Design optimization of planetary gear trains under dynamic constraints and parameter uncertainty

In this work, the vibrational behavior of planetary gear trains is of concern as this can lead to detrimental effects including fatigue, comfort and acoustics. Lumped-parameter models are useful in early development phases of planetary gear sets to assess the modal response and optimize performance. This design phase is plagued by uncertainty, which if neglected can lead to drastically suboptimal designs. Methods are demonstrated here to optimally design planetary gear sets, which ensures proper performance with respect to resonance frequencies under parameter uncertainty. A parametric model is used to ascertain the resonance behavior of such free vibration. Lumped-parameter models are accurate in terms of eigenfrequencies and their eigenmodes, yet require extremely low computational effort, allowing for numerical optimization and uncertainty analysis. Methodologies utilizing optimization are introduced to design generic planetary gear trains; three formulations are shown. Mass and inertia terms are used as design variables. The frequency ranges have been avoided by formulating the constraint functions. The stiffness values of planetary gear sets are afflicted with uncertainty and correspondingly the stiffness parameters used in this lumped-parameter model are treated as intervals. Bounded intervals are used instead of statistical distributions, which are assumed to be unavailable in such early development phases. The uncertainty analysis is carried out using an efficient optimization-based minimization-maximization method