-
摘要:
为提升弹性箔片端面气膜密封(CFFGS)综合性能，提出1种新型超椭圆织构浮动坝箔片端面气膜密封(SHFSD-CFFGS)，该结构通过在箔片区开设超椭圆型孔织构，利用二次动压效应提升了密封的开启性和气膜稳定性. 此外，在密封坝底部设计了柔性箔片支撑增强了其自适应性，并通过表面双列倾斜超椭圆型孔织构来改善控漏性能. 基于气体润滑和弹性力学相关理论，建立SHFSD-CFFGS气弹耦合润滑理论模型，研究浮动坝区型孔织构形状、倾角、方向因子和深度对SHFSD-CFFGS密封性能的影响规律并开展箔片区和坝区柔度系数优化设计. 结果表明：超椭圆织构端面结构在保证箔片密封具有较好开启力和气膜刚度的同时能够进一步减小泄漏率；且在本文中参数研究范围内，当超椭圆系数n2取1、内外侧型孔倾角θ1和θ2取40°、超椭圆织构长半轴a2取1.75 mm、短半轴b2取0.7 mm、织构深度Td2取6 μm、箔片区柔度系数α1取0.005~0.01、浮动坝区柔度系数α2取1×10−5~1×10−4时，SHFSD-CFFGS具有较优的综合密封性能.
Abstract:Dry gas seal is widely used in centrifugal compressors, pumps, fans, and other high-speed rotating equipment due to its advantages of low friction, minimal leakage, and extended operational lifespan.However, with the advancement of rotating machinery towards higher-speed conditions, intense shaft vibration can lead to grinding or crushing failures of the dry gas seal's rigid surface. Therefore, developing a novel dry gas seal structure capable of accommodating severe shaft vibration is of significant importance. To address this, foreign scholars have developed a flexible-end compliant foil face gas seal (CFFGS), drawing upon the design principles of foil bearings. Compared to traditional rigid-end dry gas seals, the CFFGS with a flexible surface exhibits clear adaptability and impact resistance. However, it does not demonstrate significant advantages in terms of opening force, gas film stiffness, and leakage rate. Enhancing these aspects while ensuring the adaptive capability of CFFGS has become a crucial focus in its application research. Additionally, incorporating hole textures on the seal end face is recognized as a critical approach to enhancing hydrodynamic lubrication performance. Super-elliptic curves can describe the boundaries of sealed interface-type holes structures, allowing for continuous shape evolution by adjusting the super-elliptic coefficients. Nonetheless, scholarly investigations into seal hole texture predominantly focus on traditional rigid surface hydrodynamic pressure seals, with relatively limited attention given to research on foil seals.
In order to improve the comprehensive performance of CFFGS, a novel super-elliptical hole floating seal dam compliant foil face gas seal (SHFSD-CFFGS) was proposed. By opening super-elliptical hole textures in the foil area, the opening force and the gas film stiffness were improved by the effect of secondary dynamic pressure. Additionally, the compliant foil support was designed at the bottom of the sealing dam to reinforce its adaptability, and the leakage control performance was improved by the double-row inclined super-elliptical hole textures on the surface. Based on the theories of gas lubrication and elastic mechanics, a theoretical model of SHFSD-CFFGS aeroelastic coupling lubricationis established. The study explored the influence of the hole texture shape, inclination, slender ratio, and depth of the floating dam area on the seal performance and conducted an optimization design for the compliant coefficients of the foil and dam area. The results showed that the super-elliptical textured foil face structure reduced the leakage rate while enhancing the foil seal’s opening force and gas film stiffness. Within the scope of parameters research in this paper, when the super-elliptical coefficient n2 was set to 1, the inner and outer hole inclination angles θ1 and θ2 were set to 40°, the super-elliptical texture major axis a2 was 1.75 mm, the minor axis b2 was 0.7 mm, the texture depth Td2 was 6 μm, the compliance coefficient of foil area α1 was set to 0.005~0.01, and the compliance coefficient of floating seal dam area α2 varied from 1×10−5 to 1×10−4, the SHFSD-CFFGS exhibited superior comprehensive sealing performance.
-
Keywords:
- foil seal /
- floating seal dam /
- super-elliptical texture /
- upstream pumping /
- sealing performance
-
干气密封是1种广泛应用于离心压缩机、泵和风机等中高速旋转设备的非接触式轴端密封技术，具有低摩擦、低泄漏和长寿命等优势[1-3]. 然而，随着旋转机械不断向更高转速工况发展，随之而来的轴系剧烈振动极易导致干气密封刚性表面发生碰磨或撞碎失效[4-5]. 因此，研发1种能适应剧烈轴振的新型干气密封结构具有重要意义.
