Mechnics & Industry 14, 247 252 (213) c AFM, EDP Sciences 213 DOI: 1.151/mec/21367 www.mechnics-industry.org Mechnics & Industry Experimentl investigtions on the effectiveness of electromgnetic ctutor s sensor Benjmin Defoy, Lurence Genty nd Jrir Mhfoud Université de Lyon, INSA-Lyon, LMCoS UMR 5259, Villeurbnne, Frnce Received 12 Februry 213, Accepted 24 June 213 Abstrct The study ims t exmining the behviour of electromgnetic ctutor s inductive sensor. The electromgnets re integrted in n lterntive Whetstone bridge nd powered with lterntive tension. This circuit llows the mesurement of the electromgnet inductnce vrition, nd s this vrition is function of the ir gp, the displcement cn be deduced. The effect of eddy currents is ssessed in order to choose the suitble bridge frequency. Finlly, demodultor is used to obtin the tension proportionl to the ir gp vlue. The behviour is ssessed experimentlly. Experiments re crried out on simple bem; clmped t one end nd simply supported t the other. The displcements could be mesured by using four eddy current sensors nd the inductive sensor. The inductive sensor displcement nd modl pproximtion of the four eddy current sensors resulting from impct testing re compred. Anlysis of the results obtined predicts n efficient nd robust behviour. Key words: Self-sensing / sensors / electromgnetic ctutor / vibrtions / experiments 1 Introduction Active Mgnetic Berings (AMB) re nowdys successfully utilized in severl industril pplictions [1, 2]. Their min dvntges re the contct-less working environment, no seling constrints, the frictionless suspension, nd tht they represent n ctive system. A typicl ctive mgnetic bering system consists of n ctutor, displcement sensor nd digitl controller. The ctutors cn only produce ttrctive electromgnetic force nd hve strongly nonliner chrcteristics due to the fct tht this force is current nd rmture position dependent [3]. Usully, nd due to technologicl constrints, the sensor is plced beside the ctutor (s close s possible) nd the rmture position is estimted from the mesurements stemming from the sensor. This estimtion is cceptble in the presence of rigid body modes but could led to undesirble effect when crossing flexible mode zones. On the other hnd, nd s consequence of the AMB success, we re looking for reducing its size such tht it could be used in smll structure like utomotive turbochrger. AMBs (or ctutors) which estimte the rotor position from informtion of the electromgnet signls re referred to s self-sensing ctutor. To our current knowledge, the notion of self sensing AMBs ws first introduced Corresponding uthor: jrir.mhfoud@ins-lyon.fr by Vischer nd Bleuler [4]. This work exmined the problem of control of single xis AMB with n opposed pir of mgnets. Self-sensing mgnetic berings hve been investigted by vrious reserchers. Their efforts cn be grouped into two min ctegories. One ctegory is prmeter estimtion where the bering ir gp is treted s time-vrying prmeter of n isolted dynmic mgnetic system nd mplifier combintion. The other pproch is to tret the mgnetic berings nd the supported object s whole. In this cse, the position of the supported object is stte rther thn prmeter [5 9]. Self-sensing mgnetic berings re not only reserch concept but now find commercil ppliction [1]. Generlly, inductive sensors hve the sme rchitecture s electromgnetic ctutors, i.e. two copper coils winded round two iron mgnetic cores. Nevertheless, the two devices hve not the sme specifictions [11]. The ctutors re designed usully for low frequency rnge (up to 2 khz) with high force cpbilities. And, the sensors re designed for high frequency rnge (1 khz 5 khz). Consequently, sensors re mde of smll mgnetic circuit in order to void losses into their iron core nd ctutors hve lrge coil in order to obtin high mgnetic field. The two objectives re opposite since the coil size defined the iron core length [3]. This work is contribution iming t the experimentl ssessment of n ElectroMgnetic Actutor (EMA) behving s inductive sensor. Only one ction line Article published by EDP Sciences
