Modal Analysis Design to Exposure Gyroscopic Effect in Rotating Machinery Using Experimental and Analytical/Computational Techniques

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1 H.A. A-Khaza et a. / nternatona ourna of Engneerng Scence and Technoogy EST Moda Anayss Desgn to Exposure Gyroscopc Effect n Rotatng Machnery Usng Expermenta and Anaytca/Computatona Technques Abstract: H.A. A-Khaza 1 1 Schoo of Mechanca & Automotve Engneerng, Kngston Unversty, London, UK, E-ma, K @ngston.ac.u M. Asar Schoo of Aerospace & Arcraft Engneerng, Kngston Unversty, London, UK, E-ma, M.Asar@Kngston.ac.u The moda anayss desgn s to estabsh a system dentfcaton methodoogy usng the anaytca/computatona technques and update the mode usng expermenta technques aready estabshed for passve structures but to actve rotatng structures, whch subsequenty hep to carry out heath montorng as we as further desgn and deveopment n rotatng machnery There are severa phenomena need to be detected such as centrfuga and gyroscopc effect whch woud create compexty n the mathematca procedures n moda anayss before they coud be used n moda testng of rotatng structures.gyroscopc acton occurs whenever the axs of the rotatng body s made to change ts drecton. Rotatng components produce a gyroscopc coupe, whch can ead to undesrabe effects,for exampe,when a road vehce traves round a bend the gyroscopc coupe produced by turnng the axes of the whees tends to overturn the vehce.n an arcraft changng drecton,the gyroscopc coupe produced due to the rotatng components of the engne cause the arcraft to ptch up or down.n shp ptchng,the turbne rotor axs of rotaton ptches wth the shp and t tend to mae the shp swng sdeways. Gyroscopc effect s can aso be used to advantage as n the case of gyro-stabzers n whch the undesrabe effect s ressted and provdes stabzaton so we study a behavors of gyroscopc. The raw data obtaned from experment was used n fnte eement FE mode for comparson. Snce t has good capabty for Egen anayss and aso good graphca facty, and obtaned good resut. The ams s to estabsh a system dentfcaton methodoogy usng the anaytca/computatona technques and update the mode usng expermenta technques aready estabshed for passve structures but to actve rotatng structures, whch subsequenty hep to carry out heath montorng as we as further desgn and deveopment n rotatng machnery Keywords: Desgn, Anaytca/Computatona Technques, Moda, Gyroscopc Effect, Vbraton. 1. ntroducton Rotatng machnes such as steam or gas turbnes, turbo-generators, nterna combuston engnes, motors, and dsc drves can deveop nerta effects that can be anayzed to mprove the desgn and decrease the possbty of faure. Current trends n rotatng equpment desgn focus on ncreased speeds, whch ncrease operatona probems caused by vbraton. At hgher rotatona speeds, the nerta effects of rotatng parts must be consstenty represented to accuratey predct rotor behavor. nerta effects n rotatng structures are usuay caused by gyroscopc moment ntroduced by the precse motons of the vbratng rotor as t spns. As spn veocty ncreases, the gyroscopc moment actng on the rotor becomes crtca. Not accountng for nerta effects at the desgn eve can ead to bearng and support structure damage [1]. t s aso mportant to consder bearng stffness, support structure fexbty, and dampng characterstcs to understand the stabty of a vbratng rotor. The best method for measurement of dynamc performance of machne s to obtan the frequency response functons at approprate ponts []. SSN : Vo. 3 No. 9 September

