[6] 葛世荣,朱华. 摩擦学的分形[M]. 北京:机械工业出版社,2005. GE Shirong,ZHU Hua. The fractal of tribology[M]. Beijing:China Machine Press,2005.
[7] 田红亮. 机械结构固定结合部动力学建模[D]. 武汉:华中科技大学,2011. TIAN Hongliang. Dynamic modeling on fixed joint interface in mechanical structure[D]. Wuhan:Huazhong University of Science and Technology,2011.
[8] 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.
[9] BUCZKOWSKI R,KLEIBER M,STARZYNSKI G. Normal contact stiffness of fractal rough surfaces[J]. Archive of Mechanics,2014,66(6):411-428.
[10] 朱华,葛世荣. 结构函数与均方根分形表征效果的比较[J]. 中国矿业大学学报, 2004,33(4):396-399. ZHU Hua,GE Shirong. Comparison of fractal characterization effects of structure function and mean square root[J]. Journal of Chain University of Mining & Technology,2004,33(4):396-399.
[11] 贺林,张长军,朱均. 金属摩擦磨损表面的分形特性[J]. 西安公路交通大学学报,1997,17(3):93-96. HE Lin,ZHANG Changjun,ZHU Jun. The fractal character of friction-worn metal surface[J]. Journal of Xi'an Highway University,1997,17(3):93-96.
[12] 温淑花,张宗阳,张学良,等. 固定结合面刚度分形模型[J]. 农业机械学报,2013,44(2):255-260. WEN Shuhua,ZHANG Zongyang,ZHANG Xueliang,et al. Stiffness fractal model for fixed joint interfaces[J]. Transactions of the Chinese Society for Agricultural Machinery,2013,44(2):255-260.
[13] PATRICK F. On the spectrum of fractional Brownian motions[J]. IEEE Transactions on Information Theory,1989,35(1):197-199.
[14] BENOIT B. MANDELBROT,JOHN W V N. Fractional Brownian motions fractional noises and applications[J]. SIAM Review,1968,10(4):422-437.
[15] 王若平,李成彬,王国林,等. 基于分形布朗运动的二维路面不平度重构[J]. 武汉理工大学学报,2010, 32(21):89-93. WANG Ruoping,LI Chengbin,WANG Guolin,et al. Reconstruction of two-dimension road roughness based on FBM[J]. Journal of Wuhan University of Technology,2010,32(21):89-93.
