Experimental identification of fluid-induced force in labyrinth seals

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1 Jounal of Mechanical Science and Technology 5 (7) (011) 485~494 DOI /s Expeimental identification of fluid-induced foce in labyinth seals Wan Fu Zhang *, Jian Gang Yang, Hao Cao and Dan Sun National Engineeing Reseach Cente of Tubo-Geneato Vibation, Southeast Univesity, Nanjing, 10096, China (Manuscipt Received Septembe 7, 010; Revised Mach 14, 011; Accepted Apil 13, 011) Abstact The seal foce is an impotant facto in tubomachineies. Theefoe, the cuent pape puts fowad an expanded seal foce identification model. A seal test ig consisting of seveal sets of seals was pepaed. Using the double-plane unbalance foce identification theoy in otodynamics, the distibuted seal foce in the cylinde became equivalent to two selected planes. Consideing the complex cylinde vibation with inceasing otating speed and inlet pessue, the cylinde was egaded as a vibation system with 4 degees of feedom. The 4 4 impedance matix was tested at the two selected planes using a shake in two othogonal diections. The equivalent seal foce can be obtained by multiplying the impedance matix with the measued change in the cylinde vibation. In the seal ig, tests wee pefomed on the influence of inlet pessue, otating speed, eccenticity atio, oto vibation, and cleaance. The seal foce inceases almost linealy with the inceasing inlet pessue, eccenticity atio, and vibation amplitude. Futhemoe, the seal foce is stongly sensitive to the change in cleaance between the cylinde and the otating oto. The phase diffeence between the seal foce and the vibation influences the wok done. If the phase diffeence is nealy 90, then the wok is at maximum. Moeove, the seal foce applies positive foce on the cylinde and negative foce on the oto. Keywods: Foce; Seal; Vibation; Wok Intoduction The seal pevents woking fluid leakage between the otating and stationay pats of tubomachines. Flow-induced foce in seals is known as one of the majo factos causing instability in tubomachines. Attention has been given to fluidinduced foce fo the impovement of tubine opeating paametes. In the past yeas, many studies [1-6] used CFD techniques to simulate the flow behavio in seals. Many factos, such as tubulent flow, bounday condition, and tempeatue vaiation, among othes, cannot be consideed accuately. Devising a moe accuate model is still unde investigation. Today, inceasing wok has been conducted in expeimental testing. Tiwai [7] gave a citical eview of the estimation of the otodynamic paametes (RDPs) of diffeent seal types. The identification pocess can be mainly divided into two methods: time-domain and fequency-domain. The timedomain method eveals insights into the dynamic chaacteistics of seals at the most fundamental levels. Rajakuma and Sisto [8] measued seal foce by integating the cicumfeential pessue ove the oto suface. Liu and Wang [9] found that the seal foce could futhe defom the flexible oto as This pape was ecommended fo publication in evised fom by Associate Edito Cheolung Cheong * Coesponding autho. Tel.: , Fax.: addess: zwf50006@163.com KSME & Spinge 011 well as educe the fist citical speed and destabilization otating speed of the oto. Etas [10] applied the dynamic pessue-esponse method to detemine the fequency-dependent foce coefficients of pocket dampe seals. The fequencydomain method can be applied though excitation expeiments to obtain the otodynamic chaacteistics; it is inceasingly adopted by eseaches. Childs and his teams [10-5] conducted poductive eseach on diffeent seals, such