On the kinematics and kinetics of mechanical seals, rotors, and wobbling bodies

Mechanical seals, rotors, and wobbling bodies whirl about a point and are characterized by a kinematical constraint that prevents them from having integral motion with respect to the axis of whirl. A valid kinematical model is a prerequisite to subsequent dynamic analyses. Three previous works have suggested distinctly different kinematical models for the same problem. The analysis herein presents yet another kinematical model that preserves (actually enforces) the proper kinematical constraint. Interestingly, it is found that although no integral rotation is allowed about the axis of whirl, the wobbling body possesses a sustained nonzero angular velocity about that axis. The derivation is done for any finite nutation angle and only final results are being degenerated to small tilt angles. The outcome reaffirms the results of a previous work. For this time-invariant problem the notion of virtual velocity and virtual power emerges, and the equations of motion are derived using Lagrange’s equations to complement results obtained previously by Newton–Euler mechanics.