高速加工HSK工具系统的力学模型_英文_

M ECHAN I CAL MOD EL OF HSK T OOL ING S Y STE M　Foundation ite m s :Suppo rted by the N ati onalN atural Science Foundati on of Ch ina (50275066,50675088);the N aturalScience Foundati on of J iangsu P rovince (BK 2005111,BK 2006077).　Rece ived date :2006-06-27;rev ision rece ived date :2007-01-09　E -ma il :w gch @ujs .edu .cnIN H IGH SPEED M ACH IN INGW ang Gu icheng 1,W u W eig uo 1,S hen Chung en 1,W ang S hu lin 1,Z uo J ianm in2(1.Schoo l of M echanical Engineering ,J iangsu U niversity ,Zhenjiang ,212013,P .R .Ch ina ;2.D epartm ent of M echanical Engineering ,N anjing Institute of T echno logy ,N anjing ,211167,P .R .Ch ina )Abstract :A cco rding to the structure of the hoh l schaft kegel (H SK )too ling system and its w o rk ing p rinci p le ,a m echanical model of the H SK too ling system is established .M aj o r facto rs influencing the stiffness of the system are analyzed and the relati onsh i p betw een the load and the m anufacturing quality is obtained .T he basic rule of the stiffness variati on is p resented and the theo retical analysis is in a good agreem ent w ith experi m ental results .T he dynam ic stiffness m ust also be considered to evaluate the perfo r m ance of the too ling system besides the static stiffness .F inally ,the selecting p rinci p les of the H SK types are p ropo sed and their op ti m um operating conditi ons are established .Key words :m echanical model ;stiffness ;load ;H SK too ling systemCLC nu m ber :T G 50611 D ocu m en t code :A Article I D :100521120(2007)022*******INTROD UCT I ONW ith the developm en t of advanced m anufac 2tu ring techno logies ,especially the h igh sp eed m a 2ch in ing (H S M )and the h igh 2p recisi on m ach in 2ing ,m any researches study on the too ling sys 2tem ,becau se the p erfo r m ance of too l in terfaces can greatly influence the m ach in ing characteristicsof m ach ine too ls [123].In H S M ,the too ling system endu res a large cen trifugal fo rce .It m akes the jo in t stiffness and the p recisi on of the traditi onal too ling system (7∶24tap er )decrease rap idly .So it is i m p erative to develop a new style too ling sys 2tem su itab le fo r H S M .In the num erou s new style too ling system s exp ected as the system of the 21st cen tu ry ,the hoh l schaft kegel (H SK )too ling sys 2tem can m eet the requ irem en ts fo r h igh sp eed m a 2ch in ing very w ell and it is app lied w idely in thew o rld [425].Since the H SK too ling system is developed on ly fo r a sho rt p eri od and the research w o rk is in sufficien t ,there are m any p rob lem s in the m anufactu ring and app licati on of H SK too lingsystem .It is necessary to fu rther the basal re 2search of H SK too ling system in o rder to tho r 2ough ly so lve the p rob lem s .1　M ECHAN I CAL MOD EL S OFHSKT he H SK shank is a ho llow and sho rt one w ith 1∶10taper .O n the acti on of the clam p ing fo rce ,H SK is pu lled in to the sp indle ho le un til tw o tap ers betw een the flange of the H SK shank and the face of the sp indle receiver are in tigh t con tact due to the elastic defo r m ati on of the shank .T he si m u ltaneou s con tact en su res h igh po siti on accu racy and stiffness ,bo th radially and ax ially .M echan ical m odel of H SK estab lished in R ef .[6]is show n in F ig .1.A cco rding to M odel,the bending m om en t M A and the radial stiff 2ness K A can be calcu lated w hen the tw o faces begin to separate .MA=12F S R P +C S C P R S 2R P(1)F ig .1　M echanical model of H SK too ling systemK A =M<=12(C P R P 2+C S R S 2)(2)w here F S is the p u lling fo rce of the clam p ing structu re ;R S the radiu s of the sp ring distribu 2ti on ;R P the average of the flange radiu s of H SK shank and the gageline radiu s ;C S the to tal stiff 2ness of the clam p ing structu re ;C P the jo in t stiff 2ness betw een the H SK shank and the sp indle re 2ceiver ,and <is the defo r m ing angle .It is no ticed that the con tact stiffness is ig 2no red in the analysis of the jo in t stiffness C P .To acco rd w ith the fact ,M echan ical m odel ,tak 2ing the con tact stiffness in to accoun t ,is estab 2lished in th is p aper (see F ig .2).T he jo in t be 2tw een the shank and the sp indle is rep laced by a soft layer with the stiffness C P ′.F ig .2　M echanical model of H SK too ling systemA ssum ed that C cont is the con tact stiffness betw een the flange and the face ,then C P ′can be calcu lated .1C P ′=1C P+1C cont(3) T he distribu ti on of the con tact p ressu re Ρ(x ,y )on the con tact