Journal of Power and Energy Engneerng, 2013, 1, 20-24 http://dx.do.org/10.4236/jpee.2013.17004 Publshed Onlne December 2013 (http://www.scrp.org/journal/jpee) Analyss of Dynamc Cross Response between Spndles n a Dual Spndle ype Mult-Functonal urnng Machne Y.. Cho 1, S.. Km 1,. Y. Seo 2, K.. Km 3 1 Department of Mechancal Engneerng, Changwon Natonal Unversty, Changwon, Korea; 2 Department of Mechancal Desgn Engneerng, Graduate School of Changwon Natonal Unversty, Changwon, Korea; 3 echnology Research Insttute, AMECO Co., Ltd., Korea. Emal: yhcho@changwon.ac.kr Receved October 2013 ABSRAC In order to meet ncreasng demand for hgher productvty and flexblty, recently many knds of mult-functonal machne tools, whch are capable of multple machnng functons or dfferent knds of machnng processes on one machne, have been developed and wdely used n manufacturng ndustres. In ths study, a mult-functonal turnng lathe, whch has two spndles and two turrets so that multple turnng operatons and varous machnng processes could be performed smultaneously, has been developed. Furthermore, the equatons of correlaton between whole responses and cross responses of the two spndles have been derved to examne to what extent the two spndles affect each other s vbratons. Keywords: Mult-Functonal Lathe; Mult-Spndles; Frequency Response; Cross Response; FEM Structural Analyss 1. Introducton In the last couple of decades, as the demands are ncreasng to produce machne parts wth hgher productvty and accuracy at reduced cost, many researches and developments on mult-functonal machne tools have been performed [1-5,10,11]. Nowadays mult-functonal machne tools are wdely used to machnng varous mechancal components n the aerospace, automoble, power plant ndustres and so on. Fgure 1 shows a bref hstory of the advancement n the confguraton of turnng center (C) [1]. And Fgure 2 shows typcal examples of machned parts as the functonalty of C was ncreased [3]. he machne tool shown n Fgure 3 s a mult-functonal turnng lathe under developng for machnng complex automotve parts. It conssts of 2 spndles and 2 turrets so that varous machnng process could be performed smultaneously. Regardng a mult-functonal turnng lathe that conssts of two spndles, the two spndles operatng smultaneously may affect each other because of nteractons between ther cuttng forces. hus resultng machnng accuracy may be worse than that of a sngle spndle only machnng. Vbraton s one of the domnant causes that most badly affect the machnng accuracy of machne tools [6, 7]. In order to examne how the two spndles affect each other s vbratons when they are operatng smultaneous- Fgure 1. Evoluton of turnng machnes (after. Morwak [1]). Fgure 2. Evoluton of parts machned by turnng machnes (after. Morwak [1]).
Analyss of Dynamc Cross Response between Spndles n a Dual Spndle ype Mult-Functonal urnng Machne Fgure 3. A mult-functonal turnng lathe for machnng automoble parts. ly, n ths study, the equatons of correlaton between whole responses and cross responses of the two spndles have been derved and FEM harmonc response analyss has been carred out of the mult-functonal turnng lathe. A generalzed machne structure model has been ntroduced for dervng the correlaton equatons. 2. Cross Response Analyss 2.1. A Generalzed Machne Model Analyss In order to derve the correlaton equaton between responses of at arbtrary two dfferent nodes on a machne structure acted on by exctaton forces, n ths study, a generalzed machne structure model s ntroduced as shown n Fgure 4. For the generalzed machne model of mult-degree-of-freedom (DOF) shown n Fgure 4, the dsplacement response, { D } due to the appled force vector, { F } can be determned from followng transfer functon relatonshp. { D} ( ω) F (1) [ ]{ } Where { } (, ) ( X,, X, ) D D1 D 2 1 1 1 2 2 2 s a dsplacement vector condensed on nodes 1 and 2, { F} ( F1, F2) ( F1 X, F1 Y, F1, F2 X, F2 Y, F2, ) s a appled force vector, [ 2 1 ( ω) ] ω [ M ] + ω[ C ] + [ K ] s a transfer functon, [ M ], [ C ], [ K] are mass, stffness, and equvalent vscous dampng coeffcent