Моделирование динамики планетарных передач с элементами повышенной податливости

I A Pushkarev

doi:10.22213/2413-1172-2018-2-43-48

Authors

I. A. Pushkarev Kalashnikov ISTU

DOI:

https://doi.org/10.22213/2413-1172-2018-2-43-48

Keywords:

planetary gear, elements flexibility, dynamic, vibrations, natural frequency

Abstract

The increased elements flexibility of planetary gear promotes load alignment in wheel meshing, but creates danger of undesirable vibrations emergence. The research problem of dynamics of planetary gears with elements of the increased flexibility is relevant. The planetary gear is presented by a set of solid bodies (gearwheels) connected by the springs modeling elastic constraints in gear pair. The flexible epicycle is presented in the form of gear rim parts and separate teeth with elastic constraint between them which are at present in meshing. The mathematical model of dynamics of the planetary mechanism is made on the basis of Lagrange’s equations of the second kind. Nine generalized coordinates are considered. The generalized forces are: moments of the engine, forces of friction and useful resistance; the moment caused by torsion of an elastic axle of a sun gearwheel; elastic forces in wheels meshing, in satellites axles, between separate teeth of an epicycle. As a first approximation it is considered that planetary carrier’s angular speed is constant. It is also accepted that the sum of the moments of the engine, forces of friction and useful resistance is equal to zero; and the mass center of the satellite with respect to the planetary carrier doesn’t move. The system of nine differential equations is reduced to two equations of free vibrations of the satellite and a sun gearwheel. The meshing rigidity is expressed via the Young modulus and face width of gearwheels. The moments of inertia of wheels are accepted as for continuous disks; masses of wheels are determined with account of the filling coefficient. Analytical dependences for natural frequencies of free vibrations of the satellite and a sun gearwheel owing to teeth flexibility are received. Influence of a sun gearwheel diameter and gear ratio of the planetary mechanism on values of natural frequencies is investigated. The conclusion is made for the influence of the increased compliance of planetary gear elements on undesirable vibrations of the satellite and the sun gearwheel.

Author Biography

I. A. Pushkarev, Kalashnikov ISTU

Post-graduate

References

Equal strength optimal design of planetary gear transmission / W. Jiao, J. Yang, F. Ma, etc. // Nongye Jixie Xuebao. 2015. Vol. 46, no. 1. Pp. 359-364, 378.

Trubachev E., Savelyeva T., Pushkareva T. Practice of designe and production of worm gears with localized contact // Mechanisms and Machine Science. 2018. Vol. 51. Pp. 327-343.

Plekhanov F., Goldfarb V. Rational designs of planetary transmission, geometry of gearing and strength parameters // Mechanisms and Machine Science. 2016. Vol. 34. Pp. 285-300.

Plekhanov F. I., Ovsyannikov A. V. Load capacity of planetary transmission with internal gear engagement // Russian Engineering Research. 2011. Vol. 31, no. 9. Pp. 825-827.

Plekhanov F. I., Kuznetsov V. S. Deformability of elements of planetary transmission // Russian Engineering Research. 2010. Vol. 30, no. 6. Pp. 557-560.

Plekhanov F. I. Influence of gear deformability in a planetary transmission on the load distribution in tooth engagement // Russian engineering research. 2015. Vol. 35, no. 7. Pp. 485-488.

Plekhanov F. I. Deformability of units of a planetary gear and its effect on load distribution in gear meshes // Journal of Machinery Manufacture and Reliability. 2015. Vol. 44, no. 3. Pp. 227-231.

Plekhanov F., Goldfarb V., Vychuzhanina E. Load distribution in meshing of planetary gearwheels and its influence on the technical and economic performance of the mechanism // Mechanisms and Machine Science. 2018. Vol. 51. Pp. 117-137.

Plekhanov F. I., Kuznetsov V. S. Deformability of elements of planetary transmission // Russian Engineering Research. 2010. Vol. 30, no. 6. Pp. 557-560.

Распределение нагрузки в зацеплениях колес рациональных конструкций планетарных передач и его влияние на технико-экономические показатели привода / Ф. И. Плеханов, Е. Ф. Вычужанина, И. А. Пушкарев, А. С. Сунцов // Вестник ИжГТУ имени М. Т. Калашникова. 2017. № 2. С. 29-35.

Plekhanov F., Pushkarev A., Pushkarev I. Influence of layout features and parameters of planetary gear on its dynamics and strength characteristics // Mechanisms and Machine Science. 2018. Vol. 51. Pp. 481-494.

Chaos control of planetary gear trainbased on strategy of speed disturbance / J. Wang, T. Li, G. Jin, etc. // Jixie Qiandu. 2016. Vol. 38, no. 1. Pp. 21-26.

Plekhanov F., Pushkarev A., Pushkarev I. Influence of layout features and parameters of planetary gear on its dynamics and strength characteristics // Mechanisms and Machine Science. 2018. Vol. 51. Pp. 481-494.

Sondkar P., Kahraman A. A Dynamic Model of a Double-helical Planetary Gear Set // Mechanism and Machine Theory. 2013. Vol. 70. Pp. 157-174.

Nikolic-Stanojevic V., Dolicanin C., Veljovic L. A new model of the fractional order dynamics of the planetary gears // Mathematical Problems in Engineering. 2013. Vol. 2013. Pp. 932150.

Chaos control of planetary gear trainbased on strategy of speed disturbance / J. Wang, T. Li, G. Jin, etc. // Jixie Qiandu. 2016. Vol. 38, no. 1. Pp. 21-26.

Batinic V. J. Planetary gear dynamic response to mesh // Vojnotehnicki glasnik. 2013. Vol. 61, no. 1. Pp. 58-68.

Вибрации в технике : cправочник. Т. 3 : Колебания машин, конструкций и их элементов / под ред. Ф. М. Диментберга и К. С. Колесникова. М. : Машиностроение, 1980. 544 с.

Там же.