FRACTAL CHARACTERIZATION AND SIMULATION OF ROUGH SURFACES
FRACTAL CHARACTERIZATION AND SIMULATION OF ROUGH SURFACES
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DOI：
10.1016/0043-1648(90)90154-3
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发表时间：
1990-03-01
期刊：
影响因子：
5
通讯作者：
TIEN, CL
中科院分区：
文献类型：
--
作者：
MAJUMDAR, A;TIEN, CL
对各种机械加工的钢表面和织构磁性薄膜盘的粗糙度测量表明，它们的形貌是多尺度的和随机的。在所考虑的长度范围内，这些表面的功率谱均遵循幂定律。这种光谱行为意味着，当表面被反复放大时，统计上相似的表面图像会不断出现。本文将分维作为这种多尺度结构的本质属性，并利用W-M分维函数提出了一种新的简单的粗糙度表征方法。不锈钢表面轮廓的功率谱在高频下重合，对应的分维为1.5。据推测，这种重合发生在较小的尺度上，因为表面在这样的尺度上仍未处理。表面处理，如磨削或研磨，在达到一定拐角频率的较低频率下会降低功率，高于此频率，所有表面都表现为未加工表面。W-M函数还用于确定性地模拟统计上与真实表面相似的布朗和非布朗粗糙表面。
Roughness measurements on a variety of machined steel surfaces and a textured magnetic thin-film disk have shown that their topographies are multiscale and random. The power spectrum of each of these surfaces follows a power law within the length scales considered. This spectral behavior implies that when the surface is repeatedly magnified, statistically similar images of the surface keep appearing. In this paper the fractal dimension is identified as an intrinsic property of such a multiscale structure and the Weierstrass-Mandelbrot (W-M) fractal function is used to introduce a new and simple method of roughness characterization.The power spectra of the stainless steel surface profiles coincide at high frequencies and correspond to a fractal dimension of 1.5. It is speculated that this coincidence occurs at small length scales because the surface remains unprocessed at such scales. Surface processing, such as grinding or lapping, reduces the power at lower frequencies up to a certain corner frequency, higher than which all surfaces behave as unprocessed ones.The W-M function is also used to simulate deterministically both brownian and non-brownian rough surfaces which exhibit statistical resemblance to real surfaces.