as the labyinth seal, smooth annula seal, hole patten stato annula seal, honeycomb seal, and pocket seal, among othes. Many factos have been consideed and tested in seveal igs, such as eccenticity atio, pe-otation, pessue atio, seal type, speed, cleaance, excitation fequency, etc. The authos obseved that the stiffness and damping coefficients ae insensitive to oto speed and vey sensitive to the inlet tangential velocity as well as incease with the inceasing inlet pessue [11]. Test esults indicate that TAMSEAL had 100 times moe diect damping than the conventional bladed seal [16]. Labyinth seals with shunt injection against otation contol otodynamic instabilities bette than seals with adial injection [18]. Wagne [6] developed a test ig supplied with N fo high pessues up to 5 MPa. The estoing foce of the honeycomb seal is seveal times highe than the tangential foce. The foce fom the labyinth seal is consideably smalle than that of the honeycomb seal and is theefoe easie to keep unde contol. Tiwai [7] indicated that the estimation of seal RDPs using

2 486 W. F. Zhang et al. / Jounal of Mechanical Science and Technology 5 (7) (011) 485~494 Fig. 1. Schematic diagam of the seal foce equivalent model. Fig.. Schematic diagam of the seal foce identification model. the fequency-domain method is moe eliable than the timedomain method. Howeve, the conical elative motion between the stato and the oto may occu duing the seal paamete identification test. Pevious tests indicate the existence of the cylinde tilting motion with an inceasing numbe of seals and otating speed. In this case, the cylinde system has moe than degees of feedom. Setting up an effective identification model should be consideed. Thus, a new identification model using the double-plane unbalance foce identification method in otodynamics is pesented. The cylinde and its suppoting stuctue ae consideed a single system with 4 degees of feedom. The seal foce is equivalent to the two selected planes. A 4 4 impedance matix is obtained by exciting the cylinde with diffeent fequencies at the two end planes in two othogonal diections. Afte measuing the cylinde vibation at diffeent inlet pessues, the equivalent seal foce can be identified. The test ig is set up, and the influence of inlet pessue, otating speed, eccenticity atio, oto vibation, and cleaance is tested and analyzed.. Equivalent seal foce identification model.1 Seal foce equivalent method Six sets of seals ae included in the test ig. The foce in each set is diffeent due to diffeent vibations along the oto axis. Thus, identifying the foce on each set of seals is difficult. Fig. 1 shows the seal foce analysis model. Two sets of seals ae taken as an example. Assume that the seal foces in sets 1 and ae f 1 and f, espectively. Then, f 1 can be divided into two components in the two selected planesⅠand Ⅱ as follows: f + f = f f L = f L 1Ⅰ 1Ⅱ 1 1Ⅰ 1 1Ⅱ (1) whee fⅠ and fⅡ ae the equivalent composite foces of the two seal foces. Similaly, the foce fom any set of seals can be decomposed into two foces in planes Ⅰ and Ⅱ. If the cylinde is a igid body, then the two foces ae equal to the distibuted seal foce in the test ig.. Seal foce identification model Taditional identification methods can excite the cylinde at its single cente plane. The cylinde is a igid body with degees of feedom. Cylindical whil could be obtained duing the tests. In the pesent test ig, the elative tilting motion of the cylinde could occu with inceasing otating speed duing the test pocess. An identification method based on 4 degees of feedom is poposed in the cuent pape. Fig. shows