Machinery's Handbook, 31st Edition
1526 Characteristics of Metal Powders Shape Factor: The second determination is defined as a shape factor that attempts to quantify the particle shape as a single number. This is not easy; and there have been many attempts to employ shape factor in the past. However, combining the flatness ratio and elongation ratio allows the shape of the particle to be described by a shape factor. Flatness ratio p is the ratio of the short length (thickness T ) to the intermediate length w : (1) The elongation ratio q is the ratio of the intermediate length w to the longest length l : (2) where T = thickness of particle, in. (mm) w = intermediate length of particle, in. (mm) l = longest length of particle, in. (mm) p T w = -- q w l = --
T w -- w l -- --
p q -- lT w 2 --- = = =
S f
(3)
where S f = shape factor p = flatness ratio
q = elongation ratio
If
S f = 1, S f 1, < S f 1, >
the particle is spherical or cubical the particle is more elongated and thin
(4)
the particle is blade-shaped
Sphericity: Sphericity is, naturally, a measure of how spherical an object is. Defined by Wadell in 1932, the sphericity y of a particle is the ratio of the surface area of a sphere with the same volume as the given particle to the surface area of the particle: (5) where V p = volume of the particle A p = the surface area of the particle A particle that is a perfect sphere has sphericity value of Ψ = 1. Friction and Flow Characteristics of Particles.— The friction characteristics of particles play a very important rule in the ability of a powder to flow readily and pack tightly. The friction of particle aggregates basically involves two aspects: inter-particle friction and friction between the aggregate and the walls of the container. Both aspects constitute challenging topics, and often both must be considered in dealing with practical problems related to powder materials. Particle mechanics is the branch of knowledge that deals with the mechanics properties and flow of particles and particle aggregates. Friction is a critical aspect of many particle mechanics problems. The most common way to quantify inter-particle friction is by measuring the angle of repose. Angle of Repose: Angle of repose, in general, is an engineering property of granular material. When powders are poured from a narrow funnel onto a horizontal surface, a conical pile will form (Fig. 4). Ψ π 1 3 -- 6 V p ( ) A p = ------------ 2 3 --
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