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.
In recent years, bond graphs have been used to analyze complex dynamic systems. In this paper a bond graph study is made of the kinematics and dynamics of a general mechanism treated as a component of a dynamic system. The method is applicable to multiple-loop, multiple degree-of-freedom mechanisms for which the displacement and velocity loop equations are known. A bond graph multiport representing the kinematic relations forms a power-conserving core to which dissipative, inertial, and compliance effects may be added to form a dynamic mechanism model. A constitutive relation suitable for automatic computation is derived in terms of system variables. A numerical example is presented illustrating an application of the technique.
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