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By H. O. Hofman

The sudden decease, April 1, 1910, in Chicago, of Dr. Franklin R. Carpenter was a shock to his many friends. He died in his sixty-second year, of heart paralysis. To most fellow-members of the Institute who have followed the progress of the last twenty-five years in the mining and treatment of non-ferrous ores, the work of Dr. Carpenter in that line is familiar; but very few, even of those who knew hinl well in the later years, are acquainted with his earlier struggles to satisfy an inborn hunger for knowledge. The story of his life resembles that of the pioneer who opens up new country; overcoming hardships with indomitable courage, meeting doubts and difficulties with an alert and open mind, and exercising in the face of reverses an unconquerable perseverance. It seems appropriate to place on record in the Transactions a brief outline of the life and work of this eminent engineer. During the past 15 years of his life Dr. Carpenter was much interested in genealogy. In the pursuit of this study as an avocation, he traced his own ancestry to the time when ((Hugh," called "le Charpentier" on account of the dexterity with which he had swung his battle-axe as a crusader, settled in Sussex on lands received from William the Conqueror. The Carpenters came to this country with William Penn. A prominent member of the family was Joshua Carpenter, the founder of Christ Church, Philadelphia. Dr. Carpenter's branch of the family moved from Pennsylvania into that part of Virginia which is now West Virginia, where his grandfather settled in Harrison county, while the grand-uncle went further west, and built the first iron-furnace at Hanging Rock, Lawrence county, Ohio. In fact, since early times, the Carpenters appear to have been iron-masters. Franklin R. Carpenter mas born, Nov. 5, 1848, in Parkers-

Jan 1, 1911

By Robert Roberts

(Butte Meeting, August, 1913.) IN order to obtain data on the thermal effect of the blast-furnace jacket and oil the water consumption in these jackets a series of tests were run on the 56 by 180 in. blast furnaces at the Great Falls Reduction Department of the Anaconda Copper Mining Co., at Great Falls, Mont. The arrangement of the jacket is shown in the transverse section of one of the furnaces (Fig. 1) on which the tests were made. The nose, spout, and breast jackets have independent water supplies and discharges. The end and side jackets are connected in pairs, as regards water supply, the feed water entering at the bottom of the lower jacket and overflowing into the bottom of the jacket immediately above it, and discharging into an independent overflow pipe for each pair of jackets. Tests were run on the main side and end jackets, the breast jacket, the spout, and the nose. Measurements were taken of the quantity of water discharged per minute and the rise in temperature of the water in its passage through the jacket. The product of these two results, expressed in the proper units, evidently gives the number of units of heat removed per minute by the water. Sufficient work was done on each type of jacket to determine its behavior under different conditions, and the results from each set of conditions were checked by repeating the work from three to six times.

Jan 7, 1913

By Chester Purington

THE AUTHOR hopes that this paper will meet with criticism and debate by fellow members of the Institute rather than with that attitude of passiv-ity and indifference which one is inclined to adopt when considering a field completely foreign to one's own experi-ence. After several years of study of voluminous literature, maps, and statistics, and many personal journeys and field inspections of various parts of Siberia, the conclusion is reached .that the area adjacent to the Stanovoi, Zhugd-Zhur, and Yablonoi ranges as below defined is that which .is most accessible to the western world and will soonest give results from exploration. HISTORY The first incursion of the Russians into Siberia east of the Yenesei River appears to have been in 1632 when the fort of Yakutsk was founded on the middle Lena. The early expeditions were in quest of furs. As the Siberians say, "the sable beckoned" and the post of Anadyr was founded in 1639, two thousand miles further northeast. Thus nineteen years after the Pilgrims landed in Massachusetts, the Russians had established a trading post within 700 miles of what is now the town of Nome, Alaska. Parties of Cossaks penetrated to the shores of the Okotsk1 Sea early in the seventeenth century, but it was not until 1688 that the town of Okotsk was founded. In 1712 a grand project was elaborated at St. Petersburg for building a port at Okotsk, but it came to nothing. Vitus Bering, the Alaska explorer, built ships at Okotsk, and made this his point of depar-ture. It is stated that the iron work used in these ships was brought overland partly from Yakutsk, and partly even from St. Petersburg, 5500 miles away. Accord-ing to report a copper deposit was worked on the river Urak, not far from the coast, and copper was smelted for sheathing the bottoms. Grassgrown mounds con-taining slag and shots of copper were inspected by the writer last summer, at the site of the ancient shipyard.

