MATHEMATICAL 3-D-SIMULATION OF ROUGHNESS AND PLASMA-SPRAYED COATING
Dirk Windelberg
AG Qualität im Institut für Mathematik - Universität Hannover Welfengartenl - D-30167 Hannover
Friedrich-Wilhelm Bach
Lehrstuhl für Werkstofftechnologie Universität Dortmund - Germany
Abstract
For plasma-coating we simulate
- substrate surface condition (for optimization adhesive strength of plasma spray coatings)
- 3-D-surface (roughness and geometry) of A1_{2}0_{3} -blasted substrates, and
- plasma-spray-coating.
We activate a surface by grit blasting (A1_{2}0_{3}-particles P_{i}). For mathematical simulation we assume spherical size (diameter d_{i}), velocity v_{i} and angle of incidence α_{i}.
Our experiments give hints to the kind of statistical distributions (hyperbolic, parabolic or constant) as well as to the power of diameter and velocity for modeling the depth of penetration for each point.
From this equation of penetration we give a mathematical definition of roughness of a grit by a vector of grit-roughness: For each pixel we look for a solid spherical particle of such a diameter, that the particle can vanish in the surface. Comparing the diameters of all pixels of the surface we define the 'quality of grit-roughness'.
In the same way we define the 'quality of spray-roughness' by a vector: For each pixel we assume the particle is liquid and then we look if it vanishes.
For evaluating and calculating the'quality of a plasma-coated material' we compare these two vectors with the results from experience.