matrces, respectvely. And the symbol ω denotes angular frequency. Equaton (1) can be denoted as Equaton (2) by dentfyng nodal degree of freedom. D F 1 11 12 1 D2 22 F2 (2) Where, sub-matrces are defned as followngs. h11 h12 h13 11 h h22 h 23 (3-a) h31 h32 h 33 h14 h15 h16 12 h24 h25 h 26 (3-b) h34 h35 h 36 Fgure 4. A generalzed mult-dof machne structure model acted on by dynamc forces at two dfferent nodes. h41 h42 h43 h51 h52 h 53 (3-c) h61 h62 h 63 h44 h45 h46 22 h54 h55 h 56 (3-d) h64 h65 h 66 In Equatons (3-a)-(3-d), f the sub-matrces were assumed as dagonal matrces, whch seems to be ratonal assumpton n most mechancal structures of sotropc materals, the whole frequency responses at nodes 1 and 2 can be obtaned, respectvely as follows. X h F + h F X + X (4-a) 1 11 1X 14 2 X 11 12 Y h F + h F Y + Y (4-b) 1 22 1Y 25 2Y 11 12 h F + h F + (4-c) 1 33 1 36 2 11 12 X h F + h F X + X (4-d) 2 44 2 X 41 1X Y h F + h F Y + Y (4-e) 2 55 2Y 52 1Y h F + h F + (4-f) 2 66 2 63 1 Where, X1111, 11 and X2222, 22 are auto-responses that are X--, -responses at nodes 1 and 2, respectvely due to the forces appled to the same node. X12, 12 and X, are cross responses that are the dsplacements brought about at one node due to the assocated forces actng on the other node. Based upon the correlaton Equatons (4-a)-(4-f), the statc cross response to total response ratos (SCR) n the X--, -drectons are defned as follows, respectvely. X SCRX 1, 2 and j 2,1 X ω 0 Y SCRY 1, 2 and j 2,1 Y ω 0 SCR 1, 2 and j 2,1 ω 0 (5-a) (5-b) (5-c) Smlarly the dynamc cross response to total response ratos (DCR) n the X--, - drectons are defned as
22 Analyss of Dynamc Cross Response between Spndles n a Dual Spndle ype Mult-Functonal urnng Machne follows, respectvely. X DCRX 1,2 and j 2,1 X Y DCRY 1, 2 and j 2,1 Y DCR 1, 2 and j 2,1 (6-a) (6-b) (6-c) Where subscrpt means the peak resonance frequency where the mum harmonc response occurs. he percent SCR and the percent DCR can be obtaned from SCR and DCR multpled by 100, respectvely. 2.2. Cross Response Analyss between Spndles of a Mult-Functonal urnng Machne In order to obtan SCRs, DCRs, and percent SCRs, percent DCRs at the 1 st and 2 nd spndles of the mult-functonal lathe, FEM harmonc response analyss has been carred out. Fnte element model s presented n Fgure 5 and modelng data are lsted n the able 1. In case of the FEM model shown n Fgure 5 of the mult-functonal turnng lathe, node numbers, j correspond to the spndle numbers. Pror to ths FEM analyss, the multfunctonal turnng lathe shown n Fgure 5 had been optmzed for lghtweght and hgh rgdty [8,9,11]. As the result of FEM harmonc response analyss, harmonc frequency responses of the mult-functonal turnng lathe are obtaned; total responses ( X, ), au- to-responses ( X, ), and cross-responses ( X, ) at the -th spndle. he responses computed at each spndle are llustrated n Fgures 6 and 7. As seen from Fgures 6 and 7, t s apparent that almost all of both percent SCRs and percent DCRs are less than 5% except the 1 st spndle s percent DCR, whch s above 10%. As stated above, statc response means the response at the frequency ω 0 and dynamc response (peak response) desgnate the mum response among resonant peak responses. Appled the Equatons (5) and (6) wth the FEM harmonc analyss results, both the percent SCRs and the percent DCRs at the 1 st spndle have been determned and lsted n able 2. Smlarly, the percent SCRs and the percent DCRs at the 2 nd spndle also have been obtaned and summarzed n able 3. Fgure 5. FEM model of the mult-functonal lathe. able 1. Modelng data for FEM structural analyss. FEM modelng Materal property Appled force at each spndle Boundary condtons Element type No. of nodes No. of elements Shell 63 Beam 189 Combne 14 8839 9198 Materal Elastcty (GPa) Posson s rato Densty (kg/m 3 ) GC 300 98 0.25 7250 SM45C 205 0.29 7850 Drecton X-dr. Y-dr. -dr. Force (N) 225 750 75 Anchorng nodes at the bottom of the bed are fxed (a) In the X-drecton (b) In the Y-drecton (c) In the -drecton Fgure 6. Computed harmonc responses, auto- and cross-responses at the 1 st spndle.
