Scientific Journal "Metallurgy"

STUDY OF ACID-BASE PROPERTIES OF PHOSPHORUS-CONTAINING TUNGSTEN MELTS UNDER EQUILIBRIUM CONDITIONS

Viktor Malyshev, Dmytro Shakhnin, Angelina Gab — Fri, 10 May 2024 00:00:00 +0300

The ionic composition of tungstate melts determines both the nature of electrode processes and equilibria, as well as the composition of cathode products. The activity of oxygen ions in the tungstate melt was studied by measuring the EMF of electrochemical cells with oxygen electrodes. A diaphragm-type platinum-oxygen electrode was used as a reference electrode. The indicator platinum electrode was immersed in the investigated melt. Potentiometric studies proved that P2O5, NaPO3, Na4P2O7 compounds are acceptors of oxygen ions, and Na3PO4 is a donor. The character of experimental dependences of the platinum-oxygen electrode on the concentration of oxygen-containing phosphorus compounds can be justified using the theory of conjugated acids-bases. Studies have shown that, when P2O5, NaPO3, Na4P2O7 are added to the tungstate melt, W2O7 2- anions are formed which is confirmed by structural methods of study of frozen melts. The agreement of the experimental and calculated dependences confirms the correctness of the proposed models of the ionic composition of melts. The possibility to control the acid-base properties of these melts is important from the point of view of tungsten electrodeposition and high-temperature electrochemical synthesis of tungsten carbides, borides, and silicides. Information on the structure of tungstate melts with oxygen-containing compounds of phosphorus makes it possible, depending on the conditions of electrolysis, to obtain purposefully tungsten deposits in the form of powders or coatings.

USTIFICATION OF THE APPLICATION OF OXYGEN ELECTRODE COMPARISON WITH β-Al2O3 MEMBRANE IN TUNGSTEN-MOLYBDATE MELTS

Victor Malyshev, Tetiana Nesterenko, Dmytro Shakhnin, Angelina Gab, Roman Volyar — Fri, 10 May 2024 00:00:00 +0300

Four conditions for using the electrode system as a reference electrode are formulated: compliance of the electrode system with the type of measurements; inertness of electrode system materials; stability and reproducibility of potential values; reversibility of the electrode system. Taking into account the physicochemical properties of tungstate-molybdate systems, melts based on sodium tungstate and chloride tungstate-(molybdate)-containing melts were selected as electrolytes for comparison electrodes. As a membrane of the reference electrode, a material based on β-Al2O3 (Na2O⋅11 Al2O3) was used. The stability of this material in both acidic and basic melts has been proven. The temperature limits for the use of this material as a membrane have been determined experimentally: 723-1073 K. It is assumed that the potential of a platinum-oxygen electrode with a membrane on the base of β-Al2O3 is determined by the partial pressure of oxygen in the atmosphere inside the membrane tube. Calculated values of the diffusion potentials on the porous diaphragm. They do not exceed 3⋅10-3 V. Diffusion potentials reach a stationary value within several minutes. The potential of the oxygen electrode relative to the reference electrode will be determined by the ratio of О2- ion activities in the investigated melt and in the melt of the reference electrode. To check the reversibility of the proposed system, the study of electrochemical equilibrium on platinum electrodes and their micropolarization studies were conducted. The absence of hysteresis on the micropolarization curves proves the reversibility of the proposed electrode system. The stability and reproducibility of potential values have been experimentally proven. The use of a comparison oxygen electrode with a β-Al2O3 membrane in melts containing compounds of carbon, boron, silicon, molybdenum, and tungsten will allow for a more reasonable solution to the issue of controlling and combining the potentials of the electroreduction processes of these compounds. The latter will make it possible to practically implement the technology of high-temperature electrochemical synthesis of carbides, borides and silicides of molybdenum and tungsten in molten salts.

