Design approach of stiffeners for frequency shifting of rotors and stators in aero-engine
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摘要:
为了解决转子叶片/叶鼓系统与静子在模态频率接近且具有相同节径数时可能发生的流致转静子耦合振动问题,提出了一种基于位移与应变能密度分布的正向加筋调频设计方法,为结构调频设计提供了理论依据。该方法适用于有限元模型,且通过一次模态计算即可初步判断加筋区域,显著缩短设计周期。以提高安全工作裕度为目标,使用该方法对某型发动机增压级转/静子进行加筋调频设计,并探究了加强筋的结构参数对转/静子模态特性的影响。通过加筋设计,该型增压级转/静子危险模态下的共振裕度从3.47%提高到10.56%。该方法具有良好的通用性,同样适用于其他型号发动机的结构加筋调频设计。
Abstract:In order to suppress the flow-induced coupling vibration of rotor blades/bladed drum and stator caused by the close modal frequencies with the same nodal diameter between the rotor and stator, an ad-hoc forward design method based on displacement and strain energy density distribution was proposed to tailor the frequency margin, providing a solid theoretical basis for designing the gap of the frequency; and the stiffened area can be preliminarily determined through a single modal analysis, which significantly shortened the design cycles. The method was then applied to an industrial rotor/stator finite element model to improve the resonance margin. The influence of structural parameters of stiffeners on the modal characteristics of rotor and stator was investigated. The resonance margin of the dangerous mode increased from 3.47% to 10.56% by stiffening. The generality of this method is good, making it suitable for other types of engines.
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表 1 悬臂梁不同位置加筋后模态频率变化情况
Table 1. Modal frequency variation of cantilever beam stiffened at different positions
阶数 加筋前模态
频率/Hz固支端加筋模态
频率/Hz自由端加筋模态
频率/Hz1 2.789 3.067 2.499 2 13.538 13.980 12.140 3 17.400 19.086 16.143 4 30.307 31.755 27.795 5 48.442 52.962 45.706 6 75.975 78.435 70.963 7 91.973 96.465 86.555 8 94.179 102.41 89.432 9 128.24 129.68 120.05 10 154.13 164.43 148.00 表 2 转子模态计算转速点
Table 2. Modal calculation speed points of rotor
相对转速 物理转速/(r/min) 相对转速 物理转速/(r/min) 0 0 0.61 2500 0.10 400 0.71 2900 0.20 800 0.80 3300 0.39 1200 0.93 3800 0.49 1600 0.98 4000 0.59 2000 1.00 4100 表 3 静子危险模态加筋位置平均位移与应变能密度
Table 3. Mean displacement and strain energy density of the stiffener positions in danger mode of stator
参数 数值 节径 3 阶数 19 模态频率/Hz 783.196 $ {U_{{\text{c}}1}} $/mm 7.459 $ {U_{{\text{c}}2}} $/mm 5.26 $ {U_{{\text{c}}3}} $/mm 3.26 $ {D}_{\mathrm{s},\mathrm{c}1} $/$ (\mathrm{N}/\text{m}{\text{m}}^{2}) $ 6.07 $ {D}_{\mathrm{s},\mathrm{c}2} $/$ (\mathrm{N}/\text{m}{\text{m}}^{2}) $ 6.95 $ {D}_{\mathrm{s},\mathrm{c}3} $/$ (\mathrm{N}/\text{m}{\text{m}}^{2}) $ 2.30 表 4 转子危险模态加筋位置平均位移与应变能密度
Table 4. Mean displacement and strain energy density of the stiffener positions in danger mode of rotor
参数 数值 节径 3 阶数 25 模态频率/Hz 1018.5 $ {U_{{\text{d}}1}} $/mm 0.164 $ {U_{{\text{d}}2}} $/mm 0.265 $ {U_{{\text{d}}3}} $/mm 0.086 $ {D}_{\mathrm{s},\mathrm{d}1} $/1010 $(\mathrm{N}/\text{m}{\text{m} }^{2})$ 6.05 $ {D}_{\mathrm{s},\mathrm{d}2} $/1010 $ (\mathrm{N}/\text{m}{\text{m}}^{2}) $ 1.35 $ {D}_{\mathrm{s},\mathrm{d}3} $/1010 $ (\mathrm{N}/\text{m}{\text{m}}^{2}) $ 12.4 表 5 加筋前后转/静子危险模态频率及共振裕度对比
Table 5. Comparison of mode frequencies of rotor and stator dangerous modes and resonance marginbefore and after stiffened
工况 静子模态
频率/Hz转子模态
频率/Hz共振裕度/% 加筋前 783.196 1018.5 3.47 加筋后 772.193 1042.7 7.58 表 6 更改加筋位置后转/静子危险模态频率及共振裕度
Table 6. Comparison of mode frequencies of rotor and stator dangerous modes and resonance margin after changing stiffened positions
工况 静子模态
频率/Hz转子模态
频率/Hz共振裕度/% 加筋前 783.196 1018.5 3.47 加筋后 780.697 1007.3 2.43 表 7 加强筋不同高度对静子危险模态频率影响
Table 7. Influence of different height of stiffener on frequency of stator dangerous mode
高度/mm 加筋后模态频率变化率/% 2 −0.092 4 −0.279 6 −0.506 8 −0.762 10 −1.10 12 −1.40 14 −1.73 16 −2.08 18 −2.43 20 −2.79 表 8 加强筋不同宽度对静子危险模态频率影响
Table 8. Influence of different widths of stiffener on frequency of stator dangerous mode
高度/mm 宽度/mm 模态频率变化率/% 10 27.0 −1.10 20 13.5 −1.66 27.0 −2.49 表 9 加强筋不同高度对转子危险模态频率影响
Table 9. Influence of different heights of stiffener on frequency of rotor dangerous mode
高度/mm 加筋后模态频率变化率/% 2 1.38 4 1.83 6 2.08 8 2.25 10 2.37 12 2.47 14 2.55 16 2.62 18 2.68 20 2.74 表 10 加强筋不同宽度对转子危险模态频率影响
Table 10. Influence of different widths of stiffener on frequency of stator dangerous mode
宽度/mm 加筋后模态频率变化率/% 2.57 0.15 5.14 0.43 7.71 0.87 10.28 1.34 12.85 1.85 15.42 2.32 17.99 2.74 -
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