2 H.A. A-Khaza et a. / nternatona ourna of Engneerng Scence and Technoogy EST n ths paper search of fndng a new technque for nterpret the resuts obtaned from experment measurement of dynamc performance of machnery for condton montorng, t s envsage that. A database coud be created. Ths database consstng of compete mathematca mode of the machne whch ncudes both the supportng structures as we as the movng parts and s based on the structura dynamcs characterstcs of the system. Lnear structures for the purpose of vbraton anayss may be modeed ether as a contnuous system or a dscrete one. n the case of the atter method, the mass of the system s umped nto a fnte number of masses connected by sprngs and dampers representng the stffness and dampng n the system respectvey. The system s then sad to posses an nfnte number of degrees of freedom. Dampng mechansm comes n dfferent forms such as vscous, structura, hysteretc and couomb.the vscous dampng beng the most common form. The equatons of moton of the dscrete mode conssts of a fnte number of second order ordnary dfferenta equatons couped together, n whch case they have to be soved smutaneousy[1,3]. The process becomes progressvey more dffcut as the number of degrees of freedom ncreases. There s a way of de-coupng the equatons of moton usng the orthogonaty propertes of the natura modes. n ths method, the system s transformed from generased coordnates to a new set of coordnates caed prncpa coordnates, n whch case the equatons are soved ndependenty and nverse transformed nto the generased coordnates. The method of de-coupng the equatons of moton s caed Moda anayss [4, 5 &6]. n moda anayss apped to passve structures non-rotatng t s assumed that the system matrces are symmetrc, whch smpfes the transformaton. Whe the symmetrc assumpton of system matrces s vad for passve structures, t s not sutabe for structures contanng rotatng eements. f the theory of moda anayss for passve structures s apped to actve structures the fu de-coupng s not acheved. However t s possbe to use a dfferent technque to acheve fu de-coupng of the dfferenta equatons of moton [7, 8& 9] Gyroscopc effect For a structure spnnng about an axs Δ, f a rotaton about an axs perpendcuar to Δ a precesson moton s apped to the structure, a reacton moment appears. That reacton s the gyroscopc moment [1, 3]. ts axs s perpendcuar to both the spn axs Δ and the precesson axs. The resutng gyroscopc matrx coupes degrees of freedom that are on panes perpendcuar to the spn axs. The resutng gyroscopc matrx, [G], w be sew symmetrc. Gyroscopc effect occurs whenever the mode shape has an anguar conca/rocng component. Aso at the same secton t s mentoned that havng an overhung oad w mae the gyroscopc occurs n both, 1 st and nd mode of vbraton that mean gyroscopc effect occurs at the ower frequences. Athough t s suffcent to aocate the experment n the 1 st mode [8, 13]. Fg. 1 The gyroscopc effect [16] Whr When a rotatng structure vbrates at ts resonant frequency, ponts on the spn axs undergo an orbta moton, caed whrng. Whr moton can be a forward whr FW f t s n the same drecton as the rotatona veocty or bacward whr BW f t s n the opposte drecton [1, 10]. SSN : Vo. 3 No. 9 September

3 . Methods.1. System mathematca mode Fg. Gyroscopc setup parameter [3]. Pcture. 1 Expermenta setup for the moda testng Equatons of moton The genera equatons of moton for a mut-degree of freedom vbratory system may be wrtten as [3, 6 & 14]: [ ]{ } [ ]{ } [ ]{ } { } ] [ ] [ ] [ t F t q K B t q C G t q M 1 n the above equatons the mass, dampng and stffness matrces are speed dependent. The dampng matrx aso ncude the gyroscopc effect of the rotatng system, so the equaton of moton for a rotor consstng of shaft and a snge over hanged dsc can be wrtten as foow:- wt Z z y z z y e F F f f Z Z c c Z Where ₀, L, j and are ; ₀ the moment of nerta of the dsc about the shaft ongtudna axs through pont 0, L,Length of the shaft, dametra moment of nerta of the dsc and, rotatona speed of the rotor respectvey. The frequency response functon pont and transfer due to a snge exctaton and snge response pont obtaned by the foowng expresson / / 4 3 c c c c F H yy yy 3 / / 4 3 c c c H yy 4. By usng the Eq. 4, the frequency response functon FRF of the rotor was found, as ths s a graphca method shown n Fg.8. The poar mass moment of nerta ₀ about the pont o can be cacuated as foows: 3 m M d 5 H.A. A-Khaza et a. / nternatona ourna of Engneerng Scence and Technoogy EST SSN : Vo. 3 No. 9 September

