Performance Evaluation of Whole-spacecraft Vibration Isolation

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1 he th Internationa Conference on Motion and Vibration MOVIC04 erformance Evauation of Whoe-spacecraft Vibration Isoation Likun LIU*, **, Jinjun SHAN** and Gangtie ZHENG*** * Institute of eecommunication Sateite, China Academy of Space echoogy 04 Youyi Street, Beijing, 00094,. R. China E-mai: hitiuk@gmai.com ** Department of Earth and Space Science and Engineering, York University 4700 Keee Street oronto, ON M3J 3 Canada E-mai: jjshan@yorku.ca *** Schoo of Aerospace, singhua University Haidian District, 0004,. R. China E-mai: gtzheng@mai.tsinghua.edu.cn Abstract Vibration isoation is traditiona technique for mitigating structura vibrations, and has been successfuy appied to whoe-spacecraft vibration isoation. ransmissibiity across the isoator, which derived from the singe degree-of-freedom vibration isoation system, is usuay used to evauate the performance of the isoator. However, it is not sufficient to evauate the performance of muti degree-of-freedom system, such as whoe-spacecraft vibration isoation. Considering the fexibiity of the origina payoad attachment fitting, the ratio of transmissibiity to transmissibiity with the payoad attachment fitting shoud be used. In order to take into account the fexibiity of the spacecraft, transmissibiity ratio of more observation nodes in the spacecraft have to be cacuated. Furthermore, in order to consider the fexibiity of aunch vehice, the response ratio or power fow ratio, which overcomes the imitation of transmissibiity, is used to quantify the vibration isoation performance. he method presented here can be appied to other compicated fexibe vibration isoation systems. Keywords : Vibration isoation, Spacecraft, ransmissibiity, erformance evauation, ayoad attachment fitting. Introduction he aunch stage is the most severe dynamic environment that a spacecraft wi experience during its whoe mission ife. Whoe-spacecraft vibration isoation (WSVI) uses an isoator to repace the payoad attachment fitting (AF) and mitigates vibration of the spacecraft during the aunch. Up to now, more than ten aunches are reported pubicy by using different isoators (Edberg etc. 997, Wike etc. 99, Denoyer etc. 00, Johnson etc. 00,). An octo-strut vibration isoation patform has been deveoped for whoe-spacecraft vibration isoation (Liu etc., 005), and its optima design is aso discussed (Wang etc., 006). he main characteristic of a WSVI system is that the base (aunch vehice) and the payoad (spacecraft) of the isoator are fexibe. hough there have been numerous pubications on the subject of isoation design, a majority of them have used a singe degree-of-freedom (DOF) mode for the isoator design, in which the fexibiity of the base and the payoad is negected. hen the performance of the isoator is evauated by the transmissibiity across the isoator. For the sake of response dissimiarity of different points on the spacecraft and fexibiity of the aunch vehice (LV), this method is not sufficient for evauating the performance of a WSVI system. Severa authors have anayzed the isoation design with fexibiity inherent in the system. Sciui and Inman(997, 99a, 99b) utiized the technique deveoped by Yang (994) to mode the system fexibiity anayticay. Yang's method can be empoyed to sove compound distributed parameter systems anayticay, but it cannot dea with the isoation design of the arge compex fexibe structure. Huang, etc. (003) presented a theoretica and experimenta 04 he Japan Society of Mechanica Engineers

