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ABSTRACT Based on mineralogical characteristics and processing techniques required, gold ores can be classified into 12 types: gold placers, quartz vein-lode ores, oxidized ores, silver-rich ores, iron oxide copper-gold ores, porphyry copper-gold ores, iron sulphide ores, arsenic sulphide ores, antimony sulphide ores, bismuth sulphide ores, telluride ores, and carbonaceous sulphide ores. The bulk mineralogy and gold deportment of each ore type differs and may have a significant impact on ore processing and metal extraction. This paper summarizes the bulk mineralogy and gold deportment in some major types of gold ore and discusses the potential impact of gold deportment on gold metallurgy.

Jan 1, 2013

By D. H. Ryan, B. Abdul, M. Pernechele, E. Asselin

Hydrometallurgical processing of sulphide concentrates at medium temperature (150°C) produces residues, which contain valuable metals (Cu, Ni) as well as sulphur and iron bearing minerals and phases. The low solubility of iron during the medium temperature processing of sulphide ores can favour the formation of poorly crystalline, nano-scale iron oxide/oxyhydroxide phases. A better understanding of the formation and structure of these iron precipitates may elucidate key factors that would ultimately result in lower valuable metal losses and more stable leach residues. Residues from two medium temperature leach processes were characterized by Mössbauer Spectroscopy. Some portions of the Mössbauer Spectrum were suspected to be linked to jarosite but could not be positively identified as such. There was a broad range of disorder and substitution present in the material and solely attributing it to jarosite proved difficult. Various synthetic jarosites with Cu substitution were precipitated for Mössbauer analysis. These were then characterized by Quantitative X-Ray Diffraction (QXRD), Scanning Electron Microscopy (SEM), Inductively Coupled Plasma Mass Spectroscopy (ICP-MS) and Mössbauer Spectroscopy. The Mössbauer Spectra of the synthetic jarosites is compared with that of the residues from medium temperature (150°C) sulphide concentrate leaching.

Jan 1, 2014

By Bert S. Hall

"The purpose of this paper is to review the evidence at hand concerning the earliest centuries of cast iron in Europe, from roughly 1400 A.D. until the second half of the sixteenth century. For the most part it is concerned with the relationship between two technologies which emerged first in China and then later appear in Western lands, gunpowder weapons and iron founding. We should not assume, as I hope to show later in this discussion, that weapons constituted the only product for which the iron founder had any market, but it is clearly true that attempts to produce weapons constituted the most severe technical challenge for the early founder. Firearms appear for the first time in Europe in the 1320s and develop into significant weapons on the field of battle by the end of the century. Theirs is a complex history, subject neither to easy summary treatment nor to simplified models of development. I hope to be able, through the analysis of the evidence concerning cast iron, to show that one important strand in the fabric of gunpowder's history concerns the materials from which cannon could be made. This question is subject to a number of shades of meaning, because ""cannon"" can be made for many purposes under a profusion of different names, and under sharply varying conditions of use. As a result, the question of materials is frequently really a question of competing materials, and involves a complex set of factors, of which production costs and the ultimate safety of the user seem the most important. Judged in this manner cast iron was an important but unsatisfactory metal for weapons purposes until 1543, at which time English founders learned to make iron muzzle-loading cannon which could rival bronze ordnance in most important performance criteria, but which cost much less to produce. With that event, the history of cast iron and the history of weapons entered into the close relationship that persisted until the advent of rifled artillery made of steel in the middle of the nineteenth century."

Jan 1, 1999

By K. Soldenhoff, D. Wilkins, E. Ho

In the processing of rare earth ores, a pure, mixed rare earth chloride solution is usually produced and used as the feed to solvent extraction circuits to separate the individual rare earths. Cerium(III) may be separated from the other rare earths by oxidising it to cerium(IV), which precipitates as cerium(IV) hydroxide in chloride liquors. This oxidation step may be inserted either before rare earth separation by solvent extraction or between solvent extraction circuits. Although oxidation of cerium by sodium hypochlorite has been known for many years, detailed conditions for oxidation are not readily available. The effect of hypochlorite addition, temperature, pH and cerium concentration on oxidation of cerium(III) from synthetic solutions was investigated

