The Impulsive Loading Evaluation of the Dynamic Technological Equipments Field

Transcription

1 he Impulsive Loing Evlution of the Dynmic echnologicl Equipments Fiel ADRIAN LEOPA Reserch Center for Mechnics of Mchines n echnologicl Equipments Engineering Fculty of Bril Dunre e Jos University of Glti Cle Clrsilor nr. 9, Bril ROMANIA leop.rin@ugl.ro, Abstrct: - In the inustril sector, continuous interest exists in orer to ientify the vible methos for environment protection ginst vibrtion from the technologicl equipments with ynmic loing. For the ynmicl moeling of the inustril equipments with impulsive loing it is necessry the exct chrcteriztion of the system excittion functions, by specific prmeters efinition: mplitue, urtion n shpe. his stuy refers to roughly metho for etermining n quntify the previous three prmeters by combining the theoreticl n experimentl nlysis methos. Key-Wors: - vibrtion, moeling, ynmic loing, forging hmmer Introuction he first step for ientifiction of efficient metho for ntivibrtory isoltion is physicl n mthemticl moeling of technologicl equipment bse on these moels by nlyzing whole ynmic system in ifferent hypothesis of work conition: ifferent loing conitions, ifferent technologicl process n ifferent isoltion systems mounte uner equipment. For this reson is very importnt to efine ccurtely of the perturbtion signl by ll chrcteristic prmeters: urtion, shpe n mplitue. Determintion of chrcteristic prmeters of technologicl equipment excittion force, who work with ynmicl loing, cn by mke from rel cse strting, in the following wy: Impct energy of equipment working element is etermine, in the forging hmmer cse since it t rm; the collision urtion between rop hmmer rm n eforme semi-prouct is experimentlly etermine; ynmicl loing shpe epening on type of technologicl process is opte; the elimite re by the ynmicl loing shpe is ctully the input system energy; by equliztion two energies will be etermine the excittion function mplitue. An very importnt prmeter for mechnicl systems ynmic loings nlyze, is their uring, in nother wor in the shock type loing cse represent the collision urtion between working element n semi-prouct who is plstic eforme. he experimentl etermintion of collision urtion he experimentl mesurements were me in PROMEX inustril compny, for the collision urtion mesuring between two metllic boies on the forging hmmers. hese technologicl equipments re use for plstic eformtion of metllic mterils, by repete strikes pplie with rm on semi-prouct. he experimentl mesurements were me on ie forging hmmer with following chrcteristics, fig. : forging hmmer cpcity - 7 kgf; piston ro imeter - 75 mm; nvil imension - 5x mm; rm isplcement - 76 mm; forging hmmer height - 75 mm; forging hmmer weight (inclusive nvil n fountion plte) - 5 kgf; nvil weight kg. ISSN: ISBN:

2 Fig. he technologicl process Fig. Die forging hmmer 7 kgf cpcity. Mesurement evices for cquisition n processing t he mesurement system n evices ws compose the following: Portble High-Spee Digitl Vieo Cmer roubleshooter me Fstec Imging; Hlogen light source (W); notebook for cquisition t Softwre Mis Express. - Winows. Experimentl etermintion on ie forging hmmer 7 kgf cpcity hrough portble high-spee igitl vieo cmer, ws cquire vieo signl uring specific cycle of semi-finishe ie forging from the current prouction of inustril fcility [6]. During experimentl etermintion fig., the high-spee igitl vieo cmer ws justment on fps, which llowe lter urtion etermintion of the elsto-plstic collision between hmmer's rm n semi-finishe. Bse on vieo recoring, ws estblishe following: rm spee of ie forging in the moment before impct is of 7.65 m/s; urtion of blow, in nother wors, urtion of collision between hmmer's rm n semi-finishe is of 7 ms. he ynmicl loing forces generte on ie forging hmmer re usully non-perioicl function. he non-perioicl function cn be consiere perioicl function with infinitely lrge perio n nturl pulstion infinitely smll ω. his non-perioicl function efinition, for grphicl representtion in frequency - mplitue coorintes is very useful [5]. he shock loing represents prticulr cse of non-perioicl functions, which mens tht whole kinemtic energy, re trnsmitte in very short time. he grphicl representtion of Fourier trnsforms moulus give s shock spectrum. F[ f ( t )] = F( ω ) = f ( t )e t= f ( t )e t () he most common use functions in ynmicl mechnicl system moeling re: hlf-cycle sine pulse, rectngulr pulse, hversine pulse, ISSN: ISBN:

