Graph-theoretic modelling of epicyclic gear systems

摘要

New graph theoretic models of gears, gear trains and geared systems are developed, which are suitable for computer aided kinematic and dynamic analyses. A lumped parameter model of ideal non-deforming gears is used. Methodologies of modelling of rigid bodies and linkages using graph theory are extended to include gear members. Rigid arms model the contact between the gear pair. Gear pair-carrier assemblies are modelled as multi-terminal subsystems. A hyper-edge in the rotation graph representing the three bodies of the gear pair-carrier trio has the fundamental law of gearing constraint as an associated terminal equation. Gear pair-carrier subassemblies are over constrained kinematically. Assuming that the gear pair and carrier dimensions are designed so that the constraints are satisfied identically, the system can be seen as having excess consistent equations kinematically and dynamically which may be set aside during the analysis of the system. The methodology is applied to planar involute profile spur gear systems but may be extended further. Example models for fixed, epicyclic and planetary gear trains are developed. A detailed model and analysis of a gear slider mechanism is given.