scholarly journals DETERMINATION OF DISPLACEMENT TRAJECTORIES AND FALLING TIME OF HINGEDLY FIXED WORKING UNITS OF AGRICULTURAL MACHINES

2018 ◽  
Vol 13 (1) ◽  
pp. 91-95
Author(s):  
Александр Акимов ◽  
Aleksandr Akimov ◽  
Юрий Константинов ◽  
Yuriy Konstantinov ◽  
Владимир Мазяров ◽  
...  
Keyword(s):  
Special Functions ◽  
Angular Position ◽  
Oscillation Period ◽  
Point Of View ◽  
Elliptic Integrals ◽  
Engineering Practice ◽  
Physical Pendulum ◽  
Elementary Functions ◽  
Operating Modes ◽  
Agricultural Machines

The solutions of many problems of agricultural engineering are expressed through special functions. In particular, such problems include the problem of determining the displacement trajectories and the falling time of the hingedly working units of agricultural machines, when the suspension axis moves horizontally at a certain speed. Such working device include: a stacker valve, falling after release from the shock, a beam of transverse rakes, that falls after the release of the roll and others. The solution of such problems is to determine the motion time of a physical pendulum to a given angular position, which is expressed in terms of elliptic integrals. And although elliptic integrals are a well-studied class of functions, in many cases an approximate solution of similar problems in elementary functions is quite sufficient both from the point of view of practical application and convenience of use. In addition, this approach makes it possible to determine the approximate law of motion of a physical pendulum in an explicit form, which makes it easier to set and solve problems of optimizing the operating modes and parameters of the above-mentioned working units. By estimating the integral, such an approximate law of motion of a mathematical pendulum was obtained. Its accuracy is sufficient for engineering practice. The obtained formula for the oscillation period of a pendulum with a large amplitude makes it possible to determine the falling time of the hinged working units of agricultural machines with high accuracy.

scholarly journals Calculation of integrals in MathPartner

2021 ◽  
Vol 29 (4) ◽  
pp. 337-346
Author(s):  
Gennadi I. Malaschonok ◽  
Alexandr V. Seliverstov
Keyword(s):  
Special Functions ◽  
Geometric Mean ◽  
Numerical Algorithms ◽  
Rational Functions ◽  
Elliptic Integrals ◽  
Software Implementation ◽  
Elementary Functions ◽  
Improper Integrals ◽  
Complete Elliptic Integrals ◽  
Rational Integral

We present the possibilities provided by the MathPartner service of calculating definite and indefinite integrals. MathPartner contains software implementation of the Risch algorithm and provides users with the ability to compute antiderivatives for elementary functions. Certain integrals, including improper integrals, can be calculated using numerical algorithms. In this case, every user has the ability to indicate the required accuracy with which he needs to know the numerical value of the integral. We highlight special functions allowing us to calculate complete elliptic integrals. These include functions for calculating the arithmetic-geometric mean and the geometric-harmonic mean, which allow us to calculate the complete elliptic integrals of the first kind. The set also includes the modified arithmetic-geometric mean, proposed by Semjon Adlaj, which allows us to calculate the complete elliptic integrals of the second kind as well as the circumference of an ellipse. The Lagutinski algorithm is of particular interest. For given differentiation in the field of bivariate rational functions, one can decide whether there exists a rational integral. The algorithm is based on calculating the Lagutinski determinant. This year we are celebrating 150th anniversary of Mikhail Lagutinski.

Elliptic integrals in engineering problems

10.12737/3391 ◽  
2014 ◽  
Vol 2 (1) ◽  
pp. 58-63 ◽  
Author(s):  
Кошкинбай Анахаев ◽  
Koshkinbay Anakhaev
Keyword(s):  
Direct Calculation ◽  
Elliptic Integrals ◽  
Engineering Practice ◽  
Elementary Functions ◽  
Thermal Dynamics ◽  
Engineering Problems ◽  
Incomplete Elliptic Integrals ◽  
Building Physics

