scholarly journals The mathematical model of engagement and analytical description of tooth profile of waveform edge kinematic reducer

2021 ◽  
pp. 22-31
Author(s):  
M. A. Jasem ◽  
◽  
P. Y. Krauinsh ◽  
◽  
Keyword(s):  
Mathematical Model ◽  
Transfer Function ◽  
Spherical Surface ◽  
Analytical Description ◽  
System Of Equations ◽  
Mathematical Experiment ◽  
Pair Mating ◽  
The Mathematical Model ◽  
Spherical Motion

The problem of creating a waveform edge kinematical reducer with multi-pair gearing brings to the fore a range of issues in the field of geometric-kinematic gearing theory, which are considered in this work. The synthesis of multi-pair gearing for a waveform edge kinematical reducer, which ensures the constancy of their transfer function, provides for: development of a mathematical model of gearing taking into account the peculiarities of the interaction of teeth during special-spherical motion; description of the profile of the teeth by a system of equations for a spherical surface and for a normal section of teeth for internal gearing; identification with the help of the MathCAD 2010 Professional program of a mathematical experiment and determination of the area of existence of 100 % multi-pair mating of teeth by comparing the shape of their profile with the nature of the analytical function of multi-pair engagement

scholarly journals DETERMINATION OF TRANSFER FUNCTION OF MAGNETIC LEVITATION MODEL AND EXPERIMENTAL VERIFICATION OF OPTICAL SENSOR

2019 ◽  
pp. 148-154
Author(s):  
Erik Prada
Keyword(s):  
Mathematical Model ◽  
Transfer Function ◽  
Experimental Verification ◽  
Optical Sensor ◽  
Magnetic Levitation ◽  
Positioning Systems ◽  
Levitation System ◽  
Magnetic Levitation System ◽  
The Mathematical Model

Urgency of the research. The potential of controlling the position of levitating objects has great application in deposition and in various positioning systems. Magnetic levitation eliminates direct mechanical friction between moving parts. Target setting. The measurement shielding method used is one of the methods of determining the position of a levitating object. By combining positioning and regulating elements, we achieve a feedback control. The use of a given type of measurement has advantages in places where the use of other methods is not appropriate. Actual scientific researches and issues analysis. The problem of magnetic levitation is addressed by several research laboratories with a direct connection to practice. The problem that is currently solved within magnetic levitation is the regulation of the levitating object using various types of regulators. The research objective. Derivation of mathematical model of magnetic levitation and examination of nonlinear system followed by linearization by Taylor series. Experimental determination of characteristics and dependence between object position, voltage and current. The statement of basic materials. The position of the levitating object is determined by the shading of the optical sensor. The light source is a laser light. Conclusions. In this work we defined the mathematical model of the magnetic levitation system and subsequently derived the transfer function of the levitation system and the position sensor. From the experimental verification of the shadow method for the determination of the position of the levitating object and the consequent need for regulation, we found that the dependence of the position of the levitating object on current and voltage on the photodiode is linear in the active region.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

scholarly journals Determination of the Vertical Load on the Carrying Structure of a Flat Wagon with the 18–100 and Y25 Bogies

2021 ◽  
Vol 11 (9) ◽  
pp. 4130
Author(s):  
Oleksij Fomin ◽  
Alyona Lovska ◽  
Václav Píštěk ◽  
Pavel Kučera
Keyword(s):  
Mathematical Model ◽  
Fatigue Strength ◽  
Service Life ◽  
Dynamic Characteristics ◽  
Dynamic Load ◽  
Field Tests ◽  
Vertical Load ◽  
Mathcad Software ◽  
The Mathematical Model

The study deals with determination of the vertical load on the carrying structure of a flat wagon on the 18–100 and Y25 bogies using mathematic modelling. The study was made for an empty wagon passing over a joint irregularity. The authors calculated the carrying structure of a flat wagon with the designed parameters and the actual features recorded during field tests. The mathematical model was solved in MathCad software. The study found that application of the Y25 bogie for a flat wagon with the designed parameters can decrease the dynamic load by 41.1% in comparison to that with the 18–100 bogie. Therefore, application of the Y25 bogie under a flat wagon with the actual parameters allows decreasing the dynamic loading by 41.4% in comparison to that with the 18–100 bogie. The study also looks at the service life of the supporting structure of a flat wagon with the Y25 bogie, which can be more than twice as long as the 18–100 bogie. The research can be of interest for specialists concerned with improvements in the dynamic characteristics and the fatigue strength of freight cars, safe rail operation, freight security, and the results of the research can be used for development of innovative wagon structures.

