考虑气动阻尼的失调叶盘强迫响应分析

房明昌; 王延荣

doi:10.13224/j.cnki.jasp.20220266

考虑气动阻尼的失调叶盘强迫响应分析

doi: 10.13224/j.cnki.jasp.20220266

房明昌^1,,
王延荣^{1, 2}

1.
北京航空航天大学能源与动力工程学院，北京 100191
2.
北京航空航天大学江西研究院，南昌 330096

基金项目: 国家科技重大专项（2017-Ⅳ-0002-0039）；国家自然科学基金（51475022）

详细信息

作者简介:
房明昌（1996-），男，博士生，主要从事航空发动机结构强度与振动研究。E-mail: fangmingchang@buaa.edu.cn

中图分类号: V232.4
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- 被引次数: 0
出版历程
- 收稿日期: 2022-04-28
- 网络出版日期: 2022-09-05

Forced response analysis of mistuned bladed disk with aerodynamic damping

FANG Mingchang^1
,,
WANG Yanrong^{1, 2}

1.
School of Energy and Power Engineering，Beihang University，Beijing 100191，China
2.
Jiangxi Research Institute，Beihang University，Nanchang 330096，China

摘要

摘要:
基于与影响系数法相结合的基础失调模型（FMM）分析多种人为失调在叠加随机失调前、后的强迫响应。采用有限元和计算流体力学方法分别计算得到协调叶盘的模态和气动力影响系数，构建考虑气动阻尼的基础失调模型。通过求解矩阵特征值得到失调叶盘的模态频率、振型和阻尼比，进而采用模态叠加法得到失调叶盘在行波激励下的强迫响应。结果表明：失调叶盘的强迫响应在考虑气动阻尼后明显减小。以交替失调叶盘为例，在适当范围内增大失调量可以减小强迫响应，该模型的相邻叶片频率差宜取6%，对应失调量为4.32。此外，增大间隔一个叶片的相邻叶片频率差有利于进一步减小强迫响应。
- 强迫响应 /
- 叶盘 /
- 人为失调 /
- 基础失调模型（FMM） /
- 气动阻尼
Abstract:
The forced response of the mistuned bladed disk was analyzed by use of the fundamental mistuning model (FMM) combined with the influence coefficient method. The finite element method and computational fluid dynamics method were used to obtain the modal results and aerodynamic influence coefficients of the tuned bladed disk, and then the FMM considering aerodynamic damping was constructed. The modal frequency, mode shape and damping ratio of the mistuned bladed disk were obtained by solving the matrix eigenvalues, and then the modal superposition method was used to calculate the forced response of the mistuned bladed disk under traveling wave excitation. The above method was used to calculate the forced responses of various intentional mistuned bladed disks before and after the superposition of random mistuning. Results indicated that the forced response of the mistuned bladed disk decreased significantly after considering aerodynamic damping. Taking the alternating mistuned bladed disk as an example, the forced response can be reduced by increasing the mistuning value within an appropriate range. The frequency difference between adjacent blades of the model should be 6%, and the corresponding mistuning value was 4.32. In addition, increasing the frequency difference between adjacent blades with an interval of one blade can further reduce the forced response.
- forced response /
- bladed disk /
- intentional mistuning /
- fundamental mistuning model (FMM) /
- aerodynamic damping

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图 1 协调叶盘模型

Figure 1. Tuned bladed disk model

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图 2 协调叶盘模态频率

Figure 2. Modal frequencies of the tuned bladed disk

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图 3 协调叶盘模态振型

Figure 3. Mode shapes of the tuned bladed disk

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图 4 含两种频率叶片的人为失调叶盘

Figure 4. Intentional mistuned bladed disks with two blade frequency types

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图 5 随机失调分布

Figure 5. Random mistuning distribution

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图 6 协调叶盘强迫响应

Figure 6. Forced response of the tuned bladed disk

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图 7 含两种频率叶片的交替失调叶盘强迫响应

Figure 7. Forced response of the alternating mistuned bladed disk with two blade frequency types

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图 8 含两种频率叶片的单个失调叶盘的强迫响应

Figure 8. Forced response of the single mistuned bladed disk with two blade frequency types