在21世纪初，Heshmat和Agrawal等[6-7]以箔片轴承设计理念为参考，提出了采用弹性结构替代刚性密封端面的新构思，设计了1款具有柔性端面的弹性箔片端面气膜密封(Compliant foil face gas seal, CFFGS). 基于此模型，Muson等[8]对CFFGS在多种工况下的密封性能进行了探讨，研究结果显示，其柔性表面表现出优异的抗变形能力，可以有效适应气膜厚度的变化，在高速高温工况下具有良好的密封性能；随后，Salehi等[9]将CFFGS引入航空发动机性能测试，而Heshmat等[10]则在飞机空气循环机的试验中采用了CFFGS，2项研究均表明CFFGS在高速高振动的极端工况下有较好的适用性. 近年来，国内学者逐步关注CFFGS并开展相关研究. Chen等[11-12]和王庆港等[13]通过建立CFFGS的气弹耦合润滑理论模型并利用有限差分法求解分析了密封的稳、动态性能并开展了结构优化设计. 研究结果发现，与传统刚性端面的干气密封相比，CFFGS在抗扰动能力上具有明显优势，但开启力和气膜刚度有一定下降. 同时，徐洁等[14-16]也研究指出在高速低压工况下引入柔性表面结构可有效提升密封的综合性能. 针对目前CFFGS结构中刚性密封坝与旋转部件接触时会引发额外的摩擦和磨损，导致密封坝表面发生碰撞和碎裂等风险以及对密封自适应性产生不利影响. 陈源等[17]对CFFGS结构进行改进，提出了抗冲击性更佳的浮动密封坝箔片端面气膜密封(Floating seal dam compliant foil face gas seal, FSD-CFFGS). 综上研究表明，具有柔性表面或柔性支撑的CFFGS相比刚性表面干气密封具有明显的自适应能力或抗冲击能力，但从开启力、气膜刚度和泄漏率角度无明显优势，如何在确保CFFGS自适应能力的同时提升开启力和气膜刚度并降低泄漏率，成为CFFGS应用研究的重要方向.
在密封端面开设型孔织构是改善流体动力润滑性能的重要方法，早在1996年，Etsion等[18]就对型孔织构端面密封性能进行了理论分析. 之后，Kligerman等[19]将圆形孔密封技术引入到气膜密封领域，并建立了相应的润滑模型. 随着研究的不断深入，椭圆孔[20]、菱形孔[21]和矩形孔[22]等不同形状的方向性孔相继出现，经过数值验证证实型孔织构能有效提升密封动压性能并降低泄漏率. 柏林清等[23]的分析表明，在型孔织构排布形式方面，双列倾斜型孔端面气体密封的低压侧型孔环带有助于将下游流体沿着型孔倾斜方向向上游进行泵送，使得泄漏率显著降低. 张璇等[24]则利用具有优异几何表征能力的超椭圆曲线来描述密封界面型孔织构边界，通过改变超椭圆系数可实现型孔织构形状的连续演变，使得型孔织构形状设计更加灵活和多样.
目前，国内外密封型孔织构研究主要集中在传统刚性表面流体动压密封中，而对于箔片密封的研究较少. 本文中针对自适应性更强的FSD-CFFGS，在箔片区和坝区分别引入超椭圆织构，研究其作用效果并开展结构优化，以期为实现超椭圆织构浮动坝弹性箔片端面气膜密封(Super-elliptical hole floatingsealdam compliant foil face gas seal, SHFSD-CFFGS)增大开启力、提高气膜刚度和减小泄漏率的设计目标提供理论依据.
1. 计算模型
1.1 物理模型
超椭圆是1种类似椭圆的封闭曲线，具有椭圆长轴、短轴和对称性的特点，同时具有形状变换平滑的特点. 随着超椭圆系数的不断变化，超椭圆形状可由星形连续演变至矩形，其方程表达式[25]如下：
$$ {\left| {\frac{x}{a}} \right|^n} + {\text{ }}{\left| {\frac{y}{b}} \right|^n} = 1 $$ (1) 式中，a和b分别为超椭圆长和短半轴，n为超椭圆系数.
SHFSD-CFFGS结构示意图如图1(a)所示，其密封端面主要分为两部分：一是由弹性波箔片支撑平箔片组成的箔片区，二是由弹性波箔片支撑密封坝组成的浮动坝区. 此外，在箔片端面斜坡区和浮动坝表面引入超椭圆型孔织构，如图1(b)所示. 图1(c)所示为不同内、外侧型孔倾角下的织构深度分布云图，可以看出箔片端面的型孔中心点位于箔片中位线上，型孔的长轴与圆周线方向垂直. 浮动坝区内、外侧型孔的中心点分别位于坝区的三等分线上，并在圆周方向上均匀分布. 通过调节箔片区和浮动坝区超椭圆系数n1和n2、箔片区和浮动坝区织构深度Td1和Td2、箔片区超椭圆横半轴a1和纵半轴b1、浮动坝区超椭圆横半轴a2和纵半轴b2以及浮动坝区内、外侧型孔的长轴与圆周线的倾角θ1和θ2，可以实现对型孔织构形状和结构的连续调控. 其中，当型孔倾角所产生的导向作用促成低压侧气体沿着超椭圆长轴方向向高压侧进行泵送时会形成上游泵送效应，而当型孔倾角促使高压侧气体沿着超椭圆长轴方向向低压侧进行泵送时，则形成下游泵送效应.
![]()
图 1 超椭圆织构浮动坝箔片密封结构示意图Figure 1. Super-elliptical hole texture floating seal dam foil sealstructure diagram1.2 数学模型
假设润滑气体为层流状态的等温等黏度理想气体，在忽略惯性力和体积力的条件下，气体稳态雷诺方程如式(2)所示.
$$ \frac{1}{{{r^2}}}\frac{\partial }{{\partial \theta }}\left( {p{h^3}\frac{{\partial p}}{{\partial \theta }}} \right) + \frac{1}{r}\frac{\partial }{{\partial r}}\left( {rp{h^3}\frac{{\partial p}}{{\partial r}}} \right) = 6\mu \omega \frac{{\partial \left( {ph} \right)}}{{\partial \theta }} $$ (2) 式中，p和h分别为密封端面任意一点的气膜压力和厚度，μ为气体黏度，ω为旋转角速度.
