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TSHBM法及其在干摩擦阻尼叶片响应计算中的应用

孙扬 周标 臧朝平

孙扬, 周标, 臧朝平. TSHBM法及其在干摩擦阻尼叶片响应计算中的应用[J]. 航空动力学报, 2024, 39(10):20220195 doi: 10.13224/j.cnki.jasp.20220195
引用本文: 孙扬, 周标, 臧朝平. TSHBM法及其在干摩擦阻尼叶片响应计算中的应用[J]. 航空动力学报, 2024, 39(10):20220195 doi: 10.13224/j.cnki.jasp.20220195
SUN Yang, ZHOU Biao, ZANG Chaoping. A TSHBM method and its application in response calculation of dry friction damped blades[J]. Journal of Aerospace Power, 2024, 39(10):20220195 doi: 10.13224/j.cnki.jasp.20220195
Citation: SUN Yang, ZHOU Biao, ZANG Chaoping. A TSHBM method and its application in response calculation of dry friction damped blades[J]. Journal of Aerospace Power, 2024, 39(10):20220195 doi: 10.13224/j.cnki.jasp.20220195

TSHBM法及其在干摩擦阻尼叶片响应计算中的应用

doi: 10.13224/j.cnki.jasp.20220195
基金项目: 航空发动机及燃气轮机重点专项基础研究项目(J2019-Ⅳ-0023-0091)
详细信息
    作者简介:

    孙扬(1997-),男,硕士生,主要从事航空发动机结构动力学研究。E-mail:sunyang97@nuaa.edu.cn

    通讯作者:

    臧朝平(1963−),男,教授、博士生导师,博士,主要从事航空发动机结构动力学研究。E-mail:c.zang@nuaa.edu.cn

  • 中图分类号: V231.92

A TSHBM method and its application in response calculation of dry friction damped blades

  • 摘要:

    建立了以时间谱形式的谐波平衡法为核心的新型非线性强迫振动响应高效计算方法,并应用于含接触界面的干摩擦阻尼叶片结构响应分析。基于时间谱形式的谐波平衡法的原理和特点,建立非线性强迫振动响应通用求解方案;根据接触非线性的特性,提出了干摩擦力及解析雅可比矩阵计算的适应性处理方案,形成了含接触界面的叶片结构新型非线性振动响应高效预测方法。数值仿真结果表明:在带燕尾型榫根的叶片单扇区有限元模型中,分别保留1阶和3阶谐波阶次时,该方法的非线性振动响应计算时间消耗相较于传统的多谐波平衡法分别削减37%和46%,因此该方法在易用性、可推广性和计算效率方面具有独特的优势。

     

  • 图 1  三维变压力接触模型

    Figure 1.  3D contact model with variable normal load

    图 2  带干摩擦单元的悬臂梁模型及正切函数描述的干摩擦力曲线

    Figure 2.  Cantilever beam with dry friction element and dry friction force curve described by tangent function

    图 3  ${\tilde {\boldsymbol{U}}_{{\mathrm{tip}}}}$的伪时间域历程曲线

    Figure 3.  Pseudo-time history of ${\tilde {\boldsymbol{U}}_{{\mathrm{tip}}}}$

    图 4  失真现象

    Figure 4.  Aliasing phenomenon

    图 5  不同方法计算的带干摩擦单元的悬臂梁模型的幅频曲线

    Figure 5.  Amplitude-frequency curve of cantilever beam with dry friction element by different methods

    图 6  不同方法结合弧长延拓法计算的杜芬振子的幅频曲线

    Figure 6.  Amplitude-frequency curve of duffing oscillator by different methods with arc-length continuation

    图 7  带燕尾型榫根的叶片单扇区有限元模型

    Figure 7.  FE model of a bladed disk sector with dovetail joint

    图 8  不同方法计算的带燕尾型榫根的叶片单扇区模型的幅频曲线

    Figure 8.  Amplitude-frequency curve of bladed disk sector with dovetail joint by different methods

    图 9  幅频曲线随激振力的变化

    Figure 9.  Amplitude-frequency curve with varying exciting force

    表  1  带干摩擦单元的悬臂梁模型的幅频曲线的归一化计算时间

    Table  1.   Normalized computational time of amplitude-frequency curve of cantilever beam with dry friction element

    计算方法 保留谐波阶次
    ${N_{\rm{h}}} = 1$ ${N_{\rm{h}}} = 3$ ${N_{\rm{h}}} = 5$ ${N_{\rm{h}}} = 7$
    MHBM 1.000 4.247 15.493 66.795
    MHBM ACC. 0.139 0.371 0.746 1.559
    TSHBM-NR 0.038 0.082 0.171 0.309
    TSHBM-PTM 0.043 0.085 0.184 0.361
    下载: 导出CSV

    表  2  杜芬振子系统的幅频曲线的归一化计算时间

    Table  2.   Normalized computational time of amplitude-frequency curve of duffing oscillator

    计算方法 保留谐波阶次
    ${N_{\rm{h}}} = 1$ ${N_{\rm{h}}} = 3$ ${N_{\rm{h}}} = 5$ ${N_{\rm{h}}} = 7$
    MHBM 1.000 1.713 2.631 4.233
    MHBM ACC. 0.719 0.984 1.161 1.454
    TSHBM-NR 0.539 0.650 0.681 0.779
    下载: 导出CSV

    表  3  主要模型参数

    Table  3.   Model parameters

    参数 数值
    弹性模量E/1011 Pa 2.1
    泊松比μ 0.3
    材料密度ρ/(kg/m3 7980
    β-阻尼系数/10−5 1
    切向接触刚度kt/105 (N/m) 1
    法向接触刚度kn/105 (N/m) 1
    摩擦因子μ 0.3
    下载: 导出CSV

    表  4  带燕尾型榫根的叶片单扇区模型的幅频曲线的归一化计算时间

    Table  4.   Normalized computational time of amplitude-frequency curve of bladed disk sector with dovetail joint

    计算方法 保留谐波阶次
    ${N_{\rm{h}}} = 1$ ${N_{\rm{h}}} = 3$
    MHBM ACC. 1.000 6.085
    TSHBM-NR 0.926 5.404
    TSHBM-PTM 0.628 3.304
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-04-07
  • 网络出版日期:  2024-05-20

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