On January 27, 2021, at the 84th year of his life, a remarkable scientist, engineer and
organizer, Doctor of Engineering Sciences, Professor Anatoly Andreevich Ryzhkin died a
sudden death.

Introduction. Currently, the obtaining of lightweight concrete and reinforced concrete products and structures with the improved structure and characteristics is a challenge. This can be achieved through centrifugation or in a more advanced way — vibro-centrifugation. At the same time, the influence of centrifugal and centripetal forces of inertia in these types of technologies causes differences in the cross-section properties of concrete products and structures. To reflect this in the calculations, it is required to experimentally and analytically investigate the qualitative and quantitative patterns of such differences in the characteristics of concretes obtained through different technologies.

Materials and Methods. The study used the cross-section averaged characteristics of concrete — “integral characteristics of concrete”. The applicable raw materials included portland cement 500, crushed stone fraction 5-20, medium sand. Nine control samples of annular cross-section obtained through vibrating, centrifuging, and vibro- centrifugation were manufactured and tested. The essence of the technique was that each manufactured experimental control sample was used in several types of tests in-parallel. From the total annular section of each sample, three conditional quadrants were distinguished, from which standard samples of small size were cut out. Subsequently, they were tested for axial compression, tension, and flexural tension. The following test equipment was used: electronically controlled mechanical press IPS-10 — for compression testing of prisms, and the breaking machine R-10 — for testing samples for axial tension. Strain sensors and dial indicators were used to measure concrete deformations. Oscilloscopes were also used to obtain the deformative and strength properties of concrete, including full deformation diagrams with descending branches.

Results. We have analyzed the calculation results of the integral design characteristics of the concretes obtained through vibration, centrifugation and vibro-centrifugation. It is established that due to the influence of centrifugal and centripetal forces of inertia under centrifugation and vibration centrifugation, the characteristics of concrete in cross-section become different. In some cases, these differences can be very significant. We have developed and tested the following: a new method for evaluating the dependence of the integral (cross–section averaged) design characteristics of concrete (density, cubic and prismatic axial compressive strength); ultimate deformations under axial compression; axial tensile and flexural tensile strength; ultimate deformations under axial tension; elasticity modulus; diagram of “stress ϭb– strain εb” under compression; diagram of “stress ϭbt–strain εbt” under tension on the manufacturing technology (vibrating, centrifuging, vibration centrifugation).

Discussion and Conclusions. Based on the results of the research, conclusions are formulated on the positive effect of the proposed technology of joint vibrating and centrifuging. It consists in improving the integral design characteristics and structure of concrete from vibrating to centrifuging and from centrifuging to vibro-centrifuging.

Introduction. A three-dimensional dry friction model in the interaction of a rectangular body and a horizontal rough surface is considered. It is assumed that there is no separation of the body from the horizontal surface. The body motion occurs under the conditions of combined dynamics when, in addition to the longitudinal movement, the body participates in twisting.

Materials and Methods. Linear fractional Pade approximations are proposed, which replaced the cumbersome analytical expressions that most accurately describe the motion of bodies on rough surfaces. New mathematical models describing sliding and twisting of bodies with a rectangular base are proposed.

Results. Analytical expressions of the principal vector and moment of friction for rectangular contact areas are developed and scientifically established. A friction model that takes into account the relationship between sliding and twisting speeds, which provides finding solutions for Pade dependences, is developed. After numerical solution to the equations of motion, the dependences of the sliding speed and angular velocity on time were obtained and constructed. Graphs of the dependences of the friction forces and their moment on two parameters (angular velocity and slip velocity) were constructed, which enabled to compare the integral and normalized models of friction. The comparison results showed good agreement of the integral model and the model based on Pade approximations.

