Search Documents

By R. E. Whippo, B. L. Murowchick

The commercially exploited sedimentary apatites exhibit a number of variable lattice substitutions which affect their chemical composition. Carbonate is a major diluent of phosphorus values in sedimentary apatites. Substantial amounts of water as hydroxyl, hydronium, and tetrahedral hydroxyl ions substitute for fluorine and oxygen, calcium, and phosphate, respectively. Calcium is also replaced by several other divalent and monovalent cations. The structural formula demonstrates the substitutions in the lattice of the sedimentary apatites studied in view of the crystal-chemical relationships which have been postulated for the isomorphous apatite series. The lattice constant a. varies from 9.29 to 9.40 A for the apatites studied. Quantitative relationships between this constant and lattice substitution are complicated by the interaction of multiple substitutions whose influence is non-additive. The mineral apatite, the principal raw material source of phosphorus for agricultural and industrial applications, offers a wide area for investigation. Considerable research effort has been expended in the study of apatite crystal-chemistry by medical, biological, and earth scientists. Few of these studies deal directly with the sedimentary apatites from the major occurrences which are widely exploited for commercial uses. It is the purpose here to present chemical analyses of several sedimentary apatites and discuss their chemical composition in relation to the structural and crystalchemical principles which have been postulated for the apatite isomorphous series. THE STRUCTURE OF FLUORAPATITE The atomic structure of fluorapatite was described, independently, by Ngray-Szabd and Mehmel in 1930 and has been accepted as presented, with only minor changes,4 since that time. The hexaogonal unit cell with dimensions of a = 9.37 0.01 A and c = 6.88 0.01 A contains two molecules of the composition "There are six (PO4) groups in the cell, four calcium ions on the trigonal axes, surrounded prismati-cally by six oxygen ions and six calcium ions surrounded by an irregular polyhedron of a fluorine and five oxygens. Fluorines are at the comers of the reflexion planes, touching three calcium ions each".l7

Jan 1, 1968

By Marco Barla, Mariacristina Bonini, Giovanni Barla

ABSTRACT: The paper describes the characterisation studies of Tectonised Clay Shales at laboratory and in situ scale. The interest relates to tunnelling under squeezing and swelling conditions, in Italy, along the Apennines. The results of monitoring during full face excavation are presented in conjunction with numerical modelling. RESUME: Cet article présente la caractérisation, à l'échelle du laboratoire et in situ, des Argiles Chaotiques. L'attention est portée sur le creusement, dans ces milieux gonflants, des tunnels, dans les zones montagneuses des Appennini, en Italie. Enfin, on présentera les résultats de la modélisation numérique et la comparaison de ces derniers avec les mesures effectuées in situ. KURZFASSUNG: Die Arbeit beschreibt die Charakterisierungsstudien von tektonisierten Schiefertonen, sowohl im Labor als auch vor Ort. Das Interesse gilt dem Tunnelbau unter Quetsch- und Schwellbedingungen in Italien entlang der Apenninen. Die Überwachungsergebnisse des ganzflächigen Ausbruchs werden mit numerischen Modellen präsentiert.

Jan 1, 2003

By Eugen Gluck, Gus Van Weert, Peter Kondos

"Microwaves have the capability to heat up sulphides, especially clusters of particles of approx. 1 mm. Some sulphides absorb microwaves more readily than others. Molybdenite is especially effective in this regard, possibly due to its flaky nature and/or electrical conductivity. Even where it occurs in low concentrations in a deposit, individual rocks may be ore grade due to the high monetary value of MoS2. Such rocks often result from crushing mined veinlets or stockwork, or are contained in the cutoff grade fraction of ROM. Machine segregation of rocks high in MoS2 by infrared sensors after microwaving could therefore advantageously be used to upgrade lower grade ore between Mine and Mill. This would reduce the size of the latter, and thus its CAPEX and OPEX. Such upgrading could also yield shipping ore for a distant Mill, or extend ore reserves.Barrick Gold Corp. has been supporting the development of MW/IR sulphide sorting for the past three years. The results of MW/IR sorting work on molybdenite and other (pyritic) ore samples from a variety of sources are being presented here.INTRODUCTIONThis paper looks at mechanized, i.e. machine ore sorting technologies currently available and under development, and what conditions would be needed for the potential application of such ore sorting to sulphide mining and milling. Current machine sorting involves no-contact sensing technology for rocks, and signal processing after sensing to activate airblast segregation of certain rocks, normally the smallest mass to keep compressed air costs down.The forerunner of modern sorting is probably magnetic separation, which utilizes an inherent property of certain ores to divert it into mag and non-mags fractions. Radiometric ore sorters, which have been applied successfully for decades in the pre-concentration of uranium ores (Wotruba and Riedel, 2006) initiated modern sorting. In the 90’s, sensor-based machine sorting became a viable means of increasing the overall economic recovery of a resource. This technology became driven by the availability of low cost computing equipment and the concurrent development of algorithms, and by the availability of extremely fast response sensors and air actuators, allowing the sorting equipment to run faster, dropping the cost per tonne. It has been in industrial minerals processing that rock sorting has been most widely adopted, not really surprising. Liberation occurs on a different scale than in the base metal industry. Most industrial minerals are mined from massive deposits, requiring (in the past) no upgrading. Many of these operations now run into product contamination problems, which ore sorting can solve. One illustration: in Finland, a quarry is separating limestone from dolomite at 500 tonnes / hour, with individual rocks weighing up to 15 kg. Many of these industrial minerals operations have stockpiles of earlier discarded below-quality rocks, now being reprocessed with the help of ore sorting. The economics of this are very favourable, going from zero or negative value (stockpiles can not be left when closing the mine) to full product value for at least a portion of the stockpile. This suggests that in the future the economics of overburden sorting could become attractive under the right circumstances and such treatment could well become an integral part of open pit mine development."

Jan 1, 2009

By J. L. Giove, J. M. Hodge, R. G. Storm

The hardenability effect of molybdenum has been evaluated by a number of investigators, including one of the present authors.1,2,3,4,6 Considerable discreMncy exists, however, among the results of these various investigators, and two of them, Brophy3 and Kramer,4 have indicated that the apparent hardenability effect of molybdenun would vary, depending upon the other alloying elements in the steels being considered. The results of previous, unpublished work conducted at the Duquesne Works Laboratory of the Carnegie-Illinois Steel Corporation also have indicated significant differences in the hardenability effect of molybdenu~n in nickel and in chromium steels. The present investigation was undertaken in an effort to establish the mechanism governing this difference in the hardenability effect of molybdenum. This work involved both end-quench hardenability and isothermal transformation tests on two series of steels of varying molybdenum content. One steel contained 3 pct nickel and the other 1 pct chromium. It was hoped that such studies would shed further light on the mechanism of this behavior. Materials and Experimental Work MATERIALS The chemical compositions of the steels used in this investigation arc shown in Table 1. These steels were furnished by Battelle Memorial Institutc in the form of 100-lb induction furnace ingots. The top half of each ingot was forged to 1 3/8-in. square billets and then rolled to I-in. round bar stock for isothermal transforma- tion studies. The bottom half of each ingot was forged into approximately 1 1/4-in. rounds for end quench tests. All of the steels were normalized from 1650°F and tempered at 1100°F before nlachming to end quench or isothermal samples. END-QUENCH TESTS standard l-in. diam end-quench tests were made on each of the steels. The test bars were austenitized at 1600°F for 30 min,, quenched in a standard Jominy jig, and hardness surveys were made in all tests. The 95 pct martensite point was deterInined from hardness values5 and cheeked by metallographic examination. The jominy distance values for 95 pct martensite were converted to hardellability values in terms of ideal diameter (Dl), using a revised carve for the relationship between Jominy distance and ideal diameter. This curve was based on the cooling time from the A1 to the bainite nose temperatures rather than on the usual criterion of half-temperature time. The cooling rates as determined by Russell and Williamson9 were used as a basis for this relationship. The derivation of this curve is described in detail in the appendix. ISOTHERMAL TRANSFORMATION STUDIES Samples for the isothermal transformation studies were quarter sectors of 1/16.is-in. thick slices from the 1-in. round bars. All samples were austenitized for a total the of 15 min., transferred rapidly to a lead bath for isothermal transformation, and brine quenched from the lead bath. A time of 3 see was allowed for the sample to come to the temperature of the lead bath, and this time was not included in the isothermal transformation times. Each sample was examined metallo-graphically at a magnification of 100 diam. The per cent transformation was estimated by comparison with standard micrographs, and the values were plotted against the on log/log coordinate paper. At least 4 and as Inany as 10. points were plotted for each steel. A line was drawn through the points for each steel, and the times for 5 pct transformation were obtained from the plot for each steel. Isothermal transformation diagrams in terms of 5 pet total transformation, covering the temperature range of 800 to 1200°F, were determined in this manner for an austenitizing temperature of 1600°F. The times for 5 pct transformation at the bainite nose for austenitizing temperatures of 1800 and 2000°F were also determined in the same manner. These times for 5 pct total transfor-

