Multiport Models for the Kinematic and Dynamic Analysis of Gear Power Transmissions

The kinematics of a gear power transmission may be characterized by a power-conserving kinematic transformation between independent and dependent angular velocities. The conjugate of this transform provides a relation between input and output torques. A bond graph multiport representing these kinematic relations provides a power-conserving core to which dissipative, inertial, and compliance effects may be added. This dynamic model of a power transmission may be connected with other machine elements (such as other kinematic mechanisms, motors, driveshafts, and loads) to form large-scale, computable dynamic models. Bond graph techniques are shown to facilitate the process of developing and assembling computable dynamic models for the study of gear trains as elements of machine systems. A numerical example is presented.