The Effect of Manufacturing Errors and Deformability of Planetary Gears Elements on Load Distribution in Contact Zones

Multi-planet epicyclic gears are widely used in engineering due to their technical and economic indicators: high bearing capacity with small dimensions and weight, low power losses due to friction, and good vibroacoustic performance. To ensure the uniform load distribution in meshed gears, the sun gear is connected to the drive shaft through the clutch gear, and the planets are mounted on spherical bearings. However, due to the limited radial dimension, it is not possible to select a planet gear bearing of the required load capacity; while mounting the planet on two bearings leads to an uneven load distribution across the width of the planet gear crown. It is advisable that the planet consist of two gear wheels mounted by means of spherical bearings on the same axle. In this case, the load across the width of the crown of each planet gear is distributed evenly, while load distribution on the individual crowns is uneven. In this regard, it is important to study the rational design of the planetary gear where the carrier cheek is located between the series of planet gears. It improves deformability of the axle and the carrier cheek mating with the axle. It also significantly compensates for the inevitable errors of the mechanism and the negative effect of the sun gear torsional deformation on load distribution along the planet gear crowns and on technical and economic indicators of the drive. When solving the problem, the planet axle at the point of interface with the carrier cheek is considered as a beam on an elastic foundation. Thus, the law of load distribution over the thickness of the cheek is determined. It has a great influence on yielding of the axle and the distribution of the load in the meshed wheels. The coefficient of uneven load distribution along the crowns of a two-series planet is determined by solving the equations of displacement compatibility that include the yield of the gear train elements (sun gear, wheel teeth, axle and bearings of the planet gear, carrier cheek) and the initial separation of the teeth. To determine the stresses in the coupling zone of the planet axle and the carrier cheek, a computer model of the unit is used to perform a strength analysis.

References

[1] Syzrantsev V.N., Golofast S.L. Drives of Pipelines Block Valve based on the Pan Precess Gear. Global journal of researches in engineering, 2014, vol. 14, no. 2, pp. 15–17.

[2] 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.

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

[4] Singh A. Epicyclic load sharing map – development and validation. Mechanism and Machine Theory, 2011, vol. 46(5), pp. 632–646.

[5] Kraynev A., Salamandra K., Raghavan M. Synthesis of the Two-Stream Transmissions. Power Transmissions Proceedings of the 4th International Conference, Sinaia, Romania, June 20–23, 2012, pp. 335–345.

[6] Kahraman A., Ligata H., Singh A. Influence of ring gear rim thickness on planetary gear set behavior. Journal of Mechanical Design, Transactions of the ASME, 2010, vol. 132, is. 2, pp. 0210021–0210028.

[7] Boguski 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, Transactions of the ASME, 2012, vol. 134, article no. 071002.

[8] 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.

[9] Nakhatakian F.G. Analiticheskoe opredelenie kontaktnoi podatlivosti rolikovykh podshipnikov [Analytical determination to contact softness roller bearing]. Privody i komponenty mashin [Machine drives and parts]. 2013, no. 5, pp. 21–22.

[10] Chermenskii O.N., Fedotov N.N. Podshipniki kacheniia. Spravochnik-katalog [The rolling bearings. Directory]. Moscow, Mashinostroenie publ., 2003. 575 p.