Open Journal of Appled Scences Supplement01 world Congress on Engneerng and Technology Dynamc Contact Problem for Slde Hnge Kazunor Shnohara JAXA's Engneerng Dgtal Innovaton Center (JEDI) Japan Aerospace Exploraton Agency (JAXA) Sagamhara, Japan shnohara@06.alumn.u-tokyo.ac.jp Ryoj Takak Insttute of Space and Astronautcal Scence (ISAS) Japan Aerospace Exploraton Agency (JAXA) Sagamhara, Japan ryo@sas.jaxa.jp Takesh Akta Faculty of Engneerng Chba Insttute of Technology Chba, Japan akta.takesh@t-chba.ac.jp Abstract Contact analyss can be ether statc or dynamc. In statc contact analyss, the poston on the contact surface s constant. In dynamc contact analyss, the poston on the contact surface changes at every tme step. In statc contact analyss, the computng results (stress, stran, etc.) of contact states have been verfed through the Hertz contact problem n lterature. On the other hand, there has been nsuffcent research nto dynamc contact analyss. The contact algorthm s nsuffcently constructed n fnte element model (FEM) dscretzaton. The gap between two objects cannot be calculated accurately. A contact method s demanded for artfcal parameters. Inapproprate settng of artfcal parameters causes artfcal numercal oscllatons on the contact surface between objects. To develop a hgh-relablty satellte, we started the development of FEM contact-frcton modelng technques n ths study. A dynamc contact method was realzed by usng the approprate parameters requred n the contact analyss. We verfed the reproducblty of the physcal behavor of the contact frcton va numercal smulaton technques by usng a computatonal model of the hnge jonts. Keywords-FEM; Contact; Frcton; Stress; Jonts; Structural Analyss; Advance/FrontSTR; Dynamc Contact Analyss; Statc Contact Analyss 1. Introducton Ths year, falures due to jonts between parts have become apparent [1]-[3], as hgh-precson equpment of space structures are demanded. Varous contamnants n the ar on the ground adhere to the contactng parts of metal surfaces. These contamnants, n turn, act as a lubrcant, thereby reducng the coeffcent of frcton. Therefore, the frctonal force on the contact surface s naturally decreased on the ground. Space, however, s a vacuum, and because metal contamnaton does not occur n space, the frcton coeffcent between the metals n space ncreases to about 10 tmes that on the ground [4]. In space, the frcton force causes ncomplete movement at jonts because of the lack of lubrcaton. In ths study, to develop the hgh-precson space structure, we construct a smulaton based on contact-frcton fnte element analyss (FEM) usng Advance/FrontSTR [5]-[7]. The accuracy of the calculated results usng Advance/FrontSTR s verfed. To develop hgh-relablty satelltes, we started the development of contact modelng technques by usng a hgh-performance computer (JSS) n ths study. The contact behavors were verfed by usng computatonal jont models of the slde hnge.. Contact-frcton analyss [6] [8] The varable represents the densty. The subscrpt curly brackets of varables represent object {1} and object {}. The superscrpt ˆ represents the known varables. The sgn and the sgn : represent the nner product of the frst order tensor and second order tensor, respectvely. The sgn {} represents the nternal doman of objects. Sgns {1} and {} represent the tracton boundary condtons. The non-ndex represents the contact surface between objects. The sgn represents nabla. The boundares {1} and {} represent the dsplacement boundary condtons. The tensor represents the Cauchy stress tensor. The vector g represents the gravty vector. The vectors v and v represent the velocty vector and acceleraton vector, respectvely. The vectors n, u, and s represent the outward normal vector, the dsplacement vector, and the surface tracton vector, respectvely. The functon u represents arbtrary weghtng functons. Governng equatons ncludng movng objects consst of the force balance, the dsplacement boundary condtons, and the tracton boundary condtons. g v n (1) n sˆ on () 8 Copyrght 01 ScRes.
