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热致混合式转子变结构与动力学特性

潘健智 魏大盛 胡伟男

潘健智, 魏大盛, 胡伟男等 . 热致混合式转子变结构与动力学特性[J]. 北京航空航天大学学报, 2020, 46(1): 67-76. doi: 10.13700/j.bh.1001-5965.2019.0150
引用本文: 潘健智, 魏大盛, 胡伟男等 . 热致混合式转子变结构与动力学特性[J]. 北京航空航天大学学报, 2020, 46(1): 67-76. doi: 10.13700/j.bh.1001-5965.2019.0150
PAN Jianzhi, WEI Dasheng, HU Weinanet al. Variable structure and dynamics properties of mixing rotor due to thermal expansion[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(1): 67-76. doi: 10.13700/j.bh.1001-5965.2019.0150(in Chinese)
Citation: PAN Jianzhi, WEI Dasheng, HU Weinanet al. Variable structure and dynamics properties of mixing rotor due to thermal expansion[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(1): 67-76. doi: 10.13700/j.bh.1001-5965.2019.0150(in Chinese)

热致混合式转子变结构与动力学特性

doi: 10.13700/j.bh.1001-5965.2019.0150
基金项目: 

江苏省自然科学基金 BK20160821

详细信息
    作者简介:

    潘健智  女, 博士, 讲师。主要研究方向:复杂旋转机械建模与动力学

    通讯作者:

    潘健智,E-mail:jzhpan@163.com

  • 中图分类号: O327;TH113.1

Variable structure and dynamics properties of mixing rotor due to thermal expansion

Funds: 

Natural Science Foundation of Jiangsu Province BK20160821

More Information
  • 摘要:

    航空发动机、汽轮机等大型旋转机械多运行在复杂多变的高温环境中,机组主转子系统在工况下因热膨胀而产生结构变化,进而影响运行特性。首先,考虑盘鼓混合式旋转构件与转轴相比具有高刚度特点,将其结构简化并建立单厚盘转子动力学模型;其次,针对热膨胀引发的系统变结构特征,以曲线拟合结合Hermite插值法描绘出圆柱厚盘窜动到任意位置时的转轴弯曲情况,根据弯曲轴所储存的弹性势能运用数值方法折算出对转盘所提供的恢复力及转轴的弯曲恢复刚度;最后,通过数值分析热膨胀诱发的轴向窜动对厚盘转子系统进动频率、临界角速度和振动响应幅值等动力学特性的影响,验证了热膨胀诱发的转轴窜动因素是影响厚盘转子系统动力学特性的主要因素之一。

     

  • 图 1  盘鼓混合旋转构件示意图

    Figure 1.  Schematic diagram of mixing rotor set with turntable and drum

    图 2  理想刚性圆柱示意图

    Figure 2.  Schematic diagram of ideal rigid cylinder

    图 3  厚盘转子系统示意图

    Figure 3.  Schematic diagram of rotor system with thick disk

    图 4  转轴轴向窜动

    Figure 4.  Axial movement of shaft

    图 5  转轴轴向窜动变形示意图(n=1, 2)

    Figure 5.  Deformable diagram of axial movement of shaft (n=1, 2)

    图 6  热膨胀转子弯曲示意图

    Figure 6.  Bending diagram of rotor after thermal expansion

    图 7  弯曲转轴的曲线拟合

    Figure 7.  Curve fitting of bending shaft

    图 8  温升曲线

    Figure 8.  Temperature rising curves

    图 9  转轴长度变化

    Figure 9.  Axial length variation

    图 10  转子进动频率

    Figure 10.  Precession frequency of rotor

    图 11  临界角速度ωαωβ变化

    Figure 11.  Changes of cirtical angular velocity ωα and ωβ

    图 12  转轴截面直径影响下响应xr的幅频曲线

    Figure 12.  Amplitude-frequency curves of response xr under influence of shaft diameter

    图 13  T1W影响下响应xr的幅频曲线

    Figure 13.  Amplitude-frequency curves of response xr under influence of T1W

    图 14  T2W影响下响应xr的幅频曲线

    Figure 14.  Amplitude-frequency curves of response xr under influence of T2W

    图 15  转盘厚度影响下响应xr的幅频曲线

    Figure 15.  Amplitude-frequency curves of response xr under influence of disk thickness

