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Analytical Determination of the Reduced Rotational Resistance Coefficient of the Construction Machine Slewing Gear
(Дніпровський національний університет залізничного транспорту імені академіка В. Лазаряна, Дніпро, 2019) Bondarenko, Leonid N.; Posmitiukha, Oleksandr P.; Hlavatskyi, Kazymyr Ts.
EN: Purpose. Designing new models of construction machines is closely related to the development of slewing gear, and that, in turn, has a drive whose power and dimensions depend on the rotational resistance and the reduced fric-tion coefficient in the units. The absence of analytical dependencies for determining the reduced coefficient of friction for the rotation of construction machines, first, restricts the designer's ability to select materials, and secondly, does not allow the adoption of optimal design solutions. Therefore, the purpose of the article is to find analytical solutions to determine the rotational resistance in the slewing gear of construction machines, which allows project-ing more advanced gears and machines in general. Existing techniques are based on empirical dependencies and experimental coefficients that reduce the accuracy of calculations, increase the size and cost of work. It is proposed to improve the accuracy and simplify the process of determining the rotational resistance and the magnitude of the reduced rotational resistance coefficient of the building tower cranes. Methodology. The set objectives can be achieved by means of analytical dependencies for determination of rolling friction coefficients over linear and point contacts. This will enable to find the more accurate value of the resistance coefficient, and the constructor during the calculations to take targeted measures to reduce it, using the mechanical constants of materials of the units and their geometric parameters. The calculation is based on Hertz contact deformation theory and the body point plane mo-tion theory. Findings. The obtained dependencies will allow analytically to find the resistance of rolling resistance of rollers in construction machines with fixed and rotating pillars, with circular rotary devices, as well as in ball and roller slewing rings. The calculated values of the rotational resistance coefficients for some types of mechanisms give similar values with those recommended, while for others they significantly differ and require their refinement in reference values. Originality of the work consists in the use of analytical dependences for determining the reduced coefficient of the rotational resistance over linear and point contacts using Hertz contact deformation theory and Tabor partial analytic dependencies theory. Practical value. The obtained dependencies will allow to design new types of slewing gear units of the construction machines and to reveal the additional rotational resistances.
Analytical Method of Determining the Movement Resistance of a Tip for Forming Rectangular Technological Hole in the Lower Structure Tracks
(IOP Publishing, 2020) Posmitiukha, Oleksandr P.; Hlavatskyi, Kazymyr Ts.; Kravets, Svyatoslav V.; Suponyev, Volodymyr; Koval, Andrey
EN: Abstract. The aim of this work is to theoretically determine the total resistance to soil pricking with a wedge-shaped tip to create a rectangular cavity and to determine the influence of the size of the working equipment and soil environment in the repair of earthenware or areas where trench technology can-not be used. To determine the forces of the recess of the replaceable pilot, the law of change of soil pressure on the working surfaces of the working equipment was first determined, which is based on the idea of the change of the soil elastic state at its compaction was determined, which is determined by the compression module of deformation of the soil. The processes occurring during the formation of wells and new approaches to the improvement of calculations have been described. On the basis of the pro-posed model of the piercing process, the laws of change of the normal pressure of soil resistance on the surface of the wedge working equipment are established. Based on its value, the results of theoretical studies have received a rational form and parameters of the tip of the work equipment.
The Calculation of Stress Intensity Factor Steel of Railway Wheels
(Silesian University of Technology, Katowice, Poland, 2020) Vakulenko, Ihor O.; Proydak, Svetlana V.; Askerov, Hangardas
EN: From an analysis of the dependence complex of carbon steel properties on structural parameters, it was found that for an isostructural state, the influence of austenite grain size on impact strength exceeds the dependence on carbon content. As a result of explaining correlation relationships between individual mechanical characteristics, to evaluate critical stress intensity factor, a relationship is proposed based on the use of impact strength. The proportionality coefficient in proposed dependence is determined by ratio of elongation to narrowing at tensile test.
Concept of Determining the Friction Stir Welding Mode
(Національний гірничий університет, Дніпро, 2018) Vakulenko, Ihor O.; Plitchenko, Serhii; Murashova, Nataliia H.; Bohomaz, Volodymyr M.
ENG: Purpose. To determine the optimal mode of friction stir welding of aluminum alloy. Methodology. 2.5 mm thick plates made of aluminum alloy AMg5 with chemical content of alloying elements within grade composition were used as a material for the research. Friction stir welding was carried out using specially designed equipment with a preselected form and dimensions of working tool. At different ratios of the working tool rotation frequency the forces of pressing and speed of its movement along the connecting edges determined the metal heating degree and the quality of welded joint formation. Temperature of the connecting edges heating was determined by thermocouples immersed in metal at different distances from the welded joint. Rotational speed of the working tool was from 800 to 1600 min-1 with the effort of pressing to the plate surface from 580 to 1370 N and the speed of movement along the joint of 50 mm/min. Findings. On the basis of different ratios of the working tool rotation speed and pressing to the connecting edges, there were determined conditions for achieving the effect of constant softening during friction stir welding. In order to achieve a high level of welding joint quality during friction stir welding it is necessary to carry out the process at high revolutions of the working tool and low levels of pressing to the connecting edges. Originality. At the constant speed of the working tool rotation proportional increase in alloy temperature from increasing the level of its pressing to the connecting edges is disturbed by achievement of conditions of the dynamic softening processes development. Practical value. The concept of choosing the technological parameters of welding process is determined, when it is preferred to increase in speed of the working tool rotation when the level of its pressing to the connecting edges decreases.
Determination Activation Energy of Friction Stir Welding
(WRTYS, Kyiv, 2017) Vakulenko, Ihor O.; Plitchenko, Serhii
EN: According to the technology of friction stir welding (FSW) heating of the edges is equal to 0.85-0.9 from the melting temperature of metal (T). Increase in temperature is accompanied by increased degree of the metal stirring, which leads to ambiguous influence on the metal density and concentration of cavities at different distances from the welding joint. At the same time, the temperature gradient across the section of joint leads to a different speed of recrystallization processes development and forming of structural heterogeneity in metal edges. Thus, the relevant question is to determine the optimal scheme of metal edges heating during the implementation of FSW technology. Material for the study was alloy AMg5. For different ratio of rotation speed and pressure on operating tool there were obtained the conditions of superplastic state of alloy at the temperatures of heating at the level of 0.45-0.5 from T, which corresponds to the beginning of dynamic recrystallization development during FSW. At the same time, it was evaluated the energy of activation (EA) of FSW process. Using the analysis of the obtained results it was determined the fact that when reaching the same temperature of alloy heating the EA value of FSW process decreases with increasing the rotation frequency of the operating tool and decreasing the degree of its pressing to the edges of welding joint. On the basis of the above mentioned the development of FSW technology should be directed toward the use of high speed rotations of the operating tool and low levels of its pressing to the alloy edges.
Determination of Equivalent and Optimal Sizes of Wedge Tip from Flange for the Static Perforation of Soil
(Український державний університет залізничного транспорту, Харків, 2018) Posmitiukha, Oleksandr P.; Kravets, Svyatoslav V.; Suponyev, Volodymyr; Glavatsky, Kazimir Ts.
EN: Abstract. The purpose of the study is to create a new design of the working tip for the perforation of the soil when laying two or more buildings trenchless way and determine its rational parameters. Method. It is known that for static perforation in the formation of cavities in the soil for communication is traditionally used cone-shaped working elements, which is the most common, cheap and reliable. However, the study revealed inefficiency. The design of the working elements of the soil perforation for trenchless laying of two or more buildings simultaneously in the form of a tip, which consists of a wedge-shaped part and a control part in the form of a rectangle with half-cylinders. The basic principles and mathematical dependences of determining the size of the working body are described. Scientific novelty. Regularities of changes in soil pressure on the lateral, conical and wedge surface, flat and cylindrical part of the tip, allowed to obtain an analytical dependence for the calculation of the resistance force depending on the physical and mechanical properties of the soil, the diameter and the number of cases established simultaneously. Also, when comparing the cone-cylindrical and flat tips, it can be argued that the breakdown force of the flat tip decreases from 1.2 to 1.7 times.
Determination of the Size of Theseal Zone and the Soil Pressure on Underground Communications in the Process of Soil Deformation by the Wedge-Shaped Tip
(НВП ПП «Технологічний Центр», Полтавська державна аграрна академія, 2018) Posmituha, Alexander; Kravets, Svyatoslav; Suponyev, Vladimir; Kulazhenko, Yevhenii Yu.
