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

风力发电行业面临的一个挑战是齿轮箱过早失效，导致严重的停机时间和重大的经济损失。这个问题的主要原因是缺乏对动态的基本理解和准确预测。因此，对齿轮箱中的行星齿轮系（PGT）的振动和动力学的详细研究是提高齿轮箱可靠性的关键步骤。在这个问题上工作了几年后，我们的团队的注意力被吸引到了环形（内）齿轮，其动态特性在现有的建模技术中还没有得到很好的解释。PGT中的齿圈同时与3至5个行星齿轮顺序啮合。为了减轻重量，它通常设计有薄的轮辋。在这种情况下，环的柔性和移动负载这两个效应变得突出，从而对系统造成更复杂的共振，并影响整个齿轮箱的动力学。本研究将集中在薄环的这两个影响的调查。本文将系统地研究薄圆环在多个连续移动随机载荷作用下的自由振动、强迫振动和稳定性。分析，数值和实验的方法将用于这项调查。第一步将是找到新的方法来计算考虑齿轮齿和一般支撑（边界条件）的环的自由振动。强迫振动将作为第二步以两种方式进行研究。首先，齿轮啮合载荷被视为移动和随机点力。其目的是获得环的动态响应，而不考虑环和PGT的其余部分之间的相互作用。其次，将环在随机移动载荷作用下的动力学模型纳入到整个PGT的动力学模型中。在此步骤中，行星架、太阳轮和行星轮被建模为通过弹簧（齿轮齿啮合）与环耦合的振动器。利用这两个模型，可以彻底研究整个PGT的随机动力学。除了齿轮动力学中固有的时变刚度之外，移动载荷还带来了额外的时变参数。存在更复杂的共振（稳定性）。因此，在第三步中，将利用Floquet理论和摄动方法系统地研究系统在两类时变参数下的稳定性。短期目标是找到提高风力涡轮机齿轮箱可靠性和预期寿命的解决方案。从长远来看，这项研究计划的成果不仅有利于风力发电行业，而且还有利于其他相关领域，因为受到移动载荷的环状结构广泛应用于汽车，直升机，电动机和发电机等，此外，在非线性和随机振动理论方面受过训练的HQP将成为加拿大工业和学术界的宝贵财富。

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.