Load Distribution in Engaged Multi-Row Planetary Gears and its Impact on Technical and Economic Performance of the Mechanism

As the radial dimension of a planetary gear is limited, it is difficult to place bearings of the required capacity in the satellites, therefore such gears are usually arranged in multiple rows. However, the torsional deformation of the sun gear, having in this case a greater width, leads to uneven load distribution on the rows of satellites, thus reducing the effect of multi-row transmission.  In this regard, the study of load distribution in the engaged gears and the development of measures aimed at reducing its unevenness is relevant. Important issues to address are the extent of the impact of the gear parameters on load distribution in the rows of satellites, development of a rational design of the carrier, and optimization of the mechanism parameters. To determine the coefficient of uneven load distribution caused by the deformation of the sun gear, the angles of the gear torsion in the section passing through the plane of symmetry of the rims of satellites are determined, and a system of equations for simultaneity of displacements of the transfer elements is formulated. Having the carrier with bridges of different widths facilitates balancing the loads in the engaged gears, so the dimensions of the bridges are chosen so that their deformation is consistent with the torsional deformation of the sun gear and bending of the satellite axes. The ratio of the gearing mass to the torque on the output shaft is determined by performing the external gear strength analysis. It has been found that when the number of satellites is equal to three or more, the coefficient of uneven load distribution in the engaged gears is unacceptably high. By using the proposed design of the carrier and selecting its rational parameters, it is possible to minimize this unevenness, reduce the gearing mass, and consequently, reduce its cost.

References

[1] Plekhanov F.I. Zubchatye planetarnye peredachi. Tipy, osnovy kinematiki, geometrii i rascheta na prochnost’ [Planetary gear transmission. Types, basics of kinematics, geometry and strength calculation]. Izhevsk, Udmurtiia publ., 2003. 200 p.

[2] Timofeev G.A., Samoilova M.V. Silovoi raschet kombinirovannogo planetarno-volnovogo mekhanizma s generatorom voln vneshnego de-formirovaniia [Stress analysis of Combined Planetary-Wave Gear with Generator of Waves of External Deformation]. Vestnik MGTU im. N.E. Baumana. Ser. Mashinostroenie [Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering]. 2010, no. 4, pp. 17–22.

[3] Talbot D., Li.S., Kahraman A. Prediction of mechanical power loss of planet gear roller bearings under combined radial and moment loading. Journal of mechanical design, 2013, vol. 135, is. 12, article no. 121007.

[4] Kissling U., Dinner H. A procedure to determine the optimum flank line modification for planetary gear configurations. International gear conference, 26–24 august 2014, France, Lyon –Villeurbanne, pp. 65–76.

[5] Reshetov L.N. Samoustanavlivaiushchiesia mekhanizmy. Spravochnik [Aligning mechanisms. Directory]. Moscow, Mashinostroenie publ., 1991. 288 p.

[6] Plekhanov F.I., Tonkikh A.S., Vychuzhanina E.F. Osobennosti proektirovaniia i tekhniko-ekonomicheskie pokazateli planetarnykh peredach burovykh ustanovok [Planetary gear rigs: design features and technical-economic indicators]. Neftianoe khoziaistvo [Oil Industry]. 2015, no. 6, pp. 44–46.

[7] Volkov G.Iu., Ratmanov E.V., Kurasov D.A. Adaptivnaia sistema korrektsii pogreshnostei naklona zub’ev v zubchatykh peredachakh [Self-organizing system of adjustment of inclination teeth error in gear units]. Vestnik mashinostroeniia [Russian Engineering Research]. 2013, no. 3, pp. 14–16.

[8] Parker R., Wu X. Parametric instability of planetary gears with elastic continuum ring gears. Journal of vibration and acoustics, 2012, vol. 134, is. 4, article no. 041011.

[9] Boduski B., Kahraman A., Nishino T. A new method to measure planet load sharing and sun gear radial orbits of planetary gear sets. Journal of mechanical design, 2012, vol. 134, is. 7, article no. 071002.

[10] Plekhanov F.I., Plekhanov A.D. Mnogoriadnaia planetarnaia peredacha [Multiple-row epicyclic gear]. Patent RF no. 2581222, 2015.

[11] Talbot D., Kahraman A., Singh A. An experimental investigation of the efficiency of planetary gear sets. Journal of mechanical design, 2012, vol. 134, is. 2, article no. 021003.