External Rolling of a Polygon on Closed Curvilinear Profile

Kresan, Tetiana; Pylypaka, Serhii; Ruzhylo, Zynovii; Rogovskii, I. L.; Trokhaniak, Oleksandra

doi:10.14311/ap.2020.60.0313

Cited by 19 publications

(7 citation statements)

References 4 publications

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“…1, c). This angle cannot be less than 90°, otherwise the transmission will be jammed [8]. For the same reasons, the angle between the curves in the depressions of the teeth should also be either right or larger than the right one.…”

Section: The Study Materials and Methodsmentioning

confidence: 99%

“…In the first case, this is the trajectory of the point of the circle, which rolls in a straight line, and in the second -on the contrary -the trajectory of the straight point, which rolls around in a circle. Rolling along a curvilinear path in a straight line is used in work [8] to construct noncircular wheels, one of which is formed by straight segments, that is, it is a polygon. The formation of congruent noncircular wheels of two symmetrical arcs of the logarithmic spiral is considered in [9].…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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Designing an outer toothed gear whose wheel teeth are outlined by the logarithmic spiral arcs

Pylypaka

Kresan

Volina

et al. 2021

EEJET

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Toothed gears are the most common mechanical gears in machine building, which are characterized by high reliability and durability, a constant transfer number, and which can transmit high torque. During toothed gear operation, the surfaces of the teeth slide, which gives rise to friction forces and wears their working surfaces. To prevent this, the surfaces of the teeth need constant lubrication. This paper considers the design of a gear tooth engagement, which does not have friction between the surfaces of the teeth since they roll over each other without slipping. The profile of the tooth of such a gear is outlined by congruent arcs, symmetrical relative to the line that connects the center of rotation of the toothed wheel with the top of the tooth. These symmetrical curves at the top of the tooth intersect at the predefined angle. In the depressions of the wheel, adjacent teeth also intersect at the same angle. Such a condition can be ensured by a curve that at all its points crosses the radius-vector emanating from the coordinate origin, also at a stable angle equal to half of the given one. This curve is a logarithmic spiral. If the number of teeth of the drive and driven wheels is the same, then their teeth are congruent. Otherwise, the profiles of the teeth would differ but they could be outlined by congruent arcs of the same logarithmic spiral of the same length taken from different areas of the curve. The minimum possible angle at the top of the teeth is straight. At acute angle, the toothed gear operation is impossible. To build gear wheels with a right angle at the top of the tooth, it would suffice to set the number of teeth of the drive and driven wheels. The center-to-center distance is calculated using the derived formula. The transfer number of such a gear is variable but, with an increase in the number of teeth, the range of its change decreases. The algorithm of wheel construction is given.

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Section: The Study Materials and Methodsmentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Designing an outer toothed gear whose wheel teeth are outlined by the logarithmic spiral arcs

Pylypaka

Kresan

Volina

et al. 2021

EEJET

Self Cite

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“…Під час роботи машин постійно виникає контакт частинок матеріалу з поверхнями робочих органів. У сільськогосподарському виробництві це стосується зокрема ґрунтообробних знарядь [5] та знарядь по видаленню навозу [6]. При сепарації матеріалу частинки рухаються по поверхні, яка здійснює коливальні рухи [7,8].…”

Section: аналіз останніх дослідженьunclassified

Research of particle movement on rough surface formed by screw movement of sinusoid under action of own weight

Volina¹

2020

Tehnìka ta energetika

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The differential equations of particle movement on a rough surface which is formed by the helical motion of a sinusoid under the action of the force of own weight were obtained in the article. The sinusoid is the axial cross-section curve of the helical surface and is located in the vertical plane. The obtained equations were solved by numerical methods and the trajectories of the particle on the helical surface were constructed. In addition, graphs of the change in the particle velocity and its distance from the axis of the surface were found, as a result of which the conditions when stabilization of the particle movement is possible were found. It is shown that in the general case, as a result of acceleration, the particle moves away from the axis of the surface and stops in one of its gutters. The depth and density of the gutters are controlled by changing the constant coefficients parameters. Also, a partial case at zero depths of the gutter, when the sinusoid turns into a straight line and the particle moves on the surface of the helical conoid, were considered.

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“…У працях більш вузького спрямування досліджуються різні аспекти покращення якості обробітку ґрунту такими знаряддями [6][7][8][9]. Визначено науковцями і перспективи подальшого вдосконалення дискових та інших ґрунтообробних знарядь [10,19,20,21,22]. В працях [11,12] теоретично обґрунтовано конструкцію грунтообробного знаряддя, в якому, в якості робочих органів використано гвинтові поверхні із відсіку розгортного гелікоїда.…”

Section: аналіз останніх дослідженьunclassified

Research of influence of constructive and technological parameters of developed variants of screws with screw working bodies rabbit

Klendii¹,

Klendii²,

Shatrov³

2020

Tehnìka ta energetika

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The purpose of the study is to establish the influence of design and technological parameters of the developed variants of the harrow with screw working bodies on the efficiency of earning plant residues. The object of research is the technological process of tillage with a harrow with screw working bodies. The subject of the study is the patterns of the process of earning crop residues depending on the change in the angle of attack of the working body, the step size of the screw working body and the depth of tillage On the basis of the complex of experimental researches the regression dependences for definition of percent of the area of a surface of a field with full earning of the vegetative rests by a harrow with screw working bodies are deduced. The response surfaces of the percentage of the surface area of the field with the full earning of crop residues ξ during tillage with a harrow with screw working bodies are constructed. It is established that the dominant influence on the percentage of the field surface area with full earnings of crop residues ξ has the depth of tillage h, then the angle of attack β of the battery of screw working bodies and the least affected step size of the screw working body T.

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External Rolling of a Polygon on Closed Curvilinear Profile

Cited by 19 publications

References 4 publications

Designing an outer toothed gear whose wheel teeth are outlined by the logarithmic spiral arcs

Designing an outer toothed gear whose wheel teeth are outlined by the logarithmic spiral arcs

Research of particle movement on rough surface formed by screw movement of sinusoid under action of own weight

Research of influence of constructive and technological parameters of developed variants of screws with screw working bodies rabbit

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