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米粉松丝机的设计
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Science in China Series E: Technological Sciences 2007 SCIENCE IN CHINA PRESS Springer Received January 5, 2005; accepted February 26, 2007 doi: 10.1007/s11431-007-0058-5 Corresponding author (email: liuying) Sci China Ser E-Tech Sci | Aug. 2007 | vol. 50 | no. 4 | 448-453 Optimization design of main parameters for double spiral grooves face seal LIU Zhong, LIU Ying & LIU XiangFeng State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China The optimization design of the parameters, such as the groove depth, groove number, ratio of the groove width to the land width, and spiral angle of a new kind of double spiral grooves face seal, which works under the condition of high velocity, high sealing pressure and ultra-low temperature, is presented under the assump-tion of fixed closure force by finite element analysis method. The results show that the stiffness of the maximum film can be obtained when the ratio of the groove width to the land width is 0.5 and the spiral angle is about 75 degrees, when the influence of the groove number on the sealing performance is not obvious. double spiral groove, face seal, optimization 1 Introduction Spiral groove face seal (SGFS) is widely used in the fields of petroleum, chemistry, aviation and aerospace because of its low abrasion, small leakage and power loss. However, with the devel-opment of new technology, more strict requirement are set forth for SGFS, such as longer service time, less leakage and power loss1. Thus, the design and development of new types of seal with higher performance are becoming a very hot research subject in the filed of fluid seal. A new kind of double spiral grooves face seal (Figure 1) has attracted much attention due to its obvious ad-vantages over traditional single spiral groove face seal. For example, it has lower or even zero leakage and better stability with larger stiffness of the fluid film than the conventional one and is self-adaptative to the disturbance caused by double spiral grooves at high pressure and high rotary speed2,3. It is reported that the double spiral grooves face seal has been applied to some critical fields such as aerospace, defense, etc.3 in some countries. In this paper, an optimization design of the main configuration parameters is carried out under the condition of constant closure force to improve the seal performance. This work could provide an important theoretical guide for the selection of the groove configuration. LIU Zhong et al. Sci China Ser E-Tech Sci | Aug. 2007 | vol. 50 | no. 4 | 448-453 449 Figure 1 Configuration of double spiral grooves face seal. (a) Surface of rotary ring; (b) assembly of static ring module. 2 Theoretical models 2.1 Optimization model The optimization model includes three elements: optimization targets, optimization variables and constraint conditions. Much less leak is the first requirement for the seal. And next, the stiffness of the fluid film between the sealing rings must be large enough to reduce the possible film pertur-bation and guarantee the sealing stability. So optimization targets should be that the fluid film axial stiffness (sk) reaches its maximum when the flow leakage (Q) is the least. The optimization function can be expressed as max()/sspf kdFdh= and 3min( ),12hpf Qr= where h