Bionic Design for Column of Gantry Machining Center Using Honeycomb Structures

Transcription

1 Procdings of th World Congrss on Enginring 01 Vol III, July 4-6, 01, London, U.K. Bionic Dsign for Column of Gantry Machining Cntr Using Honycomb Structurs Yuhong Zhang, Wnhua Y, Shng Lng, and Wnyong Shan Abstract With th aim to improv th machining prcision of a gantry machining cntr, bionic optimization dsign for ribs structur of its column was invstigatd. Firstly, basd on th analysis of honycomb structurs, thr kinds of bionic columns wr discussd and simulatd by finit lmnt analysis mthod. h column structur with th bst comprhnsiv prformanc was achivd according to th column dsign optimization systm using th Gray Analytic Hirarchy Procss. h bionics principls for ribs of column wr concludd, which providd a nw mthod for improving th traditional dsign and achiving comprhnsiv prformanc optimization structurs of machin tool componnts. Indx rms bionics dsign, honycomb structurs, analytic hirarchy procss, gantry machining cntr, finit lmnt analysis A I. INRODUCION ftr billion yars of natural slction optimization, biological structur was almost prfct and wondrful, provid a lot of dsign prototyp and crativ improvmnt mthods in ordr to solv nginring tchnical problms for human [1]. Bionic dsign of th mchanical function and structur basd on th study of th mystry and mchanism of biological structur is on of th cor contnts of th mchanical bionic dsign. Stiffnss was an important indx of machin prformanc. It not only influncd th prcision and surfac quality of work pic, but also affctd vibration rsistanc, nois and movmnt stability of th machin tool []. In addition, moving componnts in high spd machin tool with high acclration should hav light wight and strong vibration rsistanc, thn w could us last amount of matrials to suffr th biggst load [3].hr ar many organisms of high spcific stiffnss in biosphr with its uniqu structural faturs. Applying som kind of ruls and Manuscript rcivd March 6, 01; rvisd April 13, 01.his work was supportd in part by Six major talnt Summit projct of Jiangsu provinc. Yuhong Zhang is with th Collg of Mchanical and Elctrical Enginring, Nanjing Univrsity of Aronautics and Astronautics, Nanjing, 10016,P.R. China. (-mail: zhangyh @16.com). Wnhua Y is with th Collg of Mchanical and Elctrical Enginring, Nanjing Univrsity of Aronautics and Astronautics, Nanjing, 10016, P.R. China. (corrsponding author, tlphon: ;-mail: why@nuaa.du.cn). Shng Lng is with th Collg of Mchanical and Elctrical Enginring, Nanjing Univrsity of Aronautics and Astronautics, Nanjing,10016,P.R. China. (-mail: mslng@nuaa.du.cn). Wnyong Shan is with th chnology Cntr of Wuxi Qiaolian CNC Machin ool Co., Ltd. Wuxi, Jiangsu Provinc,14187,P.R. China. (-mail: swy_qlmachin@sina.com). mchanism of th bionic structur is a mthod of improving th spcific stiffnss of structur. In rcnt yars many scholars had applid th bionic structur to optimization dsign of machin tool structur. For xampl, Ling Zhao, Wuyi Chn [4] usd hollow sandwich structur of organism to th bionic dsign on ribs arrangmnt of machin tabl. Yongbin Yang [5] studid th advantags of th biologic sklton which incrasd th stiffnss of organism, finding that th biologic sklton indicatd th bst path for organism to suffr th load. h innr structur of column was rdsignd as sklton to improv th spcific stiffnss. Ling Zhao [6] carrid out structur optimization dsign for ribs of a gantry machin tool cross-bam basd on giant watrlily vin distribution, and summarizd th bionic dsign principls of cross-bam s ribs. hr ar grat advancs in th bionic structur. In th ara of th dsign of machin tool, most studis ar on basis of on singl kind of structur with som biological charactristics without considration of drivativ structurs. o obtain a structur with bst prformanc, it is ncssary to invstigat varitis of bionic structur. So far, its application in th structural dsign of machin tool is in th stag of prliminary and xprimntal rsarch bcaus of th imprfction of pilot study on th bionic structur. Aiming to improv comprhnsiv prformanc of column of larg-scal gantry machining cntr, th lightwight and high fficincy biological structur configuration law was studid which is applid to th dsign of ribs of column. h solutions wr optimizd by th Gray Analytic Hirarchy Procss (Gray-AHP). h rsults show that applying th bionic dsign mthod could improv th comprhnsiv prformanc of column. II. HE BASIC DESIGN MEHOD OF HE BIONIC SRUCURE Basd on thoroughly undrstanding th structur and function mchanism of organism, w slctd bionic objct, study similaritis btwn th larg-scal machin structur and biological structur, and thn st up th bionic organisms prototyps, and optimizd th structur of th dsigning objct. Bcaus th biological structur was mor complx than machin structur, w must considr manufacturability of th componnts, whn collcting th faturs structurs which influncd its mchanical proprtis. In this papr, a paramtrizd modl basd on studying organism structur, was st by th 3d CAD softwar, with construction form and siz of typical structur of larg-scal machin tool. W usd ANSYS softwar for simulation of column, and thn according to th simulation rsults and ISSN: (Print); ISSN: (Onlin)

2 Procdings of th World Congrss on Enginring 01 Vol III, July 4-6, 01, London, U.K. othr aspcts of prformanc, w usd Gray-AHP for optimization to gt th structur of column with comprhnsiv prformanc. h procss was shown in figur 1. Fig. 1 Column Bionic Dsign Flow Structur III. BIONIC DESIGN AND ANALYSIS OF COLUMN A. Analysis of column h rsarch objct was a kind of column of prcision gantry machining cntr (as shown in figur ). Its matrial was gray iron H300. h column was th support parts of machin tool, supporting bam of machin tool, cross slid, box and sliding bas. h load was larg. In addition, big dformation of column would dirctly affct procssing prcision of parts. hrfor assuring that column had gratr ability to rsistant to dformation is vry important undr th big dynamic and static load. ach of th diamond obtus angl was ', th acut angl was 70 3 '.h volum of ach hol was almost cm. Walls of hivs wr thin and lss than 0.1 mm on avrag [11]. o against th maximum load, th bottoms of nst room wr mutually combind. Honycomb structur, with high spcific stiffnss, high spcific strngth, light wight, xcllnt hat and sound insulation, widly applid in structur of construction, industrial boilr, aircraft and so on. For xampl glass fibr rinforcd plastic honycomb sandwich structur that th plan applid had advantags of high spcific strngth, high structur stiffnss, light wight, asy molding that wr suitabl for matrials of making wing of small UAV[1]. Honycomb cor was now applid in cast-in-plac concrt building, h hollow wall of honycomb structurs was applicabl to th nw floor systm of larg span and larg spac, not only with light wight, good sismic prformanc, good sound insulation ffct, but also matrial saving. It was rally th conomic on [13]. W wr quit familiar with th traditional singl honycomb shap structur, such as triangl honycomb (as shown in lft part of figur 5), hxagonal honycomb. What was so spcial to dsrv to b mntiond, a kind shap of "combination of honycomb " calld Kagom honycomb (as shown in right