Jan 1, 2014

By K. Maruyama, T. Nagasaka, R. d. Chairaksa-Fujimoto, T. Miki

Electric arc furnace dust or EAF dust is considered as a hazardous waste but contains a significant amount of economically attractive non-ferrous metals especially zinc as zinc ferrite (ZnFe2O4) and zincite (ZnO). The hydrometallurgical process is one alternative choice because it has the advantage of low energy consumption. The leaching of ZnO from the dust is very easy. However, the complex major zinc compound in EAF dust is ZnFe2O4, which is very stable and insoluble in alkaline or acidic media under delicate conditions, and causes the low zinc recovery yield by hydrometallurgical process. Moreover, halogens and heavy metals in the dust are also problematic. In order to develop a new effective EAF dust treatment process, the authors have proposed "CaO addition process" as pre-dust treatment to transform all of ZnFe2O4 in the EAF dust to ZnO and Ca2Fe2O5. In this study, the selective zinc leaching from the CaO treated EAF dust with NaOH and NH4Cl solutions was carried out. The effect of temperature, reaction time and solute concentration were systematically investigated. All of zinc in CaO treated EAF dust was successfully leached into both solutions.

Jan 1, 2014

"Pilot plants for pressure hydrometallurgy represent special design and project execution challenges. Over the past twenty years, Zeton has designed and fabricated a variety of world-class pressure hydrometallurgical pilot-plant facilities for the nickel industry, and this paper discusses design considerations and strategies related to such projects. Project execution methods are also discussed, and guidance is given for the selection of materials of construction and for the selection of appropriate pressure and temperature design points for pressure hydrometallurgical pilot equipment. The paper concludes with a discussion of the need for process similarity with future commercial operations and the realities of pilot-scale equipment.INTRODUCTION The process technology developer or owner and the designer/fabricator of a new pilot-plant facility are faced with some difficult technical choices even after the decision to build a dedicated plant has been taken. A pilot-plant project is usually on the critical path of a large commercial project involving investments many multiples greater than the capital cost of the pilot plant. Schedule savings in the design, manufacture, and commissioning of the pilot plant or in a rapid completion of the experimental program can be disproportionately beneficial to the overall development project. However, inappropriate shortcuts resulting in major oversights can be disproportionately problematic. A number of considerations and suggestions for both the project execution approach and the process engineering design of pressure hydrometallurgical pilot-plant facilities are presented as a guide for potential owners and operators of new pilot-plant equipment and facilities. These suggestions are particularly applicable to the nickel industry, where the majority of our firm’s prior hydrometallurgical experience was obtained. This paper is an update to an earlier publication (Martin, 2004), offering an opportunity for a new generation of metallurgists and engineers to learn the specialist requirements of pilot- and demonstration-scale plant design, which are key functions in the development and commercialization of new processes."

Jan 1, 2017

By G. Zárate, G. Tapia

Anglo American Chile has been doing copper concentrate leaching studies at the laboratory and small pilot plant scale since 1992. Among the processes evaluated are bacterial leaching and pressure leaching using Mantos Blancos, Salobo Project and Quellaveco Project concentrates. Late in the nineties, it was decided to focus the research on pressure leaching, either medium or total pressure oxidation. Preliminary scouting tests were run with Mantos Blancos concentrate samples during 2000, which were repeated during 2003 together with samples of Los Bronces and El Soldado concentrates, in order to define the most suitable concentrate for running a pilot plant campaign at AARL, which was carried out in two campaigns, a first one from November 2003 through January 2004 and a second one during April 2004. Mantos Blancos was the selected concentrate and the laboratory and pilot plant results are discussed in this paper together with some preliminary economic estimates.

Jan 1, 2004

By J. Lu, J. B. Wiskel, D. G. Ivey, E. Niemi, H. Henein

Simulated TMCP using a Gleeble was undertaken to evaluate the effect of the austenite to ferrite cooling rate, coiling temperatures of either 400°C or 500°C and the magnitude of plastic deformation at the coiling temperature on the hardness of a Grade 483 (X70) steel. For comparable apparent cooling rates and deformation conditions, the hardness of the samples were independent of coiling temperature The application of a minimum compressive deformation > 8% was required to increase hardness at both simulated coiling temperatures of 400°C and 500°C. An increase in hardness was also observed with increased cooling times between 800°C and 500°C (i.e., slower cooling rates).

Jan 1, 2005

By S. Hume, J. Shepherd

Meso-2,3-dimercaptosuccinic acid(DMSA) was studied as an additive for thiosulfate leaching of gold. DMSA was added to solutionscomposed of either sodium thiosulfate or calcium thiosulfate and the solutions were tested for their ability to leach pure gold samples as well as a calcined gold ore from Barrick Gold Corp. Results showed prolonged leaching of pure gold samples when DMSA was added at a concentration of 5µM; however, higher concentrations were shown to inhibit leaching. Differential capacitance measurements of the interface indicated that DMSA adsorbed as a defective monolayer on the surface of gold at low concentrations and formed a more compact monolayer with increased concentration. It is proposed that a concentration of 5µM DMSA produces a defectivemonolayer on the surface that still allowsthe transport of oxidants to the underling metal while inhibiting the formation of polysulfide passive layers that arise fromdecomposed thiosulfate.The 5µM DMSA/CaS2O3 system was also studied using calcined ore. Results showed that the initial leaching rates in the presence of DMSA are lower than those obtained in thiosulfate alone. However, after 10h, prolonged leaching is again observed when DMSA is included.

Jan 1, 2015

By Ki-Bok Min, Bona Park

"In spite of the applications of DEM models to emulate the elastic modulus, Poisson’s ratio and strengths of isotropic rock in laboratory scale, extensions to anisotropic rock and larger engineering scale still have many challenges to overcome such as robust verification and validation against observed field case. In this study, a discrete element modeling was performed in order to represent a transversely isotropic rock such as shale, and the upscaled model was applied to foundation and borehole problems using PFC2D. The applicability of the upscaled rock mass model was verified by an analytical solution. The DEM modeling of stress redistribution induced by an applied surface line load compares well with Boussinesq’s isotropic solution and anisotropic solution given by Bray. The borehole model with a circular opening under biaxial stress was compared with both isotropic and anisotropic solutions resulting in good agreement. The abilities of DEM model to investigate the micromechanisms accounting for complex macroscopic behaviors and to predict the macroscopic behavior are discussed.The results demonstrate that DEM modeling has the potential to be applied to anisotropic rock mechanics problems on larger engineering scales such as wellbore stability problems especially in shale formations. Furthermore, the effect of anisotropy modeled through this study may be able to explain failure behavior of anisotropic rock encountered frequently in real cases.INTRODUCTIONAnisotropy is prevalent in various types of rocks, especially in shale that contain a set of parallel bedding planes. These weak planes in various forms are sources of large deformation and low shear strength and contribute significantly to the anisotropic behavior of rocks (Amadei, 1996; Cho et al., 2012; Kim et al., 2012). As elastic and strength behavior of anisotropic rock is substantially different from that of isotropic rock, proper consideration of anisotropy is of great importance. There is extensive of experimental evidence showing the anisotropy of shale. Niandou et al. (Niandou et al., 1997) analyzed the plastic deformation and failure mechanisms of Tournemire shale were highly dependent on the orientation of bedding planes. Cho et al. (Cho et al., 2012) presented various deformations and strengths of Boryeong shale obtained from laboratory experiments. Fjaer and Nes (Fjaer and Nes, 2013) performed uniaxial and triaxial compressive strength tests using Mancos shale, and they observed that the shear sliding along the planes of weakness before the occurrence of a major failure can reduce the strength of anisotropic rock. The recent research has demonstrated that the anisotropy of rock is an important consideration in rock engineering."

Jan 1, 2015

By Mory Ghomshei

As fossil fuels become depleted over the next century, it is imperative that Canada and other countries examine ways to transition to other sources of energy, particularly renewable resources. A critical obstacle to developing Canada?s renewable energy resources is the scarcity of infrastructure to wheel the generated electricity to a viable market. For each megawatt of renewable electrical power, a maximum of 1 km of connecting power line is typically feasible. This means that hydropower, geothermal, and wind power projects with capacities up to 100 MW must be located within a maximum of 100 km of a main power line in order to be economically viable. With a total length of about 1200 km, the proposed Northern Gateway oil pipeline project creates an excellent opportunity to become a corridor that can seed renewable energy projects in Northern British Columbia and Alberta. Utility companies must build new infrastructure to provide the electricity for constructing and operating the proposed pipeline. The pipeline and linked power line infrastructure therefore, should be designed and built with consideration to create an energy highway to the significant renewable energy resources, such as hydro, wind, and geothermal, in the vicinity of the proposed pipeline. Some of the important renewable energy resources in northern British Columbia can be developed in connection with the proposed pipeline. It is estimated that close to 2,500 MW of commercially viable wind, geothermal and run-of-river power resources are present in the proximity of the proposed pipeline corridor. While oil flows westward from the Alberta bitumen fields, the generated green power can flow eastward to help the Canadian oil sand industry to offset as much as 10 Megatons of carbon emissions per year. The generated carbon credits are equivalent to 75% of the emissions associated with extraction of the 525,000 barrels per day of oil from oil sands, intended to be carried by the pipeline.

Aug 1, 2013

By S. Nafisi

Permanent mould casting may be regarded as a near net shape manufacturing process where simple to very complex shaped engineering components are fabricated with high degree of precision in a metallic mould, In this group, High Pressure Die Casting (HPDC), have attracted more attention because of its production rate, where both liquid and semisolid metals (SSM) can be cast with high degree of precision and versatility. The SEED process, Swirled Enthalpy Equilibration Device, the new process for semi solid metals slurry production route, consists of two steps: The initial step involves extracting specified amount of heat from the molten metal to generate liquid-solid slurry, i.e, mushy structure, followed by drainage of remaining liquid to produce a compact free standing feedstock for rheocasting operation. In this paper, microstructural evolution during the process and some initial casting results of automotive components an also reported.

Jan 1, 2005

By Michael Magerstädt

Material loss by abrasion of contact surfaces of pipes, chutes, pumps, and other equipment in contact with ore is one of the main reasons for downtime of mining operations. Abrasion protection materials in use range from expensive tungsten carbide overlay to hardened steels, ceramics, as well as polymers, particularly polyurethanes (PUR). This paper describes abrasion protection products made from High Performance Polyurethane Elastomers. An interior pipe coating was developed that exhibited outstanding abrasion resistance and an extremely high adhesion to steel. Years of field testing in oil sands tailings as well as applications in slurry lines (e.g., phosphate slurries) have proven the performance of this material. A proprietary field joining process was developed and successfully applied in the field. This joining process requires only one field weld per joint very similar to the joining of uncoated pipe. No internal re-coating is necessary adding savings during pipe laying to the significant savings of reduced down time. Using the building-kit chemistry of polyurethane synthesis, similar high performance elastomers were used to extend the life time of ball mills. An intelligent system was developed in which wear parts contain sensors reporting the actual wear thereby optimizing maintenance interval leading to significant cost savings for the operator. Test data as well as field experience with High Performance PUR Elastomers for abrasion protection in mining are presented.

Aug 1, 2013

By Zhenyu Han, Dion Weatherley, Ruslan Puscasu

"This study aims to demonstrate the capacity of the Discrete Element Method (DEM) to model and simulate fracture in brittle rock, capture the crack propagation process and determine crack propagation rates for various levels of external loading. In the numerical experiments reported here, a macroscopically homogeneous body of brittle rock, containing a single pre-existing crack, was subjected to tensile stress loading. Simulations concerned with model I crack growth process in 3D were carried out. The process of fracture has been observed under various steady state and dynamic conditions. The numerical results obtained reproduce qualitatively and quantitatively a variety of observed fracture phenomena. Specifically, this study examined the onset of cracks, single dominant cracks that grow across the specimen, crack bifurcations and branching. The density of fractures that can be nucleated and grow to a significant size with and without arresting each other, crack growth speed and stress distribution, all have been consistently and systematically analyzed. Suggestions on potential future developments are made and discussed.INTRODUCTIONFracture and failure mechanics are very important in mining, manufacturing, materials processing, mineral processing, civil and mechanical engineering, and many other disciplines of science and engineering. Yet, due to the complexity of fracture phenomena, no theoretical models of broad applicability are currently available (Bieniawski 1967). The simulation of crack propagation is therefore considered an open question in numerical rock mechanics. Although, a significant body of experimental research on fracture of materials was carried out since the early days of fracture mechanics (circa 1940s) (Poncelet 1946, Mott 1948), often in parallel with the development of fracture mechanics theories as well as with the development of experimental and observational techniques themselves, the experimental results were often done on particular classes of material such as glasses and other very brittle materials. Indeed, a number of specific experimental observations on the behavior of growing cracks in brittle materials were made in the 1940s for which generally accepted explanations based on physical principles are still lacking. Likewise, quantitative numerical modeling, based on both continuum and discrete methods, as a basis for understanding dynamic crack growth is still in a preliminary stage."

