Motion, Static Force, and Efficiency Analysis of Planetary Gear Transmission Based on Graph Theory

Abstract

This paper employs graph theory to analyze kinematic relationships, static force, and power flow for planetary gear systems. We start from the graphs of these trains to determine all the structurally distinct kinematic inversions. We then obtain all the constructive solutions resulting from every possible combination of gear configuration. Based on the kinematic and static force analysis model, related matrices are acquired. Hence, a kinematic and static force analysis of the planetary gear mechanism is achieved. The link power can be determined by the link speed and torque. Power flow diagrams of each gear are acquired. The efficiency is calculated by the transmission ratio method. This analysis is useful in the design of power transmission applications. A planetary gear system of a 6HP26 automatic transmission is further illustrated for the motion, static force, and efficiency calculations by using graph theory technique and matrix equations. This paper provides a guide for engineers in gear transmission fields to easily finish mechanical transmission design.

Research on Kinematics and Efficiency Calculation of Binary Logic Planetary Gearbox Based on Graph Theory

“…Many scholars began to study this. H Xue et al [17] used graph theory to analyze the kinematics, static force and power flow of planetary gear systems. EL Esmail et al [18] used graph theory to represent planetary gear trains (PGT), developed a procedure to identify fundamental leverage entities (FGE) and developed an algorithm to detect the degenerate structure of PGTs using the concept of FGEs and the notation of related adjacency matrices.…”