图2所示为SHFSD-CFFGS气膜厚度分布示意图，可以看出，气膜厚度由初始气膜厚度h0、箔片表面到密封坝表面高度差g(r,θ)、箔片区织构区域孔深Td1(r,θ)、浮动坝区织构区域孔深Td2(r,θ)以及密封端面在运行条件下箔片区形变量u1(r,θ)和浮动坝区浮动量u2(r,θ)构成.
气膜厚度h(r,θ)表达式如下：
$$ h(r,\theta ) = \left\{ \begin{aligned} &{h_0} + g(r,\theta ) + {u_1}(r,\theta )&&{\text{ (}}r,\theta {\text{)}} \in {\text{untextured area of foil}} \\ &{h_0} + g(r,\theta ) + {u_2}(r,\theta )&&{\text{ (}}r,\theta {\text{)}} \in {\text{untextured area of floating seal dam}} \\ &{h_0} + g(r,\theta ) + {u_1}(r,\theta ) + {T_{{\text{d1}}}}&&{\text{ (}}r,\theta {\text{)}} \in {\text{textured area of foil}} \\ & {h_0} + g(r,\theta ) + {u_2}(r,\theta ) + {T_{{\text{d2}}}}&&{\text{ (}}r,\theta {\text{)}} \in {\text{textured area of floating seal dam}} \end{aligned} \right. $$ (3) 上式中，初始状态下的g(r,θ)为
$$ g(r,\theta ) = \left\{ \begin{aligned} & {h_{\text{d}}}{\text{ }}&&{r_{\text{g}}} \leqslant r \leqslant {r_{\text{o}}},0 \leqslant \theta \leqslant {\beta _1} \\ &{\delta _{\text{h}}}(1 - \frac{{\theta - {\beta _1}}}{{c\beta }}){\text{ }}&&{r_{\text{g}}} \leqslant r \leqslant {r_{\text{o}}},{\beta _1} \leqslant \theta \leqslant {\beta _2} \\ & 0{\text{ }}&&{r_{\text{g}}} \leqslant r \leqslant {r_{\text{o}}},{\beta _2} \leqslant \theta \leqslant {\beta _3}{\text{ }} \\ & 0{\text{ }}&&{r_{\text{i}}} \leqslant r \leqslant {r_{\text{g}}}{\text{ }} \\ \end{aligned} \right. $$ (4) 式中，β为单周期箔片区的周向角度，c为节距比即斜坡区与箔片区的周向角度之比，hd为间隙区深度，δh为楔形高度.
本文中每个波箔片均视为刚度为kb的线性弹簧[26]，根据图3所示的波箔片和平箔片的几何特征和组装关系，刚度kb的计算表达式如式(5)所示.
$$ {k_{\text{b}}} = \frac{{{E_{\text{b}}}t_{\text{b}}^3}}{{2{l^3}(1 - v_{\text{b}}^2)}} $$ (5) 式中，Eb和vb分别为波箔片材料弹性模量和泊松系数，tb表示波箔片厚度，l是半波箔长度.
引入柔度系数α来表征箔片轴向变形能力，其定义为
$$ \alpha = \frac{{{p_{\text{a}}}s}}{{{k_{\text{b}}}{h_0}}} $$ (6) 式中，pa为大气环境压力，s为波箔片单元长度.
据此推导出箔片区形变量u1(r,θ)和浮动坝区浮动量u2(r,θ)的表达式为
$$ u(r,\theta ) = \left\{ {\begin{aligned} &{{u_1}(r,\theta ) = (p - {p_{\text{o}}}){\alpha _1}{\text{ }}\quad{r_{\text{g}}} \leqslant r \leqslant {r_{\text{o}}}} \\ &{u_2}(r,\theta ) = \left( \int_0^{2\pi } {\int_{{r_{\text{i}}}}^{{r_{\text{g}}}} {prdrd\theta - } } \int_0^{2\pi } {\int_{{r_{\text{i}}}}^{{r_{\text{g}}}} {{p_{\text{i}}}rdrd} } \theta \right) {\alpha _2}{\text{ }}\\ &\qquad\qquad\qquad\qquad\quad{r_{\text{i}}} \leqslant r \leqslant {r_{\text{g}}} \end{aligned}} \right. $$ (7) 式中，α1为箔片区支撑波箔柔度系数，α2为浮动坝区支撑波箔柔度系数，pi为密封环内径侧大气压力，po为密封环外径侧的介质压力.
根据SHFSD-CFFGS的运行环境和构造特性，稳态雷诺方程(2)的求解所采用的边界条件如下：
1) 压力边界条件：
$$ \left\{ \begin{aligned} &p(r,\theta ) = {p_{\text{i}}},&r = {r_{\text{i}}} \\ & p(r,\theta ) = {p_{\text{o}}},&r = {r_{\text{g}}} \\ & p(r,\theta ) = {p_{\text{o}}},&r = {r_{\text{o}}} \end{aligned} \right. $$ (8) 2) 周期性边界条件：
$$ p\left(r,\theta + \frac{{2\pi }}{{{N_{\text{c}}}}}\right) = p(r,\theta ) $$ (9) 式中，Nc为周期数.
基于上述边界条件，采用有限差分法对SHFSD-CFFGS气弹耦合润滑理论模型进行求解，推导出密封端面气膜压力分布. 在此基础上，进一步计算稳态密封性能参数，包括开启力Fo、气膜刚度kz、泄漏率Q和刚漏比Г.
