14.5. MECHANICAL SIZE REDUCTION

14.5A. Introduction

Many solid materials occur in sizes that are too large to be used and must be reduced. Often the solids are reduced in size so that the separation of various ingredients can be carried out. In general, the terms crushing and grinding are used to signify the subdividing of large solid particles into smaller particles.

In the food-processing industry, a large number of food products are subjected to size reduction. Roller mills are used to grind wheat and rye to flour and to grind corn. Soybeans are rolled, pressed, and ground to produce oil and flour. Hammer mills are often used to produce potato flour, tapioca, and other flours. Sugar is ground to a finer product.

Grinding operations are very extensive in the ore-processing and cement industries. Copper ores, nickel and cobalt ores, and iron ores, for example, are ground before chemical processing. Limestone, marble, gypsum, and dolomite are ground to use as fillers in paper, paint, and rubber. Raw materials for the cement industry, such as lime, alumina, and silica, are ground on a very large scale.

Solids may be reduced in size by a number of methods. Compression or crushing is generally used for reduction of hard solids to coarse sizes. Impact gives coarse, medium, or fine sizes. Attrition or rubbing yields fine products. Cutting is used to give definite sizes.

14.5B. Particle-Size Measurement

The feed-to-size reduction processes and the product are defined in terms of the particle-size distribution. One common way to plot particle sizes is to plot particle diameter (sieve opening in screen) in mm or μm versus the cumulative percent retained at that size. (Openings for various screen sizes are given in Appendix A.5.) Such a plot was given on arithmetic probability paper in Fig. 12.12-2.

Often the plot is made, instead, as the cumulative amount as percent smaller than the stated size versus particle size, as shown in Fig. 14.5-1a. In Fig. 14.5-1b the same data are plotted as a particle-distribution curve. The ordinate is obtained by taking the slopes of the 5-μm intervals of Fig. 14.5-1a and converting to percent by weight per μm. Complete particle-size analysis is necessary for most comparisons and calculations.

14.5C. Energy and Power Required in Size Reduction

1. Introduction

In size reduction of solids, feed materials of solid are reduced to a smaller size by mechanical action. The materials are fractured. The particles of feed are first distorted and strained by the action of the size-reduction machine. This work to strain the particles is first stored temporarily in the solid as strain energy. As additional force is added to the stressed particles, the strain energy exceeds a certain level, and the material fractures into smaller pieces.

When the material fractures, new surface area is created. Each new unit area of surface requires a certain amount of energy. Some of the energy added is used to create the new surface, but a large portion of it appears as heat. The energy required for fracture is a complicated function of the type of material, size, hardness, and other factors.

The magnitude of the mechanical force applied; the duration; the type of force, such as compression, shear, and impact; and other factors affect the extent and efficiency of the size-reduction process. The important factors in the size-reduction process are the amount of energy or power used and the particle size and new surface formed.

2. Power required in size reduction

The various theories or laws proposed for predicting power requirements for size reduction of solids do not apply well in practice. The most important ones will be discussed briefly. Part of the problem with the theories is estimating the theoretical amount of energy required to fracture and create new surface area. Approximate calculations give actual efficiencies of about 0.1 to 2%.

The theories derived depend upon the assumption that the energy E required to produce a change dX in a particle of size X is a power function of X:

Equation 14.5-1

where X is size or diameter of particle in mm, and n and C are constants depending upon type and size of material and type of machine.

Rittinger proposed a law which states that the work in crushing is proportional to the new surface created. This leads to a value of n = 2 in Eq. (14.5-1), since area is proportional to length squared. Integrating Eq. (14.5-1),

Equation 14.5-2

where X₁ is mean diameter of feed and X₂ is mean diameter of product. Since n = 2 for Rittinger's equation, we obtain

Equation 14.5-3

where E is work to reduce a unit mass of feed from X₁ to X₂ and K_R is a constant. The law implies that the same amount of energy is needed to reduce a material from 100 mm to 50 mm as is needed to reduce the same material from 50 mm to 33.3 mm. It has been found experimentally that this law has some validity in grinding fine powders.

Kick assumed that the energy required to reduce a material in size was directly proportional to the size-reduction ratio. This implies n = 1 in Eq. (14.5-1), giving

Equation 14.5-4

where K_K is a constant. This law implies that the same amount of energy is required to reduce a material from 100 mm to 50 mm as is needed to reduce the same material from 50 mm to 25 mm.

