Whirl Dynamics of Pendulous Flywheels Using Bond Graphs

Bond graphs are used to generate the equations of motion of a whirling flywheel. The formulation is shown to be a natural one when control forces and moments are included for active control of the whirling modes. Critical frequencies are interpreted as rotational speeds at which non-zero equilibrium configurations exist for displacements (as opposed to the more familiar momenta) and arise when the system dynamics matrix of the complete whirl motion has two zero eigenvalues. In addition, oscillatory modes corresponding to non-zero eigenvalues are examined. Time simulations and other numerical results are given for an example flywheel system which has been proposed for electric utility energy storage.