n s on (3) u ˆ (4) u on Governng equatons ncludng movng objects consst of the force balance, the dsplacement boundary condtons, and the tracton boundary condtons. Usng the force balance (1) and the arbtrary weghted functon, the resdual equaton s derved as follows: g v u d 0 n 1, (5) Usng the partal ntegraton based on Gauss-Green s theorem, (5) s transformed as follows: : u v u g u d (6) sˆ u d s u d 0 n 1, 1 1 Equaton (6) s transformed as follows: : u d 1 sˆ u d 1 v u g u d (7) 0 n s 1 u 1 u d 3. Algorthm of Contact-Frcton Analyss In ths study, the Advance/FrontSTR and JAXA supercomputer system (JSS) are appled to solve the contact-frcton problem. Advance/FrontSTR was jontly-developed as part of a government project (Mnstry of Educaton, Culture, Sports, Scence and Technology) by the Unversty of Tokyo (Prof. Hrosh Okuda) and Advance Soft Co. Ltd. Presently, Advance Soft Co. Ltd. provdes commercal versons of the software and s responsble for upgrades. The software can calculate the geometrc non-lnearty, the materal non-lnearty, and the contact non-lnearty. The JSS conssts of a massvely parallel supercomputng system, a storage system, a large-scale shared memory system, and a remote access system. We attempted to realze a large-scale FEM analyss of the hgh effcent parallel supercomputng system by Advance/FrontSTR and JSS. The ncrements of dsplacements are unknown varables at the nodes n the FEM model. The dsplacement can be obtaned by the ncrements of dsplacements. The stran can be subsequently calculated by the dsplacement. Then, the stress can be calculated by the stress-stran relatonshp. Advance/REVOCAP s appled for the pre-processng and the post-processng. Advance/REVOCAP can easly make FEM meshes, set calculaton condtons, and vsualze results from Advance/FrontSTR [5][6]. 4. Calculaton results A. Slde hnge model Fg. shows the computng model. The structure conssted of a hollow cylnder and a rng. The hollow cylnder makes physcal contact wth the rng. The outer and nner dameters of the rng were 10.0 and 1.0 (mm), respectvely. The length n the longtudnal drecton (drecton z) was 0.0 (mm). The outer and nner dameters of the hollow cylnder were 10.0 and 8.0 (mm), respectvely. The length n the longtudnal drecton (drecton z) was 150.0 (mm). There were 4640 nodes and 40 elements. The element type was appled to the frst-order hexahedral element. For the materal propertes, the Young's modulus, Posson rato, and densty were set to.03 10 5 (N/mm ), 0.3, and 7.85 10-6 (kg/mm 3 ), respectvely. The dsplacements on both sdes were fxed as boundary condtons. Usng ths computng model, we conducted the statc and dynamc contact analyses. In statc contact analyss, the poston on the contact surface does not change wth respect to tme. On the other hand, n dynamc contact analyss, the poston on the contact surface does change wth respect to tme. Fgure 1 Computer model (by Advance/REVOCAP [5]). Fgure Computng model of sldng hnge (by Advance/REVOCAP [5]) B. Statc Contact Analyss of Slde Hnge Model Fg.3 shows the stran contour and deformaton (scale factor: 1 10 5 ). The center of the cylnder bent under the nfluence of the rng weght. Fg.4 shows the stran contour. Fg.5 shows the stran dstrbuton for the red lne on the cylnder and blue lne on the rng n Fg.4. The vertcal axs represents the radal stran. The horzontal axs represents the coordnates wth respect to the z drecton n Fg.4. Red lne (1) represents the lne (x = 0, y = 10) on the cylnder. Red lne () represents the lne (x = 0, y = -10) on the cylnder. Blue lne (3) represents the lne (x = 0, y = 10) on the rng. Blue lne (4) represents the lne (x = 0, y = -10) on the rng. As shown n Fg.5, n order to deform the cylnder under the rng weght, the stran dstrbuton of the cylnder was larger than that of the rng. Fg.6 shows the radal stress dstrbuton along the cross secton z = 0. The radal stran was plotted at every angle gong n the counterclockwse drecton. The yellow crcle n Fg.6 represents 0.0. For plots nsde the yellow crcle, the drecton of the radal stran vector was nward toward the center of the Copyrght 01 ScRes. 83
