Decoupled optimization of underplatform dampers based on a parametric equivalent model
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摘要:
针对涡轮叶片缘板阻尼结构设计中存在的多目标优化机理缺失及迭代建模计算成本高昂的问题，提出了一种基于参数化等效模型的阻尼器质量-几何解耦优化设计方法。建立了叶片-缘板阻尼的等效梁模型，在准确复现其1阶弯曲模态动力学特性与非线性强迫响应的基础上，显著降低了模型自由度与计算成本。在阐明缘板阻尼关键设计参数对减振效果影响规律的基础上，提出了减振幅度、适用激振域宽度与重合度3个无量纲指标，多维度定量表征阻尼器的减振性能。研究揭示了接触倾角主要决定减振性能的“深度”与“适用宽度”，而阻尼器质量则调控其工作域与发动机流场激励的重合度。基于此，提出了先利用帕累托多目标遗传算法优化几何参数，再根据激励信息优化阻尼质量的解耦优化策略。以非对称缘板阻尼器为算例验证表明，优化后阻尼器的相对减振幅度、适用激振域宽度及重合度分别提升了13%、38%和114.6%；在目标工况激励下，叶片的一弯共振响应幅值降低了43.8%。
Abstract:A decoupled optimization method is proposed for underplatform damper (UPD) design to address the lack of multi-objective mechanism insight and the high cost of iterative blade–damper modeling. We develop a parameterized equivalent beam model of the blade–UPD system that accurately reproduces the first bending-mode dynamics and the nonlinear forced response, while keeping the model size and computational cost modest. We characterize the influence of key UPD design parameters on vibration attenuation and introduce three dimensionless metrics—reduction degree, domain width, and coincidence degree—to quantify damper performance. The results show that the contact angle primarily sets the attenuation “depth” and applicability “width,” whereas the damper mass tunes the operating domain’s overlap with engine flow-field excitation. Based on these insights, we adopt a decoupled strategy: first optimize geometric parameters using a Pareto multi-objective genetic algorithm, then set the damper mass according to the excitation characteristics. For a non-symmetric UPD case, the optimized design increases the reduction degree by 13%, the domain width by 38%, and the coincidence degree by 114.6%, yielding a 43.8% decrease in the first-bending resonance amplitude at the target operating condition.
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图 3 缘版阻尼器模型及接触力学本构
Figure 3. Model of underplatform damper with its frictional constitutive relationship
图 7 缘板倾斜角对减振效果影响
Figure 7. Influence of the contact angle on vibration reduction effectiveness
图 12 优化前后减振效果对比
Figure 12. Comparison of vibration reduction performance before and after optimization
表 1 算例参数
Table 1. Case parameters
参数 数值 $ \nu $ 0.344 $ E $/1011 $ \text{Pa} $ 1.315 $ \rho $/$ （{\text{kg/m}}^{3}） $ 8780 $ {k}_{\text{t}} $/107 $ \text{（N/m}） $ 1 $ {k}_{\text{n}} $/107 $ \text{（N/m}） $ 1.4 $ \mu $ 0.2 
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表 2 多目标参数优化方法
Table 2. Multi-objective optimization method
优化参数名称 目标函数 缘板倾斜角 减振幅度、适用激振域宽度 阻尼器质量 适用激振域重合度
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表 3 几何优化结果
Table 3. Geometric optimization results
缘板接触面倾斜角
帕累托解集/（°）减振幅度/% 适用激振域
宽度56.8 64.20 1.88 59.78 64.08 3.48 60.15 64.01 3.70
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