Non-circular wheels made by congruent arches intersected at a straight angle
DOI:
https://doi.org/10.31734/agroengineering2022.26.046Keywords:
non-circular wheels, rolling of curves, mid-center distance, arc length, quadratic polynomialAbstract
The closed flat curves being the basis for projecting gear engagements are called centroids. Their characteristic feature is the continuity of the transfer function. However, many engineering problems require centroids with different transfer functions. In addition, there are devices (for example, counters) for which the type of transfer function is not essential, but the number of whole revolutions of the wheels is essential. Non-circular wheels are a pair of closed curves that rotate around fixed centers and roll over each other without sliding. Non-circular wheels serve as centroids in the constructing of gear cylindrical gears with a variable gear ratio. The article develops a method of constructing pairs of non-circular wheels, which consist of separate symmetrical arcs intersecting at a right angle. A quadratic polynomial is used to form the corresponding curves in the polar coordinate system. This approach enables creating two types of component non-circular wheels. In one case, they consist of convex elements, in the other – elements similar to the teeth of a toothed gear. The initial data for the design of wheels are the number of elements of the driving and driven wheels. Non-circular wheels can consist of any number of symmetrical arcs that intersect in pairs at right angles. It is established that the right angle is the minimum value of the angle at which non-circular wheels designed in this way can roll without jamming. A characteristic feature of the operation of pairs of wheels is the absence of sliding between the surfaces during operation. It does not cause frictional forces and does not lead to wear of working surfaces. The gear ratio is not constant, that is, when the driving wheel rotates with a constant angular velocity, the angular velocity of the driven wheel changes according to a periodic law. The number of periods for a complete rotation of the driven wheel is equal to the number of its teeth. The center-to-center distance is not specified, but is calculated depending on the number of wheel teeth.
References
Han, J., Li, D. Z., Gao, T., & Xia, L. (2015). Research on Obtaining of Tooth Profile of Non-Circular Gear Based on Virtual Slotting. In Proceedings of the 14th IFToMM World Congress (pp. 229-233).
Kovrehin, V. V., & Malovyk, I. V. (2011). Analitychnyi opys tsentroid nekruhlykh zubchactykh kolis. Pratsi TDATU, 4: Prykladna heometriia ta inzhenerna hrafika, 49, 125-129.
Kresan, T. A., Pylypaka, S. F., Hryshchenko, I. Yu., & Kremets, Ya. S. (2020). Modeliuvannia tsentroid nekruhlykh kolis iz vnutrishnim i zovnishnim kochenniam iz duh symetrychnykh kryvykh. Machinery & Energetics. Journal of Production Research, 11(4), 23-32.
Kresan, T., Pylypaka, S., & Ruzhylo, Z. (2020). External rolling of a polygon on closed curvilinear profile. Acta Polytechnica, 60 (4), 313-317.
Leheta, Ya. P. (2014). Opys ta pobudova spriazhenykh tsentroid nekruhlykh zubchastykh kolis. Suchasni problemy modeliuvannia, 3, 87-92.
Leheta, Ya. P., & Shoman, O. V. (2016). Heometrychne modeliuvannia tsentroid nekruhlykh zubchastykh kolis za peredavalnoiu funktsiieiu. Heometrychne modeliuvannia ta informatsiini tekhnolohii, 2, 59-63.
Lin, C., & Wu, X. (2019). Calculation and characteristic analysis of tooth width of eccentric helical curve-face gear. Iranian Journal of Science and Technology – Transactions of Mechanical Engineering, 43 (4), 781-797.
Lyashkov, A. A., Panchuk, K. L., & Khasanova, I. A. (2018). Automated geometric and computer-aided noncircular gear formation modeling. Journal of Physics: Conference Series, 1050 012049.
Okudaira, R., & Aoki, T. (2018). Development of rough terrain mobile robot with non-circular wheel. In The Proceedings of JSME annual Conference on Robotics and Mechatronics (Robomec) (pp. 1P2-G05).
Padalko, A. P., & Padalko, N. A. (2013). Zubchataya peredacha s nekruglyim kolesom. Teoriya mehanizmov i mashin, 2 (11), 89-96.
Pylypaka, S. F., Nesvidomin, V. M., Klendii, M. B., Rogovskii, I. L., Kresan, T. A., & Trokhaniak, V. I. (2019). Conveyance of a particle by a vertical screw, which is limited by a coaxial fixed cylinder. Bulletin of the Karaganda University – Mathematics, 95 (3), 108-118.
Ravska, N. S., & Vorobiov, S. P. (2011). Pytannia formoutvorennia tortsevymy frezamy zubchastykh kolis. Protsesy mekhanichnoi obrobky v mashynobuduvanni: Zb. nauk. prats, 11, 231-237.
Ravska, N. S., & Vorobiov, S. P. (2014). Vidkhylennia profiliu zuba arochnoho kolesa vid evolventnoho pry formoutvorenni tortsevymy riztsevymy holovkamy. Visnyk NTUU «KPI». Seriia mashynobuduvannia, 1 (70), 19-24.
Sobolev, A. N., Nekrasov, A. Ya., & Arbuzov, M. O. (2017). Modelyrovanye mekhanycheskykh peredach s nekruhlyimy zubchatyimy kolesamy. Vestnyk MHU «Stankyn», 1 (40), 48-51.
Ututov, N. P. (2011). Tsepnyie privodyi s nekruglyimi zubchatyimi kolyosami: Monografiya. Lugansk: Noulidzh.