4 H.A. A-Khaza et a. / nternatona ourna of Engneerng Scence and Technoogy EST d Mass moment of nerta of the dsc about tsef. 4 π d d 64 m nerta due to the shaft 3 γ, Where; s the dametera mass moment of nerta and, ₀ s the poar mass moment of nerta, s the statonary natura frequency of the rotor equa to vertca and horzonta modes n our case. x a Represent the vertca mode. y b Represent the horzonta mode For rotatng condtons the natura frequences has to be cacuated from the equaton beow, γ * 6 γ * 1, ± 7 s the rotor speed. s the natura frequency of the rotor at a gven speed. Are bacward and forward whr natura frequency of the system. 1,. Rotate Acquston and Anayss n expermenta The Rotate Acquston and Anayss software pacage s part of m p nternatona's t s desgned for troubeshootng and anayzng nose or vbraton probems reated to the speed characterstcs of rotatng or recprocatng components of a machne n operaton[15,16]...1 Appcatons Rotatng machnery dagnostcs Anayss of nose and vbraton probems reated to rotatona forces, e.g. n automotve and arcraft engnes, transmssons, gearboxes, compressors, pumps, turbnes, eectrc motors Order anayss... Test setup The test rotor s shown n pcture 1. Bascay, the rotor conssted of a shaft wth a nomna dameter of 10 mm, wth an overa ength of 610 mm. Two journa bearngs, RK4 Rotor Kt made by Bentey Nevada the advanced power systems energy servces company, coud be used to extract the necessary nformaton for dagnostc of rotatng machnery, such as turbnes and compressor. Been testng the process w be conducted on the rotary machne as the project s based on rotary dynamcs reach practca resuts for the purpose of subsequenty apped machnery rotary by usng Smart offce program,and then do the expermenta testng usng the mpact test, nstaed fx two acceerometermode 333B3,senstvty 97. & 98.6 mv/g n &Z drecton and rovng the hammermode , S.N449 on each pont for the purpose of generatng strength of the Movement for the vbraton body and the creaton of vbraton for that wth creatng a computer when tang readngs n pubc that he was Dmensons and ntroducng t wth the data wthn the program Smart offce,[9,15].confgu raton for testng on the machnes wth rotary machne the creaton of a necessary equpment for that purpose wth the desgn geometry wzard see Fg.3. SSN : Vo. 3 No. 9 September

5 H.A. A-Khaza et a. / nternatona ourna of Engneerng Scence and Technoogy EST Fg.3 Geometry desgn for moda gyroscopc effect, expermenta test usng smart offce..3. Smuaton of a smpe mode n ANSS 1. A smpe mode of rotor system wth an overhung dsc wth mut degree of freedom and Z drectons has been used to demonstrate the above capabty see Fg.4. A program has been wrtten n ANSS 1, Postprocessng commands /POST1. For preparng of Campbe dagrams, CAMPBELL command was used n nput fe. Appyng of gyroscopc effect to rotatng structure was carred by usng COROLS command. Ths command aso appes the rotatng dampng effect. Another command whch was used n nput fe SNCHRO that Specfes whether the exctaton frequency s synchronous or asynchronous wth the rotatona veocty of a structure n a harmonc anayss; PLCAMP pots Campbe dagram data, PRCAMP prnts Campbe dagram data [14,16]. A-ANSS APDL. B-ANSS wor bench. Fg.4 A-Fnte eement mode gyroscopc geometry n;.3.1 Campbe dagram N a moda anayss wth mutpe oad steps correspondng to dfferent anguar veoctes, a Campbe dagram PLCAMP or PRCAMP shows the evouton of the natura frequences [14]. ANSS determnes Egen frequences at each oad step. The pot showng the varaton of Egen frequency wth respect to rotatona speed may not be ready apparent. For exampe, f the gyroscopc effect s sgnfcant on an Egen mode, ts frequency tends to spt so much that t crosses the other frequency curves as the speed ncreases..3.. Crtca speeds The PRCAMP command aso prnts out the crtca speeds for a rotatng synchronous unbaanced or asynchronous force. The crtca speeds correspond to the ntersecton ponts between frequency curves and the added ne Fs. where s represents SLOPE > 0 as specfed va PRCAMP. Because the crtca speeds are determned graphcay, ther accuracy depends upon the quaty of the Campbe dagram [14, 16]. To retreve and store crtca speeds as parameters, use the GET command. SSN : Vo. 3 No. 9 September