Jan 1, 2015

By P. E. Cavanagh

"The Davis tube test has been used for many years as a laboratory method for determining the magnetic iron re-coverable from a magnetite iron orebody. This paper de-scribes a method for determining the recoverable iron from ores of the Labrador Trough type, with the usua1 flow sheet utilizing spirals followed by magnetic separation.The mechanical structure of a metamorphosed iron ore, resulting from recrystallization over long periods of time, is the basis for the laboratory method developed. Similarities between the structures of such recrystallized ores and the structure of annealed and recrystallized steel are noted.A laboratory technique to determine the size of the different grains of gangue and iron ore minerals is de-scribed and the application of this information to arrive at recommended grinding techniques and flow sheets is demonstrated. The use of the method to determine recoverable iron in such ores is compared to actual iron recovery in the pilot-plant and commercial concentrations of the same ore.The use of a specified lower limit of recoverable iron as determined by this method, in order to design open-pit limits, achieves practical results when compared to designing a pit based on an arbitrary lower limit of total soluble iron. The Ungava Iron Ore deposits are used in giving an example of the resulting pit design changes."

Jan 1, 1968

By C. Piribauer, E. Feichtenhofer, A. McEneaney

"As part of a major diversification project, RHI AG, through its plant in Drogheda Ireland, has developed a Caustic Calcined Magnesium Oxide (CCM) for use in the Cobalt (Co) & Nickel (Ni) hydrometallurgical extraction industry. In the course of the project, the company investigated the chemical and physical properties of a number of different Magnesia’s used in Co & Ni hydrometallurgy applications and has been able to determine the important parameters for a successful Magnesia for this application. A number of live plant trials have confirmed the results of this testwork and the company is now proceeding to produce this product in commercial quantities at Premier Periclase Ltd., the RHI AG plant in Drogheda, Ireland. This paper will outline the development work conducted by the company and highlight the important chemical and physical properties that make a successful CCM. Much of the research was conducted at the RHI Technology Centre in Leoben, Austria. In addition, a number of external laboratory studies were conducted on behalf of RHI AG. The result of this work has allowed the company to develop a Magnesia product with optimised properties for use in the Cobalt and Nickel hydrometallurgical extraction process.INTRODUCTION Premier Periclase is part of RHI AG, a globally operating supplier of refractory products, systems and services, headquartered in Vienna, Austria. The company produces Magnesia from seawater at its plant in Drogheda, Ireland. While the main focus is on production of refractory grade Dead Burned Magnesia for the steel industry, the plant also produces a number of different grades of Caustic Calcined Magnesia as well as Magnesium Hydroxide products. As part of a major project to diversify the company’s product base, the use of CCM in the Cobalt (Co) & Nickel (Ni) hydrometallurgical extraction industry was investigated. One of the company’s highly reactive grades of Caustic Calcined Magnesia was found to be particularly suitable for this application. In an effort to understand what makes a successful Magnesia for hydrometallurgy the chemical and physical properties of different Magnesia’s used in Co & Ni hydrometallurgy were investigated. This paper and conference presentation outlines the findings of this process."

Jan 1, 2017

By D. J. M. Farnsworth

Since the 1.940's, the bulk of the ore production from the Sullivan Mine has come from pillars. These pillars, located from 100 to 2000 feet below surface, have been subjected to considerable ground pressure. Mining techniques were adopted to minimize the problems of deteriorating ground conditions. These techniques included an orderly sequential blasting of pillars along a retreat front, stage blasting of tall pillars in horizontal slices and utilization of broken pillars as "buffers". The latter two techniques involved leaving substantial tonnages of broken ore in place for as long as 4 years. Rapid oxidation of metal sulphides, with attendant heat and noxious gas generation, had occurred in a few very localized areas of the mine associated with a major water course. However, in a very short period starting in 1972, sulphide fires spread to several of the large blocks of broken ore that had been left inactive for lengthy periods. There proved to be no feasible method of extinguishing these fires, except by complete removal of the burning ore. The attendant problems of handling large tonnages of burning ore have had considerable negative impact on the mine operation. The chemical reactions involved in these sulphide fires have been studied by the mine staff to determine the conditions necessary for' initiation and propagation of the tires. Techniques to safely and efficiently handle hot ore have been implemented and refined. Lastly, and most important, mining methods at the Sullivan Mine have been revised to ensure that additional fires do not occur.

