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

doi:10.13700/j.bh.1001-5965.2019.0150

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

潘健智^{1, 2, ,},
魏大盛²,
胡伟男¹

1.
南京理工大学理学院, 南京 210094
2.
北京航空航天大学能源与动力工程学院, 北京 100083

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
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- 被引次数: 0
出版历程
- 收稿日期: 2019-04-03
- 录用日期: 2019-08-03
- 网络出版日期: 2020-01-20

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

PAN Jianzhi^{1, 2
, ,},
WEI Dasheng²,
HU Weinan¹

1.
School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
2.
School of Energy and Power Engineering, Beihang University, Beijing 100083, China

Funds:

Natural Science Foundation of Jiangsu Province BK20160821

More Information

Corresponding author: PAN Jianzhi, E-mail:jzhpan@163.com

摘要

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。
- 混合式转子系统 /
- 热膨胀 /
- 厚转盘 /
- 弯曲势能 /
- 弯曲刚度
Abstract:
According to complex and changeable high-temperature environments of large rotating machinery, such as aero engines or steam turbines, the main rotor system of the unit has a variable structure due to thermal expansion under operating conditions, which could also affect the operation characteristics. First, considering high stiffness of turntable-drum mixing, compared with the rotating shaft, the structure is simplified and a single-thickness disk rotor dynamic model is established. Second, aimed at the variable structure characteristics of the system caused by thermal expansion, Hermite interpolation method and curve fitting method are used to depict the bending condition of rotating shaft when the thickness table is at any position, and then bending restoring force provided to disk and the bending restoration stiffness of the shaft are calculated by using numerical methods, basing on elastic potential energy stored in the bending.Finally, through numerical analysis of precession frequency, critical angular velocity and response amplitude of thick disk rotor system, it is verified that axial movement induced by thermal expansion is one of the main factors that affect the dynamics properties of thick disk rotor system.
- mixing rotor system /
- thermal expansion /
- thick disk /
- bending potential energy /
- bending stiffness

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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

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图 2 理想刚性圆柱示意图

Figure 2. Schematic diagram of ideal rigid cylinder

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图 3 厚盘转子系统示意图

Figure 3. Schematic diagram of rotor system with thick disk

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图 4 转轴轴向窜动

Figure 4. Axial movement of shaft

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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)

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图 6 热膨胀转子弯曲示意图

Figure 6. Bending diagram of rotor after thermal expansion

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图 7 弯曲转轴的曲线拟合

Figure 7. Curve fitting of bending shaft

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图 8 温升曲线

Figure 8. Temperature rising curves

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图 9 转轴长度变化

Figure 9. Axial length variation

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图 10 转子进动频率

Figure 10. Precession frequency of rotor

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图 11 临界角速度ω_α、ω_β变化

Figure 11. Changes of cirtical angular velocity ω_α and ω_β

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图 12 转轴截面直径影响下响应x_r的幅频曲线

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

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图 13 T_1W影响下响应x_r的幅频曲线

Figure 13. Amplitude-frequency curves of response x_r under influence of T_1W

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图 14 T_2W影响下响应x_r的幅频曲线

Figure 14. Amplitude-frequency curves of response x_r under influence of T_2W

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图 15 转盘厚度影响下响应x_r的幅频曲线

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

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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R_l/m	0.03
偏心量ε/m	0.3×10^-4
比例阻尼系数β₁，β₂	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

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表 2 弯曲恢复刚度受T_1W的影响

Table 2. Bending restoration stiffness affected by T_1W

T_1W/K	k_rr/(10⁷N·m^－1)	k_θθ/(10⁶N·m^－1)	k_rθ/(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

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表 3 弯曲恢复刚度受T_2W的影响

Table 3. Bending restoration stiffness affected by T_2W

T_2W/K	k_rr/(10⁷N·m^－1)	k_θθ/(10⁶N·m^－1)	k_rθ/(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

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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	k_rr/(10⁷N·m^－1)	k_θθ/(10⁶N·m^－1)	k_rθ/(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

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表 5 临界角速度受T_1W的影响

Table 5. Cirtical angular velocity affected by T_1W

T_1W/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

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表 6 临界角速度受T_2W的影响

Table 6. Cirtical angular velocity affected by T_2W

T_2W/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

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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	Ω_A-max/s^－1	A_xr/(10^-4m)
0.04	291	4.175 7
0.05	455	2.736 9
0.06	658	1.928 3

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表 8 图 13中峰值及其对应转速

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

T_1W/K	Ω_A-max/s^－1	A_xr/(10^-4m)
302	459.2	2.717 9
572	456.5	2.739 4
932	452.9	2.768 2

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表 9 图 14中峰值及其对应转速

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

T_2W/K	Ω_A-max/s^－1	A_xr/(10^-4m)
1 832	453.7	2.758 0
2 192	455.2	2.737 0
2 732	459.8	2.733 0

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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	Ω_A-max/s^－1	A_xr/(10^-4m)
0.2	453	2.757 5
0.4	429	2.351 1
0.6	405	2.052 8

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