Contact problem and numeric method of a planetary drive with small teeth number difference

This paper deals with a theoretical study on contact problem and numeric analysis of a planetary drive with small teeth number difference (PDSTD). A mechanics model and finite element method (FEM) solution are presented in this paper to conduct three-dimensional (3D) contact analysis and load calculations of the PDSTD through developing concepts of the mathematical programming method [T.F. Conry, A. Serireg, A mathematical programming method for design of elastic bodies in contact, Transactions of ASME, Journal of Applied Mechanics 38 (6) (1971) 387–392] and finite element method [S. Li, Gear contact model and loaded tooth contact analysis of a three-dimensional, thin-rimmed gear, Transactions of ASME, Journal of Mechanical Design 124 (3) (2002) 511–517; S. Li, Finite element analyses for contact strength and bending strength of a pair of spur gears with machining errors, assembly errors and tooth modifications, Mechanism and Machine Theory 42 (1) (2007) 88–114] to solve a more complex engineering contact problem. FEM programs are developed through many years’ efforts. Contact states of teeth, pins and bearing rollers of the PDSTD are made clear through performing contact analysis of the PDSTD with the developed FEM programs. It is found that there are only four pairs of teeth in contact for the PDSTD used as research object when it is loaded with a torque 15 kg m. It is also found that these four pairs of teeth are not located in the offset direction of the external gear. They are located at an angular position of 20–30° away from the offset direction. Loads shared by teeth, pins and rollers have big difference. The maximum load shared by the teeth is much greater than the ones shared by pins and rollers. This means that strength calculations of the teeth are more important than the ones of pins and rollers for the PDSTD. It is also found that all pins share loads while only a part of rollers share loads.