Proceedngs of the ASME 21 Pressure Vessel & Ppng Dvson / K-PVP Conference PVP21 July 18-22, 21, Bellevue, Washngton, USA PVP21-25223 DETERMINATION OF GIMBAL AND HINGED EXPANSION JOINTS REACTION MOMENTS José Carlos Vega Nelson Kavanagh Ana Mara F. Sousa Teadt Juntas Ltda Campnas, SP Brazl e-mal: jccvega@teadt.com.br e-mal: nkavanagh@teadt.com.br e-mal: edph@teadt.com.br Jorvaldo Mederos Jordana Luza Vega Petrobras- Petroleo Braslero SA Research and Development Center - CENPES Ro de Janero, RJ Brazl e-mal: jorvaldo@petrobras.com.br e-mal: jordana@petrobras.com.br ABSTRACT Ths paper proposes a method to estmate the actual reacton loads n gmbal and hnged metal bellows expanson jonts. Frcton and some meda pressure forces, whch are not consdered n current EJMA Standard calculatons, are added to bellows sprng rate to estmate the expanson jont movement reacton moment. The proposed calculaton method s based upon pressure and movement tests of large sze expanson jonts. Keywords: Expanson jont reacton loads, EJMA Mpf = Moment due to pn frcton Ms = Moment due to nner sleeve seal frcton P = Pressure R = D / 2 Tf = Aeff. P = pressure thrust force calculated per EJMA equatons d = Pn dameter kα = Bellows angular sprng rate α = Movement angle µp = Pn frcton coeffcent NOMENCLATURE INTRODUCTION Ac Ad Aeff C R D Fb Fe Fp L Ma Marm Mav Mb Mejt Mlpf = Partal dfferental area = Dfferental area = Effectve bellows area = Correcton factor = Bellows nsde dameter = Force due to the dfferental area = External forces (weght, etc) = Tf + Fe = Total transversal force n the pn = Half the bellows length = Actual moment calculated from expanson jont tests = Moment due to hnges frcton = Total moment n a EJ wth angular movement = Bellows angular moment due to bellows sprng rate = Theoretcal moment n a expanson jont = Moment due to the lateral pressure force Expanson jonts are used by the ndustry n process ppng and ducts to compensate the thermal expanson and provde the proper ppe flexblty. A ppe lne s consdered flexble f the ppe stresses and the equpment connecton loads are lower than an acceptable level. The ASME Process Ppng code B31.3 [1] establshes the rules and values for the maxmum allowable stresses n a process ppng system. In addton, rotatng equpment lke steam turbnes (Fg. 1), compressors, pumps and turbo-expanders, have the maxmum allowable nozzle loads specfed by the manufacturer or by an ndustry specfc standard such as the NEMA SM23 [2] for steam turbnes and turbo-expanders. In a paper by the authors [3] metal bellows expanson jonts actual reacton forces were compared wth the theoretcal values as per standards of the Expanson Jont Manufactures Assocaton (EJMA) [4] equatons. Snce 1 Copyrght ASME 21
EJMA does not consder effects lke frcton and components nterference there s a dscrepancy n the calculatons that can show an ncrease n the actual ppe stresses and equpment nozzle loads. Ths Paper presents a seres of equatons, based upon 13 large gmbal (Fg. 2) and hnged (Fg. 3) expanson jonts pressure and movements tests, that take nto account the loads not consdered by the EJMA calculatons. These equatons can be used to estmate wth hgher precson the reacton forces n ppng systems wth metal bellows expanson jonts. FIG. 3 HINGED EXPANSION JOINT EXPANSION JOINT REACTION FORCES FIG. 1 - STEAM TURBINE The meda pressure and the movement actng n a gmbal or hnged expanson jonts causes reacton loads calculated accordng to EJMA equatons. The source of these reacton loads may be attrbuted to the followng effects: - Bellows sprng effect: a metal bellows acts lke a sprng when t s flexed by the ppng movement (Fg. 4). - Pressure thrust: as a flexble element the meda pressure creates a pressure thrust force (Fg. 5) that acts on expanson jont hnges. In addton to these loads, other loads may be attrbuted to reactons as defned bellow: - Hnges pn frcton: as the expanson jonts move, there s frcton force actng on the hnge pns (Fg. 6). Ths force s due to the pressure thrust, jont weght and external