www.erjournal.org Internatonal Engneerng Research Journal (IERJ) Specal Issue Page 558-557, 015, ISSN 395-11 ISSN 395-11 Performance Enhancement of Metal Expanson Bellows for Shell and Tube Type Heat Exchanger #1 M.M. Bagban, # A.A Keste, # S. H. Gawande 1 bagban.mohsn@redffmal.com aakeste@mescoepune.org 3 shgawande@mescoepune.org 1 PG Student Dept. of Mech. Engg, 1 Modern Educaton Socety s College of Engneerng Pune, Inda. Professor, Dept. of Mech. Engg, 1 Modern Educaton Socety s College of Engneerng Pune, Inda. 3 Assocate Professor, Dept. of Mech. Engg., 1 Modern Educaton Socety s College of Engneerng Pune, Inda. ABSTRACT The bellows are the flexble element of an expanson jont consstng of one or more convolutons and the end tangents. The number of convolutons n a bellows s n drect relatonshp to the amount of thermal or mechancal movement n the ppng system or heat exchanger. Metal bellows are elastc vessels that can be compressed when pressure s appled or extended under vacuum. When the pressure or vacuum s released, the bellows wll return to ts orgnal shape. In ths project work, objectve s to desgn & enhance the performance of the metal expanson bellows as per the ASME and EJMA. In ths work Johnson Method s used to select the optmum materal wth objectve of mnmum weght and cost. As per Johnson Method the materal selected for bellows under consderaton was SAE 40 31 for mnmum weght and cost as compared to materals lke Inconal & Hastelloy X. Analcal analyss was done for bellow wth 8, 9 and 10 convoluton and t was found that Crcumferental Membrane stress n bellow tangent (S1) s constant for bellow wth 8, 9 and 10 convoluton. Whereas End convoluton crcumferental membrane stress (SE) and Intermedate convoluton crcumferental membrane stress (SI) shows the lnear decrease n stress as the number of convoluton ncreases. In order to valdate the fndngs requred numercal analyss s also done by usng ANSYS software and by performng extensve expermentaton usng Data Acquston System. After comparng results t was found that all results are n close agreement. ARTICLE INFO Artcle Hstory Receved :18 th November 015 Receved n revsed form : 19 th November 015 Accepted : 1 st November, 015 Publshed onlne : nd November 015 Keywords Metal expanson jont, Johnson Method, FEA, Convolutons.
www.erjournal.org Internatonal Engneerng Research Journal (IERJ) Specal Issue Page 558-557, 015, ISSN 395-11 I. INTRODUCTION Normally shell tube heat exchangers are operated on large temperature dfference, nternal pressure, vbraton and aggressve corroson envronment. Due to the extreme workng condtons the shell s always stressed under axal pressure, thermal load and vbraton. Ths may lead to contracton and expanson of shell. If the rate of contracton and expanson ncreases then there may be chance of shell falure. In order to compensate the deformaton an expanson jont s used n shell and tube heat exchanger. Normally metal bellows are used as an expanson jont n shell and tube heat exchanger. Metal bellows are elastc vessels that can be compressed when pressure s appled to the outsde of the vessel, or extended under vacuum. When the pressure or vacuum s released, the bellows wll return to ts orgnal shape. The bellows s a very unque component of a ppng system. It must be desgned strong enough to accommodate the system desgn pressure, as well as, flexble enough to accept the desgn deflectons for a calculated number of occurrences, wth a mnmum resstve force. The system pressure and deflecton create the major stresses n a bellows. Typcally the deflecton stresses are hgher than the pressure stresses and are merdonal or longtudnal n drecton. These stresses are calculated and evaluated n the Standards of the Expanson Jont Manufacturers Assocaton, Inc. or EJMA. The materal used for bellows are normally stanless steel, n rare case Inconel and Alumnum. The bellows are havng wde shape verty lke