Discussion and Conclusions. The results obtained provide considering the dynamic coupling of components, which determines the force interaction of a rectangular body and a horizontal surface. These results can be used in mobile robotics. The analyzed motion of the body occurs through the motion control of a material point inside the body. Such mobile robots can be used when solving a wide class of problems: when creating autonomous robots for the exploration of outer space and planets; in the diagnosis and treatment in case of passing through complex structures of veins and arteries; in research under water, in places of large differential temperature; in underground operations.

Introduction. Cylindrical and spherical shells are extensively used in engineering. They face internal and/or external pressure and heat. Stresses and strains distribution in elastoplastic shells has been studied by many scientists. Numerous works involve the use of the von Mises yield conditions, maximum shear stress, maximum reduced stress. These condi- tions do not include the dependence on the first invariant of the stress tensor and the sign of the third invariant of the stress deviator. In some cases, it is possible to obtain numerical-analytical solutions for stresses, displacements and de- formations for bodies with spherical and cylindrical symmetry under axisymmetric thermal and force action.

Materials and Methods. The problem on the state of a thick-walled elastoplastic shell is solved within the framework of the theory of small deformations. A plasticity condition is proposed, which takes into account the dependence of the stress tensor on three independent invariants, and also considers the sign of the third invariant of the stress deviator and translational hardening of the material. A disconnected thermoelastoplastic problem is being solved. To estimate the stresses in the region of the elastic state of a spherical shell, an equivalent stress is introduced, which is similar to the selected plasticity function. The construction of the stress vector hodograph is used as a method for verification of the stress state.

Results. The problem has an analytical solution for linear plasticity functions. A solution is obtained when the strength- ening of the material is taken into account. Analytical and graphical relationships between the parameters of external action for the elastic or elastoplastic states of the sphere are determined. For a combined load, variants are possible when the plastic region is generated at the inner and outer boundaries of the sphere or between these boundaries.

Discussion and Conclusions. The calculation results have shown that taking into account the plastic compressibility and the dependence of the plastic limit on temperature can have a significant impact on the stress and strain state of a hollow sphere. In this case, taking into account the first invariant of the stress tensor under the plasticity condition leads to the fact that not only the pressure drop between the outer and inner boundaries of the spherical shell, but the pressure values at these boundaries, can vary within a limited range. In this formulation of the problem, when there is only thermal action, the hollow sphere does not completely pass into the plastic state. The research results provide predicting the behavior of an object (a hollow sphere) that experiences centrally symmetric distributed power and thermal external influences.

Introduction. A review of the application of theoretical mechanics methods for the development of algorithms of approximate analytical simulation of a motor vehicle (MV) movement in case of oblique collision with side cable barriers is performed. The representation of the MV as a material point in this type of collision is validated. The study objective is to demonstrate the application of a physical model of a material point to describe the motor vehicle dynamics in the event of its oblique collision with side cable barrier.

Materials and Methods. A new physical model that describes the opposition to the motor vehicle movement from the side of a cable barrier in an oblique collision is proposed. New methods of approximate analytical construction of the MV movements during an oblique collision with the side cable barriers are presented. The analytical calculation results are verified by the data of the finite element (FE) simulation of the collision according to the data of field tests. The FE simulation was carried out using a multi-purpose finite element complex LS-Dyna.

Results. New analytical algorithms have been developed for the MV movement in case of an oblique collision with side cable barriers, as well as a new physical model describing the opposition to the MV movement from the side of cable barriers. The application of a physical model of a material point to study the motor vehicle dynamics during an oblique collision with side cable barriers is established scientifically, including the comparative analysis of the kinematic results of the virtual test with kinematic calculations obtained on the basis of algorithms for analytical construction of the MV movements.

Discussion and Conclusions. The analysis of the kinematic results of the virtual test in  comparison  with  the analytical kinematic calculations has shown that the representation of a motor vehicle as a material point in case of an oblique collision with side cable barriers is reasonable since the MV movement is close to translational motion. The results obtained can be used in the development and analysis of the correctness of the FE modeling of a side collision of a motor vehicle with cable barriers.