METHODS AND MODELS FOR ASSESSING THE ECONOMIC SECURITY OF AN INDUSTRIAL ENTERPRISE

Natalia Metelenko, Ivan Klopov, Serhiy Pliasov, Serhiy Zagorodnyi — Fri, 10 May 2024 00:00:00 +0300

The article considers methods and models for assessing the economic security of an industrial enterprise. The aim of the research is to develop methods and models for managing the economic security of an industrial enterprise in an unstable external environment. The process of assessing the economic security of enterprise is proposed to be carried out in three stages. First stage: formation of a set of models for determining the economic security of industrial enterprise based on the composition of individual components of the economic security of enterprise. It is proposed to consider the economic security of an industrial enterprise as a system of four functional components: financial, technical and technological, personnel and intellectual, and information. The model for assessing the financial security of enterprise takes into account the level of the financial component of economic security by groups of indicators of liquidity, reliability, financial stability, and profitability. The personnel and intellectual component of the enterprise's security takes into account the level of education, qualifications, and professional characteristics of management and production personnel. The efficiency of the use of production resources and assets of an industrial enterprise is the basis for determining the level of technical and technological security of the enterprise. The level of information security of the enterprise is calculated in terms of directions, stages and bases of information activity of the enterprise At the second stage, the threats are diagnosed and their impact on the economic security of the enterprise is modelled. The method of threat diagnostics is based on determining the maximum amount of damage from the occurrence of threats in the context of the functional components of the economic security of the enterprise. The third stage is forecasting the economic security and protection of an industrial enterprise. Forecasting the economic security of an enterprise provides the basic initial information for making managerial decisions in the process of planning the modes of operation of an enterprise.

APPLIED ECONOMIC-MATHEMATICAL ANALYSIS OF FIRE-RESISTANT PRODUCTS SINTERING PROCESSES: EFFICIENCY MANAGEMENT OF PRODUCTION PLANS PJSC «ZAPORIZHVOGNETRYV»

Vyacheslav Glushchevsky, Viktoriia Ogloblina, Oleg Zhyliakov, Oleksandr Khrapkin — Fri, 10 May 2024 00:00:00 +0300

The article addresses the problem of applied economic-mathematical analysis of interrelated processes in the production, sintering, and material-resource support of fire-resistant product manufacturing. A conceptual approach to modeling the distribution of raw materials for obtaining an optimal charge is substantiated, considering the criterion of minimizing the total production cost of material and raw material expenses for fulfilling the order portfolio of PJSC «Zaporizhvognetryv». The author's modeling concept is based on the principles of a systemic approach, employing research methods such as economic-mathematical modeling, correlation-regression analysis, and groups of statistical data processing and summarization methods. This is used to create and implement a modeling toolkit – a complex of economicmathematical and information models of a specific structure (developed in MS Excel electronic spreadsheets). These models collectively realize the functionality of the "Charge Optimization" and "Raw Material Price Forecasting" modules. This ensures effective operational and tactical regulation and management of the efficiency of production plans at the level of the main links of the production activities of PJSC «Zaporizhvognetryv». A human-machine dialogue procedure has been developed for calculating the demand for raw materials in conditions of multivariate combinations of acceptable rational variants of charges. To implement this procedure, an integrated information model was developed on the MS Excel platform, automating decision support for the distribution of charge materials among different charge variants for the production of fire-resistant products, in compliance with technological norms and aligned with the volume of the planned order portfolio of PJSC «Zaporizhvognetryv». The proposed mathematical and informational support enables the automated operational verification of the compiled production plan for its resource balance and adherence to contractual business obligations through a dialog system on the MS Excel platform, using the developed economicmathematical model for charge optimization. The directions for applied economic-mathematical analysis of management decisions based on the developed toolkit are outlined. The modelalgorithmic complex was tested on the statistical data of PJSC «Zaporizhvognetryv» to assess the effectiveness of the compiled production plan (planning horizon – one month). The obtained economic effect is justified, indicating a conditional reduction in total costs (model calculations) by 8,6 million UAH compared to actual expenses. This allowed practical recommendations to be made for further improvement of the efficiency management of production plans for PJSC «Zaporizhvognetryv» based on the calculations.