part of figur 5) which was widly causd th attntion in rcnt yars, Kagom honycomb [14] comprisd of hxagonal honycomb and triangl honycomb. Fig. A Larg Gantry Machining Cntr Aftr dtrmination of shap and matrials, changing th intrnal structur of th column had significant influnc on improving th stiffnss and rducing dformation, spcially for castings of machin tool. h traditional dsigning form of ribs wr too simpl, such as paralll, # shap, X shap or othr simpl shaps[7] [9]. As shown in figur 3, it was th typical X shap arrangmnt for ribs of column of gantry machining cntr. h study found that w could improv dynamic and static charactristic by changing arrangmnt of ribs and structur paramtrs. So w dcidd to rdsign and optimiz of ribs basd on thinking of th bionic structur. Fig. 3 h Arrangmnt of Ribs of a larg Gantry Machining Cntr Column B. Rsarch of biology prformanc h b hivs that built with wax was light and strong. hy wr bautiful and practical buildings [10]. Honycomb structurs originatd from th basic structur of bs hivs (figur 4). From th outsid, th small hols in hivs wr hxagonal, which wr arrangd clos togthr. Each hol was not xact hxagonal prism, bcaus th bottom was not flat. hr wr thr qual taprd diamond prism, Fig. 4 Hxagonal Honycomb Fig. 5 riangl and Kagom Honycomb C. Bionic dsign of column h dvlopmnt dirction of modrn numrical control machin tool was high spd and high prcision, moving componnts in high spd machin tool with high acclration should hav light wight and strong vibration rsistanc, thn w could us last amount of matrials to suffr th biggst load. According to th abov spcific stiffnss of honycomb structurs, w trid to chang intrnal vnly arrangd ribs of column to honycomb structurs, which could improv th comprhnsiv prformanc of column. hrfor, by combining with procssing manufaturability and changing th ribs of column prototyp, thr bionic typ of ribs structur wr put forward as shown in tablⅠ,in ordr to study law of column structur prformanc which influncd by arrangmnt of ribs. ISSN: (Print); ISSN: (Onlin)

3 Procdings of th World Congrss on Enginring 01 Vol III, July 4-6, 01, London, U.K. ABLE 1 PROOYPE COLUMN AND HREE BIONIC YPE OF SIFFENED PLAE YPE Structur Charactristics Prototyp (first schm) h form of ribs is X shap Bionic Ⅰ typ (scond schm) h form of ribs is hxagonal honycomb shap Bionic Ⅱtyp (third schm) h form of ribs is triangl shap Bionic Ⅲ typ (fourth schm) h form of ribs is kagom shap Basd on satisfying th dsign rquirmnts of machin tool column, by dsigning th thr typ of bionic ribs, thicknss of ribs and thicknss of th prototyps wr much clos, and th numbr of rinforcd msh of bionic Ⅰ typ was clos to that of th prototyps. Bionic Ⅱ and bionic Ⅲ was transformd in th basis of bionicⅠ. In PROE modl, w could gt th following four schms (as shown in figur 6). W nd optimiz ths schms. h purpos of optimization was slcting th bst dsign of machin tools column through comparing and analyzing various optional dsign of machin column, in ordr to mak th comprhnsiv prformanc of machin tool column bst. Static prformanc, vibration rsistanc, light wight, manufacturing tchnology and conomic prformanc wr rquird to b considrd during column of machin tool dsign, to mt th dvlopmnt rqust of modrn CNC machin tool products with light wight, prformanc optimization, manufacturability and conomical fficincy. As it was a multi-objctiv optimization dcision problm, a rasonabl ffctiv optimization modl nd to b stablishd. hrough static and modal finit lmnt analysis of column, w got indx valu of static prformanc, vibration rsistanc and lightwight of all kinds of schms. It was shown in tablⅡ aftr statistical collct. Choosing th traditional column structur schm was mainly basd on xprinc of dsignr slction, it was difficult to nsuring that th slctd dsign plan was th bst on. In ordr to solv this problm, this papr usd th Gray-AHP to choos th bst comprhnsiv prformanc of column structur of column of th machin tool. ABLEⅡ INDEX VALUE OF SAIC PERFORMANCE, VIBRAION RESISANCE AND LIGHWEIGH OF ALL KINDS OF SCHEMES First Scond hird Fourth Prformanc indx schm schm schm schm Maximum strss Static prfor -manc Vibra -tion rsis -tanc Light -wight /MPa(cost) Maximum dformation /μm(cost) First stp inhrnt frquncy /Hz (fficincy) Scond stp inhrnt frquncy /Hz (fficincy) hird stp inhrnt frquncy /Hz (fficincy) Forth stp inhrnt frquncy /Hz (fficincy) Mass of column/kg(cost ) Hight of cntr of gravity of column/mm (cost) First Schm Scond Schm hird Schm Fourth Schm Fig. 6 Dsign Schm of Machin ools Column D. Finit lmnt analysis of column structur W built four kinds of column modl for th gantry machining cntr in th 3d CAD softwar. h structur of post was simplifid, and th structur of th bolt hols and small round hols, chamfring and small fillt, small stps wr all rmovd. hn import th 3d modl of machin tool column into ANSYS softwar to analyz th mchanical charactristics of ribs structur [15].Columns wr th support parts of machining cntr, baring th wight of th bam and cross slid, sliding bas, balanc wight of spindl systm, and th cutting forc. Barb bolt of column bottom was fixd connctd to lath bd. So applid fixd constraint on th bolt plac, and applid frictionlss constraints on th bottom of column to limit normal movmnt. IV. HE BASIC HEORY OF GRAY-AHP Gray-AHP includs two main contnts: apply th AHP for th wight of th valuation indxs and apply th gry thory for th comprhnsiv valuation of indxs. A. Apply th AHP for th wight of th valuation indxs Applying AHP to analyzing problm nd thr stps in gnral: 1) h stablishmnt of AHP structur modl ) Construct th judgmnt matrix W could us Dlphi mthod to dtrmin judgmnt matrix A by many xprts, this valuation matrix rquird xprts to form th rlativ importanc judgmnt of th indxs, th lmnts of matrix should b filld basd on th dfinition of tablⅢ. Evaluation matrix A was quation (1). w1 / w w1 / w n A ( w n / w1 w n / w n 1) ISSN: (Print); ISSN: (Onlin)

4 Procdings of th World Congrss on Enginring 01 Vol III, July 4-6, 01, London, U.K. ABLE Ⅲ MARIX JUDGMEN SCALE (1 ~ 9 SCALE MEHOD) Scal Maning 1 Show that th two lmnts is compard with th sam importanc 3 Show that th two lmnts is compard,th formr slightly mor important than th lattr 5 Show that th two lmnts is compard,th formr obvious mor important than th lattr 7 Show that th two lmnts is compard,th formr xtrmly mor important than th lattr 9 Show that th two lmnts is compard,th formr strong mor important than th lattr,4,6,8 Show that middl valu of th adjacnt judgmnt 3) h chck of consistncy B. Apply th gry thory for comprhnsiv valuation of indxs h main stps of comprhnsiv judgmnt which involvd two layrs wr: th dtrmination of valuation indxs, th dtrmination of th optimal indx st, th dimnsionlss procssing of data, th dtrmination of th judgmnt matrix, th dtrmination of ach wight, th comprhnsiv valuation of th scond layr, th comprhnsiv valuation of th first layr (gry comprhnsiv valuation). 1) h dtrmination of th rfrnc squnc Whn using gray incidnc mthod to do th comprhnsiv valuation, th valuation critrion was th optimal valu among indxs. Whn th indx blongd to "fficincy" indx, w took th maximum valu of ach schm; whn th indx blongd to "cost" typ indx, w took th lowst valu of ach schm. Rfrnc Sris was dnotd by quation(): X0(k)={ X0(1),X0(),X0(3),,X0(k)} () ) h dtrmination of collction of th optimal indxs h optimal indx st was an aggrgat that consists of th optimal indx of th valuating objcts,and it was also rfrnc sris of th valuation compard objcts. h optimal indxs st E * (namly rfrnc squnc X ( k ) 0 ) and th indxs of th valuation objcts composd matrix E. 1 m i i i i 1 k m E (3) n n n 1 m i In this quation: k was th original valu of th kth indx E 1,,, m in th ith valuation objct. optimal indxs st. was th 3) Dimnsionlss procssing of th data For compar, th following quation (4) was usd to nondimnsionaliz th optimal indxs st and th indxs st of ach schm in ordr to rduc th intrfrnc of random factors: 0 1 i i (4) i 0 1 In this quation: i, i rspctivly standd for th original data of th valuation indxs and th nondimnsionalization data; i was th avrag valu of th ith indx. 4) h dtrmination of judgmnt matrix According to th gry systm thory, w could obtain th ith valuation objct and th gray incidnc cofficint of th kth indx from quation (5)[16]: i min min max max i k i k max max i k k k k i k i i k k k k i k t In this quation: was rsolution ratio, gnrally took 0.5,i=1,,,m, k=1,,,n Evaluation matrix consistd of corrlation cofficint: t1 1 t1 t1 m (6) t 1 t t m t n 1 t n t n m 5) h dtrmination of wight Using AHP mthod to dtrmin wight cofficint vctor Q of th valuation indx on all layrs, two layrs of comprhnsiv valuation wight cofficint vctor wr Q A and Q B rspctivly. 6) h scond layr of gry comprhnsiv valuation h valuation matrix of th scond layr: L Q B (7) 7) h first layr of comprhnsiv valuation h first layr dirctly mad us of th scond layr valuation rsults to compos th first layr of judgmnt matrix L. Gry comprhnsiv valuation rsults vctor was: R Q L (8) A V. COLUMN OPIMIZAION PROCESS BASED ON GRAY-AHP A. h stablishmnt of comprhnsiv prformanc of column and AHP modl of machin tools (5) ISSN: (Print); ISSN: (Onlin)

5 Procdings of th World Congrss on Enginring 01 Vol III, July 4-6, 01, London, U.K. Fig. 7 h Appraisal Indx St of Column Schm and Evaluation Hirarchical Modl Multi-objctiv comprhnsiv capability analysis and schm valuation procss of column structur of gantry machining cntr was basd on Gray-AHP, which dfind gnral objctiv layr of hirarchical modl was comprhnsiv ability of column. Sub-goals layr consistd of th static prformanc, vibration rsistanc, lightwight and othr indxs; Indx layr was maximum strss, maximum dformation, th first stp inhrnt frquncy, th scond stp inhrnt frquncy, third stp inhrnt frquncy, fourth stp inhrnt frquncy, mass of column, hight of cntr of gravity of column, tchnology difficulty and conomy; Schm layr includd ths forms: th form of ribs was X shap, th form of ribs was hxagonal honycomb shap, th form of ribs was triangl, th form of ribs was Kagom shap. So far, w stablishd valuation hirarchical modl, as shown in figur 7. B. Construct judgmnt matrix and calculating wight Bcaus of importanc of valuation indx to valuation goal was diffrnt, ach indx was givn diffrnt wight cofficint.h mor important th wight cofficint of indxs wr, th biggr thy wr. his papr usd th Dlphi mthod (xprts consult mthod), and rqustd xprts to fill in fiv valuating matrix for column schm according to th rquirmnts, rspctivly was: Matrix A-Bi: th rlativ importanc of four indxs of sub-goals layr to having influnc on th total targt; Matrix B1-Ci: rlativ to th static prformanc, th rlativ importanc btwn th maximum strss and maximum dformation; Matrix B-Di:rlativ to vibration rsistanc, th rlativ importanc among th first stp inhrnt frquncy, th scond stp inhrnt frquncy, third stp inhrnt frquncy and fourth stp inhrnt frquncy; Matrix B3-Ei : rlativ to lightwight, th rlativ importanc btwn mass of column and hight of cntr of gravity of column. Matrix B4-Fi: rlativ to othr, th rlativ importanc btwn tchnology difficulty and conomy. h data which xprts valuatd in accordanc with AHP was procssd, matrix that passd th inspction form matrix wight vctor basd on maximum ignvalu mthod. h matrix and wight vctors was shown in tabl Ⅳ ~ Ⅷ. ABLE Ⅳ JUDGMEN MARIX A-BI AND WEIGH A B1 B B3 B4 Wight QA B B B3 1/ 1/ 1 3/ B4 1/ 1/3 / ABLEⅤ JUDGMEN MARIX B1-CI AND WEIGH B1 C1 C Wight QB1 C1 1 / C 5/ ABLE Ⅵ JUDGMEN MARIX B-DI AND WEIGH B D1 D D3 D4 Wight QB D D 1/ D3 1/ 1/ D4 1/ 1/3 1/ ABLE Ⅶ JUDGMEN MARIX B3-EI AND WEIGH B3 E1 E Wight QB3 E E 1/ ABLE Ⅷ JUDGMEN MARIX B4-FI AND WEIGH B4 F1 F Wight QB4 F F 1/ ISSN: (Print); ISSN: (Onlin)

6 Procdings of th World Congrss on Enginring 01 Vol III, July 4-6, 01, London, U.K. C. h scond layr of comprhnsiv valuation Profssional according to "vry asy, vry good" as th fiv points, "mor asily, bttr" as four points, "gnral" as thr points, "mor difficult, wors" as th two points, "vry hard, vry bad" as 1 point. W scord tchnology difficulty and conomy indxs of th schms, took arithmtic man for valuation of ach xprt, as shown in tablⅨ. Othr ABLE Ⅸ EVALUAION INDEX OF COLUMN 1) Confirm rfrnc squnc Slcting rfrnc squnc, according to "bnfit typ" indx took its maximum, "cost typ" indx took its minimum, got th rfrnc squnc from tablⅡand tablⅨ: X0(k)={6.54,1,3345,46.,75.7,106.7, , ,568,4.5,4} ) h static prformanc valuation indx Usd optimal indx st E * (rfrnc squnc X ( k )) 0 and th objct of th valuating indx to form th static prformanc valuation indx matrix: E= Substitution into th typ (4) and nondimnsionalization, usd th typ (5) to calculat corrlation cofficint valu ti (k), and got corrlation cofficint matrix: (10) hn calculatd th comprhnsiv valuation rsults vctor of B1 was L1 QB , (11) ,0.6450,1, ) h vibration rsistanc valuation indx Similarly, for vibration rsistanc indx, w could gt corrlation cofficint matrix: chnology difficulty (fficincy) Economy (fficincy) (9) (1) Comprhnsiv valuation rsults vctor of B was L QB ,0.995,0.1881, (13) ,1,0.4380, ISSN: (Print); ISSN: (Onlin) 4) h lightwight valuation indx Similarly, for lightwight indx, w could gt corrlation cofficint matrix: (14) Comprhnsiv valuation rsults vctor of B3 was L3 QB , (15) ,0.98,0.5000, ) Othr valuation indxs Similarly, for othr indxs, w could gt corrlation cofficint matrix: (16) Comprhnsiv valuation rsults vctor of B4 was L4 Q B , (17) ,0.5095,0.358,0.515 D. h first layr of comprhnsiv valuation Usd L1, L, L3, and L4 to structur th first layr of valuation matrix (18) L R QA L ,0.8043,0.6378,0.697 (19) E. Evaluation rsults From analysis of th scond layr of valuation rsult vctor L1, L, L3, and L4 indicatd that according to th static prformanc indx, th third schm was optimal; according to vibration rsistanc valuation indx, th scond schm was optimal; according to lightwight valuation indx, th first schm was optimal; according to othr valuation indx, th first schm optimal. It could b found that a singl indx valuation mthod couldn't masur comprhnsivly a column schm suprior or not. From th comprhnsiv valuation rsult vctor R, th comprhnsiv prformanc of th scond schm was bttr than othr schms. VI. CONCLUSION 1) h column structur of ribs with hxagonal honycomb shap has th bst comprhnsiv prformanc in comparison with that of X shap, triangl shap and kagom shap. ) h rsults of rsarch show that changing arrangmnt pattrn for ribs of column of machin tool to honycomb structurs could improv comprhnsiv prformanc.

