Sharing behavior of load transmission on gear pair systems actuated by parallel arrangements of multiple pinions

• A load sharing index is proposed based on Floquet multipliers.
• The dynamic model of a gear system actuated by many pinions is presented.
• Load sharing behavior of various gear pairs relies on their mechanical parameters.
• The bearing stiffness of pinions and gear influences their load sharing behavior.
• The load sharing behavior is dependent on the mounting locations of pinions.

The load sharing performance of every pinion plays an important role for the fatigue life of gear systems which are driven by a parallel arrangement of multiple pinions. The lumped parameter dynamic model of a gear system actuated by many pinions is presented in this study. The Floquet multipliers are calculated based on the Floquet–Lyapunov theory. A load sharing index is proposed according to the minimum and maximum of the Floquet multipliers. The simplified dynamic model of an example gear system driven by two pinions simultaneously is presented, in which mechanical parameters such as meshing frequencies, bearing stiffnesses of pinions, mounting locations of pinions, and gear configuration coefficients are involved. The correlations of the load sharing behavior of every mesh gear pair and the mechanical parameters are discussed. The numerical results show that these parameters can affect the load transmission behavior of every mesh gear pair. Suitable mechanical parameters of gear systems are important for the load sharing performance of multiple mesh gear pairs which can reduce the internal stress in the gear structure and improve their fatigue life.