Danqing, Wu

Dianxun, Huang

Jingtong, Cong

English

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Purdue UniversityPurdue e-PubsInternational Compressor Engineering Conference School of Mechanical Engineering1988The Theoretical Analysis and ExperimentalInvestigation on the Natural Frequencies andVibration Patterns of Compressor Reed ValvesWu DanqingXi'an Jiaotong UniversityCong JingtongXi'an Jiaotong UniversityHuang DianxunXi'an Jiaotong UniversityFollow this and additional works at: https://docs.lib.purdue.edu/icecThis document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu foradditional information.Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/Herrick/Events/orderlit.htmlDanqing, Wu; Jingtong, Cong; and Dianxun, Huang, "The Theoretical Analysis and Experimental Investigation on the NaturalFrequencies and Vibration Patterns of Compressor Reed Valves" (1988). International Compressor Engineering Conference. Paper 677.https://docs.lib.purdue.edu/icec/677TIH" THEOl FTICIIL II~ALYSic; AND EXf'FFT'IF~TAL T'\'VF O'RJGATI'l"' ON 'l'lll! NA1'lJRAL F'PJ':CiUENCTF!-' ~ND VIBJ<ATlON l'ATTEHNS OF C0'1PHFSSOTI HHD V;\LVrc; l11J De~nqine, Cong ,Tingtong, Huang Dianxun Dopartment of' Chemistry & Chernical Engineering; Xj 'an .Tiaotong tJnj_-ver.sity~ Xi'an, The People's Republic of China AJJSTRAC'l' It is wf'll known tl1at tt"le natural f'requencie5 ann vibration patt-erns are necessary f'or the- computer simulation of compressor reed valve , the anaJyses of' .flow, noise and stress in th~ valves, anci tho rlesign of' backer plates. J3y the finite element methoc!,this paper bas analysed the free vibration of stJcti0n anc'l di~ct1arge reed valves, anrl presented the v-jbration patterns and natur<eal f'reqencies for the first, s<econ<i and third orders under the f'ollo>~ing boundary conditions: the v,.lve fJlates are a5su1ned with one end ~ixert and tl1e othP.r ~ree, or with one end f"i:xed and th<O otl1er hing8d. Ttlrough the acoustic activation to the valves, the vi,bration p~tterns f'or the I'irst and seconrl order~ have been photoe;raghed by laser hol Of,"ram. There e:xists a good ae;reement bet"t-.·een the theoretical and P.Xperi men tal resul t.s. TN'l'HOT)UCTION To an~lyse the dynamic characteristics of compressor Tlexible reed valves, it is necessary to obtain the inf'orrnation about their natural f'requencies and vibration p:::~tterns at :first. T'heref'ore, tlle stuny con-cerninr; these asp{.~cts is very important~ and \1as been holding the attention of' many experts all over the world. Some essential data of' natu:<al frequencies and vibration patterns /1/ were reported for the mathern<'1tical simulation of' cornpre.ssor reed valves to prerlict if the valve pJates qui.ver in operation, anl.l are disclosGd anrl closed punctually, and to predict their interr:J.ctions wi..th gas pulsation. Tile kno>~ledge should be mastered of' tl1e natural freque-ncy of' ;reerl valves to indenti:ry the peak of' sound pressure spectrum .. Jf' the vibr~tion patt~rns arc solved, the stress distribution of' valve plates will be known /2/, f'nr the stress is dir<>ctly relaiive to the deflection curves, r-:1nd for the de:formed shapes of' valve plate are very similar to the f'lrst order vibration pattern. The proJ'ile d<H;i_gn of' backer p1ates ~reatly aT£'ects the impact velocity and the service Ji:fc of reed valves /J/. 'rhe optimal design to the backer plates of' discharee valves should be that, the bacl~er proTile is identical to the first order vibration pattern of' reed valve plates f'rom the ro<'t end through the port centre, and is less curved than the pattern f'rom the port centre throue;h the otl1er encl. Eecouse of' the structl1re compl e:xi ty of compressor l;"'eed valves and dif'feren t boundary conditions, it is very f'ormidabl" to obtain their vibration patterns through analytical and experimental me:thods. Sands and salt crystals /~/, and hologram method /5/ were utili7ed in exper-iments to picture the vibration pattern nodes. In tl-,is paper, the finite element method anrl laser hologram -with acotlstic activation are applied to tt1e theoretical and experimental studies on the vibration patterns and natural frequencies of reGO valves. TI-lE F1NITE I>LEMENT ANALYStS \1 ;_th the damping neglit;ible, the natural frequencies and the cor-responder~t vibration patterns can be det<>rrrl!bned by: det((KJ -W2 [MJ) ( [KJ ~W1{N]) (o) 0 0 608 (1) (2) l>hare, (K] total stiffness matrix (MJ total mass matrix IIJ natural circuJ ar frequency to be determined ({] vibration