6 H.A. A-Khaza et a. / nternatona ourna of Engneerng Scence and Technoogy EST.3.3. Whrs and stabty As Egen frequences spt wth ncreasng spn veocty, ANSS dentfes forward FW & bacward BW whrs, and unstabe frequences [1]. Because of the orbt shape the shaft maes when rotatng, ths mode s sometmes referred to as a Cyndrca mode.f t s vewed from the front, the shaft appears to be bouncng up and down.therefore ths mode s aso nown as bounce or transator mode, [1,10].Not to forget that mean whe the rotor s aso rotatng.therefore the whrng moton of the rotor orbt shape path can be n the same drecton as the shaft s rotaton or can be n an opposte drecton. Ths gves rse to the abes forward whr FW and bacward whr BW, seefg.5, shows rotor cross sectons over the course of tme for both synchronous forward and synchronous bacward whr. Fg.5 Whr sense, [4, 11]. Not that for forward whr, a pont on the surface of the rotor moves n the same drecton as the whr.thus, for synchronous forward whr.e. unbaance exctaton, a pont at the outsde of the rotor remans to the outsde of the whr orbt, [4,11]. Wth bacward whr, on the other hand, a pont at the surface of the rotor moves n the opposte drecton as the whr to the nsde of the whr orbt durng the whr. 3. Resuts, Tabes & Fgures As t can be seen from the expermenta Fg.6 & graphca cacuaton Fg.8 foows the drect reacceptance, whch assume the exctaton and response measurement are shown n fgures at varous speeds. The natura frequency of the rotor spts up nto two parts, as the rotor starts rotatng.accordng to the Eqs. 6-7 t shows the crtca speed of the statonary rotor,ths then spts nto two crtca speeds a vaue shown n Tabe.1, as t can be seen from the Fgs. 6,8,the gap wdens up as the speed ncreases. Le t was dscussed, ths phenomenon s nown as gyroscopc effect and occurs because of the Bacward BW and forward FW whr of the rotor. The Egen vectors woud show these phenomena, as the speed ncreases the gap between the two frequences becomes arger, the ant-resonance between the two peas s due to the fact that ths s a pont or drect measurement, a phenomenon n moda testng. The Fg.7A show experment & cacuaton vaue of reaton between the Natura frequences, Hz wth respect ncreasng speed of rotaton for the 1 st mode, when the speed ncreasng the two nes are dvergence the same reason before. A fgure n expermenta obtaned frequency response functons FRF of the geometry by mergng a the noda response functon nto a snge FRF, by usng the cacuator functon of the smart offce software are shown n Fg. 6, for dfferent speed of rotaton. SSN : Vo. 3 No. 9 September

7 Frequency - Hz H.A. A-Khaza et a. / nternatona ourna of Engneerng Scence and Technoogy EST 1 XAxs: Axs: Hz g/n 1 X :1 0.01m 100m Log g/n 10m 1m 100µ A-Expermenta resut speed of rotaton 30 RPM, statonary. 100m XAxs: Axs: Hz g/n X : m m 1 Log g/n 10m 1m Frequency - Hz B-Expermenta resut speed 000 RPM. C-Expermenta resut speed 3000 RPM. 100m XAxs: Hz Axs: g/n X : m m 100m 1 XAxs: Hz Axs: g/n X : m m 1 10m 10m Log g/n Log g/n 1m 1m 100µ Frequency - Hz 100µ Frequency - Hz D- Expermenta resut speed 4000 RPM. E- Expermenta resut speed 6000 RPM. Fg. 6 Expermenta resut show Frequency response functon curve FRF versus natura frequency Hz for dfferent speed of rotaton. SSN : Vo. 3 No. 9 September

8 H.A. A-Khaza et a. / nternatona ourna of Engneerng Scence and Technoogy EST Tabe 1. Bacward & Forward natura Frequences n Expermenta and Theoretca cacuatons of gyroscopc effect. Speed of RotatonRPM Expermenta ResutsHz,BW Expermenta ResutsHz,FW Theortca Vaues,1Hz,BW Theortca Vaues,Hz,FW Fg.7 A- Expermenta & Theoretca natura Frequences versus speed of rotaton for 1 st natura frequency Campbe dagram. B-ANSS, Campbe dagram cacuatons gyroscopc effect. Fg.8 More Frequency response functon FRF versus natura frequency Hz, graphca cacuatons. SSN : Vo. 3 No. 9 September

