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Ledcap Pty Ltd has developed two software tools for assisting in the determination of life-of-mine (LOM) trucking requirements. The first tool generates haul paths and the second calculates truck travel time over these paths. The two step approach allows the paths to be viewed and if required edited, to better represent the actual site haul routes.The first tool automatically creates haul paths between the mine bench and the dump. To do this the user supplies a master haul route and a scheduled block model. The master haul path and the block model are interacted to create multiple haul routes, one for each pit/dump bench pair in each scheduling period. Each path carries with it a record of the scheduling period it represents and the dry tonnage hauled over the path in that period.The second tool calculates truck travel time over the path. Data from the manufacturer's rimpull and retarder curves are used to calculate accelerations and speed over each segment of the haul path. As the paths are derived from digitised representations of mine haul routes the path f les often have over a hundred segments. This detailed representation of the haul route allows the software to automatically adjust speed for different radius corners and accurately simulates the changing accelerations over the gradient changes that occur in real life mine ramps. Rolling resistance can be specified at a global level, at a segment level and at a period level. This allows rolling resistance to be changed seasonally as well as spatially.Life-of-mine trucking studies attempt to calculate an accurate answer from extremely variable inputs. This paper will detail the features of the two software tools and how the tools provided in the software can assist the mine planner to have greater confidence in their life-of-mine trucking requirements and the subsequent production capacity inputs to their scheduling calculations.

Dec 6, 2010

By Will Jansen

When Enron rocked the United States with its Titanic-sized financial accounting scandal, miners and metallurgists were probably too busy on the mine sites in remote locations to wonder about its ripple effect. But then Enron sank, Arthur Andersen tanked and the list of scandals, costing billions of dollars, continued to ripple. Followed by the Public Company Accounting Reform and Investor Protection Act of 2002 (Sarbanes-Oxley), the recent credit crunch and weak economy, the currents from Enron?s collapse eventually washed right into the mine and the mill. These events placed intense scrutiny on metals production accounting processes as traditional semi-qualitative metal accounting practices provided insufficient credibility and transparency. ?There is growing intolerance of organizations that are unsure about the location of thousands of tonnes of ore, which will typically lose 10 to 15% of their notional value on the way to the concentrator,? Rob Morrison wrote in the opening chapter to An Introduction to Metal Accounting and Balancing. ?If the measurement and forecasts also contain qualitative (fudge) factors, a very real suspicion might emerge about just how much metal might disappear (by theft or misplacement) before detection becomes likely.? Metallurgical accounting, put simply, is the tracking and reporting of the quantity and quality (tonnage and grade, usually) of materials entering or leaving each stage from source to product for a specified accounting period. Lacking an accounting standard, metals accounting in precious metal operations has been performed in an ad-hoc, informal manner, leading to numerous errors and unidentified potentially significant inefficiencies and financial losses. As a result, mining companies are beginning to examine the quality of their metals accounting systems since they form the basis of mining company?s financial accounts and reports. As part of an effort to create that accounting standard in the mineral industry, University of Queensland?s Julius Kruttschnitt Mineral Research Centre published the textbook An Introduction to Metal Accounting and Balancing in 2009. While development of a textbook and standard are significant steps forward, the challenge in the precious metals industry is in the application of some of these suggested practices. Though improving process transparency and precious metals accounting reporting accuracy is a key driver for change from the financial side, perhaps even more important is the potential benefit to operational performance that comes with better measurement, accounting and reconciliation systems. Loss of precious metals, processing of waste and inefficient mining and processing systems are all problems that are faced in an operation on a daily basis that can help be resolved through improvements in metal accounting and reconciliation. The financial consequences of such operational inefficiencies and bad decisions based on poor information are arguably greater than consequences of fraudulent accounting. Large discrepancies between mine and mill measurement systems that measure the quantity and quality of valuable material currently exist. Some of these are expected because of statistical variation, but inherent random measurement variation is sometimes an insufficient explanation. Though the mill can usually make much better production estimates through their measurement systems (that is, less variation), this knowledge rarely benefits the mine. 3 Moreover, even if the mine does a reasonably good job of estimating expected production at the grade control level (in situ), issues such as blast movement, poor mining practice and inefficient ore/waste classification make for a disconnect between the in situ estimates of the mine and the estimates from the concentrator. This inhibits effective evaluation of the reserve and grade control models using concentrator estimates. Linking the two ends, mining and concentration, is a neglected area sorely in need of an overhaul. Hence the need for improved mine to mill reconciliation ? the area of comparing, balancing and adjusting production estimates between mine and mill for consistency in reporting.