2 investigation into an active vibration isoation system, in which the eectromagnetic actuators in parae with four passive mounts are paced between a fexibe equipment structure and a base structure, which is either fexibe or rigid. E-Sinawi (004) deat with the probem of isoating the vibration at any ocation on a fexibe structure mounted on a vibrating fexibe base by using Kaman-based active feedforward-feedback controer with noncoocated sensors and actuators. However, none of these papers provide an suitabe approach for evauating the performance of an isoator between a fexibe payoad and a fexibe base, such as the WSVI system. his paper deas with the technique to evauate the performance of the isoator for WSVI. he remainder of this paper is organized as foows. A dynamic mode of the WSVI system is deveoped in Section II. hen different evauation techniques are discussed and vaidated through numerica simuations in Section III. Section IV concudes this paper.. Description of WSVI System Engine induced vibration and thrust transients are the main sources of vibration oad appied on spacecraft during aunch. hey transmit from the bottom of LV to the bottom of spacecraft. he WSVI system, shown as in Fig., incudes the vibration isoation patform or the AF, the spacecraft and the LV, and modeed using Newton-Euer equation or finite eement method (FEM). F F L FB F FS 4 5 r 3 h 6 7 A XL XB X XS r Fig. he whoe-spacecraft vibration isoation system. Fig. he octo-strut vibration isoation patform.. Dynamics of the Vibration Isoation atform An octo-strut vibration isoation patform consists of a rigid Launch-Vehice-Interface (LVI), a rigid ayoad-interface (I) and eight fexibe struts whose ength can be changed aong axia direction. hese struts are connected to the LVI and the I using spherica joints. Based on Liu etc. (005), the dynamic mode of the patform is expressed in expicit formua constructed by the geometric parameters of the patform and the dynamic parameters of a singe strut. According to Newton-Euer equation, the dynamic equation of the patform can be expressed as M 0 X JBJ JBJ B X JKJ JKJ B X F 0 MB X B JBJ B JBJ B B X B JKJ B JKJ B B XB FB where M is mass and inertia matrix of the payoad interface, MB is mass and inertia matrix of the LV interface, X is generaized dispacement of the payoad interface, XB is generaized dispacement of the LV interface, FB is generaized force acting on the aunch vehice(lv) interface, F is generaized force acting on the payoad interface, J u u pu p u, J B u u B qu q u B K diag k k k, B diag b b b, u p q p q i i i i i and k i is stiffness of the ith strut, b i is damping of the ith strut, pi is joint points connecting the strut with the payoad interface, qi is joint points connecting the strut with the LV interface, p i is the asymmetric matrix of the vector from the I s center to point p, B q is asymmetric matrix of the vector from the LVI s centre to point q. i i () i 04 he Japan Society of Mechanica Engineers

3 A symmetric octo-strut vibration isoation patform(ovi), whose geometric configuration can be competey determined by five variabes, namey, r, r,, and h, is shown in Fig.. hen, the coefficients in Eq. () can be obtained as ui uisi 0 i i 0 ui 0 uisi 0 0 i i 0 0 ui i JKJ k () 0 su i i 0 si 0 0 i i siui si 0 i i si3 i ui uimi i i ui uimi i i ui i B k JKJ (3) B 0 su 0 sm 0 0 i i i i i i s u s m 0 i i i i i i ui uimi i i ui uimi i i i s m i3 i3 0 0 ui i B k 0 mu i i 0 mi 0 0 i i JBJ (4) mu i i mi i i i m i3 04 he Japan Society of Mechanica Engineers 3

4 where, s pu, i i i m qu, cos B i i i 4 h ui ui, i i si si i i 4rh, 4rh mi mi i i r r rr h, h ui3, i 4hrr cos r us i i us i i, i i 4hrr cos r um i i um i i, i i, si3 mi3 si3mi3, i i i 4rrh cos sm i i sm i i i i JBJ, JBJ Band B B. rr sin Other terms, such as JBJ possess the simiar matrix form. he Lapace transformation of Eq. () is where A A X F A3 A4 XB FB A M s J BJ sj KJ, A J BJ s J KJ B B 3 B s B A4 MBs JBBJBsJBKJ B A J BJ J KJ, According to the definition of receptances, we have α ( A A A A ),,i 4 3 B,i ( 3 4 ) α ( A A A A ) BB,i 4 3 α A A A A, αb,i ( A AA3 A 4) (6) where the subscript i denotes that these receptances are reated to the isoator, and if p is utiized, receptances are reated to the AF. he OVI parameters used in this paper are isted in abe. abe he parameters of the octo-strut vibration isoation patform. arameter r (m) r (m) h (m) k (N/m) b (Ns/m) Vaue Dynamics of Spacecraft he spacecraft dynamics is modeed using FEM and can be expressed as mss msi X S kss ksi XS FS SI II I SI II I 0 (7) m m X k k X where X S is generaized dispacement of the interface, and XI is the interna generaized dispacement except the interface. If the damping of the spacecraft is considered, the proportiona viscosity damping or structura damping can be used. Because of the compexity of the spacecraft, the dimension X I is usuay high, which can be condensed by the Craig-Bampton component moda synthesis (Craig and Bampton, 96). Buid a transformation as X I 0 X S S XI C N γ where C and N are the soutions to the eigenvaue probem mx II I kx II I 0, and N is the main moda matrix composed of the first N canonica modes, is the constrainted moda matrix, and is expressed as C (5) () 04 he Japan Society of Mechanica Engineers 4

C kii k IS (9) Substituting Eq. () into (7) yieds mss msi X S kss 0 XS FS SI I N N 0 (0) m γ 0 k γ where msi CmIIN m SIN, mss mss CmIIC msi m SIC, k N ΦNk IIΦ N, kss kss ksiφ C.

According to the above equation, we have α B B B B () where Φ CO and Φ NO are parts of matrix Φ C and SS 4 3 α Φ Φ B B B B B B (3) OS CO NO 4 3 4 3 Φ N with regards to node O, respectivey. Fig.

Other two observation nodes except for the interface node are taken into account.

5 C kii k IS (9) Substituting Eq. () into (7) yieds mss msi X S kss 0 XS FS SI I N N 0 (0) m γ 0 k γ where msi CmIIN m SIN, mss mss CmIIC msi m SIC, k N ΦNk IIΦ N, kss kss ksiφ C. he Lapace transformation of Eq. (0) is B BXS FS () B B γ where B msss k SS, B m s SI, B m s 3 SI, B4 I N s k N. According to the above equation, we have α B B B B () where Φ CO and Φ NO are parts of matrix Φ C and SS 4 3 α Φ Φ B B B B B B (3) OS CO NO Φ N with regards to node O, respectivey. Fig. 3 he observation nodes of the spacecraft. he spacecraft discussed in this paper is a spin-stabiized sateite as shown in Fig. 3. Other two observation nodes except for the interface node are taken into account. One is the antenna node on the top of the sateite, at which the maximum vibration usuay ocates, and the other is the attitude-contro nozze node where the vibration is supposed to be attenuated emphaticay. hree transationa DOFs of each observation node are considered in the foowing anaysis..3 Dynamics of the LV A three-stage LV can aso be modeed by FEM. hough the structure of the LV is changing with fue consuming and stage separation during the aunch, matrix forms of the FEM at each second are the same. After the dimension reduction, it can be expressed as mll ml mli X L kll kl kli XL FL ml m mi X kl k ki X F mli mi IM η kli ki km η 0 If the damping of the LV is considered, the proportiona viscosity damping or structure damping can be empoyed. he Lapace transformation of the above equation is C C C X F 3 L L C4 C5 C6X F C 7 C C9 η 0 (4) (5) 04 he Japan Society of Mechanica Engineers 5

6 where C m s k, LL LL C m s k, L L C m s k, 3 LI LI C m s k, 4 L L C m s k, 5 C m s k, 6 I I C m s k, 7 LI LI hen the receptances of the LV can be expressed as C m s k, I I C I s k. 9 M M α LL (6) (7) L () L Since the FEM of the origina AF has the same matrix form as that of the LV, the receptances of the AF wi have the same forms as Eqs. (6)~(9). 3. erformance Evauation of the WSVI erformance evauation of the WSVI is the foundation for designing an isoator. For the sake of response dissimiarity of different points on the spacecraft and fexibiity of the LV, traditiona transmissibiity is not sufficient for correcty evauating the performance of an isoator for WSVI. Based on the receptances provided in the previous section, severa methods to evauate the performance of an isoator for WSVI are presented in this section, and their appication scopes are aso discussed. 3. raditiona ransmissibiity Method In the traditiona transmissibiity method, ony subsystem A in Fig. is considered. Dispacement of point S can be expressed as XS αssfs X αbfb αf (0) Since FS F, the force acting on the spacecraft is F αss α αbf B () he dispacement at point A is XA XB αbbfb αbf () Since FB F A, from Eq. () and (), there is α AA αbb αb α αss α B (3) and - F αss α αbαaax A (4) hen the dispacement at point is - X XS αssfs αss F αss αss α αbαaax A (5) he transmissibiity matrix across the isoator is - i, αss αss α,i αb,iα AA (6) where denotes eement-by-eement compex moduus of the matrix. Sometimes, transmissibiity from the bottom of the isoator to the observation point O is considered as - i, αos αss α,i αb,iα AA (7) In fact, it is ony assumed that the AF is rigid, Eqs. (6) or (7) can be empoyed to evauate the performance. Because the AF is fexibe, the ratio of transmissibiity to transmissibiity with the AF shoud be used to evauate the performance. It is defined as R i, p, or R i, p, () where denotes the eement-by-eement division, and 04 he Japan Society of Mechanica Engineers 6