INNOVATIVE TECHNOLOGIES IN THE NON-FERROUS METALLURGY OF UKRAINE – FLUORAMMONIUM TECHNOLOGY FOR THE DISCOVERY OF ILMENITE

Yevgeny Bazhenov, Viktor Skachkov, Natalya Metelenko, Roman Volyar, Pavlo Skidin — Fri, 10 May 2024 00:00:00 +0300

The article is devoted to the generalization of the objective prerequisites of interest in titanium metal, which represents a unique combination of physical and chemical properties with significant earthly resources of titanium raw materials. The technical and economic criteria determining the rate of spread of titanium metal in innovative technologies of non-ferrous metallurgy, in particular, energy efficiency and environmental friendliness, have been updated. A critical analysis of modern technologies for obtaining titanium metal has been made, which includes the identification of problems in the technology for obtaining and further use of titanium metal; analysis of technologies for obtaining metal and derivatives based on it, which, in aggregate, combine technologies for cleaning intermediate materials; assessment of the shortcomings of chlorine technology along with its dominance in the world. The relevance of the transition from extensive efforts to revolutionary solutions for the development of technology for obtaining titanium metal has been outlined in order to solve the triune scientific task «optimization of costs for raw materials – energy efficiency – environmental conditioning of production». An initial assessment of the fluoroammonium technology for the opening of ilmenite in the production of titanium and titanium-containing materials has been made, the evolutionary path of the technology's development has been investigated, and the prospects for its development has been outlined. The principal scheme of obtaining titanium dioxide by the technology of fluoroammonium opening of ilmenite concentrate with subsequent separation of the target components has been substantiated. The advantages and prospects of the technological solution of the proposed method of opening the ilmenite concentrate and subsequent separation of the target components to obtain titanium dioxide and iron oxide has been outlined. It has been proven that the technical and economic potential of the proposed conceptual solution is enhanced due to the possibility of obtaining silicon-containing components with the prospect of obtaining silicon dioxide of high purity. The results of laboratory research towards the development of technology for the separation of works on the isolation of siliconand titanium-containing components have been proven.

USE OF ANTHROPOMETRICAL DATA OF WORKERS FOR DESIGN OF INDIVIDUAL PROTECTION EQUIPMENT

Volodymyr Gridiaiev, Yevheniia Manidina, Anna Karpenko, Oleksandr Rusakov — Fri, 10 May 2024 00:00:00 +0300

Long-term work of workers in harmful and difficult working conditions leads to the occurrence of occupational diseases in them. The largest share among all known occupational diseases caused by harmful and dangerous production factors is respiratory diseases. According to the regulations on labor protection and the collective agreement, the employer is obliged to provide the worker with personal protective equipment (PPE). The work examines the main designs of personal respiratory protection equipment (PPE), and identifies their main structural elements. A study of the anthropometric dimensions of the face of 300 workers of the coke chemical industry (KHV) was conducted. It was determined that the most influential parameters of the face for determining the protective capacity of ZIZOD are: length and width of the face, as well as the length of the lips. When comparing the research results with the data of the LANL and NIOSH tables, 20% of the agreement of the sizes of the faces of the investigated workers with the data of the first table, LANL, and 88% with the data of the second table, NIOSH, was found. It has been established that the improvement of the NIOSH table will make it possible to carry out high-precision tests of ZIZOD in domestic research laboratories. The use of such NIOSH tables is expected to allow selection of a PPE with a 90% degree of protection. On the basis of the ISO 16900-1:2020 standard "Respiratory protective devices – Methods of test and test equipment –Part 1: Determination of inward leakage" based on the standard dimensions of the Sheffield head mannequin used in determining the penetration coefficient of filtering half-masks, the face type of domestic workers was determined on KHV – medium/ wide type. Recommended main directions for improving the design of PPE to ensure their protective capacity at a high level: to produce several standard sizes of half-masks, to create an adjustable obturator according to the anthropometric parameters of the workers.

MATHEMATICAL MODELING OF METALLURGICAL ENTERPRISES HYDRO-ENERGY UTILIZATION SYSTEMS

Viktor Kovalenko, Mikhailo Paziuk, Vladimir Yefanov PhD, Iryna Ovchynnykova — Fri, 10 May 2024 00:00:00 +0300