U-shaped, sem-torodal, Torodal, S-shaped, Flat, Stepped, Sngle Sweep, Nested Rpple. II. LITERATURE SURVEY Expanson jonts used as an ntegral part of heat exchangers or other pressure vessels shall be desgned to provde flexblty for thermal expanson and also to functon as a pressure contanng element. The rules n ths Appendx n ASME VIII Dv 1 [1] are ntended to bellows-type expanson jont geometres subject to nternal pressure. And the most comprehensve and wdely accepted text on bellows desgn s the Standards of Expanson Jont Manufactures Assocaton (EJMA) []. The study on characterstcs of stress can be found n the followng papers. The development of the metal expanson bellows wth proper geometry s suggested by Hyun Wook Kang [3]. K. C. Leong, K. C. Toh, Y.C. Leong [4] gves nformaton n ther paper about a software for the thermal and hydraulc desgn of shell and tube heat exchangers wth flow nduced vbraton checks has been developed n a Wndows-based Delph programmng envronment. Its user-frendly nput format and excellent color graphcs features make t an excellent tool for the teachng, learnng and prelmnary desgn of shell and tube heat exchangers. Desgn methodology s based on the open lterature Delaware method whle flow-nduced vbraton calculatons adhere closely to the methodology prescrbed by the latest TEMA standards for ndustry practce. The formng technology wth the mechancal behavor of the metal expanson bellow s also suggested by hm. The analyss of bucklng of metal expanson jonts under nternal pressure are suggested by D.E.Newland [5]. The analyss of two types of metal expanson jonts movement test are suggested by Jorvaldo Mederos []. L [7] has nvestgated the effect of the ellptc degree of Ω-shaped bellows torod on ts stresses. The calculated stress results of Ω-shaped bellows wth ellptc torod correspond to experments. The ellptc degree of Ω-shaped torod affects the magntude of nternal pressure-nduced stress and axal deflecton-nduced stress. Especally, t produces agreat effect on the pressurenduced stress. In order to keep the bellows strength and mantan ts fatgue lfe,the torod ellptc degree should be reduced greatly n manufacturng process, for example, at least lower than15%. The man key parameter responsble n the desgn and analyss of the metal expanson jont s the effectve parameters of the metal expanson bellow are suggested by Gh Faraj [8]. Kang et al. [9] proposed the formng process of varous shape of tubular bellows usng a sngle-step hydro formng process. The conventonal manufacturng of metallc tubular bellows conssts of four-step process: deep drawng, ronng, tube bulgng, and foldng. In ther study a sngle step tube hydro formng combned wth controllng of nternal pressure and axal feedng was proposed. Those revewed papers show that there are needs for rgorous analyss and formng parameters of bellows. It s stated that the Ω-shaped bellows have much better ablty to endure hgh nternal pressure than common U-shaped bellows. He suggested most effectve parameters of the bellows are ntal length of tube, nternal pressure, axal feedng and velocty, mechancal propertes and the type of materals by fnte element (FE) analyss (LS-Dyna) and expermental tests. G.Wang et al [10] developed a new technology uses super-plastc formng (SPF) method of applyng gas pressure and compressve axal load. It s developed and can be used to manufacture large dameter U type bellows expanson jonts made of ttanum alloys. The formng technology for bellows expanson jonts made of ttanum alloys s presented to make a two-convoluton bellows expanson jont of T Al 4V alloy thn plate of 1.8mm thckness. Welded ppe bent by a hot bendng method wth a set of specfc des and welded by PAW was used as a tubular blank n the SPF. Durng the SPF process the tubular blank s restraned n a mult-layer de block assembly whch determnes the fnal shape of convoluton. The formng load route s dvded nto three steps