Mathematical calculation method for hysteresis characteristics of arc⁃shaped finger seal
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摘要:
为了预测指尖密封迟滞特性，提出了用能够直观反映指尖密封迟滞特性的最小迟滞量来表征指尖密封的迟滞，建立了指尖密封最小迟滞量计算的数学模型，确定了模型中的修正系数，并进行了试验验证，采用修正后的计算模型研究并获得了结构和工况参数对指尖密封迟滞的影响规律。研究结果表明：采用修正后的模型进行考虑迟滞效应的泄漏特性数值计算与试验结果误差最大为7.64%，最小迟滞量的计算模型合理可靠；指尖密封结构参数对其最小迟滞量影响程度从小到大依次为：指梁型线圆、指梁间隙、指梁根圆、指梁顶圆、指梁基圆、周向角、指尖片厚度。研究结果为进一步开展迟滞对指尖密封泄漏特性影响和指尖密封结构优化设计的研究提供了依据和理论基础。
Abstract:In order to predict the hysteresis characteristics of finger seal accurately,minimum hysteresis representing hysteresis characteristics of finger seal was proposed.Then minimum hysteresis mathematical calculation method was established,the correction coefficient of model was determined and verified by experiments.The influence rules of the structure and working condition parameters of finger seals on the hysteresis characteristics were studied and obtained based on the modified calculation model.Results showed that the maximum error between the numerical calculation of leakage characteristics considering the hysteresis effect based on modified calculation model and the test results was 7.64%,and the conclusion of model was reliable.The degree of influence of various structural parameters on the hysteresis characteristics of finger seal was in descending order: thickness of each finger laminate,finger repeat angle,arc radius of the finger beam arcs centers,diameter of the finger base circle,width of the interstice between fingers,and arc radius of finger beam.The results provide a theoretical basis and basis for further research on the influence of hysteresis on the finger seal leakage characteristics and the optimal design of finger seal structure.
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图 2 上下游压差作用下的指尖片受力
Figure 2. Stress of finger seal laminates under pressure difference between the upstream and downstream
图 6 转速下降阶段转子在零转速时泄漏量随压差变化的数值计算与试验结果
Figure 6. Numerical calculation and experiment results of leakage varies along with different pressures at zero rotor speed in rotor speed drop phase
图 8 指尖密封泄漏量随转速升降循环的变化
Figure 8. Leakage varies of finger seal along with rotor speed rise and fall
图 9 指尖密封最小迟滞量随参数变化系数的变化
Figure 9. Variation of the minimum hysteresis of finger seal along with variation of parameter change coefficient
图 10 指尖密封最小迟滞量随实际结构尺寸的变化趋势
Figure 10. Change trend of the minimum hysteresis of finger seal along with the practical value of structure parameters
图 11 小尺寸指尖密封的最小迟滞量随压差和摩擦因数的变化
Figure 11. Variation trend of the minimum hysteresis of small size finger seals along with pressure
表 1 指尖密封的结构参数
Table 1. Structure parameters of finger seal
结构参数 参数取值 D0/mm 190 Di/mm 150 Df/mm 152 Db/mm 170 Rc/mm 17.5 Rs/mm 75 θ/（°） 6 /（°） 6 Is/mm 0.3 Z/个 60 b/mm 0.25 
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表 2 单位参数变化量下指尖密封最小迟滞量的变化量
Table 2. Variation of the minimum hysteresis of finger seal under change of the unit parameter
结构参数 变化量 结构参数 变化量 Df/mm 0.063 3 Is/mm 0.029 7 Db/mm 0.045 4 b/mm 1.121 5 Rc/mm 0.075 θ/（°） 0.243 7 Rs/mm 0.011 5
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