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

风电行业面临的一个挑战是变速箱过早失效，造成重大停机和重大经济损失。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，对变速箱中行星轮系的振动和动力学进行详细的研究是提高变速箱可靠性的关键步骤。在这个问题上工作了几年后，我们团队的注意力被吸引到了环形(内部)齿轮上，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中的环形齿轮同时按顺序与3~5个行星齿轮啮合。为了减轻重量，它通常被设计成薄轮缘。在这种情况下，环的弹性和移动载荷两个效应变得突出，导致系统产生更复杂的共振，并影响整个变速箱的动力学。这项拟议中的研究将集中于研究薄环的这两个效应。系统地研究了薄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。本研究将采用解析、数值和实验相结合的方法。第一步是寻找新的方法，在考虑齿轮齿和一般支承(边界条件)的情况下计算环的自由振动。受迫振动将通过两种方式作为第二步进行调查。首先，齿轮啮合载荷被视为移动和随机的点力。目标是在不考虑环与PGT其余部分相互作用的情况下获得环的动态响应。其次，将随机移动载荷作用下的环件集成到整个PGT的动力学模型中。在这一步中，运载器、太阳和行星被建模为振动器，它通过弹簧(齿轮啮合)与环耦合。利用这两个模型，可以深入研究整个PGT的随机动力学。除了齿轮动力学固有的时变刚度外，移动载荷还引入了额外的时变参数。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种时变参数下的稳定性。短期目标是找到解决方案，以提高风力涡轮机变速箱的可靠性和预期寿命。从长远来看，这项研究计划的成果不仅旨在造福于风力发电行业，也将惠及其他相关领域，因为承受移动载荷的环形结构广泛应用于汽车、直升机、电机和发电机等。此外，经过非线性和随机振动理论培训的HQP将是加拿大工业界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.