is the film thickness between the static and rotational rings, and spF is the opening force produced by the fluid film between the sealing gap to open the seal. Optimization variables include the operating conditions (rotating speed, sealing pressure, fluid viscosity) and the structural parameters (outer and inner radius of the sealing rings, ratio of the groove width to the land width, ratio of the sealing dam width to the face width, groove depth, groove number, spiral angle (), etc). The possible range of the optimization variables is limited. And such limitations are regarded as the constraint conditions of the optimization. The main constraint conditions are 2 mh and 090. At present, the general idea of the optimization method for the single spiral groove face seal is as follows: select a fixed and small value of the gap, and keep one of the parameters of groove depth, groove number, ratio of the groove width to the land width and spiral angle as variable and keep others invariable, and then deduce the variation trend of the sealing performance4. Using such method, only the individual effect of every element is considered, and mutual action to sealing performance between all elements is neglected. Doing by this way cause errors, and does not re-flect the real running condition under which the closing force of the face seals is usually a fixed value. Parameters optimization with a fixed closing force should be consistent with practical con-ditions. In addition, the film thickness varies with the optimization variables, so mutual effects of synchronous variations of the optimization variables and the film thickness should be taken into 450 LIU Zhong et al. Sci China Ser E-Tech Sci | Aug. 2007 | vol. 50 | no. 4 | 448-453 consideration. The optimization process is shown in Figure 2. Figure 2 Design frame for parameters optimization. 2.2 Fundamental equations in calculation of sealing performance The governing equation for the force balance is given as follows (Figure 3): 2222222211()()44SPmPFFFDdpdDp=+, (1) where D1 is the inner radius of the stator, D2 the outer radius of the stator, d1, d2 the inner and outer radius of the corrugated pipe, Fm the closing force produced by compressed corrugated pipe, Fp the axial force caused by the fluid pressure passing through the corrugated pipe, p1 the pressure of the leakage space and p2 the pressure of the seal space. Figure 3 Sketch map of the force balance in steady-state. The opening force is composed of the static pressure and dynamic pressure of the sealing fluid. The governing equation for the fluid dynamics is a two-dimension steady-state turbulent Reynolds equation 331()0,2rhprhprhrkrkr+= (2) LIU Zhong et al. Sci China Ser E-Tech Sci | Aug. 2007 | vol. 50 | no. 4 | 448-453 451 and its dimensionless form is 331()0/12/12rHPRHPHRkRR RkR+ =, (3) where r is the radius, the fluid density, h the film thickness, the fluid viscosity, the radian, p0 the pressure at outer radius of the sealing ring, p the dynamic pressure, the rotating speed, r1 the inner radius of the sealing ring, and 0h the sealing gap; dimensionless radius 1,Rr r= dimen- sionless pressure 0,Pp p= dimensionless gap 0;Hh h= k and rk the turbulent coeffi- cients, and 22106/orp h = the compressing coefficient. The calculation region of eq. (3) is a cirque between the inner radius and the outer radius of the sealing ring, which can be