n order to obtan optmum thckness dstrbuton. Ths technology can also be used to fabrcate stanless steel bellows expanson jonts. The super-plastcty of T Al 4V ttanum alloy s the best among of them, for nstance the elongaton can exceed 1000%. G I Broman [14] suggested I DEAS software for the smulaton of the metal expanson bellows before realzaton of the bellows. At the end of the revew work now the author concludng that the remanng part of the metal expanson bellow s the key objectve for the next research work. H.Shakh [15] have performed an expermental work to analyze falure of an AM 350 steel bellows. As per the lterature survey and dscusson wth the expert n ths feld, t s very dffcult to formulate the perfect desgn and nvestgate the selecton of materals and shapes, vbraton effect, jonng of bellows to shell, stresses, flow analyss, fatgue lfe analyss and predcton of falure.as per the motvaton and problem formulaton followng am and objectve were set. conference webste
www.erjournal.org Internatonal Engneerng Research Journal (IERJ) Specal Issue Page 558-557, 015, ISSN 395-11 III. METHODS The bellows s a very unque component of a ppng system. It must be desgned strong enough to accommodate the system desgn pressure, as well as, flexble enough to accept the desgn deflectons for a calculated number of occurrences, wth a mnmum resstve force. The system pressure and deflecton create the major stresses n a bellows. Typcally the deflecton stresses are hgher than the pressure stresses and are merdonal or longtudnal n drecton. These stresses are calculated and evaluated n the Standards of the Expanson Jont Manufacturers Assocaton, (EJMA). The pressure stresses nclude crcumferental (hoop) stress n the bellows tangent as well as the convolutons. EJMA defnes the bellows tangent membrane stress due to pressure as S1. The bellows crcumferental membrane stress due to pressure s desgnated as S n the EJMA calculatons. The tangent stress (S1) and crcumferental bellows stress (S) must not exceed the mum allowable stress, whch s set as per the specfcaton. There are also merdonal pressure stresses that are evaluated n the desgn of a bellows. The bellows merdonal membrane stress due to pressure s desgnated as S3 n the EJMA calculatons. The other merdonal stress that s evaluated n EJMA s the bellows merdonal bendng stress due to pressure, or S4. If these merdonal stresses are exceeded, the convoluton sdewall wll be overstressed and ths wll lead to bellows falure. A. Termnology of Bellows In order to comprehend the desgn process of bellows, t s very mportant that, the desgner must have the knowledge of bellows termnology [Fg.1]. In ths secton dfferent terms used n bellows desgn are explan n detals as shown n Fg.1 Fg.1. Termnology of Bellow 1) Convoluton heght: The heght of the convolutons measured from the outsde- preferably wth slde gauge. ) Convoluton ptch: The dstance between the convolutons measured from crest to crest. 3) Cycle: One complete cycle s based upon movng the bellows from neutral length to poston 1,back through the neutral length to poston and then back to the neutral length. 4) Desgn Temperature: The mum and mnmum desgn, operatng and nstallaton temperatures should be accurately stated. In stuatons where the ambent temperature s expected to vary sgnfcantly durng ppe lne constructon, specal care n expanson jont postonng may be necessary. 5) Desgn Pressure: The system desgn pressure, operatng pressure and test pressure should be specfed realstcally wthout the addton of arbtrary safety factors, because ths practce necesstates greater bellows materal thckness to wthstand the overstated pressures. For standard metal expanson jonts the PN (nomnal pressure) factor can be defned as the allowed postve operatng pressure at room temperature. ) Desgn Allowable stress: Ths s the allowable stress for the bellows materal at the bellows desgn temperature. 