3 exponentil pulse, tringulr pulse, trpezoil pulse n cycloil pulse [], [7]. A π t ( cos ), t F( t ) =, < t<, < t<+ (5). he shpes of loing force. he semi-sinusoil wve form he semi-sinusoil wve form is efine ccoring to the eqution (): πt Asin, t F( t ) =, < t<, < t<+ It is pplie the Fourier trnsform on this function: iω ( ) πt A F( ω ) = Asin e t= e + ω π π () () hen we obtin the pulstion spectrum of the shock: he Fourier trnsform is pplie on this function: + iω A π t ia( e ) π = = (6) + F( ω ) ( cos )e t ωπ ω hen we obtin the pulstions spectrum of the shock: ω Aπ sin F( ω ) = (7) ωπ + ω Hversine wve form with =,7 s n A=N is presente in fig.. 8 ω cos A F( ω ) = π ω () 6 Semi-sinusoil wve form with =,7 s n A=N is presente in fig ime [s] Fig. Semi-sinusoil pulse - =,7s. Hversine wve form Hversine wve form is efine ccoring to the eqution (5): ime [s] Fig. Hversine impulse - =,7s. rpezoil wve form rpezoil wve form is efine ccoring to the eqution (8): t A, t b b F( t ) = A, b< t< c t A,c t c he Fourier trnsform is pplie on this function: (8) ISSN: ISBN:

4 b t c F( ω ) = A e t+ A e t b b ibω i( c+ ) ω i( c+ ) ω i( c+ ) ω icω t ia( e e ) + A e t= + c c ω i( + b ) ω i( + b ) ω i( + b ) ω (9) Ae ( e + ie ( i+ ω b ω )) + + ( b ) ω Ae ( e + e ( iω icω ) + ( c ) ω Hversine wve form with =,7 s n A=N is presente in fig x ime [s] Fig. 6 Semi-sinusoil pulse - =,7s 8 6 x ime [s] Fig. 5 rpezoil pulse - =,7s. he mplitue of loing force clculus he rm kinetic energy before impct cn write: mv E= () where: m - mss of the rm; m=7 kg; v - spee of the rm; v=7.65 m/s; In these hypotheses we obtin E=8.87 J. For the hversine pulse we obtin n excittion force vlue 5859 N, fig. 6, in cse of semisinusoil pulse 5969 N, fig. 7, n for trpezoil pulse 885 N, fig ime [s].5 x Fig. 7 Hversine impulse - =,7s ime [s] Fig. 8 rpezoil pulse - =,7s ISSN: ISBN:

5 Force mplitue Amplituine [N] Force mplitue 5 - Frequency [Hz] Fig. 9 Pulstions spectrum of the function semi-sinusoil impulse - =,7s Frecvent [Hz] Fig. Pulstions spectrum of the function hversine impulse - =,7s 5 Frecquency [Hz] Fig. Pulstions spectrum of the function trpezoil impulse - =,7s he shpes of excittion forces will be estblishe bse on technologicl process peculirity, becuse observe ifferences between pulstion spectrum representtions of the ech loing forces fig Conclusions he presents pper represents n efficiency metho for ynmicl loing evlution process by theoreticl n experimentl methos combine. his evlution consists into useful instrument for physicl n mthemticl moeling of the mechnicl systems with impulsive ction such s ie forging hmmers. For perfect chrcteriztion of the ynmicl loing it must eterminte the length, the shpe n the mplitue of loing. For this purpose in this pper were complete chrcterize three functions cses: semi-sinusoil, hversine n trpezoil type. he right choice of the exciting functions is very importnt becuse these moify the technologicl equipment frequency response n in consequently cn become vibrtion pollution source for ifferent neighbor objective. References: [] Brtu, P., - Sisteme elstice e rezemre pentru msini si utilje, Eitur ehnic, Bucuresti, (99); [] GfiŃenu, M., CreŃu, Sp., Drăgn, B. Dignosticre vibrocustică mşinilor şi utiljelor, Eitur ehnică, Bucureşti, 989; [] Gilt, A., MALAB: An Introuction with Applictions n Eition, Wiley eition, ; [] Hrris, C.M., Piersol A.G. Shock An Vibrtion Hnbook, McGrw Hill Book Co, ; [5] Leop, A., Nstc, S., On Disturbing Impulsive Chrges for Mchineies Fountions, he Explortory Workshop "PROBLEME MODERNE ÎN DOMENIUL MECANICII SOLIDELOR" n the CD Proceeings of the XXXII-th Ntionl Conference of Soli Mechnics - CNMS XXXII, Pitesti, Romni, 8, ISSN ; [6] Leop, A., Nstc S. Experimentl n heoreticl Anlysis of the Dynmic Behviour of the echnologicl Equipment Fountion, NAUN Interntionl Journl of Mechnics, Issue, vol., 7, ISSN 998-8, pp. 8-88; [7] Silv, C. W. Vibrtion n Shock Hnbook - ylor & Frncis Group, LLC, 5. ISSN: ISBN: