Vibrational behavior of epicyclic gear trains with lumped-parameter models: Analysis and design optimization under uncertainty

Vibrational behavior of epicyclic gearing a critical aspect as this can lead to detrimental structural-mechanical effects including fatigue, comfort and acoustics. In order to better understand this behavior, lumped-parameter models are used in early development phases. Here the eigenfrequencies as well as frequency responses are ascertained with and without consideration of uncertainty. Uncertainty is critical in the early design phases and beyond. In such systems, there is variation in parameter values from a variety of sources. Here the uncertain stiffness will be considered. It is also the goal of this work to dimension the epicyclic gear train to optimize performance. The early design phase is plagued by uncertainty and if this is neglected in the design optimization, this can lead to drastically suboptimal designs. In this work, a methodology is introduced to optimally design and dimension epicyclic gear trains under uncertainty. Though specifically aimed at epicyclic gearing, the methods developed here are general enough for further application fields. Mass and inertia terms are chosen as design variables, though others are possible in this framework. The constraints are so formulated so that the eigenfrequencies avoid the harmonics of the mesh frequencies and its side bands. The uncertain parameters are treated as bounded and therefore intervals are used instead of statistical distributions. Statistical information needed for probabilistic methods of the uncertain parameters are assumed here to be unavailable in early development phases.