EN: The object of the study is a working element with a wedge tip for static perforation of the soil with the laying of several cases for underground utilities. One of the problems that require research is the laying, location and proximity of various types of underground utilities, laid trenchless way. The study of the zone of influence of working bodies on the ground and communication will give us the opportunity to more efficiently design the use of underground space, to reduce the risks of damage to or destruction of communications and reduce the cost of the work. Studies are based on the law of conservation of mass before and after compaction of the soil with a wedge tip and on the basic theories of soil mechanics. This allows you to determine the pressure of the soil on the working element and on the communication, located nearby. The result obtained in the work shows that the pressure value is not the same in different directions of the wedge working element. It is also proved that the number of cases, which are simultaneously laid, have little effect on the zone of elastic-plastic deformation of the soil. These effects make this form of hole indispensable when you need to simultaneously lay several, more than 3, cases, compared to the traditional conical-cylindrical tip. To determine the soil pressure on underground utilities were used only the size of the working elements, and data that are easy to determine – the type and density of soil, humidity, porosity and other standardized characteristics. The use of this method has a significant advantage over other methods, which are based on empirical relationships that are either difficult to determine or their reliability is questionable. Due to the reduction of the cross-sectional area of the deformable soil, the wedge working body is indispensable for stretching the group of cases.
Dynamics of the Interbank Exchange using Neural Technologies
(Scientific Publishing Center “Sci-conf.com.ua”, Lviv, Ukraine, 2022) Volkova, Svetlana A.; Anofriev, Pavlo G.; Hiliavskyi, Denys
ENG: Artificial intelligence is used to predict various events. Recently, the direction of predicting the exchange rate of bitcoin in pair with the dollar has been actively developing. Due to volatility, it is very difficult to predict the price of cryptocurrency. Recurrent neural network are proposed in the work.
The Effect of Stress Pulses on the Cyclic Endurance of Steel Axle Wheel-Set
(Nevsehir Haci Bektas Veli University, Cappadocia, Nevsehir, Turkey, 2019) Vakulenko, Ihor A.; Bülent, Kurt; Raksha, Serhii V.; Askerov, Hangardas; Hryshchenko, Mykola A.
ENG: For different temperature and speed deformation conditions, the nature of the increase in the number of defects in the crystal structure and the achieved complex of properties are due to the peculiarities of the internal structure of the metallic material. Compared with unidirectional static loading, the violation of the monotonous nature of the effective stress is accompanied by qualitative changes in the internal structure of metals and alloys. Thus, the pulsating nature of the acting stresses in case of fatigue, depending on the degree of cyclic overload per cycle, can lead to significant changes in the development of the processes accumulation and redistribution of defects in the crystal structure and, above all, dislocations. Based on this, the rate of accumulation of dislocations per loading cycle can be considered as one factor that will allow the development of measures to increase the cyclic endurance of metallic materials during fatigue. Compared to thermal technologies, treatments that are based on the use of short stresses pulses for moving defects in a crystal structure have gained some fame. In addition to sufficiently strong magnetic fields or high-power pulses of electric current, treatments based on mechanical effects on the metal can be used.
Energy-Efficient Excavation of the Soil of the Lower Track Structure by Bulldozers with a Combined Knife System
(IOP Publishing, 2020) Hlavatskyi, Kazymyr Ts.; Raksha, Serhii V.; Gorbenko, Yu. О.
ENG: The motivation of the research and further development of the new type combined knife system on the irreversible bulldozer blade and the results of the first series of laboratory studies of the process of digging the soil with the irreversible blade of the bulldozer with the first set of its physical models, which indicate the feasibility of continuing research in this direction. The proposed combined knife system makes it possible to realize oblique digging of the soil on the irreversible blade of the bulldozer and maximally complete its orientation in the prism of the soil before the blade in order to increase the productivity of the bulldozer with irreversible blade by reducing soil losses in the side rollers, reducing the time of filling and digging the soil by reducing the coefficient of specific soil resistance to digging. The paper substantiates the technology of more efficient use of bulldozers with non-return blade compared to their traditional counterparts, which is possible due to the use of the new combined knife system, and argues in favor of expanding the technological capabilities of the bulldozer with non-return blade, equipped with the proposed solutions new type with different digging angles and a spatial inclination of the cutting edges.
Energy-Efficient Means of Transporting Oil Products to Ukraine During Martial Law
(MATEC, 2024) Zelenko, Yuliia V.; Cherkudinov, Volodymyr E.
ENG: Carrying out transportation of oil products, there is a danger of having a negative impact on the environment - a leak of liquid can create an environmental problem for a certain area. Transportation of oil-containing cargoes to Ukraine, during martial law, is carried out by multimodal transport, namely, road, sea and rail modes of transport. As of June 2023, there are 14 border railway stations connecting Ukraine with five countries: Poland, Slovakia, Hungary, Romania and Moldova. International railway transshipment stations were studied, which allow oil products to be transshipped into tankers for further customs clearance and transportation to warehouses, civilian or military recipients. The distance of the transportation path is not always decisive in the matter of energy saving. Environmental friendliness and energy consumption during the transportation of petroleum products are also affected by the topography of the road, the landscape of the area where the roads pass, and the traffic on the roads with other vehicles.
Evaluation of the Influence of Dispersion of Pearlite on the Fatigue of Carbon Steel
(Springer Link, 2020) Askerov, Khangardas; Vakulenko, Ihor O.
EN: It is shown that the slope of a tangent to the fatigue curve can be used to analyze the effect of dispersion of pearlite on the fatigue strength of carbon steel. For a constant thickness of the ferrite-pearlite layer, we established an inversely proportional relationship between the indicated parameter and the density of accumulated dislocations. We also estimated the mechanism of influence of the dispersion of pearlite on the transition from low- to high-cycle fatigue of carbon steel.
Experimental Research of Ropeway Dynamics
(Kaunas University of Technology, Kaunas, Lithuania, 2022) Kuropiatnyk, Oleksii S.; Raksha, Serhii V.; Krasnoshchok, Oleksandr L.
ENG: Research of ropeways is carried out in several directions, one of which is the establishment of dynamic characteristics of rope systems under different operating conditions. In previous works, we proposed a mathematical model for calculating the frequency spectrum of ropeway, which is based on the representation of the ropeway traction circuit as a discrete-continuous dynamic system. The main purpose of the experimental studies is to confirm the adequacy of this model; its results are presented in this article. The considered single-span ropeway is usually used as a means of industrial transport for moving goods between production and storage facilities, in the mining industry – for transporting various materials from the place of extraction to railways and highways. Studies were carried out using experimental equipment developed by us. According to the results of the experiment, we drew the frequency diagrams, which show the change of eigenfrequencies of the ropeway traction circuit during the cars movement between stations. The total array of results includes information on the decoding of about a thousand oscillograms, which were obtained and studied according to the methodology developed by us.
Formation of Carbon Steel Structure During Hot Plastic Deformation
(Dnipro National University of Railway Transport named after Academician V. Lazaryan, Dnipro, 2020) Vakulenko, Ihor O.; Bolotova, Daria M.; Proidak, Svitlana V.; Askerov, Hangardas; Cug, H.; Tchaikovska, H. O.
EN: Purpose. The main purpose of the work is to determine the peculiarities of the development of recrystallization processes of carbon steel austenite depending on the degree of hot plastic deformation and to develop proposals for improving the structural state of the metal of the railway solid-rolled wheel. Methodology. Two carbon steels of a railway wheel with a minimum and maximum carbon content of 0.55 and 0.65 % and other chemical elements within the grade composition of the steel 60 were used as research material. Samples in the form of cylinders with a diameter of 20 mm and a height of 40 mm were heated in a muffle furnace, exposed for a certain time to equalize the temperature across the cross section of the sample. After that, the samples were subjected to hot compression on Instron type test machine. The temperature interval of hot compression of the samples was 950–1100 ºС, with deformation degrees in height in the range of 10–40%. The strain rate was 10-3–10-2 sec-1 . A standard etching was used to detect the boundaries of the austenite grains. Structural studies were performed using Epikvant type light microscope at magnifications sufficient to determine the structure of austenite grains. The grain size of austenite was determined by the methods of quantitative metallography. Findings. In the case of hot compression of the railway wheel blank, increasing the concentration of carbon atoms only within the grade composition of the steel is sufficient to increase the average austenite grain size, which confirms the proposals to limit the carbon content in the metal of railway wheels. The formation of a certain degree of austenite structural heterogeneity at the cross section of the rim or hub of the railway wheel is due to a change in the development mechanism of recrystallization processes depending on the deformation value. Under conditions of the same degree of hot plastic deformation, the replacement of one-time compression by fractional one is accompanied by a violation of the conditions of formation of the recrystallization nucleus. As a result of the specified replacement of the scheme of hot plastic deformation we obtain reduction in the austenite grain size. Originality. Based on a study of the development of collective recrystallization processes during the hot compression of carbon steel of the railway wheel, it was determined that the increase in carbon content contributes to the austenite grain increase. After hot compression of the wheel blank, the structural inhomogeneity of austenite that occurs is determined by a change in the mechanism of recrystallization processes development. During deformations above the critical degree, the recrystallization nuclei are formed and successively grow, which leads to the structure refinement. In the case of deformations below the critical value, the growth of austenite grains occurs according to the coalescence mechanism, according to which fragments of boundaries with large disorientation angles consistently disappear. Practical value. For austenite grain refining in massive elements of solid-rolled railway wheel we offer to replace one-time hot compression by fractional one.