7) Modulus of elastcty at Desgn temperature: Ths s the modulus of elastcty of the bellow materal at the desgn temperature whch s used to calculate sprng rate and columns squrm pressure. 8) Modulus of elastcty at ambent temperature: The room temperature modulus of elastcty s used to calculate the deflecton stresses (S5 & S). B. Selecton of Materal Selecton of materal s very much mportant from the desgn, weght and cost pont because relablty and durablty of desgn depends on the materal only. The cost of materal vares from materal to materal therefore t s necessary to select the best sutable materal for the applcaton for the purpose of desgn and cost pont of vew. The materal for our desgn can be selected on bass of one of the well known method of optmzaton that s JOHNSON S METHOD. For the purpose of mnmzng weght and cost of bellow, Let us consder bellow as a thn cylnder wth nternal pressure. Procedure for fndng the optmum materal for bellow usng Johnson s method s as follows: 1) Prmary Desgn Equaton (P.D.E) : The most sgnfcant undesrable effect to be mnmzed s the weght of the bellow and gven by W g * volume do d * W g h 4 ) Subsdary Desgn Equaton (S.D.E) : o P d o d d d d ( P) o 3) Lmt Equaton : 0.5S N 4) Classfcaton Of Parameters: f TABLE I
www.erjournal.org Internatonal Engneerng Research Journal (IERJ) Specal Issue Page 558-557, 015, ISSN 395-11 Functonal Requremen t Parameter Undesrable Effect Parameter Geometrcal Parameter Materal Parameter Classfcaton Of Parameter Specf Lmte ed d o P d, 5) Combnng S.D.E & P.D.E : d gh d W d 4 ( P ) Unspecfe d & Unlmted W ghd P W 4 P Ths s new developed P.D.E h, S ) Combnng Lmt Equaton wth P.D.E : 0.5S N f ghd PN f W 4 0.5S PN f * *9.81*0.115*.15 1.099*10 *1.5 4 0.5* S 1.099*10 *1.5 W 1.485*10 W 0.015 0.5* S 1.485*10 TABLE II Materal Selecton Calculaton Table Materal SAE 40 31 Inconal Hastelloy X Mass Densty 8090 8440 80 (Kg/m ) Tensle 515*10 40*10 380*10 Strength (N/m ) Materal 51.45 0.0 70.71 Selecton Factor Weght 1.109 1.948 1.545 0.015*(a) (W)(Kg) Rate/Kg 70 85 0 (R) Total Materal Cost (W*R) 99.8/- 39./- 39.4/- Ths s fnal P.D.E. In order to mnmze W, the materal selecton factor 1.485*10 should be 0.5* S 1.485*10 mnmze. 7) Selecton Of Materal : From Table II t s concluded that the SAE 40 31 has mnmum weght and cost as compared to Inconal & Hastelloy X, hence SAE 40 31 s selected for our desgn purpose. C. Specfcaton of U Shaped Bellows Table.3. shows dfferent nput parameters requred n desgnng of U Shaped Bellows TABLE III Dfferent desgn parameters Parameters Symbol Values Expanson Jont Materal SA- 40 31 Materal UNS Number Bellows Desgn Allowable Stress(N / mm ) Bellows Ambent Allowable Stress(N / mm ) Bellows Yeld Stress(N/mm ) Bellows Elastc Modulus at Desgn Temp (N / mm ) Bellows Elastc Modulus at Ambent Temp (N / mm ) S3100 S 19.5 S a 137.89 S y 157.39 E b 183090 E 0 19511 Posson s Rato υ b 0.300 Bellows Materal Formed Condton Desgn Cycle Lfe, Requred number of cycles Nreq 7000 Desgn Internal pressure P 1.099 Desgn temperature for 190 0 C Internal Pressure Bellow Type U Shaped Bellows nsde D b 15.000 dameter(mm) Convoluton Depth w 10 (mm) Convoluton Ptch (mm) q 9.44 Expanson jont openng ΔQ 0.985 per convoluton (mm) Total number of N 9 convolutons Nomnal thckness of t 0.300 one ply (mm) Total number of ples n 3 End tangent Length LT 13.000 (mm) Fatgue Strength Reducton Factor Kg 1.500
