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By R. M. Jara

This work evaluates and characterizes the impact of the support size and mining dilution of a block model in the operation and selection of equipment at an open pit mine. An exploratory analysis and geostatistical modelling of the grades assayed on a set of drill hole samples is performed, which allows constructing a grade model on a dense grid by means of a conditional simulation. The grades are then averaged to greater selective mining unit supports in order to proceed with the study and methodology. First, the metal-tonnage curves are used to analyse the loss of selectivity on the in situ resources caused by a change of support. Concerning the ore reserves and their mining sequence, defined in the pit optimization and analysis process, the same curves prove that the loss of selectivity is more accentuated. Second, the importance of the block boundary dilution produced during mining operations is assessed. Its value depends on the amount of ore in contact with waste, on the loading error of the equipment and on the ore loss/waste dilution criterion assumed by the planner. The dilution percentage and the differences between waste and ore grades become higher when the block size decreases. For these reasons, considering the dilution in the production plans makes mining a small support more constraining. An adequate delimitation of the orebody can improve the mining selectivity, leading to greater income. Finally, a study of the increase in mining cost that provides a zero difference in NPV between the different block size options is carried out, in order to determine the maximum increase in mining costs for which it remains profitable to mine at a smaller block size. Keywords: Mining selectivity, support effect, block boundary dilution, selective mining unit size, block model.

Jan 1, 2006

By A. Thoraval, K. B. Slimane, O. Ozanam

The REP experiment is part of the research programme conducted by Andra to investigate the possibility of reversible radwaste disposal in a Jurassic (Callovo-Oxfordian) argillite formation at the Meuse/Haute-Marne underground laboratory site in northeastern France. The experiment focuses on the hydromechanical response of the formation to sinking the laboratory access shaft. Modelling of boreholes and shaft sinking operations has helped to optimise measurement point locations based on initial stress tensor anisotropy, while minimising interaction between instrument boreholes. Analyses were made of model sensitivity to intrinsic rock characteristics, hydromechanical coupling properties and sensor installation procedures. L’expérimentation REP fait partie du programme de recherche pluridisciplinaire engagé par l’Andra pour étudier la possibilité d’un stockage réversible des déchets radioactifs dans la formation Callovo-Oxfordienne des argilites du site de Meuse/Haute-Marne (Commune de Bure - France). Cette expérimentation permettra d’étudier la REponse hydromécanique de la formation aux sollicitations engendrées par le fonçage du Puits d’accès du laboratoire souterrain de recherche. Afin d’optimiser le positionnement des points de mesures, compte tenu de l’anisotropie du tenseur des contraintes initiales, et de minimiser les interactions entre les forages d’instrumentation, des modélisations des forages et du creusement du puits ont été conduites. Des analyses de sensibilité aux caractéristiques intrinsèques de la roche, aux propriétés de couplage HM et aux protocoles d’installation des capteurs ont été faites. Die REP-Untersuchung ist Teil des multidisziplinären Forschungsprogramms, das die ANDRA im Callovo-Oxfordian-Tonstein in situ am Standort Meuse/Haute Marne (Gemeinde Bure – Frankreich) im Hinblick auf eine Eignung zur reversiblen Lagerung radioaktiver Abfälle durchführt. Dabei soll das hydro-mechanische Verhalten der Formation auf die Beanspruchungen, die durch das Abteufen des Zugangsschachts zum Untertage-Forschungslabor erzeugt werden, untersucht werden. Zur optimalen Positionierung der Messpunkte unter Berücksichtigung der Anisotropie des Tensors der Ausgangsspannungen und zur Minimierung der gegenseitigen Beeinflussung der Instrumentierbohrungen wurden ein Schachtabteuf- und Bohrmodelle entwickelt. Zur Untersuchung der inhärenten Eigenschaften des Gesteins, des gekoppelten HM-Verhaltens und der Installationsprotokolle der Messsonden wurden Sensibilitätsanalysen durchgeführt.