divided into three parts: inner cirque, outer cirque and middle deep groove in which the fluid pressure is supposed to be equal everywhere. According to the conden-sability of the involved fluid, the fluid density and viscosity in a tiny cell are supposed to be con-sistent, but different among bordering cells. Periodicity of the spiral grooves in the sealing face causes periodic distribution of the fluid pressure. So the pressure of the whole calculation region may be gained by only considering one spiral groove, one land and its adjacent sealing dam. A coordinate switch, ln,uR= is adopted, which transforms the quadrangle with spiral and arc borders under R coordinate to parallelogram under u coordinate. The finite element analysis method with quadrangle equivalence cell is adopted to calculate fluid pressure in the sealing gap. Two boundary conditions are as follows: 1) In radial direction, at inner and outer radius, the pressure boundary condition is 1101/(1),PPppRR= 00011(/ ).PPRRrr= 2) In circumferential direction, the periodic pressure boundary condition is (2 / , )( , ).Pz RPR+= Newton-Raphson method with relaxation technique is used to solve discrete eq. (3) in order to gain the pressure distribution in the sealing gap. Then the following steady-state sealing per-formances could be obtained. 1) Opening force ,SPAFpdrd= (4) where A stands for the whole region of the sealing face, and p the dynamic pressure. 2) Flow leakage 3.12hpQr= (5) 3) The pressure loss through feeding holes 4128,QLpd = (6) where Q denotes the flow leakage in volume, L the length of feeding holes, and d the diameter of feeding holes. 4) Steady-state axial stiffness of film 452 LIU Zhong et al. Sci China Ser E-Tech Sci | Aug. 2007 | vol. 50 | no. 4 | 448-453 SP/.skdFdh= (7) 2.3 Optimization result for the structural parameters of double spiral grooves face seal The influences of the structural parameters on the sealing performance, such as groove depth, groove number, ratio of groove width to land width, spiral angle, are shown in Figure 4 in which 0/Kk k= is dimensionless axial stiffness of the film, and 0k is the axial stiffness of a benchmark seal. The parametric optimization is conducted under a specific operating state, 20000n = r/min, 01.8p = MPa, the fluid viscosity and closing force for seal are fixed. Figure 4 The influence of main structural parameters on sealing performance. (a) The influence of groove depth; (b) the in-fluence of groove number; (c) the influence of ratio of groove width to land width; (d) The influence of spiral angle. , Sealing gap (m); , dimensionless film stiffness, K; , dimensionless leakage, Q; , ratio of film stiffness to leakage, K/Q. Figure 4(a) shows that both the sealing gap and leakage increase, but the stiffness of the fluid film decreases as the groove depth grows under the condition of fixed closing force. The dynamic effect is stronger with larger groove depth, but larger groove depth (above 20 m) tends to infinity without dynamic effect and can only be treated as boundary condition. Only with smaller groove depth (below 20 m), sealing performance, e.g. film stiffness, flow leakage, is better. Figure 4(b) indicates that the effect of the groove number on the film stiffness is little in a wide range (820). Additionally, other optimization results show that the curve of the film stiffness to the groove number varies with