248 B. Defoy et l.: Mechnics & Industry 14, 247 252 (213) is considered, nd the electronic device is completely chnged to insert the electromgnets in n lterntive Whetstone bridge. Electromgnets re powered with n lterntive tension. This circuit llows the mesurement of the electromgnet inductnce. As the inductnce is function of the ir gp, the displcement cn be deduced. The effect of eddy currents is ssessed to choose the bridge frequency. Finlly, demodultor is used to obtin tension proportionl to the ir gp displcement vlue. Another objective is to ssess the possibility of estimting the displcement t the ctutor position (coloclized displcement) by using modl pproximtion. Usully, the coloclized displcement could be rebuilt by using stte estimtors [8, 9], in this study we choose to rebuilt this displcement by using modl interpoltion of the mesurement issued from the (non-coloclized) eddy current sensors utilized. This pproch hs the dvntge to be simple, esy to implement nd less time consuming. This type of estimtion ws used in previous study where the system ws controlled successfully [12]. The displcements re mesured by using four proximity sensors, locted long the bem xis. Their positions re chosen s function of the mode shpes present within the utiliztion frequency rnge. The mesurements, issued form the Inductive Sensor (IS), re compred to the vlue resulting from the modl estimtion. After this introduction, the experimentl setup is presented then; the principle of the IS will be detiled. In order to illustrte the principle of the modl pproximtion, preliminry numericl investigtion ws performed nd discussed. Finlly, the experimentl results re presented nd commented nd the conclusions re dressed. 2 Experimentl setup The experimentl pprtus is composed of steel bem with constnt rectngulr section. The bem is clmped t one end nd simply supported by 17 N.m 1 stiffness cylindricl spring t the other end. The ctutors re plced.368 m from the clmped end. This position is chosen s function of the mode shpe so tht the mesurements stemming from the ctutors cn be ssessed with the influence of the first four modes. The displcements re mesured by using four proximity sensors (Vibrometer TQ 12) locted long the y xis, nmely,c1toc4(fig.1).thereltimedtcquisition nd signl processing is performed by using the A/D-D/A nd DSP Dspce r specilized crds. The four first modes of vibrtion of the bem re considered in this study. Thus the smpling frequency ws set to 4 khz. This enbles good description of four modes. In ddition, the smpling frequency ws high enough to void using nti-lising filters for the frequency rnge studied. An impct hmmer Brüel nd Kjer (B&K) 822 supplied with piezoelectric force sensor (B&K 82) is used in order to generte the system responses to the different excittions pplied. Z X.92.552 Y.1.21.1.184 C1 C2 C3.294.478.736C4.6 Fig. 1. Experimentl setup..368 Y.2 3 Description nd principle of the sensor Since n electromgnetic ctutor (EMA) cn only produce ttrctive forces, two identicl ctutors commnded independently re necessry. Ech EMA is composed of ferromgnetic circuit nd n electricl circuit. The ferromgnetic circuit is composed of two prts; n (E) shpe tht receives the induction cooper coil nd n (I) shpe prt tht is fixed on the bem. Both prts re composed of ssemblies of insulted ferromgnetic sheets. The qulity of the ferromgnetic circuit lloy is considered high enough nd the nominl ir gp between the sttor nd the bem is smll enough to consider mgnetic loss s negligible. This EMA ws designed nd ssessed in previous study [13], it produces mximum force of 3 N for mximum current of 3.5 A (Fig. 2). Only one ction line is considered, nd the electronic device is completely chnged to insert the electromgnets in n lterntive Whetstone bridge (Fig. 3). Electromgnets re powered with n lterntive tension. This circuit llows the mesurement of the electromgnet inductnce: μ N 2 L =2f 2 δ + l (1) µ r where: μ =4π 1 7 H.m 1 the permebility of vcuum spce, = sensor geometry (Fig. 2), f = sensor geometry (Fig. 2), N is the number of turn in coils,
B. Defoy et l.: Mechnics & Industry 14, 247 252 (213) 249 x d 1 E- b f Bem 2 u dx Power 2C Fig. 3. Sensor circuit. E+ b c d Fig. 2. Sensor detils. = 1 mm b = 4 mm c = 3 mm d = 1 mm f = 21 mm N = 18 turns δ is the coloclized displcement = e ± x, e is the initil ir gp (the distnce between the I nd E shpe prts), x is the displcement, l is the middle length of mgnetic flux lines, nd μ r is the reltive permebility of the mild steel used. As the inductnce is function of the coloclized displcement, the displcement cn be deduced. Thus, the lterntive tension (U dx ) mesured hs mplitude proportionl to the displcement (x): U dx (jω)= 2 E (jω) x 2 e + l (2) µ r The sensitivity depends on the iron core permebility μ r. This chrcteristic grows with frequency nd cn vry with the temperture. Its vlue is bsed on mnufcturer specifictions nd generlly is not known with gret ccurcy. In previous study [13], its vlue ws determined experimentlly nd it ws set to be 75 for nil frequency. Hence, it is expected tht the reluctnce of iron core is superior t those of ir gp nd the sensor sensitivity will be