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首页> 外文期刊>Journal of Sound and Vibration >On blade/casing rub problems in turbomachinery: An efficient delayed differential equation approach
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On blade/casing rub problems in turbomachinery: An efficient delayed differential equation approach

机译：关于涡轮机械的叶片/壳体摩擦问题：一种有效的时滞微分方程方法

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This paper presents an alternative pathway in studying the ubiquitous blade/casing rub problem in turbomachinery. Bladed disks interfere with the stationary shroud (casing) for a variety of reasons, such as axial offsets, thermal expansions. Both components being compliant, time-varying interface characteristics, nonlinearities and uncertainties in the rub forces make this dynamics very complex to model and analyze. The main idea in this paper originates from the conjecture that this dynamics is inherently akin to internal machining operation which also deals with compliant cutters (blades) but relatively more rigid workpiece (casing). This analogy directs our attention to the fact that the blade/casing impingement dynamics manifests a 'regenerative mechanism' which is impreg-nated with time delays. The ensuing time-delayed system (TDS) can be stable, which is ideal. If it is unstable, however, the interference amplitudes between the blade and the casing grow, and the nonlinear effects become dominant. If the components survived the exercise, this evolution would reach a limit-cycle behavior. Existing literature indicates that this limit cycle mode is the common state of operation in most modern-day turbomachinery. Consequently, the state-of-the-art research effort is focused on minimizing its amplitude to alleviate the destructive levels of fatigue effect. In this article we consider a different perspective in looking at these problems, by proposing the conditions to achieve stable rub interference. For this, a recent mathematical tool of the authors' group called the Cluster Treatment of Characteristic Roots (CTCR) is deployed. CTCR declares the complete stability outlook of such time-delayed systems in the space of the operational and design parameters. We show how this new capability can assist the design process of the blade-casing interface. Simulations, relevant stability observations and comparisons with a peer technique are provided for some case studies to demonstrate the capabilities of the approach.
机译：本文提出了研究涡轮机械中普遍存在的叶片/壳体摩擦问题的另一种途径。刀片式磁盘会由于多种原因（例如轴向偏移，热膨胀）而干扰固定的护罩（外壳）。这两个组件都是合规的，时变的界面特性，非线性和摩擦力的不确定性使这种动力学的建模和分析非常复杂。本文的主要思想源于这种动力学本质上类似于内部加工操作的猜想，该内部加工操作还处理顺应性刀具（刀片），但工件相对较硬（壳体）。这种类比将我们的注意力引向一个事实，即叶片/机壳的冲击动力学表现出一种“再生机制”，该机制被时间延迟所浸渍。随后的延时系统（TDS）可以保持稳定，这是理想的。但是，如果不稳定，则叶片和壳体之间的干扰幅度会增大，并且非线性效应将占主导地位。如果组件在练习中幸存下来，则这种演变将达到极限循环行为。现有文献表明，这种极限循环模式是大多数现代涡轮机械的常见运行状态。因此，最新的研究成果集中在最小化其振幅以减轻疲劳效应的破坏性水平上。在本文中，我们通过提出实现稳定摩擦干扰的条件，来考虑这些问题时采用了不同的观点。为此，部署了作者小组最近的一种数学工具，称为特征根的聚类处理（CTCR）。 CTCR声明了此类延时系统在运行和设计参数方面的完整稳定性。我们将展示这种新功能如何协助刀片框接口的设计过程。为一些案例研究提供了仿真，相关的稳定性观测结果以及与同行技术的比较，以证明该方法的功能。

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