Equivalent Fractal Parameter Inversion for Mechanically Consistent Surface Characterization of Metallic Seals

The first step in the analysis of the contact mechanics and leakage prediction of metallic seals applied to nuclear reactor pressure vessels is the proper characterization of the surface topography. At present, two approaches are used for this characterization. On the one hand, there are non-parametric techniques such as HPD and PSD, which retain all the characteristics of the surfaces that have been measured, but the results are high dimensional; hence, they cannot be analyzed analytically. The other type is parametric fractal methods, where the parameters used are fractal dimension D and characteristic scale G, where the analytical derivations can be made; however, this leads to systematic deviations in the mechanical response due to some idealized assumptions, like isotropy, Gaussian distribution, and infinite self-similarity. In this article, we propose an equivalent fractal parameter inversion model (EFPIM) that does not rely on geometric fitting; instead, it fits the mechanical contact behavior of a physical surface. This inversion procedure reduces three errors simultaneously. Thus, the EFPIM does not use D and G as the geometrical fitting variables but rather redefines them as mechanically equivalent ones, the purpose of which is to minimize the difference between the W-M fractal surface and the real measured surface. To address the problem of constrained inversion, we adopt a genetic algorithm with BFGS. To prove its effectiveness, we carried out experiments on C-ring seal surfaces and found that the deviation in the contact area was reduced by an order of magnitude in comparison to traditional structure-function extraction, and the deviation in the approach and the maximum pressure were less than 2%. Moreover, the equivalent parameters shift systematically away from their geometric counterparts in the direction that compensates for the dominant non-ideal deficit of the W-M surface; when both parameters are free, the equivalent fractal dimension decreases, while the equivalent characteristic scale increases, compensating for the absent non-Gaussian deep valleys of ideal W-M surfaces. Existing models of analytical contact and leakage may be directly implemented using equivalent parameters and with accuracy comparable to that of FFT-based simulations, with the modest cost of the offline computations.