端面开启力Fo、气膜刚度kz表达式分别如下：
$$ {F_{\text{o}}} = \int_0^{2\pi } {\int_{{r_{\text{i}}}}^{{r_{\text{o}}}} {pr{\mathrm{d}}r{\mathrm{d}}\theta } - } \int_0^{2\pi } {\int_{{r_{\text{g}}}}^{{r_{\text{o}}}} {{p_{\text{o}}}r{\mathrm{d}}r{\mathrm{d}}\theta } } $$ (10) $$ {k_{\text{z}}} = \frac{{\partial {F_{\text{o}}}}}{{\partial h}} $$ (11) 泄漏率Q表达式为
$$ Q = \frac{{{h^3}r}}{{12\mu {p_{\text{a}}}}}\int_0^{2\pi } {\frac{{\partial p}}{{\partial r}}} p{\mathrm{d}}\theta $$ (12) 刚漏比Г是衡量密封综合性能的指标，其表达式为
$$ \varGamma=\frac{{k}_{\text{z}}}{Q} $$ (13) 为综合评价SHFSD-CFFGS稳态性能，定义密封性能变化率用以表征SHFSD-CFFGS相对于CFFGS的稳态密封性能参数的变化程度.
$$ \begin{split}&{\eta }_{F}=\frac{{F}_{\text{o}}-{F}_{(\text{CFFGS})}}{{F}_{(\text{CFFGS}）}},\;\;{\eta }_{k}=\frac{{k}_{\text{z}}-{k}_{\text{z}(\text{CFFGS})}}{{k}_{\text{z}(\text{CFFGS})}},\\ &{\eta }_{Q}=\frac{Q-{Q}_{(\text{CFFGS})}}{{Q}_{(\text{CFFGS})}},\;\;{\eta }_{\varGamma}=\frac{\varGamma-{\varGamma}_{(\text{CFFGS})}}{{\varGamma}_{(\text{CFFGS})}}\end{split} $$ (14) 2. 结果分析与讨论
本文中所采用的箔片密封结构参数、密封端面型孔织构参数以及工况参数列于表1中，在下述分析中，除特别说明外，其他参数均保持不变.
表 1 初始参数数值表Table 1. Initial parameters valuesParameters Specifications Inner radius of seal face, ri/mm 58.42 Outer radius of seal face, ro/mm 77.78 Number of cycles, Nc 8 Slope ratio, c 0.4 Foil-dam ratio, ξ 2 Compliance coefficient of foil area, α1 0.01 Compliance coefficient of floating seal dam area, α2 1×10−4 Wedge height, δh/μm 15 Balance film thickness, h0/μm 3 Major semi-axis of the super-elliptical in foil area, a1/mm 4 Major semi-axis of the super-elliptical in floating
dam area, a2/mm1.4 Minor semi-axis of the super-ellipticalin foil area, b1/mm 2 Minor semi-axis of the super-elliptical in floating
dam area, b2/mm0.7 Depth of textures in foil area, Td1/μm 5 Depth of textures in floating dam area, Td2/μm 5 Number of circumferential holes in foil area 4 Number of circumferential holes in floating dam area 13 Number of radial holes in foil area 1 Number of radial holes in floating dam area 2 Pressure at inner radius, pi/MPa 0.1 Pressure at outer radius, po/MPa 0.3 Rotational speed, ω/(r/min) 14 000 2.1 程序计算流程图及正确性验证
根据上述分析，基于有限差分法按照图4所示的流程图编程求解气弹耦合润滑理论模型. 图4中m1和m2分别为密封端面周向和径向方向上的节点数，pi,j和hi,j分别为气膜压力和气膜厚度，Δpi,j和Δhi,j分别为气膜压力和气膜厚度变化量.
CFFGS与箔片气体推力轴承理论模型相符，故将本文中程序计算结果与箔片气体推力轴承文献[27]中的数据进行了对比验证，如图5所示，结果显示两者具有良好的一致性，表明了本文中理论模型和计算程序的准确性.
2.2 超椭圆织构浮动坝箔片密封表面气膜压力和流场分布
图6所示为CFFGS和SHFSD-CFFGS的气膜压力与流场分布情况，从图6(a)和(b)的对比中可以发现，箔片区域有无织构时气膜压力分布存在显著差异. 箔片端面超椭圆型孔织构产生的额外收敛楔，推动了气膜压力进一步提升，有助于密封系统的快速开启和稳定运行. 由图6(c)和(d)的流场分布可以看出，在密封运行时，在压差和黏性剪切力作用下气流整体呈周向并偏向低压区方向流动. 从密封坝区域的超椭圆型孔内的局部流场来看，部分气体发生了向上游泵送，方向性超椭圆型孔起到了上游泵送的作用，有利于CFFGS控漏.
![]()
图 6 SHFSD-CFFGS与CFFGS气膜压力与流速分布比较Figure 6. Comparison of SHFSD-CFFGS and CFFGS gas film pressure and flow velocity distribution2.3 浮动坝区超椭圆织构参数对密封性能变化率的影响
通过协同设计浮动坝区超椭圆系数n2以及内外侧型孔倾角θ1和θ2等型孔结构参数，可以衍生出多样化的孔型结构类型，从而将密封端面织构抽象的形状优化问题具体化为参数优化问题，有助于确定SHFSD-CFFGS在性能较佳时所需的浮动坝端面织构参数.
2.3.1 超椭圆型孔倾角对密封性能变化率的影响
图7所示为不同超椭圆系数n2以及内外侧型孔倾角θ1和θ2组合条件下对应的箔片密封性能变化率. 从数值结果来看，通过超椭圆型孔织构结构的调整虽可提升开启力和气膜刚度，但往往伴随泄漏率上升. 当超椭圆系数保持不变时，最大开启力和气膜刚度对应的内外侧型孔倾角分别集中在θ1=20°~40°、θ2=120°~140°的范围内. 此时，端面外侧型孔起到下游泵送作用，而端面内侧型孔则起到上游泵送作用，有效增强了流体动压效应. 而当θ1=θ2=40°时密封控漏性能较佳，这主要是因为此时内外侧型孔均具备上游泵送作用，能有效地将低压侧的气体向高压侧进行泵送，从而实现泄漏率的最小化. 随着超椭圆系数的增大，各项超椭圆系数下开启力最优值所对应的倾角优选范围逐渐扩大，而泄漏率和刚漏比的优选倾角范围则不断缩小. 对于气膜刚度而言，超椭圆系数的变化对气膜刚度最大值影响并不显著，但会对其优选倾角范围产生影响. 值得注意的是，超椭圆系数n2为1，即菱形孔时密封开启力较小，但控漏效果较好，而当超椭圆系数n2为4，即型孔形状趋向矩形时，开启力增加，但泄漏率也增大. 上述现象主要是因为型孔边界外扩，增加了内部气体动能，但同时也扩大了泄漏通道. 根据各项密封性能变化率的极差发现密封坝区织构形状和倾角对泄漏率有显著影响，其中型孔倾角的影响最为突出，后文中重点在控漏性能较优时的型孔倾角条件(θ1=θ2=40°)下开展密封性能分析.
![]()
图 7 双列型孔倾角θ1和θ2对密封性能变化率的影响Figure 7. Influence of the double-row hole angle θ1 and θ2 on the change rate of sealing performance2.3.2 超椭圆型孔方向因子对密封性能变化率的影响
图8所示为超椭圆型孔长半轴a2固定为1.4 mm或短半轴b2固定为0.7 mm时超椭圆型孔方向因子γ (长短半轴之比)对密封性能变化率的影响规律. 结果表明，在不同型孔结构下，随着方向因子的增加，开启力、气膜刚度和泄漏率均呈减小趋势. 这是由于方向因子的增加使得超椭圆型孔形状变得细长，体积变小，这使得内部气体动能减小，削弱了动压效应，然而细长形态有利于导流，提升了上游泵送作用，故体现了一定的控漏优势. 从性能参数的降幅比率来看，开启力和气膜刚度相对于泄漏率的降幅要小得多，这为密封综合性能的提升提供有利条件. 特别当超椭圆系数n2=1、短半轴b2=0.7 mm保持不变时，通过调控方向因子γ至2.5，泄漏率降至最小值，此时密封刚漏比也较大，综合性能较优. 同时可以观察到，随着超椭圆系数的增大，织构对密封控漏的提升效果逐渐减弱. 这是因为当超椭圆系数为1时，菱形孔具有更多的尖锐边缘，增加了气体通过型孔时的阻力，降低了气体速度. 其次，细长型的菱形孔相较于其余孔型具有更明显的方向性，能更好地调控气体流动的方向，有利于泄漏气体的反向泵送. 以上结果表明，通过合理设计超椭圆型孔的长短轴比例，可有效控制泄漏. 后文中重点在b2=0.7 mm，γ=2.5条件下开展密封性能分析.
![]()
图 8 方向因子γ对密封性能变化率的影响(θ1=θ2=40°)Figure 8. Influence of slender ratio γ on the change rate of sealing performance (θ1=θ2=40°)2.3.3 超椭圆型孔深度对密封性能变化率的影响
图9所示为型孔深度Td2对SHFSD-CFFGS密封性能变化率的影响曲线. 可以看出，当超椭圆系数n2为1时，开启力和气膜刚度始终保持较高水平. 随着超椭圆系数n2的增大，开启力和气膜刚度呈先下降而后在n2为4时略有提升的趋势. 在4种超椭圆系数n2下，随着织构深度Td2的增加，SHFSD-CFFGS开启力先快速降低，而后变化趋于平缓，气膜刚度则表现出减速递减的变化趋势. 通过图7(a)和(b)的分析结果可知当倾角为θ1=θ2=40°时不利于动压效应的形成，此时增加织构深度可能会导致气膜的失稳，进而影响气膜刚度和开启力. 观察图9(c)和(d)可以发现，当超椭圆系数n2为1即菱形孔时，泄漏率呈先快速下降后缓慢上升的趋势，而刚漏比则表现为先快速上升而后缓慢下降的趋势，且近似存在1个最优织构深度Td2=6 μm. 当n2=1、Td2=6 μm时，SHFSD-CFFGS的泄漏率比普通的CFFGS降低了39.5%，刚漏比提升了66.63%. 随着超椭圆系数的增大，SHFSD-CFFGS控漏效果不仅下降，且在织构深度过大或过小时，泄漏率甚至大于坝区无织构时的情况. 总体而言，菱形孔织构相较于其余形状织构能保证密封具有较好开启性和气膜稳定性的同时拥有较优的控漏性能，且织构深度过大或过小都不利于密封控漏. 因此，在本文中研究范围内，超椭圆系数n2取1，织构深度Td2取6 μm为宜，后文中重点基于上述优选织构参数进一步开展优化研究.