different fluid viscosity5. Figure 4(c) describes the changing trend of the sealing gap, flow leakage and film stiffness with the increase of the ratio of the groove width to the land width. The dynamic effect along the LIU Zhong et al. Sci China Ser E-Tech Sci | Aug. 2007 | vol. 50 | no. 4 | 448-453 453 circumferential direction of the seal ring grows up with an increase in the ratio of the groove width to the land width, which introduces large sealing gaps and flow leakage. On the contrary, the film stiffness decreases smoothly during this process. Larger film stiffness is obtained when the ratio of the groove width to the land width is between 0.20.5. The circular velocity of the seal ring can be decomposed into shear and normal velocity. Let us consider a single calculation cell. The larger the spiral angle is and the smaller the intersection angle between shear velocity and circle velocity is, the stronger the effect of the spiral angle is. But when the spiral angle becomes much larger, the area of the calculation cell will be narrower, and the interference of the flow between adjacent cells will also become more serious which will weaken the dynamic pressure effect under some condition on the contrary. This will obviously appear under the working conditions with high rotating speed and high viscosity. Anyway, the spiral angle and the seal gap influence the performance of the face seal under the fixed closure force condition. Therefore, Figure 4(d) shows that the smaller the spiral angle (below 50 degree), the higher the film axial stiffness and the larger the ratio of the film stiffness to the flow leakage. On the other hand, when the spiral angle is above 60 degrees, the sealing gap is wider. These results suggest that the sealing gap is the main factor exerting the dynamic effects. The bumping effect of the spiral reaches the maximum when the spiral angle is approaching 90 degrees. At the same time, the sealing gap and the flow leakage augment rapidly with the growing dynamic effect. The film axial stiffness and the ratio of the film stiffness to the flow leakage arrive at their maxima with the spiral angle be-tween 7580 degrees. 4 Conclusions (1) The interaction of main structural parameters and the influence of the seal gap on the per-formance of the double spiral grooves face seal are investigated simultaneously with the fixed closure force. The optimization results of the groove depth, groove number, ratio of the groove width to the land width and spiral angle are obtained under the working condition of high speed, high pressure and ultra-low temperature. These results are different from those of single spiral groove gas face seal. The trend of optimization curves with fixed closure force is also dissimilar with that assuming fixed seal gap. (2) The optimization results show that much better sealing performance can be obtained when the ratio of the groove width to the land width is 0.5 and the spiral angle is about 75 degrees. But the influence of the groove number on the sealing performance is not obvious. (3) A small error is caused by the assumption of parallel sealing gap, which ignores the effect of coning film due to heat and elastic distortion. But it does not affect the reliability of parametric optimization results. 