航空发动机转/静子加筋调频设计方法

范雨; 钱鑫; 吴亚光; 陈璐璐; 张辉

doi:10.13224/j.cnki.jasp.20220258

航空发动机转/静子加筋调频设计方法

doi: 10.13224/j.cnki.jasp.20220258

范雨^{1, 2,},
钱鑫^{1, 2},
吴亚光^{1, 2,*, ,},
陈璐璐³,
张辉³

1.
北京航空航天大学能源与动力工程学院，北京 100191
2.
北京航空航天大学航空发动机结构强度北京市重点实验室，北京 100191
3.
中国航发商用航空发动机有限责任公司，上海 200241

基金项目: 国家科技重大专项(2017-Ⅳ-0002-0039，J2019-Ⅳ-0023-0091）；航空科学基金（2019ZB051002）；
先进航空动力创新工作站(HKCX2020-02-013，HKCX2020-02-016)

详细信息

作者简介:
范雨（1987-），男，副教授、博士生导师，博士，主要从事智能结构动力学及振动控制等研究

通讯作者:
吴亚光（1990-），男，助理研究员，博士，主要从事航空发动机薄壁结构的振动控制研究。E-mail：yaguangwu@buaa.edu.cn

中图分类号: V231.92
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- 被引次数: 0
出版历程
- 收稿日期: 2022-04-27
- 网络出版日期: 2022-09-07

Design approach of stiffeners for frequency shifting of rotors and stators in aero-engine

FAN Yu^{1, 2
,},
QIAN Xin^{1, 2},
WU Yaguang^{1, 2,*
, ,},
CHEN Lulu³,
ZHANG Hui³

1.
School of Energy and Power Engineering， Beihang University，Beijing 100191，China
2.
Beijing Key Laboratory of Aero-engine Structure and Strength， Beihang University，Beijing 100191，China
3.
Commercial Aircraft Engine Company Limited，Aero Engine Corporation of China， Shanghai 200241，China

摘要

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。
- 耦合振动 /
- 结构设计 /
- 频率优化 /
- 共振裕度 /
- 加筋结构 /
- 有限元
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.
- coupling vibration /
- structural design /
- frequency optimization /
- resonance margin /
- stiffened structure /
- finite element

HTML

图 1 加筋对模态频率影响初步判断流程图

Figure 1. Preliminary judgment flow chart of the effect of stiffening on modal frequency

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图 2 简易悬臂梁有限元模型

Figure 2. Finite element model of simple cantilever beam

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图 3 简易悬臂梁典型模态振型与应变能密度分布

Figure 3. Modal shapes and strain energy density distribution of typical modes of simple cantilever beam

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图 4 简易悬臂梁不同位置加筋有限元模型

Figure 4. Finite element models of simple cantilever beam stiffened at different positions

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图 5 增压级静子与转子单扇区有限元模型

Figure 5. Single sector finite element models of stator and rotor of turbocharged stage

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图 6 3节径下转/静子波速

Figure 6. Rotor and stator wavelet velocities at 3 nodal diameters

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图 7 3节径下转/静子危险模态振型

Figure 7. Dangerous modal shapes of rotor and stator at 3 nodal diameters

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图 8 转/静子加筋位置

Figure 8. Stiffened positions of rotor and stator

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图 9 静子加筋位置位移与应变能密度分布

Figure 9. Distributions of the displacement and strain energy density of stiffened positions of stator

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图 10 转子加筋位置位移与应变能密度分布

Figure 10. Distributions of the displacement and strain energy density of stiffened positions of rotor

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图 11 转/静子加筋后有限元模型

Figure 11. Finite element models of stiffened stator and rotor

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图 12 3节径下转/静子加筋后危险模态振型

Figure 12. Dangerous modal shapes of stiffened rotor and stator at 3 nodal diameters

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图 13 筋高度与静子模态频率关系曲线

Figure 13. Relation curve between the height of stiffener and the modal frequency of stator

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图 14 加强筋几何参数与转子模态频率关系

Figure 14. Relation curves between the geometric parameters of stiffener and the modal frequency of stator

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图 15 加筋前后3节径转/静子波速及共振裕度示意图

Figure 15. Schematic diagram of rotor and stator wavelet velocities and resonance margins before and after stiffened at 3 nodal diameters

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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/Hz
1	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

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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

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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

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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

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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

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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

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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

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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
20	27.0	−2.49

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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

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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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