基于快速傅里叶变换的三维非高斯粗糙表面数值仿真

Numerical simulation of three dimensional non-Gaussian rough surfaces based on FFT

实际工程粗糙表面多数符合非高斯分布,非高斯粗糙表面的数值仿真和生成对于研究两表面间润滑、接触行为具有重要意义。基于有限脉冲滤波技术,利用快速傅里叶变换算法,生成具有给定峰度、偏态和自相关函数的非高斯粗糙表面。当非高斯粗糙表面生成时,将其高度分布视为随机序列,用幅值和相角两个分量来表示,通过分别求解这两个分量使粗糙表面具有给定的表面粗糙度参数。结果表明,对于各向同性和各向异性表面,生成表面的自相关函数与给定的自相关函数吻合良好,并具有给定的峰度和偏态。

Numerical simulation plays an important role in the study of lubrication and contact behaviors of two mating surfaces, because most engineered rough surfaces approximately conform to non-Gaussian distribution. Based on finite impulse response filters and fast Fourier transform （FFT）, rough surfaces with given skewness, kurtosis and autocorrelation function （ACF） are generated. During computer generation, the height distribution of non-Gaussian rough surface is treated as a random sequence, and expressed as a function of amplitude and phase angle, which are iteratively calculated to obtain the given values. The results show that, isotropic and anisotropic rough surfaces can be efficiently generated by using the proposed model, which have the same skewness, kurtosis and ACF as the values of the given surfaces.