Jan 11, 1923

By E. S. Machlin, A. A. Hendrickson

Use was made of a recently developed surface-accumulation diffusion technique to measure the self-diffusivity of edge-type dislocation singular lines (Burgers vector along <110>) in a bent and polygonized single crystal of silver. Two factors are involved in obtaining a number for the diffusivity. One factor, the dislocation-line density, was measured by a microscopic technique recently developed, and the value of the other parameter, the effective "diameter" of a dislocation pipe, was estimated. With these parameters equal to 7.3 X 106 dislocations per sq cm and 10-7 cm, respectively, it was found that the self-diffusivity along edge-type dislocation lines was a factor of about two times the average grain-boundary self-diffusivity. The dislocation-pipe diffusivity is about 7x10-7 sq cm per sec at 450°C. THE possibility of short-circuit diffusion through imperfections in crystals has been recognized for some time. It was only recently, however, that concerted effort has been expended to obtain values of diffusivity for grain-boundary short circuits. The work, for example, of Hoffman and Turnbull1 on silver, Fisher&apos;s&apos; analysis of the grain-boundary dif-

Jan 1, 1955

By C. C. Harris

A critical literature review leads to a descriptive model of tumbling mill operation based upon energy partition concepts and the necessary requirements for particle fracture. As grinding proceeds into the ultra-fine region, conditions which are of little significance during normal operations gradually become controlling. These involve increasing resistance to fracture and an increasing tendency to aggregate as particles become smaller, and a growing fraction of the power input being consumed fruitlessly. The result is that fineness asymptotes to a maximum value as comminution proceeds indefinitely; thus where t is time, p and n are experimentally determined parameters, and Ø is a measure of fineness, which is presumed to be proportional to specific surface area, or proportional to the reciprocal of the size modulus (provided that the distribution modulus remains constant with time), or both. Ø, is the asymptotic value of Ø and is a measure of the grind limit. A method for its graphical determination is given. In a previous paper1 the physical and mathematical principles requisite to a study of the role of energy in comminution were reviewed. The micro-process of comminution — or the comminution event — can be investigated in terms of (a) the magnitude of the force-field localized around the individual particles which gives rise to the stresses generated in the particles, which in turn induces their fracture, and (b) the distribution of fragment sizes, should the event prove fruitful. The entire fragmentation operation can be considered to be the totality of its individual events, and in order to obtain a single independent variable of the process it is necessary to transform and sum the local stresses in terms of energy.1 This energy, however, will account for only a fraction of the energy input to the comminution process, the actual magnitude depending upon the kind of mill and several related factors. From the comminution viewpoint the primary function of a mill is that of stressing as many as possible of the individual particles of the charge to failure, with the maximum economy of energy expenditure. This is difficult indeed to achieve, for stressing a particle does not always break it, while the overwhelming portion of the energy input is involved with various internal mill processes which — almost incidentally — determine the magnitude, frequency, and manner in which the forces are applied to the particles. Essentially, these processes depend upon the mill dimensions, loading and speed, and they may be little affected whether fracture occurs or not. These processes must be delineated if a complete description of the role of energy in comminution is to be given; the energy account sheet1 (Fig. 1) in showing how the energy is partitioned for the requirements of the several functions it performs, provides a framework for the development of a model of the comminution process. Actual numerical values for the variables appearing in Fig. 1 will depend upon the mill, materials, and operating conditions. A possible general relationship between the variables will be suggested in this paper. Before proceeding further, a cautionary note must be issued. It was pointed out in an earlier paper&apos; that while energy input is not changed by increasing the power and decreasing the time in the same proportion, and vice versa, the results of the process in terms of particle fineness may be different. Thus, although energy is chosen as the independent variable of a comminution process, it is not absolutely independent, and care must be exercised to ensure that it is used within its range of valid application. Time has the necessary independence, and it will be used in place of energy where it is appropriate. The residence time in a mill is usually of the order of minutes. Under these conditions the particles are subjected to "... a relatively constant fracture producing environment".2 However, under the more rigorous conditions of greatly extended time, which pertain in ultra-fine grinding, indications are that the fracture producing environment no longer remains constant; this is the major subject of this paper. At this extreme limit the mill is probably taxed to its utmost, and at the same time the bulk material properties are becoming closer to ideal, while the physico chemical effects associated with surfaces, edges and corners are multiplying. (The edge length per unit volume is proportional to the square of the specific

