Movement of the Particle on the Internal Surface of the Spherical Segment Rotating About a Vertical Axis

Pylypaka, Serhii; Nesvidomin, Victor; Volina, Tatiana; Sirykh, Larysa; Ivashyna, Liudmyla

doi:10.35633/inmateh-62-08

Cited by 10 publications

(3 citation statements)

References 10 publications

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“…In this case, there may be difficulties of cumbersome analytical notation of the relative movement of the particle. An option to overcome these difficulties may be to use the Frenet trihedron and formulas, which were used in the study of the movement of a particle on the inner surface of a spherical segment orbiting a vertical axis, considered in paper [8], as well as on the outer surface of a horizontal cylinder with an oscillatory motion [9].…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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The possibility to apply the Frenet trihedron and formulas for the complex movement of a point on a plane with the predefined plane displacement

Volina

Pylypaka

Nesvidomin

et al. 2021

EEJET

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Material particles interact with the working moving surfaces of machines in various technological processes. Mechanics considers a technique to describe the movement of a point and decompose the speed and acceleration into single unit vectors of the accompanying trajectory trihedron for simple movement. The shape of the spatial curve uniquely sets the movement of the accompanying Frenet trihedral as a solid body. This paper has considered the relative movement of a material particle in the static plane of the accompanying Frenet trihedron, which moves along a flat curve with variable curvature. Frenet formulas were used to build a system of differential equations of relative particle movement. In contrast to the conventional approach, the chosen independent variable was not the time but the length of the arc of the guide curve along which the trihedron moves. The system of equations has been built in the projections onto the unit vectors of the moving trihedron; it has been solved by numerical methods. The use of the accompanying curve trihedron as a moving coordinate system makes it possible to solve the problems of the complex movement of a point. The shape of the curve guide assigned by parametric equations in its length function determines the portable movement of the trihedron and makes it possible to use Frenet formulas to describe the relative movement of a point in the trihedron system. This approach enables setting the portable movement of the trihedron osculating plane along a curve with variable curvature, thereby revealing additional possibilities for solving problems on a complex movement of a point at which rotational motion around a fixed axis is a partial case. The proposed approach has been considered using an example of the relative movement of cargo in the body of a truck moving along the road with a curvilinear axis of variable curvature. The charts of the relative trajectory of cargo slip and the relative speed for the predefined speed of the truck have been constructed

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Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…After multiplying the obtained results (9) by 2 e V according to (8), one can derive expressions of the absolute acceleration of point B in the projections onto the unit vectors of a trihedron:…”

Section: Constructing a System Of Differential Equations Of The Relative Movement Of A Particle On A Plane Using Frenet Formulasmentioning

confidence: 99%

The possibility to apply the Frenet trihedron and formulas for the complex movement of a point on a plane with the predefined plane displacement

Volina

Pylypaka

Nesvidomin

et al. 2021

EEJET

Self Cite

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“…The issues of theoretical design of screw reloading mechanisms with flexible lines and methods of designing and calculating their parameters, development of efficient designs of screw conveyors for transporting bulk materials along curved routes are discussed in [1; 2], and the issues of synthesis of machine structures by morphological analysis are discussed in [3] etc. Particular attention should be paid to the coverage in the literature of the issues of calculation and selection of parameters of screw working bodies and transportation of grain materials, mineral fertilisers and other bulk agricultural materials by screw conveyors [4; 5; 6] since the problem of injury to materials during the transportation is open.…”

Section: Introductionmentioning

confidence: 99%

Justification and calculation of design and strength parameters of screw loaders

Klendii¹,

Logusch²,

Dragan³

et al. 2022

Tehnìka ta energetika

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Existing designs of screw working bodies of transport and processing machines cannot always provide the required performance and avoid overloading, which causes deformation and damage to parts of the mechanisms. Thus, it is necessary to establish new efficient screw working bodies that would ensure the execution of the technological process. The purpose of the study was to substantiate and explore the design and methodology for calculating the main structural-power parameters of the developed screw loader, to synthesise screw loaders using the method of morphological analysis to obtain designs of mechanisms with better technical and economic characteristics. The methods of surface theory, analytical and differential geometry, computer graphics and mathematics were used to conduct the research. As a result of theoretical and experimental studies, the designs of screw conveyors with hopper loading and screw conveyors with nozzle loading are presented. In addition, a classification of loaders for screw transport and technological mechanisms is presented. The dependencies for calculating the design of screw conveyor loaders are determined. The synthesis of loaders and mixers by the method of morphological analysis was performed to obtain designs of mechanisms with the best technical and economic characteristics and competitive designs of mechanisms were established. A system of coding and synthesis of structural elements and mechanisms of screw implements with improved technological properties is proposed, and competitive designs of screw implement that perform technological processes efficiently and effectively are selected. A methodology for calculating the main structural and power parameters of a screw loader has been developed, which allows for determining the parameters of a screw loader. The materials of the research can be used in further studies of screw conveyors and, in particular, screw loaders to determine their design, technological, energy and power parameters

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Theoretical and Experimental Studies of the Properties of Porous Permeable Materials Obtained from Industrial Waste

Povstyanoy

Imbirovich

Tkachuk

et al. 2022

Lecture Notes in Mechanical Engineering

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Movement of the Particle on the Internal Surface of the Spherical Segment Rotating About a Vertical Axis

Cited by 10 publications

References 10 publications

The possibility to apply the Frenet trihedron and formulas for the complex movement of a point on a plane with the predefined plane displacement

The possibility to apply the Frenet trihedron and formulas for the complex movement of a point on a plane with the predefined plane displacement

Justification and calculation of design and strength parameters of screw loaders

Theoretical and Experimental Studies of the Properties of Porous Permeable Materials Obtained from Industrial Waste

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