scholarly journals RESEARCH OF THE TENSELY-DEFORMED STATE OF ELEMENTS OF MOBILE HEAT STORAGE

2020 ◽  
Vol 42 (2) ◽  
pp. 68-75
Author(s):  
V.G. Demchenko ◽  
А.S. Тrubachev ◽  
A.V. Konyk
Keyword(s):  
Mathematical Model ◽  
Heat Storage ◽  
Quantitative Estimation ◽  
The Real ◽  
State Of The Union ◽  
Real Geometry ◽  
Deformed State ◽  
The Mathematical Model ◽  
Minimization Of Functional

Worked out methodology of determination of the tensely-deformed state of elements of mobile heat storage of capacity type, that works in the real terms of temperature and power stress on allows to estimate influence of potential energy on resilient deformation that influences on reliability of construction and to give recommendations on planning of tank (capacities) of accumulator. For determination possibly of possible tension of construction of accumulator kinematics maximum terms were certain. As a tank of accumulator shows a soba the difficult geometrical system, the mathematical model of calculation of coefficient of polynomial and decision of task of minimization of functional was improved for determination of tension for Міzеs taking into account the real geometry of equipment. Conducted quantitative estimation of the tensely-deformed state of the union coupling, corps and bottom of thermal accumulator and the resource of work of these constructions is appraised. Thus admissible tension folds 225 МРа.

scholarly journals Large Deflection Model for Multiple, Inline, Interacting Cantilever Beams

2020 ◽  
Vol 88 (4) ◽  
Author(s):  
Austin Bebee ◽  
Christopher J. Stubbs ◽  
Daniel J. Robertson
Keyword(s):  
Mathematical Model ◽  
Flexural Rigidity ◽  
Cantilever Beams ◽  
Model Concept ◽  
Math Model ◽  
Rigid Body Model ◽  
High Throughput Phenotyping ◽  
Stalk Lodging ◽  
The Mathematical Model

Abstract Numerous natural and synthetic systems can be modeled as clusters of interacting cantilever beams. However, a closed-form mathematical model capable of representing the mechanics of multiple interacting cantilever beams undergoing large deflections has yet to be presented. In this work, a pioneering mathematical model of the force–deflection response of multiple, inline, interacting (i.e., contacting) cantilever beams is presented. The math model enables the determination of the force–deflection response of a system of interacting cantilever beams and is predicated upon the “Pseudo Rigid Body Model” concept. The model was validated through data triangulation experiments which included both physical and computational studies. An analysis of the mathematical model indicates it is most accurate with deflections less than 50 deg. In the future, the model may be used in high throughput phenotyping applications for investigating stalk lodging and estimating the flexural rigidity of crop stems. The model can also be used to gain intuition and aid in the design of synthetic systems composed of multiple cantilever beams.

scholarly journals THE MATHEMATICAL MODELING OF METALS CONTENT IN PEAT

2015 ◽  
Vol 1 ◽  
pp. 249
Author(s):  
Edmunds Teirumnieks ◽  
Ērika Teirumnieka ◽  
Ilmārs Kangro ◽  
Harijs Kalis
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Inductively Coupled Plasma ◽  
Optical Emission ◽  
Peat Bog ◽  
Inductively Coupled ◽  
Pollution Loading ◽  
The Mathematical Model ◽  
Optical Emission Spectrometer

