Application of computer technologies for calculation of gears at studying of a course " Details of machines"

The computer program GearKURT has been created to calculate mechanical gears. The program allows you to calculate gears: - closed cylindrical spur gear - closed cylindrical helical gear - open cylindrical spur gear - Novikov's gear - closed bevel spur gear - closed bevel gear with indirect teeth - open bevel gear - worm-gear. The computer program has a dialog interface written in the object-oriented programming language Delphi and compiled into an exe-file. The program allows you to choose the necessary material and method of heat treatment for the manufacture of gears, to calculate the optimal geometric dimensions and transmission parameters, to determine the design of gears. The program provides all the necessary reference materials in the form of tables and graphs, which must be used to select the coefficients and other values necessary for calculations. The program provides access to the theoretical material of the course "Machine Parts" and the ability to save the results of calculations in a separate file. Recommendations for using this program are given.

Methods for estimating the durability of the needle bearing of the piston head of the connecting rod of a transportation diesel

The article presents the results of an experimental study and analytical evaluation calculations to check service life and increase durability of the needle bearing of piston head of connecting rod of a transport diesel engine. The primary reasons for the violation of the nominal operation of the main units of this mechanism have been established. Corresponding recommendations are proposed for carrying out accelerated tests for durability, reducing the thermal loads of the bearing operation and, as a consequence, improving the quality and service life of its entire piston group. Theoretical and experimental methods for determining the nominal life of the needle bearing of the piston head of the connecting rod (PHCR) of a transport diesel engine are proposed. The theoretical methodology allows obtaining reliable values of durability, taking into account the distribution of the working load over the rolling elements, as well as the mobility of the piston pin and sleeve. The performed calculations make it possible to correct and clarify the standard mathematical model for determining the nominal life of the PHCR needle bearing, depending on the distribution of loads on the rolling elements (rollers) under different operating conditions. This experimental technique with an acceleration factor of 10 is based on a twofold increase in the force effect on the elements of the PHCR needle bearing. This was achieved by assembling the bearing using a special technology, which is described in detail in the work. A significant decrease in the thermal effect and a decrease in radial loads on working rollers have been established. For ensure the regular oil supply into bearing during engine operation, a technique was developed to increase the load on the roller in contact zone, which significantly influenced durability and made it possible to conduct accelerated tests with a reliable yield. Its results of operational research and experience in design work correlate and are sufficiently explained by the developed methods, which allows them to be used for the improvement and modernization of connecting rods with needle bearings in PHCR. That is a permission to use these methodic for doing perfect and modern the needle bearing of the connecting-rod piston. Keywords: diesel, test procedure, needle bearing, rollers, piston head of the connecting rod, durability.

Method and software for finite element solution of two-dimensional creep problems at large deformations

The paper presents the formulation of a two-dimensional problem of the creep theory for the case of finite strains. A description of the foundations of the calculation method presents. The method is based on the use of the generalized Lagrange-Euler (ALE) approach, in which the boundary value problem in the current solid configuration is solved by using FEM. A triangular element is involved in the numerical modeling. At each stage of creep calculations in the current configuration, the initial problem is solved numerically using the finite difference method. The preprocessing data preparation is carried out in the homemade RD program, in which two-dimensional model is surrounded by a mesh of special elements. This feature implements the ALE algorithm for the motion of material elements along the model. The examples of preprocessing as well as of the mesh rebuilding in the case of finite elements transition are given. Creep calculations are performed in the developed program, which is based on the use of the FEM Creep software package in the case of finite strains. The regular mesh is used for calculations, which allow us to use the efficient algorithm for transition between current configurations. The numerical results of the creep of specimens made from aluminum alloys are compared with the experimental and calculated ones obtained by integrating the constitutive equations. It was concluded that for material with ductile type of fracture the presented method and software allow to obtain results very close to experimental only by use of creep rate equation. Creep simulations of material with mixed brittle-ductile fracture type demand use the additional equation for damage variable.

Implementation and use of the Levenberg-Marquard algorithm in the problems of calibration of robotic manipulators

