1. Prahant Kumar TRIPATHI,. K.V. GANGADHARAN COI BASED EECTROMAGNETIC SEMI ACTIVE VIBRATION CONTRO FOR FEXIBE STRUCTURES 1. DEPARTMENT OF MECHANICA ENGINEERING, NATIONA INSTITUTE OF TECHNOOGY KARNATAKA, INDIA ABSTRACT: In thi tudy, the emi active coil baed electromagnetic vibration control wa newly employed for vibration uppreion of a cantilever beam integrated with a copper coil and a permanent magnet. The control ytem for the vibration uppreion of the beam conit of a permanent magnet attached to an aluminum beam and a coil intalled below the magnet. The witching ytem operate when the output of enor i larger than the reference et value and a Proportional feedback control wa implemented for fater ettling time. The frequency repone function of a beam with the theoretical model of the electromagnetic witching ytem wa predicted, and it accuracy wa compared with the experimentally meaured data. Alo, the time repone with and without witching control were invetigated. The teted model i uggeted to implement in vibration control of flexible tructure. KEYWORDS: Semi Active Vibration Control (SAVC), PID control, Electromagnetic Actuator INTRODUCTION Vibration accompany u everywhere and in mot cae thee vibration greatly affect the nature of engineering deign. The vibration propertie of engineering device are often limiting factor in their performance. Vibration can be harmful and hould be avoided, or it can be extremely ueful and deired. In either cae, knowledge about vibration analyi, meaure and control i deired. Vibration control trategie have been ued in many application uch a pace tructure, helicopter, aircraft tructure, wind tunnel ting, civil engineering tructure and machine tool. In all thee cae an object ha to be iolated from the ource of vibration. Automobile and truck have hock aborber to damp out the vibration experienced due to roughne of the road. However, energy in conventional hock aborber get diipated a heat and wa not ued in any way. Regenerative electromagnetic hock aborber provide a mean for recovering the energy diipated in hock aborber, A. Gupta (006). Electromagnetic device have been widely ued in variou electronic and indutrial application including power generator, electric motor, loud peaker and propulion train. A microwave coil wa employed to generate a magnetic field in the magnetic reonance force microcope (MRFM) [1]. Stepanek et al [] tudied the dynamic behavior of the movement of a magnetic micro actuator. The electromagnetic micro actuator with three diaphragm can be developed through fabrication, tet reult, or finite element analyi [3]. Chen et al [4] propoed a new type of non conventional electromagnetic actuator for micro poitioning. The electromagnetic damper alo wa ued to actively reduce the vibration of 1 D.O.F upenion ytem [5]. There are many application of the electromagnet, uch a actuator for aircraft flight control urface, long troke linear motor for high peed packaging and manufacturing, reciprocating actuator for reonant electro mechanical ytem, magnetic bearing for flywheel, olenoid actuator for dieel fuel injector control, and actuator with multiple degree offreedom [6]. The electromagnetic actuator wa developed for the vibration control of a cantilever beam with a tip ma [7]. Some reearcher [8 9] tudied the deign, modeling, and analyi of a novel magnetic pring damper and alo reported the modeling, imulation and teting of a novel eddy current damper to be ued in vehicle upenion ytem. Piezoelectric hunt damping with voltage feedback can be claified into a emi active control method with the power amplifier and the ignal proceing unit, i the mot popular technique for minimizing the vibration of a mart flexible tructure. The poibility of diipating mechanical energy with a piezoelectric material hunted with paive electrical circuit i invetigated by Hagood et al [13]. Applied witching R hunt, where a ingle reitor i either witched to, or diconnected from the piezoelectric tranducer reulting in change in patch tiffne [11]. With a heuritic witching law, they were able to damp vibration of a beam tructure. ater, witching of R_ hunt have been propoed [1]. Figure 1 how the concept of electromagnetic witching emi active vibration control with ingle degree of freedom ytem in thi tudy. It i called emi active becaue of the hunt damping act a paive damping given from the coil itelf, and there wa an external power upply for driving of the witching circuit and feedback control make it active control ytem. copyright FACUTY of ENGINEERING HUNEDOARA, ROMANIA 185