the X-diection as an example. Unde the exetion of seal and elastic foces, the kinematic equation can be pesented as follows: mx && = k1x1 c1x& 1 kx cx& + fx 1+ fx J && θ = klx clx& + kl x + cl x& + f l f l x x11 x whee f x1 is the equivalent seal foce in plane Ⅰ, f x is the equivalent seal foce in plane Ⅱ, x is the cylinde displacement, θ x is the deflection angle, and k i and c i (i=1, ) ae the stiffness and damping coefficients of the suppoting spings, espectively. Fom Fig., the following is obtained: l l x = x + x x1 x θx =. l1+ l 1 1 l1+ l l1+ l (3) (4) whee f1Ⅰ and f1Ⅱ ae the component foces of f 1 in the two selected planes Ⅰ and Ⅱ, espectively. Similaly, f can also be divided into fⅠ and fⅡ. Thus, the composite foce in the two end planes Ⅰ and Ⅱ can be obtained as follows: f + f = f f + f = f 1Ⅰ Ⅰ Ⅰ 1Ⅱ Ⅱ Ⅱ () Substituting Eq. (4) into Eq. (3) poduces the following: l l1 m && x1+ m && x + k1x1+ c1x& 1+ kx + cx& = l1+ l l1+ l fx 1+ fx J (&& x1 && x) + kl 1 1x1+ cl 1 1x& 1 klx clx& = l1+ l fx 11 l fxl. (5)

3 W. F. Zhang et al. / Jounal of Mechanical Science and Technology 5 (7) (011) 485~ Unde extenal hamonic excitation, the following can be assumed: iωt iωt iωt iωt x1 = Xe 1, x = Xe, fx 1 = Fx 1e, fx = Fxe (6) whee X 1, X, F x1, F x ae complex vaiables, including amplitudes and phases. Substituting Eq. (6) into Eq. (5) obtains X F (7) H1( ω) H( ω) 1 x1 = H3( ω) H4( ω) X Fx whee Hi( ω) (i=1,, 3, 4) is the impedance function of the test cylinde. This function can be expessed as follows: ml + J H1( ω) = - ω + k 1+ iωc1 ( l1+ l ) J mll 1 H( ω) = ω ( l1+ l) J mll 1 H3( ω) = ω ( l1+ l) ml1 + J H4( ω) = - ω + k + iωc. ( l1+ l) Eq. (8) indicates that Hi( ω) depends on the inheent chaacteistics of the system, i.e., the function of excitation fequency ω. Thus, Hi( ω) can be obtained by extenal excitation expeiments in the X-diection at the two selected planes. To conside the coupling effect between the vetical and hoizontal diections, the above model can be expanded as follows: H D= F whee H11( ω) H1( ω) H13( ω) H14( ω) H1( ω) H( ω) H3( ω) H4( ω) H = H31( ω) H3( ω) H33( ω) H34( ω), H41( ω) H4( ω) H43( ω) H44( ω) X F 1 x1 X Fx D = F = Y1 Fy 1,. Y F y In the pesent model, the dimension of the impedance function matix H is 4 4. Extenal excitation expeiments must be caied out in the vetical and the hoizontal diections at (8) (9) two selected planes, espectively, to achieve this 4 4 matix. If the impedance matix H and the cylinde vibation in diffeent woking conditions ae measued, we can calculate the equivalent seal foce by Eq. (10). F = H D q q (10) whee F q is the equivalent seal foce, and D q is the displacement vecto of the cylinde vibation at diffeent inlet pessues and speeds. 3. Test appaatus (a) Geneal view of the oto system (b) Stato suppot Fig. 3. Test setup of the oto system. 3.1 Geneal intoduction of the test ig Fig. 3(a) shows the oveall test ig. The test oto is suppoted on two jounal beaings and is diven by a 15 kw vaiable-speed moto though a geabox (4.5:1) via two igid couplings. The maximal otating speed and inlet pessue ae 6000 pm and 0.8 MPa, espectively. High-pessue ai entes the seal though fou inlet holes at the cente plane of the cylinde. Six sets of seals ae included in the ig. As shown in Fig. 3(b), the cylinde is suppoted by vetical, hoizontal, and axial spings. Fou velocity sensos and fou poximitos ae used to measue the cylinde vibation and the elative vibation between the cylinde and the oto, espectively. A key phase tansduce is used to measue the otating speed and the phase. Fig. 5 shows the dimension of a set of seals.