forces. - Lateral pressure force: n a rotated bellows the dfference between expanded and contracted sdes generates a lateral force - Hnges Arm frcton: the rubbng effect of the arms (Fg. 6) creates a frcton force that opposte to ther rotaton. - Sleeve Seal frcton: expanson jonts wth nner sleeves may have a seal to hold nsde bellows nsulaton. The seal creates a force whch opposes the angular movement as shown n Fg. 7. The forces actng on the expanson jont create an angular moment whch can be expressed as follows: Mav = Mb + Mpf + Mlpf + Marm + Ms (1) FIG. 2 GIMBAL EXPANSION JOINT In the followng paragraphs each reacton moment s analyzed. 2 Copyrght ASME 21
FIG. 4 SPRING EFFECT FIG. 7 INNER SLEEVE SEAL FRICTION MOMENT DUE TO BELLOWS SPRING RATE The standard EJMA (Expanson Jont Manufacturers Assocaton), state the sprng rate calculaton consderng only the bellows sprng effect. Mb = α * kα (2) MOMENT DUE TO PIN FRICTION FIG. 5 THRUST PRESSURE Arms frcton locaton The pressure thrust force actng on an expanson jont hnge can reach very hgh values. For examples, n one of the jonts tested, durng the preparaton of ths paper, t reached 112 ton (248 lbf) at ts maxmum test pressure. Consequently, t s necessary to account accurately and reduce the hnge pn frcton. An expanson jont, nstalled n a process ppng to compensate thermal growth, s under a low frequency movement. A process whch starts-up and stays for long perods at a steady-state, once the process temperature has been reached and hnges wll not move. In Fg. 8, see the sketch of the angular movement and the pn frcton moment, due to the pn load. The hnges pn moment can be wrtten as: Pn frcton locaton Mpf = Fp * µp * d/2 (3) FIG. 6 HINGED PIN / ARMS FRICTION 3 Copyrght ASME 21
pressures, consderng that the meda pressure would cause a pn contact pressure from 47 MPa to 73 MPa (6.8 ks to 1.5 ks). Table 1 shows the stellte frcton test results. For ths study we consdered a frcton coeffcent of.14. TABLE 1 STELLITE FRICTION TEST Contact pressure MPa (ks ) Frcton Coeffcent 21 (3.).14 52 (7.5).14 66 (9.6).13 85 (12.3).13 99 (14.4).13 114 (16.5).13 See Pn Detal Below Pn Frcton Moment Angular Movement MOMENT DUE TO THE LATERAL PRESSURE FORCE As shown n Fg. 9, as the expanson jont rotates, one sde of the bellows expands and the opposte sde contracts. The dfference between the expanded and contracted areas (Fg.1) wll generate a force n the opposte drecton of the rotaton. The moment due to the dfferental area can be wrtten as follows: Mlpf = Fb * L / 2 (4) The force due to the dfferental area can be wrtten as: Fp Fb = P * Ad (5) FIG. 8 PIN FRICTION MOMENT The pn statc frcton coeffcent value µp depends of several condtons, lke materals, hardness, surface fnshng, presence of drty and others. The most part of expanson jonts applcatons use some steel pn straght n contact wth the arms steel or wth a metal sleeve, not usng any lubrcant and usually, n ths condton the µp value s from.25 to.9 and ths values can change due to envronmental condtons. The choce of the proper pn and arm or sleeve metal must be carefully studed durng the expanson jont desgn. It s not part of ths paper to analyze pn and sleeve materals. Further studes are necessary to evaluate the best choces. The focus of ths paper s to show the mportance of pn/sleeve frcton loads. If the hnges pn and sleeves are not properly hardened, the pressure thrust force may create a gallng effect at ther contact surface, ncreasng the moment necessary to move the jont. To avod gallng the pns can be hardened or adopt some other soluton. In the expanson jonts tested, for ths paper, the pns were hardened usng stellte, wth grndng surface fnshng. In order to check the frcton coeffcent of stellte x stellte, t was developed a test usng dfferent contact Fgure 11 shows an angular sector equals to half of the total rotaton angle α. A sde vew (X-X) of ths sector s shown n Fg. 12. The shaded portons are the dfferental areas between the expanded and contracted sdes of the rotated bellows. FIG. 9 LATERAL PRESSURE FORCE 4 Copyrght ASME 21