7 - p, αss αss α,p αb,pα AA, - p, αos αss α,p αb,pα AA (9) he transmissibiity and its ratio across the isoator/af are shown in Fig. 4. ransmissibiity across the isoator is ess than that across the AF and aso ess than for most frequencies. aken into account the fexibiity of the spacecraft, transmissibiity ratios from the bottom of the isoator/af to the observation nodes are shown in Fig. 5. It can be seen that the transmissibiity ratios for the different observation nodes are dissimiar. ransmissibiity ransmissibiity ransmissibiity ratio ransmissibiity ransmissibiity ransmissibiity ratio ransmissibiity ransmissibiity Fig. 4 ransmissibiity from the bottom to the top of the isoator/af. payoad interface antenna attitude-contro nozze 0 payoad interface antenna attitude-contro nozze ransmissibiity Ratio ransmissibiity Ratio Fig. 5 ransmissibiity ratio of different observation nodes. Appying Eqs. (6)~() to evauate performance of the isoator requires two other assumption, i.e., the base of the subsystem A has infinite mechanica impedance, and the base input is not infuenced by repacement of the AF and stage jettisons. In practice, the base of the subsystem A is the fexibe LV, and the base input is infuenced. A. ratio method Mead (999) defines the isoator effectiveness, which is the ratio of the response of the receiver when it is directy couped to the source to that of its response when isoators are inserted, to investigate the probem of vibration. Here it is extended to anayze WSVI system. In order to compare to the transmissibiity ratio, the ratio of the response of the observation point when the isoator is used to that the origina AF is used, is adopted. Dispacement of point L can be expressed as X A can be expressed as X α F α F (30) L L LL L XA αaaf A (3) 04 he Japan Society of Mechanica Engineers 7

8 Since XL X A and F L F A, according to Eqs. (30) and (3), we have FB FL ( αll αaa ) α LF (3) According to Eqs. () and (3), if the spacecraft is attached to the LV, the dispacement of the observation point O on the spacecraft is X α F α α α α α α α F (33) O,p OS S OS SS,p B,p LL AA,p L If the AF is repaced by the isoator, the dispacement of the observation point O on the spacecraft is O,i OS S OS SS,i B,i LL AA,i L X α F α α α α α α α F (34) hen the response ratio is defined as Rr XO,i X O,p (35) Because of the fue consuming and stage jettisons, the LV changes significanty during its ascent. However, it is too tedious here to report resuts of the response or the response ratio at every second. herefore, ony two typica fight events were seected as exampes, the aunch time (aso caed iftoff) and the second-stage separation. Figures 6~ show the response of the payoad interface and the other two observation nodes as the unit force is appied to the engine at the bottom of the LV. For the different observation nodes at the same instant, or for the same observation nodes at different time instants, responses of the observation nodes shows great differences. But it is obvious that the responses of any observation node is greaty attenuated by repacing the origina AF. Figures ~4 show the response ratios that are compared to the transmissibiity ratio. In the ongitudina direction, the response ratio at aunch or at the second-stage separation is neary the same as the transmissibiity ratio. However, in the atera direction, they show great deviation in the ow-frequency band Fig. 6 of the payoad interface at iftoff Fig. 7 of the antenna node at iftoff. 04 he Japan Society of Mechanica Engineers

9 Fig. of the attitude-contro nozze at iftoff Fig. 9 of the payoad interface at the second-stage separation Fig. 0 of the antenna at the second-stage separation. 04 he Japan Society of Mechanica Engineers 9

10 Fig. of the attitude-contro nozze at the second-stage separation. aunch time second-stage seperation transmissibiity ratio aunch time second-stage separation transmissibiity ratio Ratio Ratio Fig. ratio of the payoad interface. aunch time second-stage separation transmissibiity ratio 0 aunch time second-stage separation ransmissibiity Ratio Ratio Fig. 3 ratio of the antenna 04 he Japan Society of Mechanica Engineers 0