Jan 1, 1968

By Allan T. Fisk, Carl R. Peterson, Richard E. Brooks, James J. Olson

Development of a continuous drill-and-blast excavation capability in mining and high-speed tunneling has been a long recognized goal. Ideally, a machine to meet the challenge should simultaneously perform drilling, explosive loading, initiation, mucking, ventilation, and other functions while remaining at the face, since the elimination or modification of the cyclic nature of the system would significantly improve the advance rate and economy of drill-and-blast tunneling. The Rapidex continuous spiral drill-and-blast concept, one of the continuous excavation schemes presently under evaluation in the US Bureau of Mines&apos; Bedded Deposits subprogram, utilizes an unusual blasting pattern that provides effective fragmentation and involves a partially self-shielding geometry that permits a lightly shielded machine to remain at the face during blasting.

Jan 6, 1977

By Charles M. Rolker

THIS remarkable and well-known district lies about 320 miles south of Salt Lake City, in Washington County, near the Arizona border of the territory. It is now reached by the Utah Southern Railroad and its extension, and the last 100 miles are run by stages. These vehicles are called "jerkies" in the West, which name conveys a good idea of the comfort they afford, and the relief experienced when you alight. Arriving at Silver Reef, the main camp of the district, one sees at once that he stands where once a surging sea had its domain, marked now by heavy sandstone deposits of a red and white color. The town itself, a neat, clean, and orderly mining town, is encircled on the north by traohyte and granite mountains, skirting to the west. They are cut through in places by deep gorges, left us as the only trace of the force of former currents, which drained the adjoining territory to the north; and which when swelled and infuriated by tempests and cloud-bursts, took in their grasp the huge blocks of

Jan 1, 1881

By Y. Zimmels, I. J. Lin, I. Yaniv

The potential application of magnetic and electric separation techniques in beneficiation of fine-particle feeds are reviewed. Special features of these techniques are considered and compared with a view to increased amenability of such feeds to separation in electro- magnetic fields. The following techniques are discussed, with reference to those already developed and in use to-date: - Differential-susceptibility separation (DSF). - High-gradient differential-dielectric separation (HGDDS). - High-gradient magneto-gravimetric separation (HGMGS). In this context the new approach - whereby selectivity of solid- solid separation processes, in wet high-gradient magnetic and electric separation, can be improved - is described, including experimental results from DSF and HGDDS tests.

Jan 1, 1980

By P. R. Kalischer

In the production of alloys by powder metallurgical processes it is often necessary or desirable to include one or more cornponents that tend to form very stable oxides. Included in this group of metals are aluminum, manganese, magnesium, silicon, and a few others. In many cases it is not necessary for the sintered compact to have full density and the other physical characteristics of a cast alloy and in that event no undue precautions need be taken. If, however, it is required that the sintered part be entirely homogeneous, and have maximum density and physical properties, some method must be found to reduce the surface films of oxide, which are always present on the metals, and for the metals mentioned above this is always extremely difficult, if not impossible. since the production of high-density alloys is of particular interest to powder metallurgists, some experiments were undertaken to devise methods of reducing the refractory oxides. For this work, alloys of iron, nickel, and aluminum were chosen because aluminum oxide is one of the most stable oxides and because these alloys in the right compositions form excellent permanent magnets. All of the pertinent properties of the magnets could be accurately and delicately measured by density measuremerits and magnetic tests of sufficient scope to give a complete demagnetization curve. From such a curve the maximum coercive force, residual magnetism, and energy products could be obtained and compared with the same properties for a cast material. Any lack of homogeneity, density, or solid diffusion would be immediately apparent as a decrease in the magnetic properties. Nature and Removal of Surface Barriers The early work of the present investigation was based upon published processes.* In the published information it was claimed that by intimately mixing iron, nickel, and iron-aluminum alloy (50 Per cent Fe, So Per cent Al) powders, compressing such a mixture into the desired shape and size, and then sintering (heating to a temperature below the melting point of the component metals) in hydrogen at 1200°C. or higher, a sound, homogeneous article could be made having the desired physical size, shape, and strength, and good magnetic characteristics. However. this early work showed clearly that something in the powder compress was inhibiting diffusion and the process was almost entirely unworkable. In the initial phase of the investigation samples of iron powder, nickel powder, and iron-aluminum alloy powder were pressed into separate bars and sintered in hydrogen. Both the iron and nickel powders sintered