New settlement dependences for expression of «not undertaking» elliptic integrals through elementary functions (with a margin error to 1–2%), received at the decision of various engineering problems hydro- and aerodynamics, the building physics, the theory of a filtration, mechanics of the continuous environment, thermal dynamics, etc. are given. In particular, on the basis of the approximately-hydromechanical decision analytical dependences for direct calculation value of incomplete elliptic integrals of 2nd sort are received. Thus their range of definition is expanded from an individual interval of a material axis to all numerical axis and to the top complex semiplane that opens new possibilities for researches of more challenges of engineering practice.

scholarly journals Simple Closed Analytic Formulas to approximate the Legendre Complete Elliptic Integrals K(k) and E(k), by a Fast Converging Recurrent-Iterative Procedure

2021 ◽  
Vol 9 ◽  
pp. 55-67
Author(s):  
Richard Selescu
Keyword(s):  
Normal Form ◽  
Iterative Procedure ◽  
Special Function ◽  
Iterative Scheme ◽  
Special Functions ◽  
Elliptic Integrals ◽  
Elementary Functions ◽  
Regression Functions ◽  
Complete Elliptic Integrals ◽  
The Right

wo sets of closed analytic functions are proposed for the approximate calculus of the complete elliptic integrals K(k) and E(k) in the normal form due to Legendre, their expressions having a remarkable simplicity and accuracy. The special usefulness of the newly proposed formulas consists in they allow performing the analytic study of variation of the functions in which they appear, using derivatives (they being expressed in terms of elementary functions only, without any special function; this would mean replacing one difficulty by another of the same kind). Comparative tables of so found approximate values with the exact ones, reproduced from special functions tables, are given (vs. the elliptic integrals’ modulus k). Both sets of formulas are given neither by spline nor by regression functions. The new functions and their derivatives coincide with the exact ones at the left domain’s end only. As for their simplicity, the formulas in k / k' do not need mathematical tables (are purely algebraic). As for accuracy, the 2nd set, more intricate, gives more accurate values and extends itself more closely to the right domain’s end. An original fast converging recurrent-iterative scheme to get sets of formulas with the desired accuracy is given in appendix.

Conditions for the Effective Use of Air Curtain on Objects of Agricultural Production

2020 ◽  
Vol 67 (1) ◽  
pp. 54-59
Author(s):  
Aleksey V. Kuz’michev ◽  
Stanislav S. Trunov ◽  
Dmitriy A. Tikhomirov
Keyword(s):  
Agricultural Production ◽  
Theoretical Models ◽  
Research Purpose ◽  
Engineering Practice ◽  
Physical Factors ◽  
Air Curtain ◽  
Operating Modes ◽  
Air Jets ◽  
Urgent Task ◽  
Design Characteristics

Creating and maintaining a microclimate in animal housing is an energy-intensive technological process that consumes up to 70 percent of the thermal energy consumed on cattle farms. Improving heating and ventilation systems aimed at reducing energy consumption is an urgent task. (Research purpose) The research purpose is to analyze the theoretical models for calculating air curtains and evaluate the possibility of their use for agricultural production facilities and to identify promising directions in the design solutions for thermal air curtains aimed at rural consumers. (Materials and methods) The article considers the theoretical justification and calculation of air curtains. The authors studied the physical model of interaction of air jets in openings, which serves as the basis for mathematical calculation of air curtains in engineering practice. The article describes the features of using the models for calculating air curtains for agricultural objects and the energy parameters of the curtains depending on the design characteristics and external environmental factors. (Results and discussion) The effect of the air curtain on the energy characteristics of the room has been studied. It was found that it is necessary to determine the type of air curtain that is optimally suitable for protecting the gate opening, with or without heating the air curtain. Authors have found that the engineering methods of calculation are based on different experimental data, which leads to a discrepancy in the results of evaluating the effectiveness of the designed curtain, overestimating its energy intensity and power. The calculation of heat curtains, operating modes should be carried out taking into account the variable effects of external physical factors, the equipment should correspond to a specific room. (Conclusions) The use of air curtains reduces or eliminates the penetration of external cold air into the room through the openings of external gates, requires a smaller volume of air supplied by the curtain, compared to the mass of the incoming air flow.

