Avalable onlne at www.scencedrect.com Proceda Engneerng 5 (0) 553 5535 Advanced n Control Engneerng and Informaton Scence Investgaton on transmsson parameters of vbraton measurement on hgh temperature envronment Xuhua Men, Fanghen Song, Hayan Shao School of Mechancal engneerng Unversty of Jnan,Jnan,550,Chna Abstract Temperature rse can lead to sgnal transmsson change of vbraton measurement durng test run of engnes. In the artcle, the effect of thermal feld on electromagnetc feld varables was studed. Combnng test transmsson network, a new approach s proposed to extract multconductor transmsson parameters. The parameters values obtaned by proposed approach are n good agreement wth classcal energy method. It can be shown that resstance and nductance of transmsson conductor ncrease wth the rsng temperature, and conductor resstance has obvous change range as compared to nductance. Temperature rse aggravates proxmate effects of conductors, and mutual electrcal parameters have mportant changes due to temperature and dstance. All the change of resstance and nductance can brng more effect on fnal sgnal processon. 0 Publshed by Elsever Ltd. Selecton and/or peer-revew under responsblty of [CEIS 0] Open access under CC BY-NC-ND lcense. Keywords: engne; vbraton measurement; hgh temperature; mult-conductor transmsson; transmsson crcut. Introducton When vbraton characterstcs of the engne was detected, not only the parts vbraton characterstcs [, ] (such as the rotors and the blades)but also the accuracy of characterstc sgnal were affected by the hgh temperature. Transmsson lne or transmsson cable s the vector of characterstc sgnal. Thee electrcal parameters of transmsson conductor were no longer constant due to effect from changng ambent temperature. Therefore, n order to mprove the test precson of the engne, t s sgnfcant to analye the parameters change of transmsson conductor n the hgh-temperature envronment. The present researches on transmsson parameters of test sgnal were concentrated on the parameters extracton of mcrowave sgnal or mult-conductor couplng parameters of hgh speed sgnal crcut [3, 4]. a There are some nvestgatons on the responses of hgh frequency sgnal n termnal nterconnected lnes [5, 6, 7] and the extracton of frequency-dependent transmsson parameters [7, 8, 9] etc. However, the studes on the mpacts of transent or steady temperature to transmsson parameters were few. In fact, the test sgnal of engne vbraton characterstcs s dfferent to mcrowave and hgh speed sgnal. The frequency of test sgnal s often md or low frequency whch s lower than that of hgh speed sgnal. So, applyng the prevous methods to extract the transmsson parameters has certan lmtatons. When the model s multa * Correspondng author. Tel.: +0-086-55-656593 E-mal address: me_menxh@ujn.edu.cn. 877-7058 0 Publshed by Elsever Ltd. do:0.06/j.proeng.0.08.06 Open access under CC BY-NC-ND lcense.
553 Xuhua Men et al. / Proceda Engneerng 5 (0) 553 5535 output responses, the nducton among conductors and thermal envronment were merged, whch brngs more complcate to solve model. In the artcle, an effectve method s proposed to get the transent characterstcs of transmsson parameters changng wth ambent temperature. The result s of better applcatons for the collect sgnal processng. Nomenclature H Vector of magnetc feld densty J vector of total current densty J S Vector of source current densty J E vector of nduced eddy current D vector of electrc dsplacement E vector of electrc feld densty B Vector of flux densty μ permeablty ε Delectrc constant σ conductvty E electrc feld ntensty J current densty respectvely t temperature ρ conductor resstvty α temperature coeffcent of resstvty V the voltage drop column vector I column vector of the current n the conductor Z mpedance matrx Y admttance matrx.. Electromagnetc-thermal couplng soluton.. The electromagnetc fled theory of transmsson conductor The complete measure system s composed of three parts, ncludng generatng, transmttng and recevng of the electromagnetc energy. When the sgnal generatng part and the sgnal recevng part were defnted, test sgnal transmtted by sgnal cable s dstrbuted spatally n the form of electromagnetc fled varable, whch followed the Maxwell equaton D D H = J + = J S + J E + () τ τ B E = () τ Denote the current n transmsson conductor along the drecton of, and E = ẑe. Introducng governng equatons of Maxwell to Helmholt equaton, t s obtaned wth tme-harmonc converson of Eq.(), by J S = J and J = σe, J + μσω ε jωμσ J = (3) ( ) 0 Smplfyng the characterstc equaton, the egenvalue k s equal to.. The establshment of temperature parameters equaton μσω ε jωμσ of Eq.(3). The effects from temperature of test envronment on conductor resstvty ρ were obvously. When the conductvty σ s the recprocal of the resstvty ρ, the relatonshp between σ and temperature t s obtaned σ σ( T ) = 0 (4) ( + αt) Where, σ 0 s the conductvty when the temperature s 0 o C. So, the egenvalue k n Eq.(4) s changed nto the parameter of temperature. σ 0μω k() t = μω εσ() t jωμ σ () t = ( ωε( + αt) jσ 0 ) (5) + αt
