Magnetostrictive Dynamic Vibration Absorber (DVA) for Passive and Active Damping

Transcription

1 aer : 59 /. Magnetostrictive ynamic Vibration Absorber (VA) for Passive and Active aming C. May a,. uhnen b, P. Pagliarulo b and H. Janocha b a Centre for nnovative Production (ZP), Saarbrücken, ermany, c.may@zi.uni-sb.de b Laboratory for Process Automation (LPA), Saarland University, Saarbrücken, ermany, k.kuhnen@la.uni-saarland.de,.agliarulo@la.uni-saarland.de, janocha@la.uni-saarland.de Several artners within the consortium of the Euroean 5 th ramework roject MESA (Magnetostrictive Equiment and Systems for More Electric Aircraft) are working together to tackle the roblem of vibration and noise disturbance in turboro aircraft. The vibration sectrum is characterised by ronounced eaks at aroximately Hz, Hz and 3 Hz corresonding to the first, second and third blade ass frequencies (BPs). mlementing a novel actuator design with mechanical transformation to achieve secified acceleration forces the resulting VA assively absorbs vibrations at its resonance frequency tuned to the fundamental frequency of disturbance while oerating actively over the range of 5-4 Hz. Otimised with resect to weight and size, the VA design is resented, illustrating the dislacement amlification feature based on elastic members. An electromechanical model of device behaviour is develoed followed by a descrition of a closed-loo control algorithm for effective imlementation of the active VA. Exerimentally obtained vibration absorbing characteristics are resented. Laboratory measurements indicate fulfilment of secifications for reducing vibrations in turboro aircraft, while the VA design could be alied to vibration roblems in other vehicles of transortation such as trains and shis or for imroving manufacturing quality in machine tools.. NTROUCTON The active dynamic vibration absorbers (VAs) described in this aer were develoed within the Euroean 5 th ramework R& roject MESA [] to solve roblems of vibration and noise in turboro aircraft. The reduction of structural vibrations by alying VAs on frame members is an effective means of reducing the cabin sound ressure level and was the selected aroach defining the scoe of the resent develoment []. The vibration disturbance contains ronounced tonal comonents corresonding to the first three blade ass frequencies (BPs) close to Hz, Hz and 3 Hz. Alenia Aeronautica, roducer of the ATR4 turboro aircraft and MESA roject artner, defined the secifications for the active VAs based on measurements on an exerimental mock-u. A VA air, which should weigh less than 5 g, should fulfil in articular the dynamic force requirements of 9 N, 8 N and N at the three BPs, resectively [3]. n order to ermit its mounting on the structural frame members in the aircraft, each VA should fit in the rectangular volume defined by the dimensions 3 x 5 x 5 mm 3. By imlementing active magnetostrictive materials in the VA, the device should be caable of generating forces over the entire frequency band 6-36 Hz.. ESN Early in the concet hase of develoment, it was decided to combine assive and active functionality resulting in a so-called hybrid VA. With a resonance frequency corresonding to the first BP, the hybrid VA can assively absorb the main vibration disturbance while actively oerating as an effective force generator for all other frequencies within the oerating band.

2 aer : 59 /. n order to achieve the low weight and size requirements, it was necessary to develo a design in which most of the total VA mass is effective in generating dynamic forces, i.e. the ratio of seismic mass to static mass should be as great as ossible. This design consideration demanded a solution in which the coil(s) used to excite the magnetostrictive material should be art of the seismic mass. urthermore, the force and mass requirements demand VA dislacements on the order of 5 µm as determined by Newton s law ma m(πf) xˆ. This dislacement is necessary in resonance at about Hz. ue to the size limitations of the VA and a tyical achievable magnetostrictive strain of about m, the design would have to incororate a mechanical transformation to amlify the dislacement roduced by the active rod. A 4 mm long rod laced along one of the two 5 mm axes of the device could roduce about 4 µm unloaded dislacement. To achieve the required 5 µm VA mass dislacement under load conditions, a mechanical transformation with a dislacement amlification ü is necessary. An additional imortant design requirement is to achieve a robust VA structure that exhibits the desired directional resonance at the first BP while exhibiting no other structural vibration modes within the intended frequency range of oeration. igure : Cross-sectional view of discretely built VA (left) and hoto of assembled VA with wire-eroded frame (right) These and other design criteria resulted in the VA structure deicted in igure. The seismic mass is comrised of the coils, the backing lates and the magnetostrictive rod connected to the mechanical fixation beams via elastic susension arms. The elastic susension achieves a 9 mechanical transformation of the rod elongation with a dislacement amlification of about 6. The elastic susension also fulfils the function of reload sring, is longitudinally stiff and laterally soft. As a result the overall VA stiffness is dominated by the contribution of the magnetostrictive rod. Two different VA versions were roduced. The cross-sectional view in the left of igure deicts a VA whose structure is comrised of discrete mechanical comonents, while the hoto on the right shows the VA achieved by wire erosion manufacturing. The overall VA mass is about 35 g of which the seismic mass is about 9%.