Jan 1, 1941

By P. R. Kalischer

In the production of alloys by powder metallurgical processes it is often necessary or desirable to include one or more cornponents that tend to form very stable oxides. Included in this group of metals are aluminum, manganese, magnesium, silicon, and a few others. In many cases it is not necessary for the sintered compact to have full density and the other physical characteristics of a cast alloy and in that event no undue precautions need be taken. If, however, it is required that the sintered part be entirely homogeneous, and have maximum density and physical properties, some method must be found to reduce the surface films of oxide, which are always present on the metals, and for the metals mentioned above this is always extremely difficult, if not impossible. since the production of high-density alloys is of particular interest to powder metallurgists, some experiments were undertaken to devise methods of reducing the refractory oxides. For this work, alloys of iron, nickel, and aluminum were chosen because aluminum oxide is one of the most stable oxides and because these alloys in the right compositions form excellent permanent magnets. All of the pertinent properties of the magnets could be accurately and delicately measured by density measuremerits and magnetic tests of sufficient scope to give a complete demagnetization curve. From such a curve the maximum coercive force, residual magnetism, and energy products could be obtained and compared with the same properties for a cast material. Any lack of homogeneity, density, or solid diffusion would be immediately apparent as a decrease in the magnetic properties. Nature and Removal of Surface Barriers The early work of the present investigation was based upon published processes.* In the published information it was claimed that by intimately mixing iron, nickel, and iron-aluminum alloy (50 Per cent Fe, So Per cent Al) powders, compressing such a mixture into the desired shape and size, and then sintering (heating to a temperature below the melting point of the component metals) in hydrogen at 1200°C. or higher, a sound, homogeneous article could be made having the desired physical size, shape, and strength, and good magnetic characteristics. However. this early work showed clearly that something in the powder compress was inhibiting diffusion and the process was almost entirely unworkable. In the initial phase of the investigation samples of iron powder, nickel powder, and iron-aluminum alloy powder were pressed into separate bars and sintered in hydrogen. Both the iron and nickel powders sintered

Jan 1, 1941

By Ottey M. Bishop, William G. Peryam, Fred E. Johnson

THE Lepanto Consolidated Mining Company is the largest copper producer in the Philippines, and the only one that makes a concentrate valuable principally for its copper; also, it has the only productive copper mine situated at considerable distance from the sea, and is the only one in the islands operating its own smelter. The Lepanto mine is in the Municipal District of Mankayan, sub-province of Benguet, near the heart of the Mountain Province of Northern Luzon. It is 165 km. from its shipping point at San Fernando, Province of La Union, on the shore of the China Sea. Elevations at the property range from 3200 to 4500 ft. The climate is very mild; temperatures are seldom below 50° or above 80°F. Annual rainfall approaches 170 in. and is mainly confined to a rainy season lasting from May to October. The months from December to April, inclusive, are usually extremely dry. This climatic pecularity entails the problems of landslides on the roads during the rainy season and water shortage during the dry season. The Mountain Trail, an improved rocksurfaced toll road maintained by the Commonwealth Government, gives access to the property. The 105 km. over this road may be traveled in about 4 ½ hr. during the dry season. Very few sections of the road are straight for more than 100 meters, and about one third of it is a one-way road controlled by gates. All freight for the property is delivered by the Manila Railroad Company to Bauang, La Union, 45 km. west of Baguio and at sea level, where it is picked up by freight trucks and hauled via Baguio to Lepanto. Granulated matte is hauled in bulk from Lepanto in four-ton lots on freight trucks to the storage bins at San Fernando. Freight rates from Bauang to the property amount to [P]8.oo per ton, and from the property to San Fernando the rate is [P]16.00 per ton. The company pays the road toll, [P] 1.00 per truck, each way. THE CAMP The company maintains a modern camp, well separated from the mine and reduction plant. Comfortable and sanitary living quarters, water, and light, as well as free medical service are provided all employees. A hospital staffed by a doctor and two nurses takes care of all medical treatment. Considering recreational facilities of great importance, the company has provided two tennis courts, two basketball courts, and badminton courts for employees. Bowling alleys and a motion picture theater are operated by the company, the profits being expended for other recreational purposes. A moderate sized recreation hall serves for barrio dances, meetings,

