Vibration Analysis and Health Diagnosis of Spinning Cyclic Symmetric Rotors with Flexible Bearing and Housing Supports

本文研究了具有柔性轴承和壳体支撑的旋转循环对称转子的振动和健康监测问题。有三个具体目标。第一个目标是建立一个数学模型来预测具有柔性轴承和外壳支撑的旋转循环对称转子的地面振动响应。基本思想是一个组件模式的综合允许转子和外壳假设任意几何。并对模型进行了实验验证。第二个目标是开发一种有效的算法来加速地面响应的计算。其基本思想是通过使用“平衡模式”来降低控制方程的阶数，这种模式不存在转子和壳体之间的耦合。第三个目标是研究通过壳体和轴承的振动特征监测转子健康的可行性。研究的主要焦点是循环对称转子，它经常出现在旋转机械中，如喷气发动机和冰箱压缩机。每台旋转机器由三个基本部件组成：一个旋转部件（转子），一个固定部件（外壳），以及连接旋转部件和固定部件的多个轴承。当转子由N个相同的子结构在圆周方向上重复时，转子被称为“循环对称”。循环对称转子的例子包括风力涡轮机和螺旋桨。传统的循环对称转子的振动分析假设(a)没有轴承和外壳支撑和(b)基于转子的公式。然而，最近的工业需求对这两种假设的有效性提出了挑战。随着材料和燃料成本的增加，航空工业寻求减轻发动机的重量和刚度，从而增加转子-轴承-壳体耦合振动。随着维护成本的增加，工业界寻求监测地面机器的响应，以评估高速旋转系统的健康状况。提出的研究不仅将通过消除两个主要假设来扩大对循环对称转子的认识，而且还将为行业提供基本的理解，以推进其产品。

This research is to study vibration and health monitoring of spinning cyclic symmetric rotors with flexible bearing and housing supports. There are three specific goals. The first goal is to develop a mathematical model to predict ground-based vibration response of a spinning cyclic symmetric rotor with flexible bearing and housing supports. The basic idea is a component mode synthesis allowing the rotor and housing to assume arbitrary geometry. Also, the model will be validated experimentally. The second goal is to develop an efficient algorithm to speed up calculations of the ground-based response. The basic idea is to reduce the order of the governing equation through use of "balanced modes" that do not present coupling between the rotor and the housing. The third goal is to study the feasibility to monitor rotor health via vibration signatures of the housing and bearings.The main focus of the research is cyclic symmetric rotors, which appear very often in rotary machines, such as jet engines and refrigerator compressors. Every rotary machine consists of three basic components: a rotary part (rotor), a stationary part (housing), and multiple bearings that connect the rotary and stationary parts. When a rotor consists of N identical substructures repeating themselves in the circumferential direction, the rotor is called "cyclic symmetric." Examples of cyclic symmetric rotors include wind turbines and propellers.Traditional vibration analyses of cyclic symmetric rotors assume (a) no bearing and housing supports and (b) rotor-based formulations. Recent industrial needs, however, challenge the validity of these two assumptions. With increased material and fuel costs, aviation industry seeks to reduce weight and rigidity of engines, thus increasing coupled rotor-bearing-housing vibration. With increased maintenance costs, industries seek to monitor ground-based machine response to evaluate the health of high-speed rotary systems. The proposed research will not only broaden the knowledge on cyclic symmetric rotors by removing the two major assumptions, but also provide the industry with fundamental understanding to advance its products.