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Seal performance analysis of double-faced gas film in counter-rotating intershafts
LIU Xiaoyu, WANG Zhili, DING Lei, WANG Bowen, LIU Likun
School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2016-03-18; Accepted: 2016-04-15; Published online: 2016-05-09
Corresponding author. WANG Zhili, E-mail:wang_zl@buaa.edu.cn
Abstract: The performance of a double-faced gas film seal system used in counter-rotating intershafts was analyzed. The system's two-degree-of-freedom force balance equation was established. The thickness and force of the film were calculated with finite element method. The seal system's dynamic response to seal disturbance simulated by instantaneous disturbing force and exciting force was solved with the direct numerical simulation. The vibration signal was processed by fast Fourier transform (FFT). The results show that the hydrodynamic-hydrostatic hybrid structure maintains a higher stiffness in a wider thickness range and improves the seal system performance with a good stability. When disturbed by instantaneous force, the seal system's convergence time is impacted by the mass ratio of track and sealing ring. When the exciting force's frequency is not the natural frequency, the seal system is in good stability. Exciting force with resonance frequency strengthens the vibration, increases the leakage and even damages system stability. Thus, this situation should be avoided in the design.
Key words: double-faced gas film     performance analysis     dynamic analysis     direct numerical simulation     fast Fourier transform (FFT)

1 密封结构及工作原理

 图 1 反转轴间双端面气膜密封系统 Fig. 1 Double-faced gas film seal system in counter-rotating intershafts

2 密封系统稳态求解 2.1 密封系统受力分析

 (1)
 (2)

 Ro—密封跑道外径；Ri—密封跑道内径；Rm—密封跑道结构尺寸；F(hF)—前端面密封气膜力；F(hB)—后端面密封气膜力。 图 2 密封件受力图 Fig. 2 Force diagram of seal components

2.2 端面气膜稳态压场

 (3)

 (4)

1) 已知压力边界：p|r=ri=pip|r=ro=po

2) 周期性边界：p(θ)=p(θ+2π/z)，z为节流孔数量。

3) 节流孔边界：在连续性方程中增加了ρ，为节流孔单位面积流入的质量流量，将雷诺方程和节流孔流量方程联立求解得到节流孔出口压力。

2.3 稳态密封性能

1) 气膜反力：

2) 气膜刚度：

3) 泄漏量：泄漏量由前后端面节流孔质量流量QK1QK2及前端面环形汇流质量流量QH三部分组成。

 (5)

 (6)

3 密封系统动态求解

3.1 密封系统动力学方程

 (7)

 (8)

t>t0Fs=0，摩擦力的正负号取决于密封件运动方向，式中x1x2分别表示密封跑道、主密封环偏离平衡位置位移。

 (9)

 (10)

 (11)
 (12)

3.2 端面气膜动态压场

 (13)

 (14)

4 计算结果及分析 4.1 结构参数

 参数 密封环外径Do/mm 密封环内径Ds/mm 节流孔直径Dk/mm 节流孔数量z 弹簧预紧力F/N 进口压力PH/MPa 出口压力PL/MPa 旋转速度n/(r·min-1) 数值 170 150 0.65 20 30 0.6 0.1 15 000

 参数 前端面膜厚hF0/μm 后端面膜厚hB0/μm 前端面反力FF/N 后端面反力FB/N 前端面刚度KF/(107N·m-1) 后端面刚度KB/(107N·m-1) 泄漏量Qr/(kg·s-1) 数值 17.27 22.93 1 480.8 1 483.3 3.16 4.96 0.009 4

4.2 动静压混合密封稳态密封性能

 图 3 气膜支反力随膜厚的变化趋势 Fig. 3 Variation trend of gas film reaction force with film thickness
 图 4 气膜刚度随膜厚的变化趋势 Fig. 4 Variation trend of gas film stiffness with film thickness
 图 5 泄漏量随膜厚的变化趋势 Fig. 5 Variation trend of leakage with film thickness

4.3 密封系统动态性能分析

4.3.1 瞬时力扰动下密封系统的动态响应

 图 6 不同质量比系统动态响应 Fig. 6 System dynamic response of different mass ratio

 图 7 振动收敛时间随质量比变化趋势 Fig. 7 Variation trend of vibration convergence time with mass ratio

 图 8 系统响应频谱图 Fig. 8 Spectrum of system response

 图 9 系统固有频率随质量比变化趋势 Fig. 9 Variation trend of natural frequency of system with mass ratio

4.3.2 激振力扰动下密封系统的动态响应

 图 10 不同激振频率密封系统动态响应曲线 Fig. 10 Seal system dynamic response curves of different excitation frequency
5 结论

1) 所述动静压混合气膜密封结构能在较大膜厚范围内保持较高的气膜刚度，气膜的工作范围增加允许系统更大的轴向跳动，且密封系统仍保持良好的稳定性。

2) 双端面气膜密封系统具有二自由度振动系统特征，在相同扰动下，振动收敛时间分布存在非线性区域、类线性增加区域以及类线性减少区域，且主密封环与密封跑道质量差距越大，其收敛时间越长。

3) 分析自由振动信号的频域，系统具有两阶固有频率，当激振频率位于系统固有频率附近时，密封系统振幅显著增加，可能导致系统失稳，在共振频率之外，振幅较小，密封系统稳定性较好。

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#### 文章信息

LIU Xiaoyu, WANG Zhili, DING Lei, WANG Bowen, LIU Likun

Seal performance analysis of double-faced gas film in counter-rotating intershafts

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(3): 608-614
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0216