Identification of damping parameters for particle damper from the response of SDOF harmonically forced linear oscillator

Transcription

1 Iteratioal Joural o Egieerig Treds ad Techology (IJETT) Volume 23 Number 6- May 2015 Idetiicatio o dampig parameters or particle damper rom the respose o SDOF harmoically orced liear oscillator Mr.Uttam L.Ause 1, Pro.S.B.Tuljapure 2 1 P.G.Studet, 2 Assistat Proessor, Departmet o Mechaical Egieerig, Walchad Istitute o Techology, Solapur Solapur Uiversity, Solapur, Maharashtra, Idia Abstract This paper deals with Experimetal methods or idetiicatio o Particle dampig parameters rom the respose o Sigle degree o reedom harmoically orced liear oscillator whe system damped with sprig ad particle dampig,which parameter is resposible or the cotrol o resoat respose o vibratig systems, ad calculatio o dampig parameters or the cases such as sprig + particle damper i experimetal method setup have bee preseted to ivestigate steady state respose amplitude xi or SDOF system or dieret values o amplitude Yi o the base excitatio rom this relatioship o (Xi,Yi) or particle dampig by usig hal power bad-width method ad the Frequecy 1 ad 2 calculated usig FFT aalyser. Keywords dampig ratio; Dampig Coeiciet; Resoat requecy; Excitatio requecy; 1. I. INTRODUCTION Particle Dampig Particle dampig techology is a derivative o impact dampig with several advatages. Particle dampers sigiicatly reduce the oise ad impact orces geerated by a impact damper ad are less sesitive to chages i the cavity dimesios or excitatio amplitude.[2] The advatages o impact dampers are that these dampers are iexpesive, simple desigs that provide eective dampig perormace over a rage o acceleratios ad requecies. I additio, impact dampers are robust ad ca operate i eviromets that are too harsh or other traditioal dampig methods. Vibratio dampig with impact dampers has bee used i a wide variety o applicatios icludig vibratio atteuatio o cuttig tools, turbie blades, televisio aerials, structures, plates, tubig, ad shats. [3] Particle Vibratio Dampig (PVD or the short) is a combiatio o impact dampig ad rictio dampig. I a PVD, metal or ceramic particles or powders o small size (0.05 to 5 mm i diameter) are placed iside cavities Withi or attached to the vibratig structure. Metal particles o high desity such as lead or tugste give high dampig perormace due to dissipatio o kietic eergy. Particle Vibratio Dampig ivolves the potetial eergy absorptios ad dissipatio through mometum exchage betwee movig particles ad vibratig walls, rictio impact restitutio. [4] Particle Impact Dampig (PID or the short) is a meas or achievig high structural dampig by the use o a particleilled eclosure attached to the structure i a regio o high displacemets. The particles absorb kietic eergy o the structure ad covert it ito heat through ielastic collisios betwee the particles ad the eclosure, ad amogst the particles. 2. II. RELEVANCE I may situatios, it is importat to idetiy dampig iormatio rom a vibratio system with both Coulomb ad Viscous sources o dampig. Their requet occurrece i practical egieerig has arised or a log time the iterest o may researchers i the vibratio ield. Frictio dampers (with ISSN: Page 275

2 Iteratioal Joural o Egieerig Treds ad Techology (IJETT) Volume 23 Number 6- May 2015 viscous dampig as the system dampig) are used i gas turbie egies, high speed turbo pumps, large lexible space structures uder carriage o railway bogie, vehicle suspesio systems etc. These dampers are used to reduce resoat stresses by providig slidig cotact betwee poits experiecig relative motio due to vibratio, thereby dissipatig resoat vibratio eergy. The distributio ad arragemet o the multiple particle dampers o the structure usually have a sigiicat impact o the dampig eect o the dampers. It is see that the idetiicatio ad estimatio o the umerous orms o dampig preset i a dyamic system is helpul i improvig the cotrol o resoat respose. As such, some theoretical ad experimetal studies o Developmet o Theoretical ad Experimetal Methods or Idetiicatio o Coulomb, Viscous ad Particle Dampig Parameters rom the Resposes o a SDOF Harmoically Forced Liear Oscillator have bee carried out. Whe a vibratig system is damped with more tha oe type o models o dampig, it is ecessary to determie which o these types o dampig are more eective to cotrol the resoat respose. I such case, it is importat to idetiy dampig parameters rom the resposes o a vibratig system. Thereore whe a system is damped due to Coulomb rictio, viscous rictio ad Particle dampig, it is ecessary to develop theoretical & Experimetal methods or idetiicatio o these dampig parameters rom the resposes o the vibratig system. As such, it is proposed to develop methods or idetiicatio o Coulomb ad Viscous rictio (ad also with Particle dampig) parameters resposible or the cotrol o resoat respose o vibratig systems. For this purpose, ollowig work has bee carried out. Fig.1 Schematic o the experimetal arragemet (b) A magiied view o the particles iside the eclosure [21] Fig.2The model o a sigle degree o reedom system o a particle vibratio damper22] ISSN: Page 276

3 Iteratioal Joural o Egieerig Treds ad Techology (IJETT) Volume 23 Number 6- May 2015 Fig. 3 particle vibratio damper (let) ad the particle cotacts the base o the sprigs has bee excited by a electrodyamic (right).[22] Hal Power Bad-Width Method: To estimate dampig ratio rom requecy domai, (requecy respose curve) hal-power badwidth method ca be used. I this method, resoat amplitude o the system is obtaied irst. Correspodig to each atural requecy, there is a peak i Frequecy Respose Fuctio (FRF) amplitude. O decibel scale, 3 db dow rom the peak there are two poits correspodig to hal power poit. The more the dampig, more the requecy rage betwee this two poits. Hal-power badwidth Bad width is deied as the ratio o the requecy rage ( 2-1 ) betwee the two hal power poits to the atural requecy ( ) at this mode. It is related to dampig ratio as, 2 1. IV. EXPERIMENTALTEST SET-UP AND THE PLAN OF INSTRUMENTATION A schematic o the experimetal test set-up is show i the ig. (4.1).A plate which is made to move i the horizotal directio i two guide bars, represets the mass m o the system. It is coected o two parallel sprigs o equal stiess k 1 /2 each as show i igure (4.1). Liear bearigs have bee used to reduce rictio i betwee the mass plate ad guide bars. A heavy C rame has bee used or ixig the guide bars as show i igure. O the let side o mass, a viscous damper, two Coulomb dampers ad two particle dampers have bee attached. While, o the right side o mass, exciter. The Viscous damper is attached betwee Ceters o the mass ad the C rame. Two Particle dampers have bee attached. Oe ed o the particle damper is coected to the mass ad other ed o the damper is kept ree. Two Coulomb dampers have bee attached betwee the mass ad ed plate o the C rame. The requecy respose curve o the system is obtaied usig the accelerometer pick up with its ecessary attedat equipmet ad a FFT aalyzer, over a small rage o excitatio requecy. SYSTEM PARAMETERS k, m A plate o 1.0 kg has bee used ad the atural requecy o system aloe was chose as 8.75 Hz, (54.97 rad/sec) ad k usig the equatio, sprig stiess k was obtaied m as 3022 N/m. Thus the values o the parameters o SDOF system are m=1.0 kg ad k= 3022 N/m. Desig o sprigs o Stiess k 1 /2 Two parallel sprigs each o stiess o k 1 /2 = 1511 N/m have bee desiged or the experimetal work. The sprigs selected are helical compressio with both eds squared ad groud. The dimesios o sprigs are obtaied usig stadard ormulae o desig o helical compressio sprig. The material o sprigs is selected as high grade sprig steel. The ial dimesios o the sprig are as ollows. Followig are the desig speciicatios. TABLE 1 DESIGN SPECIFICATION OF SPRINGS FOR SDOF SYSTEM Parameters Sprig stiess k 1 /2=1511 N/m Number o turs (N) 14 Wire diameter (d) Mea diameter (D) Outer diameter (D 0 ) Ier diameter (D i ) 4mm 38 mm 42 mm 34 mm Sprig idex (C) 10 ISSN: Page 277