4 488 W. F. Zhang et al. / Jounal of Mechanical Science and Technology 5 (7) (011) 485~494 Shake Poximito Velocity senso Shake Plane Keyphaso tansduce Velocity senso Y-diection Plane Cylinde X-diection Y1-diection Shake Roto X1-diection Poximito Shake Fig. 4. Schematic diagam of the measuement system. (a) H 11 (ω) Seal Roto Unit mm Fig. 5. Dimensions of the test seal. (b) H 1 (ω) (a) Wavefom unde the nomal condition (c) H 31 (ω) (b) Spectum unde nomal condition (d) H 41 (ω) (c) Wavefom unde ubbing condition (d) Spectum unde the ubbing condition Fig. 6. Wavefom and spectum unde nomal and ubbing conditions. Fig. 7. Typical impedance function H ij (ω). 3. Seal ub diagnosis and pevention The seal gap is quite small, easily causing ubbing between the cylinde and the oto. This ubbing foce may poduce eos in the identification esults. Fig. 6 shows the wavefom and spectum unde nomal and ubbing conditions, espectively. Unde nomal conditions, the vibation is nealy a sinusoidal wavefom. Fequency coesponding to the otating speed is the main component in the spectum. Howeve, the wavefom unde ubbing conditions is iegula, and many fequency components exist in

5 W. F. Zhang et al. / Jounal of Mechanical Science and Technology 5 (7) (011) 485~ Table 1. Test points. Speeds (pm) Eccenticity atio 0, 0.4, 0.6 Inlet pessues (MPa) 0.1, 0., 0.3, 0.4, 0.5, 0.6 Cleaance (mm) 0., 0.5 Unbalance (g) 30, 7 Exciting fequency (Hz) (a) n = 800 pm the spectum. The ubbing may be detemined by monitoing the wavefom and the spectum duing the test pocess. 3.3 Impedance function Fig. 7 shows a typical, measued impedance function. The cylinde is excited in the Y-diection at planeⅠ. Although the coss-tems H 1 (ω ) and H 41 (ω ) ae elatively small compaed with the lage diect-tems H11 (ω ) and H 31 (ω ), the coss-tems cannot be neglected to obtain accuate identification esults. (b) n = 100 pm 4. Test conditions In the cuent pape, the test ig is used to study the influence of otating speed, inlet pessue, elative vibation, eccenticity atio, and seal gap. The test conditions ae shown in Table 1. (c) n = 1600 pm Fig. 8. Motion obit of the test cylinde. 5. Test esults and discussion 5.1 Motion obit of the test cylinde Fig. 8 shows the motion obits of the cylinde at diffeent otating speeds. As shown in Fig. 8(a), the cylinde is in a tanslational motion with a elatively low otating speed (n = 800 pm). Convesely, the cylinde is in a tilting motion with an inceasing otating speed (n = 100 pm, 1600 pm). Accodingly, the cylinde should be taken as a vibation system with 4 degees of feedom. (a) Phase vs. inlet pessue 5. Influence of inlet pessue on seal foce Fig. 9 illustates the measued seal foce change vesus the inlet pessue. In Fig. 9(b), the seal foce amplitudes incease almost linealy with the inceasing inlet pessue. The phases change smoothly with the inceasing inlet pessue, as shown in Fig. 9(a). Fig. 10 shows the two equivalent seal foces in a pola coodinates system at the two selected planes. The seal foce is not symmetical at the two end planes of the test cylinde. The phase diffeence between the X1-diection and the X. The phase diffeence between the Y1diection is nealy 80, which is caused by diection and Y-diection is nealy 180 the tilting vibation of the cylinde. (b) Amplitude vs. inlet pessue Fig. 9. Seal foce vs. inlet pessue (C = 0.5 mm, ε = 0.4, n = 1400 pm).

6 490 W. F. Zhang et al. / Jounal of Mechanical Science and Technology 5 (7) (011) 485~ Influence of eccenticity atio on seal foce Table gives the seal foce unde diffeent eccenticity atios ε. The amplitudes of the seal foces in the fou diections incease with the inceasing eccenticity atio. The pessue diffeence aound the cylinde cicumfeence in the seal ig becomes lage and lage with the inceasing eccenticity atio. This esult poduces a lage seal foce, which is obtained by integating the pessue aound the cylinde cicumfeence. 