FEM NUMERICAL ANALYSIS OF TOOL HOLDER OF TURNING LATHE. Aleksandras Stulginskis University

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1 ENGNEERNG FOR RUR DEVEOPMENT Jelgava, FEM NUMERC NYSS OF TOO HODER OF TURNNG THE ndrus Senkus, Egle Jotautene leksandras Stulgnsks Unversty bstract. Fnte element modelng provdes a method n understandng vbraton processes. study of a tool holder by a numercal Fnte Element Method (FEM) was conducted. To analyze the modal propertes of the tool holder, a D fnte element model was developed usng NSYS software. t was found that decrease of the ampltude of a cantlever structure n vbro-mpact moton depends on the locaton of the supports. n the expermental modal analyss, natural frequences and mode shapes were measured for statc condtons. The fnte element model s valdated by comparng the numercal to expermental results. The cantlever type tool holder tends to functon as an effectve dampng element, whch abates detrmental nfluence of unwanted vbratons. Ths phenomenon could be useful for cantlever type cuttng tools, when t s necessary to ncrease the qualty of the machnng surface by decreasng the ampltudes of cuttng edge vbratons. Keywords: tool holder, FEM analyss, vbraton. ntroducton The stablty of a cuttng process drectly nfluences the qualty of a fnal surface. The control of the cuttng process s an mportant problem for machnng technology. nstabltes usually manfest as harmful chatter vbratons generated durng cuttng. Recently many studes have been conducted on ths problem by focusng on the condtons of appearance of such unwanted vbratons [; ]. Undesrable vbratons can be reduced by ether usng passve or actve dampng control methods. The passve methods can be mplemented by ncreasng dampng constant or by modfyng the structure by addng constraned layer dampng, damped lnks, tuned mass dampers, nterface dampng, sold-spacer dampng, etc. The passve vbraton control strategy can be qute effectve and desrable for ts smplcty []. One of the approaches s smart tools whch reduce forced vbratons, chatter and heat durng machnng. The Smart Tool proposed by B.-K. Mn et al. has a fast tool servo that utlzes a pezoelectrc actuator and two laser photo sensors to actvely solate the cuttng nsert from erroneous bar motons whle rejectng cuttng force dsturbances. The purpose of the tool tp servo s to solate the cuttng nsert from erroneous borng bar motons (.e., devatons from a perfectly cylndrcal path) whle rejectng cuttng force dsturbance. The servo has to be fast enough to compensate for at least the forced vbraton due to spndle rotaton at rpm. The majorty of the studes dealng wth the cuttng process of the turnng lathe are manly focused on the analyss of tool wear and dynamc cuttng force smulaton [4; 5]. The revew of ths research ndcates that the numercal smulaton of ths process s condtoned upon a number of assumptons and uncertantes as well as hghly dependent on varous factors such as the materal propertes, cuttng regmes, geometrc parameters of a tool, etc. [; ]. method to detect the presence of cross secton changes n beams and to determne ther locaton and sze has been developed based on the results of expermental modal analyss []. The changes of the natural frequences and frequency response functon ampltudes as a functon of the cross secton depths and ts locatons are mplemented. n Ref., a comparson between expermental and numercal results of the vbratng cantlever type tool structure led to the concluson that the best results were obtaned when the second flexural mode of the cantlever type tool concentrator s excted. The mplementaton of structural modfcatons by changng the cross secton at dfferent locatons that ntensfed hgher natural vbraton modes resulted n reducton of magntude of unwanted deleterous vbratons. Ths suggests, that exctaton of hgher natural vbraton modes could be advantageous, snce the ampltude of hgher modes becomes more ntensve, the energy dsspaton nsde the structure materal ncreases sgnfcantly [] makng the tool holder nto a passve damper. The man focus of ths research s based on treatng the tool holder of the turnng lathe as a flexble crcular hallow cantlever structure of whch vbratons are characterzed by several natural modes. The study presents several sample smulatons and expermental verfcatons of the tool holder vbratons. 55