Jan 1, 2009

By Mario Paredes Malca

El presente trabajo describe el sistema experto por circuito de molienda desarrollado en la Concentradora Toquepala, donde se aplica la tecnología del control experto-basada en conjuntos difusos y modelos matemáticos. Las ventajas que presenta la aplicación de los sistemas expertos comprenden el aumento de la capacidad de tratamiento, la disminución del costo de operación y del porcentaje del producto que no cumple las especificaciones. Asímismo, el sistema experto se integra al sistema de control para asistir al operador en la detección de los casos, donde las operaciones se puedan descontrolar, aunque ésta no sea realmente su principal función. Si se le configura y sintoniza correctamente, el sistema experto detecta, diagnostica en forma continua los problemas de operación y aplica modelos matemáticos y estadísticos de optimización, interactúando con un sistema de control DCS o PLC.

Sep 12, 2005

By V. O. Tenorio, D. Tolmachoff, K. Willa Brown, K. J. Kingsbury, J. B. Nickels, G. J. Nail

A major design feature to consider from the initial pioneering works until reaching full mine production of icy regolith at the South Pole of Moon will be the ramp. This will allow the access of equipment and personnel in and out of the excavation area. Although most of the requirements considered when designing a ramp on the Earth are similar, the fact of working in low gravity, with zero atmosphere, the potential exposure to high radiation, extreme temperature levels and drastic changes of illumination, from intense light to total darkness, are new factors to be included. Transversal sections are obtained according to the progression sequence of the production levels, with changes in length, gradient, friction factor of the terrain and curvature when required by the location characteristics and the specification of the equipment utilized. A MATLAB script was developed to calculate all the variables, in order to obtain 3D generated surfaces from the range of possible profiles.

Mar 2, 2022

By Paul S. Fisk, Arne Fareth, Julie Frietas, Francis Lo, Fidel L. Mallonga

INTRODUCTION This report describes the inspection of parts of the New Croton Aqueduct (NCA)undertaken for the New York City Department of Environmental Protection (NYCDEP)by Parsons Brinckerhoff Quade & Douglas, Inc., (PB) in association with Montgomery Watson Engineers of New York, P.C. (MWH). Support for the inspection was provided by AFC Enterprises, Inc., under Construction Contract CRO-333, “WM-11 New Croton Aqueduct Rehabilitation and Inspection Program.” The scope of the inspection work under CRO-333 included assessing the condition of the 10.3 km (6.4 mile) long, pressurized section of NCA and inspection of shafts, head houses and blow-off structures in both the pressurized and gravity sections. The CRO-333 inspection continued investigation work begun under ContractCRO-196, which ran from 1993 to 1997. The CRO-333 inspections were conducted from November 2004 to September 2005. Background The New Croton Aqueduct was put into service in 1891 to deliver water from the Croton River Watershed in Westchester County to consumers in New York City. Figure 1 shows the location plan of Croton Water Supply System. The design flow into Jerome Park Reservoir was 12.7 m3/s (290 mgd) and into the135th Street Gate House, further south, was 10.9 m3/s (250 mgd). The NCA has been operated as a gravity conduit from Croton Lake to Gate House No. 1, just north of Jerome Park Reservoir, since its original construction. The length from Gate House No. 1to 135th Street, which includes a major siphon under the Harlem River, has been operated under pressure. Croton Lake gate house, the north end of the alignment lies at Station 4+75; Shaft 33, the south end of the alignment lies at Station 1628+05. The diameter of the tunnel is 3.2 m (10.5 ft) in the siphon and 3.7 m (12.3 ft) in the Bronx and Manhattan sections. The pressurized sections, constructed in rock, consist of a brick lining surrounded by a mortared and grouted rubble backing. Figure 2depicts a typical tunnel cross section. The objective of the shaft and tunnel inspections was to locate and document defects, such as leaks, deterioration of lining material, cracks, spalls, delaminations,