Jan 1, 1942

Steel Tape The new Lufkin Royal Ni-Clad steel tape, made in 25, 50, 75, and 100-ft sizes, is stated to cost less than any other steel tape on the market. Figures and graduations are an integral part of the steel and the nickel plated surface is rust and corrosion resistant. Circle No. 1 Lift A manually operated and propelled hydraulic lift marketed by Century Products Co. weighs only [ ] 150 lb, but the 23x24 in. platform will raise 1000 lb from floor level to 4 ft height. Circle No. 2 Scintillation Counter The Scintillator from Precision Radiation Instruments, stated to have 100 times the sensitivity of the Geiger counter, is suitable for prospecting and may be operated from plane or moving vehicle. The instrument is contained in a 2-lb probe and the belt mounted battery box weighs less than 4 lb. Circle No. 3 Generators Wincharger Corp. announces development of a Speedy-Shift wheel-barrow base type attachment for model 700, 1800 and 5000 engine-generator sets. Portability of the engine-generator sets themselves has been improved by belted construction for higher operating speed and maximum weight reduction. Circle No. 4

Jan 1, 1952

By E. O. Wagner, V. F. Parry

This paper summarizes investigations during 1949 on three pilot plants for drying low-rank fine coal by entrainment in hot gases. Detailed operating results on processing seven coals having moisture ranging from 24 to 62 pct, formulas and data for calculating performance of large units, and general conclusions on the problem of drying fine coal are presented.

Jan 9, 1950

By J. K. Furst

THE reasons for manufacturing steel by the duplex process are, briefly: saving of time; increasing output for capital invested; and avoiding the difficulty sometimes experienced in obtaining scrap. On account of the latter reason, some plants duplex only at such times as the price and quantity of scrap in the open market warrant. At some plants the use of the duplex process enables, the blast-furnace practice to be simplified, because the furnaces run more smoothly and produce more iron when not held to a strict specification as to the silicon and phosphorus therein. The duplex process was practiced in Witkowitz as far back as 1878, but it was left to the steel makers of this country to develop it along practical, commercial lines. The American companies manufacturing steel by the duplex process at the present time are: Tennessee Coal, Iron & Railroad Co., Maryland Steel Co., Bethlehem Steel Co., Pennsylvania Steel Co.; Jones & Laughlin Steel Co., Colorado Fuel & Iron Co., Lacka-wanna Steel Co., Dominion Iron & Steel Co. of Canada. All of these companies, except the Dominion Iron & Steel Co., combine the acid Bessemer with the basic open-hearth process, while the latter combines the basic Bessemer with the basic open hearth. The Tennessee Coal, Iron & Railroad Co.&apos;s Plant The installation of a converter of 15 tons capacity at the Ensley plant of the Tennessee Coal, Iron & Railroad Co. in 1904 marked the introduction into this country of the duplex system. The experience gained in the employment of the Bessemer converter had demonstrated that there was a shortening of .the time required in the open-hearth furnace and a reduction of the outlay for fuel and lime, thus affording substantial evidence of the economies resulting from this method.