Xuhua Men et al. / Proceda Engneerng 5 (0) 553 5535 5533 Known from Eq.(5), the egenvalue k decreases wth the ncreasng temperature. Put Eq.(5) nto Eq.() (3), the current densty and electrc feld ntensty become the functon of temperature. By J = σe and d d Laplac e s equaton σ V (, t) = 0, we have d d dv () () () ()( ( ) () (, t) J t = σ t E t = σ t grad V, t = σ t (6) d When recevng mult-output response, more conductor models were needed. In that case, couplng effect between conductors couldn t be gnored, the matrx form about J s as followed J j, J j, J j, J j,n σ j Ej, J j, J j, J j, J j,n σ j Ej, = = (7) J j,n J j,n J j,n J j,nn σ j Ej,N J corresponds to dfferent temperatures, and =,, N means the number of transmsson conductor. 3. Method of transmsson crcut The vbraton frequency of aeroengne parts s always concentrated on low or md frequency. Because the length of the sgnal transmsson cable s much smaller than the wavelength of electromagnetc waves, test sgnal transmsson path can be acheved easly by the crcut model. Based on quas-statc electromagnetc feld theory, test sgnal transmts along the Z-axs wthn the transmsson lne n the form of transverse electromagnetc mode (TEM). Fg. s the sgnal transmsson model of unconductor or multconductor (a) shelded cable. The transmttng form of sgnal n frequency doman can be obtaned as follows dv = ZI = ( R + jωl) I d (8) di = YV d The electrcal parameters dstrbuton of Multconductor transmsson cable s N*N matrx. By Eq.(6)and Fg. Sgnal transmsson usng transmsson cable (b) Eq.(8), we have (a) s network of sgnal transmsson; (b)s dv J = σ = σzi = σ( R + jωl)i confguraton of multconductor cable d (9) In multconductor model, the electromagnetc feld s mutual couplng between nner conductor and neghbourng conductor. So, the parameters R, L, C and G are composed of two parts: sngle parameters and mutual parameters. The paper frstly bulds the deal reference ground loops. Set the sheldng layer N conductor to conductor and other N-conductors crcut conductor satsfes I = I. Now loadng condtons meet I = I I = 0, I + = I (, j =,, N, j ), j = N.Set the sheldng layer outer conductor that along -axs source current densty as J ( ), conductvty as σ, then we have
5534 Xuhua Men et al. / Proceda Engneerng 5 (0) 553 5535 J j J ( ) Rj = Re I σ σ J j J ( ) =,, N ( ) Z = (0) j J J I σ σ j Im j =,, N I σ σ Lj = ω As the current densty and electrcal conductvty are functon of temperature, the temperature characterstcs of electrcal parameters can be obtaned by solvng Eq.(9). Applyng Eq.(0), we can avod calculatng complex ntegral, whch s also apt to use FEM method to smulate the whole model. 4. Smulaton calculaton and dscusson In the paper, the coaxal cable s used to set up a test sgnal transmsson network. The radus of nner conductor s 0.4mm, and sheldng layer s as the outsde conductor. In mult-output model, seven wres are parallel, as Fg. shown. The materal of nternal and external conductor s copper, and the conductvty σ 0 s 5.8 0 7 S/m at 0 o C. The transmsson model s bult usng fnte element theory. Eq.(0) s appled to calculate resstance and nductance parameters. Because the engne can reach over 300 o C n a hgh temperature envronment, so we calculate 0~500 o C n a certan range n ths paper. Fg. and Fg. 3 respectvely show the temperature characterstc of resstance and nductance n mult-conductor model. Fg. Temperature characterstc of resstance Fg.3 Temperature characterstc of nductance As shown by the Fg., the parameter value of the self-resstance and the mutual resstance ncrease wth the rsng temperature. The relatonshp bascally appears lnear varaton. At the same tme, we can observe that the self-resstance s nfluenced markedly by the rsng temperature. Among 0 o C~500 o C, the ncrease range of the electrc resstance can reach to 300%. The mutual resstance caused by proxmty effect between conductors can reach up to % of the self-resstance. It can be demonstrated that the couplng effect for output response of the multconductor not be gnored. Here, the resstvty ncreases n lnear wth the ncreasng of temperature, whch played a decsve role on temperature varaton characterstcs of the resstance. Dramatc change of resstance appears wth the ncreasng of temperature. It wll necessarly make the test sgnal change along characterstcs of wave propagaton, whch becomes the mportant part effectng on test precson. As shown n Fg.3, the self- nductance and the mutual nductance of the wre are n lnear wth temperature ncrease, and the couplng effect between conductors becomes more evdent wth small space. The varaton curves of the self-nductance and mutual nductance are successvely from the top down. Compared to resstance, nductance s smaller affected by temperature varaton, but at 500 o C, and nductance value rses about 50% than 0 o C. Analyng Eq.