3 aer : 59 /.3 3. MATHEMATCAL MOEL The electromechanical equivalent circuit diagram of the active magnetostrictive vibration absorber is shown in igure. igure : Electromechanical model of the active magnetostrictive VA As a first aroximation the relationshi between the force, the current and the dislacement s of the magnetostrictive material can be described by the actuator equation d c s m where c reresents the mechanical stiffness and d m the effective magnetostrictive constant of the active material. The VA structure has a dislacement amlification factor of ü. The linear damer with the daming constant k is a first aroximation of the system s natural daming. The magnetostrictive transducer with electrical inductance L is driven by a voltage-controlled current source with gain v and internal resistance R. The acceleration a of the base structure is a measure for the vibration comensation effect. t can be described in the Lalace domain in terms of the electrical and mechanical excitations and the electromechanical transfer functions. u r V U a. n terms of the comlex Lalace variable σ j, the current source transfer function is U V V r V, where L R V. The hybrid VA can be described by the guiding and disturbance transfer functions a and a u,

4 aer : 59 /.4 where the single arameters are: m m, k ( m m), c ((4 ü ) m m m ) m d m ü m m k, c ((4 ü ) m ) c ( m m, (4 ü ) m m m ) c (4 ü ) m 4. CLOSE-LOOP ORCE COMPENSATON The active comensation of the disturbing forces u can now be achieved by a suitable feedback of the measured base acceleration a to the inut of the current source. The corresonding acceleration feedback loo is reresented in igure 3a with S as the sensor transfer function and with C as the controller transfer function. The acceleration sensor has a low-ass characteristic which is assumed here as a second order filter S ( ) ( ) S S with S, S > V > >. n ractice it is mandatory that for each bounded inut signal vector X T (a md a d U Rd d ) the signal vectors Y T (a m a U R ) and Z T (a mu a u U Ru u ), i.e. all signals which occur in a feedback loo, remain bounded and furthermore that the condition Z L X and Y L X is fulfilled with the constants L, L. n such case the feedback loo according to igure 3a is characterized as internally stable [4]. u j U Rd d a md a m U Ru U R u a u C V - a mu a d a σ S a) b) igure 3: a) orce comensation within a closed control loo, b) Root locus grah of the characteristic equation

5 According to [4] this is equivalent to the fact that the roots of the characteristic equation PC PV P PS ZC ZV Z Z S aer : 59 /.5 are in the oen left-half -lane whereby the denominators of the transfer functions C, V, and S are given by P C, P V, P and P S and the numerators by Z C, Z V, Z and Z S. rom this for the control loo according to igure 3a follows the characteristic equation ( ) ( ) ( ) ( ) P ZC C V V S S deending on the controller transfer function C. A more careful consideration of this equation shows that integral arts in the controller transfer function always roduce oles at and thus violate the demand for internal stability of the feedback loo. Whereas the use of a simle roortional controller with the controller transfer function C C leads to a root locus grah of the characteristic equation as shown in igure 3b, and thus to an internally stable feedback loo for a sufficiently small gain C [5]. The disturbing transfer function of the closed loo describes the relationshi between the disturbing force u and the base acceleration a in the Lalace domain. Based on the fact that the controller gain C can only influence the coefficient of the ower in the denominator of this transfer function, the feedback has no effect on low and high frequencies. or this reason, the active daming of the disturbance u emerging through feedback is only ossible in a middle frequency band. 5. EXPERMENTAL RESULTS The test and measurement set-u for verifying the erformance of the hybrid VA consists of a base mass m to which an electro-dynamic shaker is attached for generating the external disturbance u. The solid line in igure 4 shows the constant amlitude resonse of the acceleration a relative to the disturbance force u over the frequency range of interest. The dashed line shows the amlitude resonse of the entire system consisting of mass m, the electrodynamic shaker and the assively working VA. The assive VA achieves a narrowband daming of about 6 db at anti-resonance and an acceleration increase of arox. 4 db in resonance. The dash-dot line shows the amlitude resonse of the system with the VA oerating actively in the closed control loo. n contrast to assive oeration, the active VA achieves broadband daming of acceleration with a maximum of nearly db. After characterizing the VA devices, six units were sent to the MESA artners eartment of Aeronautical Engineering at the University of Nales ederico and the eartment of Comuter Science at the Second University of Nales for testing the devices on a rectified frame member together with control hardware roduced by Newlands Technologies, Ltd. These tests simulate the vibration disturbance within the ATR4 aircraft and allow a verification of the hybrid VA erformance [].

6 aer : 59 /.6 igure 4: Amlitude resonse a / u in the test rig without VA (original system) as well as with the hybrid VA acting assively (dashed curve) and actively (dash-dot curve) 6. CONCLUSONS A hybrid magnetostrictive dynamic vibration absorber with a assive resonance tuned to about Hz has been develoed that fulfils the functional requirements for combating vibration and noise disturbances in the frequency band 5-4 Hz. This hybrid VA design is therefore suitable for reducing the sound ressure level in the cabin of turboro aircraft where tonal disturbances at the first three blade ass frequencies near Hz, Hz and 3 Hz are redominant. As disturbances of this nature can be found in many transortation alications, the achieved VA design, for which a atent is ending, has large alication otential. ACNOWLEEMENTS This work has been financially suorted by the Euroean Commission under the research roject MESA "Magnetostrictive Equiment and Systems for More Electric Aircraft" (contract number 4R-CT ). urthermore, the authors wish to exress their areciation for the kind and roductive co-oeration of the MESA consortium artners. REERENCES. MESA roject website resentation: htt:// Aurilio, A. Cavallo, L. Lecce, E. Monaco, L. Naolitano and C. Natale, "uselage rame Vibration Control Using Magnetostrictive Hybrid ynamic Vibration Absorbers", in Proceedings of Euronoise 3, Naoli, taly, ranco, E. Monaco and L. Lecce, Vibrations Control Using Hybrid ynamic Vibration Absorber (HVAs) Based on Magnetostrictive Active Material, in Proceedings of Actuator, 8 th nternational Conference on New Actuators, Bremen, ermany,. 4. M. Vidyasagar, Control System Synthesis - A actorization Aroach, M..T. Press, Cambridge, Massachusetts, uhnen and H. Janocha, Smart iezoelectric vibration absorber, in Proceedings of the 8 th Mechatronics orum nt. Conf. Mechatronics, Twente Enschede, Netherlands,,