Jan 10, 1914

By R. E. Zimmerman

WITH coal-preparation plants becoming more complex and containing widely diversified types of equipment and processes, it is necessary that considerable control be exercised in their operation. Rising mine costs make it imperative that close check be made of plant efficiencies to assure a minimum loss of coal to the refuse bank. Further, much of the coal sold today is sold on a competitive specification basis, and this makes it necessary to provide frequent analyses and inspections. Many &apos; plants are required to operate on a two or three-shift basis, and as a con- sequence an efficient organization is required to eliminate down time and provide for smooth low-cost operation. ORGANIZATION Probably the most important item for successful operation of a preparation plant is a capable, properly organized staff, with the individual workers properly informed and well trained for their particular jobs, clear-cut lines of authority among the supervisors and in general a standard operating procedure for most conceivable conditions that may occur. The idea of placing the older, partially disabled and generally incompetent coal miner in the cleaning plant, as was the practice on the earlier tipples, is entirely inadequate in a modern complex cleaning plant. The new plants require intelligent, alert, and reasonably educated men. With perhaps millions of dollars invested in an installation, it is poor business to use other than a well organized, well trained, and properly supervised force. Organizations naturally must vary with the size of the plant and local conditions; whether it is a central cleaning plant at a distance from the mine organization or one of several cleaning plants operated by the company. Smaller operations can be operated by a washery foreman, under the supervision of the mine superintendent or perhaps the "outside" superintendent. Large installations should have a plant superintendent either responsible to the mine superintendent or preferably, where possible, responsible to a preparation manager or engineer. A typical organization chart for companies operating in the anthracite region of Pennsylvania is shown in Fig. 1. Breaker (preparation plant)

Jan 1, 1950

By R. C. Wilmoth, R. D. Hill, R. B. Scott

A cost breakdown is given for reclamation and mine drainage abatement conducted by the Federal Water Quality Administration&apos;s demonstration project near Elkins, W. Va. Costs for construction of control measures have been developed and include backfilling strip mines, sealing subsidence areas, reconstructing stream channels, and installing mine seals to prevent the entrance of water and air.

Jan 1, 1973

E. K. Landis, Philadelphia, Pa. (communication to the Secretary) : Mr. Firmstone&apos;s paper is of great interest; but he has unfortunately otnitted to state the most important point, viz., the percentage of sulphur in the two materials he compares; and this omission vitiates the conclusions which he draws. Comparing by grade, instead of silicon-contents (as in his Table III.), the iron made using limestone with that made using dolomite, we find for gray-forge the average of four analyses under limestone to be, Si, 0.644; S, 0.089 ; while one analysis under dolomite gives Si, 0.508 ; S, 0.070. For No. 2 iron, the limestone flux gives, as an average of 19 analyses, Si, 1.107; S, 0.051; while the average of 4 analyses made with dolomite flux gives Si, 0.630; S, 0.056. It will be observed, that no No. 1 pig is given under limestone, while 14 analyses appear under dolomite, averaging Si, 0.950 ; S, 0.028. As nothing is said about changed conditions, it is Fair to presume that the ore and fuel, as well as the blast-temperature (which is stated to have been uniform at about 750&apos; F.) remained practically the same; and since the sulphur in the two fluxes is not given, it is impossible to know whether the lower sulphur for equal silicon-contents is due to the use of dolomite or to other conditions. The use of dolomite would produce a more fusible cinder, and the furnace would be hotter than when using limestone; therefore, we might expect to see a grayer iron. The amount of So. 1 iron made with dolomite seems to confirm this supposition; and, under these conditions, we might expect more of the sulphur to be volatilized, and to pass off in the gases. The easier fusibility of the cinder would also permit more rapid driving; and this should reduce the amount of silicon and sulphur in the iron, as the amount of reduced metalloids in the pig is directly proportional to the length of time it remains in the reducing-zone.