face is suppo sed to be lin 2ear .W hen the face con tact begin s to separate ,the con tact p ressu re can be exp ressed asΡ(x ,y )=F SΠ(R 12-R 22)yR 1+1(4)w here R 1is the flange radiu s of the H SK shank and R 2the gageline radiu s .A cco rding to M odel ,the bending m om en tMAand the radial stiffness K A can be ob tainedw hen the con tacted faces begin s to separate .MA=κΡ(x ,y )y d x d y +12F S C S R S 2C P ′R 1=12F S R 12+R 222R 1+C S R S 2C P ′R 1(5)K A =M<=C P ′(R 12+R 22)4+12C S R S 2(6) A fter the face con tact disapp ears ,the stiff 2ness K B of the second part of the in terface can be calcu lated .K B =∃M∃<=∃FR 1∃F(K ax R 1)=K ax R 12(7)w here K ax is the ax ial stiffness of the in terface af 2ter the face con tact disapp ears .2　RESUL TS AND D ISCUSSI ONS211　Com par ison of ca lcula ted and m ea sured re 2sultsT he exp eri m en tal cu rves of radial and ax ial stiffness of the H SK too ling system are show n inF ig .3[6].F rom the defo r m ati on cu rve ,it is foundthat the stiffness of H SK is com posed of tw o parts .W hen the bending load is s m all ,the stiff 2ness is h igh .How ever ,it rap idly decreases w hen the load increases .T he phenom enon is related toF ig .3　R adial and axial stiffness of H SK too ling systemthe con tact state of the face.W hen the load is s m aller than a certain value,the face con tact is p reserved.B ecau se of its suppo rting effect,the defo r m ati on of the system is s m all and the in ter2 face stiffness is h igh.W hen the load is b igger than a th resho ld,the face con tact disapp ears and the stiffness rap idly decreases w ithou t the sup2 po rting effect.T he face con tact stiffness co rrelates w ith the p ressu re.A cco rding to ISO standards[7],the p ressu re is abou t11M Pa w hen the H SK shank is clam p ed.In R ef.[8],the distribu ting con tact stiffness of the face w as abou t3×1013N m3.So the con tact stiffness of the face can be calcu lated byC f=C cont×Π(R12-R22)(8) U sing Eqs.(527),the bending m om en t M A and radial stiffness K A,K B can be ob tained w hen the face con tact begin s to be separate.R esu lts are listed in T ab les124.Table1　Calculational results of load and stiffnessT ype C P (N・mm-1)C S (N・mm-1)C cont (N・mm-3)C f (N・mm-1)C P′ (N・mm-1)F S kNH SK2A405129×1062134×1063×10131615×1064101×106618H SK2A506139×1063103×1063×10132419×1065109×10611H SK2A638112×1063181×1063×10133912×1066173×10618 Table2　Radi al stiffness K A before face con t act disappearsM ethodK A (N・m2・mm-1)H SK2A40H SK2A50H SK2A63M odel 104920434128M odel 86617513629Experi m entin R ef.[2]90018103600Table3　Radi al stiffness K B of the second part af ter face con t act beg i n s to separateM ethodK B (N・m2・mm-1)H SK2A50H SK2A63M odel 294629Table4　Bendi ng load M A when face con t act beg i n s to sep-arateM ethodM A (N・m)H SK2A40H SK2A50H SK2A63M odel 77160329M odel 73151308Experi m entin R ef.[2]—150—170300—340T ab le2show s that radial stiffness resu lts calcu lated by M odel are abou t15%h igher than exp eri m en tal resu lts in R ef.[2]and tho se calcu lated by M odel are clo se to experi m en tal resu lts.T herefo re,it can be concluded that the difference is cau sed by the con tact stiffness of the face.F rom T ab le3,the radial stiffness of the sec2 ond p art K B is on ly abou t1 6as m uch as the first part K A.It acco rds w ith the experi m en tal resu lt.T he sep arati on of the face con tact is gradual. T herefo re,it is hard to exactly deter m ine the bending load M A.T ab le4also show s that resu lts calcu lated from M odels and are all in the range of experi m en tal resu lts.212　I nf luence of clam p i ng syste m on i n terface stiffnessT he clam p ing fo rce is non linearly related to the con tact stiffness C f.A cco rding to Eqs.(3,6), if the clam p ing fo rce is sufficien t,increasing the clam p ing fo rce al m o st does no t influence the in2 terface radial stiffness K A.B u t if it is too s m all, K A w ill decrease w ith the decrease of the con tact stiffness.In additi on,the face roughness has a great influence on the con tact stiffness.To ob tain h igh stiffness of the in terface,the face roughness betw een the H SK shank and sp indle m u st be s m all.Eq.(7)show s that the second radial stiffness K B is related to the ax ial stiffness deter m ined by the stiffness of the clam p ing system after the face con tact disappears.So the radial and ax ial stiff2 ness of the in terface can be i m p roved by increas2 ing the stiffness of the clam p ing system after the face con tact disappears.741N o.2W ang Guicheng,et al.M echanicalM odel of H SK Too ling System in H igh Speed……213　I nf luence of load on i n terface stiffnessF ig.3show s that bo th static and dynam ic ra2 dial stiffness is all h igh w hen M<M A.W hen M> M A,although the static stiffness is still m uch h igher than the steep tap er shank,the dynam ic stiffness is low,thu s directly influencing the m a2 ch in ing quality and the too l life.So exceeding the load M A m u st be avo ided.T hen M A can be de2 fined as the no r m al load li m it of the H SK too l in2 terface.T he load s m aller than M A belongs to the no r m al load,and the load b igger than M A belongs to the heavy load.A s know n from Eq.(5),increasing the clam p ing fo rce is help fu l to increase the no r m al load li m it M A.214　I nf luence of shank d i m en sion on i n terface stiffnessIncreasing the flange radiu s R1can increase the in terface stiffness and the no r m al load li m it. W ith the sam e gageline diam eter,the flange of H SK2B is b igger than H SK2A.So w hen the load is heavy,H SK2B is p referred.In additi on,in the p rocess of m anufactu ring the H SK shank and sp indle,it is very i m po rtan t to en su re the p rop er radial to lerance of the H SK shank sp indle.O n one hand,w hen the radial to l2 erance of the H SK shank sp indle is too large,the clam p ing fo rce tran sferred to the con tact faces be2 com es s m all,thu s leading to the decrease of the stiffness and the no r m al load li m it of the H SK too ling in terface.O n the o ther hand,w hen the radial to lerance is s m all,the m ax i m um per m issi2 b le ro tati onal sp eed of the H SK too ling system can be reduced.3　CONCL USI ONSA cco rding to the above analyses,the fo llow2 ing conclu si on s can be draw n:(1)T he m echan ical m odel of H SK estab2 lished in th is p ap er is in acco rd w ith the p ractical situ tati on.T he in terface stiffness K A and the no r m al load li m it M A calcu lated by the m odel are in agreem en t w ith experi m en tal resu lts.(2)T he clam p ing fo rce is an i m po rtan t facto r that affects the p erfo r m ance of the H SK too ling system.Fo r ob tain ing the excellen t perfo r m ance of the H SK too ling system,the clam p ing fo rce canno t be s m aller than the recomm ended value in R ef.[7].(3)T he no r m al load li m it M A is a u sefu l li m it fo r the H SK too ling system.T he m ach in ing load m u st be s m aller than it in o rder to en su re h igh static and dynam ic stiffness of the H SK too l2 ing system.Fu rther m o re,increasing the clam p2 ing fo rce help s to increase M A.(4)W hen the m ach in ing load is heavy,the clam p ing system w ith b ig stiffness m u st be adop t2 ed to i m p rove the dynam ic stiffness at the second part of in terfaces.M o reover,H SK2B is m uch m o re su itab le fo r heavy m ach in ing.(5)T he radial to lerance of the H SK shank sp indle has a great influence on the perfo r m ance of the H SK too ling system.(6)Bo th static and dynam ic stiffness m u st be con sidered in evaluating the perfo r m ance of the too ling system.References:[1]　A oyam a T,Inasak i I.Perfo r m ances of H SK too l in2terfaces under h igh ro tati onal speed[J].A nnals ofthe C I R P,2001,50(1):2812284.[2]　W ang Shulin.Study on perfo r m ances of H SK too l2ing system and its app licati on foundati on in h igh m a2ch ining[D].Zhenjiang:J iangsu U niversity,2003.(in Ch inese)[3]　W ang Guicheng,W ang Shulin,W u W eiguo.Stiff2ness of H SK too ling system in h igh speed m ach ining[J].M aterials Science Fo rum,2006,5052507:4692474.(in Ch inese)[4]　Kocherovsky E.H SK H andbook[M].IntelligentConcep t,U SA:[s.n.],1999.[5]　W ang Guicheng,W ang Shulin.Too ling system fo rh igh speed m ach ining[M].Beijing:N ati onalD efenseIndustry P ress,2005.(in Ch inese)[6]　L em bke D,W eck M.Study on design po ssibilitiesfo r the connecti on m ach ine too l[R].F inal repo rt onR esearch P ro ject,A achen:W Z L L abo rato ry fo r M a2ch ine Too ls and A pp lied Econom ics,1991:8.841T ransacti ons of N anjing U niversity of A eronautics&A stronautics V o l.24[7]　ISO1216422001.Ho llow taper interface w ith flangecontact surface[S].[S.l.]:Internati onal O rganiza2ti on fo r Standardizati on,2001.[8]　R ao Zhush i.A study of contact stiffness of flatrough surfaces[J].Journal of M echanical Strength,1994,16(2):72275.(in Ch inese)高速加工HSK工具系统的力学模型王贵成1　吴卫国1　沈春根1　王树林1　左健民2(1.江苏大学机械工程学院,镇江,212013,中国;2.南京工程学院机械工程系,南京,211167,中国)摘要:根据H SK工具系统的结构和工作机理建立了H SK工具系统的力学模型,分析了影响工具系统刚度的主要因素和载荷与加工质量之间的关系,揭示出H SK工具系统刚度变化的基本规律,理论分析结果与实验结果吻合。