scholarly journals Mathematical modeling of a self-propelled scraper at the beginning of soil set

2021 ◽  
Vol 1 (92) ◽  
pp. 154
Author(s):  
Sergii Kovalevskyi
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Dynamic Change ◽  
Vertical Force ◽  
Horizontal Force ◽  
Small Influence ◽  
Rate Of Increase ◽  
Draw Conclusion ◽  
External Forces

The process of filling of scoop of dragshovel consists of a few operations which periodically repeat oneself in the working loop. Each of these stages is accompanied the different moving of dragshovel and his separate knots, conditioned actions of external forces, at cutting and load of soil in a scoop, that needs separate consideration of the tense state of dragshovel equipment in a few calculation positions. The analysis of the modes of ladening of metallokonstrukcii of dragshovel during implementation of basic operations of digging allows to define the rational modes of operations of machine. For the decision of the put tasks the calculation chart of self-propelled dragshovel was developed in the process of zaglubleniya of knife in soil, on the basis of which taking into account the grounded limitations and scope terms, a twomass mathematical model, having degrees of freedom in horizontal and vertical directions, is created. With the purpose of simplification of mathematical model the angular vibrations of tractor and dragshovel were not taken into account, in connection with their small influence on the operating loadings at zaglublenii of scoop. Realization of mathematical model allowed to get the charts of dynamic change of horizontal and vertical force, operating in the hinges of hauling frame. Swaying character of loadings rotined that maximal values were arrived at almost for the identical interval of time in the first semiperiod, and horizontal and vertical efforts increase with the increase of intensity of resistance digging. The results of researches rotined that forces operating in the front hinge of hauling frame grow with the increase of intensity of resistance digging, arriving at the maximal values of 195 and 78 kN. Horizontal efforts to a great extent exceed vertical and increased with growth of intensity of resistance digging. The rate of increase of maximums of horizontal force can be considered even, because at megascopic intensities from 150 to 250 kN/m, most values grow approximately on 32 %, that enables to draw conclusion about expedience of work with the less rates of movement of dragshovel, taking into account loading of metallokonstrukcii. The rate of growth of maximums of vertical force can be considered even, approximately on 7 %, with the increase of rate of climb of knife of dragshovel, that far fewer as compared to growth of efforts, operating in horizontal direction. Therefore diminishing of speed of zaglubleniya will not result in the substantial diminishing of loading on the hauling frame of dragshovel.

Fore-Aft Forces in Tire-Wheel Assemblies Generated by Unbalances and the Influence of Balancing

1991 ◽  
Vol 19 (3) ◽  
pp. 142-162 ◽  
Author(s):  
D. S. Stutts ◽  
W. Soedel ◽  
S. K. Jha
Keyword(s):  
Mathematical Model ◽  
Elastic Foundation ◽  
Torsional Oscillation ◽  
Vertical Direction ◽  
Torsional Stiffness ◽  
Rolling Motion ◽  
Vertical Force ◽  
Horizontal Force ◽  
Wheel Rim ◽  
Open Question

Abstract When measuring bearing forces of the tire-wheel assembly during drum tests, it was found that beyond certain speeds, the horizontal force variations or so-called fore-aft forces were larger than the force variations in the vertical direction. The explanation of this phenomenon is still somewhat an open question. One of the hypothetical models argues in favor of torsional oscillations caused by a changing rolling radius. But it appears that there is a simpler answer. In this paper, a mathematical model of a tire consisting of a rigid tread ring connected to a freely rotating wheel or hub through an elastic foundation which has radial and torsional stiffness was developed. This model shows that an unbalanced mass on the tread ring will cause an oscillatory rolling motion of the tread ring on the drum which is superimposed on the nominal rolling. This will indeed result in larger fore-aft than vertical force variations beyond certain speeds, which are a function of run-out. The rolling motion is in a certain sense a torsional oscillation, but postulation of a changing rolling radius is not necessary for its creation. The model also shows the limitation on balancing the tire-wheel assembly at the wheel rim if the unbalance occurs at the tread band.

