Vibration Absorbers for Systems with Cyclic Symmetry

本工作的目的是研究阶调谐吸振器在循环和近循环系统中的减振性能。感兴趣的应用是结构系统，如涡轮叶片，叶片盘组件，圆盘（整体圆盘-叶片系统），和直升机旋翼叶片。这些柔性结构以恒定的速度旋转，并受到行波动载荷的影响，导致组件振动，从而导致高周疲劳失效、噪音、性能降低和其他不良影响。减少这些振动及其伴随问题的自然方法是实现调谐振动吸收器。离心驱动的、有序调谐的吸振器非常适合这项任务，但迄今为止，这种方法很少受到关注。本项目将考虑对单个旋转柔性部件和相互连接子结构的循环系统中有序调谐吸振器的性能进行系统研究。这些吸波器的基本设计特征将通过考虑装有吸波器的旋转结构元件的层次模型来探讨。结构构件的模型将从单自由度振荡器到基于工业的有限元模型。吸收器模型的特征将集中在与设计相关的参数上，具体而言：吸收器在主结构上的位置，吸收器相对于主结构的质量比，吸收器行进的路径（设置其线性和非线性调谐参数），以及当吸收器达到其振动空间限制时的冲击影响。这些系统的响应将通过利用系统的对称性来分析，并将利用一系列工具，包括循环系统的线性振动分析，对称非线性系统的摄动和分岔技术，冲击运动的匹配方法，混合时频域技术和运动方程的模拟。不可避免的破坏完美循环对称的缺陷（如叶片失谐）的影响也将被考虑。众所周知，子系统之间的某些失谐模式可以大大降低最坏情况下的强制响应水平，我们将检查使用调谐到不同阶的吸收器来实现这些效果的有效性。在这种情况下，减振器将起到双重作用：减弱它们所附着的叶片的振动，以及提供一种系统失谐模式，以减少整体结构的振动。这些分析的总体目的是提供预测工具，可用于帮助选择吸收器参数以获得最佳性能。如上所述，拟议的研究将影响对减振器性能的基本理解，并且还将涉及教育，推广和技术转让。在教育方面，pi将包括这些系统的线性振动分析，在本科生和研究生水平的标准振动课程中，系统的一些非线性方面将被用作非线性振动研究生课程的激励例子和练习。此外，密歇根州立大学的pi还参与了一个暑期拓展项目，让高中生接触机械工程专业。向学生们展示的一个主题是减振器的实际应用，而减振器在喷气发动机涡轮叶片等系统中的应用将是该项目的自然选择。在技术转让领域，密歇根大学的pi在涡轮机械领域有相当丰富的经验，并有一些工业联系。研究结果将与飞机发动机制造商的代表分享，预计吸收器的工作将部分以与他们讨论期间提出的考虑为指导。总的来说，我们的目标是将这项研究获得的基本知识转化为课堂、年轻的有抱负的工程师和工业。

The goal of this work is to investigate the performance of order-tuned absorbers for vibration reduction in cyclic and nearly cyclic systems. The applications of interest are structural systems such as turbine blades, bladed disk assemblies, blisks (integral disk-blade systems), and helicopter rotor blades. These flexible structures rotate at a constant speed and are subjected to traveling wave dynamic loading, resulting in component vibrations that can cause high cycle fatigue failure, noise, reduced performance, and other undesirable effects. A natural means of reducing these vibrations and their attendant problems is the implementation of tuned vibration absorbers. Centrifugally-driven, order-tuned vibration absorbers are ideally suited for this task, yet this approach has received scant attention to date.This project will consider a systematic study of the performance of order-tuned vibration absorbers in individual rotating flexible components and in cyclic systems of interconnected substructures. The basic design features of these absorbers will be explored by considering a hierarchy of models for rotating structural elements fitted with absorbers. The models for the structural members will range from single-degree-of-freedom oscillators to industry-based finite element models. The features of the absorber models will be focused on design-related parameters, specifically: the placement of the absorber on the primary structure, the absorber mass ratio relative to that of the primary structure, the path along which the absorber travels (which sets its linear and nonlinear tuning parameters), and the effects of impacts when the absorber reaches its rattle space limitations. The response of these systems will be analyzed by exploiting the symmetry of the system and will utilize a range of tools that includes linear vibration analysis for cyclic systems, perturbation and bifurcation techniques for symmetric nonlinear systems, matching methods for impacting motions, hybrid time-frequency domain techniques, and simulations of equations of motion. The effects of unavoidable imperfections that destroy the perfect cyclic symmetry (such as blade mistuning) will also be considered. It is known that certain patterns of mistuning among subsystems can drastically reduce worst-case forced response levels, and we will examine the effectiveness of using absorbers tuned to different orders to achieve these effects. In this case the absorbers will serve a dual purpose: to attenuate vibrations in the blade to which they are attached, as well as to provide a pattern of system detuning that reduces vibrations in the overall structure. The general aim of these analyses will be to provide predictive tools that can be used to help select absorber parameters for optimal performance.The proposed research will impact the fundamental understanding of the performance of vibration absorbers, as described above, and will also involve education, outreach, and technology transfer. In terms of education, the PIs will include the linear vibration analyses of these systems in standard vibration courses at both the undergraduate and graduate levels, and some of the nonlinear aspects of the systems will be used as motivating examples and exercises for graduate courses in nonlinear vibrations. In addition, the Michigan State University PIs are involved in a summer outreach program that exposes high school students to the mechanical engineering profession. One topic presented to the students is the practical use of vibration absorbers, and their application to systems such as turbine blades in jet engines will be a natural fit into that program. In the area of technology transfer, the University of Michigan PIs have considerable experience in the area of turbomachinery, and a number of industrial contacts. The results of the research will be shared with representatives from aircraft engine manufacturers, and it is anticipated that the work on absorbers will be guided in part by considerations raised during discussions with them. Overall, the goal will be to transfer the basic knowledge gained by this research into the classroom, to young aspiring engineers, and to industry.