The well-known problem of calibration of an arbitrary robotic manipulator, which is formulated in the most general form, is considered. To solve the direct problem of kinematics, an alternative to the Denavit-Hartenberg method, a universal analytical description of the kinematic scheme, taking into account possible errors in the manufacture and assembly of robot parts, is proposed. At the same time, a universal description of the errors in the orientation of the axes of the articulated joints of the links is proposed. On the basis of such a description, the direct and inverse problem of kinematics of robots as spatial mechanisms can be solved, taking into account the distortions of dimensions, the position of the axes of the joints and the positions of the zeros of the angles of their rotation. The problem of calibration of manipulators is formulated as a problem of the least squares method. Analytical formulas of the objective function of the least squares method for solving the problem are obtained. Expressions for the gradient vector and the Hessian of the objective function for the direct algorithm, Newton-Gauss and Levenberg-Marquardt algorithms are obtained by analytical differentiation using a special computer algebra system KiDyM. The procedures in the C ++ language for calculating the elements of the gradient and hessian are automatically generated. On the example of a projected angular 6-degree robot-manipulator, the results of modeling the solution to the problem of its calibration, that is, determination of 36 unknown angular and linear errors, are presented. A comparison is made of the solution of the calibration problem for simulated 64 and 729 experiments, in which the generalized coordinates - the angles in the joints took the values ±90° and -90°, 0, +90°.

Dynamics of an oscillator with a quadratic nonlinearity in the expression of the elastic force loaded with a step pulse

The unsteady oscillations of an oscillator with a quadratic nonlinearity in the expression of the elastic force under the action of an instantaneously applied constant force are described. The analytical solution of a second-order nonlinear differential equation is expressed in terms of periodic Jacobi elliptic functions. It is shown that the dynamic coefficient of a nonlinear system depends on the value of the instantaneously applied force and the direction of its action, since the elasticity characteristic of the system is asymmetric. If the force is directed towards positive displacements, then the characteristic of the system is "rigid" and the dynamic coefficient is in the interval , that is, it is smaller than that of a linear system. In the case when the force is directed towards negative displacements, the elasticity characteristic of the system is «soft» and the dynamic coefficient falls into the gap (2, 3), that is, it is larger than in the linear system. In the second case of deformation, there are static and dynamic critical values of the force, the excess of which leads to a loss of stability of the system. The dynamic critical force value is less than the static one. Since the displacement of the oscillator is expressed in terms of the Jacobi functions, the proposed formula for their approximate calculation using the table of the full elliptic integral of the first kind. The results of calculations are given, which illustrate the possibilities of the stated theory. For comparison, in parallel with the use of analytical solutions, numerical computer integration of the differential equation of motion was carried out. The convergence of the calculation results in two ways confirmed the adequacy of the derived formulas, which are also suitable for analyzing the motion of a quadratically nonlinear oscillator with a symmetric elastic characteristic. Thus, the considered nonlinear problem has an analytical solution in elliptic functions, and the process of motion depends on the direction in which the external force acts. In addition, when a force is applied towards a lower rigidity, a loss of system stability is possible. Keywords: nonlinear oscillator, quadratic nonlinearity, stepwise force impulse, Jacobi elliptic functions.

Influence of stresses on deformation process under the irradiation creep and swelling

Approaches for describing the deformation of structural elements made from the material, in which radiation creep and swelling strains develop simultaneously, are discussed. The technique for description of irradiation swelling strains, which is used for calculational analysis of stress-strain state arising in structural elements under the joint action of irradiation and thermal-stress fields, is regarded. A complete system of equations of the boundary –initial value problem is presented, in which elastic and thermal strains, strains of radiation creep and swelling are taken into account. Numerical modelling was carried out using the specialized software FEM Creep, in which the boundary value problem is solved by the Finite Element Method, and the initial one is integrated in time by the difference predictor-corrector method. Two forms are given for the equation of state describing the radiation swelling strains: first is for the components of the strain tensor as well as second is prepared for their rates. The hypothesis about the linear correspondence of the received radiation dose and the deformation time, during which radiation swelling strains develop, are analyzed. A number of questions that require answers when using equations with a complex stress state in which the radiation swelling strains are directly depend on stresses, are discussed. Based on the processing of experimental data on the swelling of tubes made of steel 316Ti in the temperature range of 450-460 °С, a form of the equation for the radiation swelling strain rate is proposed, and the constants included in it are determined. Using the example of numerical modelling of the deformation of tubes were made of steel 316Ti and loaded by inner pressure, the applicability of the classical approach for the analysis of the stress-strain state in the presence of radiation swelling strains is shown.