www.erjournal.org Internatonal Engneerng Research Journal (IERJ) Specal Issue Page 558-557, 015, ISSN 395-11 IV. DESIGN OF BELLOWS A. Determnaton of U-shaped Bellows Parameters: In ths secton dfferent parameter requred to perform bellow desgn are determned. 1. Mean dameter of bellows convolutons (D): = D b + W + n * t. Thckness of one ply, corrected for Thnnng durng formng (tp): = t * Db/ D 3. Convoluton Ptch ( q): N q 85 10.5 mm N 8 m 4. Bellows cross sectonal area of One convoluton (A): (3.1411 ) = * q * W * n * tp 5. Stffenng effect factor (k): Lt = MIN 1, 1.5* ( Db* t). Coeffcent (C1) q = * W 7. Coeffcent (C) q =.* D m* t p TABLE IV Parameters Of Bellows Types Of Stress Convolutons 8 9 10 Convoluton Ptch 10.5 9.44 8.5 ( q) (mm) Bellows cross.7.104 1. sectonal area of One convoluton ( A) (mm ) Coeffcent (C 1 ) 0.5313 0.47 0.45 Coeffcent (C ) 0.94 0.17 0.5 B. Analcal Stress Analyss of U-shaped bellows: In ths secton stresses nduced n dfferent drecton n U- shaped bellow are determned. 1. Crcumferental membrane stress n bellows tangent ( S1 ) : 1 Lt * Eb * K * P( Db n* t) [ n* t *( Db n* t)* Lt * Eb tc* Dc * Lc* Ec* K]. End convoluton crcumferental membrane stress ( SE ) : 1 [ q* Dm Lt *( Db n* t)]* P ( An* tp* Lt tc* Lc) 3. Intermedate convoluton crcumferental membrane stress (SI) : 1 P* q* Dm A 4. Merdonal membrane stress (S3) : 1 W* P n* tp 5. Merdonal bendng stress (S4) : 1 W * * P* Cp * n tp. Unrenforced Merdonal stress summaton : S3 S4 7. Unrenforced Bellow axal stffness (sprng rate ) [ Kb] 1 n tp 1 * * Eb* Dm* * (1 b ) N W Cf 8. Allowable pressure for unrenforced column stablty ( Psc) : Kb 0.34*3.141* N* q S 4 3* SI 1 * 1 4 4 9. Allowable pressure for In- plane stablty ( Ps ) : SYSTAR ( )* A* Dm* q* Types Of Stresses TABLE V Summary of Analcal Results Convolutons 3 Allowable Streses 8 (N/mm ) 9 (N/mm ) 10 (N/mm ) (N/mm ) (S1) 95.8 95.8 95.8 19.5 (SE) 0.95 58.7 57.03 19.5 (SI) 4.97 39.13 3.0 19.5 (S3 + S4) 139.1 149.8 17.3 388.94 (Psc) 3.84 3.34 3.39 5.153 (Ps).3.17.04 3.450 S1 = Crcumferental membrane stress n bellows tangent. SE = End convoluton crcumferental membrane stress. SI = Intermedate convoluton crcumferental membrane stress. S3 + S4 = Unrenforced Merdonal stress summaton. Psc = Pressure for unrenforced column stablty. Ps = Pressure for In- plane stablty Bref summary of analcally calculated values of stresses (as per EJMA & ASME Code) s gven n TABLE V. Calculated stresses.e, Crcumferental membrane stress n bellows tangent (S1), End convoluton crcumferental membrane stress (SE), Intermedate convoluton crcumferental membrane stress (SI), Unrenforced Merdonal stress summaton (S3+S4), are wthn good
www.erjournal.org Internatonal Engneerng Research Journal (IERJ) Specal Issue Page 558-557, 015, ISSN 395-11 agreement when compared wth allowable stresses. Hence performed desgn of bellow wth 8,9 & 10 convoluton s safe. TABLE V. shows that there Crcumferental Membrane stress n bellow tangent(s1) s constant rrespectve of ncrease or decrease of the number of stress. And End convoluton crcumferental membrane stress ( SE) and Intermedate convoluton crcumferental membrane stress (SI) shows the lnear decrease n stress as the number of convoluton ncreases. Smlarly Pressure for unrenforced column stablty (Psc) also decreases as the number of the convoluton ncreases. Whereas Unrenforced Merdonal stress summaton (S3 + S4) ncreases as the number of convoluton ncreases. C. Fatgue Calculaton 1. Unrenforced Merdonal membrane stress due to axal dsplacement ( S 5) : Q E * t * (* w * C ) = b p 3. Unrenforced Merdonal bendng stress due to axal dsplacement ( S ) : Q = 5* Eb* tp * (3* w * Cd ) 3. Unrenforced total stress range due to cyclc dsplacement ( St): K g Factor = 0.7*( S S ) ( S S ) = 3 4 5 K E 0 g* * Eb 4. Allowable number of Fatgue Cycles (Nallw) : K E g b K * E * S t 0 0 S t S 0 TABLE VI Summary of Fatgue Results Types Of Stresses Convolutons 8 (N/mm) 9 (N/mm) 10 (N/mm) (S5) 1.45 1.44 1.4589 (S) 0.1 153. 