Jan 1, 1895

By S. Singh, R. C. Deshpande

RECENTLY metallographic studies of copper slugs recovered after firing shaped charges in deep containers of water were reported.&apos; The present note describes the metallographic examination of a steel

Jan 1, 1960

By Fred C. Bond

MOST investigators are aware of the present unsatisfactory investigatorsstate of information concerning the fundamentals of crushing and grinding. Considerable scattered empirical data exist, which andare useful for predicting machine performance and give acceptable accuracy when the installations and materials compared are quite similar. However, there is no widely accepted unifying principle or theory that can explain satisfactorily the actual energy input necessary canexplain commercial installations, or can greatly extend the range of empirical comparisons. Two mutually contradictory theories have long existed in the literature, the Rittinger and Kick. They were derived from different viewpoints and logically lead to different results. The Rittinger theory is the older and more widely accepted.&apos;TheRittinger In its first form, as stated by P. R. Ritted.&apos;tinger, it postulates that the useful work done in crushing and grinding is directly proportional to the new surface area produced and hence inversely proportional to the product diameter. In its second form it has been amplified and enlarged to include the concept of surface energy; in this form it was precisely stated by A. M. Gaudin&apos; as follows: "The efficiency of a comminution operation is the ratio of the surface energy produced to the kinetic energy expended." According to the theory in its second form, measurements of the surface areas of the feed and product and determinations of the surface energy per unit of new surface area produced give the useful work accomplished. Computations using the best values of surface energy obtainable indicate that perhaps 99 pct of the work input in crushing and grinding is wasted. However, no method of comminution has yet been devised which results in a reasonably high mechanical efficiency under this definition. Laboratory tests have been reported- hat support the theory in its first form by indicating that the new surface produced in different grinds is proportional to the work input. However, most of these tests employ an unnatural feed consisting either of screened particles of one sieve size or a scalped feed which has had the fines removed. In these cases the proportion of work done on the finer product particles is greatly increased and distorted beyond that to be expected with a normal feed containing the natural fines. Tests on pure crystallized quartz are likely to be misleading, since it does not follow the regular breakage pattern of most materials but is regularrelativelybreakage harder to grind patternat the finer sizes, as will be shown later. This theory appears to be indefensible mathematically, since work is the product of force multiplied by distance, and the distance factor (particle deformation before breakage) is ignored. The Kick theory4 is based primarily upon the stress-strain diagram of cubes under compression, or the deformation factor. It states that the work required is proportional to the reduction in volume of the particles concerned. Where F represents the diameter of the feed particles and P is the diameter of the product particles, the reduction ratio Rr is F/P, and according to Kick the work input required for reduction to different sizes is proportional to log Rr /log 2." The Kick theory is mathematically more tenable than the Rittinger when cubes under compression are considered, but it obviously fails to assign a sufficient proportion of the total work in reduction to the production of fine particles. According to the Rittinger theory as demonstrated by the theoretical breakage of cubes the new surface produced, and consequently the useful work input, is proportional to Rr-l.V f a given reduction takes place in two or more stages, the overall reduction ratio is the product of the Rr values for each stage, and the sum of the work accomplished in all stages is proportional to the sum of each Rr-1 value multiplied by the relative surface area before each reduction stage. It appears that neither the Rittinger theory, which is concerned only with surface, nor the Kick theory, which is concerned only with volume, can be completely correct. Crushing and grinding are concerned both with surface and volume; the absorption of evenly applied stresses is proportional to the volume concerned, but breakage starts with a crack tip, usually on the surface, and the concentration of stresses on the surface motivates the formation of the crack tips. The evaluation of grinding results in terms of surface tons per kw-hr, based upon screen analysis, involves an assumption of the surface area of the subsieve product, which may cause important errors. The evaluation in terms of kw-hr per net ton of —200 mesh produced often leads to erroneous results when grinds of appreciably different fineness are compared, since the amount of —200 mesh material produced varies with the size distribution characteristics of the feed. This paper is concerned primarily with the development, proof, and application of a new Third Theory, which should eliminate the objections to the two old theories and serve as a practical unifying principle for comminution in all size ranges. Both of the old theories have been remarkably barren of practical results when applied to actual crushing and grinding installations. The need for a new satisfactory theory is more acute than those not directly concerned with crushing and grinding calculations can realize. In developing a new theory it is first necessary to re-examine critically the assumptions underlying

