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Research on kinematics of contact interaction of cycloidal profiles in gerotor gearing

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Category: Geotechnical and mining mechanical engineering, machine building

Last Updated on 11 January 2018

Published on 11 January 2018

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Authors:

O.I. Skibinskyi, Candidate of Technical Science, Associate Professor, Central Ukrainian National Technical University, Senior Lecturer of the Department of Machinebuilding Technology, Kropyvnytskyi, Ukraine

A.O. Hnatiuk, Central Ukrainian National Technical University, Postgraduate Student, Kropyvnytskyi, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

Abstract:

Purpose. Determination of laws of movement of contact points of the conjugate profiles of the wheels of a gerotor gearing in the process of relative motion, analytical determination of motion velocities, identification of the nature of friction which results in gearing, identification of profile zones with the highest degree of friction.

Methodology. The research is based on the theory of non-centroidal cycloidal gearings, statements of differential geometry, and the laws of motion of the material point according to the trajectory which is defined by the function.

Findings. The result of the research is the identification of the accurate mathematical relations of the relative velocities of the contact point of two conjugate profiles in gerotor gearing. It was identified that there are two simultaneous velocities of contact points along the cycloidal profile and along the profile of the lantern gear. In this case the velocity vectors are located on the common tangent at the point of conjugation. They are different by module and their index depends on the phase of operation cycle.

Originality. The laws of movement of contact points in gerotor gearing were determined and the changing velocity mode in gearing was reliably established. In the process of research the universal formula of the relationship between the motion velocity of the points along the curved trajectory and its equidistant curve which takes account of trajectory curvature was obtained. It was established that in the interaction of the convex area of the equidistant curve with the cycloidal curve with conjugated lantern there is a sliding friction, while in the generating process of the concave area there is a rolling friction. The linearization functions which allow stabilizing the changing velocity mode were obtained.

Practical value. The research results enabled us to assess the impact of the velocity mode on the degree of friction in the points of conjugation of the profile surfaces, to localize the areas with the highest degree of friction and to find the ways of reducing the destructive impact of friction and to increase the stability of the profiles while gearing. The results may also be used in the process of development of the processing technology of the cycloidal profiles in the conditions of generating process with the linearization function of the velocity of relative generating process of the tool profiles and the workpiece. The linearization will stabilize the load and increase the processing accuracy.

References

1. Borislavov, B., Borisov, I. and Panchev, V., 2012. Design of a planetary-cyclo-drive speed reducer. Cycloid stage, geometry, element analyses. SwePart Transmission AB.

2. Lozica, I., Mirko, B., Goran, D. and Yasmina, A., 2010. Analitycal and numerical analysis of load gerotor pumps. Scientific and Technical Review Jornal, 60(1), pp. 30‒38 [online]. Available at: <http://is.fink.rs/podaci/Mirko_Blagojevic/63/4.pdf> [Accessed 24 May 2017].

3. Hao, L., Jae-Cheon, L., Yoon, A. and Sang-Tae, K., 2014. Profile design and numerical calculation of instantaneous flow rate of a gerotor pump. Journal of Applied Mathematics and Physics, 3, pp. 92‒97.

4. Skibinskyi, O. I., Hutsul, V. I., Hnatiuk, A. O., 2012. Research on terms of existence of working profile of center epicyclic transmission internal gear. Collection of scientific papers of KNTU, 1(25), pp. 238‒241.

5. Lozica, I. and Danica, J., 2006. Specific sliding of trochoidal gearing profile in the gerotor pumps. FME Transactions Jornal, 34, pp. 121‒127 [pdf]. Available at: <http://www.mas.bg.ac.rs/_media/istrazivanje/fme/vol34/3/1_lozica_ivanovic_121-127> [Accessed 24 May 2017].

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