Jan 1, 2007

By G. C. Smith

Process control applications in the minerals processing industry have grown extensively over the years due to the many benefits derived, both financially and operation-wise. Although control theory is widely known, conventional control does not address many of the problems posed by minerals processing circuits. Some of these problems include interactions between process units, large dead times, few and sometimes unreliable measurements of process variables, non-linear systems, disturbances entering the process, processes with varying dynamics, and many more. For the past 26 years Mintek has been active in the field of providing specific, customized solutions for the minerals processing industry. This paper focuses specifically on applications in milling and flotation control. The underlying control principles have been applied to a wide range of other processes including submerged arc furnaces. Advanced control application is implemented on a common advanced control platform, called the PlantStar. Much innovation has been brought to the fore in terms of adapting theoretical techniques and developing new methods to resolve specific milling and flotation circuit issues by using process control. The general approach adopted by Mintek when implementing advanced control is to enforce stabilization of the process as a solid foundation for optimization strategies to be built upon. In doing this, a robust control solution is presented, and the end result is flow and level stability, better product quality regulation, increase in throughput and a stable feed to downstream processes. The MillStar advanced milling control system ensures that the milling circuit is at all times easy to operate while achieving optimum product quality and throughput. Stabilization should include product size regulation and sump level control. Another important aspect of stabilization control is the handling of milling circuit constraints without introducing cyclical behaviour and with minimal disturbance to the final product quality. Process constraints may include factors such as process water limitations, cyclone feed density, and cyclone underflow angle. An optimization strategy should be developed to increase the mill throughput without affecting product quality or introducing mill overloads. The relationship between solids feed and power draw is examined and manipulated for optimization. The interactive nature of flotation circuits and the presence of recirculating streams tend to make satisfactory control almost impossible with conventional techniques such as PI (Proportional plus Integral) or PID (Proportional, Integral and Derivative) control. The FloatStar Level Stabilizer simultaneously considers all the flotation levels in a circuit by use of a multivariable algorithm, and takes compensating action in anticipation of disturbances. The FloatStar Flow Optimizer is an optimization strategy that controls the concentrate flow rate between various sections of a flotation circuit (e.g. Rougher ?Cleaner; Cleaner ?Recleaner). By controlling the concentrate flow between the sections, the mass pull, circulating loads and residence times of the circuit can be stabilized, thereby enhancing the performance of the flotation process. Optimizing grade and recovery are coupled with the dynamic optimization of circulating flows. The FloatStar Grade-Recovery Optimizer will maximize the grade in a section, whilst ensuring that recovery or any other process specific limits remain within predefined limits. With successful applications on several milling and flotation plants worldwide processing amongst others PGMs, gold, copper and nickel, Mintek has shown that it is a leader in milling and flotation control innovation