Jan 1, 1953

By Fred C. Bond

MOST investigators are aware of the present unsatisfactory investigatorsstate of information concerning the fundamentals of crushing and grinding. Considerable scattered empirical data exist, which andare useful for predicting machine performance and give acceptable accuracy when the installations and materials compared are quite similar. However, there is no widely accepted unifying principle or theory that can explain satisfactorily the actual energy input necessary canexplain commercial installations, or can greatly extend the range of empirical comparisons. Two mutually contradictory theories have long existed in the literature, the Rittinger and Kick. They were derived from different viewpoints and logically lead to different results. The Rittinger theory is the older and more widely accepted.&apos;TheRittinger In its first form, as stated by P. R. Ritted.&apos;tinger, it postulates that the useful work done in crushing and grinding is directly proportional to the new surface area produced and hence inversely proportional to the product diameter. In its second form it has been amplified and enlarged to include the concept of surface energy; in this form it was precisely stated by A. M. Gaudin&apos; as follows: "The efficiency of a comminution operation is the ratio of the surface energy produced to the kinetic energy expended." According to the theory in its second form, measurements of the surface areas of the feed and product and determinations of the surface energy per unit of new surface area produced give the useful work accomplished. Computations using the best values of surface energy obtainable indicate that perhaps 99 pct of the work input in crushing and grinding is wasted. However, no method of comminution has yet been devised which results in a reasonably high mechanical efficiency under this definition. Laboratory tests have been reported- hat support the theory in its first form by indicating that the new surface produced in different grinds is proportional to the work input. However, most of these tests employ an unnatural feed consisting either of screened particles of one sieve size or a scalped feed which has had the fines removed. In these cases the proportion of work done on the finer product particles is greatly increased and distorted beyond that to be expected with a normal feed containing the natural fines. Tests on pure crystallized quartz are likely to be misleading, since it does not follow the regular breakage pattern of most materials but is regularrelativelybreakage harder to grind patternat the finer sizes, as will be shown later. This theory appears to be indefensible mathematically, since work is the product of force multiplied by distance, and the distance factor (particle deformation before breakage) is ignored. The Kick theory4 is based primarily upon the stress-strain diagram of cubes under compression, or the deformation factor. It states that the work required is proportional to the reduction in volume of the particles concerned. Where F represents the diameter of the feed particles and P is the diameter of the product particles, the reduction ratio Rr is F/P, and according to Kick the work input required for reduction to different sizes is proportional to log Rr /log 2." The Kick theory is mathematically more tenable than the Rittinger when cubes under compression are considered, but it obviously fails to assign a sufficient proportion of the total work in reduction to the production of fine particles. According to the Rittinger theory as demonstrated by the theoretical breakage of cubes the new surface produced, and consequently the useful work input, is proportional to Rr-l.V f a given reduction takes place in two or more stages, the overall reduction ratio is the product of the Rr values for each stage, and the sum of the work accomplished in all stages is proportional to the sum of each Rr-1 value multiplied by the relative surface area before each reduction stage. It appears that neither the Rittinger theory, which is concerned only with surface, nor the Kick theory, which is concerned only with volume, can be completely correct. Crushing and grinding are concerned both with surface and volume; the absorption of evenly applied stresses is proportional to the volume concerned, but breakage starts with a crack tip, usually on the surface, and the concentration of stresses on the surface motivates the formation of the crack tips. The evaluation of grinding results in terms of surface tons per kw-hr, based upon screen analysis, involves an assumption of the surface area of the subsieve product, which may cause important errors. The evaluation in terms of kw-hr per net ton of —200 mesh produced often leads to erroneous results when grinds of appreciably different fineness are compared, since the amount of —200 mesh material produced varies with the size distribution characteristics of the feed. This paper is concerned primarily with the development, proof, and application of a new Third Theory, which should eliminate the objections to the two old theories and serve as a practical unifying principle for comminution in all size ranges. Both of the old theories have been remarkably barren of practical results when applied to actual crushing and grinding installations. The need for a new satisfactory theory is more acute than those not directly concerned with crushing and grinding calculations can realize. In developing a new theory it is first necessary to re-examine critically the assumptions underlying

Jan 1, 1953