scholarly journals Cavitation Erosion and Sliding Wear of MCrAlY and NiCrMo Coatings Deposited by HVOF Thermal Spraying

2020 ◽  
Vol 20 (2) ◽  
pp. 26-38 ◽  
Author(s):  
M. Szala ◽  
M. Walczak ◽  
L. Łatka ◽  
K. Gancarczyk ◽  
D. Özkan
Keyword(s):  
Wear Resistance ◽  
Sliding Wear ◽  
Cavitation Erosion ◽  
Erosion Resistance ◽  
Nickel Content ◽  
Thermal Spraying ◽  
Point Of View ◽  
Engineering Practice ◽  
Hvof Thermal Spraying ◽  
Cavitation Erosion Resistance

AbstractThe investigation into wear resistance is an up-to-date problem from the point of view of both scientific and engineering practice. In this study, HVOF coatings such as MCrAlY (CoNiCrAlY and NiCoCrAlY) and NiCrMo were deposited on AISI 310 (X15CrNi25-20) stainless steel substrates. The microstructural properties and surface morphology of the as-sprayed coatings were examined. Cavitation erosion tests were conducted using the vibratory method in accordance with the ASTM G32 standard. Sliding wear was examined with the use of a ball-on-disc tribometer, and friction coefficients were measured. The sliding and cavitation wear mechanisms were identified with the SEM-EDS method. In comparison to the NiCrMo coating, the MCrAlY coatings have lower wear resistance. The cavitation erosion resistance of the as-sprayed M(Co,Ni)CrAlY coatings is almost two times lower than that of the as-sprayed NiCrMoFeCo deposit. Moreover, the sliding wear resistance increases with increasing the nickel content as follows: CoNiCrAlY < NiCoCrAlY < NiCrMoFeCo. The mean friction coefficient of CoNiCrAlY coating equals of 0.873, which almost 50% exceed those reported for coating NiCrMoFeCo of 0.573. The as-sprayed NiCrMoFeCo coating presents superior sliding wear and cavitation erosion resistance to the as-sprayed MCrAlY (CoNiCrAlY and NiCoCrAlY) coatings.

Optimization of Trimaran Design Configuration in Calm and Deep Water

2020 ◽  
Author(s):  
Renato Skejic ◽  
Sverre A. Alterskjær
Keyword(s):  
Deep Water ◽  
Optimization Procedure ◽  
Wave Theory ◽  
Point Of View ◽  
Engineering Practice ◽  
Total Resistance ◽  
Operational Parameters ◽  
Viscous Effects ◽  
Greenhouse Gasses ◽  
Hard Particles

The field of sea based modern shipping activities is constantly seeking for its improvements to achieve the economically justified operational patterns. In the same time, the sea transportation activities also need to satisfy currently imposed and, as well as, upcoming in the near future, safety and ecologically friendly footprint characteristics when it comes to the emission of greenhouse gasses and hard particles [1]. Fulfilment of the stated requirements consequently asks for the determination of certain vessels operational parameters such as the total resistance of a vessel which estimation is frequently carried out for predefined calm and deep-water environmental scenario. Current work is dealing with investigation of the total resistance parameter in calm and deep water for the preselected types of the trimaran ship hull configurations. The total resistance is estimated according to [2] recommended procedure through applicability of the robust and reliable method which is capable to address the problem of wave resistance prediction in calm and deep water. The method has origin in ordinary and modified Michell thin – ship wave theory by considering the viscous effects [3]. The differences between the utilized theories are discussed from the qualitative and quantitative point of view of the obtained results in comparison to the open source available theoretical experimental data and from the perspective of common engineering practice. Finally, based on the above description, the performed total resistance studies are used as a base for formulation of the optimization procedure which may be used in the trimaran vessel preliminary designs in the range of the forward speeds commonly expected during the normal operational life of the investigated trimaran vessel.

scholarly journals Self-Inductance of the Circular Coils of the Rectangular Cross-Section with the Radial and Azimuthal Current Densities