Jan 1, 1977

By R. Carrier

"There has been a continuous evolution with the use of pre-cast concrete elements in the construction of aluminum smelters. In 1990, Phase I of Alouette was built using cast-in-place concrete exclusively. Whereas, other AP 30 technology plants such as Hillside 2 in the mid-1990s used pre-cast concrete beams with cast-in-place floors. Mozal 2, in 2002, used pre-cast concrete beams with pre-cast partial-slab operating floors. Alouette Phase II went further. Not only were the potroom building beams and floors pre-cast, but the entire pot support system, insulating walls and basement jersey walls were pre-cast. Once the techniques for bending and welding the reinforcement bars and the design for attaching electrical insulating plates to the concrete was perfected, the challenge for the project remained only in the logistics of transporting the pieces to site and simple erection. The overall impact on the project was dramatic. Using prefabricated concrete not only allowed advancement of the schedule, but totally eliminated formwork, re-bar installation, and form removal activities along with the handling of all the materials involved with these activities. With the elimination of these labour and material-intensive portions of the job, exposure to work injuries was dramatically reduced. The most prevalent activity for lost time accidents is during the rough work associated with concrete formwork, placing concrete and form removal. Another area where prefabricated elements were successfully used on Alouette Phase II was for the insulating walls enclosing the pot area, known as the ""claustra walls"". Usually these walls are constructed in-situ using mortar and breeze block. Success was also achieved with prefabrication of the perimetric walls that are installed at the lower floor of the potroom. A big advantage of using prefabricated concrete in the electrolysis area is in assuring electrical isolation for the operating floors. Poured concrete requires a meticulous clean-up effort before commissioning to establish the electrically ""floating"" characteristics of the operating floors. Poured concrete results in ""wash"", stray wood,"

Jan 1, 2006

By J. G. A. Stevenson

"IntroductionDURING the past quarter of a century diamond drilling, in all its phases, has increased in Canada to a very impressive total of more than 10,000,000 feet annually. Since the art of diamond drilling became recognized, some seventy-five years ago, there has been considerable improvement in both equipment and technique. The steam-powered drill rig and the hand-set diamond bit are things of the past.The purpose of this paper is to review some drilling trends •and practices over the past few years. In the preparation of the paper, the author wishes to acknowledge kind assistance of Mr. J. D. Cumming, Dr. C. H. Hitchcock, Mr. Robert H. Quintal, and many others, including staff members of the Longyear organization.Figures provided by the Dominion Bureau of Statistics for the year 1954 show that Canadian production of metallic and non-metallic minerals and structural materials had a value of $1,454.2 million, excluding radioactive products for which figures are not available. Approximately 61 per cent of this valuation comprised production of nickel, copper, gold, coal, asbestos, zinc, lead, and iron. It is certain that diamond drilling played a major role in the discovery and development of the orebodies from which these minerals were obtained.After the surface examination of an ore deposit, diamond drilling will automatically follow, in order to determine structure, grade, and tonnage.Footage drilled by mining companies and contractors on mineral exploration and blast-hole work since 1945, as reported by the Do-minion Bureau of Statistics, is shown in Figure 1."

Jan 1, 1955

By N. Tounsi

The use of analytical modeling of continuous chip formation in conjunction with orthogonal cutting experiments was presented in the open literature to identify the coefficients of material constitutive equation within the practical range of stress, strain, strain rate, and temperature encountered in metal cutting. Identification of reliable constitutive data was hampered by a lack of a reliable model for the prediction of the primary shear zone thickness that affects directly the effective strain rate field. An original analytical model to determine the primary shear zone thickness is proposed in this paper. It is based on the mechanics governing the material flow in the primary shear zone. Based on the distribution of the hydrostatic pressure and the forces measured from orthogonal cutting tests, the model that describes the thickness of the primary shear zone is derived. To validate the model, FE simulations of chip formation using DEFORM3D were carried out for different materials and cutting conditions. The results of the analytical model are in reasonable agreement with FEM results.

Jan 1, 2006