Investigation of mechanical characteristics of braided carbon fiber

The use of composite materials in various branches of modern industry is rapidly increasing due to their high strength properties, low weight and good manufacturability. A wide variety of materials used, types of reinforcement and internal structures creates a need for studies of the static and dynamic properties of composite materials. Due to the latest advances in technology, composite materials are widely used in a variety of industrial applications. As a result, there is considerable interest in studying and understanding the behavior of composite structures. Analysis of composite structures, study of resonance frequencies, damping factors and modal shapes played an important role in determining the dynamic characteristics of the structure, detecting damage and monitoring the state of the composite structure. In this paper, the results of computational and experimental researches of the Young’s modulus, natural frequencies and modes of vibration, damping properties of the composite material are presented. The researches were carried out on samples of the woven ten-layer carbon fiber reinforced plastic. The investigated carbon fiber reinforced plastic has a plain weave. Samples were cut in three directions: warp (0 °), weft (90 °) and 45 °. Nine samples were prepared for each direction. To study the Young’s modulus, a tensile testing machine was used, and a vibration stand was used to determine the natural frequencies and modes of vibration. Damping properties are calculated by the Oberst method, based on the amplitude-frequency characteristics of the samples. Statistical processing of the experimental results was carried out and the values ​​of the mathematical expectation and variance were obtained. Geometric and finite element models of сarbon fiber reinforced plastic samples were built, their natural frequencies and vibration modes were determined. Comparison of the computational and experimental data with numerous calculations using the finite element method is carried out.

Investigation of error in evaluation of spectral statistical characteristics of numerical solution of stochastic dynamic system

In this paper, an algorithm for numerical simulations is developed for calculating a discrete dynamic system with a stochastic perturbation and an analysis of the quality of numerical solutions is carried out. For this, an algorithm for the numerical solution of a second-order differential equation with a stochastic right-hand side was developed and this algorithm was implemented as a program. The next step was to carry out a set of computational studies by varying the parameters of numerical integration with the subsequent assessment of their impact on the error and accuracy of simulations. To estimate the spectral density, the Welch periodogram method was used. To check the quality of simulations and assess the accuracy of solutions, it is proposed to compare the results of numerical integration and subsequent digital processing with analytical solutions that are known for the linear problem, given by the equation. As a result of the work, a comparative analysis of the dispersion of displacements relative to the lengths of signals from a different number of blocks was carried out, into which the signal is divided for the Welch method; the confidence interval of the error at different signal lengths and the confidence interval of the error with a different number of blocks at a certain signal length. Comparison of the variance with a different number of blocks showed that with a signal length of 30 s and from 90 s, there is a slight scatter of the variance values within an error of ± 5%.

Software tool for recognition of Ukrainian-language scientific articles

The problem of computer recognition, both separately printed characters and whole texts, which may contain mathematical formulas, and further saving the resulting document in the "Latex" format, is considered. The developed software implements the ability to recognize printable Latin, Cyrillic, Greek letters and special mathematical symbols. For this, a multilayer convolutional neural network built using the Keras machine learning library and additional validation heuristics are used. To improve the quality of neural network recognition, a sophisticated image processing mechanism has been developed that helps to remove noise from the image, eliminate errors associated with the inclination of characters, and correct character defects associated with the quality of the input image. Also implemented are mechanisms for collecting individual characters into words or mathematical formulas, reproducing the position of signs of indices and degrees, forming ordinary fractions and expressions under the root sign. The results of the recognized text are saved in a file with the simultaneous construction of the "latex" document structure. To demonstrate the capabilities of the developed software, a graphical user interface has been added, with which you can select and inspect the input image even before the start of recognition. During testing of the software, the recognition of images of different types was carried out: completely textual, mathematical formulas without text, mathematical formulas that are between blocks of text.

Specific features of thermal deforming of composite inductors during magnetic-pulse processing of materials

The problem of taking into account a non-stationary inhomogeneous temperature field in the analysis of the stress-strain state of inductor systems for magnetic-pulse processing of materials is considered. It follows from the analysis of open information sources that the problem of analyzing a non-stationary temperature field arising from the presence of a non-uniform electromagnetic field and its effect on deformation has been sufficiently studied in relation to induction heating. At the same time, during other operations of magnetic-pulse processing of materials, heating of equipment can cause additional deformations of a significant magnitude, which, in turn, can lead to a loss of equipment performance due to destruction or irreversible deformation. A general approach to the analysis of such problems is proposed, which involves the determination of the spatial-temporal distributions of the quantitative characteristics of the electromagnetic field, temperature field and stress-strain state. The necessity of using numerical methods for carrying out such an analysis has been substantiated. The most effective numerical method is the finite element method, which makes it possible to analyze the unsteady electromagnetic field, temperature field, and stress-strain state within the same calculation scheme. In this case, within the framework of the finite element method, iterative schemes can be created that allow taking into account nonlinear effects. Here, nonlinear effects can be due to the dependence of the mechanical and electro-physical properties of the material on temperature, the plastic nature of deformation, and the need to take into account contact phenomena. The results of complex analysis for a composite single-turn inductor with a dielectric band are presented. The features of contact interaction were taken into account by introducing layers of contact finite elements. The stress-strain state of the inductor is estimated for two variants of the materials used: copper and non-magnetic steel.