Mathematical modeling of water purification in a bioplato filter

2021 ◽  
pp. 56-57
Author(s):  
Ivanchuk Natalya ◽  
Sergiy Kunytskyi
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Water Purification ◽  
Dynamic Change ◽  
Filtration Coefficient ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Filter System ◽  
Physical Effects ◽  
Change Of Porosity

A mathematical model of filtration taking into account clogging and suffusion in the bioplato filter system in the two-dimensional case was built. The constructed mathematical model takes into account the physical effects of the dynamic change of porosity and the dependence of the filtration coefficient on the concentration of contaminants, which is not in the known analogues

scholarly journals MATHEMATICAL MODEL OF THE DYNAMICS OF A SIX-MASS SYSTEM OF A PARALLEL STRUCTURE MANIPULATOR MECHANISM

2021 ◽  
pp. 32-37
Author(s):  
V. V. Dyashkin-Titov ◽  
N. S. Vorob’eva ◽  
V. V. Zhoga
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Kinetic Energy ◽  
Quadratic Form ◽  
Degrees Of Freedom ◽  
Parallel Structure ◽  
Mass System ◽  
Generalized Coordinates ◽  
Comparative Results

The paper is devoted to the construction of a mathematical model of the dynamics of a parallel structure manipulator with three controlled degrees of freedom, based on the reduction of the kinetic energy of the manipulator to a quadratic form relative to three independent generalized coordinates, comparative results of mathematical modeling are presented.

Application of the method of mathematical modeling for forecasting channel deformations at the underwater crossing of the main pipeline

2020 ◽  
Vol 10 (6) ◽  
pp. 599-609
Author(s):  
Valery А. Gruzdev ◽  
◽  
Georgy V. Mosolov ◽  
Ekaterina A. Sabayda ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Roughness Coefficient ◽  
Computational Domain ◽  
Channel Deformations ◽  
Geological Surveys ◽  
Kuban River ◽  
The Stability ◽  
Protective Structures

In order to determine the possibility of using the method of mathematical modeling for making long-term forecasts of channel deformations of trunk line underwater crossing (TLUC) through water obstacles, a methodology for performing and analyzing the results of mathematical modeling of channel deformations in the TLUC zone across the Kuban River is considered. Within the framework of the work, the following tasks were solved: 1) the format and composition of the initial data necessary for mathematical modeling were determined; 2) the procedure for assigning the boundaries of the computational domain of the model was considered, the computational domain was broken down into the computational grid, the zoning of the computational domain was performed by the value of the roughness coefficient; 3) the analysis of the results of modeling the water flow was carried out without taking the bottom deformations into account, as well as modeling the bottom deformations, the specifics of the verification and calibration calculations were determined to build a reliable mathematical model; 4) considered the possibility of using the method of mathematical modeling to check the stability of the bottom in the area of TLUC in the presence of man-made dumping or protective structure. It has been established that modeling the flow hydraulics and structure of currents, making short-term forecasts of local high-altitude reshaping of the bottom, determining the tendencies of erosion and accumulation of sediments upstream and downstream of protective structures are applicable for predicting channel deformations in the zone of the TLUC. In all these cases, it is mandatory to have materials from engineering-hydro-meteorological and engineering-geological surveys in an amount sufficient to compile a reliable mathematical model.

On the displacements of the contours of the optic-electronic space images. Mathematical modeling of displacement

2017 ◽  
Vol 992 (4) ◽  
pp. 32-38 ◽  
Author(s):  
E.G. Voronin
Keyword(s):  
Mathematical Modeling ◽  
Remote Sensing ◽  
Mathematical Model ◽  
Point Of View ◽  
Design Features ◽  
Space Images ◽  
Electronic Imaging ◽  
Measuring Accuracy ◽  
Physical Laws