poor. Finlly, demodultor is used to obtin tension proportionl to the ir gp displcement vlue. The effect of eddy currents is ssessed to choose the bridge frequency. When the frequency of the crrier wve increses up to vlue greter thn 1 khz nd up to 1 khz the sensitivity of the IS decreses progressively. For frequency of 2 khz the sensitivity of the sensor becomes lmost nil [14]. Hence, the frequency of the crrier wve must be chosen s low s possible, but since the crrier wve must be suppress with low pss filter fter demodultion, it must be high enough s function of the opertionl frequency rnge. Severl tests were performed in order to set the mesurement prmeters. In our cse crrier wve of 1 khz enbles sufficient frequency bndwidth ( 1 khz). The mplitude of the crrier wve ws chosen such to hve significnt vlue nd not to exceed the circuit cpcity. Also, nd s shown by eqution (2), the IS is expected to hve good linerity properties over the totl rnge of studied displcement. 4 Preliminry numericl investigtions This step is necessry in order to djust nd to estblish reference results to be compred to those stemming from the sensor. Numericl simultions re done in configurtion s similr s possible to experiments. The bem is represented by 25 Timoshenko bem elements, tking into ccount the sher effect, with two nodes nd 4 degrees of freedom; two displcements nd two rottions per node long x nd z directions. The spring is modeled by supplementry stiffness element nd the (I) shpe prts of the sensor re modeled by supplementry mss. The structure hs four bending modes in the studied frequency rnge. The dmping effects re essentilly induced by the structure. The dmping ws introduced by using the modl dmping fctor. Its vlue ws djusted ccording to experimentl observtions. Even if there were slight vritions of their vlues for the different modes, men vlue of.3 ws used for ll modes (Tb. 1). In this study, the reference distnce is rebuilt by using pssge mtrix [H] stemming from cubic interpoltion of the modes considered for the structure: [H] =g(y i,y, [ϕ]) (3)
25 B. Defoy et l.: Mechnics & Industry 14, 247 252 (213) 5 x 1-4 1 6 Amplitude (m) Amplitude (m) 4 3 2 5 4 3 2 1 x 1-4.1.15.2.25.3 Time (sec) FE Response Modl estimtion Liner estimtion FE Response Modl estimtion Liner estimtion.1.2.3.4.5.6.7 Time (sec) Fig. 4. Modl nd liner estimtion of the coloclized displcement. Tble 1. Chrcteristics of the model. Mode Frequency (Hz) Dmping fctor 1 28.15.3 2 58.57.3 3 155.81.3 4 317.2.3 where y i is the position of the ith sensor, y is the ctutor position nd [ϕ] is the mode shpe mtrix. The modes were rel, nd were normlized by setting the gretest vlue equl to one. As we use four displcement sensors, only the four first modes re considered. The reference distnce δ (coloclized displcement) is then clculted in function of the mesured displcements stemming for the displcement sensors {δ} s: δ =[ϕ] 1 {δ} [H] (4) In Figure 4 the reference distnce clculted by using the finite element model is compred with tht rebuilt either by modl estimtion s described previously, or by liner interpoltion of the displcements clculted t nodes #9 nd #14, which correspond to the positions of sensors C2 nd C3 plced on ech side of the EMA. The ccurcy of the modl estimtion is cceptble nd the ltter is the vlue used for the experimentl comprison. Amplitude ( µm ) 2-2 -6-1 5 1 15 2 4 3 2 1-1 -2 C2.2.4.6.8.1 Fig. 5. Sensor clibrtion ccording to the ir gp. 5 Experimentl investigtions The IS ws clibrted ccording to the ir gp. This ir gp ws mesured first by using clssicl fillers nd its totl vlue ws 1.65 mm. Then, the bem ws pushed until the contct with ech sttor. The delivered tension ws mesured nd the sensitivity ws set to be 1.3 μm.mv 1 (Fig. 5). In ddition, when compring the signl of the displcement sensor C2 to tht issued form the inductive sensor, it could be noticed tht the signl to noise rtio of the inductive sensor is very similr to commercil eddy current sensors (Fig. 5b). Impct testing ws performed; severl impcts were pplied t different positions. The impcts were done by using the impct hmmer. The impct forces mesured by using the piezoelectric force sensor nd the displcements by using the IS nd the eddy current sensors. The signl cquisition nd dt processing were done by using Dspce crds, s described in the following: clcultion crd (DS15) equipped with digitl signl processor (DSP TMS32C4), 12 bit cquisition crd (DS22) with nlog to digitl time conversion rte of 3.3 μs per chnnel, 12 bit restitution crd (DS211) with digitl to nlog time conversion rte of 3.3 μs per chnnel. b