Jan 1, 2004

By F. R. Camisani-Calzolari

Surface defects on continuously cast slabs require treatment by grinding. This extra phase in the process causes lower throughput of final product and extra energy costs. The elimination of slab treatment after casting implies that slabs can be direct rolled or hot charged, resulting in higher throughput and lower energy costs. To increase the number of slabs that can be direct rolled or hot charged, defects have to be predicted before a slab has completed the casting process. Transversal and longitudinal cracking, casting powder entrapment and other inclusions, bleeders, deep and uneven oscillation marks, stop marks and depressions are the defects thatare considered for prediction. A structure with two models is proposed. The first model describes the effect of mould level, water inlet temperature and casting speed (MV?manipulated variables) on 38 thermocouple temperatures (IV?intermediate variable). Casting speed is a manipulated variable while mould level and water inlet temperature are treated as measured disturbances. This model is known as the MV to IV model, and is used to control the occurrence of defects. The second model describes the effect of the thermocouple temperatures on the defects at different positions and locations on the slabs (OV?output variables). This model is known as the IV to OV model and is the predictor of defects. The models are determined using time-series methods in the form of auto regression with exogenous input using data of approximately 500 slabs cast over a period of 6 months. The models are validated using plant data from 44 slabs gathered three years later, with good results. As an example, published results give a sensitivity and specificity of 61.5 per cent and 75 per cent respectively for longitudinal cracks on validation data, while the presented method gives 63.6 per cent and 93.5 percent, respectively. The IV to OV model is used in an inversion to determine the optimal thermocouple temperatures for each slab width. Keywords: Continuous casting, model, defect, prediction, direct rolling, hot charging, goodness-of-fit, correlation, time-series, soft sensor, ARX.

Jan 1, 2003

By John R. Zelonka

Models made by encasing strain-gage networks in epoxy are described and evaluated. With this technique relatively complex models can be constructed in which any number of gages can be located and alined precisely. Although the gages are an integral part of the model matrix, they create no important mechanical or thermal stresses. Model construction techniques and experimental data proved reproducible and reliable. In addition, the sGlution obtained with these models to the problem of the state of stress around a circular hole in a plate subject to a plane stress condition was in agreement with theoretical, photoelastic, and finite-element solutions.

Jan 1, 1970

By J. O. Marsden

Over the past eight years, Phelps Dodge (a subsidiary of Freeport-McMoRan Copper & Gold, Inc.) devoted a significant amount of effort to the development of a suite of processes for the effective hydrometallurgical treatment of copper sulfide concentrates. This effort resulted in the development of high-temperature (>200ºC) and medium-temperature (150° to 165ºC) pressure leaching processes. Specific configurations of both processes have been commercially demonstrated at Phelps Dodge?s facility in Bagdad, Arizona. This paper reviews in detail the chemistry of medium-temperature pressure leaching of copper concentrates and reports on the process development work conducted by Phelps Dodge and others for this technology. This paper is Part I of a four-part series on this technology. Part II covers the development of medium-temperature pressure leaching and direct electrowinning technology; Part III considers the large-scale demonstration of the MT-DEW-SX process at Bagdad, Arizona; and Part IV addresses the development and design of a full-scale commercial application at Morenci, Arizona.

Jan 1, 2007

By Richard S. Fowkes

This Bureau of Mines report describes the Human Factors in Mining Search System (HFMSS), a computerized information retrieval system that provides relevant human factors information from journal articles, research reports, seminars, conferences, etc. in terms of 19 mining-related categories. It is the only existing data base that stresses all of the areas of human factors as applied to mining. Examples of these categories are biomechanics and work physiology, human error and human reliability, work design and task analysis, manual materials handling and back injuries, hand tools, organizational and management practices, psychological factors, and training. Although the emphasis is on literature dealing directly with mining, applicable material from other areas of research is included for those categories in which little research has been done in mining. Each record in HFMSS can be recalled by any field such as title, author, date, source, descriptive terms or key words, as well as by any words found in an abstract that describes the purpose, procedure, and results of the research. This report describes HFMSS fields and subject categories, the annotated bibliography, user's manual, and thesaurus of key words. Example printouts in both brief and full formats are included as an appendix.

Jan 1, 1990

By A. K. Raji, E. F. Orumwense, M. O. Ojumu

The Fourth Industrial Revolution has driven significant advancements in autonomous robotic systems, particularly in subsea exploration and offshore mineral dredging. This review examines the latest developments in electrically powered quadrotor-track subsea robotic crawlers, highlighting their potential to enhance efficiency, mobility, and adaptability in challenging underwater environments. The integration of advanced automation, artificial intelligence, and real-time control systems has paved the way for more effective robotic solutions in offshore mining. This study explores the dynamic performance of hydraulic crawlers to quadrotortrack robotic dredgers, focusing on their propulsion, navigation, and stability under high hydrodynamic conditions. By leveraging state-of-the-art technologies such as lithium-ion battery power systems, intelligent microprocessors, and sensor-based control mechanisms, these robotic crawlers offer a promising alternative to conventional subsea excavation methods. Furthermore, the review analyses recent experimental and simulation-based studies that assess the feasibility and performance of these systems in real-world applications. The findings of this review provide valuable insights into the role of 4IR in transforming subsea robotics for offshore mineral dredging. By addressing existing limitations and identifying key technological advancements, this study contributes to the ongoing development of nextgeneration robotic systems capable of operating efficiently in extreme underwater conditions

Jan 30, 2026

By J. P. Welsh

Ground Modification construction is rapidly evolving in the United States. An assessment of the construction status of Ground Modification methods with their dates of introduction and general acceptance in the United States is summarized. Seven of these techniques are discussed in depth with short case histories; namely, Dynamic Deep Compaction, vibro-compaction, vibro-Replacement, chemical grouting, compaction grouting, slurry grouting and jet grouting. Additional case histories are presented to illustrate the trend of combining Ground Modification techniques to solve specific site problems.

Jan 1, 2010

By M. Q. W. Jones

This paper presents a compilation of physical properties of rocks from the Bushveld Complex. The database consists of more than 900 measurements each of thermal conductivity and density. The data are well distributed from localities around the Complex and most rock types are well represented. Thermal conductivity and density are shown to vary widely in the ranges 1.8-4.2 W m-1K-1and 2600-4200 kg m-3respectively. Although only 190 heat capacity measurements are available, this parameter is quite uniform for most rock types present, 800-900 J kg-1K-1, except for chromitite, which has a lower average, 750 J kg-1K-1. Rocks encountered in deep platinum mines are particularly well characterized and this has important implications for prediction of mine refrigeration requirements. The heat flux into a semi-infinite region with properties typical of the Bushveld Complex as a function of time is substantially lower than an equivalent model for the Witwatersrand Basin.

Jan 1, 2015

By R. Webber, D. Averill, L. Whittle, D. Moffeti, G. Kassakhian

"This paper describes the recent pilot-plant work carried out on two alternative processes capable of producing an effluent containing less than 10 pCi/L total radium-226 activity and very close to 3 pCi/L dissolved radium-226. The processes incorporate coprecipitation of radium with barium sulphate by the addition of barium chloride in continuously stirred tank reactors followed by either chemical coagulation with ferric chloride, flocculation and clarification, or polymer-aided dual-media filtration. IntroductionUranium mines in Canada have practiced radium removal from tailings basin effluents since 1965. Treatment consists of addition of barium chloride to precipitate radium as barium- radium sulphate and provision of natural or constructed settling ponds for sedimentation. This process, however, has been identified as being deficient in that it allows particulate or suspended radium-226 releases which are higher than the regulated dissolved values». Also, the large size of some of the settling ponds is believed to represent a real limitation of the present technology because of inferred difficulty in recovery of barium-radium sulphate precipitates.The Federal Government Mining Task Force established a Radioactivity Sub-Group in 1974 to assist in the development of effluent regulations and guidelines for the uranium mining industry. Among the recommendations of the Sub-Group was the need to seek more effective methods of radium removal, including development of physical/chemical treatment systems as an alternative to settling ponds. In response to the SubGroup recommendations, a bench-scale study began in March 1976at the Wastewater Technology Centre (WTC) of Environment Canada . The results of this study indicated that coagulation and flocculation of the precipitate from barium chloride addition is a viable alternative to sedimentation in settling ponds(3). The bench work was expanded and accelerated in 1977, with financial assistance provided by the Atomic Energy Control Board. Subsequently, a research program with a larger scope was developed; this program is jointly managed and funded by government and industry, as shown in Table I.One of the goals of the joint program is to develop, at pilot scale, a physicalI chemical process to reduce the radium-226 content of uranium mining and milling effluents. Target radium-226 activities for treated tailings basin effluents were set: namely, 10 pCil L total and 3 pCil L dissolved radium 226. Extensive bench-scale and pilot-scale work was conducted through 1978 and 1979 and has culminated in the development of two physical/chemical processes. This paper describes work carried out at a pilot plant which led to the selection of the two physical I chemical processes for demonstration. In short-term tests, the processes produced effluents meeting the radium-226 target activities."

Jan 1, 1980

By L. W. Higley

Electrowinning metals from solutions leached from low-grade ores is becoming an increasingly important extraction method as the metal industry turns to pollution-free recovery processes. Lead-alloy anodes are used industrially in the electrolytic recovery of zinc and copper. However, associated with the use of these anodes are the inherent problems of stability and lead contamination of the cathode. In an effort to eliminate these problems, the Bureau of Mines has developed a relatively inexpensive lead dioxide anode for electrowinning metals from strong acid solutions. The anode was prepared by depositing Pb02 directly on a titanium blank in a strong HN03-Pb(N03)2 solution at 2.15 to 6.45 A/dm2 and 60° C. This anode was tested in zinc and copper electrowinning cells containing 200 gpl H2S04 and 35 to 100 gpl metal ions at the current density of 3.23 to 6.45 A/dm2. Contamination of the cathode by lead was =0.005 pet. A 30-day test at 6.45 to 12.90 A/dm2 in an electrolyte containing 200 gpl H2S04 and no metal ions resulted in a slight change in surface morphology of the Pb02 anode but no measurable change in anode weight or dimensions.

Jan 1, 1976

D. HARRINGTON: Owing to lack of funds, the United States Bureau of Mines have made no experiments in the Bruceton mines in the use of mudite. MR. McAULIFFE: I doubt that mudite cam be delivered at fifty cents a ton and that a mile of heading can be treated with mudite for ten dollars. You could not dig a ton of sand out of a sand hank for that money. L. C. CLARE: The tram road leading to Wattis mine crosses a shale bed and it is easy to screen the shale through a %-inch sieve and load it into a mine car. W. J. REID: A slow trip passing through a mudited entry will dislodge practically no dust, a rapid trip will make air disturbance enough to coat the cars with fine dust. MR. PRYDE: We have used mudite on stoppings around a fire in Reliance and for two months thought they were getting good results, but the fire was found to be drawing air and to be spreading. This mudite was smeared over the stoppings with a trowel. After this apparently failed we used dry adobe.

Jan 1, 1925

By T. Celik, B. Genc, C. Musingwini

"This paper discusses a new methodology for defining and measuring mine planning software utilization in the South African gold mining sector within an evolving data-set framework. An initial data-set showing the mine planning software providers, their corresponding software solutions, as well as the software capabilities and information on the number of licences was collected and compiled in 2012 in an online database for software utilized in the South African mining industry. Details of the database development and implementation were published in the Journal of the Southern African Institute of Mining and Metallurgyin 2013. In 2014 the data-set was updated with additional and new information. Using the 2012 and 2014 timestamps, a methodology for estimating the software utilization was developed. In this methodology, the three variables of commodity, functionality, and time factor were used to define and measure the software utilization in order to ultimately inform decision-making strategies for optimal software utilization. Using six different functionalities, namely Geological Data Management, Geological Modelling and Resource Estimation, Design and Layout, Scheduling, Financial Valuation, and Optimization, utilization in the gold sector was measured. This paper presents the methodology employed for measuring the mine planning software utilization. The methodology is useful for stakeholders reviewing existing software combinations or intending to purchase new software in the near future and who want to estimate the comparative attractiveness of a certain software package. These stakeholders include mining companies, consulting companies, educational institutions, and software providers. The work presented in this paper is part of a PhD research study in the School of Mining Engineering at the University of the Witwatersrand."

