This article is devoted to the development of methods of mathematical simulation techniques for modeling machine tools’ guideway wear. An example of calculation of pressure curves in the edges of the machine tool’s guideways was presented; values of pressure were determined according to the scheme of the forces and reactions. The fundamentals of method for calculating wear of guideway friction pairs developed by prof. A.S. Pronikovd were considered. Possibility of improving the method was demonstrated for the case, when greater accuracy for modeling wear process is required. Algorithm of wear simulation with the possibility of calculating guideways wear with any complexity of changes in pressure curves along the trajectory of working body on the bedplate. The only requirement for the calculation is that the pressure curve remains constant at the elementary step of modeling. Experimental data which verify the accuracy of modeling by the example of study of the wear process of guideways and changes in the trajectory of the movable working body of machine tools under operating conditions were also presented in this article.

In this article the authors consider methods of determination of total absorbing ability of high-vacuum cylindrical cryoadsorption pumps: average temperature calculation and integrated calculation. These two methods were compared with each other. The authors also considered an algorithm of calculation of a relative error of the method of determination of total absorbing ability by using an average temperature. Influence of various parameters, such as temperature on the periphery of the adsorptive layer, the radius of a cryogenic vessel, etc., on the mistake value was revealed. Results of calculation were presented in graphic and analytical interpretations. On the basis of the conducted researches several conclusions were drawn.

This article describes an estimation technique of the contact area in the “spindle-tool” cone joint used at NC machine tools. This method was developed as an alternative for quality control of the contact area in the cone joint and may be interesting for machine-tool builders during the stage of manufacturing the spindle’s cone sleeve. The proposed method contains calculations of transient electrical resistivity and coupling capacitance. The relations obtained during the investigation allowed to establish a connection between the contact area and specified electric parameters. The results can be useful for postgraduates and researchers.

The author considers problems of increasing plasticity of welded TRIP-steel joints at resistance spot welding. Special attention is paid to application of using an additional heat treatment pulse and its parameters. The author investigated the influence of the pause between the basic and secondary pulse currents, as well as the volume of the heat treatment current on mechanical properties of welded joints. The author gives an assessment of the influence of electro heat treatment on micro-hardness parameters and mechanical properties of welded joints; this allows to optimize the pause duration and the volume of the heat treatment current. Practicability of applying the additional pulse current to increase the plasticity of spot welds was proved on the basis of the obtained results.

Heavy rotating shafts with radial bearings require an additional axial support. Axial support in some mechanisms is designed poorly. This article describes a developed design of an axial support and results of its structural analysis. This design is patented in the Russian Federation. The proposed support is designed for installation on the free end of the shaft and does not interfere with the shaft’s radial float and rotation of its axis. The admissible lateral displacement of the shaft in the axial installation is 1-2 mm, and the maximum rotation of the shaft axis is 30 arc minutes. The support is suitable for the shaft of an oil turbo pump unit. This shaft is mounted with bearings; its axis has radial and angular displacements during the operation.

The results of the investigation of a combined method of the final processing which is called “surface plastic deformation - smooth finish” are presented in this article. It was experimentally determined that application of this technology allows one to combine the advantages of both mechanical hardening of a work-piece surface (improving operational properties) and abrasive machining (providing high accuracy and fine finish of a surface) methods. For example, the fatigue resistance σ_-1 of samples made of 12H18N10Т and 37H12N8G8МFB steels after the proposed combined “surface plastic deformation - smooth finish” processing is increased by 28-42% in comparison with the resistance of samples processed by smooth finish only. Besides, grinding of previously deformed samples tends to be smoother than the traditional grinding at the equivalent modes. Geometrical errors of sample surfaces obtained with the use of both methods are approximately the same.

A new deterministic global minimization method based on the numerical solution of the convection-diffusion boundary problem was developed. With the help of this method, the inverse problem of chemical kinetics was solved. Problems of identification of speed constants in chemical reactions are usually based on minimization of functions. In most cases it is necessary to deal with "stiff" systems of differential equations and, respectively, with many objective functions with ravine surface and local extremums, which makes application of existing multidimensional minimization methods complicated. Two main conceptions are included in this method: diffuse overcoming of local extremums and transforming multivariable minimization to one-dimensional minimization.