B. Defoy et l.: Mechnics & Industry 14, 247 252 (213) 251 15 1 Modl Approximtion 1 Modl Approximtion 5-5 1-2 -1-15 1 2 3 4 5 1 5-5 -1 Modl Approximtion.1.12.14.16.18.2 Fig. 6. Impulse response, time domin. The displcements stemming from the eddy current sensors were recorded; were used in order to estimte, by modl pproximtion, the coloclized displcement. The mode shpe mtrix issued from the numericl clcultions ws utilized. In this study the first four modes were only considered. The results obtined in time domin (Fig. 6) show good consistency. Mesurements were done for severl impct loctions tht were selected depending on the mode shpes of the first four modes. In this study, only the results stemming from impcts performed t.11 m from the clmping end re presented. Sme trends were observed for the different impct loctions. Sme behvior ws observed when processing the signl in frequency domin (Fig. 7). The presented frequency response ws clculted s the men vlue of ten time signls of.1 s without overlp. Hnning window nd zero pdding were used. The frequency nlysis enbled to verify tht the dynmic of the four first modes ws well cught without gin reduction for higher mode. Therefore, the IS hs frequency bndwidth superior to the frequency rnge studied. It is worth mentioning tht even if modl pproximtion ws performed by using the first four modes, sme trends were noticed for higher modes. 1-4 1 2 3 4 5 6 Frequency (Hz) Fig. 7. Impulse response, frequency domin. The results obtined were repetitive for different impulse testing. 6 Conclusion This study is contribution iming t the experimentl ssessment of n electromgnetic ctutor to behving s inductive sensor. The electronic device ws dpted in order to insert the electromgnets in n lterntive Whetstone bridge tht llows the mesurement of the electromgnet inductnce nd consequently the displcement vrition. This modifiction is simple nd could be esily implemented in industril pplictions. The results obtined demonstrte the effectiveness of the EMA behving s sensor. The signl to noise rtio is equivlent to commercil eddy current sensors nd IS exhibits sufficient linerity over the utiliztion frequency rnge. The obtined mesurements were repetitive. The results show tht the sme electromgnet configurtion is suitble to ctute nd to sense. In ddition, the two signls hve frequency bndwidth extremely different which mens tht self-sensing depends on the technicl possibility of providing power nd the mesurement signl in the sme device. Modl pproximtion of the coloclized displcement ws performed nd compred to the mesured one by using the IS. Good greement ws observed. This is n encourging result towrd the development of methodology using minimum number of sensors. References [1] G. Schweitzer, H. Bleuler, A. Trxler, Active Mgnetic Berings Bsics, Properties nd Applictions, vdf Hochschulverlg AG, ETH, Zurich, 23 [2] E.H. Mslen, Smrt Mchine Advnces in Rotting Mchinery, Proceeding of the 9th Interntionl Conference on Vibrtions in Rotting Mchinery, IMechE, Exeter, UK, 28, pp. 3 14
252 B. Defoy et l.: Mechnics & Industry 14, 247 252 (213) [3] G. Schweitzer, E.H. Mslen, Mgnetic Berings, Theory, Design, nd Appliction to Rotting Mchinery, Springer-Verlg, 29 [4] D. Vischer, H. Bleuler, A new pproch to sensorless nd voltge controlled AMBs bsed on network theory concepts, Proceedings of the 2nd ISMB, 199 [5] E.H. Mslen, Self sensing for ctive mgnetic berings: overview nd sttus, Proceedings of the 12th ISMB, 21 [6] L. Kucer, Robustness of self-sensing mgnetic bering, Proceedings of MAG 97 Industril Conference nd Exhibition on Mgnetic Berings, 1997 [7] N.M. Thibeult, R.S. Smith, Mgnetic bering mesurement configurtions nd ssocited robustness nd performnce limittions, ASME J. Dyn. Syst. Mes. Control 124-4 (22) 589 598 [8] M.D. Noh, E.H. Mslen, Self Sensing Active Mgnetic Berings Bsed on Prmeter Estimtion, IEEE Trns. Instrum. Mes. 46-1 (1997) 45 5 [9] T. Mizuno, K. Arki, H. Bleuler, Stbility nlysis of self sensing mgnetic bering controllers, IEEE Trns. Control Systems Technol. 4-5 (1996) 572 579 [1] M. Brunet, B. Wgner, Innovtion: Self-sensing technology, simplified mechnicl design, In S2M News (25) [11] H. Hbermnn, Pliers mgnétiques, Techniques de l ingénieur, trité Génie mécnique B 5 345, 1984 [12] J. Mhfoud, J. Der Hgopin, Fuzzy Active Control Of Flexible Structures By Using Electromgnetic Actutors, ASCE s Journl of Aerospce Engineering 24 (211) 329 337 [13] J. Der Hgopin, J. Mhfoud, Electromgnetic Actutor Design for the Control of Light Structures, Smrt Structures nd Systems 6 (21) 29 38 [14] J.-L. Chrron, Mesures sns contct, Techniques de l ingénieur, Mesures Anlyses R1331, 23