基于三维的摩擦表面分形维数计算方法

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The calculation results of fractal dimension by the method based two-dimensional surface are uncertainty and randomness. Four kinds of three-dimensional calculation methods, Fractal Brown Act method, the original box dimension Act method, improved differential box-counting method and wavelet transform method were used respectively to calculate fraetal dimension of the three-dimensional surface constructed with W-M function, and the calculation results were com- pared with the standard value Of fractal dimension. The result shows that box-counting method has the largest error because of the restriction on the number of sampling points the calculation scale cannot be too large, therefore only in small scale it has good linearity. Wavelet Transform has little error, but the calculation is complex, and the filter influences the calcu- lation result severely, therefore it is crucial to choose a suitable filter. Fractal Brown Act method has better linearity and litter error which is less than 3%. Therefore Fractal Brown Act is a suitable method to calculate the 3D fractal dimension of friction surface.利用二维表面形貌计算分形维数具有随意性和不确定性。采用分形布朗法、原始盒维数法、改进差分盒维数法和小波变换法计算标准三维曲面的分形维数值，并与标准值进行比较，得到误差较小的三维表面分形维数计算方法。计算结果表明：盒维数法计算结果误差最大，受采样点数量的限制，选择的尺度不能太大，只有在小尺度时，才具有较好的直线性；小波变换法误差较小，但计算复杂，且使用的滤波器不同结果也不同，因此选择合适的滤波器非常重要；分形布朗法直线性较好，误差也较小，误差基本在3％以内，是计算三维摩擦表面分形维数的合适方法。