In this article the process of two-dimensional autoregression of order (1,1) is considered. Distribution of the innovation field of the autoregressive model was assumed to be unknown. Definitions of the influence functional and the gross error sensitivity coefficient for autoregressive field parameter estimation were given. An explicit expression for the influence functional of sign estimation of the equation coefficients of the autoregressive field was obtained. It was shown that the sign estimation was robust. Sign estimation could be recommended as an alternative to least squares estimation with anomalously large errors when observing an autoregressive field.

A six-dimensional model, where the aircraft is treated as a material point, is used for planning trajectories of aircraft. In this case, the state variables are the coordinates of the aircraft in the trajectory coordinate system, and controls are longitudinal and transversal overloads and the roll angle of the transversal overload vector. In the context of this model, the author considers a terminal control problem in which it’s required to find such controls at which the aircraft is transferred from a specified initial point of the phase space to a specified destination point. Methods of solving this terminal control problem are well known if the flight time is given. Selection of flight time, if it is not known, is not an easy task, as this choice influences the shape of the flight trajectory. One of the methods to solve the terminal control problem with unknown time is the energy method based on replacement of the independent variable (time) by the normalized mechanical energy of the system. The energy method leads to flight trajectories with a monotonic variation of energy. It provides good solutions for landing and take-off of aircraft, but may not be applicable for complex maneuvers. The author considers methods of planning trajectories with non-monotonic variation of energy, which, nevertheless, are based on the energy method. These methods are based on special short-term maneuvers at the beginning and end of the trajectory (so-called transient maneuvers), and on selection of certain intermediate points through which the trajectory must pass.

The conjugacy problem is one of the three fundamental algorithmic problems of the group theory, formulated by M. Dehn in 1912. The negative answer to this problem was obtained by P.S. Novikov in 1955: he created a finitely presented group with an unsolvable word equality problem; so he proved that in the class of finitely presented groups the conjugacy problem is also unsolvable. After that one began to study the conjugacy problem in particular classes of finitely presented groups and their subgroups. In 1971 C.F. Miller III constructed a subdirect product of free groups with the unsolvable conjugacy problem. This subdirect product is almost never finitely presented. In 2000 G. Baumslag et al. proved that there exist torsion-free word hyperbolic groups the direct product of which contains a finitely presented subgroup with the unsolvable conjugacy problem. For a direct product of free and surface groups M.R.Bridson and. Ch.F.Miller III proved in 2009 that any finitely presented subgroup of this direct product has a solvable conjugacy problem. The present paper is a sequel of the paper in which the conjugacy problem for subdirect products was studied with the use of pictures; and, in particular, it was proved that solvability of the conjugacy problem for subdirect products follows from atoricity and the small cancellation condition C(6). Pictures are geometric objects dual to van Kampen diagrams. In 1968 P. Schupp was the first to use van Kampen diagrams to solve the conjugacy problem in a group under the non-metric conditions C(p) and T(q). In this paper it is proved that under atoricity and the condition C(4)-T(4) or C(3)-T(6), the conjugacy problem for subdirect products is solvable. Also in this paper the sufficient condition for solvability of the conjugacy problem for subdirect products is expressed with small cancellation conditions only.

The author considers the problem of movement stabilization along the given path for a two-wheeled robot with a differential drive. Wheeled robots belong to the class of non-holonomic systems, which, as it is generally known, cannot be stabilized in the vicinity of the equilibrium position of a continuously differentiable stationary state feedback. But the task of stabilizing the motion along the given curve is formulated only for part of the variables, so that the use of stationary feedback is possible. The robot model was transformed into a quasi-canonical form, all possible functions which allow one to obtain it were determined. The normal form for the system was built with the use of the distance to the target curve; its zero dynamics was investigated. On the basis of this form the problem of movement stabilization along the path was solved with the use of feedback linearization. The results of computer modeling are presented for particular cases: a circle and a line.

Mathematical model of a dynamically tuned gyroscope (DTG) includes an elastic and not ideal ball bearings of the gyro spin motor. The DTG is considered as a mechanical system with eight degrees of freedom. Selection of the number of degrees of freedom is based on the gyroscope design features. The angular and linear displacements of the gyro spin shaft, suspension ring and rotor became possible due to deformation of ball bearings. This model is necessary for modeling the DTG dynamics caused by natural vibration of bearings, for calculation of natural frequencies and for considering the influence of particular defects of ball bearings on the gyroscope drifts.