The analog witch i connected with electromagnetic actuator which wa placed on a ma, damper and pring ytem. The witch operating condition depend on the diturbance to the ytem. Switch on control when the diplacement i more than reference diplacement value, ele off. Here the diplacement value mean the vibration amplitude which increae with increaing of diturbance of ytem. In thi tudy, the emi active electromagnetic ANNAS OF FACUTY ENGINEERING HUNEDOARA International Journal Of Engineering witching hunt damper wa newly employed for vibration uppreion of cantilever beam. The electromagnetic witching hunt damper conit of a magnet attached on a cantilever and a conducting coil placed under the bottom of the tack of permanent magnet, and both end of the coil were connected to the witching circuit and amplifier. The reult howed good vibration damping effect with electromagnetic witching emi active control. There ha been 6.5 mm amplitude reduction at firt mode of flexible beam tructure in frequency domain. EECTROMECHANICA COUPING MATHEMATICA FORMUATION When a conducting coil move through a non uniform magnetic field or i in a region where there i a change in the magnetic flux, an electric current can be induced within the conducting media. Although the eddy current can be induced in any electrical conductor, the eddy current i mot pronounced in olid metallic conductor. Eddy current are utilized to induce heat and to damp ocillation in variou device. In order to analytically model the dynamic governing equation of the cantilever beam with the copper coil, an unorthodox approach wa ued [10]. Uing Hamilton principle, the kinetic and potential energy of the vibrating flexible beam can be written by conidering the tip ma effect of the copper coil a: w w ( ) + Mc ( x xc ) dx 1 T = A ρ δ t t 0 1 U = EI w dx x (1) 0 Here, M C and x C are the ma and location of the coil, repectively, and w denote the tranvere diplacement of the cantilever beam. ρ, A, E, and I are the denity, cro ectional area, Young modulu, and ma moment of inertia of the cantilever beam, repectively. The virtual work conit of two term: the firt term i for work done by the external force, the econd i due to the inherent damping force of a bae: w δw = fext ( x,t) c δwdx () x 0 The equation of motion and all the natural and geometric boundary condition can be obtained by applying Hamilton principle: t = δ H (T U + W )dt = 0 (3) t1 Figure1. Schematic on electromagnetic witching emi active control for 1DOF ytem where t 1 and t are the end point in the time domain and δ i the virtual work parameter. Subtituting the train energy and kinetic energy into Hamilton principle yield the following equation of motion: 4 y w w ( ρ A+ Mc δ ( x xc )) + c + EI = fext ( x,t) (4) 4 t t x The ingle mode approach can be ued to create a dicrete partial differential equation (4) into an ordinary differential equation. The flexural motion for a cantilever beam i imply approximated with a hape function, ψ (x) w(x,t) = ψ (x)w(t) (5) 186 Tome X (Year 01). Facicule. ISSN 1584 665
ANNAS OF FACUTY ENGINEERING HUNEDOARA International Journal Of Engineering where x x x x ψ ( x) = coh α co α β inh α in α (6) Here, the frequency coefficient, α, and the mode hape coefficient, β. By applying the aumed olution (5) to the equation of motion (4) and integrating the equation (4) multiplied with the hape function ψ(x), within the domain a ingle mode ordinary differential equation can be obtained. M W(t) & + CW(t) & + KW(t) = F(t) (7) where, M = ψ (x) 0 C = ( ρa + M δ (x x ) ψ (x) dx) 0 dψ dx c ( x) dψ ( x) C dx d ψ (x) d ψ (x) K EI dx 0 dx dx = F(t)) =ψ fext(x,t)dx The electro magnetic force due to the induced eddy current, which i generated in the mechanim of the electro magneto mechanical coupling in the conductive coil that i located at x =x C, can be formulated in the following form through a point load of the input force that i located at x = x S. F(t) = f ( x,t) ψdx = ( φi(t) δ (x x ) + f (t) δ (x x )) ψdx o ext dx ( (x )) i(t) ψ ( x ) f (t) = φψ c + c = φ i(t) + F f (t) (9) where φ =NB i electromechanical coupling coefficient and i(t) i the induced current in the coil, f S (t) and x S are the exciting force and the location, repectively. The ingle mode governing equation can be written a: Figure. Circuit diagram of the witching hunt damper with voltage input. c c MW(t) & S + CW(t) & + KW(t) + Φi(t) = F f (t) (10) S (8) Figure how the circuit diagram of the witching hunt damper. The copper coil ha the electrical propertie of inductance and reitance. The meaured inductance and the electrical reitance of the coil are C = 