As shown n Fg. 13, t was consdered a partal area, from the total dfferental area, to calculate n an easest way. So the equaton s: Ad = 8* Ac (6) FIG. 1 BELLOWS SIDES AREA DIFFERENCES, UNDER ANGULAR MOVEMENT FIG. 13 DIFFERENTIAL AREAS Consderng the radus R n the vew XX dvded n n equal parts, the partal dfferental area can be calculated as follows: Ac L1 L n 1 = + 1 = 2 ( ( A A ) ) (7) In ths study, t was adopted a dvson n 1 equal parts, so the equaton becomes: FIG. 11 BELLOWS ANGULAR SECTOR Ac L1 L 9 = + 1 = 2 ( ( A A ) ) L 1 L = B tan α 2 4 (8) (9) B 2 2 ( R ). 5 = A (1) So the equaton becomes: FIG. 12 BELLOWS ANGULAR VIEW X-X Ac 9.5 = + 1 = 4 2 2 ( ( R A ) ( A A ) ) tan α (11) 5 Copyrght ASME 21
Table 2 shows values of the dfferental areas Ad for the dameters and movements of ths paper. TABLE 2 BELLOWS SIDES AREA DIFFERENCES ID mm (n) α ( ) 165 (65) 19 (75) Ad (cm²) 193 (76) 1 196,3 262,4 268,5 1,5 294,4 393,7 42,8 2 392,5 524,9 537,1 2,5 49,7 656,1 671,4 3 588,8 787,4 85,6 3,5 687, 918,6 939,9 4 785,2 149,9 174,2 4,5 883,3 1181,2 128,6 5 981,5 1312,4 1342,9 FIG. 14 SLEEVE SEAL CENTERED MOMENT DUE TO HINGES FRICTION The frcton between hnges wll ncrease the moment requred to move the expanson jont. Ths frcton can not be accurately accounted for. Bendng due to weldng thermal stresses can reduce the gap between arms ncreasng ther rubbng. MOMENT DUE TO INNER SLEEVE SEAL The expanson jonts, wth nternal refractory nsulaton, may be ftted wth a metal seal between sleeves as shown n Fg. 14. Ths seal usually s a steel wre brad wth steel mesh fller. If the seal s algned wth the hnge pn, t wll slde between the nternal sleeves when the expanson jont s subjected to an angular movement as shown n Fg. 14. If the seal s not algned t wll slde as well as compress wth the jont rotaton as shown n Fg. 15. Both the sldng movement and the seal compresson wll generate a force, and consequently, a moment that can not be accurately calculated. FIG. 15 SLEEVE SEAL NOT CENTERED ANALYSIS OF LARGE EXPANSION JOINTS TEST RESULTS Pressure and movement tests were performed by the authors [3] wth 13 large expanson jonts. A summary of the test results are shown n Fg. 18 to 23. The actual moment values (black lnes) are larger than the values calculated by the EJMA equatons (green lnes). Fgure 16 shows a pcture of a jont beng tested and Fg. 17 shows a schematc drawng of the test devce. The force on hnges s affected by the weght of the test devce and ts value was excluded from calculatons. The actual values can be as hgh as 3 tmes when compared wth the EJMA equatons results. Angles n the 1 to 2 degrees range ncrease the error. Ths dfference can result large errors n the ppe flexblty analyss. To mnmze ths error, at the ppng desgn tme, the actual values were compared wth the theoretcal values n order to defne a correcton factor (C R ) to account for the uncertantes. We have seen that s possble to calculate moment due to bellows sprng rate (Mb), meda pressure (Mlpf) and pn 6 Copyrght ASME 21
frcton (Mpf), so the eq. (1) n theory can be calculated and becomes as eq. (12). Mavt = Mb + Mlpf + Mpf (12) The value of C R can be used as a correcton factor to adjust the Eq. (12) n order to have values closer to the actual expanded jont. Moment (N.m) EJ ID193mm P=3.6bar 9 8 7 1 2 3 4 5 6 FIG. 18 TEST RESULT 1 VS. THEORY FIG. 16 MOVEMENT TEST Moment (N.m) EJ ID193mm P=2.3bar 9 8 7 1 2 3 4 5 6 FIG. 19 TEST RESULT 2 VS. THEORY Moment (N.m) EJ ID198mm P=3.6bar 9 8 7 1 2 3 4 5 6 FIG. 2 TEST RESULT 3 VS. THEORY FIG. 17 MOVEMENT TEST 7 Copyrght ASME 21