![]()
图 9 织构深度Td2对密封性能变化率的影响(θ1=θ2=40°, b2=0.7mm, γ=2.5)Figure 9. Influence of texture depth Td2 on the change rate of sealing performance (θ1=θ2=40°, b2=0.7mm, γ=2.5)2.4 柔度系数优化设计
2.4.1 箔片区柔度系数优化设计
图10所示为箔片区柔度系数α1对密封性能变化率的影响规律，从图10中可以看到，随着箔片区柔度系数α1的增加，具有表面超椭圆型孔织构的SHFSD-CFFGS开启力、气膜刚度以及刚漏比呈逐渐减小的趋势，而泄漏率则保持不变. 这一现象产生的原因在于箔片区柔度系数α1较大时，箔片本身的变形能力增强，这使得其表面织构在接触外力时更容易发生形变，这种形变会导致织构表面原有的动压效应减弱. 而箔片区柔度系数的变动并未影响密封坝区的流场，泄漏通道保持不变. 进一步从图10(a)和(b)可以发现，仅在箔片柔度系数α1小于0.01时，SHFSD-CFFGS的开启性和稳定性才均优于未开设织构的CFFGS，而α1越小，箔片端面逐渐趋于刚性. 基于此，为确保SHFSD-CFFGS具有一定自适应能力，α1取0.005~0.01为宜.
![]()
图 10 箔片区柔度系数优化设计(θ1=θ2=40°, b2=0.7 mm, γ=2.5, Td2=6 μm, n2=1)Figure 10. Optimal design of compliance coefficient of foil area (θ1=θ2=40°, b2=0.7 mm, γ=2.5, Td2=6 μm, n2=1)2.4.2 浮动坝区柔度系数优化设计
图11所示为浮动坝区柔度系数α2对密封性能变化率的影响规律. 从图11(a)和(b)的结果来看，浮动坝区柔度系数α2对开启力和气膜刚度影响相对较小，可在一定程度上忽略. 如图11(c)所示，泄漏率Q受浮动坝区柔度系数α2的影响较大，因为α2的变化会影响密封坝的浮动量，从而改变了浮动坝区的气膜厚度，进而影响泄漏率. 同时较小的柔度系数α2意味着更好的密封控漏性能，而过大柔度会增加气膜的不稳定性，特别是在高压情况下会增加气膜泄漏的风险. 根据图11中的结果可知，通过适当调整α2，能够获得更优异的综合密封性能. 为了保证密封端面具有一定的自适应变形能力，α2取1×10−5~1×10−4时，密封综合性能较为理想.
![]()
图 11 浮动坝区柔度系数优化设计(θ1=θ2=40°, b2=0.7 mm, γ=2.5, Td2=6 μm, n2=1)Figure 11. Optimal design of compliance coefficient of floating seal dam area (θ1=θ2=40°, b2=0.7 mm, γ=2.5, Td2=6 μm, n2=1)综上所述，浮动坝区织构结构参数和柔度系数对开启力和气膜刚度的影响较小，但对泄漏率的影响显著. 在对SHFSD-CFFGS开展增大开启力、提高气膜刚度和减小泄漏率设计时，考虑箔片区承担动压弹性支承作用，控漏依赖密封坝区，因此主要通过箔片区织构和柔度系数合理设计以提高开启力和气膜刚度，重点通过坝区织构及柔度系数的设计控制泄漏，进而实现箔片密封在具有较好开启力和气膜刚度的同时能够进一步减小泄漏率.
3. 结论
a. 箔片区引入超椭圆织构能有效提高CFFGS的开启力和气膜刚度，而浮动坝区引入超椭圆织构虽对开启力和气膜刚度影响微弱，但在控漏方面有显著效果.
b. 合理设计浮动坝区超椭圆织构结构参数是保证密封控漏性能提升的关键因素. 在本文中参数研究范围内，超椭圆系数n2取1、超椭圆短半轴b2为0.7 mm、方向因子γ为2.5、织构深度Td2为6 µm时，SHFSD-CFFGS的泄漏率较普通CFFGS降低了39.5%，刚漏比提升了66.63%.
c. 箔片区柔度系数α1和浮动坝区柔度系数α2的合理配置是确保织构有效性的关键因素. 当α1在0.005~0.01，α2在1×10−5~1×10−4范围内取值时，SHFSD-CFFGS不仅具备一定的自适应变形能力，同时还表现出较好的开启性、稳定性和控漏性.
-
![]()
图 1 超椭圆织构浮动坝箔片密封结构示意图
Figure 1. Super-elliptical hole texture floating seal dam foil sealstructure diagram
![]()
图 6 SHFSD-CFFGS与CFFGS气膜压力与流速分布比较
Figure 6. Comparison of SHFSD-CFFGS and CFFGS gas film pressure and flow velocity distribution
![]()
图 7 双列型孔倾角θ1和θ2对密封性能变化率的影响
Figure 7. Influence of the double-row hole angle θ1 and θ2 on the change rate of sealing performance
![]()
图 8 方向因子γ对密封性能变化率的影响(θ1=θ2=40°)
Figure 8. Influence of slender ratio γ on the change rate of sealing performance (θ1=θ2=40°)
![]()
图 9 织构深度Td2对密封性能变化率的影响(θ1=θ2=40°, b2=0.7mm, γ=2.5)
Figure 9. Influence of texture depth Td2 on the change rate of sealing performance (θ1=θ2=40°, b2=0.7mm, γ=2.5)
![]()
图 10 箔片区柔度系数优化设计(θ1=θ2=40°, b2=0.7 mm, γ=2.5, Td2=6 μm, n2=1)
Figure 10. Optimal design of compliance coefficient of foil area (θ1=θ2=40°, b2=0.7 mm, γ=2.5, Td2=6 μm, n2=1)
![]()
图 11 浮动坝区柔度系数优化设计(θ1=θ2=40°, b2=0.7 mm, γ=2.5, Td2=6 μm, n2=1)
Figure 11. Optimal design of compliance coefficient of floating seal dam area (θ1=θ2=40°, b2=0.7 mm, γ=2.5, Td2=6 μm, n2=1)
表 1 初始参数数值表
Table 1 Initial parameters values
Parameters Specifications Inner radius of seal face, ri/mm 58.42 Outer radius of seal face, ro/mm 77.78 Number of cycles, Nc 8 Slope ratio, c 0.4 Foil-dam ratio, ξ 2 Compliance coefficient of foil area, α1 0.01 Compliance coefficient of floating seal dam area, α2 1×10−4 Wedge height, δh/μm 15 Balance film thickness, h0/μm 3 Major semi-axis of the super-elliptical in foil area, a1/mm 4 Major semi-axis of the super-elliptical in floating
dam area, a2/mm1.4 Minor semi-axis of the super-ellipticalin foil area, b1/mm 2 Minor semi-axis of the super-elliptical in floating
dam area, b2/mm0.7 Depth of textures in foil area, Td1/μm 5 Depth of textures in floating dam area, Td2/μm 5 Number of circumferential holes in foil area 4 Number of circumferential holes in floating dam area 13 Number of radial holes in foil area 1 Number of radial holes in floating dam area 2 Pressure at inner radius, pi/MPa 0.1 Pressure at outer radius, po/MPa 0.3 Rotational speed, ω/(r/min) 14 000 
下载: 导出CSV
-
[1] Liu Zhengxian, Wang Musu, Zhou Yue, et al. Dynamic coupling correlation of gas film in dry gas seal with spiral groove[J]. Chinese Journal of Mechanical Engineering, 2014, 27(4): 853–859. doi: 10.3901/cjme.2014.0508.090.