Metals deposition in peat can aid to evaluate impact of atmospheric or wastewaters pollution and thus can be a good indicator of recent and historical changes in the pollution loading. For peat using in agriculture, industrial, heat production etc. knowledge of peat metals content is important. Experimental determination of metals in peat is very long and expensive work. Using experimental data the mathematical model for calculation of concentrations of metals in different points for different layers is developed. The values of the metals (Ca, Mg, Fe, Sr, Cu, Zn, Mn, Pb, Cr, Ni, Se, Co, Cd, V, Mo) concentrations in different layers in peat taken from Knavu peat bog from four sites are determined using inductively coupled plasma optical emission spectrometer. Mathematical model for calculation of concentrations of metal has been described in the paper. As an example, mathematical models for calculation of Pb concentrations have been analyzed.

scholarly journals APPLICATION OF MATHEMATICAL PLANNING OF THE EXPERIMENT IN THE CHOOSING THE OPTIMUM CONDITIONS OF THE VAPOR-PHASE GAS-CHROMATOGRAPHIC DETERMINATION OF FORMALDEHYDE IN THE URINE

2018 ◽  
Vol 97 (10) ◽  
pp. 985-989 ◽  
Author(s):  
Аnton N. Alekseenko ◽  
O. M. Zhurba
Keyword(s):  
Mathematical Model ◽  
Vapor Phase ◽  
Statistical Processing ◽  
Analytical Signal ◽  
Heating Time ◽  
Gas Extraction ◽  
Optimal Conditions ◽  
Steep Ascent ◽  
The Mathematical Model

Introduction. There was substantiated a method for the determination of formaldehyde by vapor-phase gas chromatography by the use of derivatizing reagent o-(2,3,4,5,6-pentafluorbenzyl)hydroxylamine. Material and methods. Formaldehyde in urine was derivatized to o-pentafluorobenzyloxime and recovered to the vapor phase by heating the urine sample with o-(2,3,4,5,6-pentafluorbenzyl)hydroxylamine in a sealed vial. Gas-chromatographic analysis of the vapor-air phase was performed in a mode of the temperature gradient on a capillary column HP-5 with a flame ionization detector. Identification of the analyte in the form of the derivative-o- pentafluorobenzyloxime of formaldehyde was carried out according to the absolute retention time, which was established by comparing the chromatograms of model formaldehyde mixtures in the urine of different concentrations. Results. The optimal conditions for gas extraction are selected using mathematical experimental planning. The most important factors of gas extraction in the vapor-phase analysis are the temperature and time of the establishment of the interphase equilibrium with heating. From the experimentally obtained curves of the analytical signal on the temperature and the heating time, the zero level and the interval of variation of these factors are chosen. A matrix for planning a 2-factor experiment was constructed. The coefficients of the mathematical model are determined. There was carried out statistical processing of the experimental data, which was reduced to the estimation of the reproducibility of the optimization parameter and to the evaluation of the significance of the coefficient of the mathematical model. The adequacy of the mathematical model was evaluated, its interpretation was carried out. Discussion. The peak area of the analyte increases with the elevating the temperature and heating time, due to an increase in the analyte concentration in the vapor phase. Moreover, the heating time makes a greater contribution to the formation of the analytical signal than the temperature. The step of motion along the gradient was calculated and the experiments of steep ascent were carried out. Conclusion. According to the results of the steep ascent experiments, the optimal conditions for the gas extraction of formaldehyde in the form of a derivative were chosen.

scholarly journals Reduction of Grain Loss During Harvesting Due to the Rational Distribution of Vehicles

2021 ◽  
Vol 334 ◽  
pp. 02025
Author(s):  
Konstantin Esin ◽  
Andrei Bodrov ◽  
Denis Lomakin ◽  
Maxim Kulev ◽  
Andrew Kulev
Keyword(s):  
Mathematical Model ◽  
Carrying Capacity ◽  
Grain Storage ◽  
Rational Distribution ◽  
Agricultural Organizations ◽  
Combine Harvesters ◽  
The Mathematical Model ◽  
Storage Facilities

The paper deals with the mathematical model of the rational distribution of vehicles, which allows attaching them to a group of combine harvesters during harvesting, depending on the carrying capacity of vehicles, the productivity of combine harvesters and the capacity of grain storage facilities. In addition, it presents a formula which allows determining the required number of vehicles that will deliver grain from a group of combine harvesters. Further the article presents calculations of routes of vehicles movement and determination of the required number of vehicles de-pending on the carrying capacity of one of the operating agricultural organizations.

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