温度梯度下高速旋转叶片的非线性振动特性研究

High speed rotating blade is the critical hot end part of turbine, and it has a wide application background. During the operation of the gas turbine, high-temperature-burned gas impacts directly on the concave airfoil surface of the blade; however, the gas temperature near the convex surface is relatively low. Hence, there will exist a huge thermal gradient along the blade thickness, and slender blade will be pre-deformed. The presented project is aimed at the pre-deformed blade under thermal gradient, and trying to establish a nonlinear dynamic model of rotating blade, which is closer to the actual situation. The natural frequencies are calculated and the commensurable relationship of frequencies, which could introduce the internal resonance phenomenon, are determined under some parameter conditions, such as, thermal gradient, rotating speed and so on. Internal resonances are depended on the nonlinear order of the blade system and can cause the corresponding modes to be strongly coupled. The presented project intends to utilize the assumed mode method and multi-scale method to establish multi-dimensional nonlinear analysis system and reveal the energy interchange mechanism between the corresponding modes of the system. This study will help to understand the complex double-jumping, hysteresis, saturation phenomenon and evolution betweent the hardening spring and the softening spring. The results of present project will enrich the theory of nonlinear dynamics, and provide valuable information for the design of the turbine blade.

高速旋转叶片是涡轮机最关键的热端部件，具有广阔的工程应用背景。涡轮机工作过程中，高温燃气直接作用在叶片压力面，而叶片吸力面附近的燃气温度相对较低，导致叶片内部存在较大的温度梯度。对于细长叶片来说，其中轴线会产生弯曲，造成一定程度的预变形。本项目研究温度梯度作用下，考虑一定预变形的旋转叶片，建立更符合实际情况的动力学模型。在温度梯度、旋转速度等参数条件下，计算出系统的各阶固有频率，最终确定各阶固有频率之间可公度的关系，这就确立了内共振现象。内共振依赖于叶片系统中的非线性阶数，会引起相应模态之间很强的耦合效应。项目拟采用假设模态法和多尺度近似解析法，建立高维非线性的分析模型，去揭示叶片系统之间耦合的能量交换机制，有助于理解复杂的双跳跃现象、滞后现象、饱和现象以及软硬特性变化过程，探求出一些参数变化的规律。研究结果将丰富非线性动力学理论，并为涡轮机叶片的前期设计提供参考。

高速旋转叶片是涡轮机最关键的热端部件，具有广阔的工程应用背景。涡轮机工作过程中.，叶片内部存在温度梯度是不可避免的。本项目针对由温度梯度产生的具有一定预变形的旋转叶片，建立其精确的非线性动力学模型，从理论分析和数值仿真两个方面，讨论了预变形旋转叶片在2:1和3:1内共振条件下主共振、超谐波共振、亚谐波共振、组合共振、参数共振等十余种不同共振形式的可能性。阐释了预变形旋转叶片动力学模型所蕴含的不同形式共振机理。揭示了不同系数参数对旋转叶片在不同共振条件下的频响曲线，力响应曲线以及稳态区域的演变规律。探析了不同共振形式下单模态解和双模态解的存在性和稳定性。研究发现2:1内共振下单模态解和双模态解都是无条件存在的。而对于3:1内共振，只有单模态解是无条件存在的。在两种内共振下，稳定的单模态解和双模态解可能同时存在。在准确掌握预变形旋转叶片运动规律的基础上，研究了基于压电纤维复合材料的预变形旋转叶片内共振主动控制。发现当超过临界时滞时，闭环受控系统原有的平衡点失稳，系统将缓慢进入一个大振幅周期运动，从而丧失控制效果。本项目研究工作为深入掌握涡轮叶片服役环境下的非线性动力学行为，进而发展相应的振动抑制提供了理论基础。