The analytic expression for the normal connection dynamic stiffness of whole bolted joint interface was deduced using a modified two-variable Weierstrass-Mandelbrot function. Theoretical and experimental methods to identify the fractal dimension and fractal roughness of the joint interface were presented with the structure function for the equivalent surface. A beam-rail joint interface was selected as a research object at the pentahedral machining center of a wind turbine
and experimental modes of test specimen were viewed as reference. The theoretical solution to the normal connection dynamic stiffness of the bolted joint interface ensemble was validated by the correlative analysis of analogous vibration shape and the quantitative comparison of natural frequencies. The theoretical vibration shapes agree with the experimental ones. The relative deviation of the theoretical natural frequencies from the experimental results is from -4.3% to 5.1%.
LAN Guosheng, ZHANG Xueliang, DING Hongqin, et al. Modified contact model of joint interfaces based on fractal theory [J]. Transactions of the Chinese Society for Agricultural Machinery,2011,42(10):217-223,229.
JIANG Shuyun, ZHENG Yunjian, ZHU Hua. A contact stiffness model of machined plane joint based on fractal theory [J]. ASME Journal of Tribology, 2010,132(1):1-7.
CHANG W R, ETSION I, BOGY D B. Adhesion model for metallic rough surfaces [J]. ASME Journal of Tribology, 1988, 110(1):50-56.
YAN W, KOMVOPOULOS K. Contact analysis of elastic-plastic fractal surfaces [J]. Journal of Applied Physics, 1998, 84(7):3617-3624.
GREENWOOD J A,WILLIAMSON J B P. Contact of nominally flat surfaces [J]. Proceedings of the Royal Society of London: Series A Mathematical and Physical Sciences, 1996, 295(1442):300-319.
TIAN Hongliang, ZHU Dalin, FANG Zifan, et al. 129 years of Hertz contact [J]. Journal of China Three Gorges University: Natural Sciences, 2011, 33(6):61-71.
WANG S, KOMVOPOULOS K. A fractal theory of the interfacial temperature distribution in the slow sliding regime: part Ⅰ Elastic contact and heat transfer analysis [J]. ASME Journal of Tribology, 1994, 116(4):812-823.
TIAN Hongliang, ZHAO Chunhua, ZHU Dalin, et al. Contact analysis of elastoplastic three-dimensional anisotropic fractal surfaces [J]. Journal of China Three Gorges University: Natural Sciences, 2012, 34(1):69-73.
《数学手册》编写组. 数学手册 [M]. 北京:高等教育出版社, 2008:282,590.
WANG S, KOMVOPOULOS K. A fractal theory of the temperature distribution at elastic contacts of fast sliding surfaces [J]. ASME Journal of Tribology, 1995, 117(2):203-215.