5.4 Influence of the oto vibation on seal foce The oto is balanced befoe the expeiment; the identification of two unbalance levels is then tested. Table 3 pesents the changes in the seal foce with the elative vibation. The seal foce inceases with the unbalanced foce. Fo a small motion at a centeed position, the seal foce can Table. Seal foce F (N) vs. eccenticity atio ε (C = 0.5 mm, ε = 0.4, n = 1600 pm, P in = 0.5 MPa). ε F y1 F x1 F y F x Table 3. Seal foce vs. elative displacement (n = 1800 pm, ε = 0, P in = 0.5 MPa). Unbalance (g) F y1 (N) F x1 (N) F y (N) F x (N) be expessed linealy as the function of the elative vibation: fx K k x C c x& = f + y k K y c C y& (11) whee x and y define the elative oto position, f x and f y ae the eaction-foce components acting on the oto, K is the diect coefficient, k is the coss-coupled stiffness, and C and c ae the damping coefficients. Clealy, the elative vibation between the oto and cylinde has a stong influence on seal foce. 5.5 Influence of cleaance on seal foce Fig. 11 illustates the seal foce changes vesus cleaances. Compaed with that fo C = 0.5 mm, the seal foce fo C = 0.3 mm is lage. The influence of the seal gap becomes lage with inceasing inlet pessue. 5.6 Wok done by the seal foce The fluid otation amplifies the oto vibation by feeding enegy into the whil obit, esulting in otodynamic instability. The wok done by the seal foce in one cycle can be epesented as follows: W = [ f ( t) x& ( t) + f ( t) y& ( t)] dt+ 0 T 0 T 1x 1 1y 1 [ f ( t) x& ( t) + f ( t) y& ( t)] dt. x y (1) Unde the conditions of hamonic excitation, f 1x, x 1, f 1y, y 1, f x, x, f y, y can be stated as follows: (a) P in =0.1 Mpa (b) P in = 0. Mpa (c) P in = 0.3 MPa (d) P in = 0.4 Mpa (e) P in = 0.5 Mpa (f) P in = 0.6 MPa Fig. 10. Two equivalent seal foces in a pola coodinate system (C = 0.5 mm, ε = 0.4, n = 1400 pm).

7 W. F. Zhang et al. / Jounal of Mechanical Science and Technology 5 (7) (011) 485~ (a) Y1-diection (b) X1-diection (c) Y-diection (d) X-diection Fig. 11. Seal foce vs. cleaance (ε = 0.4, n = 100 pm). Fig. 1. Schematic diagam of the whiling motion. f1x = Fx 1cos( ωt+ ϕfx 1) f1y = Fy 1cos( ωt+ ϕfy 1) x1 = X1cos( ωt+ ϕx 1), y1 = Y1cos( ωt+ ϕy 1) fx = Fxcos( ωt+ ϕfx) fy = Fycos( ωt+ ϕfy) x = Xcos( ωt+ ϕx) y = Ycos( ωt+ ϕy). Substituting these vaiables into Eq. (1), we have W = π Fx1X1sin( ϕfx 1 ϕx 1) + Fy 1Y1sin( ϕfy 1 ϕy 1) + π F X sin( ϕ ϕ ) + F Y sin( ϕ ϕ ). x fx x y fy y (13) (14) Evaluation of Eq. (14) eveals that the wok W done by the seal foce is the sinusoidal function of fou phase diffeences between the seal foce and vibation. As shown in Fig. 1, the tangential component foce F τ is othogonal to the adial deflection of the oto elative to the cylinde. When the phase diffeence Δφ is 90, the tangential foce F τ is at its maximum, which is the main facto in oto whil instabilities. Consequently, the wok done by the total seal foce is at a maximum, which is likely to cause oto instability. The phase diffeence deceases gadually with inceasing inlet pessue, as shown in Fig. 13. The damping effect of the seal foce has inceasing influence on the vibation unde inceasing inlet pessue. The change in foce acting on the cylinde and the oto is shown in Figs. 14 and 15, espectively, in efeence to the otating speed fo vaious inlet pessues. The wok done by the seal foce in the two conditions clealy shows a high dependency on inlet pessue. In Fig. 14, wok on the test cylinde is at maximum at the speed of appoximately 1400 pm. This finding indicates that the citical value of the test cylinde is nealy 1400 pm, and the seal foce is at maximum unde this condition. In Fig. 15, the wok done by the seal foce inceases with the inceasing inlet pessue and otating speed due to an inceased magnitude of tangential foce with inceasing speed. The figues also show that the wok acting on the test cylinde and the oto is positive and negative, espectively. The positive wok causes cylinde vibation by feeding enegy to the cylinde, wheeas the negative wok inceases oto stability by exhausting enegy.