pattern vectors to be determined The problem like this is named characteristic value problem in '1athematics. There exist many solution metllods and the correspondent computer programmes, ~hich are different only on the solution manners. '!'he method in this paper is characterized f"or adopting a series of" effective means to make rapid the convergence: l<'or matrj_x (M), a consi-stent mass matrix was adopted, and ttle qwmti ties at the riiagonal line were amplified under the condition o:f constant total mass; and flfler the Cholesky' s Decomposition to [Ml, the problem of generalized eigen-value was changed into a problem of standard characteristic value; acc-ording to Gi vans-Householder's Method, a series of orthogonal transfor-mati.on converted the Ftew matrix in the stanCiard eir.;envalue equation into a trjple diagonalmatrix; the OR method """ applj ed to transform the triple di.,gonalmatrix into an upper triagular matrix, and all the characteristic values were at the diagonal line. The drift coordinate method was also utili7ed in the iterative process to shorten the time of convereence. In this paper, the finite element analyses are carried out to the natural f'requencies anct vibration patterns of suction and disd1arc;e Feed valves with an air compressor typed 2V-0.6/7. The layout of finite eJ.ements is sho-wn in Fi.g. 1. Considering their symrnet.ry, hal£" of' the suction valve pl~te and one fourt~ of the discharRe are calculated, and divi''led :bnto ten elements respectively. ES-Eh of' them is isoparame-tric element "i th eiel"lt nodes. There are 53 nodes and 159 degre<>s of freedom in the suction valve plate, and 45 nodes and 135 deerees of freedom in the discharge valve plate. There exist t""'o kinds of boundary condition during the operati.on of suction valve plate: the plate is assumed one enct fixed and the other free, or called tc1e F'irst Kind of Boundary rondi tion, if the plate is in thO? process from the bet;,tnning of' operat; on to the moment it barely ~raps the backer pJate; anct at the moment the valve plat~ wraps the backer plate, it is assumed one enct fixed and the other hinged "ith point contact at node 1, or called the Second Kind of Boundary Condi-tion. There exists only the First Kind of Boundary Condition for the discharge valve plate. EXI'fRT'WN'l"AL Al'PIIPNfUS To obtain the precist~ natural pfitterfls,. the l<.9Ser hol oe-ram method with acoustic activation 'h'as applied to measurC? the vibration pararnet~ ers of the testP-d reed vaJve plate~ a very li&ht and thin spring~steel pJ ate. ·f3ecouse th.e aCOl.Istic excitation does not contact the tested platet no actdi.tional m'ilsS will be broul:;ht out. Through the J aser holo-~ram, the '"'hole distriiJiltion of' vibration amplitude can be obtainect ~ith the precision in the order of ~aveJenghth. The experiment n'as con(luctcQ with laser holot-;ra.phic interferome-ter on an apparatus with gas shockproof, as shown in Ficr. 2. In Fig. 2 ~ the units numclered from 1 to 8 arc the laser clevice and lights system, 9 is the tested plata, 10 is the hologrAphic negative, and from ll to 16 arc the acoustic !'Ctllvation and vibration pick-up sy~tems. The tested pl atG 9 was installed firmly rl.ccordinc; to the t\oo'O kinds of bourtdRry condj_tion in operation respectively. 'The acoustic activator 13 si imulat<Orl tile plRte 9 to vibratG, ana the vortex flow tr<>nsducer 111 sensed the vibration p<:>r<lmeter~. Jn ord<-'r to find the accur<~te res-onanc~ fr~u1uency, an oscillograph -was L3pp)ied to monjtor the exciting vibration and the ncbtal vibration. And mearlwhile the laser interlero-meter photographect the te5 ted plate continuously. The hol agraphic pic-tnre of vibrRtion p;gttF-;-rn at resc;m~nce was tr•e8ted to ml?ll<e clear th~ int~rfe:rent stre.;k CR\lt-.erl by the interference of the testerl plate wJth 609 laser. f\.ccording to tl1e order of' i nt~S,rf'er.~cn l- ~ trPak, v.-e can c'loterrnine ttH:~ vibration ampJitud(?, for the amplitude trans,rnissivity is dir'ectJy proportional to the ~:xposure. CALCULATED i\'ID E). n fl_I'IEN'I'A L fll'SULTS In Table,; l "'"d 2, we pre:oent the the<>ret:i,cal rt~ta by :finite ele-ment method and the tes terl results conccrni.ng the natural f'r42quencie~ of suction ~nd dischar~e reed valve plates. Table 1. The Th~oretical ann ,,.:xperirnenta1 HesuJ ts of t11e Naturr:~1 Frequencies for Suct.ion V~lve PJ <;a.tc ,------------------·--,-----·------------ - ---1\!"tur"l l<""~re(J11 en ci. e s (T-\7) Conrlition Results ls t or•der 2nd order Jrd ord -Type~ of' Boundary~e Sources o The First )(jnd of Theoretical 2~1. 