Recent data by Bond (B3) on correlating extensive experimental data suggest that the work required using a large-size feed is proportional to the square root of the surface/volume ratio of the product. This corresponds to n = 1.5 in Eq. (14.5-1), giving

Equation 14.5-5

where K_B is a constant. To use Eq. (14.4-5), Bond proposed a work index E_i as the work in kW · h/ton required to reduce a unit weight from a very large size to 80% passing a 100-μm screen. Then the work E is the gross work required to reduce a unit weight of feed with 80% passing a diameter X_F μm to a product with 80% passing X_P μm.

Bond's final equation, in terms of English units, is

Equation 14.5-6

where P is hp, T is feed rate in tons/min, D_F is size of feed in ft, and D_P is product size in ft. Typical values of E_i for various types of materials are given in Perry and Green (P1) and by Bond (B3). Some typical values are bauxite (E_i = 9.45), coal (11.37), potash salt (8.23), shale (16.4), and granite (14.39). These values should be multiplied by 1.34 for dry grinding.

EXAMPLE 14.5-1. Power to Crush Iron Ore by Bond's Theory It is desired to crush 10 ton/h of iron ore hematite. The size of the feed is such that 80% passes a 3-in. (76.2-mm) screen and 80% of the product is to pass a -in. (3.175-mm) screen. Calculate the gross power required. Use a work index Ei for iron ore hematite of 12.68 (P1). Solution: The feed size is DF = = 0.250 ft (76.2 mm) and the product size is DP = /12 = 0.0104 ft (3.175 mm). The feed rate is T = 10/60 = 0.167 ton/min. Substituting into Eq. (14.5-6) and solving for P,

14.5D. Equipment for Size Reduction

1. Introduction and classification

Size-reduction equipment may be classified according to the way the forces are applied as follows: between two surfaces, as in crushing and shearing; at one solid surface, as in impact; and by action of the surrounding medium, as in a colloid mill. A more practical classification is to divide the equipment into crushers, grinders, fine grinders, and cutters.

2. Jaw crushers

Equipment for coarse reduction of large amounts of solids consists of slow-speed machines called crushers. Several types are in common use. In the first type, a jaw crusher, the material is fed between two heavy jaws or flat plates. As shown in the Dodge crusher in Fig. 14.5-2a, one jaw is fixed and the other reciprocating and movable on a pivot point at the bottom. The jaw swings back and forth, pivoting at the bottom of the V. The material is gradually worked down into a narrower space, being crushed as it moves.

The Blake crusher in Fig. 14.5-2b is more commonly used, where the pivot point is at the top of the movable jaw. The reduction ratios average about 8:1 in the Blake crusher. Jaw crushers are used mainly for primary crushing of hard materials and are usually followed by other types of crushers.

3. Gyratory crushers

The gyratory crusher shown in Fig. 14.5-3a has to a large extent taken over in the field of large hard-ore and mineral crushing applications. Basically it is like a mortar-and-pestle crusher. The movable crushing head is shaped like an inverted truncated cone and is inside a truncated cone casing. The crushing head rotates eccentrically and the material being crushed is trapped between the outer fixed cone and the inner gyrating cone.

4. Roll crushers

In Fig. 14.5-3b a typical smooth roll crusher is shown. The rolls are rotated toward each other at the same or different speeds. Wear of the rolls is a serious problem. The reduction ratio varies from about 4:1 to 2.5:1. Single rolls are often used, rotating against a fixed surface, and corrugated and toothed rolls are also used. Many food products that are not hard materials, such as flour, soybeans, and starch, are ground on rolls.

5. Hammer mill grinders

Hammer mill devices are used to reduce intermediate-sized material to small sizes or powder. Often the product from jaw and gyratory crushers is the feed to the hammer mill. In the hammer mill a high-speed rotor turns inside a cylindrical casing. Sets of hammers are attached to pivot points at the outside of the rotor. The feed enters the top of the casing and the particles are broken as they fall through the cylinder. The material is broken by the impact of the hammers and pulverized into powder between the hammers and casing. The powder then passes through a grate or screen at the discharge end.

6. Revolving grinding mills

For intermediate and fine reduction of materials, revolving grinding mills are often used. In such mills a cylindrical or conical shell rotating on a horizontal axis is charged with a grinding medium such as steel, flint, or porcelain balls, or with steel rods. The size reduction is effected by the tumbling of the balls or rods on the material between them. In the revolving mill, the grinding elements are carried up the side of the shell and fall on the particles underneath. These mills may operate wet or dry.

Equipment for very fine grinding is highly specialized. In some cases two flat disks are used, where one or both disks rotate and grind the material caught between the disks (P1).