8 49 W. F. Zhang et al. / Jounal of Mechanical Science and Technology 5 (7) (011) 485~494 (a) Y1-diection (b) X1-diection (c) Y-diection (d) X-diection Fig. 13. Phase diffeence vs. inlet pessue (C = 0.3 mm, ε = 0.4, n = 100 pm). Fig. 14. Wok acting on the cylinde vs. otating speed. 6. Conclusions An expeimental seal test ig is established in the cuent pape. An expanded identification model fo the seal foce based on the double-plane balance theoy in otodynamics is set up. Numeous tests ae pefomed to investigate the influence of inlet pessue, otating speed, eccenticity atio, oto vibation, and cleaance on the seal foce in the ig. The seal foce inceases almost linealy with the inceasing inlet pessue, eccenticity atio, and oto vibation amplitude. In addition, the seal foce is notably sensitive to changes in the cleaance between the cylinde and the otating oto. Wok done by the seal foce is influenced by the phase diffeence between the seal foce and the elative vibation. If the phase diffeence is nealy 90, the wok done is at its maximum. The wok done by the seal foce acting on the test cylinde and oto is positive and negative, espectively. Acknowledgments This wok was suppoted by the National Natual Science Foundation of China (No ). Nomenclatue Fig. 15. Wok acting on the oto vs. otating speed. f 1, f fⅠ, fⅡ : Foces in two sets seals [N] : Equivalent composite foces [N]

9 W. F. Zhang et al. / Jounal of Mechanical Science and Technology 5 (7) (011) 485~ f 1 Ⅰ, f 1 Ⅱ : Component foces of f 1 in the two selected planes [N] f Ⅰ, f Ⅱ : Component foces of f in the two selected planes [N] m : Mass of the cylinde [kg] θ x : Deflection angle of the cylinde [ ] k 1, k : Stiffness coefficients [N/m] c 1, c : Damping coefficients [N s/m] J : Moment of inetia [kg m ] L : Length of the cylinde [m] H : Impedance function matix [N/m] F q : Equivalent seal foce [N] D q : Displacement vecto of the cylinde vibation [m] ω : Excitation fequency [Hz] n : Rotation speed [pm] C : Cleaance [mm] P : Inlet pessue [MPa] ε : Eccenticity atio W : Wok done [J] φ : Phase [ ] F τ : Tangential foce [N] Subscipt τ in Refeences : Tangential diection : Inlet [1] L. Jian, CFD development fo otodynamic foce coefficients of plain and labyinth seals, Ph.D. Texas A&M Univesity (1997). [] J. J. Mooe and A. B. Palazzolo, CFD Compaison to 3D Lase anemomete and otodynamic foce measuements fo gooved liquid annula seals, ASME Jounal of Tibology, 11 (1999 ) [3] J. J. Mooe and A. B. Palazzolo, Rotodynamic foce pediction of centifugal impelle shoud passages using computational fluid dynamic techniques, ASME Intenational Gas Tubine and Aeoengine Congess and Exposition, Indianapolis, Indiana (1999). [4] N. Kim and D. L. Rhode, A New CFD-petubation model fo the otodynamics of incompessible flow seals, ASME Intenational Gas Tubine and Aeoengine Congess and Exposition, May 8-11, Munich, Gemany (000). [5] J. J. Mooe, Thee-dimensional CFD otodynamic analysis of gas labyinth seals, Jounal of Vibation and Acoustics (003) [6] Hiano et al., Application of computational fluid dynamics analysis fo otating machiney-pat Ⅱ: Labyinth Seal Analysis, ASME Jounal of Engineeing fo Gas Tubines and Powe. [7] Tiwai et al., A eview of the expeimental estimation of the oto dynamic paametes of seals, The Shock and Vibation Digest, 37 (005) [8] C. Rajakuma and F. Sisto, Expeimental investigations of oto whil excitation foces induced by labyinth seal flow, ASME Jounal of Vibation and Acoustics, 11 (1990). [9] Liu et al., Influence of leakage flow though labyinth seals on otodynamics: numeical calculations and expeimental measuements, Ach. Appl. Mech. (007). [10] B. H. Etas, Rotodynamic foce coefficients of pocket dampe