Generalized mathematical model of the transfer processes in the enclosing structures of buildings, constructions, thermal and engineering networks

Mathematical Modeling, Vol. 8 (2024), Issue 1, pg(s) 7-9

The problems of heat and moisture transfer, air permeability in single and enclosure constructions (EC) of buildings, facilities and heat, engineering and electrical networks under the influence of environmental factors and the work of heating, ventilation and air conditioning has been analyzed. A general definition of the problem taking into account the transfer processes of internal voluminous or local heat source (drainage) has been considered. A generalized mathematical model (MM) of unsteady heat and mass transfer process for bodies of different canonical form (half-plate, hollow cylinder and sphere) and their analogues has been developed. In particular cases of the mathematical model, the dependence of the physical characteristics of the (solid isotropic) medium, the boundary conditions parameters, the capacity of the mass substance transfer sources (drains) from the transfer potentials (temperature, moisture content) or the space-time continuum has been taken into consideration. The analytical solution of the generalized non-stationary and stationary heat and mass transfer problem under the general boundary conditions of different (first, second, third and mixed) kind on the outline of the researched area has been scrutinized. For constant system parameters of non-stationary transfer processes an algorithm for solving differential transfer equations using Fourier transformation with variable parameters of different kind of boundary conditions has been shown. For large-scale transitions, practical applications, parametric analysis of the solutions obtained, setting optimization and automation tasks for process control systems, the obtained MM, analytical and approximate solutions of direct transfer short circuits are given a criterion form convenient for these purposes.

Mathematical modelling of oscillatory movements cleaner of the heads of root cultures from remains on the root

Harvesting root crops still poses a challenging problem for the agricultural mechanization industry. Even though the technology of separate harvesting of tops and roots has undoubted advantages, the quality of the final product, i.e. roots, depends significantly on the accuracy of cutting tops from their heads to the roots and the thoroughness of their final cleaning from residues. One of the ways to solve this problem is to create improved constructions of peelers and their further testing, experimental and theoretical studies to determine their optimal structural and kinematic parameters. To implement the above, a new mathematical model was constructed, the study of which made it possible to assess the influence of the construction parameters of the root crop head cleaner from the residues of tops on the root on the indicators of its oscillatory process in the longitudinal-vertical plane when moving along uneven soil surfaces. Numerical calculations of the obtained mathematical model were carried out on a PC using the PTC Mathcad 15 software environment and the previously determined input numerical parameters. The amplitude-frequency and phase-frequency characteristics were constructed, which made it possible to determine the optimal parameters of this oscillatory system. Based on the mathematical modelling performed, the influence of irregularities in the longitudinal profile of the soil surface on the angular oscillations of the cleaner, as well as the influence of different values of the stiffness coefficient c and the damping coefficient μ of its two copy wheels, as well as the length l, or the longitudinal coordinate of their placement on the cleaner frame, was first of all determined. The mathematical modelling of the oscillatory movements of the cleaner made it possible to establish that the value of the stiffness coefficient c of the pneumatic tires of its trailing wheels should be not less than 315 kNm–1, which is ensured by the air pressure in its tires, which should be equal to 135 kPa. In addition, it has been established that the change in the value of the coefficient μ of damping of the tires of the cleaner’s tracking wheels should be in the following range 350…1350 Nsm–1 and this parameter does not affect the amplitude and phase frequency characteristics of oscillations under the influence of oscillations of the ordinates of the longitudinal profile of field surface irregularities in the frequency range 0…24 s–1. Also, the influence of oscillations of the longitudinal profile ordinates of the field in the specified frequency range of 0…24 s–1 depends little on the change in the value of the longitudinal coordinate l of the location of its tracing wheels. Therefore, the placement of the tracing wheels on the frame should be determined based on the constructional features of the cleaner.

Matematical models for assessing the quality of functioning of the motor transport company

Mathematical Modeling, Vol. 7 (2023), Issue 1, pg(s) 34-35

In order to obtain the methods of assessing the quality of the functioning of the motor transport company, it is necessary to develop a methodology for quantitative evaluation of this quality. This methodology should be based on mathematical models of the quality of operations of the motor transport firm.
For purposeful formation of quality, the paper proposes an adequate method of analysis of this quality. At the same time, a method of evaluating the quality of the functioning of the automobile enterprise, evaluating the quality of the decisions taken to improve this property, and forecasting the expected quality of the functioning have been developed.

Modeling the estimate of the volume of recreational fishing based on the Bayesian approach

Mathematical Modeling, Vol. 6 (2022), Issue 3, pg(s) 92-95

In this paper we consider the task of estimating the volume of recreational fish catch yield in a water body. We design mathematical models for the tasks varying in complexity and generality and demonstrate how they can be solved using Bayesian approach. A Markov Chain Monte Carlo (MCMC)-based Bayesian approach is widely used as a solution for stochastic models. To solve the simplest case of a proposed model we have used the PyMC library. The proposed models were later used to estimate the recreational fishing capacity of the water bodies in Qazaqstan.