The article opens a cycle of three consecutive publications dedicated to the phenomenon of the displacement of the same points in overlapping scans obtained adjacent CCD matrices with opto-electronic imagery. This phenomenon was noticed by other authors, but the proposed explanation for the origin of displacements and the resulting estimates are insufficient, and developed their solutions seem controversial from the point of view of recovery of the measuring accuracy of opticalelectronic space images, determined by the physical laws of their formation. In the first article the mathematical modeling of the expected displacements based on the design features of a scanning opto-electronic imaging equipment. It is shown that actual bias cannot be forecast, because they include additional terms, which may be gross, systematic and random values. The proposed algorithm for computing the most probable values of the additional displacement and ways to address some of the systematic components of these displacements in a mathematical model of optical-electronic remote sensing.

scholarly journals Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model

2021 ◽  
Vol 11 (2) ◽  
pp. 787
Author(s):  
Bartłomiej Ambrożkiewicz ◽  
Grzegorz Litak ◽  
Anthimos Georgiadis ◽  
Nicolas Meier ◽  
Alexander Gassner
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Hertzian Contact ◽  
Two Degrees Of Freedom ◽  
Wide Range ◽  
Shape Errors ◽  
Nonlinear Features ◽  
Fourier Transform Phase ◽  
Hertzian Contact Theory

Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.

scholarly journals Report of the Kew Committee for the fourteen months ending December 31, 1891

1892 ◽  
Vol 51 (308-314) ◽  
pp. 152-182
Keyword(s):  
Vertical Force ◽  
Horizontal Force ◽  
Increased Activity

The operations of The Kew Observatory, in the Old Deer Park, Richmond, Surrey, are controlled by the Kew Committee, which is constituted as follows: The magnetographs have worked satisfactorily all through since last report. The curves obtained, representing Declination, Horizontal Force, and Vertical Force, have shown a marked increased activity in terrestrial magnetic changes as compared with the preceding year, although no very large disturbances have been registered.

Mathematical modeling of fluid movement inside the eyeball during intravitreal injection

2021 ◽  
pp. 106-109
Author(s):  
D.V. Lipatov ◽  
◽  
S.A. Skladchikov ◽  
N.P. Savenkova ◽  
V.V. Novoderezkin ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Residence Time ◽  
Complex Structure ◽  
Posterior Vitreous Detachment ◽  
Vitreous Body ◽  
Complete Removal ◽  
Intravitreal Injections ◽  
The World

Background. The avalanche-like growth of intravitreal injections in the world has significantly increased interest in the hemodynamics of the processes that occur in the eye when a drug is injected into the vitreous cavity. Every year, the number of intravitreally used drugs and promising areas in which they can be used is growing. This also applies to the creation of new combined medicines and the development of drugs with a long-term therapeutic effect. Aims. Create mathematical model of eyeball to evaluate the movement of the drug substance in it; to estimate the time of the drug's presence in the eye cavity before its complete removal, to characterize the ways of its removal from the eye cavity; to assess the significance of posterior vitreous detachment during the time when the drug is present in the eye cavity; to evaluate the effect on the hydrodynamics of the depth of drug administration. Results. When the drug is administered closer to the center of the eyeball, its residence time increases in comparison with the parietal administration. With a complete posterior detachment of the vitreous body, the time of finding the drug in the eye is prolonged compared to its absence. The obtained results of mathematical modeling of the movement of the drug administered intravitreally cannot be mechanically transferred to the human eye, due to the more complex structure of the latter. Key words: intravitreal injections, vitreous body, mathematic computing.

