Mathematical modeling of the working surface of the wheel in the conditions of electroerosive diamond grinding

Abstract

The paper presents an analysis of formulas for calculating the number of grains of the diamond wheel, the distances between them, and their distributions. The results are based on experimental studies and calculation methods with simulation of a specific shape of grains. The discrepancy in the quantitative data is explained by a different methodological approach - profiling, imprint method, optical, thermocouple method, planimetric, microsections, and others, and in calculation methods - by the difference in the accepted grain shape and initial grain sizes, based on the designation of the grain size of the powder. In addition, in order to establish reliable results, each of the noted methods gives rise to a number of special techniques and original approaches. Profiling of the working surface of the circle can be carried out with a diamond needle, a chisel-like probe, with the recording of profilograms along two auxiliary lines, equidistantly located relative to the controlled one, with an assessment of the relief of the conductive needle for more distinct recognition of diamond grains and protrusions of a metal bond, etc. each method. Moreover, the corresponding distinctive method provides an analysis of the advantages of one and the disadvantages of another approach.
The most reliable calculation method can be considered the one in which the results correspond to experimental data obtained by piecewise counting the number of grains in one carat and, respectively, per unit volume of the diamondiferous layer. In the calculations, this correspondence made it possible to judge the reliability of the results.
The analysis and calculation of grains held on the working surface of the circle at the smallest embedment depth in the bundle was carried out. Many researchers as the determining parameter accept the maximum height of the protrusion of grains above the ligament level. In this regard, we note that the minimum embedment depth is more reliable (stable), physically determined value, at least depending on randomly acting factors.