9 H.A. A-Khaza et a. / nternatona ourna of Engneerng Scence and Technoogy EST 4. Dscasson and concuson n ths paper nvestgate the behavour of a rotor system wth gyroscopc effect has been careed out, by ncreasng the rotona speed,the dstance between the forwared whr and bacwared whr ncreasees reated to the mode-shape and the rato of the poar mass moment of nerta 0 to the dametera mass moment of nerta.draw the campbe dagram and the outcom resut Fg.7-A,B. The cacuaton vaues obtaned from the Eq.7 are perfecty nearby to the vaues obtaned from the expermenta that shown n Tabe 1, tae cognzance Fg. 7-A and comparson wth ANSS Fg.7-B. By usng Eq.4 Frequency response functon FRF of the rotor was found as ths s a graphca method see Fg.8, n ths fgure we see the approva to expermenta and ANSS smuaton the gap wdens up as the speed ncreases due to BW& FW whr. n ths paper a smpe mathematca mode has been used, however more eaborate modes based on a much arge degree of freedom may be used based on suppeness or stffness nfuence coeffcents. The mathematca modes may aso be used to refne the measured data and hep n remova of contamnated data. t s therefore feasbe to create a mathematca mode as a database for varous systems for condton montorng durng ther fe tme of the machnes Summarse what have earened The rotor whr s ether n the same drecton as rotaton or aganst rotaton, whch resuts nto both forward and bacward whr mode.the frequences are affected by both the mass m and dametera mass moment of nerta. The gyroscopc effect enhances are sgnfcanty by owerng between the overhung oad and the nward bearng. By ncreasng the rotona speed,the dstance between the forward whr and bacward whr ncreases reated to the mode-shape and the rato of the poar mass moment of nerta 0 to the dameter mass moment of nerta. The expanaton for ths surprsng behavour s a gyroscopc effect that occurs whenever the mode shape has an anguar conca/ rocng component. Consder the forward whr as shaft speed ncreases, the gyroscopc effects essentay act e an ncreasngy stff sprng on the centra dsc for the rocng moton. ncreasng stffness acts to ncrease the natura frequency. For bacward whr, the effect s reversed. ncreasng rotor spn speed acts to reduce the effectve stffness, thus reducng the natura frequency as a sde note, the gyroscopc terms are generay wrtten as a sew-symmetrc matrx added to the dampng matrx-the net resut, though, s a stffenng /softenng effect.n the case of the frst modes of the machnes cyndrca modes, very tte effect of the gyroscopc terms was noted, because the centre dsc was whrng wthout any conca moton. So t can be sad that, wthout the conca moton, the gyroscopc effects do not appear. Therefore, for the soft bearng case,whch has a very cyndrca moton, no effect was observed, whe for the stff bearng case, whch has a bugng cynder and thus conca type moton near the bearng,a sght effect was noted, [1,1]. Acnowedgments The author s deepy apprecatve support derved from the raq Mnstry of Hgher Educaton, raq cutura attaché n London and Kngston Unversty for supportng ths research. References [1] Laanne M and Ferrars G 1998 Rotor dynamcs predcton n engneerng, pubshng by ohn Wey & Sons Ltd, nd edton, Engand. [] Asar M R 1997, 000 System dentfcaton usng vbraton montorng for faut dagnostcs n manufacturng machnery, Proceedng of 5 th nternatona Conference on Factory, Cambrdge, UK. [3] Sngresu S Rao 005 Mechanca vbratons, Prentce-Ha, nc. S Edton, Sngapore. [4] Muszynsa A 1989 Shaft vbraton versus shaft stress, orbt, BNC, vo.10, no.3, U.S.A, [5] Gnsberg H 001 Mechanca and structura vbraton, theory and appcatons, Georga nsttute of Technoogy, ohn Wy & Sons,nc, Unted States. [6] Ewns D 1995 Moda testng: theory and practce. ohn wy, Exeter, Engand. [7] Benty D E 1984 What happened to the dampng orbt. BNC, V 5, no., 1631 Bentey par way south,mnden,nevada,u.s.a, ,pp [8] mn He and Zh-Fang Fu 001 Moda anayss. Actve Oxford, Butterworth-Henemann, Oxford. [9] Reynods P and Pavce A 000 mpuse hammer versus shaer exctaton for the moda testng of budng. Foors, Expermenta Technques 43 : [10] Muszynsa A 1986 Fundamenta response of rotor. BNC/ BRDRC, Report 1/86, pp. 1-. SSN : Vo. 3 No. 9 September

10 H.A. A-Khaza et a. / nternatona ourna of Engneerng Scence and Technoogy EST [11] Swanson E, Pow C D and Wesmann S 1991 A practca revew of rotatng machnery crtca speeds and modes.111: [1] Ferrars G, Masonneuve V and Laanne M 1996 Predcton of the dynamc behavour of non symmetrc coaxa co or counter rotatng rotor. ourna Sound vbraton 1954: [13] [14] [15] [16] ANSS 1 Hep Menu can be found wth ANSS 1. SSN : Vo. 3 No. 9 September