Frequency Analysis of Vehicle Drive with Cable Traction
(Український державний університет залізничного транспорту, Харків, 2018) Raksha, Serhii V.; Kuropiatnyk, Oleksii S.; Anofriev, Pavlo G.; Onopreychuk, Dmytro V.; Kovalov, Ihor
ENG: Abstract. The paper outlines the basic principles of constructing frequency diagrams and specifies the features of their application for the analysis of the dynamic state of the vehicle drive with cable traction on the example of a ropeway. To draw up the frequency diagrams, the ropeway traction circuit was presented as a dynamic system containing lumped masses and elements with distributed parameters. In this case, the moments of inertia of the rotating masses of the drive were brought to the traction pulley as a lumped mass. The traction cable segments are represented as elements with distributed parameters. The mathematical model describing the dynamic state of the drive consists of equations in the form of deformations of the traction cable segments using the positions of wave mechanics. Studies have shown that in most cases there is a fairly wide inter-resonance band, limited by the first and second eigenfrequencies. This phenomenon may be the basis for justifying the rational values of the rotational speed of the pulley as one of the kinematic parameters of the ropeway drive.
Improving the Performance Parameters of Railway Wheels with the Help of Optimal Design Technologies of their Electric Pulse Processing
(Dnipro National University of Railway Transport named after Academician V. Lazaryan, 2019) Vakulenko, Igor A.; Kuzin, Nickolai O.; Vakulenko, Leonid I.; Raksha, Sergey V.; Proidak, Svetlana V.
ENG: Abstract. The processing by pulses of electric current (PEC) of a fragment of the rim of a railway wheel was carried out on the DS10D equipment. When the density of the electric current is from 3 to 17 A/mm2, the processing cycle consisted of the action of a pulse with a duration of 2.5-3 s and a pause between pulses of 4 s. After 150 cycles of PEC, the hardness of cold-formed metal was reduced from 10 to 20%. Studies of the parameters of the metal structure of the wheels have determined that the processing of PEC leads to a decrease in the number of defects in the internal structure, which are accumulated as a result of cold deformation of the rim along the rolling surface of the railway wheel. It has been established that, according to the nature of the influence on the hardness distribution of carbon steel, the PEC treatment corresponds to changes during tempering in the average temperature range and allows to significantly increase the operating parameters of the wheels of railway equipment.
