Active Magnetic Bearings for Frictionless Rotating Machineries

Transcription

1 Ative Magneti Bearings for Fritionless Rotating Mahineries Joga Dharma Setiawan Abstrat Ative magneti bearing (AMB systems an support a rotor without physial ontat and enable users to preisely ontrol rotor position and vibration as funtion of time or other parameters. These fritionless and programmable features have made AMB suitable to meeting the demand for higher speed, higher effiieny and reliability of rotating mahineries in many industrial appliation inluding oil and gas prodution, power generation and energy onservation, lean manufaturing and transportation. This paper reviews the omponents and working priniples of AMB, whih requires basi understanding of rotordynamis, eletromagnetisms, power eletronis and ontrol theories. Several onfigurations and appliations of AMB are presented inluding design and ost issues. The apabilities of several major AMB world manufaturers are evaluated. The paper onludes with the summary of investigation topis at several leading AMB researh enters. It is hoped that this paper an provide an up-to-date, brief and yet omprehensive introdution of the AMB tehnology for potential users and industrial ommunities in general. Keywords : Control, magneti bearing, magneti levitation, rotordynamis 1. Introdution Ative magneti bearings have several attrative advantages over onventional bearings beause magneti bearings levitate rotors and therefore have no physial ontat with the spinning rotors. The use of magneti bearings an signifiantly eliminate the fritions that usually exist in onventional bearings. Thus, in rotating systems, magneti bearings an ontribute to effiieny in energy, longer life, and the ability to operate at very high RPM. Other advantages inlude the elimination of mehanial maintenane of the bearing and lubriation, suitability for lean or vauum room operation. The programmable feature typialy inludes the ability to adjust stiffness, damping, and periodi fore as funtion of time or other parameters suh as bearing temperature, RPM and angular aeleration. Ative magneti bearings have been implemented in rotating systems in a variety of industrial appliations. These appliations inlude flywheel energy storages, momentum wheels, turbomahineries, preision mahineries, vauum pumps, and medial devies. This paper reviews the omponents, working priniples and harateristis of ative magneti bearing (AMB systems. The most popular onfiguration as shown in Fig.1 is introdued [1-8] in whih the AMB provides radial fores generated by four poles magneti oils that are driven by power amplifiers operating in urrent mode.. AMB Components The design of AMB systems requires the knowledge of several disiplines inluding rotordynamis, eletromagnetisms, power eletronis and ontrol feedbak theories. This is driven to the fat that the omponents of AMB systems inlude position sensors with signal onditioning, swithing-power amplifiers, either analog iruits or Digital Signal Proessor (DSP, and magneti oils/eletromagnet as the atuators. The onnetion of AMB omponents are shown by the blok diagram in Fig..

2 Radial Position Sensor Magneti oils Figure 1. Rotor equipped with Radial AMB The dynami of the rotor an be simplified by fousing on the rotor motion along x axis shown in Fig. 1. The equation of motion beomes, m & x = Fb mg + F d (1 where m is the effetive mass of the rotor seen in the x axis, x is the rotor position, and F b is the bearing fore i 10 + i i0 i Fb = k ( l x l + x k = magneti fore onstant l = nominal air gap i 10,i 0 = bias urrents in the top and bottom eletromagnets i = ontrol urrent g = aeleration along x axis due to gravity The nonlinear bearing fore in Eq. ( an be linearized about x=0 and i =0, thus F b = K s x + K i (3 where k( i10 + i0 K s = ; position stiffness 3 l k( i10 + i0 K = ; urrent stiffness l Figure. AMB system blok diagram 3. Modeling The integration of a feedbak ontrol in AMB systems shown in Fig. must arefully onsider the dynamis of the rotor. This is due to the fat that a rotor, supported by magneti bearings is an open-loop unstable system as will be shown in this setion. Thus, an aurate model of the system is always needed for stabilization. For simpliity, we an assume the sensor runout E=0 in Fig. and the unbalane fore F d =0 in Eq. (1. Proper hoie of i 10 and i 0 an be made to anel the gravity term in Eq. (1 while K s and and K an be set to preferrable values. Thus, we an write the plant transfer funtion as shown in Fig. 3. The plant is an unstable system. The simplest way to stabilize the plant is by losing the loop with a proportional-derivative (PD ontroller shown in Eq. (4. i ( K x + K x& = (4 p The losed-loop system dynami then an be represented by Eq.(5. As long as the d