The aim of this work is to optimize parameters of onboard laser ranging systems (LRS) in order to control rendezvous and docking of spacecraft. Systematic analysis of the factors that have to be considered when developing onboard laser ranging systems of spacecraft was carried out. The authors developed a computer program designed to simulate characteristics of onboard laser ranging systems with different values of their parameters. The authors solved the problem of multi-criteria optimization of parameters of laser ranging systems by criteria of maximum range and safe viewing distance. Use of Pareto optimization provides a set of solutions from which developers can choose the most suitable for technical implementation.

The authors describe a laser lidar model for remote measurement of instantaneous speed and direction of atmospheric winds. The authors provide the results of experimental studies in the surface layer of the remote correlation laser method for measuring instantaneous wind speed and characteristics of aerosol backscatter coefficient heterogeneities of the atmosphere. It is shown that the measurement of aerosol size heterogeneities and adaptive selection of size measurement framework in accordance with the found criterion can increase determination accuracy of instantaneous wind speed by correlation lidars.

This article describes development of an algorithm for recognizing assembly parts which can be used in computer vision systems of robotized manufacturing units. The problem of development has several distinctive features. First of all, assembly units have a fairly simple shape. That means their contours characterize their shape in a unique fashion. Secondly, all assembly units to be recognized are placed on an open conveyer belt and are oriented randomly. This problem formulation allows to use various recognition algorithms based on the contour analysis. This approach eliminates all inner points of images from the analysis; it leads to reduction in the volume of processing information at the expense of transition from two-variable function analysis to one-variable function analysis.

The authors carried out an electro-dynamic analysis of the line parameters’ dispersion characteristics of the segments of balanced stripline-slot antennas of traveling waves with different configuration. A dispersion model of the twin-strip line was presented. Dispersion equations were obtained by reduction of the original system of integral equations relating the currents and the electric fields in the cross section of the transmission line to a homogeneous system of linear algebraic equations by means of the spectral Galerkin method. In order to find the components of the two-dimensional Green tensor function the method of spectral immitances was used. Analysis of test line geometries was carried out.

The authors consider several signal processing algorithms in an on-board radar system with a multi-channel phased antenna array used for detection of small, low-speed targets. These are: split space and time non-adaptive processing, space-time adaptive processing and space-time adaptive processing with pre-beam forming in elevation plane. A simple method of result comparison for mentioned algorithms is described. The results of computer simulation of the output signal-to-(noise + interference) ratio are also presented. The particular results were obtained for a coherent impulse sequence with mean repetition frequencies.

This article considers stochastic control systems with impulses that are generated by hyper-Erlangian flows of events and lead to discontinuities of system trajectories. The authors solve the problem of finding a probability density function for the system state. The solution is based on usage of the spectral form of mathematical description. The purpose of this paper is to develop a spectral method for analysis of this kind of systems, based on function expansion by a series of orthonormal functions. This approach simplifies the process of solving analysis problems, making it convenient for use of modern high-performance computers.

This article deals with a review of modern interactive methods for solving the multi-objective optimization problem. The most advanced class of interactive methods is represented by techniques based on estimations offered by the system of multi-objective optimization of alternatives. Depending on the form of the decision maker’s estimates one can separate two classes of interactive methods: methods based on estimations of DM’s preference function and methods based on the pairwise comparison of solutions. Precisely these two classes of interactive methods are described in more detail in this article; directions for their further development are proposed.

Works of Lode V., Yagna Yu. I. and other researchers point to the presence of deviations from the laws of plasticity that found wide application in scientific literature. Analysis of the results of studies with such materials as steel, nickel, copper, and duralumin shows the possibility of studying and description of marked deviations from the standpoint of modern representations of the tensor of nonlinearity. In this work, on the basis of the results of the mentioned works, it was shown that consideration of this non-linearity leads to increases in accuracy of determination of both stresses and deformations, if we reject a single relation between intensity of stress and intensity of deformations. For this purpose, derivation of determining equations of the deformation theory of plasticity, which takes into account the effect of loosening, a form of hardening curves and their dependence on the kind of stressed state was performed using one of the variants of the theory of V. V. Novozhilova.