()-(3),
Xuhua Men et al. / Proceda Engneerng 5 (0) 553 5535 5535 t s shown that resstvty varaton can make the whole electromagnetc feld ntensty and stored energy change, whch also can t keep the nductance n steady state value as the temperature change. Accordng to the analyss, the hgh-temperature envronment nsde the arcraft engne s extremely obvous to the effects of test transmsson parameters. In vbraton performance test procedure process, t wll make the termnal test sgnals dffcult to fully reflect the top test sgnals f the varaton of parameter value affected by the hgh-temperature s gnored. It would brng nto more questons to dentfy the vbraton character of the parts by analysng such test sgnal. 5. Conclusons The mpact of hgh-temperature envronment nsde the engne over test sgnal transmsson comes to true for affectng the transmsson parameters after all. Ths artcle has bult a effected method to extract the transmsson parameters of test sgnal, and analysed detaledly the mpact of the temperature over transmsson parameters characterstc. In the hgh-temperature test envronment, the proposed Transmsson Crcut Method s easy to mplement vbraton test sgnal transmsson network. Moreover, the obtaned transmsson electrcty parameters are consstent wth results obtaned by the classcal energy method. The electrc resstance parameter whch takes sheldng layer as crcut s obvously greater than the transmsson network reference to the grand. The temperature change of resstvty leads to resstance and nductance parameters ncreasng lnearly wth ncreasng temperature, whch s partcularly evdent on the mpact resstance. When the ambent temperature reaches to 500 C, the resstance changes more than 300%, and the nductance s also ncreased to 50% of the ntal temperature. On the engne nternal vbraton characterstc test processon, sgnal transmsson parameters change fercely along wth the temperature whch wll affect the accuracy of test sgnals. Ganng the effectve transmsson parameter temperature change characterstc s helpful to mprove the valdty and the precson of the vbraton characterstc test. Acknowledgments Ths research was supported by the Doctoral Foundaton of Jnan Unversty (Grant No.XBS003). References [] Sun Qang, Zhang Zhongpng, Cha Qao, Wang Bo, Lu Suol. Temperature effect on vbraton frequency of aeroengne compressor blade [J]. Chnese Journal of Appled Mechancs, 004, (4):37-39. (n Chnese) [] Zhu Xang-he, Yuan Hu-qun, He We. Effect of steady thermal feld on crtcal speeds of a rotor system [J]. Journal of Vbraton and Shock, 007, 6():3-6. (n Chnese) [3] Mchael J. Tsuk, Jn Au Kong. A hybrd method for the calculaton of the resstance and Inductance of transmsson lnes wth arbtrary cross sectons[j]. IEEE Trans on Mcrowave Theory and Technques, 99, 39(8):338-347. [4] Enrque E.Mombello. Impedances for the calculaton of electromagnetc transents wthn transformers[j]. IEEE Trans on Power Delvery, 00, 7(): 479-488. [5] Clayton R.Paul. Incorporaton of termnal constrants n the FDTD analyss of transmsson lnes[j]. IEEE Trans. Electromagn. Compat., 994, 36():85-9. [6] Omar M. Ramah, Vnay Subramanan, Bruce Archambeault. A smple fnte-dfference frequency-doman (FDFD) algorthm for analyss of swtchng nose n prnted crcut boards and packages[j]. IEEE Trans on Advanced Packagng, 003, 6():9-98. [7] Zhao Jn, L Zhenfan. A Tme Doman Full Wave Method for extracton of frequency-dependent equvalent crcut parameters of multconducor [J]. Acta Electronca Snca, 997, 5(4):33-38. (n Chnese) [8] Yanan Yn, Hermann W.Dommel. Calculaton of frequency-dependent mpedances of underground power cables wth fnte element method[j]. IEEE Trans on Magnetcs, 989, 5(4):305-307. [9] Karen M. Coperch, Jason Morsey, Vladmr I. Okhmatovsk, Andreas C. Cangellars, Albert E. Ruehl. Systematc development of transmsson-lne models for nterconnects wth frequency-dependent losses[j]. IEEE Trans on Mcrowave Theory and Technques, 00, 49(0):677-685.