Moment (N.m) EJ ID198mm P=2.3bar 9 8 7 1 2 3 4 5 6 7 FIG. 21 TEST RESULT 4 VS. THEORY EJ ID165mm P=3.5bar TABLE 3 - M R IN TEST PRESSURE 2.2bar Angle (degree) Run 1 1,5 2 2,5 3 3,5 4 4,5 5 1 1, 1,7 1,12 1,15 1,17 1,18 1,2 1,21 1,21 2,54,66,74,79,82,85,87,89,91 3,52,64,72,77,81,83,86,87,89 4 - -,61,7,76,81,85,89,91 5,75,86,93,98 1,2 1,4 1,6 1,8 1,9 6,86,89,91,93,94,95,95,96,96 7 1,1 1,2 1,3 1,4 1,4 1,4 1,5 1,5 1,5 8 1,15 1,16 1,16 1,17 1,17 1,17 1,17 1,17 1,17 9,81,88,92,95,97,99 1, 1,1 1,2 1,49,59,66,7,73,76,78,79,8 11,59,69,75,79,81,84,85,87,88 12,61,73,8,84,88,9,92,94,95 13,58,7,78,83,87,9,92,94,96 Moment (N.m) Moment (N.m) 1 2 3 4 5 6 FIG. 22 TEST RESULT 5 VS. THEORY EJ ID165mm P=2.1bar 1 2 3 4 5 6 FIG. 23 TEST RESULT 6 VS. THEORY TABLE 4 - M R IN TEST PRESSURE 3.5bar Angle (degree) Run 1 1,5 2 2,5 3 3,5 4 4,5 5 1 1,1 1,6 1,1 1,12 1,14 1,15 1,16 1,17 1,18 2,82,86,89,91,92,94,94,95,96 3,52,63,7,75,78,81,84,85,87 4 -,51,63,71,77,82,86,89,91 5,55,71,82,9,95 1, 1,3 1,6 1,8 6,86,9,93,95,96,97,98,99 1, 7 1,2 1,2 1,3 1,3 1,3 1,3 1,3 1,3 1,3 8 1,14 1,15 1,15 1,16 1,16 1,16 1,16 1,16 1,17 9,75,82,87,9,93,95,96,98,99 1,51,59,65,69,73,75,77,79,8 11,64,72,77,81,83,86,87,89,9 12,7,78,84,88,91,93,95,97,98 13,65,75,81,86,89,92,94,96,97 Accordng to box-and-whsker plot for each pressure test, shown n Fg. 24, the varablty s smlar wthn each sample. The mean comparson shows the same behavor of varablty, as shown n Fg. 25. It means that pressure does not have nfluence on M R; consequently all data can be used to determne the probablty dstrbuton. Thus, the rato of actual value and Mavt s defned as moment Rato (M R ) shown n Eq. (13). M R = Ma / Mavt (13) The moment ratos calculated usng Eq.(13) are shown n Tables 3 and 4, for test pressures of 2.2 bar and 3.5 bar respectvely. These values were feed nto the Statgraphcs Centuron software [5] to determne the best probablty dstrbuton for the data. FIG. 24 BOX AND WHISKER PLOT 8 Copyrght ASME 21
The values shown n Table 5 can be used as a correcton factor (C R ). The selecton of the M R value, used as C R, wll depend upon how crtcal the applcaton s. Thus the expanson jont estmated moment can be expressed as n Eq. (14) below. Mejt=Mavt* C R (14) FIG. 25 MEANS CONFIDENCE INTERVALS A dstrbuton fttng procedure was performed to fnd a probablty that provdes a sutable model for the expermental data n order to determne M R tolerance lmts. From ths procedure, expermental data of M R can be adequately modeled by Webull, as shown n Fg. 26, whch compare frequency hstogram to the estmated probablty densty accordng Webull dstrbuton. For example, the respectve M R value of a probablty of 99.5% s 1.26. Usng ths number as C R, the Mejt calculated from Eq. (14) s plotted, n red lnes, aganst the jont actual test results, as shown n Fg. 18 to 23. CONCLUSION Based upon test values t s possble to mprove the EJMA reacton moment, represented by Eq. (2), whch s consderng just the bellows sprng effect, by addng the frcton and pressure forces effects wth a correcton factor. So, t s suggested to use Eq. (15), to calculate the angular moment for gmbal and hnged expanson jonts, due to angular rotaton. Mejt=(Mb + Mlpf + Mpf )* C R (15) Usng ths equaton at the desgn tme wll prevent an underestmaton of the expanson jonts reacton loads, whch are crtcal n rotatng equpment lke turbnes and turboexpanders. Addtonal studes are necessary to evaluate the C R varaton accordng to the pn/sleeve dfferent materals and envronment exposure. REFERENCES FIG. 26 - M R HISTOGRAM VS. WEIBULL DISTRIBUTION Table 5 shows the calculated M R and ts respectve probablty obtaned from the ftted Webull dstrbuton. TABLE 5 - M R VALUES PROBABILITIES M R Probablty, % 1.15 95. 1.19 97.5 1.23 99. 1.26 99,5 1.31 99.9 [1] ASME B31.3 26 Process Ppng, chapter II and appendx A, ASME Code for Pressure Ppng, B31, New York, NY, USA. [2] NEMA SM23 1991(R1997, R22), Steam Turbnes for Mechancal Drve Servce, secton 8.4, Steam Ppng Systems, NEMA Standards, Rosslyn, VA, USA. [3] Vega J.C., Mederos J., Vega J.L.B.C., PVP29-77828, Analyss of FCC Expanson Jonts Movement Test, 29 ASME Pressure Vessel and Ppng Conference, Prague, Czech Republc. [4] EJMA 28, 9 th edton, secton 4, Standards of the Expanson Jont Manufacturers Assocaton, Inc., Terrytown, NY, USA. [5] Statgraphcs Centuron XV - 26, verson 15.2. Edton Profssonal, StatPont Technologes, Inc., Warrenton, VA, USA. 9 Copyrght ASME 21