Jan 1, 1950

FEB. 17-The past month found the average citizen backed off just a little more into his blind corner staring glassily at hydrogen bombs, unbalanced budgets, John L. Lewis, more inflation, a rising wave of strikes, the country's only active battleship on a mudbank, a famous scientist in gaol as a traitor, a favorite actress on a Roman holiday, and rising mountains of potatoes, butter and eggs begging for destruction. About the only bright spot has been industrial activity and employment, but even these are menaced by the coal shortage. Most industries have orders on hand or in prospect to warrant high operations for some time to come. The trend of the Reserve Board's production index is upward except as strikes may interfere. There has been heavy buying at the seasonal merchandise shows, particularly in furniture and house-hold goods. The demand for goods of this kind illustrates greater confidence in the Spring outlook than was generally felt a year ago. Further, the demand also reflects improved market positions due to curtailment of output and reduction of inventories in 1949 and sustained consumer buying power. It demonstrates the strong support that is given directly to many businesses, and indirectly to all, by the phenomenal construction activity that is now under way. The Commerce Department places the number of new dwelling units started in 1949 at the new all-time high of 1,019,000.

Jan 3, 1950

By J. A. Finch, D. Lin

The robustness of the large-sections correction procedure, Hill's fast approximation, Barbery's correction and the PARGEN correction was examined by comparing their ability to reconstruct the true liberation distribution using sectioning data from computer-generated spheres. The results indicate that the flexibility of a correction procedure is related to the assumptions it makes about the continuity of the liberation distribution, locked-particle characteristics and ore texture. Overall, the large-sections procedure appeared to be the most generally applicable. The Hill fast approximation performed well, but this was probably because it partially incorporates the sphere model; the performance of the PARGEN and Barbery corrections varied from case to case.

Dec 1, 1995

The Honor Roll includes the names of all members of the Institute whom we know to be on active military duty at the date of its compilation, February 7, 1918. We are aware that there are many others of whose activities we have not been informed, and we shall be grateful for information as to any such omissions from the Roll. 1. MEMBERS ON ACTIVE MILITARY SERVICE Mail addressed to members on the first division of the Roll and sent to the office of the Institute Will be forwarded according to the best of our knowledge at the time. AARONS, J. BOYD, Capt., 4th Reinforcements, 11th Infantry, Australian Imperial Force. '05 ADAMS, HENRY, Capt Asst. to Dept. Engr., Northeastern Department. '02 AGNEW, FRANK VANS '04 ARBE, FREDERICK R., Capt 33d Engineers. '97 ALDER, ALFRED Engineers' Reserve Corps. '17 ALFORD, NEWELL G., Sgt., Bureau of War Risk Insurance, Headquarters 84th Division. '14 ALLEN, HEMAN H., Private Co. D., 8th Reserve Engineers. '17 AMBLER, HARRY A., Lieut 30th Infantry. '16 ANDERSON, ALEXANDER, Lieut Royal Garrison Artillery. '07 ANDERSON, GEORGE K., JR., See. C, 1st Co., 3d Officers' Training Camp. '17 ANDREWS, CLARENCE W., 1st Infantry Co., Officers' Training Camp, 83d Division. '13