11 aunch time second-stage separation transmissibiity 0 aunch time second-stage separation transmissibiity ratio Ratio Ratio Fig. 4 ratio of the attitude-contro nozze ower Fig. 5 ower fow into the spacecraft. B. ower fow ratio method ime-averaged power fow(goyder and White, 90) into the spacecraft from the LV can be expressed as * * ImFSα SSF S (36) where Im and * denote the imaginary part and the compex conjugate of the associated compex quantities. Substituting Eq. (3) into (3), the power fow is derived. hen, the power fow without the isoator can be derived by substituting α i, and α i,b in the expression of α AA with α p, and α p,b. Fig. 5 shows the time-averaged power fow into the spacecraft at the iftoff. he power fow is obviousy ower than that except for in the ow-frequency band. hough the power fow can evauate the performance of the isoator in a direction together, it cannot count the vibration ampitude of sensitive equipment in the spacecraft. 4. Concusion In this paper, severa techniques used to evauate the performance of vibration isoator for WSVI are discussed. Concusions can be summarized as foows: a) For the sake of response dissimiarity of different points on the spacecraft, the traditiona transmissibiity across the isoator is not sufficient for correcty evauating the performance of an isoator for WSVI. ransmissibiity from the bottom of the isoator to the different observations nodes has to be used. Furthermore, the ratio of transmissibiity with the isoator to transmissibiity with the AF shoud be used to evauate the performance for the fexibiity of the AF. 04 he Japan Society of Mechanica Engineers

12 b) ratio is used to evauate performance of the isoator for considering the fexibiity of the LV. In the ongitudina direction, response ratio at the iftoff or at the second-stage separation is neary the same as the transmissibiity ratio. However, in the atera direction, they show great deviation in the ow-frequency band. c) ime-averaged power fow can be used to evauate the isoator performance in a direction. However, it cannot count the vibration ampitude of sensitive equipment in the spacecraft. It can be used together with the response ratio to evauate the performance. Acknowedgments he authors woud ike to acknowedge the China Schoarship Counci for the support. References Craig, R. R., Bampton, M. C. C., Couping of Substructures for Dynamic Anaysis, AIAA Journa, Vo. 6, No. 7 (96), pp Denoyer, K. K., and Johnson, C. D., Recent Achievements in Vibration Isoation Systems for Space Launch and On-Orbit Appication, 5nd Internationa Astronautica Congress (00b). Edberg, D. L., and Johnson, C. D., On the Deveopment of a Launch Vibration Isoation System, roceedings of Smart Structures, Vo. 3045, Society of hoto-optica Instrumentation Engineers, Beingham,WA (997), pp E-sinawi, A. H., Active vibration isoation of a fexibe structure mounted on a vibration eastic base, Journa of Sound and Vibration. Vo. 7 (004), pp Goyder H. G. D., White R. G., Vibrationa power fow from machines into buidup structures, part I: introduction and approximate anaysis of beam and pate-ike foundations, Journa of Sound and Vibration, Vo. 6 (90), pp Huang, X., Eiott, S. J., Brennan, M. J., Active Isoation of a Fexibe structure from base vibration, Journa of Sound and Vibration. Vo. 63 (003), pp Johnson, C. D., Wike,. S., and Daring, K. R., Muti-Axis Whoe-Spacecraft Vibration Isoation for Sma Launch Vehices, roceedings of Smart Structures and Materias, Vo. 433, Society of hoto-optica Instrumentation Engineers, Beingham, WA (00a), pp Liu, L. K., Liang, L., Zheng, G.., and Huang, W. H., Dynamic Design of Octo-Strut atform for Launch Stage Whoe-Spacecraft Vibration Isoation, Journa of spacecraft and rocket, Vo. 4, No. 4 (005), pp Mead, D. J., assive Vibration Contro, John Wiey & Sons (999), pp Sciui, D., Dynamics and Contro for Vibration Isoation Design. h.d. dissertation, Virginia oytechnic Institute and State University, May 997 Sciui, D., Inman, D. J., Isoation Design for Systems with Fexibe Base and Equipment, roceedings of SIE - he Internationa Society for Optica Engineering. Vo. 337 (99a), pp Sciui, D., Inman, D. J., Isoation Design for a Fexibe System. Journa of Sound and Vibration. Vo. 6, No. (99b), pp Wang, Z., Liu, L. K., Zheng, G.., Optima Design of Octo-strut Vibration Isoation atform, Journa of Guidance, Contro, and Dynamics, Vo. 9, No. 3 (006), pp Wike,. S., and Johnson, C. D., Whoe-Spacecraft assive Launch Isoation, Journa of Spacecraft and Rockets, Vo. 35, No. 5 (99), pp Yang B., Distributed transfer function anaysis of compex distributed parameter systems, Journa of Appied Mechanics Vo. 50 (994), pp he Japan Society of Mechanica Engineers

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