Leakage characteristics and formula construction of W-shaped elastic metal seals
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摘要:
基于Weierstrass-Mandelbrot（W-M）分形理论建立了考虑实际粗糙接触表面的W形弹性金属密封泄漏特性求解模型，设计搭建W形弹性金属密封泄漏特性实验装置，在实验验证数值求解模型准确性基础上，研究了W形弹性金属密封在不同内外腔压差、压缩量以及来流温度下的力学特性、流场特性与泄漏特性，提出了基于多元回归方法综合考虑工况参数与表面粗糙度的W形弹性金属密封泄漏量理论公式。研究结果表明：接触应力随着内外腔压差的增大、温度的升高以及压缩量的增加而不断增大，接触宽度随着接触应力的增加而增大。密封系统的泄漏量随着表面粗糙度降低、内外腔压差减小以及来流温度的升高而逐渐减小。降低表面粗糙度能显著提升密封系统的封严性能，表面粗糙度由3.2 μm减小至1.6 μm时，泄漏量平均减小50%；表面粗糙度由1.6 μm减小至0.8 μm，泄漏量平均减小62%。所构造的泄漏量理论公式能够准确预测考虑实际粗糙接触表面的W形弹性金属密封的泄漏量，为W形弹性金属密封泄漏特性分析提供理论依据。
Abstract:Based on Weierstrass-Mandelbrot geometric fractal theory, a W-shaped elastic metal leakage model considering the actual rough contact surface was established. The experimental device for leakage characteristics of W-shaped elastic metal seal was designed and built, and the accuracy of numerical solution model for leakage characteristics of W-shaped elastic metal seal was verified by experiments. The flow field characteristics and leakage characteristics of W-shaped elastic metal seals under different internal and external cavity pressure differences, compression and flow temperature were studied. At the same time, the theoretical formula of W-shaped elastic metal seal leakage was proposed based on multiple regression methods considering the working condition parameters and surface roughness. The results showed that the contact stress increased with the increase of pressure difference, temperature and compression, and the contact width increased with the increase of contact stress. The leakage of the sealing system gradually decreased with the decrease of surface roughness, the pressure difference between internal and external cavities and the increase of inlet temperature. Reducing the surface roughness can significantly improve the sealing performance of the sealing system. When the surface roughness Ra reduced from 3.2 μm to 1.6 μm, the leakage decreased by 50% on average. The surface roughness Ra reduced from 1.6 μm to 0.8 μm, and the leakage rate decreased by 62% on average. The constructed theoretical formula of leakage can accurately predict the leakage of W-shaped elastic metal seal considering the roughness of contact surface, thus providing a theoretical basis for analysis of leakage characteristics of W-shaped metal seal.
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图 6 W形弹性金属密封泄漏通道模型构建流程
Figure 6. Model construction flow of W-shaped elastic metal seal leakage channel
图 11 数值计算与实验之间的泄漏结果比较
Figure 11. Comparison of leakage results between numerical calculation and experiment
图 12 接触应力随温度与内外腔压差的变化规律
Figure 12. Variation of contact stress with temperature and pressure difference between inner and outer cavities
图 13 接触应力随压缩量与温度的变化规律
Figure 13. Variation of contact stress with compression and temperature
图 14 接触应力随内外腔压差与压缩量的变化规律
Figure 14. Variation law of contact stress with the pressure difference between the inner and outer cavities and the compression amount
图 15 不同内外腔压差下金属密封环总体变形以及受力
Figure 15. Overall deformation and stress of the metal sealing ring under different internal and external cavity pressure differences
图 17 W形弹性金属密封环与法兰接触面的流场分布
Figure 17. Flow field distribution on the contact surface between W-shaped elastic metal sealing ring and flange
图 18 不同表面粗糙度下的泄漏因子随接触间隙的变化规律
Figure 18. Variation of leakage factor with contact clearance under different surfaceness
图 19 不同表面粗糙度下泄漏量随内外腔压差的变化曲线
Figure 19. Variation curve of leakage volume with the pressure difference between the inner and outer cavities under different surfaceness
图 20 不同内外腔压差下泄漏量随温度的变化规律
Figure 20. Variation law of leakage with temperature under different pressure differences between the inner and outer cavities
图 21 不同温度下泄漏量随表面粗糙度的变化曲线
Figure 21. Variation curves of leakage volume with roughness at different temperatures
图 22 考虑粗糙接触表面的W形弹性金属密封理论公式与数值计算结果对比
Figure 22. Comparison of theoretical formulas and numerical results of W-shaped elastic metal seals considering rough contact surfaces
图 23 考虑粗糙接触表面的W形弹性金属密封理论公式与实验测量结果对比
Figure 23. Comparison of theoretical formulas and experimental measurements for W-shaped elastic metal seals considering rough contact surfaces
表 1 W形密封环结构参数
Table 1. Structure parameters of W-shaped sealing ring
参数 数值 外径d/mm 300.00 环高h/mm 6.00 波峰半径R1/mm 0.75 波谷半径R2/mm 0.90 接触曲率半径R3/mm 3.00 壁厚ts/mm 0.30 
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表 2 材料参数
Table 2. Material parameters
温度
t/℃抗拉强度
σb/MPa屈服强度
σs/MPa弹性模量
E/GPa热导率
W/（m·℃）密度
ρ/（g/cm3）20 1465 1265 203 0.92 8.24 650 1180 1030 167 15.49
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表 3 密封模型工况参数
Table 3. Operating parameters of the leakage model
参数 数值及说明 流体属性 理想空气 流体状态 层流流动 出口压力/MPa 0.1 进口压比 1～5 接触应力/MPa 60～160 表面粗糙度/μm 0.8～3.2
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