Vibration of High-Speed, Lightweight Gears

Planetary and other gears offer exceptional efficiency benefits in aircraft engines. The extremely high rotation speeds, need for lightweight components, and importance of avoiding any type of failure require new understanding and new methods to analyze the vibration of high-speed, lightweight gears. The Dynamics and Vibrations Lab initiated gear vibration research in 1996 working on helicopter, automotive, and wind turbine applications. The lab is among the most recognized research teams worldwide in gear and power transmission system vibration. Recently we have focused intensively on the emerging application of aircraft engine gears that demand new computational tools and analytical models compared to classical gear vibration research.

Unique Features and Methods in the Vibration of General Symmetric Systems

Symmetric systems have especially fascinating and highly structured vibration properties. Throughout the literature, symmetric systems are usually examined based on their own individual models. Recently lab members have pioneered the application of group theory, an elegant tool from mathematics, to analyze general symmetric systems. One can learn a great deal about vibration properties of a symmetric system based solely on its symmetry, without extensive computation and even without deriving the equations of motion for a system. When seeking to go further to calculate the response of a specific system, group theory offers tremendous computational advantages. It permits, for example, efficient analysis of aircraft engine bladed-disk assemblies with many millions of degrees of freedom. We plan to use these powerful tools to tailor specific and unusual material properties of metamaterials (materials specifically designed to behave in ways not possible with conventional solids) based on symmetry.

Computational Methods for the Vibration of Spinning Bodies

For a few reasons, it is difficult to apply finite element analysis and similar methods to rotating systems. One is the need to include Coriolis and centripetal acceleration terms that arise from high-speed rotation. These terms are usually formulated in a rotating reference frame and difficult to include in a fixed frame. In addition, rotating systems often couple with space-fixed components like contacting gear teeth, tire/road contact, disk brake/caliper interface, and so on. This also demands a fixed frame formulation that is not suitable for general spinning bodies. When the spinning bodies can be approximated as axisymmetric, which is common, an efficient fixed frame formulation is possible using a harmonic finite element (HFE) formulation we are developing. In addition to solving the problems mentioned, HFE is especially computationally efficient because it requires only a finite element mesh of a radial cross-section rather than the entire 3-dimensional body.