To utilize the maximum amount of potential energy of the flow of secondary water, which is diverted from technological equipment, and the amount of which depends on the topology of such sources and the configuration of the collection system, it is necessary to create a mathematical model of the latter and optimize its structure and parameters. In order to predict the energy characteristics of the water flow that will flow to the hydro turbine, statistical information on the actual water consumption by the equipment in the system of the reversible cycle of the metallurgical enterprise of the Zaporizhzhia region was collected. It has been established that the condition for the creation of energy-efficient hydropower utilization systems in the conditions of industrial enterprises is the selection of their structure at the optimization level and the determination of the technical characteristics of its elements, as well as taking into account the modes and specifics of water consumption of technological units, which will depend on the energy indicators of the real total water flow entering the hydro turbine micro hydropower plant. The paper developed a mathematical model of a stochastic generator of secondary water consumption of an industrial metallurgical enterprise, which allows to more accurately determine the parameters of hydropower utilization systems. The modeling of the flow of technical water is performed taking into account the dynamic nature of water consumption for the needs of cooling technological equipment. Statistical data obtained experimentally were used to determine the distribution law of the random amount of expenditure. It has been established that experimental observations of water consumption are most accurately described by the Poisson distribution law with parameters 4,12 і k = 1...14 . For the implementation of this method, the autocorrelation function of technical water consumption is preliminarily constructed and the coefficients bk are determined by solving the system of equations. The applied approach makes it possible to create stochastic generators of secondary water consumption of any metallurgical enterprise based on their predicted values and to calculate the approximate hydropower potential of their watercourse, to select the parameters of the necessary equipment.

CONTROL OF AGGLOMERATE DISTRIBUTION BY LAYER HEIGHT ON THE AGGLOMERATING CONVEYOR UNDER DIFFERENT LOADING CONDITIONS

Iryna Ovchynnykova, Mikhailo Paziuk, Olena Barishenko, Viktor Kovalenko — Fri, 10 May 2024 00:00:00 +0300

The article addresses the issue of managing the distribution of agglomerate charge by the height of the layer on the agglomerating conveyor during its loading. It is noted that the segregation of material particles affects key parameters such as gas permeability and fuel distribution within the layer. The task of solving this problem is formulated as finding the distribution of size classes of agglomerate charge by the height of the layer without segregation. The article utilizes models described in other studies to determine the distribution of size classes by the height of the agglomerate charge layer. The model is calibrated based on experimental data and loading device parameters. Calculation results for specific enterprises confirm the adequacy of the model, where the modeling error does not exceed 5.1%. The research also highlights the influence of loading device parameters and properties of the agglomerate charge on the distribution of fractions by height. Changes in the average particle diameter, tilt angle, and length of the loading chute affect segregation within the layer. Modeling results indicate that altering the average particle diameter significantly impacts the distribution of size classes in the agglomerate charge. The article addresses the challenge of managing the structure of the agglomerate charge layer on the agglomerating conveyor by altering loading device parameters, particularly the tilt angle. Results suggest the effectiveness of changing the tilt angle to control particle segregation.

MONITORING OF THE FINANCIAL STATE OF PJSC “ZAPORIZHSTAL” AS A MECHANISM FOR INCREASING THE EFFICIENCY OF MANAGEMENT

Tetyana Melikhova, Andriy Makarenko, Yevgenii Melikhov, Ksenia Skachkova — Fri, 10 May 2024 00:00:00 +0300

Metallurgy is traditionally a basic branch of industry and plays an important role in the economy of Ukraine as a supplier of basic construction materials and an indicator of the country's socioeconomic development. Therefore, the research topic is very relevant for the economy of Ukraine. The state and trends of the development of metallurgy in Ukraine are analyzed. The main problems of the metallurgical industry of Ukraine are: a decrease in the share of the domestic market of Ukraine in the world volume of consumption of finished metal products, the growth of exports, which is connected with the surplus of steel products on the domestic market, the lack of innovations in the metallurgical industry, low investment activity. A financial analysis of the largest enterprise of the metallurgical industry of Ukraine was carried out PJSC "Zaporizhstal". Based on the analysis, the following suggestions are given for the development of metallurgical enterprises of Ukraine: attraction of foreign investors; attraction of additional cash flows of the founders through the revision of the dividend payment policy; modernization of the main production assets; review of product range; reduction of tax rates for metallurgical products when consumed in the domestic market; application of modern production technologies; reduction of sales for export of raw materials and semi-finished products. Based on the financial analysis, the following proposals are given for the development of metallurgical enterprises of Ukraine: attraction of foreign investors; attraction of additional cash flows of the founders through the revision of the dividend payment policy; modernization of the main production assets; review of product range; reduction of tax rates for metallurgical products when consumed in the domestic market; application of modern production technologies; reduction of sales for export of raw materials and semi-finished products.

CRITERIA AND METHODOLOGY FOR EVALUATING POTENTIALLY DANGEROUS PRODUCTION TECHNOLOGIES

Vladislav Rumyantsev, Tatiana Sharapova, Andriy Hnatyshak, Radion Skachkov — Fri, 10 May 2024 00:00:00 +0300

The proposed work examines the criteria for evaluating potentially hazardous production technologies on the example of metallurgical production. The main criterion is proposed to use the coefficient of labor protection. To determine the safety of technological processes (BTP), it is necessary to take into account the normative parameters of labor safety BP. Factors affecting the level of labor protection are given. To determine the level of safety of processes, it is advisable to carry out calculations for a certain period of time, during which the technological process proceeds without violating safety standards. Special attention is paid to the safety assessment of technological processes. The main factors affecting the safety of the technological process are analyzed. All devices that do not participate in the technological process are suitable for ensuring the convenience of work and the safety of workers. It has been proven that the optimal way to increase the safety level of technological processes is their mechanization and automation.

SIMULATION OF COMPOSITE MATERIALS COMPOSITION PROCESSES WITH SILICON PYROCARBIDE

Fri, 10 May 2024 00:00:00 +0300

The paper examines the peculiarities of obtaining and using materials of the C/SiC class in the form of carbon-silicon carbide structures in various fields of technology. The work is aimed at developing a mathematical model of the deposition of pyrolytic silicon carbide on the porous surface of carbon-carbon composite materials from a mixture of gases based on methane CH4 and SiCl4. Pyrolytic silicon carbide is formed as a result of thermal dissociation of organosilicon compounds of silicon tetrachloride (SiCl4) or methyltrichlorosilane (CH3SiH3). When compacting reinforced composite materials with pyrolytic silicon carbide, organosilicon compounds enter the reaction zone together with hydrogen or methane, which are both a reducing gas and a carrier gas. The deposition process of pure silicon carbide competes with the deposition of carbon and mixtures of silicon carbide with carbon. Therefore, one of the tasks of the work is to ensure such conditions for the flow of homogeneous-heterogeneous processes, which would realize the deposition of pure SiC. During the pyrolysis of methyltrichlorosilane in the temperature range of 800-1000 °C, highdensity SiC with a purple hue is formed. As the pyrolysis temperature of methyltrichlorosilane increases, the color of the coating changes to gray. The size of the crystals is about 22 nm. The yield of SiC is in the range of 25-35%. The maximum yield of silicon carbide is observed in the temperature range of 1250 – 1500 °C. Increasing the temperature to 1600 °C does not significantly affect the yield of SiC. During the research, it was established that the most relevant is chemical-thermal deposition from a gaseous mixture of methane and silicon tetrachloride, during which stoichiometric deposition of SiC is achieved without damage to carbon fibers in carbonized carbon plastics with a carbidized matrix. The paper defines the theoretical equilibrium constants of representations of thermochemical reactions. Formulas for evaluating the productivity of a thermochemical reactor under the conditions of a quasi-equilibrium regime of silicon carbide deposition have been determined.

"SILICON FROM SAND" – STAGE OF DEVELOPMENT OF SEMICONDUCTOR SILICON TECHNOLOGY: EXPERIENCE AND PROSPECTS

Tetiana Kritska, Yevhenii Vasylovych Bazhenov — Fri, 10 May 2024 00:00:00 +0300

On the basis of the analysis of modern methods of obtaining semiconductor silicon, critical factors affecting the prospects of the industry's development are identified – these are the problems of raw material supply and the high energy intensity of production processes. As an alternative solution, a method of obtaining semiconductor-quality silicon directly from quartz sand is proposed, which excludes the use of expensive, scarce quartzites and charcoal. Ensuring the energy efficiency of the method is carried out due to the exclusion from the technology of the multi-tonnage, energy-intensive process of carbothermic reduction of quartzites in ore-thermal furnaces (stage of obtaining metallurgical silicon, temperature up to 2000°С, 12 17 MW∙g/t), exclusion from further technologies of methods of high-energy-consuming operations of distributive condensation of PGS (temperature below 60°C), explosive high-temperature hydrogen chloride synthesis process (temperature up to 2300°C), as well as operations of high-temperature hydrogenation of silicon tetrachloride (temperature ~ 1270°C). The advantage of the new technology is also the possibility of disposal of man-made waste from the abrasive, electrode industry, organic silicon and other silicon-containing waste. Activation of the charge composition in the solid phase ensures its effective low-temperature chlorination in the mine chlorinator. Further stages of the technology are rectification purification of silicon tetrachloride, low-temperature hydrogenation to obtain silanes, gradual separation of PGS components (mixture of silanes, hydrogen chloride, hydrogen). The new technology provides the possibility of further production of polycrystalline silicon rods using the following methods: pyrolysis of monosilane (Dupon process), hydrogen reduction of silicon (CVD process), or granular silicon (pyrolysis of monosilane in a pseudo-liquefied layer of silicon particles – Dassel process). The use of low-energy-intensive processes for the production and purification of silanes, the utilization and reversal of intermediate technological products in the new technology opens up the possibility of variable use of known technologies in relation to the current demands of consumers for the quality of polycrystalline silicon.

STUDY OF FLUCTUATIONS OF METAL LEVEL IN CRYSTALLISERS OF CONTINUOUS STEEL CASTING MACHINE

Natalya Volosova, Ihor Mazur, Vitaly Volokh — Fri, 10 May 2024 00:00:00 +0300

Steel production is of great importance in the country's defense capability. Today, there are four active metallurgical enterprises in Ukraine that produce steel both for military needs and for the construction industry. Continuous casting of steel in modern conditions is a promising direction in the metallurgical industry. Due to the economic impracticality of casting steel in a foundry, there is a transition to methods of continuous casting of blanks, therefore it is necessary to increase the requirements for diagnosis and technical condition of the structural elements of the continuous casting machine (CBM). In order to reduce the duration of unforeseeable downtimes caused by technical malfunctions, as well as to avoid accidents with severe economic consequences, it is necessary to increase the requirements for diagnostics and the technical condition of the elements of equipment structures used at MBLZ. One of the main factors that affects the performance of the MBLZ is the methods of diagnosing the equipment based on the results of the crystalliser oscillation diagrams, which is generally determined by the stable operation of the machine. Since the beginning of the construction of the MBLZ, namely from 2003 to the present, research and improvement of diagnostic methods, both of individual nodes and of the machine's performance as a whole, has been continued, therefore this work should be considered relevant. The presented work is aimed at improving the efficiency of the MBLZ nodes due to timely determination and identification of breakdowns by determining the level of oscillation bursts in the crystallizer. In the work, an analysis was carried out with the determination of the main deviations in the work of the MBLZ. The main deviations are summarized in a classification list with a definition of the relative impact on the stream as a whole. In the work, the main attention is paid to diagnosing the equipment and determining the breakdown of this or that node, where it is necessary to perform preventive maintenance or replace the node as a whole. The paper presents practical calculations with the probable determination of deviations in the operation of the MBLZ equipment.

A NEW DIRECTION OF MANUFACTURING PREPARATION FOR METALLURGY AND MECHANICAL BUILDING

Fri, 10 May 2024 00:00:00 +0300

A fundamentally new method of obtaining blanks for grade rolling, pipe production and machine building has been developed. The method is based on the use of the roll castingrolling process. A fundamentally new design of the casting-rolling installation has been developed, it includes three crystallizer rolls, which, together with other equipment of the installation, form a volumetric inter-roll space, where a three-dimensional massive body of the workpiece is created, the design device is protected by a patent of Ukraine for an invention. The method and device make it possible to obtain solid and hollow blanks that can have a dual purpose. Design solutions are based on proven original analogs. The developments have undergone initial testing in the laboratory of the department of metallurgical equipment of the Zaporizhia National University. The testing was experimental in nature, the main task was to test the design of the installation and the new method. As a result of the approbation, the manufacturability of the method and device was established, the prospects of their development and application in industrial conditions were confirmed. The workability of the method of obtaining blanks and the device for its implementation has been confirmed. The industrial production of solid and hollow billets by the roll casting-rolling method will improve the technical and economic indicators of metallurgical and machine-building enterprises: shorten the metallurgical cycle, reduce energy costs, reduce the metal capacity of equipment, and improve the environmental condition. The results of the development can be used by enterprises of metallurgical, machine-building complexes, and the defense industry. The availability of new type of blanks allows to revise the composition of the equipment of rolling mills and pipe shops in the direction of reducing its volume and energy consumption. In the future, new developments become the basis for the creation of endless graded rolling.