Swimbladder Function and Buoyancy Regulation in the Killifish Fundulus Heterochtus

1992 ◽  
Vol 166 (1) ◽  
pp. 61-81
Author(s):  
EDWARD M. GOOLISH
Keyword(s):  
Body Weight ◽  
Center Of Gravity ◽  
Water Current ◽  
Control Fish ◽  
Vertical Position ◽  
Vertical Force ◽  
Water Currents ◽  
Pectoral Fins ◽  
Artificial Lift ◽  
Rate Of Increase

Killifish, Fundulus heteroclitus, subjected to artificial lift above their center of gravity (10% of body weight) required a minimum of 7–8 days to resorb swimbladder gases completely. The swimbladders of some fish, however, did not fall below 50% of normal volume. The rate of increase in swimbladder volume upon removal of lift varied little among individuals, with approximately 6 days required for complete refilling. Previous deflation of the swimbladder (by syringe) did not result in faster or more complete gas resorption when the fish were subjected to artificial lift. This suggests that the constraint to resorption observed in some fish is not mechanical, e.g. connective tissue, but may reflect individual variability in perception of the stimulus. Swimbladder dry mass, which scaled as (body mass)0.79, was not affected by exposure to artificial lift. However, fish subjected to 7–11 days of artificial lift displayed slower rates of gas secretion upon removal of lift than control fish whose swimbladders had been evacuated by syringe. The initial rate was 65 % of that of control fish, with two additional days required to achieve normal buoyancy. Also, the rate of swimbladder gas resorption was 24 % faster the second time fish were exposed to artificial lift. These results demonstrate that the capacity for gas secretion and resorption can be altered by previous exposure to hydrostatic challenges. Killifish buoyancy, expressed as swimbladder volume per weight of the gas-free fish in water, fell from 0.95 to 0.70 mlg−1 after 5 days of exposure to water current. Removal of the pectoral fins eliminated 70% of this decrease, while removal of the pelvic fins had no effect. The rate of gas resorption by fish subjected to artificial lift was also not affected by removal of the pectoral fins. From these results it appears that the decrease in swimbladder volume in fish exposed to water currents is a consequence of lift forces produced by the pectoral fins, but that they are not required for regulation. Fish exposed to water currents or artificial lift swim with a head-down angle of attack. Theoretical estimates show that the vertical force component generated by this swimming behavior is of the appropriate magnitude to compensate for the additional lift. Fish confined in transparent cages near the surface of the water were less buoyant (0.91 mlg−1) than fish similarly maintained at the bottom of the tank (0.98mlg−1). However, because this effect was small, 10% of swimbladder volume, visual perception of vertical position is apparently not the primary stimulus for volume regulation. Partial lift (2.65 % of body weight) resulted in the resorption of twice as much swimbladder gas when attachment was anterior to the fish's center of gravity than when it was an equal distance posterior to the center of gravity. When equal amounts of partial lift and weight were added, lift anterior and weight posterior, no change in swimbladder volume occurred. With the position of these forces reversed, swimbladder volume increased by 31 % to 1.27 ml g−1. These results suggest that fish respond to pitching forces, i.e. longitudinal lift moments, as a stimulus for swimbladder gas secretion and resorption.

MATHEMATICAL MODELING OF CONCRETE STRUCTURE CORROSION IN BIOLOGICALLY AGGRESSIVE ENVIRONMENTS

2021 ◽  
Vol 3 (102) ◽  
pp. 55-67
Author(s):  
VARVARA E. RUMYANTSEVA ◽  
SVETLANA A. LOGINOVA ◽  
NATALIA E. KARTSEVA
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mass Transfer ◽  
Parabolic Type ◽  
Cement Concrete ◽  
Mass Conductivity ◽  
Kinetics And Dynamics ◽  
Biological Corrosion ◽  
First Time ◽  
Fourth Kind

In the aquatic environment, biocorrosion is an important factor affecting the reliability and durability of concrete structures. The destruction of cement concretes during biological corrosion is determined by the processes of mass transfer. The article presents the development of a calculated mathematical model of liquid corrosion in cement concrete, taking into account the biogenic factor. For the first time, a model of mass transfer in an unbounded two-layer plate is considered in the form of differential equations of parabolic type in partial derivatives with boundary conditions of the second kind at the interface between concrete and liquid and of the fourth kind at the interface between concrete and biofilm. The results of a numerical experiment are presented to study the influence of the coefficients of mass conductivity and mass transfer on the kinetics and dynamics of the process.

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