2 ENGNEERNG FOR RUR DEVEOPMENT Jelgava, Materals and methods The majorty of analytcal and numercal methods use modal dentfcaton technques to obtan natural frequences and mode shapes. The fnte element numercal method s used n ths paper. Snce the cantlever structure has dstrbuted mass, stffness and other parameters, t s necessary to model the dynamc characterstcs of such an elastc structure by ncludng several modes of natural vbratons. The mpulse force that s produced durng spnnng, when the cuttng tool breaks away from the surface, has wde band spectral contents that are capable of exctng many natural modes of the cuttng tool. The sudden movement of ths structural component could be constraned by supports. The developed -D fnte element model of mpactng tool holder (Fg. ) represents the general case of the vbro mpact system. For numercal calculatons, the mpactng tool s represented by a -D model snce flexural vbraton modes have a much more sgnfcant nfluence on the vbro-mpact process n comparson to torson modes []. The numercal model conssts of =,..., m lnear beam elements located n a sngle layer and j =,..., k moton lmters or supports ( < k < m) that are located at =,,...,m nodes. Each beam element has two nodes wth three degrees of freedom (DOF) at each: dsplacement n x- and y-axs drectons and rotaton n xy plane. The model s meshed manually wth a number of fnte element m equal to 5, resultng n 5 total DOFs. mpact modelng s based on a cantlever approach and makes use of the Kelvn-Vogt (vscoelastc) rheologcal model, n whch a lnear sprng s connected n parallel wth a damper the former represents the mpact force and the latter accounts for energy dsspaton durng the mpact [7]. Fg.. Schematc of -D fnte element model of mpactng cantlever Model dynamcs s descrbed by the followng equaton of moton gven n a general matrx form [7]: [ M] {&& y( t) } + [ C] { y& ( t) } + [ K] { y( t) } = Q t, f > y t < y t f y, y&, t ; () { ( )} { j} ( ) { Q( t) } + F( y, y&, t), { } { j} { ( )} ( ) { } f{ } { y ( t) } { } y ( t) j j { } f ( y, y&, t) <, where [M] mass matrx; [C] dampng matrx; [K] stffness matrx; {y(t)} dsplacement vector; {ẏ(t)} velocty vector; {ẏ (t)} acceleraton vector; {Q(t)} vector representng the external forces actng on the structure. Ths vector s used purely as a mechancal load durng smulatons; f (y,ẏ,t ) reacton of the mpactng structure; {F(y,ẏ,t)} vector of mpact nteracton between the cantlever mcrostructure and the support; j dstance from the -th nodal pont of the structure to the j-th surface of the support located at the correspondng nodal pont. The mass and stffness matrces are expressed respectvely as shown n equatons () and () [5-7]. The obtaned results ndcate a process of free vbratons of a crcular hollow cantlever structure. n order to analyze the modal propertes of the tool holder, a D fnte element model of the hollow 5

3 ENGNEERNG FOR RUR DEVEOPMENT Jelgava, crcular cantlever was developed usng NSYS software. Numercal fnte element models were constructed usng the nformaton of geometry and materal propertes of the structure. The requred parameters were chosen to be representatve of a real tool holder from the standards [8]. For the numercal analyss, the cantlever wth the followng parameters has been analyzed: outsde dameter s.7 mm, nner dameter s.5 mm length s mm and cross sectonal area s 7. mm. cantlever wth smlar geometrc and materal parameters was also chosen for expermental study. Tool holders are usually made of hgh strength steel, so the materal parameters for numercal smulaton were chosen accordngly as (DN.) steel. ts modulus of elastcty s N m -, densty s 787 kg m -, moment of nerta s mm 4. fter creatng a geometrc model of the holder, the fnte element mesh was generated. The structure s meshed by m=5 fnte elements and the rgd support s located at the free end of the cantlever (Fg. ). = ] [ M ρ () [ ] = E K 4 4 () where E modulus of elastcty, N m - ; cross sectonal area of beam, mm ; length of element dsplacement, m; ρ densty of cantlever materal, kg m - ; second moment of nerta, mm 4. To perform the expermental modal analyss of the crcular hollow cantlever, the beam was nstalled n the bench (grps) of a planers lathe. The vbratons of the lathe components were measured by PUSE software developed by Brüel&Kjær together wth the PUSE data acquston module 58, the mpact hammer 8 for creatng known or controlled exctaton and type 47 pezoelectrc charge accelerometers. The expermental modal analyss was performed by exctng the crcular hollow cantlever that was supported at the free end. The chosen length of the hollow cantlever s 5 mm, the outer dameter s.7 mm and the wall thckness s.5 mm. The experment modal analyss was performed at the SU laboratory.

