Rough Surfaces

All of the below functions can be found in the rough_surfaces module of the package.

This module contains functions related to rough surfaces. Please see the /demo directory for minimum examples.

abbottfirestone(trace, num_bins=100)

Calculate the Abbott-Firestone curve for a 1D profile trace.

Parameters:

• trace (ndarray) – The profile heights of the 1D trace.
• num_bins (positive int, optional) – The number of bins for the calculation of the profile height probability distribution.

Returns:

• bins (ndarray) – The bins used for the calculation of the profile height probability distribution (= x-axis data for Abbott-Firestone plot).
• prob_dist (ndarray) – The probability distribution of the profile (= y-axis data for Abbott- Firestone plot).

randsurf(n_x, n_y, delta_x, delta_y, s_q, lambda_x, lambda_y)

Generate a random rough surface in the x-y-plane. The surface has a Gaussian roughness distribution, a mean surface roughness of (approximately) 0, and a standard deviation of s_a.

The correlation length can be specified separately in x and y; however, the correlation length and grid spacing need to be constant in both directions. The computational cost increases with increasing correlation length in either direction.

The implementation follows the approach described in the appendix of:

N. Patir and H. S. Cheng, An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication, Journal of Lubrication Technology, 100(1), pages 12-17, 1978. doi:10.1115/1.3453103

The implementation is similar to that used by Björklund and Andersson:

S. Björklund and S. Andersson, A numerical method for real elastic contacts subjected to normal and tangential loading, Wear, 179, pages 117-122, 1994. doi: 10.1016/0043-1648(94)90228-3

Parameters:

• n_x (int) – Number of grid points along x-axis.
• n_y (int) – Number of grid points along y-axis.
• delta_x (float) – Distance between grid points along the x-axis
• delta_y (float) – Distance between grid points along the y-axis.
• s_q (float) – Standard deviation of the surface roughness.
• lambda_x (float) – Correlation length along the x-axis.
• lambda_y (float) – Correlation length along the y-axis.

Returns:

heights – Surface heights in the x-y-plane.

Return type:

ndarray