    表  1  厚盘转子系统参数

    Table  1.   Parameters of rotor system with thick disk

    参数 数值
    弹性模量E/(N·m-2) 2.058×1011
    泊松比μ 0.28
    材料密度ρ/(kg·m-3) 7 800
    转盘质量m/kg 100
    转盘半径R/m 0.12
    转轴半径Rl/m 0.03
    偏心量ε/m 0.3×10-4
    比例阻尼系数β1β2 0.2×10-3
    转轴总长l0/m 1.5
    轴段长l10/m 0.6
    轴段长l20/m 0.9
    下载: 导出CSV

    表  2  弯曲恢复刚度受T1W的影响

    Table  2.   Bending restoration stiffness affected by T1W

    T1W/K krr/(107N·m-1) kθθ/(106N·m-1) k/(106N·m-1)
    248 3.770 6 5.869 3 -4.078 4
    356 3.751 7 5.863 7 -4.058 2
    428 3.739 2 5.860 0 -4.044 7
    482 3.729 8 5.857 3 -4.034 7
    536 3.720 5 5.854 5 -4.024 6
    572 3.714 3 5.852 7 -4.018 0
    608 3.701 8 5.850 9 -4.011 3
    下载: 导出CSV

    表  3  弯曲恢复刚度受T2W的影响

    Table  3.   Bending restoration stiffness affected by T2W

    T2W/K krr/(107N·m-1) kθθ/(106N·m-1) k/(106N·m-1)
    1 472 3.692 6 5.862 4 -3.985 6
    1 652 3.701 8 5.850 9 -4.011 3
    1 742 3.715 8 5.845 1 -4.024 2
    1 796 3.720 5 5.841 7 -4.031 9
    1 868 3.726 7 5.837 2 -4.042 2
    2 012 3.739 2 5.828 1 -4.062 9
    2 192 3.754 9 5.816 8 -4.088 8
    下载: 导出CSV

    表  4  弯曲恢复刚度受转盘厚度的影响

    Table  4.   Bending restoration stiffness affected by disk thickness

    b/m krr/(107N·m-1) kθθ/(106N·m-1) k/(106N·m-1)
    0.05 3.754 9 5.070 7 -2.553 2
    0.08 3.754 9 5.500 7 -3.474 5
    0.1 3.754 9 5.816 8 -4.088 8
    0.12 3.754 9 6.156 5 -4.703 0
    0.15 3.754 9 6.710 4 -5.624 3
    0.2 3.754 9 7.751 6 -7.159 9
    0.22 3.754 9 8.209 3 -7.774 1
    下载: 导出CSV

    表  5  临界角速度受T1W的影响

    Table  5.   Cirtical angular velocity affected by T1W

    T1W/K ω1/s-1 ω2/s-1 ω3/s-1
    248 566 620 2 219
    392 564 618 2 218
    482 563 617 2 218
    608 562 615 2 217
    下载: 导出CSV

    表  6  临界角速度受T2W的影响

    Table  6.   Cirtical angular velocity affected by T2W

    T2W/K ω1/s-1 ω2/s-1 ω3/s-1
    1 472 561 614 2 220
    1 652 562 615 2 217
    1 832 563 616 2 214
    2 192 565 619 2 209
    下载: 导出CSV

    表  7  图 12中峰值及其对应转速

    Table  7.   Peak value and corresponding rotation speed of Fig. 12

    d0/m ΩA-max/s-1 Axr/(10-4m)
    0.04 291 4.175 7
    0.05 455 2.736 9
    0.06 658 1.928 3
    下载: 导出CSV

    表  8  图 13中峰值及其对应转速

    Table  8.   Peak value and corresponding rotation speed of Fig. 13

    T1W/K ΩA-max/s-1 Axr/(10-4m)
    302 459.2 2.717 9
    572 456.5 2.739 4
    932 452.9 2.768 2
    下载: 导出CSV

    表  9  图 14中峰值及其对应转速

    Table  9.   Peak value and corresponding rotation speed of Fig. 14

    T2W/K ΩA-max/s-1 Axr/(10-4m)
    1 832 453.7 2.758 0
    2 192 455.2 2.737 0
    2 732 459.8 2.733 0
    下载: 导出CSV

    表  10  图 15中峰值及其对应转速

    Table  10.   Peak value and corresponding rotation speed of Fig. 15

    2b/m ΩA-max/s-1 Axr/(10-4m)
    0.2 453 2.757 5
    0.4 429 2.351 1
    0.6 405 2.052 8
    下载: 导出CSV
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  • 收稿日期:  2019-04-03
  • 录用日期:  2019-08-03
  • 刊出日期:  2020-01-20

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