Jan 1, 2015

By Nicholas G. Theofilos

The Bahamian economy weathered the worldwide recession of the last few years better than most developing countries. This was mainly owing to the ties between the tourist industry of the Bahamas and the U.S. economy. The mineral industry played a minor role in the country's economy. The chief mineral exports included an increasing amount of petroleum products horn the country?s 500,000-barrel-per-day refinery, steel pipe, salt, and aragonite. A 60,001)-barrel-per-day desulfurization facility was completed by Bahamas Oil Refinery Co. (BORCO) in Freeport. The project included vacuum gas oil desulfurization, hydrogen and sulfur recovery, steam generation, water desalinization, and offsite facilities.

Jan 1, 1980

By S. q. Honingh, G. Van Weert

Currently produced zinc-enriched blast furnace dust is stored on site at CORUS IJmuiden. To end this practise, a research program was started in 1996. Four technologies were studied: oxidative autoclave leaching in a chloride medium, fluid bed pyrohydrochloridisation (pyrohydrolysis) to yield lead-zinc-free (hematite) calcine, EAF (plasma) smelting/zinc fuming, and incorporation of the dust in 'iron foundry cupola charges. All aim to remove zinc and lead, recycle the iron residue internally, and produce a saleable zinc-lead product.

Jan 1, 2000

By F. W. Bowdish

A theoretical and experimental laboratory study has shown that the rate of breaking of oversized particles in a ball mill is proportional to 1) the concentration of such particles, and 2) the area of the balls, provided that the balls are larger than a certain size relative to the particles. If all undersized material were removed as formed, the rate of breaking would be almost independent of the quantity in the mill. Rate equations are given which are similar to those for zero, first, and second order reactions. Deviations of small balls from the equation for a second order phenomena are quantified by a factor called "nipping efficiency." Some data are correlated by a dimension-less equation, which is used to estimate nipping efficiencies from data not in the correlation. The investigation described here was undertaken after a literature survey revealed that little was known concerning the mechanism of breaking of particles within a ball mill and the effect of this mechanism upon grinding rates. One paper, by Roberts1 , offered a theory concerning the mechanism of breaking, and a rate equation for the breaking of particles larger than some size to particles smaller than that size. That paper provided the starting point for a theoretical and experimental investigation of grinding under carefully controlled conditions. THEORETICAL CONSIDERATIONS In his paper on the probability theory of ball mill grinding, Roberts theorized that "... a given expenditure of power leads either to a certain number of point to point blows per bp-hr or to a certain distance of line contact per hp-hr ..." He assumed that the balls touch each other during each blow or during moving contact. Then he said that a volume of pulp, dependent upon the size being considered, would be covered per minute within which all oversized particles would be crushed to particles smaller than that size. Naturally, the higher the concentration of oversized particles in the pulp, the higher the rate of which they would be broken. From this reasoning Roberts obtained the differential equation -dC/dt = k hp/ton C (1) where k is a constant for any size of particle, density of particle, and moisture content of pulp. C is the percentage of oversize in the material to be ground, t is the time, and hp/ton is the power input per ton of material in the mill. He then integrated the equation to log Co/Ct = k/2.3 hp/ton t , where Co and Ct are the percentage of oversize at time zero and t respectively. By always using the same quantity of material in a mill and assuming that it required constant power to run the mill, he was able to combine the horsepower per ton factor with the other constants to give an equation for a first order rate.

Jan 1, 1961