7 Procdings of th World Congrss on Enginring 01 Vol III, July 4-6, 01, London, U.K. 3) h Gray Analytic Hirarchy Procss givn in th papr is ffctiv for valuation of comprhnsiv prformanc of machin tool. 4) Bionic dsign could improv th structur of gantry machin cntr. It was an ffctiv and innovativ mthod for machin tool dsign. REFERENCES [1] Lu Y X, Significanc and progrss of Bionics, Journal of Bionics Enginring, vol.1,no.1,pp.1-3,004. []. Fu, Hongshng Ding, Jinquan Li, Siqin Pang, Rviw on Stiffnss of Variabl- axis NC Machin ools, Machin ool &Hydraulics, no.3,pp.9-1,003. [3] H. Cn. Study on Structural Bionics hory, Light Wight Structur Bionics Dsign and Rapid Prototyping sting. Bijing: School of Mchanical Enginring and Automation of Bijing Univrsity of Aronautics and Astronautics,004 [4] L. Zhao, W.Y. Chn, J.F. Ma, Lightwight Dsign of High-spd Working abl Basd on Structural Bionic, Modular Machin ool & Automatic Manufacturing chniqu,no.1,pp.1-4, 008. [5] Y.B. Yang,W.Y. Chn,D.H. Zhao, Bionic Dsign of Column Structur of Machin ool for High Spcific Stiffnss, Journal of Bijing Univrsity of Aronautics and Astronautics, vol..34, no. 9,pp ,008 [6] L. Zhao,W.Y.Chn, J.F. Ma, Structural Bionic Optimization of Stiffning Ribs of a Machin ool Crossbam Basd on Giant Watrlily Vin Distribution, Chins High chnology Lttrs vol.19,no.9,pp ,008. [7] John Higgins P E, Wgnr P, Viisoranu A, Dsign and tsting of th Minotaur advancd grid-stiffnd fairing, Composit Structurs, no.66,pp, ,004. [8] Liu J S, Hollaway L, Disign optimization of composit panl structur with stiffring ribs undr multipl loading cass, Computrs & Structurs, vol.78,no.4,pp ,000. [9] Gosowski B, Non-uniform torsion of stiffnd opn thin-walld mnmbrs of stl structurs., Joural of Constructional Stl Rsarch, vol.63,no.6,pp ,007. [10] D.Q. Jiang, Bionic Building Matrialsand Application, oday Scinc and chnology, no.6,pp.3-4,1999. [11] W. Z. Cai, Structur and Bionics of Honycomb, Entomological Knowldg,no.,pp ,001. [1] Y.B. Fng, Biomchanics, Bijing : Bijing Scinc Publishing Hous,1983 [13].P. Yu, Projct Application Honycomb Cor Hollow Concrt Floor Construction chnology, Sichuan Building Matrials,vol.36, no.,pp ,010. [14] Hyun S, orquato S, Optimal and manufacturabl two-dimnsional, Kagom-lik cllular solids, J. Mastr.Rs,no.17,pp ,00. [15] David S.Hardag,Gloria J.Wins, Modal analysis and modling of a paralll kinmatic machin, Manufacturing Scinc and Enginring,no.10.pp ,1999. [16] S.F. Liu,ianbang Guo,Yaoguo Dang, hory and Application of Gry Systm.Bijing:Scinc Prss,1999. ISSN: (Print); ISSN: (Onlin)