Introduction. When organizing drilling operations, one of the major problems is the accuracy and smoothness of lowering bundles of pipes into the shaft of the drilling rig. This depends on many factors, including the operation of the hydraulic brake of the lifting device. The objectives of this work are to create and study a mathematical model of hydrodynamic ballast in a drilling rig. Using the inverse analysis method, the effect of some performance indicators on the braking torque of the hydraulic brake is studied.

Materials and Methods. The experiments were performed using a laboratory setup, which is a model of a hydrobrake. Its valve was closed under various conditions to obtain several pressure values with the calculation of the braking torque when a certain weight was suspended. The real (field) operating conditions of the hydromatic brake were simulated, and the results obtained were compared. When creating a mathematical model, the inverse analysis method is used. It is based on the results of experimental measurements and provides expressing the totality of the effects of individual variables on the braking torque.

Results. A mathematical model of the hydraulic brake has been created and tested. The dependence of the braking torque on the pressure, density, and viscosity of the ballast fluid is determined. The influence of each variable is determined experimentally since the dependence under consideration cannot be represented as a direct relationship. The inverse analysis method is used to obtain a set of constant values that give the optimal solution. Taking into account the standard error array and the minimum standard error, the statistical errors made during experimental measurements are considered. The physically acceptable range of values of the proposed mathematical model is visualized. Using a basic (nonlinear) mathematical model, the auxiliary braking torque of a hydrobrake is calculated as a function of pressure, density, and viscosity. The proposed model validity is established. The calculated values of the braking torque were used as a criterion of correctness. The erroneous discrepancy did not exceed 6 %. For additional testing of the model, a computational experiment simulating field conditions was performed.

Discussion and Conclusions. For mathematical modeling of hydrodynamic ballast in a drilling rig, it is advisable to use the inverse analysis method. The model proposed in this paper relates the braking torque of a hydrobrake to the operating parameters of the fluid inside the ballast: pressure, viscosity, and density. The objectivity of the model is validated. An amendment to it is proposed to simulate the operation of the brake in the field. Based on the results obtained, in future studies it is advisable to test the created model in the field with a real payload.

Introduction. Currently, Russia has adopted a course towards the creation of intelligent machines and equipment. The same holds for mobile technological machines for road construction and public utilities. Therefore, the design and creation of this type of actuators with a self-adaptation function is a critical task.

Materials and Methods. A device equipped with a hydraulic drive with self-adaptation to load and coordination of kinematic and power parameters of the principal motion and the feed movement of the working body of the rock- drilling rig, is presented. To study and design the device based on the mathematical modeling methods of a hydraulic drive and adaptive systems, a mathematical model is proposed. It is developed using the foundations of the theory of volumetric stiffness of hydraulic systems. This enables to accurately describe the impact of the dynamic properties of the hydraulic system (compressibility of the working fluid, elastic properties of pipelines, high-pressure  hoses, hydraulic apparatuses) on the dynamic properties of the system as a whole.

Results. The mathematical model for a device with self-adaptation includes submodels of adaptive communication, interrelations of power, kinematic and process parameters of rock drilling, as well as mathematical description of the movement of system elements. The solution to the developed mathematical model was performed in the software environment for dynamic modeling of technical systems SimInTech. As a result, general dependences of the adaptive system on the design parameters of the system and the operating conditions are obtained.

Discussion and Conclusion. The mathematical model of the presented device shows the fundamental possibility of implementing the principle of self-adaptation in terms of load under external and internal disturbing actions during operation. The results obtained can be used under designing adaptive systems of other technological equipment, for example, for the implementation of deep drilling in workpieces with variable properties in its depth.

Introduction. Arc surfacing through feeding an additional filler wire heated by an additional arc burning between the filler wire and the electrode wire is considered. Under the conditions of such surfacing, the minimization of the input of the remelted substrate metal into the weld metal is studied. The research objectives are to examine the conditions providing self-regulation of this advanced arc surfacing process, and to evaluate control capabilities of the heat impact power on the metal and on the weld metal flow.

Materials and Methods. In solving a wide range of welding and surfacing tasks, it is advisable to use engineering analysis methods based on physicomathematical modeling of processes and phenomena. These include:

• self-regulation of the arc process under joint melting of the electrode and the filler wires;
• assessment of the possibilities to control the heat impact power on the metal and on the weld metal flow during the formation of the weld The features of the arc surfacing of anticorrosive chromium-nickel steels on low-alloy steel are considered in the paper.

Results. New mathematical dependences are proposed that describe physical phenomena under surfacing with an arc interaction between the electrode and filler wire. A physicomathematical model of the joint melting of the electrode and filler wire is developed. It provides determining the values of the control parameters. In addition, you can find out how much heat affects the substrate from:

• heat release in the main arc,
• droplet flows of the weld electrode and filler metal,
• arc plasma

Discussion and Conclusions. It is established how the current and the lengths of the main and additional arcs are affected by the supply voltages. The feed rate of the electrode and filler wire with a diameter of 1.6 mm and 1.2 mm made of Inconel 625 alloy is determined. It is shown what thermal effect the substrate undergoes in this case. It is noted that due to the larger value of the main arc current, the diameter of the electrode wire should be larger than that of the filler wire. The heat flow in the substrate is created mainly by the flow of the weld metal droplets.

Introduction. The relevance of the presented paper is due to the widespread use of plunger pumps in industrial practice, in particular, in gas and oil production. The quality of working operations and the efficiency of further well operation depend largely on their reliability. The improvement of plunger pumps involves increasing their reliability, increasing their service life, efficiency, downsizing, reduction in weight, labor intensity of installation and repair work. The modernization of the mechanism includes its power study since the found forces are used for subsequent strength calculations. Before the appearance of programs for the numerical analysis of solid objects, the analytical solution to the problem of strength calculation of the high-pressure pump drive frame was a very time-consuming and expensive procedure. The situation has changed with the development of computer technologies and the inclusion of the finite element method in the computer-aided design systems. The objective of this work is to perform a strength calculationon the TWS 600 plunger pump body made of 09G2S steel. 

Materials and Methods. A method for determining the reactions of the crank shaft supports of a high-pressure plunger pump and strength calculation of the drive part housing is developed. The direction and magnitude of the resulting forces and reactions of the supports are determined graphically according to the superposition principle of the force action on the supports. Strength calculations were performed using the finite element method in the computer-aided design system Solid Works Simulation. In this case, solid and finite-element models of the body with imposed boundary conditions were used, which were identified during the analysis of the design and the calculation of the forces arising under the pump operation.

Results. The reactions in the crankshaft supports are described with account for the forces generated by the plunger depending on its operating mode and the crank position. The forces acting on each of the plungers and the resulting reactions in each of the supports are determined. The diagrams of stresses and the safety factor are presented, which provide assessing the strength of the body and developing recommendations for creating a more rational design.

Discussion and Conclusions. As a result of the calculations, we have identified areas of the structure with minimum safety factors, and areas that are several times higher than the recommended values. This provides optimizing the designunder study through strengthening the first and reducing the thickness of the metal on the second. From the point of view of weight and size characteristics and maintainability, the results of the strength calculation performed can be used to optimize the design of the pump body under typical operating conditions.

Introduction. The power analysis of a chain transmission with a toothed chain and involute sprockets considers the centrifugal forces and the friction coefficients between the plate and the sprocket tooth. The work objectives are to determine all meshing forces, and to calculate the coupling coefficient of the gear chain with the involute sprocket in the drive gears.

Materials and Methods. When evaluating the traction capacity of a chain transmission, such parameters as the power analysis and the coupling coefficient of the gear chain with the sprocket are important (it shows what fold the pressure on a given tooth is greater than the pressure perceived by the tooth in front). In the presented paper, the following diagrams are visualized: the arrangement of the plates in gearing with the involute sprocket teeth and the meshing forces. The factors that affect the involute profile of the sprocket tooth are considered. This includes the weight of the chain plate package and the force: centrifugal, friction, normal pressure and tension. At the same time, changes in the coupling coefficient for the subsequent teeth involved in traction are taken into account. The balance of the links i and i

+ 1 of the gear chain is studied in the coordinate system XOY with the center on the axis of rotation of the involute sprocket. The method enables to determine all the desired forces through the geometric calculation of the values of the angular transmission parameters. Using the equations obtained, the following parameters are specified: the coupling coefficient Bi, the tension of the driving branch S1 and the slack branch S2.

Results. A patented transmission stand with a gear chain and involute sprockets is presented. The tests carried out on it

validated the study results of a chain transmission with a toothed gear and involute sprockets with the specified parameters. The correctness of the power analysis of the transmission with account for the centrifugal forces and the friction coefficients of the plates and the sprocket teeth was proved.

Discussion and Conclusions. It is noted that the centrifugal forces and the friction coefficients during engagement affect significantly the traction capacity of a transmission with a toothed chain and involute sprockets. The data obtained can be used to accurately estimate the traction capacity of such gears.

Introduction. The research materials devoted to the operability assurance of welded structures of hazardous technical devices — components of oil and gas production equipment are summarized. The factors determining the operational strength of welded joints and structures are systematized and diagrammed. The causes for the decrease in their service properties are described. We have defined the role of volumetric and crack-like welding defects, which were not detected during quality control at the manufacturing stage and in determining the residual life while in operation, in ensuring the life cycle of the structure. Measures to improve the practice of detecting crack-like defects under visual- and-dimensional and ultrasonic methods of quality control of welded joints are proposed.

Materials and Methods. In accordance with SNiP 2.05.06–85, the structures of main oil and gas pipelines, vertical cylindrical tanks, and other oil and gas production equipment (OGPE) are made of dead-killed and semikilled low- carbon and low-alloy steels with tensile strength of up to 686.5 MPa. Regardless of the class and strength level of steel, it should be well welded by all methods prescribed by standard process documentation (SPD). At the same time, regardless of the state of supply, the carbon equivalent С_экв should not exceed 0.46 %. The research methods are calculation-experimental ones. To calculate the stress-strain state of welded joints, the following methods were used:

• finite elements (FEM),
• fracture mechanics using the stress intensity coefficient K_t.

Methods of mathematical statistics were used to estimate the geometric dimensions of crack-like welding defects. Welding defects were detected by standard quality control methods prescribed by the SPD and GOST standards.

Results. Welded structures operating in the fatigue mode are considered. Some factors characteristic of welded joints are analyzed. It is shown how they affect the formation of strength performance properties. The role of dangerous crack-like defects, which with high probability can be formed in welded joints in the manufacture of structures and during operation, is established. Often, the reason is a decrease in mechanical properties due to aging and loss of plasticity caused by accidental mechanical actions. Note that it is impossible to identify these defects by existing quality control methods, both during the control process under production and during diagnostics while in operation. This reduces the accuracy of predicting the operational life of the welded structure.

Discussion and Conclusion. It is proposed to include the following requirements in the SPD:

• to the quality of welded joints of hazardous technical devices of OGPE,
• to detection of sharp crack-like defects with a radius of curvature in the range of 1-0.25 mm.

However, the reliability of detection of such defects by the control methods used remains low due to the human factor. To increase the reliability of detection of sharp crack-like defects, the directions of improvement of ultrasonic quality control of welded joints are determined.

Introduction. In all types of digital communication, error control coding techniques are used. Many digital communication standards, such as Wi-Fi and 5G, use low density parity check (LDPC) codes. These codes are popular because they provide building encoders and decoders with low computational complexity. This work objective is to increase the error correcting capability of the well-known bit-flipping decoder (BF) of LDPC-codes. For this purpose, a modification of the decoder is built, which enables to dynamically control one of its main parameters whose choice affects significantly the quality of decoding.

