円弧法による粒子の形状係数について

抄録

An attempt to obtain a three-dimensional shape factor of a particle, Ψ_R, was made by determining the two-dimensional shape factors of projected particle figure, φ_R and φ_R', and by considering the wave and roughness of the surface of projection.
In‘Circular arc method’, the ratio of similarity to circle, φ_R is defined as A_m/A₀, where A₀ is the area of minimum circle circumscribing the projection of particle.
The circumcribed circle is appropriately divided into equal parts by the lines passing through the circumcenter. Each divided part of the projection is again circumscribed by the maximum and the minimum circular arcs which contact with the contour line of the projection at more than one point. A_m is defined as an area of the circle with the mean radius of the above circles for each part of projections. Thus A_m represents an approximate area of the projection.
By taking into consideration the characteristics of plane and side figures, an equation Ψ_R=φ_R √φ_R' is more appropriate than Ψ_R'={(√φ_R+√φ_R')/2}³.
Comparison was carried out with various kinds of model particles and degrees of ratio to sphere.
The results clearly demonstrated that Ψ_R determined by the‘Curve-fitting method’was nearly equal to the degree of ratio to sphere for the model particles calculated from the ratio between the true area and the area of its circumscribed circle of the projection.