15.44 (St) 304.93 0 71.0 (Nallw) 5740 Cycles f 50978 Cycles 4315 Cycles S5 = Unrenforced Merdonal membrane stress due to axal dsplacement. S = Unrenforced Merdonal bendng stress due to axal dsplacement. St = Unrenforced total stress range due to cyclc dsplacement. Nallw = Allowable number of Fatgue Cycles TABLE.VI shows that Unrenforced Merdonal membrane stress due to axal dsplacement (S 5) s approxmately same for all the bellows wth dfferent convoluton. Whereas Unrenforced Merdonal bendng stress due to axal dsplacement (S) and Unrenforced total stress range due to cyclc dsplacement ( St) goes on decreasng as the number of convoluton ncreased from 8 to 10. Allowable number of Fatgue Cycles (Nallw) shows the anonymous behavor that s number of fatgue cycle frst ncreases as the number of cycle ncreases from 8 convoluton to 9 convoluton but t decreases as the number of convoluton s further ncreased from the 9 convoluton to 10 convoluton. V.MODELLING & FEA ANALYSIS Modelng and analyss of bellows wth 8,9 and 10 convoluton s done usng ANSYS 14.0 software. Modelng of bellow s done usng the Desgn Modular of ANSYS software and analyss s done usng Mult-Physcs module of ANSYS software. Axs symmetry method s used to do the analyss as bellow s symmetry about the axs and t reduces the number of nodes and element whch ultmately the reduces the meshng and solvng tme. Analyss s done usng Couple Feld Analyss method as we have to calculate the thermal stresses by gvng two boundary condton that s temperature (190 0 C) and pressure (1.099MPa).Fg.,3 & 4 shows the Von Msses stress dstrbuton for bellow wth 8,9 & 10 convoluton respectvely. Fg.. Von Msses Stresses For 8 Convoluton Fg..shows the Von Msses Stress for 8 Convolutons. Fg.. shows the four stresses that s Crcumferental membrane stress n bellows tangent (S1), End convoluton crcumferental membrane stress ( SE), Merdonal bendng stress (S4) and Unrenforced Merdonal bendng stress due to axal dsplacement ( S ) respectvely. Fg.3. Von Msses Stresses For 9 Convoluton Fg.3.shows the Von Msses Stress for 8 Convoluton. Fg.3. shows the four stresses that s Crcumferental membrane stress n bellows tangent (S1), End convoluton crcumferental membrane stress ( SE), Merdonal bendng stress (S4) and Unrenforced Merdonal bendng stress due to axal dsplacement ( S ) respectvely.
www.erjournal.org Internatonal Engneerng Research Journal (IERJ) Specal Issue Page 558-557, 015, ISSN 395-11 In order to study the effect of pressure on bellow stresses and valdate the results, the actual experment was conducted on bellow wth 10 convolutons by varyng the pressure from 1 bar to bar.fg.7. and Fg.8. shows the actual pcture of the expermental setup and Data acquston system respectvely. Fg.4. Von Msses Stresses For 10 Convoluton Fg.4.shows the Von Msses Stress for 8 Convoluton. Fg.3. shows the four stresses that s Crcumferental membrane stress n bellows tangent (S1), End convoluton crcumferental membrane stress ( SE), Merdonal bendng stress (S4) and Unrenforced Merdonal bendng stress due to axal dsplacement ( S ) respectvely. A. Comparson of Analcal and FEA Results TABLE VII.Comparson of Analcal and FEA Results Types Convolutons Of Stress 8 (N/mm) 9 (N/mm) 10 (N/mm) Anal FEA Anal FEA Anal FEA cal ca l ca l S1 95.8 98.9 95.8 97. 95.8 9.0 SE 0.95 3.1 58.7 58. 57.0 59.5 7 3 S4 13.8 13. 143.5 145. 11 17. 9 S 0.1 199. 4 153. 15. 7 15. 4 151.9 TABLE VII.shows the analcal and FEA stress value for Crcumferental membrane stress n bellows tangent (S1), End convoluton crcumferental membrane stress (SE), Merdonal bendng stress (S4) and Unrenforced Merdonal bendng stress due to axal dsplacement (S ) and t found that the FEA results are n close agreement wth the analcal results. VI.EXPERIMENTAL SETUP a In order to perform the experment, we had developed the expermental setup. Expermental setup consst of boler, bellow, stran gauges and NI Data Acquston System. Boler s used to gve boundary condton that s pressure and temperature and NI Data Acquston System s used to capture the data that s stran and stress wth the help of stran gauges. Fg.. show the schematc dagram of expermental setup. Fg.7.Actual Expermental Setup Fg.8. Data Acquston System Fg.9.Locaton of Stran Gauges S1 = Crcumferental membrane stress n bellows tangent S = End Convoluton crcumferental membrane stress Fg.9. shows the locaton of stran gauges. We can get only two types of stresses n expermental setup that are Crcumferental membrane stress n bellows tangent (S1) and end convoluton crcumferental membrane stress (S) that are shown n Fg.9. Other stresses are merdonal stresses whch are on the cross sectonal area hence cannot be evaluated. Followng Fgures shows the screen shot of the evaluated results from LabVew software wth dfferent pressure condton. Fg.10.Results wth Pressure 1 bar Fg..Schematc Dagram of Expermental Setup