Jan 1, 2003

By Ike Madingoana, Stephan van Zyl, Antoine F. Mulaba-Bafubiandi

"The study presents a control strategy implemented at the Nkomati nickel mine flotation plant for process stabilization and improvement. The control strategy involves flotation concentrate volumetric flow rate stabilization and the flotation cell mass pull control. The flotation concentrate volumetric flow rate is operated at a fixed set point. The initial control strategy involved varying the flow rate to maintain the concentrate tank level thereby reducing pump cavitation. The flotation cells mass pull control comprises air rate manipulation into the cells with the exception of the recleaners. The air rate into cells is automated to adjust based on the concentrate tank level variation. The control strategy was implemented on the roughers, cleaners and the recleaner circuit. The recleaner cells air flow rate is adjusted based on the MgO content in the concentrate. The stabilization of the flotation concentrate volumetric flow rate and the mass pull by aerate automation will increase the scope of optimization for further process improvement. The immediate benefit of the control strategy implementation was plant stability. Disturbance to the flotation cells downstream was minimized due to stable flow rate, and the air addition manipulation ensured that the concentrate tank levels are maintained, minimizing pump cavitation. INTRODUCTION Froth flotation is a challenging process because it is influenced by a large number of factors, including the flotation feed characteristics. One of the ore types mined at Nkomati nickel mine is the main mineralized zone (MMZ). The MMZ ore is hosted in the Uikomst complex, a Ni-Cu-PGE-Cr- mineralized, layered basic to ultra-basic intrusion which hosts commercially viable magmatic base-metal sulphides (De Waal et al., 2001). The MMZ ore is a heterogeneous sulphide mineral resource with a varying sulphide mode of occurrence and texture. The beneficiation of the complex sulphide ore is challenging due to the presence of impurities in the ore. The impurities report to the flotation final concentrate and penalties are levied if the impurities are beyond the contractual limits."

Jan 1, 2015

In recent years several mine researchers have studied the optimization of cutoff grade with the purpose of maximizing Net Present Value (NPV). The best and most popular one is the Lane algorithm. Based upon the Lane algorithm it is possible to calculate the optimum cutoff grade for mine, mill, and refinery capacities for single metal deposits with variable grades. The Lane algorithm cannot be used in multiple metal deposits. The reason is that, while in single metal deposits six points are possible candidates for the optimum cutoff grade, in multiple metal deposits an infinite number points are possible candidates for the optimum cutoff grades and objective function evaluation of these infinite points is impossible. In this study the Golden Section search method was used to calculate optimum cutoff grades of multiple metal deposits for the same conditions as Lane assumed in single metal deposits. Based on this method, grade-tonnage distribution uncertainty space of problem is guessed. In the next step, by selecting test points in uncertainty space and evaluating the objective function at these points, a part of uncertainty space will be eliminated. The procedure is then repeated until the uncertainty space has been sufficiently reduced to ensure that the optimum cutoff grades have been located to the required accuracy. Key words: Optimum cutoff grades, Optimization, Net Present Value (NPV), Golden Section search method

Jan 1, 2003

By James M. Link

Slurry transport of industrial minerals has proven to be practical, economical, and efficient. Industrial minerals currently being pumped for long distances include cement, clay, phosphate, sand, and various waste product from industrial mineral processing operations. This paper will touch upon the basic theory of hydraulic transport of solids and then consider the economic and engineering considerations upon which construction and operation of such a line would be based. Where possible, actual cost data will be presented.

Jan 1, 1974

By D. H. Diering

The paper deals with the technologies required for opening up anew idealized ultra-deep level mine. First the overall philosophy of accessing ore at ultra depths is discussed. Then the individual technologies which will be required are explored. Finally a detailed overview on one of the key technologies, namely tunnel support, is given. Because this project is still in its infancy, few definitive answers are provided; instead each of the envisaged technologies are briefly discussed, with emphasis on those which require the element of speed for rapidly accessing the ore body.

