Superfinishing with the use of diamond lapping films differs to a significant extent from other machining methods. This is finishing surface machining, one which is realized by a slow rewinding of a microfinishing film, putting it in an oscillating motion and pressing the tool to the surface being machined. The surface being machined moves with a speed which is substantially greater than that of the tool feed. A characteristic feature of the process is a one-time use of the tool, the result being a need of an optimal selection of the machining parameters. Investigations of the topography of the microfinishing film surface were conducted with the use of new parameters that describe the arrangement and the shape of the vertices of active grains. The following were used for the purpose of assessment: coefficients that had been developed that describe the features of the shape of the tool surface, such as the standardized coefficient of the flatness of vertices wNki, the standardized number of vertices in relation to an area unit LNwi and the dissipation coefficient of the height of the location of vertices wNrwi. For the purpose of the assessment of the smoothening ability of diamond lapping films the smoothening potential coefficient wp was developed, which is defined as the geometric mean of the abovementioned indices.
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