Materials and Methods. The well-known bit-flipping decoder of binary LDPC-codes is considered. This decoder has several parameters that are not rigidly bound with the code parameters. The dependence of the decoding quality on the selection of the output parameters of the bit-flipping decoder was investigated through simulation modeling. It is shown that the decoding results in this case are significantly affected by the input parameter of the decoder — threshold T. A modification of the BF-decoder of binary LDPC-codes has been developed, in which it is proposed to set the threshold dynamically during the execution of the algorithm depending on the error rate. A comparative analysis of the error- correcting capability of decoders is carried out by the simulation modeling method.

Results. A lemma on the maximum value of the decoder threshold T is formulated and proved. Upper bounds for the number of operations are found for the original and modified decoders. A simulation model that implements a digital noise-immune communication channel has been built. In the model, the initial data is encoded with a given LDPC-code, then it is made noisy by additive uniformly distributed errors, and thereafter, it is decoded in turn by the bit-flipping algorithm with different threshold T parameters, as well as by a modified decoder. Based on the input and output data, the correction capacity of the decoders used is estimated. Experiments have shown that the error-correcting capability of the modified decoder in the range of the real error rate is higher than that of the original decoder, regardless of the selection of its parameters.

Discussion and Conclusions. The lemma, proved in the paper, sets the upper bound on the threshold value in the original decoder, which simplifies its adjustment. The developed modification of the decoder has a better error- correcting capability compared to the original decoder. Nevertheless, the complexity of the modification is slightly increased compared to the original algorithm. It has been pointed out that the decoding quality of a modified decoder develops with a decrease in the number of cycles in the Tanner graph and an increase in the length of the code.

Introduction. This paper is devoted to the development of a method for estimating the current  time-frequency parameters of each of a set of simultaneously and independently operating generators in the radio electronic system. A general case is considered, in which the deviation of true values of the nominal generator parameters from the assumed values of these parameters is determined not only by random, but also by long-term frequency deviation. The work objective is to generalize the method for estimating the time-frequency parameters of signals (long-term nominal frequency and current frequency deviation from the nominal value) based on the simultaneous measurement of the phases of signals generated in the system of independently functioning generators. The research task is to consider a system of simultaneously and independently operating generators. Each of them generates harmonic signals, whose time-frequency parameters, such as the average frequency, are constant during a certain interval of observation. But herewith, these time-frequency parameters are known with insufficient accuracy due to the influence of external factors (changes in temperature, pressure, supply voltage, etc.). It is required to obtain estimates of the time-frequency parameters of signals (the duration of the measuring interval, values of the long-term frequency and the standard deviation) from the results of measurements of the phases of signals formed by the generators at measuring intervals belonging to the observation interval, within which the average frequency remains constant.

Materials and Methods. A system of simultaneously and independently functioning generators is considered. The long- term value of signal frequency for each of the generators over the observation interval remains constant, but it is known with some margin of error. During the observation interval, several measurements of the signal phase of each of the generators are performed. At the same time, the current values of the signal frequency and the duration of the measuring interval have random deviations from the long-term values, and follow the normal distribution law with zero mathematical expectation and a known variance. The estimation of time-frequency parameters based on the results of measuring the signal phases is carried out using a multidimensional likelihood function. The maximum is found on the base of solving the redefined system of linear algebraic equations.

Results. A new mathematical model and a numerical-analytical method for determining the time-frequency parameters of signals are developed. They take into account both the long-term constant frequency deviation and short-term random deviations.

Discussion and Conclusions. The results obtained can be used under the development and creation of data-measuring and information-telecommunication systems, including geographically distributed systems. The resulting estimates of the time-frequency parameters enable to increase the signal frequency stability and, accordingly, to improve the accuracy of measurements and the quality of information transfer.