4 Iteratioal Joural o Egieerig Treds ad Techology (IJETT) Volume 23 Number 6- May 2015 Determiatio o system dampig + particle The requecy respose curve or 300 balls iside the dampig ( s+p ) Particle Vibratio Dampig is a combiatio o impact dampig ad rictio dampig. I a PVD, metal or ceramic particles or powders o small size (0.05 to 5 mm i diameter) are placed iside cavities withi or attached to the vibratig structure. The particles absorb kietic eergy o the structure ad covert it ito heat through ielastic collisios betwee the particles ad the eclosure, ad amogst the particles. I the experimetal set-up, stailess steel balls o small size (3.18 mm i diameter) are placed iside pipe (o diameter 20mm ad legth 80 mm). The pipe is closed rom both eds. Oe ed o pipe is attached to the vibratig mass ad other ed is kept ree. I this case, the SDOF sprig mass system with particle dampig has bee excited rom 5 Hz to 12 Hz usig electro dyamic exciter ad the steady state respose X has bee measured usig a accelerometer ad FFT aalyzer. The readigs were take by icreasig the umber o balls iside the pipe, startig rom o balls to ull illed balls iside the pipe. i) Particle dampig with o balls iside pipe The requecy respose curve or o balls iside the pipe case is show i igure (4.7). Usig the hal power badwidth method, the value o system dampig ratio s+p with o balls has bee determied as, = ii) Particle dampig with 200 balls iside pipe The requecy respose curve or 200 balls iside the pipe case is show i igure (4.8). Usig the hal power badwidth method, the value o system dampig ratio s+p with o balls has bee determied as, = iii) Particle dampig with 300 balls iside pipe pipe case is show i igure (4.9). Usig the hal power badwidth method, the value o system dampig ratio s+p with o balls has bee determied as, = iv) Particle dampig with ully illed balls iside pipe The requecy respose curve or ully illed balls iside the pipe case is show i igure (4.10). Usig the hal power bad-width method, the value o system dampig ratio s+p with o balls has bee determied as, = TABLE 2. DAMPING RATIO OF VARIOUS DAMPING COMBINATION Type o dampig r (Hz) X r (micros) 1 2 S No balls) balls) balls) ully illed with balls) Fig.4. Experimetal Setup with particle damper ISSN: Page 278

5 X (micros) Iteratioal Joural o Egieerig Treds ad Techology (IJETT) Volume 23 Number 6- May 2015 S+P(ull balls) (Hz) Fig.4.9. Frequecy respose curve or ξs+p =7.5 Hz ; 1 = 6.92 Hz ; 2 = 8.08 Hz ξ=0.0778; Xr=4395 µm 3. V. CONCLUSION Particle dampers sigiicatly reduce the oise ad impact orces geerated by a impact damper ad are less sesitive to chages i the cavity dimesios or excitatio amplitude.[2] The advatages o impact dampers are that these dampers are iexpesive, simple desigs that provide eective dampig perormace over a rage o acceleratios ad requecies. i) For s+p (o ball coditio)with resoat requecy equal to 7.5 Hz. Usig the hal power bad-width method, the value o system dampig ratio has bee determied as s+p = For s+p (200 balls) with resoat requecy equal to 7.5 Hz. Usig the hal power bad-width method, the value o system dampig ratio has bee determied as s+p = For s+p (300 balls)with resoat requecy equal to 7.5 Hz. Usig the hal power bad-width method, the value o system dampig ratio has bee determied as s = iv) For s+p (ully illed) with resoat requecy equal to 7.5 Hz. Usig the hal power bad-width method, the value o system dampig ratio has bee determied as s+p = ISSN: Page 279

6 Iteratioal Joural o Egieerig Treds ad Techology (IJETT) Volume 23 Number 6- May 2015 REFERENCES 1. [1] J.W. Liag, ad B.F. Feey, 2004, Idetiyig Coulomb ad Viscous Frictio i Forced Dual-Damped Oscillators, ASME J. Vib. Acoust., 126, pp [2] Steve E. Olso, 2003, A aalytical particle dampig model J. Soud Vib. 264, pp [3] M.R. Duca, C.R. Wassgre ad C.M. Krousgrill 2005, The dampig perormace o a sigle particle impact damper, J. Soud Vib. 286, pp [4] Mao, K. M., Wag, M. Y., Xu, Z. W., ad Che, T. N., 2004, Simulatio ad Characterizatio o Particle Dampig i Trasiet Vibratios, ASME J. Vib. Acoust., 26,pp [5] De Hartog, J. P., 1931, Forced Vibratios with Combied Coulomb ad Viscous Frictio, Tras. ASME, 53, pp [6] Hudal, M. S., 1979, Respose o a Base Excited System with Coulomb ad Viscous Frictio, J. Soud Vib.,64, pp E.S. Levita, 1960, Forced Oscillatio o a sprig-mass system havig combied Coulomb ad Viscous dampig, Joural o the Acoustical Society o America 32, pp [8]Thomas A. Perls ad Emile S. Sherrard 1956, Frequecy Respose o Secod Order Systems with Combied Coulomb ad Viscous Dampig, Joural o Research o the Natioal Bureau o Stadards, 57, pp [9] J.W.Liag, ad.f.,feey, 1999, The Estimatio o Viscous ad Coulomb Dampig i Harmoically Excited Oscillators, Proceedigs o DETC 99, Las Vegas, ISSN: Page 280