Analyss of Dynamc Cross Response between Spndles n a Dual Spndle ype Mult-Functonal urnng Machne 23 (a) In the X-drecton (b) In the Y-drecton (c) In the -drecton Fgure 7. Computed harmonc responses, auto- and cross-responses at the 2 nd spndle. able 2. Percent cross response to total response ratos at the 1 st spndle. Percent Statc Cross Response to otal Response Rato, SCR (%) Percent Dynamc Cross Response to otal Response Rato, DCR (%) X-drecton, SCR X 12 Y-drecton, SCR Y12 -drecton, SCR 12 2.50 0.55 0.81 X-drecton, DCR X 12 Y-drecton, DCR Y12 -drecton, DCR 12 10.59 1.17 4.19 able 3. Percent cross response to total response ratos at the 2 nd spndle. Percent Statc Cross Response to otal Response Rato, SCR (%) Percent Dynamc Cross Response to otal Response Rato, DCR (%) 3. Results and Dscusson From the harmonc response analyss results as shown graphcally n Fgures 6 and 7 and the percent SCRs and DCRs summarzed n ables 2 and 3, the percent SCRs at both the 1 st and 2 nd spndle noses were less than 4%. owever the percent DCRs were around 4% - 7% at both spndle noses. Furthermore, the bggest percent DCR exceeds 10% even though the turnng lathe had been optmum desgned prevously. hus, careful consderaton should be gven to the effect of cross response on whole (or total) vbraton response at each spndle n order to develop or desgn mult-spndle type mult-functonal machne tools. 4. Concludng Remarks In order to analyze how the two spndles affect each other s vbratons n a dual spndle type mult-functonal turnng lathe when they are dong machnng operatons smultaneously, n ths study, a generalzed machne structure model under harmonc forces actng on two dfferent nodes has been ntroduced and the correlaton equatons of the structural responses at the two nodes have been derved. Furthermore, the derved correlaton equatons of the structural responses of the generalzed machne structure model have been appled to the dual spndle type mult-functonal turnng lathe. As the results wth FEM structural analyss of the turnng lathe, the percent SCR and the percent DCR of each spndle of the mult-functonal turnng lathe have been obtaned; Computed X-drecton, SCR X Y-drecton, SCR Y -drecton, SCR 2.37 3.52 3.60 X-drecton, DCR X Y-drecton, DCR Y -drecton, DCR 4.25 6.27 6.30 percent SCRs at both spndle noses are less than 4%, but most of computed percent DCRs are around 4% - 6.3% and the bggest one reaches about 10.6%. In concluson, careful consderaton should be gven to the effect of cross response on whole vbraton response at each spndle to develop hgh precson mult-spndle type machne tools. 5. Acknowledgements hs work was supported by the project Development of a two-spndle and two-turret mult-taskng lathe for a producton lne supportng the hgh precson processng for automoble small-parts (Grant S2071895) sponsored by the small and medum busness admnstraton Korea, and AMECO Co., Ltd. REFERENCES [1]. Morwak, Mult-Functonal Machne ool, CIRP Annals Manufacturng echnology, Vol. 57, 2008, pp. 736-749. [2] A. Nagae, Development rend of Mult-askng Machnes, Proceedngs of the 11 th Internatonal Conference on Machne ool Engneers, 2004, pp. 312-323. [3] M. Nakamnam,. okuma, M. Morwak and K. Nakamoto, Optmal Structure Desgn Methodology for Compound Multaxs Machne ools, I Analyss of Requrements and Specfcatons, Internatonal Journal of Automaton echnology, Vol. 1, No. 2, 2007, pp. 78-86. [4] M. Nakamnam,. okuma, K. Matsumoto, S. Sakashta,
24 Analyss of Dynamc Cross Response between Spndles n a Dual Spndle ype Mult-Functonal urnng Machne. Morwak and K. Nakamoto, Optmal Structure Desgn Methodology for Compound Multaxs Machne ools; II Investgaton of Basc Structure, Internatonal Journal of Automaton echnology, Vol. 1, No. 2, 2007, pp. 87-93. [5] Y.. Cho, S.. Jang,. M. Park, S. J. Jang and J. Y. Cho, A Genetc Algorthm Based Mult-Step Desgn Optmzaton of a Machne Structure for Mnmum Weght and Complance, Proceedng of SICE, 2005, pp. 476-481. [6] U. esel and M. Grngel, Machne ool Desgn Requrements for gh-speed Machnng, Annals of the CIRP, Vol. 45, No. 1, 1996, pp. 389-392. http://dx.do.org/10.1016/s0007-8506(07)63087-x [7] U. esel and A. Fenauer, Dynamc Influence on Workpece Qualty n gh Speed Mllng, Annals of the CIRP, Vol. 48, No. 1, 1999, pp. 3-324. http://dx.do.org/10.1016/s0007-8506(07)63193-x [8] S.. Jang, J.. Oh,. S. An and Y.. Cho, Mult- Objectve Structural Optmzaton of a Pn urnng Devce by Usng ybrd Optmzaton Algorthm, Proceedngs of the Internatonal Conference of Manufacturng echnology Engneers, Seoul, Korea, 2012. p. 73. [9] S.. Jang, W. Y. Jeong, B. C. Kwon and Y.. Cho, A Study on the Statc Optmzaton of Mult-Axs Mllng Machne Usng MSA, Proceedngs of KSPE 2009 Annual Sprng Conference, 2009, pp. 227-228. [10] S.. Jang.. Cho and J. S. a, A Study on Analyss of Dynamc Complance of a 5-Axs Mult-taskng Machne ool by Usng F.E.M and Excter est, ransacton of the Korean Socety of Machne ool Engneers, Vol. 18, No. 2, 2009, pp. 162-169. [11] Y.. Cho, J.. Oh, D.. Km,. Y. Seo and K.. Km, Structural Desgn Optmzaton of a 2-Spndle 2- urret ype Mult-taskng Lathe, Proceedngs of KSME 2013 Annual Sprng Conference, Jeju, Korea, 2013, pp. 535-536.