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|Introduction Grinding is the reduction of ore and similar raw materials to particle sizes below the practical limits of commercial crushing ma¬chines. This size is about 36 in. (1 cm), in most cases, although some finer crushing machines are in regular use. The feed size to grinding machines may range upward to S in. in rod mills, and 12 in. or more in autogenous mills. The finest particle sizes produced in mineral processing operations result from grinding. Ordinary grinding of brittle materials is the result of impacting, rolling, and abrasion of heavy bodies, moving freely under the influ¬ence of gravity. These falling and rolling grinding bodies, which are usually of metal, must be much heavier and larger than the ore parti¬cles they break. This weight relationship is usually in excess of 100: 1. The sustained fall of the grinding bodies is obtained by placing them, together with the rock particles they grind, in a rotating drum or cylinder with horizontal axis, called a tumbling mill. The mill is nearly half full of grinding bodies and ore particles, which may be fed into one end and exit from the other through hollow trunnions which usually serve as the mill bearings. The mill lining must be thick to absorb wear and rough to prevent excessive slippage of the charge. The breakage of brittle rock or ore is accomplished by compression. The compression may be a rapid impact, from the fall and roll of a grinding ball, or it may result from the relatively slow and constrained motion as in a jaw crusher. Breakage by shear is a secondary result of the compressive motion. Ordinary rock has an extremely heterogenous structure with innumerable zones of weakness in which cracks, fractures, and breakages can form. When a rock is subjected to com¬pression it deforms. If the compressive force exceeds a certain critical value an incipient crack appears in the most fragile zones of weakness. This crack tip may first form on the particle surface or in its interior. When the first crack tip forms the compressive stresses immediately surrounding it flow to it, and this concentration of forces extends the crack and splits the rock. Other adjacent cracks may form during this extremely rapid process. Because of the nature of brittle particles, the work done in breaking them consists essentially of the work input required to compress them to the point at which the first crack tip forms. Breakage requires no appreciable additional energy input be¬yond that required for the deformation, since the stress energy already imported to the rock flows to the crack tip and extends it to breakage. Types of Tumbling Mills The general term tumbling mill includes the rod mill, ball mill, pebble mill, autogenous mill, and tube mill. It is of cylindrical or cylindro-conical shape and rotates about its horizontal axis. Rotational speed, liner type, and size and shape of tumbling media are selected to provide the desired operating conditions for the specific grinding application. Openings are provided through the mill ends for feed and discharge of the material being ground. A common feature of tumbling mills is the use of tumbling media|