0.096 H and R C = 1Ω repectively. Therefore the differential equation of the circuit can be written a: di(t) C + RCi(t) = φ w& δ (x xc ) = Φw(t) & (11) dt The electro magneto mechanical coupled equation can be expreed with x matrice. M 0 W&& C 0 W K Φ W F = in( ωt) 0 0 i + & Φ c i + 0 R c i && & 0 Therefore, the magnitude of the frequency repone function of the flexible beam integrated with the cloed coil obtained by olving above equation. For free Vibration ubtitute f S in above matrice equal to zero. (1) Figure 3. Cantilever geometry and ening/actuator coil point location. Figure 4. Experiment etup with aer Pickup (optoncdt). copyright FACUTY of ENGINEERING HUNEDOARA, ROMANIA 187
ANNAS OF FACUTY ENGINEERING HUNEDOARA International Journal Of Engineering EXPERIMENTA VERIFICATION OF EECTROMAGNETIC SEMI ACTIVE DAMPING CONCEPT Electro mechanical coupling mathematical model wa validated by conducting experiment. The experimental tet were performed with an aluminum beam of denity (ρ) =700 kg/m 3, Young modulu of Elaticity (E) = 70 x 10 9 N/m and thickne (t) = 1.5 mm a hown in Figure. 3. The tructural dimenion and location of the laer diplacement enor (Micro Epilon optoncdt 1400), and the conductive coil are depicted. The electromagnetic tranducer conited of a copper coil and a permanent magnet attached to flexible beam. The permanent magnet with a cylindrical neodymium wa ued to induce the magnet field in the coil. Conidering the ma effect due to magnet attachment, the poition of the copper coil in the cantilever beam wa determined a 30 mm. A big ma i located at the end of the cantilever, the econd mode will be imilar, in term of the hape, to the firt mode of the Free clamped beam. Figure 4 how the experimental etup for the meaurement of the frequencyrepone function of the integrated cantilever beam with an electromagnetic hunt damper. An external reitor wa ued for paive hunt circuit for tuning the reonant vibration of the cantilever beam. The National Intrument PXI 1031 a 4 lot PXI chai with Analog input module PXI 4496 at lot and the abview program were ued to obtain the time and frequency domain repone by giving an initial diplacement of 8.5 mm with the electromagnet witching mode. Active vibration control i achieved by providing a voltage to the coil proportional to diplacement. A coil draw more current, TECHRON model 5507 wa ued a dual channel power amplifier deigned for ue in medium power ytem. Figure 5. GUI with real time video treaming to viualize vibration control RESUTS AND DISCUSSION To predict the vibration characteritic of the cantilever beam with the electromagnetic hunt damper, the electro magneto mechanically coupled ingle mode equation were reformulated in thi tudy. Figure 6 how the time repone of cantilever beam with and without witching emi active control. A clear reduction in amplitude of vibration wa oberved. Alo, time repone of the cantilever beam under an initial condition of a tip diplacement of 8.5 mm at the ening point were examined under both controlled and uncontrolled condition a how in Figure 7. The low decay of the time repone of the uncontrolled beam accelerate through the incorporation of the electromagnetic witching circuit. Figure 9 how the experimental frequency domain graph of the controlled and uncontrolled cantilever beam for firt mode of beam. The electromechanical coupling matrice were olved uing MATAB and the reulting graph are hown in Figure 10. Figure 6. Time repone of cantilever beam with and without control 188 Tome X (Year 01). Facicule. ISSN 1584 665
ANNAS OF FACUTY ENGINEERING HUNEDOARA International Journal Of Engineering Figure 7. Time repone of cantilever beam with initial diplacement Figure 8.Control voltage with amplification gain equal to one of TECHRON amplifier Figure 9. Experimental amplitude reduction with/without electromagnetic emi active vibration control Figure 10. Analytical amplitude reduction with/without electromagnetic emi active vibration control The predicted reult are conitent with the experimental data. Thi mean that the ued analytical model can provide a good olution for the deign of the multi mode electromagnetic hunt damper. From the fine tuning of the PID control, a dramatic reduction of 6.5 mm wa obtained for the firt mode with peak ytem diturbance amplitude of 8.5 mm. CONCUSIONS In thi tudy, emi active vibration control ha been achieved uing coil baed electromagnetic circuit. The advantage of thi deign i that if active voltage feedback control fail, paive hunt damping will control the vibration. The deign wa newly contructed for vibration uppreion of flexible tructure. The ued analytical formulation of the electromagnetic witching ytem provide a good olution for the deign of the hunt circuit and the dynamic analyi of the integrated cantilever beam with experimental reult. Thi can be manufactured with large electromagnet on both ide and permanent magnet at the center for emi active vibration uppreion in automobile. A the reult copyright FACUTY of ENGINEERING HUNEDOARA, ROMANIA 189