www.erjournal.org Internatonal Engneerng Research Journal (IERJ) Specal Issue Page 558-557, 015, ISSN 395-11 Fg.11.Results wth Pressure 1.5 bar Fg.1.Results wth Pressure 1.5 bar Fg.13.Results wth Pressure 1.75 bar Fg.14.Results wth Pressure bar Fg 10,11,1,13 & 14 shows the results of Labvew software of wth dfferent pressures that are 1,1.5,1.5,1.75 & bar respectvely. A. Comparson of Analcal and Expermental Results TABLE VIII.Comparson of crcumferental membrane stress n bellows tangent at dfferent pressure Pressure Descrpton (Bar) Analcal Expermental 1 7.111 9.871 1.5 8.9513 11.419 1.5 10.741 13.83 1.75 1.5319 14.775 14.3 17.8301 TABLE IX.Comparson of End Convoluton crcumferental membrane stress at dfferent pressure Pressure Descrpton (Bar) Analcal Expermental 1 4.3889 7.051 1.5 5.48 8.981 1.5.5834 9.095 1.75 7.807 10.7358 8.7779 11.094 Table VIII & IX shows the value of crcumferental membrane stress n bellows tangent and end convoluton crcumferental membrane stress at dfferent pressure. It shows that as the pressure ncreases, stresses also ncrease smultaneously. It s also found that the expermental results are n close agreement wth the analcal results. VII.CONCLUSIONS Materal for bellows was selected on the bass of Johnson method and t was that SAE 40 31 s the optmum n terms of weght and cost. Bellows wth 8,9 & 10 convoluton s desgned as the ASME and EJMA code. All the stresses are calculated and t s found that the stresses are under allowable lmts, hence the s safe. Analcal results show that there Crcumferental Membrane stress n bellow tangent (S1) s constant rrespectve of ncrease or decrease of the number of stress. And End convoluton crcumferental membrane stress( SE) and Intermedate convoluton crcumferental membrane stress (SI) shows the lnear decrease n stress as the number of convoluton ncreases. Smlarly Pressure for unrenforced column stablty (Psc) also decreases as the number of the convoluton ncreases. Whereas Unrenforced Merdonal stress summaton (S3 + S4) ncreases as the number of convoluton ncreases. Unrenforced Merdonal membrane stress due to axal dsplacement (S 5) s approxmately same for all the bellows wth dfferent convoluton. Whereas Unrenforced Merdonal bendng stress due to axal dsplacement (S) and Unrenforced total stress range due to cyclc dsplacement ( St) goes on decreasng as the number of convoluton ncreased from 8 to 10. Allowable number of Fatgue Cycles (Nallw) shows the anonymous behavour that s number of fatgue cycle frst ncreases as the number of cycle ncreases from 8 convolutons to 9 convolutons but t decreases as the number of convoluton s further ncreased from the 9 convolutons to 10 convolutons. In order to valdate the fndngs requred numercal analyss s also done by usng ANSYS software and by performng extensve expermentaton usng Data Acquston System. After comparng results t was found that all results are n close agreement. ACKNOWLEDGMENT The authors would lke to acknowledge the contnuous gudance and encouragement of Mr.Umesh Ubale and Prof.A.Mtra. Many thanks to MES College of Engneerng and MESCOE NI Labvew Academy for ther help n the experments. REFERENCES [1] ASME, ASME Boler and Pressure Vessel Code- Secton VIII, Dvson 1, Appendx Pressure Vessel and Heat Exchanger Jonts, New York, 000. [] EJMA, Standards of Expanson Jont Manufacturers Assocaton, nnth edton, New York, 008S.
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