[2] 丁俊华, 俞树荣, 王世鹏, 等. 多重效应下超高速干气密封流场模拟及密封性能试验[J]. 化工学报, 2023, 74(5): 2088–2099]. doi: 10.11949/0438-1157.20230285. Ding Junhua, Yu Shurong, Wang Shipeng, et al. Flow simulation and sealing performance test of ultra-high speed dry gas seal under multiple effects[J]. CIESC Journal, 2023, 74(5): 2088–2099 doi: 10.11949/0438-1157.20230285
[3] 王衍, 谢雪非, 何一鸣, 等. 基于特斯拉阀的新型非接触式流体密封技术研究[J]. 摩擦学学报, 2023, 43(9): 975–985]. doi: 10.16078/j.tribology.2022044. Wang Yan, Xie Xuefei, He Yiming, et al. A new non-contact fluid seal technology based on tesla valve[J]. Tribology, 2023, 43(9): 975–985 doi: 10.16078/j.tribology.2022044
[4] Jiang Jinbo, Peng Xudong, Li Jiyun, et al. Leakage and stiffness characteristics of bionic cluster spiral groove dry gas seal[J]. Chinese Journal of Mechanical Engineering, 2018, 31(1): 21. doi: 10.1186/s10033-018-0227-4.
[5] ] [卓志愿, 陈源, 李运堂, 等. 随机工况主动式动压型干气密封调控力智能预测及其算法性能对比研究[J]. 摩擦学学报, 2023, 43(11): 1370–1380]. doi: 10.16078/j.tribology.2023231. Zhuo Zhiyuan, Chen Yuan, Li Yuntang, et al. Intelligent prediction of control force of active hydrodynamic pressure dry gas seal under random conditions and comparative study of its algorithm performance[J]. Tribology, 2023, 43(11): 1370–1380 doi: 10.16078/j.tribology.2023231
[6] Heshmat H. Compliant foil seal[P]. US6505837, 2003-01-14.
[7] Agrawal G L, Patel K H, Munson J H. Hydrodynamic foil face seal[P]. US7261300, 2007-08-28.
[8] Munson J, Grant D, Agrawal G. Foil face seal development[C]//Proceedings of the 37th Joint Propulsion Conference and Exhibit. Salt Lake City, 2001: 3483. doi: 10.2514/6.2001-3483.
[9] Salehi M, Heshmat H. Evaluation of large compliant gas foil seals under engine simulated conditions[C]//Proceedings of the 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. Indianapolis, 2002: 3792. doi: 10.2514/6.2002-3792.
[10] Heshmat H, Walton J. Innovative high-temperature compliant surface foil face seal development[C]//Proceedings of the 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. Hartford, 2008: 4505. doi: 10.2514/6.2008-4505.
[11] Chen Yuan, Chen Kai, Peng Xudong, et al. Research on the operation mechanism and performance of bump-type compliant foil face gas seal[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2022, 44(8): 325. doi: 10.1007/s40430-022-03606-8.
[12] Chen Yuan, Wang Qinggang, Peng Xudong, et al. Flow field and sealing performance analysis of compliant foil face gas seal[J]. Advances in Mechanical Engineering, 2022, 14(6): 168781322211084. doi: 10.1177/16878132221108488.