seals, Ph.D. Texas A&M Univesity (005). [11] D. W. Childs and J. K. Schae, Expeimental otodynamic coefficient esults fo teeth-on-oto and teeth-onstato labyinth gas seals, ASME Jounal of Engineeing fo Gas Tubines and Powe, 108 (1986) [1] D. W. Childs et al., Theoy vesus expeiment fo the otodynamic coefficients of annula gas seals: Pat I - Test facility and appaatus, ASME Jounal of Tibology, 108 (1986) [13] D. W. Childs and J. K. Schae, Theoy vesus expeiment fo the otodynamic coefficient of labyinth gas seals: Pat II - A compaison to expeiment, Tansactions of the ASME Jounal of Vibation, Acoustics, Stess and Reliability in Design, 110 (1988) [14] D. W. Childs et al., Annula honeycomb seals: Test esults fo leakage and otodynamic coefficients; compaison to labyinth and smooth configuations, ASME Jounal of Tibology, 111 (1989) [15] D. W. Childs and K. Hale, A test appaatus and facility to identify the otodynamic coefficients of high-speed hydostatic beaings, ASME Jounal of Tibology, 116 (1994) [16] J. M. Vance and J. Li, Test esults of a new dampe seal fo vibation eduction in tubomachiney, ASME Jounal of Engineeing fo Gas Tubines and Powe, 118 (1996) [17] Z. Yu and D.W. Childs, A compaison of expeimental otodynamic coefficients and leakage chaacteistics between hole-patten gas dampe seals and a honeycomb seal, ASME Jounal of Engineeing fo Gas Tubines and Powe, 10 (1998). [18] E. A. Soto and D. W. Childs, Honeycomb geometies, ASME Jounal of Engineeing fo Gas Tubines and Powe, 14 (00). [19] L. Todd, The effects of conveging and diveging axial tape on the otodynamic coefficients of liquid annula pessue seals: theoy vesus expeiment, ASME Jounal of Vibation and Acoustics, 1 (000). [0] M. P. Dawson and D. W. Childs, Measuements vesus pedictions fo the dynamic impedance of annula gas seals - Pat Ⅱ: Smooth and honeycomb geometies, ASME Jounal of Engineeing fo Gas Tubines and Powe, 14 (00). [1] D. W. Childs and J. Wade, Rotodynamic coefficient and leakage chaacteistics fo hole-patten-stato annula gas seals - measuements vesus pedictions, ASME Jounal of Tibology, 16 (004) [] D. W. Childs and W. Jonathan, Rotodynamic coefficient and leakage chaacteistics fo hole-patten-stato annula gas seals-measuements vesus pedictions, ASME Jounal of Tibology, 16 (004).

10 494 W. F. Zhang et al. / Jounal of Mechanical Science and Technology 5 (7) (011) 485~494 [3] P. Athu and D. W. Childs, Rotodynamic coefficients fo a tooth-on-stato labyinth seal at 70 ba supply pessues: measuements vesus theoy and compaisons to a holepatten stato seal, ASME Jounal of Engineeing fo Gas Tubines and Powe, 17 (005). [4] A. Delgado and L. S. Andes, Identification of stuctual stiffness and damping coefficients of a shoed-bush seal, ASME Jounal of Vibation and Acoustics, 19 (007). [5] J. E. Bake, Measuements of leakage, powe loss and otodynamic foce coefficients in a hybid bush seal, Ph.D. Texas A&M Univesity (008). [6] N. G. Wagne, Reliable oto dynamic design of highpessue compessos based on test ig data, ASME Jounal of Tibology, 13 (001). Jian Gang Yang eceived his Ph.D degee fom the Depatment of Powe Engineeing, Southeast Univesity in He is cuently the deputy diecto of the National Engineeing Reseach Cente of Tubo-Geneato Vibation. His eseach inteests ae otating machiney fault monitoing and diagnosis, and oto dynamics and flow-induced vibation. Wan Fu Zhang is studying fo his Ph.D degee fom the National Engineeing Reseach Cente of Tubo GeneationVibation, Southeast Univesity, Nanjing, 10096, China. His eseach inteests include oto dynamics, flowinduced vibation in tubo-machiney, advanced sealing technology, advanced computational fluid dynamics, and otating machiney fault diagnosis.