This article presents a methodology dedicated to the vibration analysis of turbomachine blades accounting for both geometric nonlinearities and nonlinear blade-tip/casing contacts in a numerically efficient way through the use of reduced order models. Contact is numerically handled with Lagrange multipliers and the equation of motion is integrated forward in time using an explicit central difference time integration scheme. Nonlinear internal forces caused by large displacements are evaluated using the stiffness evaluation procedure. Three reduction techniques are compared in this article, namely a nonlinear extension of the Craig–Bampton method, the proper orthogonal decomposition and a modal derivatives-based approach. These numerical methods are applied on an open industrial compressor blade model, the NASA rotor 37 blade, in order to promote reproducibility of results. The reduction methods are first applied to the blade subjected to a harmonic excitation, without contact interactions. An indicator accounting for both local and global comparison criteria is defined to more easily compare the performance of each method. When also accounting for blade-tip/casing contacts, the presented results underline that the modal derivatives-based approach is particularly well-suited for an accurate description of the blade’s dynamics. This method is then employed for an in-depth analysis of the NASA rotor 37 vibration response over a wide angular speed range considering a typical contact scenario. Obtained results feature time and frequency domain signals along with stress fields. They suggest that accounting for geometric nonlinearities has a strong impact on the prediction of contact initiated interactions.

本文介绍了一种专用于涡轮机叶片振动分析的方法，该方法通过使用降阶模型以数值有效的方式解决了几何非线性和非线性叶尖/壳体接触问题。使用拉格朗日乘数对接触进行数值处理，并且使用明确的中心差时间积分方案将运动方程及时向前积分。使用刚度评估程序评估由大位移引起的非线性内力。本文比较了三种还原技术，即Craig–Bampton方法的非线性扩展，适当的正交分解和基于模态导数的方法。这些数值方法适用于开放式工业压缩机叶片模型，NASA转子37叶片，为了促进结果的可重复性。还原方法首先应用于受到谐波激励的叶片，没有接触相互作用。定义了一个说明本地和全局比较标准的指标，可以更轻松地比较每种方法的性能。当还考虑叶片尖端/壳体接触时，所呈现的结果强调，基于模态导数的方法特别适合精确描述叶片动力学。然后，考虑到典型的接触情况，将该方法用于对NASA转子37在宽角速度范围内的振动响应进行深入分析。获得的结果包括时域和频域信号以及应力场。