[13] 王庆港, 陈源, 彭旭东, 等. 三自由度微扰下箔片端面气膜密封动态特性分析[J]. 中国机械工程, 2022, 33(15): 1828–1840]. doi: 10.3969/j.issn.1004-132X.2022.15.009. Wang Qinggang, Chen Yuan, Peng Xudong, et al. Analysis on dynamic characteristics of compliant foil face gas seals with three degrees of freedom perturbation[J]. China Mechanical Engineering, 2022, 33(15): 1828–1840 doi: 10.3969/j.issn.1004-132X.2022.15.009
[14] 徐洁, 俞树荣, 严如奇, 等. 柔性端面气膜密封流场分析及密封特性研究[J]. 中国机械工程, 2022, 33(6): 656–663]. doi: 10.3969/j.issn.1004-132X.2022.06.004. Xu Jie, Yu Shurong, Yan Ruqi, et al. Flow field analysis and sealing characteristics research of flexible end face gas film seals[J]. China Mechanical Engineering, 2022, 33(6): 656–663 doi: 10.3969/j.issn.1004-132X.2022.06.004
[15] 徐洁, 俞树荣, 丁雪兴, 等. 基于波箔片变形的浮动式箔片气膜密封性能分析[J]. 化工学报, 2022, 73(5): 2083–2093]. doi: 10.11949/0438-1157.20220119. Xu Jie, Yu Shurong, Ding Xuexing, et al. Analysis of floating foil gas seal performance based on bump foil deformation[J]. CIESC Journal, 2022, 73(5): 2083–2093 doi: 10.11949/0438-1157.20220119
[16] 徐洁, 俞树荣, 杨小成, 等. 表面形貌对浮动式箔片气膜密封性能的影响分析[J]. 摩擦学学报, 2023, 43(11): 1341–1352]. doi: 10.16078/j.tribology.2022147. Xu Jie, Yu Shurong, Yang Xiaocheng, et al. Impact analysis of surface morphology on floating foil film sealing performance[J]. Tribology, 2023, 43(11): 1341–1352 doi: 10.16078/j.tribology.2022147
[17] 陈源, 熊聪, 彭旭东, 等. 不同箔坝位置关系下浮动坝箔片端面气膜密封性能研究[J]. 摩擦学学报, 2023, 43(5): 481–491]. doi: 10.16078/j.tribology.2022111. Chen Yuan, Xiong Cong, Peng Xudong, et al. Performance of floating seal dam compliant foil face gas seal under different foil-dam positions[J]. Tribology, 2023, 43(5): 481–491 doi: 10.16078/j.tribology.2022111
[18] Etsion I, Burstein L. A model for mechanical seals with regular microsurface structure[J]. Tribology Transactions, 1996, 39(3): 677–683. doi: 10.1080/10402009608983582.
[19] Kligerman Y, Etsion I. Analysis of the hydrodynamic effects in a surface textured circumferential gas seal[J]. Tribology Transactions, 2001, 44(3): 472–478. doi: 10.1080/10402000108982483.
[20] 彭旭东, 佘宝瑛, 孟祥铠, 等. 不同排布方向性椭圆孔液体润滑机械密封性能的研究[J]. 摩擦学学报, 2013, 33(5): 481–487]. doi: 10.16078/j.tribology.2013.05.011. Peng Xudong, She Baoying, Meng Xiangkai, et al. Sealing performance of liquid-lubricated mechanical seals with different arrangements inclined elliptical dimples[J]. Tribology, 2013, 33(5): 481–487 doi: 10.16078/j.tribology.2013.05.011
[21] 程香平, 彭旭东, 孟祥铠. 菱形孔密封环端面密封性能分析[J]. 上海交通大学学报, 2014, 48(1): 33–38]. doi: 10.16183/j.cnki.jsjtu.2014.01.007. Cheng Xiangping, Peng Xudong, Meng Xiangkai. Analysis of sealing performance of seal ring end face with diamond pores[J]. Journal of Shanghai Jiao Tong University, 2014, 48(1): 33–38 doi: 10.16183/j.cnki.jsjtu.2014.01.007
[22] Meng Xiangkai, Bai Shaoxian, Peng Xudong. Lubrication film flow control by oriented dimples for liquid lubricated mechanical seals[J]. Tribology International, 2014, 77: 132–141. doi: 10.1016/j.triboint.2014.04.020.
[23] 柏林清, 白少先, 彭旭东, 等. 倾斜微孔端面气体密封的动压特性研究[J]. 摩擦学学报, 2011, 31(2): 97–103]. doi: 10.16078/j.tribology.2011.02.012. Bai Linqing, Bai Shaoxian, Peng Xudong, et al. Hydrodynamic performance of inclination-dimpled face gas seal[J]. Tribology, 2011, 31(2): 97–103 doi: 10.16078/j.tribology.2011.02.012
[24] 张璇, 彭旭东, 江锦波, 等. 型孔形状和方向对孔型阻尼密封泄漏特性影响[J]. 摩擦学学报, 2020, 40(1): 117–127]. doi: 10.16078/j.tribology.2019119. Zhang Xuan, Peng Xudong, Jiang Jinbo, et al. The influence of shape and directionality of hole on leakage characteristics of hole-pattern damping seals[J]. Tribology, 2020, 40(1): 117–127 doi: 10.16078/j.tribology.2019119
[25] Kou Guiyue, Li Xinghu, Wang Yan, et al. Steady performance and dynamic characteristics of a superellipse groove dry gas seal at a high-speed condition[J]. Industrial Lubrication and Tribology, 2020, 72(6): 789–796. doi: 10.1108/ilt-05-2019-0171.
[26] Heshmat H, Walowit J A, Pinkus O. Analysis of gas-lubricated foil journal bearings[J]. Journal of Lubrication Technology, 1983, 105(4): 647–655. doi: 10.1115/1.3254697.
[27] 闫佳佳, 刘占生, 王铮, 等. 基于Newton-Raphson迭代的动压气体止推箔片轴承特性研究[J]. 汽轮机技术, 2017, 59(2): 116–120,124]. doi: 10.3969/j.issn.1001-5884.2017.02.011. Yan Jiajia, Liu Zhansheng, Wang Zheng, et al. Performance aanalysis of hydrodynamic gas foil thrust bearingbased on newton-raphson iterative method[J]. Turbine Technology, 2017, 59(2): 116–120,124 doi: 10.3969/j.issn.1001-5884.2017.02.011
计量
- 文章访问数: 43
- HTML全文浏览量: 19
- PDF下载量: 7
