Dynamic Analysis Based On ANSYS of Turning and Grinding Compound Machine Spindle Box Zanhui Shu and Qiushi Han

Transcription

1 Advanced Materals Research Onlne: ISSN: , Vols , pp do: / Trans Tech Publcatons, Swtzerland Dynamc Analyss Based On ANSYS of Turnng and Grndng Compound Machne Spndle Box Zanhu Shu and Qush Han School of Mechancal and Electrcal Engneerng, Bejng Informaton Scence & Technology Unversty, Bejng, Chna E-mal: Keywords: FEM; dynamc characterstcs; modal analyss; harmonc response analyss Abstract. Wth constant development of machne tools toward the drecton of hgh speed, hgh precson, hgh effcency and hgh compound rapdly. The performance of hgh-speed machne tools s affected by the dynamc characterstc of machne tools n the very great degree. More and more attenton s played to them and hgher and hgher demands are proposed. Fnte element method s a knd of fast and effcent auxlary tools n modern engneerng analyss and desgn. Three-dmensonal fnte element model of spndle box s establshed n ths paper based on large fnte element analyss software ANSYS. Through modal analyss, the frst fve order natural frequency, vbraton mode and varous order vbratng modal characterstcs are obtaned. These results are verfed by usng the method of expermental modal. Harmonc response analyss s carred after dong modal analyss on spndle box. Response and stress under dfferent frequency are obtaned. Contnuous dynamc characterstcs are forecasted. Introducton The hgher requests of CNC machne tools desgn and manufacturng putted forward wth CNC machne tools are headng n the drecton of hgh speed, hgh precson and hgh effcency, composte, ntellgent and envronmental protecton rapdly[1]. Because of precson grndng and rough turnng, hgh-precson and hgh effcency are requred for turnng-grndng compound machnng. Therefore, the hgher requests of statc and dynamc characterstcs of the spndle box components are putted forward. The key components of turnng-grndng compound machnng are spndle box. Chuck and work pece are nstalled n ts front department partcpatng n cuttng or grndng drectly [2]. Its performance effects machnng performance greatly especally n low order natural frequency and endpont dynamc soft degree. Vbraton of work pece spndle box s produced by grndng, turnng and nternal ncentve other equpment. Bend and torson resonances can be produced f some unreasonable structural desgned. Severe bendng deformaton, torson of spndle box and grndng wheel frame structures are caused. Fatgue damage of local structural s made. Roughness and accuracy of grndng work pece surface s reduced [3]. WangFeYue analyses the types of machne tools vbraton and vbraton sources, then ponted out the major ndexes of the dynamc characterstcs of the machne tool. Through contrast the dynamc and statc stffness, measures mprovng machne dynamc stffness s obtaned [4]. The mode analyss of machne tool spndle s conducted by LuXuLan through fnte element method. Dynamc stffness of machne tool spndle s analyzed systematcally provdng theory bass for the dynamc desgn [5]. Theoretcal modal analyss of work pece spndle box of turnng-grndng compound machnng s calculated n ths paper usng ANSYS analyss software. Low-order mode frequency and modal shape of work pece spndle box of turnng-grndng compound machne s acqured. Harmonc response analyss s conducted based on modal analyss. Response and stress of spndle box n dfferent frequency. Contnuous dynamc characterstcs of spndle box are predcted.. All rghts reserved. No part of contents of ths paper may be reproduced or transmtted n any form or by any means wthout the wrtten permsson of Trans Tech Publcatons, (ID: , Pennsylvana State Unversty, Unversty Park, USA-06/03/16,02:57:16)

2 Advanced Materals Research Vols Modal Analyss and Theory For mult-freedom system, usng matrx analyss method and fnte element method of elastc mechancs can get spndle box of general moton dfferental equaton for [6]: M X + C X + KX = F (1) Among them, M, C, K separately ndcate system of qualty, dampng and stffness matrx ( N N matrx); X, F ndcate dsplacement response and exctng force vector of each pont poston of system; Ẋ, X.. ndcate velocty and acceleraton. It can be turned to the flow form, for the lnear system: { X} = { φ} cosϖ t { φ } s the frst order natural frequency of vbraton model functon; ϖ s the frst order natural crcular frequences. (2) substtuted n (1). ϖ { φ} { } 2 ( [ M ] + [ K]) = 0 To enable the type holds, then there are two possble: { φ } = { 0} or ϖ 2 [ ] [ ] 0 M + K =. There s not practcal sgnfcance for the former soluton obvously, so: (2) (3) ϖ 2 [ M ] + [ K] = 0 (4)s system characterstc equaton,whch can be wrtten: (4) k ω m k ω m k ω m n 1n ω ω 22 2n ω 2n k m k m k m k ω m k ω m k ω m n1 n1 n2 n2 nn nn 2 (5) s solved for n solutons. If λ = ϖ, several expressons of characterstc values λ are solved. λ[ M ] + [ K] = 0 In (6), [M] - mass matrx, s total matrx of dvson all qualty unt, [K] - s total matrx of ϖ dvson element stffness. The relatonal expresson of Frequency and crcular frequences f = 2π are obtaned by transformaton formula n the output. The natural frequency of spndle box s acqured [7]. Because of the bolts connected of spndle box and the base, exertng constrants n modal analyss, X, Z's dsplacement of the center holes poston s lmted. Spndle box s used to nstall the spndle. The anchorage force of spndle t to support n analyss can be smplfed as two central concentrated load. = 0 (5) (6) Harmonc Response Analyss and Theory There wll be a perodc exctng force (cuttng force) exerted on the spndle box durng workng of the machne tool. When a frequency of exctng force s equvalent to the natural frequency of the spndle box, the spndle box wll resonate. Ths condton wll not only reduce the processng precson of cuttng but also damage the spndle box. Therefore t s sgnfcant to study the dynamc response of the spndle box. Harmonc analyss s conducted followng mode analyss. The modelng process of harmonc response s same as the process of mode analyss. Harmonc response analyss s structural technology to determne the response of structure under the nfluence of known load whose frequency changes by sne (harmonc) regular over tme. To conduct harmonc response analyss, the load changes by sne regular over tme must frst be defned,

3 526 Materals Scence and Informaton Technology whch s also to determned exctaton force. A complete exctaton force s composed of ampltude, ntal phase, and forced vbraton frequency. It s F( t) = f cos( ωt + ϕ).in ths equaton, f, ω, ϕ s respectvely exctaton force ampltude, forced vbraton frequency and ntal phase Angle. Soluton can be made by FULL,Reduced and Mode Superposton[8]. For harmonc analyss, plural response { x1} and{ x 2} can be obtaned soluton from the matrx equaton. 2 ( Ω [ M ] + jω [ C] + [ K]){ x1 + jx2} = { F1 + jf2 } Hypothess [M], [C], [K] wth constant. Materals are supposed as small deformaton of lnear elastc hypothess, not exstng nonlnear dampng matrx contans [C]. Response wll be nfnte, f stmulatng frequency Ω and the structure nherent frequency omega s the same. Although there are phase n exstence, but load {F} and response {x}) s stll accordng to the frequency Ω makng sne changes gven. Vbraton force comes from cuttng force or grndng force, to turnng grndng compound machne. Generally speakng, cuttng force s large whle and grndng force s hgh frequency. In the analyss, take cuttng force as exctaton force ampltude and frequency of grndng force as the exctaton frequency. Durng the process of analyss, exctng force frequency range s 0 ~ 800HZ selected, consderng of the spndle box low-order fundamental frequency and harmoncs comprehensvely. A total of 80 groups selected force s analyzed takng a each 10HZ force. Establshment of the Analytcal Model Showng as Fg.1, machne s composed of by servo motorzed spndle, grndng head, turnnggrndng operatng platform, tool holder, X axs, talstock, and Z axs and lathe bed. Machne s conssted of four CNC shafts, whch s C axs, the X axs, Z axs and B axs. X axs s drven by lnear motor, whle C axs, X axs and Z axs are drven by rotatng motor. The spndle box of machne s shown as Fg.2. (7) Fg.1 Structure of machne tools Fg.2 Spndle box of machne tools Fg.3 Spndle box 3d model and fnte element mesh model

4 Advanced Materals Research Vols The spndle box of the three-dmensonal entty modelng s establshed usng Pro/e software n ths paper, shown as Fg.3.Determnng the number of classfcaton fnte element s the key factors of establshng fnte element model. to one of, relatonshp to solvng the computaton The precson speed and expenses etc of calculaton are related to the unts quantty. In fact, t s not the more unts number the hgher calculaton accuracy, especally for dynamc calculaton. The effect of some holes and chamferng, convex platform and small characterstcs of parts was small to the dynamc characterstcs. Small characterstcs of spndle box are overlooked accordng to the holy dmenson south prncple dong fnte element model. Because the ntensty and rgdty were affected by spndle hole much, spndle hole and spndle box were consdered together when modelng. The overall sze of spndle box s 520mm 320mm 580mm, whose materal s HT200, modulus of elastcty s 2.07E11, Posson rato s 0.3 and densty scale s 7.8E3. The threedmensonal entty model s mported nto ANSYS usng generc nterface. Mesh the model usng sutable to ts structural 10 node sold92 unts selected gettng the spndle box fnte model s shown n fgure nodes and unts are obtaned by ntellgent meshng. Smulaton Results and Analyss Modal Analyss Results. Spndle box modal analyss s solved usng Lanczos method n ths paper. Due to low modes of the modal analyss has great nfluence on vbraton system, frst order frequency of fnte element model s solved usually n order to satsfy the requrements of analyss. For the model analyss, fve model extracton methods are gven n the analyss process of ANSYS as follows: Block Lanczos, Subspace, Power Dynamcs, Reduced, Asymmetrc and Damped [9]. Through a comprehensve analyss for characterstcs of a varety of extracton methods, Block Lanczos s used to analyze the spndle box because ts convergence rate s much hgher than Subspace and ts accuracy meets the requrements too[10]. The process to use an analyss model of ANSYS ncludes four steps: modelng, Loadng and Soluton, expanson mode, and post-processng. The frst fve modes of vbraton system cabnet are solved n analyss, gettng natural frequency and the ampltude. Modal analyss results such shows as table1; correspondng vbraton model and the stress cloud shown n fgure 5. Accordng to Table1 when the frst-order natural frequency s Hz, the crtcal rotatng speed reaches to 11286r/mn, much hgher than the maxmum rotatng speed of 2400r/mn to the spndle. The result shows that the spndle box desgned n ths paper can be avoded n the crtcal rotatng speed. In addton, n order to guarantee the dynamc performance durng workng, the maxmum rotatng speed of the spndle n work condton should not exceed 75% of the frst order crtcal rotatng speed. From Table 1, the maxmum rotatng speed of the spndle desgned should be less than 8465r/mn (11286*75%=8465r/mn). The maxmum rotatng speed of the spndle desgned n ths paper s 2400r/mn; far less than 75% of the frst-order crtcal rotatng speed, therefore the spndle box can avod the resonance areas effectvely even f t works n the maxmum rotatng speed. Table 1 Frequency of each order Order Frequency(HZ)

5 528 Materals Scence and Informaton Technology Fg.5 The frst three order modes deformaton Fg.6 The frst three order stress cloud Fg.7 Harmonc response stress cloud fgure Fg.8 Harmonc response stran fgure Fg.9 Z axs harmonc response dsplacement frequency curve Fg.10 Y axs harmonc response dsplacement frequency curve Harmonc response analyss results. Forced vbraton of frequency range for (100 ~ 8) Hz, the load fashon of phase step and modal superposton method are adopted n ths paper. The dynamc response of box s acqured. The dsplacement response cloud of harmonc response of spndle, deformaton fgure and dsplacement frequency of harmonc response are obtaned takng a node on the edge of spndle hole. They are shown as fgure 6 ~ 9 below. 1. The dynamc response of some pont of the spndle box at the Z drecton shown as n fgure 8 under the acton of Z drecton harmonc exctaton force. Seeng from fgure 8, ampltude has obvous peak near the frst order natural frequency (frequency Hz) under the acton of Z axs exctaton force to spndle box. The dynamc dsplacement of Z axs to s about mm. Known from the modal analyss of deformaton fgure, the frst mode s noddng acton of Z axs of spndle box. Dynamc dsplacement of Z s the largest happenng stmulated vbratng under the acton of Z exctaton force. 2. The dynamc response of some pont of the spndle box at the X drecton shown as n fgure 9 under the acton of Z drecton harmonc exctaton force. Seeng from fgure 9, ampltude has obvous peak near the frst order natural frequency (frequency Hz) under the acton of X axs exctaton force to spndle box. The dynamc dsplacement of X axs to s about mm. Known from the modal analyss of deformaton fgure, the frst mode s noddng acton of X axs of spndle box. Dynamc dsplacement of X s the largest happenng stmulated vbratng under the acton of X exctaton force.

6 Advanced Materals Research Vols Summary Structure, materal characterstcs, boundary condtons and bearng of the turnng-grndng compound CNC machne tool of spndle box are analyzed n ths paper. The three-dmensonal entty model and fnte element model of spndle box s establshed. The models of mode analyss and harmonc response are developed wth FEM for the axs of motorzed spndle, and the smulatons are conducted usng ANSYS commercal software for the models. (1) The results of mode analyss show that the frst-order natural frequency of the axs of the motorzed spndle s Hz, the frst-order crtcal rotatng speed of the spndle shaft s 11286r/mn whch s away from the maxmum rotatng speed of the spndle 2400r/mn. (2) Inferred from harmonc response curve peak of correspondng frequency, the frst fve orders natural frequency extracted from modal analyss are correct and resstance capacty of outsde resonance of spndle box s relatvely strong. (3) Because the frst order natural frequency spndle box s hgher away from the frequency of outsde exctaton force of normal processng and each order natural frequency values dffer much, generally spndle box wll not occur resonance n normal condtons. (4) Harmonc response s essentally forced vbraton. Through a seres of approprate exctaton force smulaton, the nherent frequency of structure tself can be found. The bass for the judgment of the accuracy of modal analyss results s provded. (5) Theoretcal bass for desgnng s provded by usng ANSYS to conduct modal analyss and harmonc response for machne tool. Calculaton accuracy s mproved and desgn cycle s shortened. Acknowledgment Ths research was supported by the project of the muncpal educaton commsson technology development plan of Bejng of Chna (No. KZ ). References [1] Jn Kyung Cho, and Da Gl Lee, Thermal characterstcs of the spndle bearng system wth a gear located on the bearng span, Internatonal Journal of Machne Tool & Manufacture Pergamon, 1998, pp [2] XnaSun,QushHan, ZhanxYang, The development stuaton of turnng-grndng compound machne and key technology, Precson Manufacturng and Automaton, 2008, (1) : [3] YouhaWang, HujunYan, ChangshengHu, Large fnte element analyss software ANSYS characterstcs,journal of Constructon Machnery, 2000, (9) : [4] WangFeYue, The dynamc characterstc analyss tool,hebe Industral Technology, 2001,18 (4). [5] LuXuLan, CNC machne tool spndle dynamc stffness propertes of study and test, Coal Mne Machnery,2008,29 (7). [6] NanYang, HengLngTang, BoYuLao, Machne dynamcs (I),New Machnery Industry Press. 1983,5:3 ~ 1 7. [7] NaXongZhu, Machne dynamc desgn prncple and applcaton [M].Shangha,Tongj Unversty Press, [8] YDu, MSY7115 Flat Grnder Expermental Modal Analyss and the Dynamc Characterstcs Modfy. Kunmng Polytechnc Learn, 2002,3:1 ~ 2.. [9] Mostaka.Yoshmeura.Analyss and optmzaton of Structural Dynamcs of Machne Tool by a Synthess of Dynamc Rgdty Program System.MTDR,16th,1975:201~203 [10] MnShu, HongRongJng, Hgh-speed mllng spndle box fnte element analyss and optmzaton desgn,journal of Chnese Manufacturng's Informatzaton, 2006 (9) : 34 ~ 36..

7 Materals Scence and Informaton Technology / Dynamc Analyss Based on ANSYS of Turnng and Grndng Compound Machne Spndle Box /