Random Vibration of an Internal Gear in Planetary Gear Trains Subjected to Sequential Moving Loads.

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A challenge faced by the wind power industry is the premature failure of gearboxes, causing significant downtime and major economic losses. The principal cause of this problem is a lack of fundamental understanding and accurate predictions of the dynamics. Thus, a detailed investigation on the vibrations and dynamics of the planetary gear train (PGT) in the gearbox is a critical step to improve the reliability of the gearbox. After working on this issue for several years, our team's attention was drawn to the ring (internal) gear whose dynamic properties are not yet well accounted for in existing modeling techniques. The ring gear in a PGT meshes with 3 to 5 planet gears in sequence simultaneously. It is generally designed with a thin rim for the sake of weight saving. In this case, two effects, the flexibility of the ring and the moving loads, become outstanding, causing more complicated resonances to the system, and affecting the dynamics of the whole gearbox. This proposed research will focus on the investigation of these two effects of a thin ring. The free vibration, forced vibration and stability of a thin ring under multiple, sequential moving random loads will be systematically investigated. Analytical, numerical and experimental methods will be used in this investigation. The first step will be to find new ways to calculate the free vibration of the ring with the gear teeth and general supports (boundary conditions) considered. The forced vibration will be investigated as the second step in two ways. First, the gear mesh loads are treated as moving and random point forces. The objective is to obtain the ring's dynamic response without considering the interaction between the ring and the remaining parts of the PGT. Secondly, the ring under random moving loads is integrated into the dynamics model of the whole PGT. The carrier, the sun, and the planets are modeled in this step as a vibrator which is coupled with the ring through springs (gear tooth meshes). Using these two models, the random dynamics of the whole PGT can be thoroughly investigated. The moving loads bring in extra time-varying parameters in addition to the inherent time-varying stiffness in gear dynamics. More complicated resonances (stability) exist. Thus, the stability of the system under the two types of time-varying parameters will be systematically investigated, in the third step, with the Floquet theory and perturbation methods. The short-term objective is to find solutions to improve the reliability and life expectancy of wind turbine gearboxes. In the long term, the outcome of this research program aims to benefit not only the wind power industry, but also other related areas given that ring-like structures subjected to moving loads are widely used in automotive, helicopters, electric motors, and power generators, etc. In addition, the HQP trained in nonlinear and random vibration theory will be a valuable asset to Canadian industry and academics.