Physics ◽  
2020 ◽  
Vol 2 (3) ◽  
pp. 352-367
Author(s):  
Slobodan Babic ◽  
Cevdet Akyel
Keyword(s):  
Cross Sections ◽  
Special Functions ◽  
Rectangular Cross Section ◽  
The Self ◽  
Thin Wall ◽  
Elementary Functions ◽  
Special Cases ◽  
Current Densities ◽  
New Formula ◽  
Azimuthal Current

In this paper, we give new formulas for calculating the self-inductance for circular coils of the rectangular cross-sections with the radial and the azimuthal current densities. These formulas are given by the single integration of the elementary functions which are integrable on the interval of the integration. From these new expressions, we can obtain the special cases for the self-inductance of the thin-disk pancake and the thin-wall solenoids that confirm the validity of this approach. For the asymptotic cases, the new formula for the self-inductance of the thin-wall solenoid is obtained for the first time in the literature. In this paper, we do not use special functions such as the elliptical integrals of the first, second and third kind, nor Struve and Bessel functions because that is very tedious work. The results of this work are compared with already different known methods and all results are in excellent agreement. We consider this approach novel because of its simplicity in the self-inductance calculation of the previously-mentioned configurations.

Managing Enterprise Architecture Change

2007 ◽  
pp. 192-205 ◽  
Author(s):  
T. O’Neill ◽  
M. Denford ◽  
J. Leaney ◽  
K. Dunsire
Keyword(s):  
Enterprise Architecture ◽  
Point Of View ◽  
Emergent Properties ◽  
Engineering Practice ◽  
Top Down ◽  
Systems Architecture ◽  
Architectural Model ◽  
Complex Architectures ◽  
Computer Based ◽  
And Control

Enterprise architecture (EA) is the recognised place where the engineering practice of systems architecture meets real-world enterprise needs. The enterprise computer-based systems employed by organisations today can be extremely complex. These systems are essential for undertaking business and general operations in the modern environment, and yet the ability of organisations to control their evolution is questionable. The emerging practice of enterprise architecture seeks to control that complexity through the use of a holistic and top-down perspective. However, the methodologies and toolsets already in use are very much bottom-up by nature. An architecture-based approach is herein proposed; one that has at its base a complete and formal architectural description (or model). This allows enterprise architects, strategists, and designers to confidently model, predict, and control the emergent properties of their respective systems from an architectural point of view. The authors conclude that by using an approach founded upon an architectural model to analyse software and enterprise systems, architects can guide the design and evolution of architectures based on quantifiable nonfunctional requirements. Furthermore, hierarchical 3D visualisation provides a meaningful and intuitive means for conceiving and communicating complex architectures.

scholarly journals A practical solution of the Bethe equation in the energy range applicable to radiotherapy and radionuclide production

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
D. M. Martinez ◽  
M. Rahmani ◽  
C. Burbadge ◽  
C. Hoehr
Keyword(s):  
Special Functions ◽  
Computational Cost ◽  
Target Material ◽  
Relativistic Effects ◽  
Phase Changes ◽  
Bethe Equation ◽  
Great Success ◽  
Elementary Functions ◽  
Regular Perturbation ◽  
Radionuclide Production

AbstractWhile the dose deposition of charged hadrons has received much attention over the last decades starting in 1930 with the publication of the Bethe equation, there are still practical obstacles in implementing it in fields like radiotherapy and isotope production on cyclotrons. This is especially true if the target material consists of non-homogeneous materials, either consisting of a mixture of different elements or experiencing phase changes during irradiation. While Monte-Carlo methods have had great success in describing these more difficult target materials, they come at a computational cost, especially if the problem is time-dependent. This can greatly hinder optimal advancement in therapy and isotope targetry. Here, a regular perturbation method is used to solve the Bethe equation in the limit of small relativistic effects. Particular focus is given to incident energy level relevant to radionuclide production and radiotherapy applications, i.e. 10–200 MeV. We present a series solution for the range and dose distribution in terms of elementary functions, as opposed to special functions which will aid in uptake by practitioners.

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