Influence Factors on Electrophysical Parameters of Composite Varistors
(Український державний університет науки і технологій, м. Дніпро, 2023) Ahadzade, Shafag; Vakulenko, Igor A.; Asgarov, Hangardash
ENG: Purpose. The work is aimed to evaluate the influence of the structural state of polymer phase on the response voltage and nonlinearity coefficient of a multilayer varistor based on zinc oxide. Methodology. Zinc oxide consisted of 97% zinc oxide and 3% total oxides of Bi2O3, Co3O4, MnO2, B2O3, SbO3, ZrO2, Al2O3. To obtain the composite of thermoplastic polymers and zinc oxide, non-polar and polar polymers, high pressure polyethylene and polyvinyli-denefluoride were used. The composites were obtained by hot pressing at the melting temperature of the polymer phase and a pressure of 15 MPa. After that, using silver paste measuring electrodes 10 mm in diameter were applied to the surface of the synthesized samples and then current–voltage characteristics were measured. Modification of composites under the action of gas-discharge plasma was carried out in a special cell that creates a dielectric-gas-composite system. The composites structure was studied by X-ray diffraction analysis and IR spectroscopy. Findings. The obtained experimental results show that the size of inorganic phase particles significantly affects the cur-rent-voltage characteristics of the composite varistor: at a given thickness of the composite varistor, the operation voltage decreases markedly, and the nonlinearity coefficient increases. The influence of electric discharge plasma on the polymer zinc oxide-composite results in a significant change in the permittivity and the concentration of local levels at the separation boundary of the composite. The results research showed that electrical plasma effect on the response voltage depends on the polarity of polymer matrices. Moreover, plasma processing itself significantly changes the structure of the polymer phase in the composite. Originality. The magnitude of the potential barrier at the phase boundary is mainly determined by the volume fraction and size of the main structural element of ZnO ceramics. The change in the structural state of the polymer matrix allows adjusting the response voltage and nonlinearity coefficient of volt-ampere characteristic of the multilayer varistor. Practical value. The discovered development of electron-ion processes in the polymer phase of the varistor indicates the need of taking into account the change in its service characteristics from the duration and intensity of use. The result obtained shows not only the reason for the properties change, but also the need to develop the measures to increase the service life of varistor.
Influence Ferrite Grain Size on the Development of Discontinuons Flow at Lowcarbon Steel
(Nevsehir University, Turkey, 2021) Vakulenko, Igor A.; Kurt, Bulent; Erdogdu, Ahmet Emrah; Asgarov, Khangardash
ENG: On example of low-carbon steel, it is shown that development of strain hardening processes, starting from the moment initiation of plastic deformation, determines nature behavior of the metal at all subsequent stages of loading. The conditions formation of deformation bands and reasons for the disappearance of intermittent yield section on the deformation curves are considered. The use of the dependence characteristics of strain hardening on the size ferrite grain made it possible to explain evolution structure of low-carbon steel at region of intermittent flow.
Influence of Current Shunting and Technological Parameters of Spot Welding on the Strength of Joints of Dimensional Products
(Dniprovsky State Technical University, Kamianske, 2024) Nosov, Denys; Peremitko, Valerii; Plitchenko, Serhii O.; Makarenko, Mykola; Shevtsov, Viktor
ENG: The effect of current shunting and technological parameters of spot welding on the strength of joints of dimensional products was studied. Experiments were carried out using a spot contact welding machine type MT-1614. As the main material to be joined, structural carbon steel of the 08Yu brand was chosen in the form of plates of various thicknesses. After welding, samples were made for testing according to standard techniques for shearing, tearing, or twisting. The experimental part of the study included determining the dependence of the fracture force and weld nugget diameter on the welding current, the distance between welded spots, and the duration of the welding current pulse. It was determined that the optimal welding current to ensure high strength of welded points is 7400…8000 A. Exceeding this value leads to a decrease in strength, especially when the distance between welded spots increases. The duration of the welding current pulse also plays a significant role: the optimal increase in strength is observed with pulses lasting 0.18…0.22 s. for currents of 7900…8200 A. The dependence of the diameter of the welded spot on the distance between the welded spots and the duration of the pulse was also established. A significant increase in the distance between the welded points leads to a decrease in their diameter. On the other hand, the duration of the current pulse in the range of 0.22...0.24 s increases the diameter of the points to 22 % on average. Based on the results of the experiments, mathematical models were developed that quantitatively evaluate the influence of the investigated parameters on the strength and diameter of the welded spot. Practical recommendations include optimizing welding parameters and implementing mathematical models in the production process to predict the quality of welded joints. The obtained results will contribute to improving the quality of welded joints and the efficiency of production processes in the manufacture of large-scale products.
Influence of Grain Size Ferrite on Speed of Distribution Sonic Vibrations in Alloy Steel
(China, 2016) Vakulenko, Ihor O.; Nadezhdin, Yurii L.; Sokyrko, V. A.; Yaremchuk, A.
ENG: On the example of steel XI8TI after cold rolling and annealing influence of grain size ferrite and texture is investigational on speed of distribution sonic vibrations. Character influence of grain size and texture is set on correlation of hardness and speed of distribution sonic vibrations.

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