1 Peng X D, Jiao Y R, Ye Z W, et al. The hotspots in mechanical face seals. Gener Mech (in Chinese), 2003, 3: 5457 2 Liu Z, Liu Y, Liu X F. Static performance analysis of a new double spiral groove face seals. Lubric Engin (in Chinese), 2005, 167: 6365 3 Zheng X Q, Berard G. Large diameter spiral groove face seal development, PerkinElmer fluid sciences. Centurion Me-chanical Seals, 2000, 107134 4 Hu D M, Hao M M, Peng X D, et al. Geometry optimization of spiral groove upstream pumping mechanical seals. Lubric Engin (in Chinese), 2003, (1): 3541 5 Liu Z, Liu Y, Liu X F. Effect of low temperature fluid viscosity on geometry optimization of double spiral groove mechanical seals. Lubric Engin (in Chinese), 2006, 182: 7981 双螺旋槽端面密封结构参数的优化设计 刘 忠 刘 莹* 刘向锋 (清华大学摩擦学国家重点实验室, 北京 100084) 摘要 在定闭合力假设条件下, 采用有限元方法对工作在高速、高密封腔压力和超低温工况下的一种双螺旋槽端面密封的主要结构参数, 如: 槽深、槽数、槽台宽比和螺旋角等进行了优化设计. 结果表明, 当槽台宽比为 0.5, 螺旋角约 75时, 可以获得最大的密封油膜刚度, 而槽数对密封性能的影响并不显著. 关键词 双螺旋槽 端面密封 优化设计 1 概述 螺旋槽端面密封因其具有低磨损、低泄漏、低能耗等优点, 目前广泛应用于石油、化工、航空和航天等领域. 但是随着高新技术和工业的高速发展, 对流体密封的性能也提出更高的要求, 如: 环保、最大限度降低能耗、长寿命(或重复使用性)等1, 因此, 研究和设计新型密封以满足高性能要求, 成为流体密封研究领域的新热点, 其中一种新型双螺旋槽端面密封结构(图 1)受到人们的关注. 它与传统的单螺旋槽密封相比除具有低泄漏的特点外, 在高速、 高压等极端环境中还具有更好的稳定性(密封膜刚度较大, 并可以依靠双边螺旋槽结构实现对外扰动的自平衡)2,3. 资料表明3, 此类双螺旋密封结构在国外已经应用于航天、国防等重要领域. 图 1 双螺旋端面密封槽型与装配结构示意图 (a) 动环端面; (b) 静环组件 本文作者采用等闭合力条件对双螺旋端面密封的主要结构参数进行了优化设计, 为密封端面槽型设计选择提供了理论基础. 2 密封结构参数优化设计的理论基础 2.1 优化设计模型 优化设计模型包括 3 个要素: 目标函数、设计变量和约束条件. 螺旋槽端面密封首先要求密封性, 即泄漏量要小; 其次, 应保证密封间隙内的液膜轴向刚度足够大, 这样才能减小外界干扰带来的膜厚偏差, 提高密封运行的稳定性. 因此, 优化目标选为在泄漏量(Q)较小时的最大液膜轴向刚度(sk). 优化的目标函数可以表示为 max()d/d ,sspf kFh= 3min( )12hpf Qr=, 式中 h 为静环与动环之间的液膜间隙; spF为密封开启力. 设计变量包括两类: 工况参数(转速、压力比、黏度)和结构参数(内外径、槽台宽比、密封坝宽度比、槽深、槽数、螺旋角等). 设计变量一般不允许任意取值而是受到一些限制, 这些限制称为约束条件. 优化方程的主要约束条件是: 2 m,h 090 .? 目前对单螺旋气体密封的优化设计一般是选取一个固定的较小密封间隙0h, 然后将槽深hg、槽数z、槽宽比、螺旋角中的一个作为变量而固定其余参数, 得出密封性能的变化趋势. 此方法仅考虑了每个因素的单独作用, 忽略了各因素之间对目标函数的交互作用, 这样会产生一定的误差, 且与密封装置的实际运行工况不相吻合. 因为在实际的工程应用中, 端面密封闭合力的大小一般是给定的, 因而在定闭合力的条件下进行优化设计更符合实际工况. 此时, 当某一个设计变量发生变化时, 密封间隙也随之发生改变; 因此得出的结论是综合考虑了密封间隙和相应优化参数同时发生改变对密封性能的影响. 本文采用定闭合力条件下的优化方法. 优化算法框图如图 2. 2.2 密封性能计算的基本方程 双螺旋端面密封稳定工作状态下的力平衡方程为(参见图 3): 2222222211()(),44spmPFFFDdpdDp=+ (1) 式中 D1为石墨环内径; D2为石墨环外径; d1为波纹管内径; d2为波纹管外径; Fsp为密封缝隙中流体压力将密封两端面打开力, 即开启力; Fm为由于波纹管受压缩而作用在密封端面的力; 其中开启力包括流体静压力和动压力两部分. 流体动压求解的基本方程为稳态下的二维紊流Reynolds 方程 331()0,2rhprhprhrkrkr+= (2) 其无量纲形式为 331()0,/12/12rHPRHPHRkRR RkR+= (3) 式中 r 为半径; 为介质密度; h 为液膜厚度; 为介质黏度; 为弧度; p0为外压力; p 为流体压力; 为动环角速度; r1为内径; h0为密封间隙; R=r/r1为无量纲半径; P=p/p0为无量纲压力; H=h/h0为无量纲间隙; k, rk为紊流系数; 为压缩系数, 2210 06/rp h=. 图 2 结构参数优化设计框图 图 3 稳定工作状态端面密封的力平衡示意图 (3)式的定解区域为内径和外径之间的圆环, 可分为 3 部分: 内圈、外圈和中间的深槽, 假设深槽内的流体压力处处相等. 针对所研究介质的可压缩性, 假设在一个单元体内流体的密度和黏度不变, 而不同单元内的密度和黏度不相同. 由于密封端面上螺旋槽的均布性, 流体压力沿圆周方向以 2/Ng为周期分布(Ng为槽数), 只需分别取内圈和外圈上一对槽台及和它们相连的密封坝区作为计算区域即可. 为获得好的边界逼近性, 采用坐标变换: u =lnR, 将 R 坐标下的对数螺旋线弧形四边形区域转化为 u直角坐标下的平行四边形区域. 采用四边形等参元有限元法求解密封间隙内的流体动压分布. 存在两种边界条件: 强制性边界条件和周期性边界条件. 强制性边界条件为: 内径处压力已知: 11101, /RRPPpp=; 外径处压力已知: 0010/ ,1RRrr PP=. 开启力计算公式为 d d ,SPAFp r= (4) 式中 A 为整个密封端面, p 为密封流体压力. 泄漏量计算公式 3.12hpQr= (5) 式(4)为单位圆周长度上的体积流量, 沿整个圆周积分可得到总的泄漏量. 根据 Poiseuille 公式可知, 供液小孔压力损失为 4128,QLpd = (6) 式中 Q 为体积流量; L 为小孔长度; d 为小孔直径. 静态轴向刚度定义为 d,dspsFkh= (7) 式中spF为开启力 N. 3 双螺旋槽端面密封结构参数优化设计结果 针对某组固定工作参数, 即保证轴径转速(20000 r/min)、介质黏度、密封压力(1.8 MPa)、密封闭合力等均不变的条件下, 对双螺旋槽端面密封的主要结构参数, 如: 槽深、槽数、槽区宽度比(指同一半径上槽区周向宽度与槽台区周向宽度的比值, 槽区宽度比为 0 或 1 时, 密封端面就是没有沟槽的平面)、螺旋角对密封泄漏量、液膜刚度和刚漏比的影响进行了分析计算, 其结果如图 4. 图 4 中无量纲液膜轴向刚度: 0/Kk k=, 0k为基准密封结构的液膜轴向刚度. 由图 4(a)可以看出, 在一定范围内, 槽深增大, 密封间隙内流场的动压效应增强; 在
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