Theoretical investigation of the removal of halfrums from sugar beet root heads

Removal of the haulm from the heads of sugar beet to the roots during their harvesting (cutting the main mass) or separation of its residues (when finishing the heads) is a complex technological process associated with either a significant loss of sugar-bearing mass (low cut), or not complete removal of residues (high cut), which significantly degrades the quality of root crops. Therefore, ways to find a complete removal of haulm and its residues from the heads of root crops require research and development of such devices capable of performing this process qualitatively. However, first it is necessary to determine theoretically and experimentally the basic initial conditions under which high quality indicators will be achieved, and losses of sugar-bearing mass during cutting the haulm will be minimal, with the remaining haulm being as small as possible (or they will be absent at all). This paper theoretically and experimentally investigates and determines the loss of sugar mass and remnants of the bud on the heads of sugar beet roots during the separation of the bud and its remnants. It is established that in the interval of working heights of a cut which is equal to 20 … 60 mm deviation of theoretical calculations from experimental does not exceed on the average 1%.

Features of modeling of ultralow power electric fields

Mathematical Modeling, Vol. 5 (2021), Issue 1, pg(s) 31-35

The article presents the results of modeling quasi-stationary ultralow power electric fields (the order of tens of nanowatts) and establishes ranges of rational values of parameters (average density of electric voltage, specific potential) of these fields. As a result of mathematical modeling (based on a system of Gaussian equations) and subsequent numerical experiment, it is shown that an instantaneous increase in the average electric density of a quasi-static electric field in 2 times in one part of the field leads to an increase in charge redistribution time from 34 ns (at an initial density of electric tension of 17 nN/Ku.μm 3) to 189 ns (at a density of electric tension of 145 nN/Ku.μm3). This redistribution allows us to determine the range of rational values of the specific potential, which is 1.1… 9 nV/μm 2. In this case, the maximum specific power that can occur in such a field is 0.5… 0.77 nW/μm 2.

On the question of the rational distribution of power between the hydrostatic and hydrodynamic branches of the complex steering mechanism for the tracked vehicle

Mathematical Modeling, Vol. 5 (2021), Issue 1, pg(s) 17-20

The article presents a description of the mathematical model of the curvilinear movement of a tracked vehicle with a complex steering mechanism, which contains a control hydrostatic branch and an additional hydrodynamic branch for unloading the first. The adequacy of the presented mathematical model was verified by calculating the characteristics of the turn in place of the Leop ard-2 tank. The resulting tool can become the basis for parametric optimization of similar steering mechanisms for tracked vehicles.

Construction of a new calculation mathematical model of the vibration process of excavation of the root body from the soil, taking into account its elastic damping properties

The equation of shock interaction of the vibrating digging working body with the body of the sugar beet root, fixed in the soil, which occurs in the process of vibratory digging of the roots, is made. Based on the shock interaction equation, the shock pulse and the maximum shock force that occur during this interaction were determined, which allowed to further assess the degree of damage and knocking out of root heads in the process of vibration digging of sugar beet. From the conditions of non-damage of root crops the expression for definition of admissible frequency of fluctuations of the vibrating digging working body taking into account its design parameters and translational speed of movement of the beet harvester is received. Based on the obtained equations describing this process, the optimal values of the kinematic and structural parameters of the working plow for vibration digging of sugar beets are found.

Synthesis and design of hyperboloid gear drives: Methodology and aspects

Machines. Technologies. Materials., Vol. 13 (2019), Issue 7, pg(s) 285-290

The high current requirements for the characteristics determining the accuracy, reliability and efficient manufacturing of modern machines, apparatus and devices applicable in various fields of industry and transport in a big extend dictate the applied scientific methodology to the technological synthesis, design and production of gears. In the processes of synthesis and design of the different types of gear transmissions, the designer faces an extremely complex set of questions to solve, which together define the desired optimal construction.
In this case, an optimal design means a gear transmission that is capable of delivering preliminary defined kinematic and / or strength requirements at minimum design, production and operation costs (including the repair costs during their exploitation). This work presents a review of the methodology, developed by the authors, oriented towards the synthesis and design of spatial gear mechanisms (hyperboloid gear drives), realizing rotations transformation between crossed shafts. The main principles, on which the construction of adequate software programs are based for the synthesis of treated transmissions, are presented.

Research on characteristics of failures flow according to the maintenance and repair strategy

In the practice of repairing the machines in agriculture, the following strategies are mainly applied: forced repairs; conducting repairs in plan order and a combined strategy with elements of both strategies.
An investigation was carried out and analytical dependencies were obtained to determine the function of the recovery (characteristic of the failure flow) of the machine components in the forced repairs (after failure), to carry out repairs in a planned order and a combined strategy with elements of the first two strategies to calculate the required pool of spare parts to maintain machine performance.

• On a mathematical model of land-use change

Mathematical Modeling, Vol. 2 (2018), Issue 4, pg(s) 153-155

The paper is devoted to a mathematical model of land-use change proposed by Dobson et. al. We formulate and investigate some quantitative properties of the corresponding Cauchy problem. We construct a numerical algorithm for approximate solution of the problem and present some of the numerical results. Their meaning is explained and discussed.

• Development of methods for calculating the nonequilibrium phase transformations during the condensation of supercooled steam in the turbine flow path

Methods for calculating the nonequilibrium phase transformations during the condensation of supercooled steam in the turbine flow path are developed. In the process of realization, the development of the classical Zel’dovich-Frenckel’s theory for the case of nonstationary nucleation of a new phase with fast extensions of supercooled steam is considered. A numerical-analytical method for calculating condensation was designed and implemented in the form of a software package, which consistently takes into account the nonstationarity of the process. Numerical studies have shown high efficiency and accuracy of the method.