Nowadays small plants for tire recycling based on milling and with an annual consumption of raw materials up to 5000 tons are widespread in Russia. The authors research the problem of extreme vibrations in such equipment when used tires are disposed. Analysis is based on the developed setup and its prototype. This article describes the main causes of these vibrations, their adverse effects, as well as an example of a mathematical model of the process, which takes into account parameters of the technological system, mutual influence of the cutting tool kinematics and dynamics of the cutting force formation.

A mathematical model of heat transfer in a composite material with identically oriented anisotropic ellipsoidal inclusions was created. Formulae for calculating effective thermal conductivity of composite materials, which are anisotropic with respect to the property of thermal conductivity, were obtained on the basis of a developed mathematical model. To estimate the possible error of the results, a dual formulation of the variational problem of stationary heat conduction in a heterogeneous solid body was applied. These results can be used to predict effective thermal conductivity of composite materials with ellipsoidal inclusions, which are among other nanostructured elements (including carbon nanotubes). The obtained formulas can be used for estimating electric conductivity of composite materials with identically oriented anisotropic ellipsoidal inclusions due to electro thermal analogy.

In this article the authors propose methods of quantitative estimation of the processes’ gas-dynamic parameters in gaseous media, based on the results of optical recording. The basis of this technique is a well-known dependence of a directly proportional relationship between the brightness of the image and the second derivative of gas flow density with respect to the coordinates. Comparison of experimental and calculated data showed that the developed method allowed to perform a quantitative estimation of the processes’ gas-dynamic parameters in gaseous medium correctly. It leads to a significant increase in the number of possibilities of optical registration of aero-physical and ballistic experiments and makes these experiments cheaper and simpler.

The author considers factors of abrasive finishing of details at finishing machines by a loose abrasive; these factors determine the output of the process. It was noted that the physical basis of abrasive finishing is an abrasive destruction of the detail material and lap material which is the result of the influence of forces occurring during machining; however, the majority of factors are not power ones but they do influence the result of machining. A new characteristic of the abrasive finishing process was proposed; this is a spectrum of the force influencing the surface element of a detail. This parameter allowed to unite all basic technological, kinematical and dynamical factors of the abrasive finishing process into a single power characteristic. This will lead to simplification of the control system and increase its efficiency.

Detection of substances with the use of their infrared spectra is carried out by means of statistical analysis of experimental and reference spectra. This analysis is conducted by calculating the correlation parameter. In this work dependences of correlation parameters of reference and noisy spectra on the signal-to-noise ratio were obtained. Dependence of substance recognition thresholds on the signal-to-noise ratio within the experimental spectra was obtained for the given probability of substance recognition. The authors consider the possibility of applying these dependences to calculation of recognition thresholds in view of the signal-to-noise ratio during the experiment.

Application of protective coatings is one of the promising areas to increase durability of the "pipe-coupling" threaded junction of tubing pipes for oil production. The authors investigated the structure, mechanical and corrosion properties of electroplating, thermal diffusion and hot zinc coatings on steel pipes 45, 30G2 and 37G2F 37G2S with a varying strength group. Thickness of the structure, phase composition, microhardness and pitting resistance of coatings were determined. Zinc coatings of different application techniques differ significantly in thickness, hardness, corrosion resistance and structure, but values ​​of these parameters within a single technology are virtually independent of the base metal. Hot Zn-coating of 100 microns is composed of several layers: T, T1-, δ₁-, ζ - and η-phases with a  different content of zinc in accordance with the phase diagram of Fe-Zn. Thermal diffusion coating (40 m) is composed of phases D and T1 with a complex cubic lattice, and the δ₁-phase with a hexagonal lattice. The composition of plating (20 microns) are η-phase - solid solution of iron in zinc, Zn and zinc oxide ZnO on the surface. GC and GVC coatings have significantly lower hardness as opposed to thermal diffusion, which is caused by the presence of the solid phase δ₁. Pitting resistance of uncoated steel is lower than with coatings. Coating has a maximum resistance of MCC, which has zinc oxide on the surface, and a minimum - GC coating with a two-phase η + ζ-structure. The most resistant to pitting corrosion coating on steel was 37G2S doped by1% silicon, and the most unstable was on steel 45. It is shown that chemical composition and heat treatment of the investigated pipe steels have practically no influence on thickness of coatings, but steel after rolling provides a more uniform plating without obvious lamination.