Mathematical descripton of winding helicoid section construction based on the predefined structural parameters
DOI:
https://doi.org/10.15587/1729-4061.2025.324542Keywords:
helicoid torso, return edge, parametric equations, tapering screw, support coilAbstract
The object of this study is a helical sweeping surface or a helicoid torso and the process of its design according to predefined structural parameters. Helical surfaces are widely used in engineering practice. They have become widespread in devices for transporting various materials, as well as in agricultural machinery. The problem is that when they are manufactured, the technique of their formation from the point of view of analytical description is not always taken into account. Helical surfaces can be linear and nonlinear. Linear surfaces, or helicoids, are formed by the helical motion of a straight-line generatrix around an axis, and the generatrix can intersect it or be coincident. If the straight-line generatrix intersects the axis at a right angle, then the helicoid will be a helical conoid, which is very common in technology under the name of a screw. Certain conditions are imposed on the helical motion of the straight-line generatrix of a helicoid torso. Its main advantage among other helicoids is the possibility of constructing an exact sweep. All other helicoids cannot be swept. For their manufacture, an approximate sweep is found, which is deformed into the desired shape. At the same time, the energy intensity of the process of deformation of this sweep into the finished product increases due to overcoming significant plastic deformations.
As a result of this research, dependences were established that make it possible to construct a set of helicoid torsos that pass through the predefined helical line. The results are based on the differential characteristics of the surface. These are their distinctive features from known results, according to which only one helicoid torso corresponds to the predefined helical line.
This paper shows the practical application of the helicoid torso as a supporting turn of the narrowing screw of a forage harvester with a radius of R=0.25 m of the outer edge and r=0.125 m of the inner one
References
- Klendii, M., Logusch, I., Dragan, A., Tsvartazkii, I., Grabar, A. (2022). Justification and calculation of design and strength parameters of screw loaders. Machinery & Energetics, 13 (4). https://doi.org/10.31548/machenergy.13(4).2022.48-59
- Trokhaniak, O. (2022). Estimation of eddy currents and power losses in the rotor of a screw electrothermomechanical converter for additive manufacturing. Machinery & Energetics, 13 (3). https://doi.org/10.31548/machenergy.13(3).2022.92-98
- He, K., Li, G., Du, Y., Tang, Y. (2019). A digital method for calculation the forming cutter profile in machining helical surface. International Journal of Mechanical Sciences, 155, 370–380. https://doi.org/10.1016/j.ijmecsci.2019.03.018
- Kresan, Т., Ahmed, A. K., Pylypaka, S., Volina, T., Voloshko, T. (2024). Construction of the working surfaces of the tillage screw body from the compartments of the developable helicoid. Machinery & Energetics, 15 (3), 9–21. https://doi.org/10.31548/machinery/3.2024.09
- Lyashuk, O. L., Gypka, A. B., Pundys, Y. I., Gypka, V. V. (2019). Development of design and study of screw working surfaces of auger mechanisms of agricultural machines. Machinery & Energetics, 10 (4). Available at: https://technicalscience.com.ua/en/journals/t-10-4-2019/rozrobka-konstruktsiyi-ta-doslidzhyennya-gvintovikh-robochikh-povyerkhon-shnyekovikh-myekhanizmiv-silskogospodarskikh-mashin
- Tian, F., Xia, K., Wang, J., Song, Z., Yan, Y., Li, F., Wang, F. (2021). Design and experiment of self-propelled straw forage crop harvester. Advances in Mechanical Engineering, 13 (7). https://doi.org/10.1177/16878140211024455
- Rynkovskaya, M. (2018). Support Draft Calculation for a Ramp in the Form of Developable Helicoid. IOP Conference Series: Materials Science and Engineering, 371, 012041. https://doi.org/10.1088/1757-899x/371/1/012041
- Junge, S., Zablodskiy, M., Zaiets, N., Chuenko, R., Kovalchuk, S. (2023). The screw-type electrothermomechanical converter as a source of multiphysical influence on the technological environment. Machinery & Energetics, 14 (3), 34–46. https://doi.org/10.31548/machinery/3.2023.34
- Zablodskiy, M., Kovalchuk, S., Gritsyuk, V., Subramanian, P. (2023). Screw electromechanical hydrolyzer for processing poultry by-products. Machinery & Energetics, 14 (1). https://doi.org/10.31548/machinery/1.2023.36
- Mushtruk, M., Gudzenko, M., Palamarchuk, I., Vasyliv, V., Slobodyanyuk, N., Kuts, A. et al. (2020). Mathematical modeling of the oil extrusion process with pre-grinding of raw materials in a twin-screw extruder. Potravinarstvo Slovak Journal of Food Sciences, 14, 937–944. https://doi.org/10.5219/1436
- Trokhaniak, O. (2023). Determination of optimal parameters of hinged operating elements of screw conveyers. Machinery & Energetics, 14 (1). https://doi.org/10.31548/machinery/1.2023.79
- Romasevych, Y., Loveikin, V., Malinevsky, O. (2022). The method of calculating the maximum torque when jamming the auger of the screw conveyor. Machinery & Energetics, 13 (2). https://doi.org/10.31548/machenergy.13(2).2022.83-90
- Pylypaka, S., Kresan, Т., Hropost, V., Babka, V., Hryshchenko, I. (2022). Calculation of the bending parameters of a flat workpiece into a twist of a helicoid torso. Machinery & Energetics, 13 (4). https://doi.org/10.31548/machenergy.13(4).2022.81-88
- Nieszporek, T., Gołębski, R., Boral, P. (2017). Shaping the Helical Surface by the Hobbing Method. Procedia Engineering, 177, 49–56. https://doi.org/10.1016/j.proeng.2017.02.181
- Tarelnyk, V. B., Gaponova, O. P., Konoplianchenko, Ye. V., Martsynkovskyy, V. S., Tarelnyk, N. V., Vasylenko, O. O. (2019). Improvement of Quality of the Surface Electroerosive Alloyed Layers by the Combined Coatings and the Surface Plastic Deformation. III. The Influence of the Main Technological Parameters on Microgeometry, Structure and Properties of Electrolytic Erosion Coatings. Metallofizika I Noveishie Tekhnologii, 41 (3), 313–335. https://doi.org/10.15407/mfint.41.03.0313
- Tarelnyk, V. B., Gaponova, O. P., Konoplianchenko, Ye. V., Martsynkovskyy, V. S., Tarelnyk, N. V., Vasylenko, O. O. (2019). Improvement of Quality of the Surface Electroerosive Alloyed Layers by the Combined Coatings and the Surface Plastic Deformation. II. The Analysis of a Stressedly-Deformed State of Surface Layer after a Surface Plastic Deformation of Electroerosive Coatings. Metallofizika I Noveishie Tekhnologii, 41 (2), 173–192. https://doi.org/10.15407/mfint.41.02.0173
- Chvartatskiy, I., Flonts, I., Grabar, A., Shatrov, R. (2021). Synthesis of energy-saving transport-technological systems with screw working bodies. Machinery & Energetics, 12 (4). Internet Archive. https://doi.org/10.31548/machenergy2021.04.077
- Gritsyuk, V., Nevliudov, I., Zablodskiy, M., Subramanian, P. (2022). Estimation of eddy currents and power losses in the rotor of a screw electrothermomechanical converter for additive manufacturing. Machinery & Energetics, 13 (2). https://doi.org/10.31548/machenergy.13(2).2022.41-49
- Klendiy, M. B., Drahan, A. P. (2021). Substantiation of the design of the working body of the screw section of the combined tillage tool. Perspective technologies and devices, 18, 66–72. https://doi.org/10.36910/6775-2313-5352-2021-18-10
- Kresan, T. (2021). Movement of soil particles on surface of developable helicoid with horizontal axis of rotation with given angle of attack. Machinery & Energetics, 12 (2). https://doi.org/10.31548/machenergy2021.02.067
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Copyright (c) 2025 Andrii Nesvidomin, Serhii Pylypaka, Tetiana Volina, Zinovii Ruzhilo, Olena Kozlova, Ivan Shuliak, Taras Pylypaka, Yaroslav Kremets, Olena Nalobina, Alla Rebrii
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