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图 9 含两种频率叶片的扇区失调叶盘强迫响应

Figure 9. Forced response of the sector mistuned bladed disk with two blade frequency types

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图 10 失调量为0.72的交替失调叶盘强迫响应

Figure 10. Forced response of the alternating mistuned bladed disk with a mistuning value of 0.72

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图 11 失调量为2.16的交替失调叶盘强迫响应

Figure 11. Forced response of the alternating mistuned bladed disk with a mistuning value of 2.16

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图 12 失调量为6.48的交替失调叶盘强迫响应

Figure 12. Forced response of the alternating mistuned bladed disk with a mistuning value of 6.48

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图 13 含3或4种频率叶片的交替失调叶盘

Figure 13. Alternating mistuned bladed disks with three or four blade frequency types

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图 14 含3种频率叶片的交替失调叶盘强迫响应

Figure 14. Forced response of the alternating mistuned bladed disk with three blade frequency types

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图 15 含4种频率叶片的交替失调叶盘强迫响应

Figure 15. Forced response of the alternating mistuned bladed disk with four blade frequency types

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表 1 叶片的气动力影响系数

Table 1. Aerodynamic influence coefficients of the blades

叶片编号$ n $	实部$ {a_r}^n $/ （N/m）	虚部$ {a_i}^n $/ （N/m）	气动力幅值/ （N/m）
N−4	305.7	329.4	449.5
N−3	−56.1	−2710.8	2711.4
N−2	1587.2	−553.9	1681.1
N−1	96068.9	87834.8	130169.9
0	12764.0	−314417.7	314676.7
1	30406.2	190507.5	192918.8
2	−16868.0	16008.8	23255.3
3	−3644.7	6388.2	7354.8
4	557.7	−258.7	614.8

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表 2 含两种频率叶片的人为失调叶盘分布特征参数

Table 2. Distribution characteristic parameters of intentional mistuned bladed disk with two blade frequency types

叶盘类型	失调量$ \delta $	频率邻差$\,{\beta _0}$	频率间一邻差$\,{\beta _1}$	频率间二邻差$\,{\beta _2}$
交替失调	4.32	5.89	1.63	5.66
单个失调	1.16	1.63	1.63	1.63
扇区失调	4.16	1.63	2.31	2.83

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表 3 含两种频率叶片的人为失调叶盘强迫响应最大值

Table 3. Maximum forced response of the intentional mistuned bladed disks with two blade frequency types

叶盘类型	强迫响应/10⁻⁵	叠加随机失调的强迫响应/10⁻⁵
协调	1.85	3.99
交替失调	0.77	1.91
单个失调	2.77	4.55
扇区失调	1.87	2.54

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表 4 不同失调量的交替失调叶盘强迫响应最大值

Table 4. Maximum forced response of the alternating mistuned bladed disks with different mistuning value

失调量	强迫响应/10⁻⁵	叠加随机失调的强迫响应/10⁻⁵
0	1.85	3.99
0.72	1.81	3.68
2.16	1.21	3.29
4.32	0.77	1.91
6.48	0.73	1.55

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表 5 不同种数的频率叶片的交替失调叶盘分布特征参数

Table 5. Distribution parameters of the alternating mistuned bladed disk with different number of blade frequency types

叶盘类型	失调量$ \delta $	频率邻差$\,{\beta _0}$	频率间一邻差$\,{\beta _1}$	频率间二邻差$\,{\beta _2}$
交替失调（两种频率叶片）	4.32	5.89	1.63	5.66
交替失调（3种频率叶片）	3.87	4.24	4.24	0.00
交替失调（4种频率叶片）	3.81	3.40	3.89	3.27

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表 6 不同种数频率叶片的交替失调叶盘强迫响应最大值

Table 6. Maximum forced response of the alternating mistuned bladed disks with different number of blade frequency types

叶盘类型	强迫响应/10⁻⁵	叠加随机失调的强迫响应/10⁻⁵
交替失调（两种频率叶片）	0.77	1.91
交替失调（3种频率叶片）	0.44	1.53
交替失调（4种频率叶片）	0.89	1.69

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