Vibration Absorbers for Systems with Cyclic Symmetry

这项工作的目的是研究阶调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、叶盘(整体盘叶片系统)和直升机旋翼叶片。这些柔性结构以恒定速度旋转，并受到行波动态载荷的影响，导致部件振动，可能导致高周疲劳失效、噪声、性能降低等不良影响。减少这些振动和随之而来的问题的一个自然方法是实施调谐吸振器。离心力驱动的阶调吸振器非常适合于这项任务，然而这种方法迄今很少受到关注。本项目将考虑系统地研究阶调吸振器在单个旋转柔性部件和相互连接的子结构的循环系统中的性能。这些减振器的基本设计特征将通过考虑装有减振器的旋转结构元件的模型层级来探索。结构构件的模型范围从单自由度振子到基于工业的有限元模型。减振器模型的特点将集中在与设计相关的参数上，特别是：减振器在主结构上的位置、减振器相对于主结构的质量比、减振器行进的路径(设置其线性和非线性调谐参数)以及当减振器达到其发出响声的空间限制时的冲击效果。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叉技术、冲击运动的匹配方法、混合时频域技术和运动方程的模拟。破坏完美循环对称性的不可避免的缺陷(如叶片失谐)的影响也将被考虑在内。众所周知，子系统之间的某些模式的失谐可以显著降低最坏情况下的强迫响应水平，我们将检查使用调谐到不同阶次的吸振器来实现这些效果的有效性。在这种情况下，吸振器将起到双重作用：减弱它们所连接的叶片中的振动，以及提供一种系统失谐模式，以减少整个结构中的振动。这些分析的总体目标是提供可用于帮助选择吸振器参数以获得最佳性能的预测工具。如上所述，拟议的研究将影响对吸振器性能的基本理解，还将涉及教育、推广和技术转让。在教育方面，PIS将在本科和研究生的标准振动课程中包括对这些系统的线性振动分析，系统的一些非线性方面将被用作研究生课程中关于非线性振动的激励范例和练习。此外，密歇根州立大学PI还参与了一个暑期推广计划，让高中生接触机械工程专业。向学生介绍的一个主题是减振器的实际应用，它们在喷气发动机涡轮叶片等系统中的应用将自然而然地符合该课程的要求。在技术转让领域，密歇根大学PIS在透平机械领域拥有丰富的经验，并与许多行业联系。研究结果将与飞机发动机制造商的代表分享，预计吸波装置的工作将在一定程度上受到与他们讨论期间提出的考虑的指导。总体而言，目标将是将通过这项研究获得的基本知识转移到课堂上，转移到有抱负的年轻工程师和行业中。

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.