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Static Torque Sharing Distribution of Planetary Gear Sets Generated by Manufacturing Error Distribution

Article of Honda R&D Technical Review Vol.22 No.1

Summary

Creating an appropriate design for gear strength in a planetary gear set requires that manufacturing errors be grasped statistically and that the distribution of torque to the planet gears due to manufacturing errors be projected. This article describes the derivation of an expression of relation between manufacturing errors and the torque applied to planet gears in a common n-planet planetary gear set. As a result, a formula expressing the distribution of torque to the planet gears could be obtained. Tests were also conducted to verify the relational expression, and its validity was confirmed. In order to project the distribution of torque, it was necessary to estimate the stiffness of the planetary gear set in the relational expression. Those stiffness values were calculated by numerical analysis using a 3D finite element model (FEM) to which the plan values and material property values were entered. The accuracy of the estimated stiffness values was verified by testing, and it was confirmed that the stiffness values could be estimated with a high degree of accuracy. Given the above, the distribution of torque to planet gears due to manufacturing error in a common n-planet planetary gear set could be estimated with a high degree of accuracy using only estimated data obtained by desktop methods.

Reference

(1) Hayashi, T., Takahashi, T., Ishikawa, J.: Load Balancing Theory on a Planetary Gearing, Transactions of the Japan Society of Mechanical Engineers, Vol. 36, No. 288, p.1394-1404 (1970)
(2) Hidaka, T., Terauchi, Y., Dohi, K.: On the Relation between the Run-Out Errors and the Motion of the Center of Sun Gear in a Stoekicht Planetary Gear, Transactions of the Japan Society of Mechanical Engineers, Vol. 44, No. 385, p. 3221-3230 (1978)
(3) Hidaka, T., Sugimoto, N., Ishida, T.: Effects of Errors of Elements on Load Distribution in Planetary Gears with Various Load Equalizing Mechanisms, Transactions of the Japan Society of Mechanical Engineers. C, Vol. 52, No. 480, p. 2200-2206 (1986)
(4) Shirokoshi, N., Hidaka, T., Kasei, S.: Studies on Influences of Geometrical Errors to Final Performances in Small Backlash Planetary Gear: Modeling and Simulations on Load Distribution, Transmission Error, and Sun Gear Radial Displacement, Transactions of the Japan Society of Mechanical Engineers. C, Vol. 65, No. 633, p. 2014-2021 (1999)

Author (organization or company)

Hiroki KAKIUCHI(Automobile R&D Center)

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