DETERMINING THE MAXIMUM SPEED BORNE BY THE ELASTIC STRUCTURE OF A MACHINE TOOL, PREVIONSTY ITS REMANUFACTURING

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1 THE ITERATIOAL COFERECE OF THE CARPATHIA EURO-REGIO SPECIALISTS I IDUSTRIAL SYSTEMS 7 th EDITIO DETERMIIG THE MAXIMUM SPEED BORE BY THE ELASTIC STRUCTURE OF A MACHIE TOOL, PREVIOSTY ITS REMAUFACTURIG Din DARABĂ, Constantin DOGARIU, Dorel Florea Anania Assoiate Letrer Eng. and Eonomist orth Uniersity of Baia Mare, 6A Dr. V. Babeş street, Romania Professor PHd. eng. Uniersity POLITEHICA of Bharest, Letrer PHd. Uniersity POLITEHICA of Bharest splail independentei. ddin_dmd@yahoo.om dogari@gamil.om, dorel.anania@yahoo.om. Abstrat: The finite element method is a nmerial method sed for soling the omplex isses of engineering.. The method omprises of disreting the ontinos enironment throgh assemble of finite elements, whih interat between them in a finite nmber of nodes. The interating fores of the nodes of the model haraterize the ations of the interior fores or stresses that are applied pon the ontors of the neighboring elements. Key words: finit elements method, remanfatring, modal analyses, ibration models. ITRODUCTIO The finite elements method omprises of replaing the real strtre (ontinos) with an ideal strtre (not ontinos), diided or disreted into smaller sbsets named finite elements. The ontinos adane in ompters tehnology paed the way for simlating the different omponents in exploitation mode, ths onrring to the dereasing or een totally eliminating the neessary osts of the prototypes maing and researh. The finite element method is a nmerial method sed for soling the omplex isses of engineering. This method was applied for the first time more than 5 years ago and it was ontinosly deeloped, so today it is onsidered to be one of the best methods of effiiently soling a large ariety of pratial isses..work STAGES The method omprises of disreting the ontinos enironment throgh assemble of finite elements, whih interat between them in a finite nmber of nodes. The interating fores of the nodes of the model haraterize the ations of the interior fores or stresses that are applied pon the ontors of the neighboring elements. So, allating of a strength element whih is onsidered as a ontinos enironment with an infinite nmber of onnetions has been reded to allating of a system with a finite nmber of onnetions or degrees of freedom. Disreting the strtres an be arried ot with linear, plane or spatial finite elements. The strtres analysis imposes sing two systems of referene []: One system whih is assoiated to the strtre named global system in whih the position is defined and its moements are determined; One system whih is assoiated to eah element named loal system.

2 One of the nown oordinate systems: Cartesian, ylindrial or spherial, an be hosen as systems of referene. Finite elements of sare linear type, stressed within the loal plane (, ), with two degrees of freedom on eery node were sed, in order to disrete the analyzed strtre. The approximation fntion of moements (,) is as it follows []: O (.) The interpolation fntions sed in the alls hae the following form []: for node D; for node C; (.) for node B; for node A. It is nown that: The geometry of the strtre of the FUS 5 milling mahine was arried ot sing a CAD program; afterwards it was disreted sing sare type finite elements. The model presented in Fig. is prepared for the finite elements analysis, after imposing the onditions of stress and spport. The ibration modes of strtres an be ibration modes for rigid bodies and ibration modes for elasti bodies. All strtres an hae the six ibration modes of the rigid solid: three translations and three rotations. Assming that the analyzed strtre is positioned on elasti elements, then the displaement is approximated with a rigid solid mode. Fig.. The disreted geometri model

3 Fig. shows the onditions of fastening and stress for the analysis of the strtre behaior to stati stress (the fore F = 598 has its appliation point on the ase of the main shaft, and the fore that ations on the mahine table has the ale of F = ). The strtre is freed from bonds, in the finite elements modal analyses. The first six own freenies, relatie to the six degrees of freedom of the strtre (three translations and three rotations) are not taen into aont. The strtre analysis begins from the 7 th own freeny. Fig.. Mode of fastening and stress The first own freenies obtained by theoreti analysis are low. For example, the freeny of.6 Hz, aording to Fig., is a false freeny that an be orreted by stiffening the table spport, as from the analysis it is fond that the table spport an be broen at this freeny. The. Hz own ibration, Fig. leads the mahine tool to a resonane state that ontribtes to displaements of the mahine strtre elements, seerely affeting the proessing aray. A rotation of the mahine body and table arond the Z axis bt in ontrary diretions is noted in Fig., leading to the modifiation of the position of the tool against the proessed part. Fig..Moements of the strtre by f =,6 Hz Fig.. Moements of the strtre by = Hz

4 The own mode presented in Fig.5 at the freeny of,8 Hz mars ot a bending of the mahine body and table within the X-Z plane, atastrophially affeting the tool-part position. The theoretial freeny obtained by modal FEM analysis were alidate by experimental data aisition (fig.6) with a Shen Vibroport (fig.7) [5] from the ational Researh Centre for Performanes of Tehnologial Systems Optimm ( Fig.5. Moements of the strtre by f = Hz. Fig.6. Transfer fntion experimental data aisition Fig.7. Vibroport

5 The resonane danger does not appear anymore from the Hz own freeny of the analyzed strtre, as the sbseent freenies are off the domain of the wor freenies. In the iew of this analyses, it an be asserted that the own freeny that imposes the maximm ale of the remanfatred mahine speed is Hz. The relation (.6) is sed for the allation of the maximm speed that an be attained after the remanfatring proess, ths[]: rad s Hz rot / min (..) 6 / Assming that the proessing speed is: 6 a / mm/ min rot / min f mm / rot rad / s f mm rot (..) Maing the redtion, it reslts that : 6 rot / min rad / s (.5.) Bt: f, then: 6 f [re/min] (.6) Ths the maximm speed will be 67 re/ min..coclusios In order to set p a methodology of assessing the dynami performanes of the remanfatred mahine tools, preiosly from ommening their remanfatring, we hose a milling mahine for the theoreti researh, as the milling proess is a proedre of generating the srfaes, whih is highly generating fored ibrations. The dynami aspets met by the milling mahines an be onsidered as oering for most of the mahine tools. The reslts of the researh shold ontribte to obtain a alid analytial model that is to haraterize the ftre dynami behaior of the remanfatred tehnologi eipment, and whih is to offer information that are less eident in the design stage of remanfatring.. REFERECES []. Darabă, D., Analyses of tehnologial eipment strtral elements for remanfatring sing the finite element method, mirocad 8 Inter. Sientifi Conferene. Mahine and Constrtion Design, Uniersity of Misol, 8. []. Mogan, Gh. L., Metoda elementelor finite în inginerie, Editra Lx Libris, Braşo, 997. []. Morar, V.,Ghionea, A., Predinea,., Arite, T., Eni, G., ioles, A., Dogari, C., Teoria şi proietarea maşinilo-nelte. Îndrmar de proietare, Partea a III-a, Litografia I. P. Breşti, 987. [] Morar, V., Ispas, C., Rs, St., Vibratiile si stabilitatea Masinilor-Unelte, Editra Tehnia, Bresti, 98. [5] Ispas, C., Basi, F., Zapi, M., Parasan, I., Mohora,C., Dinamia masinilor si tilajelor, Ed. AGIR, bresti, 8 [5].