双通道旋转输流管临界流速和振动模态分析

张博; 郑昊楷; 孙东生; 丁虎; 陈立群

doi:10.6052/0459-1879-22-456

双通道旋转输流管临界流速和振动模态分析

doi: 10.6052/0459-1879-22-456

张博^{*, †,},
郑昊楷^*,
孙东生^*,
丁虎^†,
陈立群^†, ,

*.
长安大学理学院, 西安 710064
†.
上海大学力学与工程科学学院, 上海 200444

基金项目: 陕西省自然科学基金(2022JQ-019), 上海市教委创新项目(2017-01-07-00-09-E00019) 和陕西省国家级大学生创新创业训练计划 (G202210710094)资助

详细信息

作者简介:
通讯作者: 张博, 副教授, 主要研究方向为非线性动力学与振动控制. E-mail: zhang_bo@chd.edu.cn

通讯作者:
陈立群, 教授, 主要研究方向为非线性动力学和振动控制. E-mail: lqchen@shu.edu.cn

中图分类号: O321
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- 文章访问数: 358
- HTML全文浏览量: 132
- PDF下载量: 76
- 被引次数: 0
出版历程
- 收稿日期: 2022-09-27
- 录用日期: 2022-11-18
- 网络出版日期: 2022-11-19
- 刊出日期: 2023-01-04

THEORETICAL ANALYSIS ON THE CRITICAL FLOW VELOCITY AND VIBRATION MODE OF A TWIN-CHANNEL ROTATING PIPE

Zhang Bo^{*, †
,},
Zheng Haokai^*,
Sun Dongsheng^*,
Ding Hu^†,
Chen Liqun^{†
, ,}

*.
School of Science, Chang’an University, Xi’an 710064, China
†.
School of Mechanics and Engineering Sciences, Shanghai University, Shanghai 200444, China

摘要

摘要: 旋转叶片是航空发动机重要零件之一, 服役条件十分恶劣, 常常因振动过量导致其失效. 为了合理设计含冷却通道的叶片, 保证其可靠性与安全性, 需对含冷却通道的叶片的振动特性进行研究. 基于Euler-Bernoulli梁理论, 将叶片简化为含两通道的悬臂旋转输流管, 考虑了通道轴线偏移量对流体动能的影响, 采用Lagrange原理结合假设模态法建立包含双陀螺效应的运动控制方程, 采用降阶扩维的方法求解系统特征值. 研究两通道模型的流速比、转速和长细比等对前3阶特征根曲线影响. 将文章模型退化为简支单通道输流管, 与文献报道结果进行对比, 部分验证建模方法的正确性. 研究发现: 在相同的管道截面积下, 两通道模型的临界流速值大于单通道模型的; 旋转运动引入的陀螺效应会使得第2, 3阶特征根轨迹发生绕圈现象, 并多次穿越虚轴; 随着长细比的增大, 系统会表现出类似非旋转的悬臂输流管的动力学行为; 系统的横向位移模态响应呈现出行波特性, 且在不同参数组合下, 阻尼因子对前3阶模态产生不同的增强或减弱作用.
- 旋转输流管 /
- 假设模态法 /
- 复模态 /
- 稳定性 /
- 临界流速
Abstract: Rotating blade is an essential part of aero-engine. It serves in harsh conditions. Its failure is often caused by excessive vibration. To design the blade properly and to ensure the reliability and safety, the vibration characteristics of the blade need to be revealed. The blade is simplified as a cantilever rotating pipe with double cooling channels based on the Euler-Bernoulli beam theory. The influences of channel axis offset on fluid kinetic energy are considered in the present study. The motion governing equation of the blade is established including the bi-gyroscopic effects with the combination of Lagrange principle and assumed mode method. The method of order reduction and dimension expansion is applied to solve the eigenvalue of the system. The influences of the fluid velocity ratio, rotating speed, slenderness et al. on the first three order eigenvalue curves are studied. The present model degenerates into a simply supported pipe conveying fluid with a single channel to compare with the results reported in literature. The correctness of the present modeling method is verified, partly. The velocity ratio of two channels has great influence on the first three order critical flow velocity values. For a given value of the cross-section area of the cooling passage, the critical flow velocity of the twin-channel model is higher than the single-channel model. A circling phenomenon is introduced to on the second and the third eigenvalue curves by the gyroscopic effect due to the rotating motion. The second and the third eigenvalue curves travel through the imaginary axis several times. With the increase of the slenderness ratio, the system’s dynamic behaviors are similar to the non-rotating cantilever pipe. Moreover, due to the gyroscopic effect, the modal response of the lateral displacement presents a traveling wave property. And the damping factor has different enhancement or weakening effects on the first three modes under different parameter conditions.
- rotating fluid conveying pipe /
- assumed mode method /
- complex mode /
- stability /
- critical flow velocity

HTML全文

图 1 含两通道的旋转输流管

Figure 1. Sketch of a rotating cantilever double channel pipe

下载: 全尺寸图片幻灯片

图 2 不同试探函数个数下前3阶特征根轨迹曲线 (Ω^* = 0)

Figure 2. The trajectories of the first three eigenvalues for different trail function numbers (Ω^* = 0)

下载: 全尺寸图片幻灯片

图 3 两端简支的单通道输流管系统的前两阶特征根轨迹

Figure 3. The trajectories of the first two eigenvalues for simple supported flow pipe

下载: 全尺寸图片幻灯片

图 4 单、双通道模型的临界流速随转速的变化曲线

Figure 4. The curves of critical flow velocity with rotating speed for the single/twin-channel models

下载: 全尺寸图片幻灯片

图 5 不同流速比下前3阶特征根轨迹(u_cr = u₂, Ω^* = 5)

Figure 5. The trajectories of the first three eigenvalues for different velocity ratios (u_cr = u₂, Ω^* = 5)

下载: 全尺寸图片幻灯片

图 6 不同转速下前3阶特征根轨迹曲线(κ = 35)

Figure 6. The trajectories of the first three eigenvalues for different rotating speeds (κ = 35)

下载: 全尺寸图片幻灯片

图 7 不同长细比下前3阶特征根轨迹曲线(Ω^* = 5)

Figure 7. The trajectories of the first three eigenvalues for different slenderness ratios (Ω^* = 5)

下载: 全尺寸图片幻灯片

图 8 相位变化对前3阶模态响应的影响(u₁ = u₂ = 8, Ω^* = 10)

Figure 8. The curves of the first three modal responses for different phase changes (u₁ = u₂ = 8, Ω^* = 10)

下载: 全尺寸图片幻灯片

图 9 不同流速和转速下阻尼因子对前3阶模态响应的影响

Figure 9. The effects of damping factor on the first three mode responses for different flow rates and rotating speeds

下载: 全尺寸图片幻灯片

表 1 两端简支单通道输流管系统的前两阶临界流速对比

Table 1. Comparison of the first two critical flow velocities for simply supported flow pipe

Critical flow vewary Result Ref. [43]

first 3.14 3.14
second 6.28 6.28

下载: 导出CSV

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