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TECHNICAL BRIEFS

Mesh Phasing Relationships in Planetary and Epicyclic Gears

[+] Author and Article Information
R. G. Parker

Department of Mechanical Engineering, Ohio State University, Columbus, OH 43210 e-mail: parker.242@osu.edu

J. Lin

John Deere Corporation, Waterloo, IA 50704-8000

J. Mech. Des 126(2), 365-370 (May 05, 2004) (6 pages) doi:10.1115/1.1667892 History: Received January 01, 2003; Revised July 01, 2003; Online May 05, 2004
Copyright © 2004 by ASME
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References

Figures

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Planetary (or epicyclic) gear system. us,uc,ur,u1,2,3 denote vibrational degrees of freedom (not nominal rotation direction or speed)
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Definition of mesh phase quantities γsnrnrs. Without loss of generality, γs1=0 and t=0 corresponds to pitch point contact at the sun-planet 1 mesh. The symbol *   denotes pitch point contact.
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(a) Example mesh tooth variation functions showing the number of teeth in contact. P is the pitch point. p denotes the base pitch. (b) Sun-planet and ring-planet mesh details. Rsb,Rpb,Rrb denotes base radii. Rso,Rpo indicate sun and planet outer radii; Rro is the inner radius of the ring gear teeth. α1,2 are pressure angles. The points B , C , P , D , and E at each of the two meshes correspond to the points indicated in (a).
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Mesh tooth variations at each of the sun-planet and ring-planet meshes for the example system with fixed ring and counter-clockwise carrier input (clockwise planet rotation) as derived using finite element/contact mechanics software for involute teeth at no load. Each curve fluctuates between one and two. The symbol* denotes pitch point contact. The results agree with (1), (20), and the sign of γrs>0 as dictated by Table 1 and Table 2.
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Mesh tooth variations at each of the sun-planet and ring-planet meshes for the example system with fixed ring and clockwise sun input (counter-clockwise planet rotation) as derived using finite element/contact mechanics software for involute teeth at no load. Each curve fluctuates between one and two. The symbol* denotes pitch point contact. The results agree with (2), (20), and the sign of γrs<0 as dictated Table 1 and Table 2.

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