基于变参数环板等效叶片组的叶盘模型耦合振动分析方法

转子系统常见于旋转机械装置中,在航空、电力、化工等工业和民用的诸多行业中发挥着重要作用.转子系统一般由轴和多级叶轮组成,存在强度、疲劳、振动和噪声等一系列问题,亟待通过优化设计等手段提高产品的各项性能.由于每级叶轮都含有由多条叶片构成的叶片组,因此在应用有限元等方法分析时,即便利用了回转周期的性质,转子系统的整体自由度数目依然庞大,优化设计的计算效率有待提高.为了提高转子系统分析的效率,可将根据气动性能要求设计的单级叶盘视为状态已经确定的子系统,在具备足够计算精度的前提下对其有限元模型进行缩聚或简化,以降低整体系统的自由度.文章介绍叶片组模型的等效建模方法,以固有振动特性相近为等效准则,将有限元模型中周向环绕的叶片组等效为变参数圆柱型正交各向异性环形板,并通过理论推导和计算得到了环板模型的几何与材料等物理参数.以航空发动机低压涡轮叶盘模型为例,实现了叶片组的模型等效过程.结果表明,等效方法可在保证精度的前提下大大降低模型的自由度数目,为后续整体转子系统的优化设计提供了高效的叶盘建模方法.

A coupled vibration analysis method of bladed disk modelbased on equivalent blade group of annular plate with variable parameters

Rotor systems are mostly applied in rotary mechanical devices, which play important roles in aviation, electric power, mechanical and many other industries. These systems usually consist of shafts with multistage impellers, but a series of issues related to strength, fatigue, vibration and noise are needed to be solved. It is in an urgent to improve the performance of such products by optimization method. In rotor system, each impeller contains a blade group that composed of dozens of blades, so the DOF of the entire rotor system is still large, although the rotation period characteristics of bladed disk is used in finite element method. Therefore, the calculating efficiency is still needed to be improved. For this purpose, the single bladed disk can be regarded as a designed subsystem according to aerodynamic performance requirements, and the simplification of the finite element model for the blade group is an effective way to improve the computational efficiency of coupled vibration of bladed disk under the premise of obtaining enough precision. In this paper, an equivalent analysis method is put forward to simplify the blade group into an annular plate with variable parameters based on the criterion that dynamic characteristics can be approximately the same. Physical parameters of annular plate including geometric and material parameters are obtained by theoretical derivation and calculation. Eventually, the equivalent method is verified by taking a bladed disk model of aero engine as an example. It shows that model reduction can ensure the precision with improving computational efficiency. Therefore, the equivalent analysis method is an efficient modeling approach of bladed disk for the future optimization of the whole rotor systems.