Jan 1, 1923

Abstract : The computation of reliability index or failure probability of slopes can be transformed into an optimisation problem. In high rock slope engineering, it is usually a multimodal optimization problem. The traditional optimization techniques are difficulty to find out the global optimal solution because of their easily falling into local optimal value. Recently, a new kind of bionic algorithm - ant colony algorithm (ACA) - has been used to solve this problem. In this paper, the structure of ant colony algorithm and the transfer probability of ants are modified to evaluate the failure probability of complicated slopes. A new adaptive ant colony algorithm (AACA) is proposed to determine critical slip surface and its corresponding failure probability of complicated slopes. A case study is given to verify the proposed approach. The results show that the presented method has obvious advantages compared with traditional methods. ZUSAMMENFASSUNG: Die Rechnung des Zuverlaessigkeitindexes oder der Zerstoerungswahrscheinlichkeit kann sich in einer Optimierungsfrage umwandeln, im Bauprojekt an hoehe Gebirgehang, handelt es sich meistens um eine Optimierungsfrage ueber Multi- Spitzenwert. Mit der traditionelle Optimierungsmethode ist es schwer eine umfassende Loesung fuer die Optimierung zu finden wegen des leichte Verfallens in Beschraenkung der Teiloptimierungsloesung. Mit dem neue Bionik- Algorithmus —— Ameisen - Kolonie- Algorithmus wird dieses Problem geloest. In diesem Text hat man eine Strukturverbesserungsloesung fuer das Ameisen- Kolonie -system und die Wahrscheinlichkeit der Ameisenkolonie erwaehnt, und damit wird man die Zerstoerungswahrscheinlichkeit des komplizierte Hangs feststellen. Mit dem neuen Ameisen- Kolonie- Algorithmus kann man die gefaehrlichste Gleitflaeche und die entsprechende Zerstoerungswahrscheinlichkeit herausfinden. Die in diesem Text beschriebene Methode wurde durch Praxis geprueft. Durch die Pruefergebnisse wurde es gezeigt und bestaetigt, dass der neue Bionik- Algorithmus vorteilhafter als der traditionelle Algorithmus ist. Résumé : Le calcul de l’indice la fiabilité ou de la probabilité de ruptures peut être transformé en un problème de l’optimisation. Pour le cas du génie des pentes de haut rocher , le problème se pose en général en l’optimisation de multi-crêtes. Les techniques traditionnelles conduisent facilement à la solution optimal partielle au lieu de celle globale. Récemment un nouveau type de bionique algorithmique a été appliqué pour la solution de ce genre de problèmes, c’est l’Algorithme Colonie de Fourmis. Dans l’article il est proposé de modifier la structure du système de la colonie de fourmis et la probabilité de transfert des fourmis en vue d’évaluer la probabilité de ruptures des pentes de haut rocher complexes, par ailleurs un nouveau algorithme adapté de colonie de fourmis est formulé pour déterminer la surface glissante critique et la probabilité de ruptures correspondante. Les techniques proposées dans l’article sont vérifiées à travers des expérimentations dont les résultats ont prouvé que les techniques présentées dans l’article sont évidemment meilleures que celles traditionnelles.

Jan 1, 2003

Jan 1, 1995

By S. R. L. Harding

"Introduction0N MAY 2th, 1953, Socony Seaboard Pembina No. 1 well, located 70 miles west-southwest of Edmonton, was completed as a producer of high-gravity oil from the Cretaceous Cardinm sand. This event is possibly the most significant in the development of the oil industry in Western Canada since the Devonian discovery at Leduc in 1947. The result of the Pembina discovery and the follow-up drilling has been a tremendous increase in interest in the Cardium formation.Descriptions of the Cardium formation, as it occurs in the 'Central Foothills' and in the 'Southern British Columbia Foothills' have been presented by R. E. Folinsbee (9)-and C. R. Stelck (21), respectively. The purpose of this paper is to discuss the more regional aspects of the subject.The name Cardium was first used .as a stratigraphic term in 1863. Dr. James Hector ( l2), geologist attached to Captain John Palliser's exploratory expedition, gave the name 'Cardium to the whole section of marine Cretaceous beds exposed along the Bow river west of Calgary."

Jan 1, 1955

By D P. Yang, Yang R. G

The laws of throwing and heaping of engineering blast are important for making use of throwing and heaping of thrown body to form certain shape, such as building dams by directional blast. The article is to apply Ballistic theory of single thrown body to take the throwing course of thrown body as the movement of particle system, and then delimit the total of thrown body into units of thrown bodies, and regard the heaping shape of single thrown body as a perfect triangle, and found a quantitative relation between macro-geometry parameters of perfect triangle and designed parameters of explosives. The theory has been adopted in blast practice and gotten good effects.

Jan 1, 1999

By L. Russell Van Wert

DURING an investigation in which the solubility relations of the phases in Muntz metal (60 per cent. copper, 40 per cent. zinc) were under study, certain phenomena that had no immediate connection with the main problem were observed, which were thought sufficiently interesting to study further. Because of lack of time, only a preliminary survey was made of two of these; namely, the cleavage structure developed under certain conditions in a 60:40 brass and abnormal grain growth in this alloy. CLEAVAGE STRUCTURE IN HEAT-TREATED MUNTZ METAL Carpenter noted many years ago that cold-working a brass of the Muntz metal type, which had been quenched previously from within the beta field, results in a partial breakdown of the supersaturated beta solution and the precipitation of the solute (the alpha solution) in the cleavage planes of the beta grains. This manner of rejection of a solute from a metastable solid solution is not peculiar to this particular alloy, for among others, it occurs in the cold-working of certain austenitic steels; for example, the austenitic nickel steels. In these ferrous alloys, cold deformation produces a partial decomposition of the austenite, with the formation of martensitic "needles" and zigzags in the austenitic poly-hedra. It is interesting to note that while the two solid solutions-austenite and quenched Muntz metal- are metastable and in their mode of decomposition behave quite alike when deformed in the cold, the metastability of each results from a different cause; viz., that of the austenite from the fact that it is a supercooled solution (its solvent, gamma iron, at ordinary temperatures is below its normal stable range) whereas the metastability of the quenched Muntz metal is the result of supersaturation.

Jan 1, 1929

By Larry R. Powell

As part of the Bureau of Mines effort to establish a comprehensive subsidence data base for subsidence technology development, subsidence and related data are being compiled for various mining, geological, and environmental situations. This publication presents data for two longwall mining operations in the Northern Appalachian Coal Region. Vertical displacements and relative face positions are tabulated for 104 subsidence monuments. Brief physiographic and geological descriptions of the mining sites are presented along with a general account of the mining and subsidence monitoring methods.

Jan 1, 1981

By J. Willan

This paper addresses the problem of designing a destress blasting procedure to reduce the incidence of rockbursting in hard rock mines. A review is made of the developed theory and practice of destress blasting in rockburst-prone ground. Specific reference is made to a recent survey of past and current practice with particular reference to Ontario mining operations. The need is identified for a more scientific basis for destress blast design and monitoring. Reference to developments in blasting technology as well as rock mechanics are then made to support a proposed, integrated design procedure and research strategy.

Jan 1, 1984

By Hui-bin Wu, Rui Yuan, Yang Gu, Peng-cheng Zhang, Zheng-zhi Zhao

The corrosion behavior of three kinds of medium-Cr rolled steel pipeline steels in carbon dioxide collecting and transporting environment at different temperatures was studied. The results shew that the 5Cr sample was most affected by temperature. When the temperature rised from 30 °C to 90 °C, the corrosion rate increased from 0.12 mm/a to 1.87 mm/a, which was increased 15.6 times. The corrosion rate of 7Cr steel at 30 °C was similar to that of 5Cr steel. However, as the temperature increased, the corrosion rate rised slowly, increasing by 2.4 times at 90 °C. The corrosion rate of 9Cr steel was not obvious with temperature, and it was always below 0.06 mm/a. The thickness of the corrosion product film of the three samples gradually increased below 70 °C, and suddenly increased above 70 °C. This was related to the negative temperature coefficient of the solubility of FeCO3, and the thickening of the product film also affected the ion exchange of the cathodic reaction. An increase in the Cr content contributed to grain refinement and increased the proportion of the small-angle grain boundaries. More fine grains mean an increase in the total length of the grain boundaries, which could provide a diffusion channel for the free Cr element; on the other hand, the low-angle grain boundary structure was more orderly, with a lower free volume and lower interface energy. Under the combined effect of both, 9Cr steel and 7Cr steel had high volta potential and better corrosion

Oct 1, 2019

By J. Luxford

The last decade has seen an enormous increase in the use of contractors right across the Australian mining industry. So much so that contractors now operate 33 of the 68 underground metalliferous mines around Australia and are making significant inroads into iron ore in the west and coal in the east. Safety used to be a low priority for many contractors. The picture has changed dramatically in recent years as most contractors take a far more professional approach to safety management. This paper examines the changes that have occurred and the requirements for effectively managing safety in a contracting environment.

Jan 1, 2000

By D. R. Babich, E. R. Bauer

National Institute for Occupational Safety and Health (NIOSH) researchers are conducting a cross-sectional survey of equipment noise and worker noise exposures in the mining industry. Surface and underground limestone is one commodity recently surveyed. The sound levels of mining and processing equipment were recorded to identify noise sources. Full-shift worker noise exposures were completed to determine the exposure of various occupations. This paper presents the results of the noise research conducted in both underground and surface limestone mines, detailing the equipment likely to cause worker overexposures, and the occupations experiencing overexposures. Implications for worker noise exposure reduction are also reported.

By Paulo F. T. Sachs

ERP systems have been widely implemented nowadays in several industries. However, ERP was originally designed to fit former MRP and MRP II users, and most of the ERP research has been focused on discrete manufacturing . On the other hand, process industries ? and mining in particular ? present many peculiar characteristics, which are difficult to comply with ERP systems standard functionalities. Again, very limited research has been developed covering enterprise management systems in mining. The objective of this paper is to identify, through an explanatory study that includes a case study methodology, how ERP systems manage the functional areas of the mining industry, and how they fit into the mineral value chain IT requirements. A secondary objective is to identify the gaps between ERP?s functional capabilities and the mining industry business requirements, and to point out the perceived benefits they generate to the companies.

May 1, 2004

By R. J. Wasilewski

The variation of elastic modulus with terrzperature between -150° and 600°C has been investigated. Compounds close to equiatomic cornposition exhibit very low modulus values and very high damping near room temperature. The modulus rises steeply with both decreasing and increasing temperature. The modulus minimum and the high damping are believed to be connected with a martensitic transformation of TiNi. In bulk material this transition takes place slightly above room temperature quite rapidly and reversibly, with a hysteresis of some 30°C, depending on the Ti:Ni ratio. Oxygen impurity affects the reaction time. THE inter metallic compound TiNi has been reported to exist in an ordered CsCl (B2) structure,l-6 the homogeneity range varying rather markedly with temperature.7 Some investigators reported this compound to decompose peritectoidally to Ti2Ni and TiNi, between 650° and 800°C,3 or below,',g the latter workers also suggesting the decomposition to be strain-sensitive. Purdy and Parr were the first to report a structural transformation to a new, possibly hexagonal, structure at 36°C,7 a temperature indubitably too low to allow the significant amount of diffusion necessary for a peritectoid reaction. Mechanical-property investigations of compositions close to TiNi just above room temperature have qualitatively shown remarkable anomalies, particularly with respect to clamping,' and to a "memory" effect, that is, plastically deformed material returning to its original shape on being heated through the "decomposition" temperature.9 The original explanation of this effect—based on the apparent experimental observation of Ti2Ni or TiNi, formation in the material subjected to tensile or compressive stresses, respectivelp—does not appear plausible. It appeared more probable that the change involved may be a martensitic, diffusionless structural transformation, similar to those observed in other B2 structures such as 0 brass,'' AuCd,ll and AuZn.12 The existence of such transformation has been established recently,', although the symmetry of the low-temperature structure is not yet known. The present paper describes the elastic modulus and damping behavior of polycrystalline TiNi in both structures. EXPERIMENTAL METHOD 1) Specimens. All the specimens to be investigated were prepared from premelted electrolytic nickel and iodide titanium by nonconsumable arc melting and casting in a water-cooled copper mold. The cast billets were canned in mild steel, extruded, and swaged to approximately 0.375 in. diam. The cans were then removed by pickling or machining. Preliminary material balance checks indicated no significant weight losses on melting (less than 5 mg on a 50-g button); hence nominal compositions have been used throughout. In agreement with previously reported observations7 no single-phase material was obtained at—or close to—Ti 1.00 Ni1.00 a small amount of finely divided second phase always being present. It was found that most of the oxygen impurity was associated with this minor phase, which was identified as oxygen-bearing Ti2Ni—possibly Ti,Ni,O. The amount of this phase—at any given Ti:Ni composi-

Jan 1, 1965

By Ragnhild E. Aune, Mark William Kennedy, Shahid Akhtar, Jon Arne Bakken

"In the present study classical induction design tools are applied to the problem of heating nonmagnetic metal billets, using 50 Hz AC. As an example of great practical industrial interest, the induction heating of aluminum billets is addressed specifically. The predicted work piece power is compared with the measured work piece power for a long and a short coil, using well established methods, such as those of Burch and Davis, introduced in 1926/28, Dwight and Bagai in 1935, Baker in 1944/57, Vaughan and Williamson in 1945, and by Tudbury in 1960. A calculation methodology based on a combination of the available tools is also introduced and discussed. The method has proven to give an error of <10% of the actual work piece power. An equation for Tudbury's work piece shortness correction factor is disclosed for the first time.IntroductionInduction heating of metal billets is a practical problem, with a geometry suitable for solution using analytical methods. This paper will examine solutions related specifically to round work pieces in round coils, although the methods presented can be extended to other regular shapes of work pieces and coils[l]. The methods can also be extended to ferromagnetic materials with slight changes[2-3]. It is assumed that the coil and work piece have a consistent diameter over their entire length and that the work piece is at least as long as the coil. Correction factors can be derived for the cases where the work piece is shorter than the coil.The study of induction heating by coils began in the late 19th century with theoreticians like Heaviside[ 4]. The work of Burch and Davis[ 5-7] in the 1920' s greatly improved the theoretical understanding of induction applied to metallurgy. Many investigators in the 1930's-1950's: Dwight and Bagai[8], Baker[l-2, 9], Vaughan and Williamson[3, 10] and others[l 1-12] added to our understanding with clearer mathematics, solutions for specific applications, semi-empirical modifications and practical design tools. Much of the accumulated knowledge is available in books, such as Tudbury's practical text or Simpson's engineering guide from 1960[13-14]. Perhaps the best description and derivation of the theoretical and semi-empirical solutions can be found in Davies[15]."

Jan 1, 2011