Testing and Calculations

Bond, F. C.
Organization: Society for Mining, Metallurgy & Exploration
Pages: 11
Publication Date: Jan 1, 1985
Nature of Empirical Calculations The size reduction of large tonnages of ore and rock is an operation of great magnitude. It is a necessary and important part of industry. Its development has been motivated by practical need and has followed the path of an industrial art without much help from theoretical science. Knowledge has been accumulated from experience. Trial and error established the methods; then collected data were tabulated and served as the basis for empirical equations that have been continually modi¬fied and amplified as new data became available. These equations now constitute the bulk of our present knowledge of comminution. There is no accepted scientific theory that is basic to comminution. In electrical, mechanical, and civil engineering, as well as in many other industrial activities, such theories exist and are extremely help¬ful, but rock is essentially heterogeneous, and the zones of weakness that control its breakage are thoroughly diversified. No theory has yet been discovered which can account for the variability of rock, although many attempts have been made. Empirical equations tell nothing of the why of a phenomenon, but if they are properly derived they can tell much about the how. They always represent only an approximation of behavior but never a law. In a proper empirical equation a symbol is assigned for each of the variable quantities that obviously affect the relationship. In a grinding mill these include mill diameter, mill speed, and feed rate among them. In setting up and revising an empirical equation the cardinal princi¬ple in establishing and modifying it is this: any change must be strictly ascribed to the variable which caused it. A useful empirical equation is rendered useless when a change in any convenient coefficient or exponent is made to make it fit a particular set of data, without certainty that the altered coefficient or exponent is the responsible variable in the new data. Such indiscriminate revisions have brought the use of empirical equations into some disrepute. When existing equations are changed to accommodate new data it is a good rule to make a change which gives results intermediate between the new and the old. A halfway point is usually a good choice.
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