Jan 1, 1997

By R. S. Montgomery

Laboratory experiments simulating rock drilling were conducted on a number of commercial grades of tungsten carbide in order to determine their wear rates when they are used as inserts in percussive rock drill bits. The test rock was Barre granite and tests were made at conditions similar to those of the carbide buttons near the periphery of a large, down-hole, button bit. In addition, some wear rate measurements were made at a low blow energy. Wear rates of these carbide buttons were an extremely sensitive function of their cobalt contents and hardnesses and were proportional to e-°.57Hup to a hardness of about 91 RA. The point of minimum wear rate, which occurs at about 92 RA, corresponds to the point of maximum compressive strength. Modern percussive rock drill bits have inserts of cemented tungsten carbide on their wear faces. These inserts have drastically reduced bit wear in comparison to that of earlier all steel bits. The most common cemented carbide grade used in percussive rock drill bits contains about ten weight percent cobalt, although grades containing more or less cobalt are also used. Contrary to the case with carbide in metal-cutting tools, alloying materials are rarely used in mining grades. There are a number of designs of rock bits in current use. The most common form is an X bit which has four chisel-form radial wings. The button bit is another important design and one which has been recently developed. This design uses a flat steel face studded with relatively small hemispherically tipped carbide buttons. These types are illustrated in Fig. 1. Studies have been made of the sliding wear of cemented tungsten carbide on rock 1-4 and multiple-impact fracture', 5-6, b~t there has been comparatively little published on the percussive wear of this material although the wear of the impact face is the most important. There is some available data on the rate of dulling of rock bit inserts in actual drilling 7 but no laboratory studies. Sliding wear studies are useful for understanding the wear of coal and mineral cutting tools and gauge wear of percussive drill bits. but the

Jan 1, 1970

By N. Kornelius

In recent years there has been an increased focus on corporate governance matters worldwide. The duties and responsibilities of directors of companies have come under close scrutiny, with shareholders increasing their demands for greater responsibility and accountability. Media attention and pressure groups have also had their effect. Governmental actions have supported these demands and directors have witnessed sweeping legislative changes imposing more onerous duties and liabilities than formerly imposed upon them at common law and in terms of the Companies Act. At the same time, the power of regulatory bodies has been increased to enforce this legislation and make someone pay to remedy an alleged infringement. Breach of such duties may incur personal or criminal liability, or both. Environmental protection legislation has become a particularly prevalent feature in this regard, and the number and complexity of statutes concerning the environment have increased over the past few years. Directors of South African companies will be familiar with relevant acts such as the National Environmental Management Act 107 of 1998; Conservation of Agricultural Resources Act 43 of 1983;Hazardous Substances Act 15 of 1973, as well as the National Water Act 36 of 1998. Now the directors of mining companies are faced with the Mineral and Petroleum Resources Development Act 28 of 2002.