4 ENGNEERNG FOR RUR DEVEOPMENT Jelgava, Results and dscusson The mode shapes provde mportant nformaton on the vbraton response characterstcs. The four calculated natural modes are shown n Fg.. a) b) c) d) Fg.. Mode shapes of tool holder: a frst mode shape; b second mode shape; c thrd mode shape; d fourth mode shape Ffteen modes of vbraton of cantlever beam were calculated durng the FEM analyss. The natural frequences of the rest of the calculated modes obtaned from FEM are presented n Table. The obtaned numercal results of ths analyss show that the ampltudes of free vbraton from the mpact can be markedly decreased at the free end of the cantlever where the support s located. Ths s due to the dynamcal ntensfcaton of the hgher modes that ncrease the cantlever vbraton frequency and decrease the vbraton ampltudes. Ths numercal smulaton could be useful for cantlever type cuttng tools, when t s necessary to ncrease the qualty of the machnng surface by decreasng the ampltudes of the cuttng edge vbratons. Table Natural frequences of tool holder Mode number Numercal frequency, Hz Mode number Numercal frequency, Hz n the expermental modal analyss, natural frequences and mode shapes were measured for statc condtons usng accelerometers and an mpact hammer. The excted frequences were recorded for

5 ENGNEERNG FOR RUR DEVEOPMENT Jelgava, statc condtons wth no load. Durng the machnng process, t s dffcult to measure vbraton response. The measurements were obtaned usng the mpulse response generated by the mpact hammer and the mpact force measured by the sensor located at the hammer tp. Only the frst two modes were dentfed expermentally. The frequency response functon of the tool holder s shown n Fg.. Dsplacement, m Frequency, Hz Fg.. Frequency response functon (FFT) of tool holder Havng the frequency response the functon, modes, modal frequences and modal dampng of the tool holder of the turnng lathe can be obtaned. By comparng the numercal and expermental results t was determned that the numercal model s adequate. Ths model could be useful for cantlever type cuttng tools, when t s necessary to ncrease the qualty of the machnng surface by decreasng the ampltudes of the cuttng edge vbratons. Conclusons. numercal vbraton analyss by the FEM and experments were conducted of a tool holder of a turnng lathe. t was found that the decrease of the vbraton ampltude of the cantlever structure tool holder n the process of vbro-mpact moton can be sgnfcantly nfluenced by the locaton of the support. Ths s due to dynamc ntensfcaton of the hgher modes that ncreases the cantlever vbraton frequency and decreases the vbraton ampltudes.. By comparng the numercal and expermental results, t s concluded that the presented numercal model s adequate. Ths model could be useful for cantlever type cuttng tools, when t s necessary to ncrease the qualty of the machnng surface by decreasng the ampltudes of the cuttng edge vbratons. References. t-sghra K., El Badaoua M., Gulleta F., Drss boutajdnea D., Drona J-P. pplcaton of the cyclostatonarty for the cuttng tool dagnoss. Mechancs & ndustry, 5(), 4, pp Desforges X., Habbad., rchmede B. Machnng control and montorng. Robotcs and Computer-ntegrated Manufacturng, vol. 7,, pp

6 ENGNEERNG FOR RUR DEVEOPMENT Jelgava, Penga, Ch., Wanga,., T. Warren aob. new method for the predcton of chatter stablty lobes based on dynamc cuttng force smulaton model and support vector machne. Journal of Sound and Vbraton, vol 54, 5, pp Chena.Q., Zhangb G. C., Dngb H., nternal resonance n forced vbraton of coupled cantlevers subjected to magnetc nteracton. Journal of Sound and Vbraton, vol. 54, 5, pp Owolab G.M., Swamdas.S.J., Seshadr R. Crack Detecton n Beams Usng Changes n Frequences and mpltudes of Frequency Response Functons. Journal of Sound and Vbraton, vol. 5,, pp. -.. Ostasevcus V., Gadys R., Rmkevcenė J., Dauksevcus R. n approach based on tool mode control for surface roughness reducton n hgh-frequency vbraton cuttng. Journal of Sound and Vbraton, vol. 9,, pp Žlukas P., Barauskas R. Mechanna vrpesa (Mechancal vbratons). Vlnus: Pedagogno unversteto ledykla, 8. 4 p. (n thuanan). 8. Cook R. D., Malkus D. S., Plesha M. E., Wtt R., J. Concepts and applcatons of fnte element analyss.john Wley&sons, NC,. 79 p 9. Rao S. S. The fnte element method n engneerng. Fourth edton. New York: Elsever nc, 5. p.. Barauskas R., Belevčus R., Kačanauskas R. Bagtnų elementų metodo pagrnda (Basc of fnte element method). Vlnus: Technka, 4.- p. (n thuanan).. Turnng tools. General turnng. Cuttng tools from Sandvk Coromant, [onlne] [..]. valable at: