Numerical and Experimental Approach for Roll Grinding Process

Transcription

1 Numerical ad Experimetal Approach for Roll Gridig Process Lihog Yua, Veli-Matti Järvepää, Seppo Virtae ad Hessam K. Shiravai Departmet of Egieerig Desig Tampere Uiversity of Techology P.O.BOX 589, 330 Tampere, Filad {lihog.yua, veli-matti.jarvepaa, seppo.virtae, Abstract This paper presets a study of a vibratio problem i a roll gridig machie. The rollig cotact betwee a metal roll ad the gridstoe may cause the patter formatio o the roll surface durig the gridig operatio. A self-excited vibratio excitatio or so-called regeerative chatter excitatio is preset i the process. The chatter vibratios are described by a mathematic model icludig time delay effects. The umerical results of frequecy resposes are illustrated ad they are cosistet with the o-site measuremets i a workshop of a roll factory. Itroductio I paper machie idustry, a roll gridig machie is used to fiish or maitai roll surface. Excellet surface fiish should be homogeous oe with silky shee, free of scratches ad ay other blemishes. Precisio roll provides more efficiet roll operatio ad better paper quality. To uderstad the dyamic behaviour of gridig machie towards these aspects is very importat. A typical gridig machie cosists of work piece-roll (metal) ad gridig wheel (stoe) which keep cotact iteractio durig the process. The cotact vibratio problem of such kid of system is studied i this work. I order to esure the fiishig the etire surface of o roll, techically there are always overlaps betwee the revolutio paths related the width of the gridig wheel. Therefore the retard effect may cause vibratio ad the cosequece is the geeratio of patter formatio occurred o the surface of the roll (Figure ). Figure : Patter deformatio geerated o the roll surface with overlap. I this roll gridig process, there are additioal time delay effects, which are origiated from the overlap of the gridig path o the surface of the roll (the work piece) groud by a cylidrical gridstoe. Geerally, the gridig system may be ustable due to the delay effect ad this chatter growth rate problem has bee

2 aalyses widely i literature [-9]. The gridstoe s rotatioal speed is high ad the roll is rotatig very slowly due to the requiremets of the fiishig process. The cotact zoe betwee the roll ad the gridstoe is assumed as a isigificatly small area. I the mathematic model, the roll is described as a simply supported cotiuous beam elemet expressed i a eigevector basis ad i a rotatig coordiate frame. The cotact betwee the roll ad the gridstoe is described by cotact dyamics formulatio ad the ormal ad tagetial forces of the cotact are based o the wear theory. I this work, the double delays will be ivolved i the model. Based o the above cosideratios a experimet is set up o a gridig machie of a real factory. The resposes of a idustrial roll gridig machie are measured by usig Pietzo-electric displacemet sesors, rotatio speed laser ad accelerometers. The correspodig results should verify the simulatio oes i tolerace rages. This provides a more precise view to observe the dyamic behavior of the system ad suggest ways to cotrol the whole process i order to miimize chatter s detrimetal effects. The mai objectives of this work are to detect ucotrollable situatios, idetify causes, determie process limits ad suggest reasoable actios i order to cotrol ad optimize the system. I this work, measuremets ad dyamical aalysis of the gridig process of paper machie rolls are studied. The measuremets have bee carried out i real factory workshop with various rotatig speed. A mathematic model describig this system is illustrated. Numerical ad experimetal results will be give. The effects from the parameters of iterest i rollig cotact will be discussed. Formulatio of Problem The vibratio problem i the gridig machie ca be modeled as a lumped sprig-mass system as i Figure. The double time delays from both roll ad grider are also cosidered [0-].The equatios of motio of the dyamic system are give by, m x c x ( ) x ( t ) x m x c x k x ( ) x ( t ) x k x k ( t k ( t ( ) om x x x ( t ) x( t ) ) ( ) om x x x( t ) x( t ) ) () () The coefficiet k is cotact stiffess. The time delay, are related to the rotatio speed of the roll ad gridig stoe. The overlap rate of gridig path is i percetage. The coefficiet idicates the elasticity of materials betwee the cotact surfaces. The coefficiet om is omial cuttig depth. Workpiece. k k k N. Gridstoe m m F N c x() t x() t Figure : Equivalet sprig-mass system. c 3 Methods ad aalysis Firstly, the respose i frequecy domai ca be obtaied; secodly the clasical stability theory ca be carried out i a simplified model. 3. Frequecy respose

3 The frequecy respose of the system ca be obtaied by addig excitatio force. The steady state solutios i matrix take the form X X ic k om (3) where m 0 0 c 0 k B A m, C, 0 c A k B ad where i A k k e k ( ) e i i B k k e k ( ) e i 3. Classical stability aalysis For simplicity, the motio of the roll is oly cosidered. The model with oe-degree freedom ca be writte as m x c x k k ) x k x ( t ) 0 (4) ( Performig variable trasformatio equatio is obtaied t ad Laplace trasform, the correspodig characteristic s s m sc ( k k ) k e 0 (5) Substitutig the characteristic complex roots s j ito above (5), ad let both real ad imagiary parts of the equatio be zero. Based o cotrol theory, we kow that whe the real part is positive 0, the system is ustable; it is egative, the system is stable. Moreover, the imagiary part is related with the wave umber of the patter deformatio geerated o the surface of the work piece [3]. 4 Measuremet set up The physical model of the roll gridig system measuremets[4] is illustrated i Figure. For the roll there are two types of sesors: two laser sesors ad two iductive displacemet sesors; all of these are o the sledge of the gridstoe, movig horizotally alog the roll durig gridig. The first laser sesor is a socalled Doppler velocity laser (LDV) ad it measures the horizotal velocity of the cross-sectio of the roll. The secod laser measures the vertical displacemet of the cross-sectio (V-directio). The iductive sesors measure the displacemets i the same directios as the lasers. At the ed of the roll there are two types of sesors for measurig the rotatioal speed of the roll: oe is a pulse sesor ad the other oe is a wheel sesor. For the gridstoe, oe pulse rotatioal speed sesor is located at ed of the drive. Oe accelerometer is o the sledge of the gridstoe the i U-directio. All the electrical sigals from the sesors go ito correspodig amplifiers ad oscilloscopes ad fially are iput ito a computer. The computer displays the measuremet data ad additioal aalysis ad data processig ca be carried out after the measuremets are fiished. 3

4 The whole machiig process was performed as ormal cuttig. The operator is able to adjust the speed of the gridstoe, workpiece roll, ad cuttig feed of the stoe i order to excite the roll durig measuremets. Figure 4 illustrates oe 3-D plot with the respose i time ad frequecy domais. There are two resoace frequecies about 3Hz ad.5 Hz. Figure 3: Measuremet illustratio of gridig machie Figure 4: Respose i time- ad frequecy- domai 4

5 5 Numerical results The simulatios have bee carried out by Mathcad programmig. The umerical results based o parameter values i Table are illustrated i followig text. The relevat observatios have bee discovered. Parameter m c k m c k k r Value x x x Uit kg Ns/m N/m kg Ns/m N/m N/m Table : Parameter values of gridig system for the computatios The frequecy resposes are computed accordig to the equatios (3). The umerical results are i figure5. The amplitude of the stoe with much less mass is much bigger tha the oe of the roll. Both cases (up ad dow) have two reouces at about 3. Hz ad.39 Hz, which is cosistet with the measuremet i figure 4. The case (dow) has satellite beak due to the time delays. The time delay from roll is s; the other oe from grider is 0.s X( ) X( ) X( ) X( ) Figure 5: Frequecy respose without time delays (up); frequecy respose with time delays (dow). 5

6 The stability aalysis is calculated from equatio (5). I Figure 6 whe real part is positive the the system should be stable; whe real part is egative it becomes ustable. The the stability regios are alteratively chagig stable ad ustable with excitatio frequecy. Furthermore because the imagiary part is related with the umber of the patter deformatio of the roll surface, we ca judge how the wave umber is movig with the excitatio frequecy Real( ) Imag( ) Figure 6: Real part of characteristic root versus rotatig agular velocity of stoe (up); Imagie part of characteristic root versus rotatig agular velocity of stoe (dow). 6 Coclusios The measuremet i the workshop has bee successfully carried out ad the results are illustrated with reouce frequecies. The frequecy resposes of umerical aalyses are obtaied ad cosistet with the measuremet results. Moreover the stability aalysis has bee give i a oe-degree case. The patter deformatio o the roll surface ca be more deeply ivestigated i the future work. Subsequetly this study provides the guidace for further desig of suppressio ad cotrol the vibratio for gridig machie. Ackowledgmets This work is fiacially supported by Academy of Filad. 6

7 Refereces [] I. Iasaki, B. Karpuschewski, H.S. Lee, Gridig Chatter-Origi ad Suppressio, CIRP Aals-Maufacturig Techology, ScieceDirect, Vol. 50, Issue, 00. [] J.F.G. Oliverira, E.J. Silva, C. Guo, F. Hashimoto, Idustrial Challeges i Gridig, CIRPAals-Maufacturig Techology, 58(009) , Elsevier. [3] G. Stepa, Modellig Noliear Regeerative Effects i Metal Cuttig, Philos. Tras. Royal Soc. Lodo A, Vol.8 No.4., 00. [4] Y. Altitas, M. Wech, Chatter Stability of Metal Cuttig ad Gridig, CIRP Aals- Maufacturig Techology, Vol. 53,Issue, 004, Elsevier. [5] Y.Altitas, M. Eyia, H. Oozuka, Idetificatio of Dyamic Cuttig Force Coefficiets ad Chatter Stability with Process Dampig, CIRP Aals-Maufacturig Techology, 57(008)37-374, Elsevier. [6] J. Gradisek, A. Baus, E. Govekar, F. Klocke,I. Grabec, Automatic chatter detectio i Gridig, Iteratioal Joual of Machie Tools ad Maufacture, Vol. 43,Issue 4, 003. [7] E. Govekar, A. Baus, J. Gradisek, F.Klocke, I. Grabec, A New Method for Chatter Detectio i Gridig, Iteratioal Joural of Machie Tools ad Maufacture, Vol. 4, Issue 5, 00. [8] B.I. Eprueau, E.H. Dowell ad F. M. Motoya, Patter formatio ad liear stability aalysis i cetreless gridig, Proceesid of istitutio of Mechaical Egieers,PartB: joual of Egieerig Maufacture, Sage, Vol, 997,. [9] A. Sueoka, T. Ryu, M. Yoshikawa, M. Kodou, T. Tsuda, Patter Formatio Geerated i a Wider System of Tactile Machie, JSME iteratioal joural, Series C, Vol.4, No.3, 998. [0] R.A. Thompso, O the Double Regeerative Stability of Grider: the theory of Chatter Growth, Joual of Egieerig for Idustry, Vol.08/75, 986. [] L. Yua, Aalysis of Delay Pheomea i Roll Dyamics, doctor thesis, TUT, 00. [] L.Yua, E.Keskie ad V.M. Järvepää, Stability Aalysis of Roll Gridig System with Double Time Delay Effects, IUTAM Symposium o Vibratio Cotrol of Noliear Mechaisms ad Structures, edited by H. Ulbrich, Spriger, 005. [3] A. Karttue, V.H. Raimo, Stability Aalysis of Rotatig Nipped Rolls with Memory, proceedig of the 0 th Fiish Mechaics DAYS, 009. [4] A. S. Kobayashi, Hadbook o Experimetal mechaics, VCH publishers, Ic.,