Jan 1, 2003

By S. Saito, P. A. Beck

The crystal structure of MoNi3 was determined by means of X-ray diffraction. This structure is isotype with that of ovgered TiCu3. The lattice parameters are: a. = 5.064A, bo = 4.224A, co = 4.448A, and zf 0.157. If the orthorhombic distortion (slight relative to the corresponding orthohexagonal unit cell) is disregarded, the structure may be described in terms of a close-packed ordered atomic layer, stacked in the sequence: abab. The structztres of ordered TiCu3 and TiAl3 are homotectic. The three types of ordered hexagonal phases, iso-structural with TiNi3, MgCd3, and VCo3, are known to occur in AB3 alloys of transition elements of the first, second, ad third long periods. It was noted1 that phases with the TiNi3 structure occur selectively in alloys of Ti-group elements with Ni-group elements. In AB3 alloys of Ti-group and V-group elements with Co-group elements the AuCu3-type structure predominates.' The vCO3 structure, which was determined very recently,' has hexagonal symmetry, but the actual atomic arrangement here, too, is rather closely related to the ordered cubic structure of AuCu3-type. However, an ordered hexagonal close-packed structure of the MgCd3-type occurs in MOCO33 and WCO3.4 Consequently, the question arises as to whether or not the crystal structure of MoNi3 is also of the MgCd3-type. Grube and winkler5 found that MoNi3 has a hexagonal close-packed structure with a = 2.54A and c/a = 1.65. They pointed out that some additional weak diffraction lines could be observed in the powder pattern, which may have been due to an ordered atomic arrangement in this phase. However, no detailed information was obtained by them and the structure was apparently not further investigated by others. The present work was, therefore, undertaken in an attempt to determine in detail the structure of MoNi3, and to investigate the possibility of ordering. EXPERIMENTAL METHODS Alloys used in the present work were arc-melted in a water-cooled copper crucible under helium atmosphere. Electrolytic nickel and molybdenum, both 99.9 pct pure, were used. Chemical analyses were not made, but the melting loss was not higher than 2 pct for any alloy. Ingots were first homogenized at 1200°C for 48hr, quenched, heavily cold worked, and then annealed at 820" or 860°C for 1 week, followed by quenching in cold water. Powder specimens for X-ray work were prepared by crushing the heat-treated solid specimens. In order to remove strains, the powders were reannealed in evacuated scaled fused silica capsules for 6 hr at the same temperature at which the corresponding solid specimens were annealed. X-ray photographs were taken with an asymmetric focussing camera, using unfiltered CrK or CuK radiation. EXPERIMENTAL RESULTS The X-ray diffraction patterns of alloys containing 20.8, 25, and 26.4 at. pct Mo, homogenized at 1200°C, showed the face-centered-cubic structure of the Ni-base a-solid solution. It was revealed, however, by micrographic examination that the 26.4 at. pct Mo alloy contained in addition very small amounts of a second phase, in accordance with the phase diagram.6 On the other hand, the 20.8 at. pct Mo alloy after annealing at 820°C gave the X-ray diffraction pattern of the ordered face-centered-tetragonal MONi4.7 In this pattern several additional weak diffraction lines were also observed, corresponding to the strongest diffraction lines of MoNi3. The alloys containing 25 and 26.4 at. pct Mo after annealing at 820" or 860°C gave X-ray diffraction patterns, as shown in Tables I and 11, corresponding to MoNi3. Each one of the reflections which could be tentatively indexed on the hexagonal close-packed cell of Grube and Winkler,5 with the exception of the basal plane reflections, was split into a doublet, as seen in Table I. Since microscopically the alloy consisted of a single phase, it seemed probable that the lattice of MoNi3 is actually slightly deformed, as compared with the tentative hexagonal unit cell. In addition to these diffraction lines, several weak lines were also present, as shown in Table 11, which could not be indexed at all on the hexagonal close-packed cell considered. Satisfactory indexing of all diffraction lines observed was found to be possible by using an orthorhombic unit cell with ao = 5.064A, ft = 4.224A, and c = 4.448A. These values, whose accuracy is estimated to approximately ± 0.008A, correspond to 95.14A3 for the volume of the unit cell, and to an X-ray density of 9.50 g per cm3. If no attention were paid to the weak reflections listed in Table II, a reduced -unit cell of half the volume (a = 2.532A, b = 4.448A, and c = 4.224A), closely related to the orthohexagonal cell, might be used. The dimensions of the orthohexagonal cell of the same volume as the reduced cell are: a = 2.562A, b = 4.437 A, and c = 4.183A. It may be seen that in the reduced cell the a axis is slightly shorter, while the b and c axes are slightly longer than those corresponding to the orthohexagonal cell of the same volume. This slight orthorhombic distortion is re-

Jan 1, 1960

By A. J. Lynch

Mineral processing models have been discussed for many years but it was not until digital computers became available about 1960 that serious attempts at circuit simulation could be carried out. Even then the work was primarily academic until PCs could be used by engineers in plants and design offices in the mid-1980s. Since then simulation has moved quickly and it is now at the point that most processes can be simulated reasonably accurately for purposes of design and optimization. There are still some significant deficiencies, notably in dry grinding and separation, and in the chemical interactions in flotation. Future work will involve: ?improvements of existing models ?dynamic simulation for automatic control and, in particular ,for training which is a weak link ?using advanced simulation models to predict liberation and separation from data acquired from SEM-based liberation analysers. Eventually mineral processes models will be part of total simulation systems which will incorporate mining and downstream processes including all environmental impacts.

Jan 1, 1999

By R. G. B. Pickering

Over the last few years Lonmin Platinum and Sandvik have embarked on a unique partnership of collaboration through a systematic approach to developing equipment to mechanize and automate narrow reef platinum mining. After the initial design and manufacture of the equipment the key aspect is the integrating equipment, people and method into a mining system. Another key aspect of mechanization is the optimization of equipment utilization, and this philosophy has ensured continual evolvement of mining methods. This paper describes the trials and development that have resulted in the mining method described as Lonmin mechanized breast.

Jan 1, 2007

By S. D. Thompson

An AIME transaction by P.L. Allsman (1960), "Analysis of Explosive Action in Breaking Rock," contains many useful concepts applicable to blast design. Of special interest was the derivation of a heave blasting burden formula, which is important in establishing the maximum burden. Unfortunately, its derivation contains a fundamental error and then a compensating one. This formula was: [ ] The derivation used the impulse-momentum principle, with a 0.3 m thick (1 ft thick) radius of rock mass being acted on by an explosive impulse. However, the rock weight was not converted to mass by dividing by the gravitational constant. This mistake can be verified by checking the units in the formula, which resolve into m%-sec instead of meters. Adding the gravitational constant corrects this: [ ] If the minimum velocity is now taken as 0.3 m/sec (1 ft per sec), as was recommended, excessively large burdens result. Any appropriate rock velocity should be capable of throwing the rock mass a minimum distance so that the swell needed for breakage can occur. Unless the burden is extremely small and the bench height is very high, it is unlikely that a velocity of only 0.3 m/sec (1 ft per sec) will be sufficient. A review of the literature indicates that average rock velocities observed by camera studies typically range from 15 to 30 m/sec (50 to 100 ft per sec) (duPont deNemours and Co., 1977; Tansey, 1979). On this basis, a minimum rock velocity of about 15 m/sec (49 ft per sec) would be expected and not 0.3 m/sec (1 ft per sec). When a velocity of 15 m/sec (49 ft per sec) is inserted into the corrected formula, the results approximate those of the original formula with a velocity of 0.3 m/sec (1 ft per sec). The errors were approximately self-compensating [ ] References Allsman, P.L., 1960, "Analysis of Explosive Action in Breaking Rock," Transactions, AIME, Vol. 217, pp. 475-476. E. I. duPont deNemours and Co., 1977, Blasters' Handbook, 175th Anniversary Edition, Dupont, Wilmington, DE, pp. 233. Tansey, D.O., 1979, "The DuPont Sequential Blasting System," CIM Bulletin, Vol. 72, July, p. 80. Thompson, S.D., 1981, "Critical Review and Revision of Surface Blasting Practice," MS thesis, West Virginia University, pp. 308-316.

Jan 3, 1985

By P. B. Baxendell

The appraial of producing properties and profitability ntzalysis of a proposed capital expenditure are based on the same principles. In both problems a projection of future cash income is. cornpared to one or more capital expenditures. Several different methods have been in use either to compute a price to obtain a given earning power on the investment or to compute the earning power which will result from a given capital expenditure. One of these, the "Average Annual Rate of Return" method, computes in a simple manner the ratio of the present value of the future earnings after amortization to the present value of the undepreciated balances of the investment over the life of a project. This method, not well known generally, appears to have some rather unique advantages in reducing the computation work required, eliminating trial-and-error solutions, and providing a more accurate answer when applied to oil industry investments subject to the unit-of-production basis of amortization. Its derivation is given and its versatility demonstrated in the solution of certain everyday investment problems. A number of charts, useful in applying this method to profitability analysis and appraisal work, are provided. The current trend in the market values of producing properties is shown. INTRODUCTION Making sound capital expenditure decisions requires an objective means of measuring the productivity of individual investment proposals. Since the best measure of the economic worth of such proposals is their ability to produce profits, it is common practice to grade proposed capital expenditures according to their annual earning power as a percentage of the outstanding capital. The same principles which govern the determination of the rate of return of proposed capital expenditures also apply generally to the problem of determining the appraisal value or purchase price of income-producing oil and gas properties. Both problems are of prime importance in the producing phase of the oil business, where management is faced daily with decisions to drill or not to drill certain development wells, or with the determination of the appraisal value of producing properties. The common feature in both problems is that a projection of future cash income is compared with a known or estimated capital investment to determine itsiearning power or annual rate of return. In the case of development drilling, the cost of the proposed well can usually be estimated with a fair degree of accuracy and the problem consists of finding the rate of return on the invested capital. In the case of appraising producing properties, on the other hand, the desired rate of return is usually known in advance and the problem consists of determining the purchase price which, for the given income projection, results in the fequired rate of return. Certain accounting procedures common to the oil and gas producing business make these two problems and their solutions somewhat different from corresponding problems in other industries, and, in certain ways, simpler. The main difference is in the amortization policy which, for oil and gas production, is frequently on a unit-of-production basis, compared to the amortization on a time basis used in many other industries. The purpose of this paper is to discuss briefly the various methods currently in use for the measurement of productivity of invested capital in producing properties and, in more detail, the derivation and application of what will be called the "Average Annual Rate of Return Method". This rather interesting and not too well known method has some very definite advantages in the solution of many problems common to the oil industry. For the sake of simplicity, federal income tax considerations have been disregarded in the examples used, since they do not affect the principles involved. The use of the production payment route in the sale or purchase of producing properties, which has been amply covered in many other publications, has also not been included in this analysis. METHODS FOK MEASUKING THE EARNING POWER OF INVESTED CAPITAL, Of the many different methods used to measure the earning power of invested capital, four are applicable to oil or gas production ventures. Depending on whether these four methods utilize one or two interest rates, and whether a fixed amortization pattern is used, they may be classified as follows.

Study on Desulfurisation and Deashing for Medium-High Sulfur Coal Using Shaking Table As important coal resources, medium- high sulfur accounts for a significant part of the coal reserve in China. The environmental regulations and fuel standard requires sulfur and ash to be removed before it is used, so as to save energy and decrease the emission. Therefore, the effective desulfurisation and deashing technologies are urgent needed. However, due to the local characteristics of the coal, specific technology with optimum operation parameters is required to develop for different local coal. Qinglong is a district of Guizhou Province, which has large medium to high sulfur contained coal reserve. In this paper, medium-high sulfur coal is sampled from Qinglong, Guizhou province. Some basic characteristics such as the mineralogical composition of the coal rock, the monomer existing state and the granulometric composition are determined by X-ray diffraction quantitative analysis and polarisation microscope analysis respectively. Adopting the classified feed method, shaking table tests show that the feed pulp concentration is 20 per cent, the stroke is 13mm, the frequency of the stroke is 380 per min, the cross slope is 3¦ and the volume of wash water is 5.2 L per min. Under such condition, aggregate processed coal yield is 72.87 per cent and sulfur content decrease to 1.31 per cent With shaking table technology of 'First stage rough and intermediate further fine benefication', the yield of concentrate coal increased from 72.87 per cent to 81.21 per cent, while the sulfur content reduced to 1.35 per cent.

Sep 13, 2010

By David Schroeder, John Chipman

Jan 1, 1964

PRODUCTION of cesium, cesium salts, and rubidium salts in the United States declined somewhat from 1961 levels; rubidium production was virtually unchanged. Imports of pollucite declined because consumption was supplied partially out of inventory. Domestic Production.-About 50 tons of pollucite was reported mined at the Tin Mountain mine in the Black Hills of South Dakota. The Dow Chemical Co., Midland, Mich., MSA Research Corp., Callery, Pa., and Penn Rare Metals, Inc., Revere, Pa., produced a total of 159 pounds of cesium. Rubidium production remained essentially the same as in 1961. Shipments of the two metals by these companies and by American Potash & Chemical Corp., Trona, Calif., totaled 279 pounds. Production of cesium and rubidium salts by American Potash & Chemical Corp., Penn Rare Metals, Inc., and Rocky Mountain Research, Inc., Denver, Colo., declined substantially during 1962.

Jan 1, 1963

By David Norval

The increased tendency to use hydrometallurgy as an extraction step towards final refining following a pyrometallurgical smelting process requires melts which have to be cast and or comminuted which can then be taken up into solution or leached. To generate surface area for optimal leaching, a common process is to granulate and in many cases mill, which is a general practice with friable material with properties associated with higher sulphur, carbon and silicon levels. However, in the case of metallic melts milling can be unfeasible due to the ductility of the granulated particles. Water solidification is capable of producing either fine particles by means of granulation or atomisation. Atomisation however, can produce particles as fine as 40 microns without a milling circuit.

Jan 1, 2005

Longwall mining originated in the early 18th century in the county of Shropshire in England, where it was known as the longway method. Its name implies the extraction of the seam over a long continuous length or wall of exposed coal. Until the late 19608 and early 1970s the use of the longwall system with a few exceptions was confined to the United Kingdom and Europe. It was not until the early 19708 that the highly productive longwall faces we now know, were developed and the application of the longwall system extended to Australia, South Africa, United states of America and other parts of the world. The modern longwall face has three major components, namely: +         the machine to break and load the coal +         the face conveyor; +         and a system of roof support.   This paper reviews the development of longwall mining technology. The parameters directly influencing the production 'of a modern longwall face are considered, as are the possible constraints to the further development of the longwall system.

Jan 1, 1991

By Enrique Touceda

FOR a number of years prior to the world war, the firm of Geo. H. Thacher & Co., of Albany, N. Y., was engaged in the manufacture of marine and other gray-iron castings. At -the outbreak of the war the firm decided to specialize in the manufacture f propeller wheels. It attacked the problem, therefore, from a foundry point of view, seeking to produce a casting that would be so accurate that no subsequent machining would be required on the blades, also from the point of view of the ship builder. There were two general methods f manufacture, the shortcomings of which have been freely acknowledged. In the sweep method, the nowel, or bottom half-mold, for each blade is swept up by a spindle beam and pitch race, while the top half-mold for each blade is built up individually. In the pattern method one individual blade, with the hub or hub portion, is mounted on a spindle and the individual -blade mold formed, the pattern is then rotated on the spindle to the position- for the next blade, etc. In rare cases wheels were made from a solid pattern. Owing to the cost of the pattern, its failure in many instances to be correctly made, and (when made of wood) its early and sure distortion the disadvantage of this practice is obvious, while metal patterns in most instances were prohibitive in cost. In these methods both green-sand and loam molding was practiced. The casting produced by either method can be considered only as a blank from which the propeller must be machined. The back surface f each blade must be chipped too the templet and through this procedure chipped to such accuracy, as will be required for a static balance. Inasmuch as the' work done by the machine tool is confined to the driving face of the blades, not only is perfection most difficult, but corrosion will be greater because of the removal of the dense skin f the casting and the local strains set up by the pneumatic tool in chipping. To produce a finished 9-ft. propeller for a Navy destroyer required from 8 to 21 days f foundry work and about the same length of, time for the machining. Through the use f the Thacher process, only as many hours are required, besides it is possible to produce a finished casting in perfect conformity, with any particular propeller-wheel design,

Jan 4, 1921

By C. C. Harris

An analytical solution of the integro-differential equation of batch grinding is proposed as a first appoximation to the xYt surface. The size distribution equation (xY plane) is a three parameter equation previously suggested. Possible refinements are outlined. Comminution kinetics research is presently following several related courses. Some are equivalent, in that they represent different ways of viewing the same facet of the problem, though the entire endeavor cannot be described as being completely integrated. The purpose of this note is to propose and discuss a framework into which the various approaches might be fitted. This must clearly be founded upon an analysis of the xYt surface.' (See also Fig. 1 of Reference 26.) The investigations referred to above comprise mainly researches into the following: (1) The kinetics of the creation of the finer sizes during relatively small grinding times. This is the Fahrenwald-Arbiter-Bhrany 2-3 approach which leads to equations equivalent to a special case of the charles4 relationship. It emerges that initial production of fines follow essentially zero order* kinetics. (2) Disappearance kinetics of the coarser fractions. This appears to be a first order relationship.5-6 (3) Prediction of the xYt surface via the selection and breakage functions utilizing computer-programmed or approximate solutions of the integro-differential equation of batch grinding.5,8-17 A recent discussion by Mika et al.5 references the relevant literature up to about 1966. In addition to these main-stream researches there is some work on the minor topic of extremely long grinding time considered as a limiting case.18-19 The field is supported by investigations into the size distribution of fragments produced by breakage processes, some of this work being most valuably statistical-mechanical in nature.20-25 Better fitting equations, however, are obtained by statistical and curve-fitting methods.26 This

Jan 1, 1969