3 effetive damping, K K d >0 and the effetive stiffness, (K K p -K s >0 the system is stable. ( K K K = 0 m& x + K K x& + x (5 d i p K x ms Ks Plant = rotor+oil Figure 3. Single-DOF AMB Plant Transfer Funtion A more aurate AMB model onsider the gyrosopi oupling in the rotor and also other external fores ie. the unbalaned magneti pull (UMP of motor, K m as shown in Eq.(6 and Fig. 4. Mx && Kmxm = F1 ( i1 + F ( i My && Km ym = F3 ( i3 + F4 ( i4 I && Tθ + IPΩψ& LmK m ym = Lt F3 ( i3 Lb F4 ( i I && Tψ IPΩ & θ LmtKmxm = Lt F1 ( i1 Lb F ( i z (6 L t L b L m Ω Figure 4. Model of Rigid Rotor with AMB s y ψ y m θ 4 3 AMB 1 x m x motor AMB M= total rotor mass 4 For robustness, a state feedbak ontroller (entralized ontrol is generally implemented in AMB systems, espeially for high RPM operation and when I p /I T (polar inertia over transverse inertia is not negligible. Additionally high order filters or ompensators are usually needed in eah axis in order to avoid resonanes and instabilities at rotor bending frequenies. 4. Design, Cost & Performane Issues Currently, there is still no industrial or international standard for AMB design proedures and performane requirements. The International Organization for Standardization (ISO and International Eletrotehnial Commitee (IEC are still preparing a draft of ISO for this purpose. The AMB ISO draft an be aessed at an internet address shown in referene [9]. There are several variations in the AMB systems onfiguration. These variations exist beause of the need for lower hardware ost and more fault tolerant AMB systems. For example, an AMB system whih is so alled self-sensing, does not require position sensors whih means lower hardware ost. However, the stability margin and robustness an easily degrade. So does the AMB system that only has 3 poles of eletromagnets in eah bearing. A redundant system whih is more fault tolerant usually an ause the ost of prodution. to inrease signifiantly ie. at least by 4 times. Two examples of redundant AMB systems are shown in Fig. 5. The design of AMB systems need to onsider the worst ase senario suh as loss of ontrol due to faulty hardware/software omponents, and due to large external disturbanes suh as an earthquake or other vibrations. For this purpose, auxiliary bearings are always inorporated as a bak-up. The diameter of auxiliary bearings is sized suh that the

4 eletromagnets are well proteted during the rash and during power start-up and termination. It is a ommon pratie to generate an aurate Campbell diagram of free-free beam mode of rotors that will be supported by AMB systems. A Finite element sofware an be used to reate a Campbell diagram that shows the loation of rotor eigen-frequenies at different spin speed inluding the rigid body and bending modes. In pratie AMB an still be designed to support a rotor that spins near or above the first rotor bending mode. However, this design demands a more powerful DSP in order to perform more omplex omputation to aommodate higher order ompensators. If possible the operation near or above the first bending mode should be avoided beause it inreases ontrol design omplexity and ost. An example of hardware ost in the year of 006 for typial AMB systems is shown in Table 1 assuming a mass prodution ie. at least a thousand AMB units for a vertial rotor with mass of 50 kg, diameter about 5 m, maximum speed about 5 thousand RPM, distane between bearings about 0.5 meter, and maximum fore per axis about 50 N. Table 1. AMB omponents ost estimate AMB omponents eletromagnets+ position sensors 8 PWM power 50 watt max DSP+eletronis +power supplies Estimated ost (US Dollar wiring auxiliary bearings Total It is worth noted that in some designs and appliations, the total eletrial loss of AMB systems may be higher than the power loss due to mehanial frition of onventional bearings. The wiring of power lines from power amplifiers to eletromagnets should be made as short as possible in order to redue eletrial resistane. However, in many appliations the other benefits of AMB already overome this eletrial loss suh that AMB is still an attrative hoie. Adaptive Vibration Control (AVC feature in AMB systems is useful after a ertain RPM. Using a gradient method to minimize ost funtion of influene effiient matrix, AVC an on-the-fly redue or eliminate synhronous vibration due to mass unbalane. Beause of its great advantage, this feature is almost always inorporated in the AMB systems. The stiffness and damping of AMB systems an be adjusted by hanging the bias urrents or the feedbak ontrol gains as shown previously in Eqs (3-5. For example, due to a gyrosopi stiffening effet in rotors with I p /I T <1, the AMB stiffness or bias urrent in equivalent an be dereased after ertain high speed; thus the AMB power onsumption is redued. 6. Major Players in AMB Tehnology There have been numerous AMB manufaturer in the world [10-1]. The two most industrious ones are SM in Frane and Revolve in Calgary, Canada. SM has sold thousands AMB systems primary for ompression systems for oil and gas prodution industry. Another AMB ompany, Synhrony fouses on high grade fault tolerant AMB systems that an be used by aerospae industries and future airraft engines. One of Synhony s approah is to use redundant AMB and multiple DSP as shown in Fig. 5. Due to the rapid progress in eletronis inluding DSP tehnology, there are abundant

5 of avenues for further researh in AMB. Performane improvement, ost redution, and additional design objetives within speifi appliations are some of the examples. In the reent years, researhers working on magneti bearings have been aggressively fousing in areas suh as (1 studies to utilize modern ontrol methods inluding multi-variable ontrols, robust ontrols, non-linear ontrols, and adaptive ontrols in order to minimize rotor vibration; ( studies of levitating more flexible rotors; (3 studies of self-sensing magneti bearings; (4 studies on the joint use of magneti bearings for levitation and motor-stators for rotation; (5 hybrid passive and AMB; and (5 studies on zero-power magneti bearings using superondutor materials. Most of the above researh topis are onduted at the three most notable AMB researh and aademi enters in the world [13-15]: (1 Rotating Mahinery and Controls Laboratory (ROMAC at the University of Virginia, Virginia, USA; ( The International Center for Magneti Bearings (ICMB at The Institute of Robotis, ETH Zurih, Switzerland; and (3 Institute for Mahine Dynamis and Measurements (MTMD, Viena University of Tehnology, Vienna, Austria. 6. Conlusions The AMB tehnology has been briefly reviewed inluding its advantages, omponents, working priniples, ost and performane. Some design and implementation issues have been also disussed. The authors believe that AMB systems are still relatively more expensive than onventional mehanial bearings; therefore the massive used of AMB in industries is still prohibitive despite of the many benefits offered. The AMB will still not ompletely replae onventional bearings in rotating mahineries in the near future. However, AMB an find its plae well in a limited volumes of high performane rotating mahines. Referenes 1. Setiawan, J.D and R. Mukherjee, Adaptive Compensation of Sensor Runout and Mass Unbalane in Magneti Bearings without Changing Rotor Speed. United States Patent number: 6,763,85 B, July 13,004.. Setiawan, J.D., R. Mukherjee, and E.H. Maslen, Synhronous Sensor Runout and Unbalane Compensation in Ative Magneti Bearings Using Bias Current Exitation, ASME Journal of Dynamis, Systems, Measurements and Controls, Marh Setiawan, J.D., R. Mukherjee, and E.H. Maslen, Adaptive Compensation of Sensor Runout for Magneti Bearings with Unertain Parameters: Theory and Experiments, ASME Journal of Dynamis, Systems, Measurements and Controls, June Setiawan, J.D., R. Mukherjee, and E.H. Maslen, Variable Magneti Stiffness Approah for Simultaneous Sensor Runout and Mass Unbalane Compensation in Magneti Bearings, Proeeding of the 7 th International Symposium on Magneti Bearings, Zurih, Switzerland, August 3-5, Setiawan, J.D., R. Mukherjee, and E.H. Maslen, Adaptive Compensation of Sensor Runout for Magneti Bearings with Unertain parameters: Theory and Experiments, Proeeding of the 5 th International Symposium of Magneti Suspension Tehnology, Santa Barbara, CA, Setiawan, J.D., R. Mukherjee, E.H. Maslen, G. Song, Adaptive Compensation of Sensor Runout and

6 Mass Unbalane in Magneti Bearing Systems, Proeeding of ASME/IEEE Mehatronis Conferene, Atlanta, GA, Shweitzer, G, Ative magneti bearings Chanes and Limits, Proeeding of the 6th Internat. IFToMM Conf. on Rotor Dynamis, Sydney, Sept. 30-Ot. 3, Maslen, E.H., Magneti Bearings, ourse notes, June 5, 000 revision, free for download from website: agnetibearings 9. AMB ISO draft web site: O/ISO.html 10. SM web site: Revolve Magneti Bearings In. web site: 1. Synhrony In. web site: Rotating Mahinery and Controls Laboratory (ROMAC web site: International Center for Magneti Bearings (ICMB web site: Institute for Mahine Dynamis and Measurements (MTMD web site: Figure 5. Redundant AMB System with multiple Digital Signal Proessors (DSP, Courtesy of Synhrony In.