Research of the movement of a material particle on the surface of an oblique helicoid under the action of the force of own weight
DOI:
https://doi.org/10.31548/energiya2022.06.076Abstract
The problem that describes the movement of a particle along a helical surface is used in the design of spiral separators. Modeling the motion of a material particle on helical surfaces and its investigation by modern methods of numerical integration and visualization makes it possible to obtain a real picture of motion in the absence of full-scale models of such surfaces. This makes it possible to search for helical surfaces to improve their operational characteristics.
The purpose of the study was to establish the regularity of the movement of a material particle along an oblique helicoid depending on the structural parameters of the surface.
The oblique helicoid has two design parameters - the pitch h and the angle b of the inclination of the rectilinear generating surfaces to the horizontal plane. With the help of these parameters, there are more opportunities to influence the nature of the movement of a particle along an oblique helicoid compared to a helical conoid and a wide helicoid.
The differential equations of motion of a material particle on the surface of an oblique helicoid under the action of its own weight were formulated. The equations are solved by numerical methods. The obtained results were visualized
It has been established that the movement of a material particle with a known coefficient of friction along the surface of an oblique helicoid can be ensured at a given distance from its axis by combinations of structural parameters of the surface. At the same time, the resolution of the surface during the separation of particles with different friction coefficients practically does not change. However, in the transition period (before the stabilization of the motion), there is a significant difference in the trajectories of particle motion, which increases as the angle of inclination of the rectilinear generating surfaces decreases. This gives reason to consider material separation at the stage of the transition period, which requires further theoretical and experimental research.
Key words: oblique helicoid, material particle, trajectory of motionReferences
Vasilenko, P. M. (1960). Teoriya dvizheniya chastitsy po sherokhovatym poverkhnostyam sel'skokhozyaystvennykh mashin [Theory of particles movement on rough surfaces of agricultural machines]. Kyiv: UASKHN, 283.
Zaika, P. M., Maznev, G. E. (1978). Separatsiya semyan po kompleksu fiziko-mekhanicheskikh svoystv [Separation of seeds according to the complex of physical and mechanical properties]. Moskow: Kolos, 287.
Zaika, P. M. (1992). Izbrann·yye zadachi zemledel'cheskoy mekhaniki [Selected tasks of agricultural mechanics]. Kyiv: Izd-vo USKHA, 507.
Sysoyev N. I. (1949). Teoreticheskiye osnovy i raschet sortirovki “Zmeyka” [Theoretical basis and calculation of the "Snake" sorting]. Sel'khozmashina, 8, 5 – 8.
Voitiuk D. H., Pylypaka S. F. (2002). Znakhodzhennia traiektorii rukhu materialnoi chastynky po hravitatsiinykh liniichatykh poverkhniakh iz horyzontalnymy tvirnymy [Finding the trajectory of the movement of a material particle along gravitational linear surfaces with horizontal generators]. Zbirnyk naukovykh prats NAU “Mekhanizatsiia silskohospodarskoho vyrobnytstva”, 12, Kyiv: NAU, 58-69.
Voitiuk D. H., Pylypaka S. F. (2003). Znakhodzhennia traiektorii rukhu materialnoi tochky po hravitatsiinii rozghortnii poverkhni na prykladi rozghortnoho helikoida [Finding the trajectory of the movement of a material point along a gravitational unfolding surface on the example of an unfolding helicoid]. Mekhanizatsiia i enerhetyka silskoho hospodarstva. IV mizhnarodna naukovo-tekhnichna konferentsiia MOTROL-2003. Kyiv: NAU, 6, 113-126.
Pogorelov A. V. (1969). Differentsial'naya geometriya [Differential geometry]. Moskow: “Nauka, 176.
Voitiuk D. H., Pylypaka S. F. (2003). Osoblyvosti rukhu materialnoi chastynky po hravitatsiinykh liniichatykh poverkhniakh [Peculiarities of the movement of a material particle along gravitational linear surfaces]. Visnyk Kharkivskoho derzhavnoho tekhnichnoho universytetu silskoho hospodarstva. Mekhanizatsiia silskoho hospodarstva. 21, 75-88.
Downloads
Published
Issue
Section
License
Relationship between right holders and users shall be governed by the terms of the license Creative Commons Attribution – non-commercial – Distribution On Same Conditions 4.0 international (CC BY-NC-SA 4.0):https://creativecommons.org/licenses/by-nc-sa/4.0/deed.uk
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