2 93 .I+ 178.9 Bounrl.ary Condition 1 F..xperimentaJ 22.8 77-7 The second Kind o;t 'l'hcoretic-~-J----+----­jBo,ndary Condi t_~o~~~_::_i_rn_e_n_t __ a_l_"'----93-4 128.2 342.2 il0.7 I 140.0 --~·-Table 2_ The Theoretical and E:xrerimental Results of the Natural F'reqnencies :for T1i schargc Valve F'J ate i --·· ---··--· Natural Frequencies (Hz) Condi t1or1 of' ResuJ ts Types of Boundary j T11e Source,; l.st order 2nd order Jrd order ~-- -~-~---~ ~~-~ ·--· 1'r1e Fo_rst Kinrl of Theoretical 302-7 655-8 1261.1 Boundary Conditi~~-- !~yerimen~~ J04.o ---· -- ~"--The computed results to the vibration patterns of suction valve plate are shov.:n in Fig. 3, where a, b and c represent the vibration patterns f'or the f~i.rs t ~ SC?conci and third orders respectively under the First T(ind of' Bounrlary Condition, and b, d and e the vibration patterns for ~he first, second and thirrl orders respectively un~er the Seconrl Kind of' Boundary Condition. ~~e experimentRl results of vibration patterns to suction valve p.l ate are shol\'rt in F'lg. l..j, 'Where a and b represent the vibration patt-erns f'or tl1e first and seconrl orders respectively t1nrler the F'irst l{ind of 13ounclary Codl tion, and b anrl c the p?tterns under tt1e Seconcl !\ind of Boundary Condition. In Fig. 5 are shO'tll.'n -.:;he the ore ticaJ and experimcn tal results of' vibration patterns of' rlischarr-;e valve plate, "\nihere a, band c are the tbeoretical results :for the first, second and third orders, and d is the holographic picture o:f the first order vibration pattern. CONCLUSIONS In this paper, we have ctescrbed theoretical ancl experimental meth-ods, i.e., the finite elem~nt method and the Jaser hologram with acou-stic activation, to analy~e the natural f'reg1,:~encies anrl vibration patt-erns of' compressor reed valves. Through tbe&e mett1ods, we hc::J.V€' obtairled satisfactory res11lts, and can supply the reliabl" "'nd ess<'ntial data neces:::;ary to the dynamic analyses of reed valves. The requirement can also be met only by the computer programme about finite element ana.ly-5PS if no experimental moans available. 1, Soedel, \L," Introductton to Computer Sirnula tion of Positive Displ-acement Type Compressors ", I'urclue Univ-ersity l 972 610 2. Soedel, 11., 11 Desir,n and :-lechanics of Compressor Valves ", Purdue University 1984 3. Maclaren, J .F.T., 11 Impact Velocities of Valve Reeds ", 1982 Purdue Compressor Technology Conference 4. ID-crainete, P.R., " Compressor Valve Stress Studies in Conjunction with Accelerated Life Tests ", Ph.D. thesis, Purdue University -l96J 5. Papastergiou, s., et al., " The Dynamic Behavior of lialf-annular Valve Re.,ds in Reciprocating Compressors 1', 1982 Purdue Compressor Technology Conference 6. Zienkiewiez, O.C., " The Finite Flement Method "• McGraw-Hill, 1977 7. Bathe, K •. r., et al., 1' Numeri.cal ~etbods in Finite 'Element Analysi.s'i Prentice-Tiill, 1976 8, WiJkinson, ,J,£-I., "The Algebraic Eigenvalue Problem", Clarendon Press, O~ford, 1965 9, Bathe, K .. J., et al., "Solution !Iethods for Eigenvalue Problems in Structural Dynamics "• Int. ,J, Num, Meth. Icng., 1973 611 :'\ : ~ ~ ~ ~ ~ ::: ~ ::: :: ~ :::; ;: ':' ~ ::: :: ;:; a. Suction Valve Plate b. Discharge Valve Plate F':i(;.l The Layout of' ~'j_nite Elements for Suction and Dischart;e Valve Plates l. Laser Device 2. Switch J. Spectroscope 4,5,6 TotRl Ref-lector 7,8 Di.ff'ussion Mirrors 9. Test Plate 10. Ho.lographic Negative ll. XD2 Signal Generator 12. PrNer Amp.lif'ier lJ. Acoustic Activator 14. Vibration Pick-up 15. l<FC-1 Vibration ~eter 16. Oscillograph Fig. 2 'I'he Sketch o:f lcxperimental Apparutus 612 I. 24.2 [!7 (a) I. II. 93.11 (b) I. 178.9 (c) TI. 128.2 (d) TI. J42.2 (e) Fig.J The Computed Results for Vibration Patterns of Suction Valve I. 22.8 \·]L (a) I - - ----..!1 1. 77.7/Il. 80.7 ll>: (b) :n. 14o.o (c) Fig. 4 The Holor;raphic T'ictures of VibraU on l'atterns for Suction ]']ate 613 ;:: .. .-302.7 Hz (a) I .,1 ... - .~ ;;;: "' •'l2fil.O Hz (c) 304.0 Hz (d) :F'ic~5 The Thoeretical r:3:rJcl txperirnental Hesults of' Vibratlon Patterns of Discharr,-e Valve Plate 614 

The Theoretical Analysis and Experimental Investigation on the Natural Frequencies and Vibration Patterns of Compressor Reed Valves

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The Theoretical Analysis and Experimental Investigation on the Natural Frequencies and Vibration Patterns of Compressor Reed Valves

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