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The paper presents a mathematical model developed for calculating the force effect on the punch in the process of high-speed combined hot extrusion of bimetallic road milling picks under plane deformation conditions. To solve the problem, the process is divided into two phases: acceleration phase and braking phase, which consists of two stages. A distinctive feature of the acceleration phase is that it allows the analysis of reverse extrusion, in the process of which the metal flows in the opposite direction to the punch stroke. A method for calculating the force acting on the punch at each phase of the process of plastic flow of a bimetallic workpiece into a matrix cavity with three deformation zones is presented in the paper. While solving the problem in a quasi-static formulation and proceeding from the conditions of the minimum power of internal forces, equations have been obtained for calculating the optimal field parameters aopt, bopt, gopt, depending on the elongation coefficients l and the friction coefficient m. The equations obtained within the framework of the developed model are quite correct, since they allow determining the minimum force acting on the punch. The considered calculation model and equations can be used in the development of industrial technology for high-speed combined hot extrusion of flat-step bimetallic road milling picks.

At this moment we know a great variety of identification objects, tasks and methods and its significance is constantly increasing in various fields of science and technology. The identification problem is dependent on a priori information about identification object, besides that the existing approaches and methods of identification are determined by the form of mathematical models (deterministic, stochastic, frequency, temporal, spectral etc.). The paper considers a problem for determination of system parameters (identification object) which is assigned by the stochastic mathematical model including random functions of time. It has been shown that while making optimization of the stochastic systems subject to random actions deterministic methods can be applied only for a limited approximate optimization of the system by taking into account average random effects and fixed structure of the system. The paper proposes an algorithm for identification of parameters in a mathematical model of the stochastic system by non-gradient random searching. A specific feature of the algorithm is its applicability practically to mathematic models of any type because the applied algorithm does not depend on linearization and differentiability of functions included in the mathematical model of the system. The proposed algorithm ensures searching of an extremum for the specified quality criteria in terms of external uncertainties and limitations while using random searching of parameters for a mathematical model of the system. The paper presents results of the investigations on operational capability of the considered identification method while using mathematical simulation of hypothetical control system with a priori unknown parameter values of the mathematical model. The presented results of the mathematical simulation obviously demonstrate the operational capability of the proposed identification method.

A large class of systems that have found application in various industries and households, electrified transportation facilities and energy sector has been classified as electrical engineering systems. Their characteristic feature is a combination of continuous and discontinuous modes of operation, which is reflected in the appearance of a relatively new term “hybrid systems”. A wide class of hybrid systems is pulsed DC converters operating in a pulse width modulation, which are non-linear systems with variable structure. Using various methods for linearization it is possible to obtain linear mathematical models that rather accurately simulate behavior of such systems. However, the presence in the mathematical models of exponential nonlinearities creates considerable difficulties in the implementation of digital hardware. The solution can be found while using an approximation of exponential functions by polynomials of the first order, that, however, violates the rigor accordance of the analytical model with characteristics of a real object. There are two practical approaches to synthesize algorithms for control of hybrid systems. The first approach is based on the representation of the whole system by a discrete model which is described by difference equations that makes it possible to synthesize discrete algorithms. The second approach is based on description of the system by differential equations. The equations describe synthesis of continuous algorithms and their further implementation in a digital computer included in the control loop system. The paper considers modeling of a hybrid electrical engineering system using differential equations. Neglecting the pulse duration, it has been proposed to describe behavior of vector components in phase coordinates of the hybrid system by stochastic differential equations containing generally non-linear differentiable random functions. A stochastic vector-matrix equation describing dynamics of the processes has been obtained in the paper. The equation contains both continuous and discrete components, which characterize an amplitude signal modulation. An equation for probability density of phase coordinate distribution in the system has been developed on the basis of a mathematical model for a hybrid system.

The paper presents a mathematical model for electronic control system of the angular ignition timing (AIT) in the (ICE), which is running on ozonized fuel. An algorithm for ignition system control of internal combustion engine using ozonized fuel has been developed in the paper. A structure of the dynamic ignition system while using a control unit for supplying ozone into fuel with a purpose to improve automobile ecological and economical indices adapted to operational conditions. Application of the given system allows to ensure minimum reduction of operational petrol consumption and concentration of incomplete combustion products due to optimum ozone dosage into the fuel. The paper proposes a controlled automobile ignition system as a sequential scheme which has a great number of discrete inputs and outputs and many discrete internal states. The scheme establishes a functional dependence between input and output states. The paper provides an assessment of ecological indices according to massive emissions of carbon monoxide СО, hydrocarbon СпНт and nitric oxide NOx . The analysis of investigations results has been carried out in the paper.

In recent years, the economic factor has played an increasingly important role in the selection of technologies for manufacturing machine parts with specified values of normalized parameters of geometric accuracy and quality of working surfaces. As applied to surface plastic deformation processes, this is noticeably manifested in the search for effective friction control methods in the “tool – workpiece” pair, which ultimately determines the distribution pattern and the magnitude of stresses and strains in the workpiece and the tool. It is not possible to obtain a rigorous analytical solution to the problem of establishing a connection between surface conditions, friction, and the stress-strain state of the contacted bodies. In this regard, the construction of mathematical models comes to the fore, the solution of which is possible by numerical methods. The paper presents the results of a numerical study (computational experiment) of a finite-element model of workpiece deformation under various conditions of contact interaction and friction by one of the methods of surface plastic deformation – surface mandrel drilling. The friction coefficient has been chosen as the criterion for assessing the conditions of contact interaction and friction. It is shown that a change in the friction coefficient in the process of surface mandrel has no noticeable effect on the formation of a stress field in the deformable workpiece both in the axial, and in the radial and circumferential directions. At the same time, with an increase in the value of the friction coefficient in the “tool – workpiece” pair and with the associated increase in the force of mechanical resistance to deformation of the workpiece, their growth is observed. A computational experiment has confirmed the presence of non-contact deformations of the workpiece and tool during surface mandrel drilling, as well as as a decrease in the value of residual deformations in the workpiece with a decrease in the coefficient of friction. Balance assessment of contact surface displacements in the workpiece (the inner surface of the hole to be machined) and the tool (mandrel) has shown that the deformations of the tool in the elastic region can lead to a significant decrease in the real tightness of surface mandrel drilling.

Investment volume is considered as an important factor in regional development under current conditions. Logistical infrastructure which ensures a complex transport, distributive, information and other services exerts a significant influence on regional investment attractiveness. Lack of clear vision on development and execution of development strategy for logistics infrastructure from the side of regional authorities results in unwillingness of large federal and transnational companies to provide investments in infrastructure projects. Network of automotive transport terminals is one of the main elements in logistics infrastructure. The network allows to optimize a flow of material goods from the point of their origin to the point of their consumption with the lowest possible costs and the required level of service. Automobile transport is one of the main objects of transport infrastructure and it is characterized by rather high flexibility in comparison with other types of transport facilities that preconditions its widespread application. Network of automobile fleets (terminals) has been formed for redistribution of goods traffic within the concerned regions. The purpose of the present research is to develop a mathematical model for formation of transport infrastructure on the territory of regions. The paper proposes an approach for formation of automobile fleet (terminal) network on the territory of a large region with due account of the established network of distribution and sorting-out warehouse facilities. A model has been developed for solving the problem pertaining to minimization of aggregate costs related to maintenance of automobile fleets, delivery of goods to and from distribution and sorting-out warehouse facilities to consumers, ferry of empty trucks and goods handling. The model makes it possible to determine optimal number and location area of automobile fleets (terminals) while accounting for their possible locations, capacity and limitations on type and number of transport facilities.