crcle. For plots outsde the yellow crcle, the drecton of the radal stran vector was outward toward the center of the crcle. In statc contact analyss, the stran dstrbuton on the rng surface dd not agree wth that on the cylnder surface. The radal stran on the cylnder surface was greater than that on the rng surface. Fgure 3 Stran dstrbuton and deformaton (Scale factor: 1 10 5 ) Fgure 4 Stran contour Fgure 6 Radal stran dstrbuton wth respect to crcumferental drecton C. Dynamc contact analyss of slde hnge model The cylnder was nclned at a 45 angle wth respect to the gravty vector. Stran dstrbutons were calculated when the rng slpped to 33 (mm) n the z drecton. The slp velocty of the rng was 8.3 (mm/s). The coeffcent of frcton was set to 0.0. The radal stran dstrbuton s shown n Fg.1. The horzontal axs represents the dstance along the z axs. As shown n Fg.9, the orgnal pont o represents the slp pont 33 (mm) from the orgnal pont o n the ntal poston (Fg.4). The vertcal axs represents the radal stran. The radal stran ncreased monotoncally from the negatve sde of the z coordnate to the postve sde of the z coordnate. The stran calculated by dynamc contact analyss was greater than that calculated by statc contact analyss, shown n Fg.6. As shown n Fg.13, the stran dstrbuton wth respect to the crcumferental drecton was vsualzed along the cross secton z = 0. The radal stran on the contact surface of both the cylnder and the rng was postve at every angle. Radal strans on the upsde and the downsde were greater than those on the rght and left sdes. In statc contact analyss, the radal stran dstrbuton of the rng was dfferent from that of the cylnder. On the other hand, n dynamc contact analyss, the radal stran dstrbutons of the rng and cylnder almost agreed wth each other. Fgs.10 and 11 show the tme hstory of the slp velocty of the rng. The slp velocty n the z drecton ncreased. The slp velocty n the y drecton caused a vbraton, as shown n Fg.11. Vbraton dampened wth tme. Fgure 5 Radal stran dstrbuton wth respect to z axs Fgure 7 Stran contour fgure (1.9 (s)) Fgure 8 Stran contour fgure (4.6 (s)) 84 Copyrght 01 ScRes.
Fgure 9 Stran contour fgure (6. (s)) Fgure 1 Radal stran dstrbuton wth respect to z axs Fgure 10 Velocty of rng wth respect to z axs Fgure 13 Radal stran dstrbuton wth respect to crcumferental drecton 5. Concluson Usng fnte element model contact analyss based on advance/frontstr, we present a slde hnge model. Our conclusons are as follows: Dynamc contact analyss found a larger stran dstrbuton on the contact surface than statc contact analyss. Therefore, the dfference n mechansms between the statc and dynamc contacts caused dsplacement hysteress when the slde hnge moved under the contact state. In contrast to the stran dstrbuton n statc contact analyss, a dscontnuous stran dstrbuton was formed n dynamc contact analyss. In future studes, we wll try to execute large-scale contact analyss by usng a supercomputer. Fgure 11 Velocty of rng wth respect to y axs REFERENCES [1] Kose Ishmura, Tsuneo K, Kej Komatsu, Ken Goto, Ken Hguch, Kazuro Matsumoto, Shoch Ikura, Makoto Copyrght 01 ScRes. 85
Yoshhara, and Masaharu Tsuchya, Shape Predcton of Large Deployable Antenna Structure on Orbt, Transactons of the Japan Socety for Aeronautcal and Space Scences, Aerospace Technology Japan, 10(01). [] Hrosh Ktahara, Kku-6's Unsuccessful Injecton nto GEO: Then and Afterwards, The Journal of the Insttute of Electroncs, Informaton, and Communcaton Engneers 80(1997), pp. 570-575. [3] Hraku Sakamoto, Ncholas Ragosta, and Mor Osamu, Fnte-element Analyss of Membrane Deployment and Its Valdaton, Proceedngs of 55th Space Scences and Technology Conference, paper No.1B08, (011). [4] Donald H. Buckley, Frcton, Wear and Lubrcaton n Vacuum, NASA-SP-77, 1971. [5] AdvanceSoft. Co., Ltd., http://www.advancesoft.jp/. [6] X Yuan, Theory reference on nonlnear analyss of Advance/FrontSTR Ver.3.0, Advance Smulaton, vol. 4, pp. 6 59, 010. [7] FrontISTR, http://www.css.s.u-tokyo.ac.jp/. [8] Klaus Jurgen Bathe, Fnte Element Procedures, New Jersey, Prentce Hall, 1995. 86 Copyrght 01 ScRes.