ANNAS OF FACUTY ENGINEERING HUNEDOARA International Journal Of Engineering how that the theoretical data are in good agreement with meaured data. One poible method to enhance the ytem broadband performance i to ue erie of coil and permanent magnet with individual witching control with repect to vibration amplitude. REFERENCES [1.] D. Rugar, R. Budakian, H. J. Mamin and B. W. Chui, ingle pin detection by magnetic reonance force microcopy, Naure vol.430, pp. 39 33, 004. [.] J. Stepanek, H. Rotaing, J. Delmare and O. Cugat, Fat dynamic modeling of magnetic micro actuator, Journal of Magnetim and Magnetic Material vol.7, pp.669 671, 004. [3.] K. H. Kim, H. J. Yoon, O. C. Jeong and S. S. Yang, Fabrication and tet of a micro electromagnetic actuator, Senor and Actuator APhyical vol.117, pp.8 16, 005. [4.] M. Y. Chen, H. W. Tzeng and S. K. Hung, A new mechanim deign of electro magnetic actuator for a micropoitioner, ISA Tranaction vol.46, pp.41 48, 007. [5.] Y. B. Kim, W. G. Hwang, C. D. Kee and H. B. Yi, Active vibration control of a upenion ytem uing an electromagnetic damper, Proceeding of The Intitution of Mechanical Engineer Part Journal of Automobile of Engineering vol.15, pp.865 873, 001. [6.] D. Howe, Magnetic actuator, Senor and Actuator A Phyical vol.81, pp.68 74, 000. [7.] R. F. Fung, Y. T. iu and C. C. Wang, Dynamic model of an electromagnetic actuator for vibration control of a cantilever beam with a tip ma, Journal of Sound and Vibration, vol.88 pp.957 980,005. [8.] B. Ebrahimi, M. B. Khameee and M. F. Golnarahi Modeling of a magnetic hock aborber baed on eddy current damping effect, Journal of Sound and Vibration vol. 315, pp.875 889, 008. [9.] B. Ebrahimi B, M. B. Khameee and F. Golnaraghi, Eddy current damper feaibility in automobile upenion: modeling, imulation and teting, Smart Material and Structure vol.18, 009. [10.] Tai Hong Cheng, Yong i, Ming Ren, Yun De Shen, Coil Baed Electromagnetic Damper Uing Semi Paive Switching Method, 010 International Conference on Intelligent Computation Technology and Automation. [11.] C. Richard, D. Guyomar, D. Audigier and H. Baaler, Enhanced emi Paive damping uing continuou witching of a piezoelectric device on an inductor, In Proc. SPIE Smart Structure and Material, Damping and Iolation, SPIE vol.3989, pp.88 99, New port Beach, CA, March 000. [1.]. R. Corr and W. W. Clark, A novel emi active multi modal vibration control law for a piezoelectric actuator. Journal of Vibration and Acoutic, Tranaction on the ASME, vol.15, pp.14, April 003. [13.] N. W. Hagood and A. von Flotow, Damping of tructural vibration with piezoelectric material and paive electrical network, Journal of Sound and Vibration vol.146, pp.43 68, 1991. [14.] S. Mirzaei, S. M. Saghaiannejad, V. Tahani, and M. Moallem, inear electric actuator and generator, IEEE Tranaction on Energy Converion 14, pp. 71 717, September 1999. [15.] S. S. Rao, Mechanical Vibration, Addion Weley Publihing Company, 3rd ed., 1995. [16.] B. M. Hanon, M. D. Brown, and J. Fiher, Self ening: Cloed loop etimation for a linear electromagnetic actuator, in Proc. IEEE American Control Conference, pp. 1650 1655, (Arlington, VA USA), June 001. [17.] C. R. Fuller, S. J. Elliott, and P. A. Nelon, Active Control of Vibration, Academic Pre, 1996. [18.] R. Amirtharajah and A. P. Chandrakaan, Self powered ignal proceing uing vibration baed power generation, IEEE Journal of Solid State Circuit 33, pp. 687 695, May 1998. [19.] Y. B. Kim, W. G. Hwang, C. D. Kee, and H. B. Yi, Active vibration control of upenion ytem uing an electromagnetic damper, in Proc. of the I MECH E part D Journal of Automoblie Engineering (Profeional Engineering Publihing), 15(8), pp. 865 873, 001. [0.] J. Shaw, Active vibration iolation by adaptive control, in Proc. IEEE International Conference on Control Application, pp. 1509 1514, (Hawaii, USA), Augut 1999. ANNAS OF FACUTY ENGINEERING HUNEDOARA INTERNATIONA JOURNA OF ENGINEERING copyright UNIVERSITY POITEHNICA TIMISOARA, FACUTY OF ENGINEERING HUNEDOARA, 5, REVOUTIEI, 33118, HUNEDOARA, ROMANIA http://annal.fih.upt.ro 190 Tome X (Year 01). Facicule. ISSN 1584 665