- Email: [email protected]
Active Magnetic Bearings For Machining Applications
Copyright © IFAC Mechatronic Systems, Sydney, Australia, 2004
ElSEVIER
IFAC PUBLICATIONS www.elsevier.comllocate1ifac
ACTIVE MAGNETIC BEARINGS FOR MACHINING APPLICATIONS
Carl R. Knospe Department of Mechanical & Aerospace Engineerillg Unil'ersi(v of Virginia. Charlottesville, VA. USA [email protected]
Abstract: High speed machining is galtlltlg greater attention duc to the substantial economic benefits that result from incrcased metal cutting productivity. Critical to realizing this technology's promise are thc intertwined challenges of spindlc dynamic stiffness and cutting process stability. Active magnetic bearings enable greater spindle dynamic stiffness through higher attainable bearing surface speeds, and also provide a means for the active control of chatter. Herein, experimental results are presented with two test rigs illustrating the potential of this technology. Design and application challenges are also examined. Copyright ([: 2004 IFAC Keywords: Magnetic bearings, multivariable control, machining. model-based control. mechanical systems.
I. INTRODUCTION
impacting many of the others is the spindle bearing system. Most spindles presently employ rolling element bearings, which limit spindle capabilities in a number of ways. In this paper, we will review over a decade of research at the University of Virginia on active magnetic bearing (AMB) technology for high speed machining applications.
It is estimated that machining operations account for 15%, of the value of all mechanical parts manufactured worldwide . Expenditures on machining operations in the United States are believed to be over $250 billion per year. Even small improvements to the productivity of machining operations can result in substantial economic benefit. Such reasoning 'has spurred increasing interest over the past 30 years in high speed machining (HSM). For many industries, high speed machining is seen as critical to increasing manufacturing productivity, rcduci ng thermal and mechanical stress in the tool and workpiece. enhancing the stability of machining, Il11provltlg part surface finish, and reducing 1V0rkpiece inventory. It is viewed as pm1icularly promising for the aerospace industry where high volumetric metal removal rates (MRR) are sought for manufacture of monolithic aluminium the components. For the achievement of high speed machining, progress along several directions in machine tool technology is critical. These include cutting tools. machine tool structures. machinc drives and controls. and spindles .
2. ACTIVE MAGNETIC BEARINGS Active magnetic bearings are a very promising technology and are now being employed for a variety of industrial rotating machinery applications. These non-contacting bearings use magnetic forces to firmly hold the rotor and maintain separation between it and the machine's stationary components (Sc~weitzer, et aI., 1994). A typical magnetic bearing system consists of two radial AM Bs and an axial AMB that together constrain 5 degrees-of-freedom of the rotor. Active magnetic bearing systems consist of electromagnetic actuators. position sensors. power amplifiers, ancl a feedback controller. Each actuator is composed of ferromagnetic component attached to the rotor (called the journal for a radial bearing. the thrusr disk for an axial bearing) and opposing pairs of stationary electromagnets (known as the sfator) . Radial magnetic bearing components are typically laminated to increase actuator bandwidth and reduce losses, while axial bearings are usually not due to the
1\ numbcr of challenges t~lce developers of spindles
for high speed machining including tool holding. thermal management, spindle dynamic stiffness, and balancing. Chief among these and strongly
7
difficulty of ensuring mechanical integrity in the face uf centrifugal loads and the cost of manufacture .
bandwidth and control authority, AMBs can provide significantly more damping to spindle modes than conventional bearings (Fittro, 1998). This results in greater tool dynamic stiffness and consequently a higher achievable metal removal rate without encountering chatter. As active devices, AMBs allow (in principle) the tailoring of the spindle dynamics so as to achieve optimal MRR for any specific combination of tool geometry, spindle speed. feed rate, and workpiece. . Finally, the forcing capability of these bemings and the position signals made available by employing them may be used to identify the cutting dynamics process which may be useful for monitoring tool wear and for further optimizing spindle operation (Chen and Knospe,
3. ADVANTAGES FOR HIGH SPEED MACHINING Conventional ball bearings are the source of a number of problems when employed in high speed machining spindles including thermal lock-up, poor damping, low dynamic stability, a tendency for I:hatter onset, and limited surface speeds that yield slender spindles with lower stiffness. The later of these presents a particularly compelling argument for the use of active magnetic bearings for high-speed spindles. For conventional bearings, maximum bearing surface speed is limited due to the high I:cntrifugal force s exerted on the rolling elements. As a wnsequence of this constraint, smaller diameter rutors must be used as rotational speed is increased . With this trend toward slenderer spindles at higher speeds comes an increased tendency for both tool vibration and chatter, an instability of the cutting process that results in increased tool wear, tool breakage, and poorer workpiece surface finish. Such problems strongly impact the benetits in MRR that accrue from the use of higher speed.
2003).
While AMBs are a very promising technology for machine tools, there are a number of significant technical challenges that must be overcome to capture their full potential. These include their relatively low specific load capacity; the difficulty encountered in achieving high bandwidth operation: the challenge' of feedback controller design considering the complexity of spindle dynamics and actuator non linearity; and the complex nature of the cutting process itsel f.
The surface speed of the spindle at the bearing is conventionally measured in DN, which may be calculated by multiplying the spindle diameter in millimeters by its rotational speed in revolutions per minute (RPM). For magnetic bearings, surface speed is limited only by the rotor lamination material strength and fracture propel1ies. Studies indicate that J\MBs I:an achieve more than twice the bearing surface speed of the most advanced contact bearing tcchnology (greater than 4 million DN versus less than 2 million DN) (Stephens, 1995). This allows for the same diameter rotor to be employed at speeds greater than twice that achievable with conventional bearings . [n comparison to a conventional spindle sized f(lr this higher speed, an AM 13 spindle would therefore have greater than 16 times the spindle rotor stiffness and greater than twice the first bending modc frequency . (While these figures are for the unsupP0l1ed spindle rotor, they will translate into significant improvements for the levitated spindle as well when the bearings are taken into account.)
3.1 Specific Load Capacity Specific load capacity is the ratio of the load carrying capability of a bearing to its volume. This figure of merit is typically more than one hundred times smaller for an AMB than for a conventional bearing (Stephens. 1995). This is cel1ainly the most significant and fundamental limitation of J\MBs for machining applications. While it is certainly possible to develop the necessalY forces to counteract cutting forces by using longer radial bearings, such a design increases shaft length, reducing both spindle stiffness and the frequency of rotor bending modes. and thus increases the difficulty of effective control. (We assume here that journal diameter has already been chosen to be the maximum possible for the operating speed range considered, hence larger bearings means longer bearings.) Therefore, it is critical in AMB spindle design to optimize the actuator design so as to yield the necessary force capabi lity in the smallest possible bearing. Of interest to the designer are both the peak specific load capacity, which IS fundamentally constrained by saturation value of magnetic flux density, and the RMS specific load capacity, which is essentially limited by coil thennal behaviour. The RMS specific load capacity is a fUIlction of a number of parameters, most importantly the allowable coil CUITent density and the air gap size. While some improvements to the former can be achieve by effective water cooling of the housing and careful design of the coils so as to enhance conduction to the back iron, minimization of the bearing air gap is the most effective approach to maximizing both RMS and peak specific load capacity. Decreasing clearances from the values typically employed in AMB systems (0.5 - I mm) does not pose any particular concern from an
J\s active devices, magnetic bearings also offer a
number of additional advantages to HSM spindles. Halmonic forces may be applied by the bearings so as to effectively counteract the imbalance of the rotor. This may be done in an adaptive fashion (Hope. et aI., 1998) so as to eliminate the rotor vibration over the entire operating speed. Modelbased control may be used so as to render infinite static stiffness at the tool (Stephens, 1995). With this type of control. the AMBs "lift" the rotor so as to yield zero deflection at the tool in response to a static clltting load. Such control capability may be useful in Improving the aCl:uracy of machined surfaces. While rolling element bearings are very stiff. the damping that they provide to the rotor's modes is rather poor. Provided that their feedback loops have sufficient
8
application viewpoint as we expect that the spindle will be precisely manufactured and that its motion within the clearances will be kept small during operation so as to provide machining accuracy. But, smaller clearances will require tight tolerances on both the joull1al and the stator, significantly increasing actuator cost. Furthermore, special care must be taken in bearing design to consider thermal and centrifugal growth of the joull1al in operation. It has been demonstrated that through careful design the specific load capacity of AMBs can be increased by over 60'}1, without changing ferromagnetic material or coi I control approach. Furthell110re, by employing individual coil control, a doubling of specifiC load capacity is possible (Stephens, 1995). For a cobalt-iron radial AMB, this means that a specific load capacity of 23 Ibf/in) is possible.
Fig. I. Block diagram of the chatter control problem; upper loop is the cutting process dynamics. be examined herein is to minimize the tool dynamic compliance so as to gain stabilize this loop (Fittro, 1998). Such controllers increase the allowable width of cut at all speeds and are tenned here as speedindependent. Another approach is to tailor the tool compliance via the control so that it has a favourable interaction with the cutting process, more akin to phase stabilization of the loop. Controllers of this type, referred to as speed-specified, increase the allowable width of cut at the design speed. For implementation over a range of speeds, such controllers would need to be gain scheduled.
4. THE MACHINING CONTROL PROBLEM From a pelioll1lance viewpoint, the efficacy of the bearing feedback control can be evaluated in terms of the tool compliance. This frequency response dictates the quality of machining in three ways: (I) profiling accuracy of the cutter is determined by the low frequency compliance; (2) surface finish of the workpicce is govell1ed by the high frequency compliance; and (3) the achievable width of chip without chatter (hence MRR) is determined by the compliance over the entire frequency range (Stephens, 1995: Chen and Knospe, 2002).
5. CONTROL OF A HIGH SPEED SPINDLE In this paper we will repoli on research conducted on two different test rigs. The first is a 32,000 RPM prototype magnetic bearing spindle, shown in Figure 2, designed and constructed in cooperation with Cincinnati Milaeron (Stephens, 1995; Knospe, et aI., 1997; Fittro, 1998; Fittro, et aI. , 1999; Fittro, et aI., 2003). The rotor is 638 mm (25.1 inch) long with a diameter that varies between 85 mm and 52.8 mm (without journals, motor rotor, and thrust disk) . Inside the rotor shaft is a 14.2 mm (0.56 inch) diameter drawbar. The rotor is supported by 3 radial bearings and a single axial bearing. These are capable of maintaining rotor levitation under cutting loads greater than 4450 N (1000 Ibf) . The radial
Chatter is a self~excited instability resulting from the feedback interaction of the dynamics of the cutting tool (and supporting machine) and the dynamics of the cutting process, see Fig. I. The occurrence of chatter depends on many factors including the structure of the machine and workpiece (stiffness, damping and orientation of modes of vibration) and the cutting conditions (workpiece material, chip Ividth, and rotational speed) (Tlusty, 1984). Key to the onset of chatter is the gain of the cutting process within the feedback loop. This is linearly dependent on the width of cut, which we wish to maximize in order to increase MRR. To achieve high width of cut without the onset of chatter, one approach that will
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9
bearings were constmeted from cobalt-iron laminations with an air gap clearance of 241 mm (0.0095 inch). The journal of the nose bearing, i.e., that closest to the cutting tool, has a diameter of IOX.4 mm and therefore reaches 3.5 million ON at the maximum operating speed. Three radial magnetic bearings were used as analysis during the design ~tage indicated that significant improvements in closed-loop tool dynamic behaviour could be obtained with an additional radial bearing in spite of the increase in rotor length that accompanies its introduction.
locations and the perturbation currents to be applied to generate forces in the x-direction by three actuators. Thus, identical 3-input I 3-output radial control algorithms are applied for the x-plane and yplane of the rotor. Control of the axial direction is established separately by single-input I single output controller. Radial controllers were developed from this plant description using: decentralized PlO design via parameter optimization; complex /1-synthesis via OK iteration; and mixed /1-synthesis via D-G-K iteration. Multivariable controllers typically contained between 100 and 200 states after synthesis. Controller reduction was carried out using a combination of techniques including balance-andtruncate (Fittro. I <')98). Reduction was quite successful with the radial controller for each plane reduced to typically fewer than 22 states.
Occlusion-based optical sensors. consisting of thermally compensated LED/phototransistor pairs operated differentially, measure displacements of the rotor adjacent to the radial bearings. Such sensors allow position measurement with very little noise «0 .5 /1m) induced by AMB fields. Axial displacement is measured in a similar fashion. Eighth order Caucr anti-aliasing filters with a corner frequency of 4.4 kHz are used to minimize the phase lag introduced into the feedback loop below 1000 kHz. The bearings are driven by 150 V switching amplifiers with 30 amp peak current capabilities. This allows force slew rates (when operated about their bias currents) of 8.4 N/ms (1.88 Ibf//1s) for the nose bearing and 5.6 Nlms (1.26 Ibfl/1s) for the middle and tail bearings. The spindle's rotation is driven by a 3-phase AC induction motor rated at 67.1 kW (9() HP). Feedback control algorithms are exec uted on a parallel processing digital controller consisting of four Texas Instnll11ents TMS320C40 DSP chips running at 40 MHz. 14 bit AID converters, and I fi bit D/A converters. Typically, a ~ampling rate of 12 kHz is used (Fittro. 1998).
Several theoretical perfollllance benchmarks were also established via alternative controller design approaches: (I) Hoc design without considering plant uncertainty or any constraint on controller gain/bandwidth ("Hoc"); (11) ~l-synthesis where controller gain/bandwidth is constrained to that practically achievable but no model unceliainty was included ("optimal /1") ; (Ill) /1-synthesis where model unceliainty was included but no constraint was placed on the controller ("high gain /1" ); and (IV) /1-synthesis where both modelling uncertainty and controller limitations were included hut the design controller sampling frequency (i.c .. throughput) was increased to 18 kHz and the antialiasing corner frequency was increased commensurately (" 18 kHz /1"). Table I presents the peak nominal and peak worst-case tool compliances for these designs, as well as experimental results (Fittro, 1998).
Detailed models of the rotor, actuators. amplifiers. and anti-aliasing filter were developed from lest data and finite element modelling techniques. These along with unceliainty descriptions for each component were assembled to form a complete mockl of the spindle system for robust controller design. This synthesis model incorporates nornlhounded uncertainty blocks. For controller design and evaluation. the performance metric used was the peak dynamic compliance of the tool. This cOITesponds to the Hoc n0I111 of the transfer function bdween cutting force and tool displacement. M inimization of this metric results in both greater accuracy in cutting and a reduction in the tendency to chatter as the cutting process feedback loop resulting from the regeneration of waviness is gain-stabilized (i .e.. this is a speed-independent approach). To ohtain designs suitable for implementation on the available hardware, the controller gain and bandwidth must be restricted in synthesis. This is easily done in the robust control framework via the inclusion of a tictitious uncel1ainty block that feeds the controller output back to its input. In this paper, we will discuss only the results for the radial tool compliance (Fittro, 199R). The multivariable controllers developed for radial control has three inputs and three outputs, corresponding to the displacements in the x-direction at the three sensor ~ensors.
Several conclusions may be developed from this data: ( I) Multivariable controllers developed via ~l synthesis can yield significant improvements in tool compliance over that attainable with conventional magnetic bearing feedback control. Experimental data indicates that a 40'Yc, reduction in compliance is achievable. (2) Elimination of plant model uncel1ainty would in principle result in nearly a 50'% reduction in Table I. Peak Tool Compliance Olinch/lbf) for nominal system model. worst-case svstem model and experiment for a variety of controllers including henchmark desil!ns.
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peak tool compliance for multivariable controllers. However, removing the restriction on controller gain/bandwidth would yield a much I,lrger improvement in tool dynamic behaviour. Of course, neither is practically achievable, but thi~ analysis nevertheless indicates the relative benefits of higher accuracy models and higher authority hardware. Cl) ;\ 50'Y<, increase in controller sampling rate (assuming that throughput could be similarly improved) would result in a 15'Yo reduction in peak tool compliance. Fig. 4. Chatter control experiment. Cutting tool and tool platform on tlexures at left AMB and actuator platform (beneath) on right.
rigure :; shows the tool compliance frequency response for both PlO and complex fl-colltrol as nhtained from experiment. It should be noted that the lI -controller has sie-nificantly lower compliance than ~lptimal PlO over ~nost of the frequency range, and that significantly more damping is introduced into the tir~t bending mode (",650 Hz) by the fl-col1troller than by PlO (over 60% reduction in compliance at this frequency).
platform and hence the air gap clearance. This entire assembly is mounted to a lathe such th
h. ACTIVE CONTROL OF CHATTER
The second experiment that will be examined herein, ;Ictive control of chatter in a turning operation. is shown in Fie-ure 4 (Chen and Knospe, 2002; Chen :1I1d Kllospe~ 20(3). This test rig consists of two platfolll1s connected by a leaf spring and constrained to sine-le-axis. rectilinear motion along the feed directi;n bv tlexures. The tool platform holds a cuttine- tool' and the actuator platfolll1 has a journal hearing rigidly mounted upon it. An AM B stator nllJuntcd above the actuator platform can apply a non-c(llltacting force to the journal along the feed direction. thus controlling its motion. The stator used is constructed from cobalt-iron laminations and is of ;1 clln\"cntional radial eight-pole deSign. Two sets of (ni Is nn opposite sides of the stator are wired t()L'ether and each driven by ISO V pulse-widthm;ldulated switching amplifiers. A bias CUITent of I amp is cmployed so as to guarantee sufficient forceslew-rate for the application . The air gap of thc hearing is 250 flm. An eddy current position probe is used to measure the displacement of the actuator
Feedback lineari zation was used (with the amplifiers operated in current mode) to ' render the bearingplatform-sensor system as linear over the entire range of journal travel and perturbation current. For this purpose, more than 600 experimental data points (current/position/force triplets) were experimentally obtained to develop a 5th order static nonlinear model of the actuator. F = ((r.i). This was used to develop a look-up-table that implements the inverse function. i = / - I ( .\" • F ). for execution on the digital controller. Experimental results obtained with this feedback linearization implemented have demonstrated that the variability of plant behaviour across the range of operating points has beell reduced by over 9()'1.1. This allows the use of smaller mCle-nitutles in ullcertainty description for controller synthesis . Thus . higher closed-loop perfOlll1anCe is obtainable over Cl larger range of displacements anti clltting forces.
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Two types of controller were developed for the interconnection depicted in Figure I (ullcertainty representations not shown but similar to those discussed ill (Fittro I l)9X)) . !)/7 eeli-inliepClldellt controllers were developed via fl-synthesis by using a unit complex unceliainty to cover the time-delay
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Frequency (Hz) figure ) . Comparison of tool compliance with PlO and ~l-synthesized controllers
11
transfer function e- T1i • This has been shown not to introduce any conservatism with regard to the speedindependent problem . The pelformance goal of such controllers is to push up the stability lobe curve across all cutting speeds. Speed-specified controllers were developed via )l-synthesis by first replacing the time-delay by a finite dimensional approximation. For accuracy over the frequency range of interest, a 40th order Pacle approximation was used . Of course, to employ thi s approach the delay (hence the wo rk piece speed) must be given. The perfonnance goal of these controllers is to push up the stability lobe curve at the given cutting speed.
7. CONCLUSION Active magnetic bearings hold considerable promise for high speed machining applications. A number of difficult technical challenges need to be tackled to realize this application's potential, including actuator design , sensor noise, and high perfomlance feedback control. Considerable progress has been made on a number of fronts over the last decade, but there will continue to be increasing demand from the application for higher performance in tenns of speed, power, dynamic stiffness, and chatter suppression. 8. ACKNOWLEDGEMENTS
Both speed-independent controller and speedspecified controller were implemented on the test rig. Figure 5 and 6 shows the tool compliance frequency n:sponscs and the stability charts, respectively, for the controlled machine tool. Compared to traditional riD controller that have been tested, these 11controllers achieve significantly better machining performance . As can be seen, the speed-specified controller yields n substantial incrense in allowable cutting stiffness (hence MRR) at the designated speed (here 2800 RPM).
The author gratefully acknowledges the help of many colleagues: Prof. L. Scott Stephens. Dr. Roger Fittro, Mr. Min Chen. Or. Stephen Fedigan. Prof. Marcio deQuieroz, Prof. Eric Maslen, Prof. Ronald Williams, Mr. David Wood. and Mr. Eclwanl Rou sc h. This work was pat1ially supported by Cincinnati Milacron an d the National Science Foundation (Grant DMI-9713488).
REFERENCES Chen, M. and Knospe. C.R. (2002)_ Experiments in Chatter Control with Magnetic Bearings . In: Proceedings of'the 2002 NSF Design. Service. and Manufacturing Grantees and Research Conference, San Juan, Jan. 7-10,1082-1095 . Chen, M_ and Knospe, C.R. (2003). A new approach to the estimation of cutting dynamics using active magnetic bearings, submitted to ASM E Journal of' Manufc/cturing Science (1nd Engineering. Fittro. R.L. (199R). A High Speed Machining Spindle with Active Magnetic Bearings: Control Theorl'. Design. and Application. Doctoral Disscl1ation . University of Virginia . Fittro, R.L. and Knospe, C.R. (1999). i control of a high-speed spindle thrust magnetic bearing. In: Proceedings of' the 1999 IEEE Illternational Conference on Control Applications, 570 - 575. Fittro, R.L., Knospe. CR., and Stephens, L.S ., (2003). Il-synthesis applied to the compliance minimization of an active magnetic bearing HSM spindle's thrust axis. Machining Science and Technology, 7. 19-51 . Hope, R.W .. Tessier, L., Knospe, C.R., and Miyamji. T. (1998). Adaptive vibration control of industrial turbomachinery. In : Proceedings of the ASMEI1GTf Turbo Expo, Stockholm. Sweden. Knospe, C.R .. Fittro, R.L., Stephens. L.S. (1997) Control of a high speed machining spindle via isynthesis. In: Proc. of 1997 IEEE International Conference 011 Con trol Applications, 912 - 917. Schweitzer, G_, Bleuler. H., and Traxler, A. (1994) Active Magnetic Bl!arings. Hochschulverlag AG an der ETH Zurich. Zurich, Switzerland. Stephens. L.S. (1995). Design and COllfrol o(Actil'£, Magnetic Bearings ./f)f- a High Speed Spindle. Doctoral Di ssertation. University of Virginia. Tlusty, J. (1984) . Dynamics of high-speed milling . ASME Produ ction Engineering, 12. 101-127.
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12
ElSEVIER
IFAC PUBLICATIONS www.elsevier.comllocate1ifac
ACTIVE MAGNETIC BEARINGS FOR MACHINING APPLICATIONS
Carl R. Knospe Department of Mechanical & Aerospace Engineerillg Unil'ersi(v of Virginia. Charlottesville, VA. USA [email protected]
Abstract: High speed machining is galtlltlg greater attention duc to the substantial economic benefits that result from incrcased metal cutting productivity. Critical to realizing this technology's promise are thc intertwined challenges of spindlc dynamic stiffness and cutting process stability. Active magnetic bearings enable greater spindle dynamic stiffness through higher attainable bearing surface speeds, and also provide a means for the active control of chatter. Herein, experimental results are presented with two test rigs illustrating the potential of this technology. Design and application challenges are also examined. Copyright ([: 2004 IFAC Keywords: Magnetic bearings, multivariable control, machining. model-based control. mechanical systems.
I. INTRODUCTION
impacting many of the others is the spindle bearing system. Most spindles presently employ rolling element bearings, which limit spindle capabilities in a number of ways. In this paper, we will review over a decade of research at the University of Virginia on active magnetic bearing (AMB) technology for high speed machining applications.
It is estimated that machining operations account for 15%, of the value of all mechanical parts manufactured worldwide . Expenditures on machining operations in the United States are believed to be over $250 billion per year. Even small improvements to the productivity of machining operations can result in substantial economic benefit. Such reasoning 'has spurred increasing interest over the past 30 years in high speed machining (HSM). For many industries, high speed machining is seen as critical to increasing manufacturing productivity, rcduci ng thermal and mechanical stress in the tool and workpiece. enhancing the stability of machining, Il11provltlg part surface finish, and reducing 1V0rkpiece inventory. It is viewed as pm1icularly promising for the aerospace industry where high volumetric metal removal rates (MRR) are sought for manufacture of monolithic aluminium the components. For the achievement of high speed machining, progress along several directions in machine tool technology is critical. These include cutting tools. machine tool structures. machinc drives and controls. and spindles .
2. ACTIVE MAGNETIC BEARINGS Active magnetic bearings are a very promising technology and are now being employed for a variety of industrial rotating machinery applications. These non-contacting bearings use magnetic forces to firmly hold the rotor and maintain separation between it and the machine's stationary components (Sc~weitzer, et aI., 1994). A typical magnetic bearing system consists of two radial AM Bs and an axial AMB that together constrain 5 degrees-of-freedom of the rotor. Active magnetic bearing systems consist of electromagnetic actuators. position sensors. power amplifiers, ancl a feedback controller. Each actuator is composed of ferromagnetic component attached to the rotor (called the journal for a radial bearing. the thrusr disk for an axial bearing) and opposing pairs of stationary electromagnets (known as the sfator) . Radial magnetic bearing components are typically laminated to increase actuator bandwidth and reduce losses, while axial bearings are usually not due to the
1\ numbcr of challenges t~lce developers of spindles
for high speed machining including tool holding. thermal management, spindle dynamic stiffness, and balancing. Chief among these and strongly
7
difficulty of ensuring mechanical integrity in the face uf centrifugal loads and the cost of manufacture .
bandwidth and control authority, AMBs can provide significantly more damping to spindle modes than conventional bearings (Fittro, 1998). This results in greater tool dynamic stiffness and consequently a higher achievable metal removal rate without encountering chatter. As active devices, AMBs allow (in principle) the tailoring of the spindle dynamics so as to achieve optimal MRR for any specific combination of tool geometry, spindle speed. feed rate, and workpiece. . Finally, the forcing capability of these bemings and the position signals made available by employing them may be used to identify the cutting dynamics process which may be useful for monitoring tool wear and for further optimizing spindle operation (Chen and Knospe,
3. ADVANTAGES FOR HIGH SPEED MACHINING Conventional ball bearings are the source of a number of problems when employed in high speed machining spindles including thermal lock-up, poor damping, low dynamic stability, a tendency for I:hatter onset, and limited surface speeds that yield slender spindles with lower stiffness. The later of these presents a particularly compelling argument for the use of active magnetic bearings for high-speed spindles. For conventional bearings, maximum bearing surface speed is limited due to the high I:cntrifugal force s exerted on the rolling elements. As a wnsequence of this constraint, smaller diameter rutors must be used as rotational speed is increased . With this trend toward slenderer spindles at higher speeds comes an increased tendency for both tool vibration and chatter, an instability of the cutting process that results in increased tool wear, tool breakage, and poorer workpiece surface finish. Such problems strongly impact the benetits in MRR that accrue from the use of higher speed.
2003).
While AMBs are a very promising technology for machine tools, there are a number of significant technical challenges that must be overcome to capture their full potential. These include their relatively low specific load capacity; the difficulty encountered in achieving high bandwidth operation: the challenge' of feedback controller design considering the complexity of spindle dynamics and actuator non linearity; and the complex nature of the cutting process itsel f.
The surface speed of the spindle at the bearing is conventionally measured in DN, which may be calculated by multiplying the spindle diameter in millimeters by its rotational speed in revolutions per minute (RPM). For magnetic bearings, surface speed is limited only by the rotor lamination material strength and fracture propel1ies. Studies indicate that J\MBs I:an achieve more than twice the bearing surface speed of the most advanced contact bearing tcchnology (greater than 4 million DN versus less than 2 million DN) (Stephens, 1995). This allows for the same diameter rotor to be employed at speeds greater than twice that achievable with conventional bearings . [n comparison to a conventional spindle sized f(lr this higher speed, an AM 13 spindle would therefore have greater than 16 times the spindle rotor stiffness and greater than twice the first bending modc frequency . (While these figures are for the unsupP0l1ed spindle rotor, they will translate into significant improvements for the levitated spindle as well when the bearings are taken into account.)
3.1 Specific Load Capacity Specific load capacity is the ratio of the load carrying capability of a bearing to its volume. This figure of merit is typically more than one hundred times smaller for an AMB than for a conventional bearing (Stephens. 1995). This is cel1ainly the most significant and fundamental limitation of J\MBs for machining applications. While it is certainly possible to develop the necessalY forces to counteract cutting forces by using longer radial bearings, such a design increases shaft length, reducing both spindle stiffness and the frequency of rotor bending modes. and thus increases the difficulty of effective control. (We assume here that journal diameter has already been chosen to be the maximum possible for the operating speed range considered, hence larger bearings means longer bearings.) Therefore, it is critical in AMB spindle design to optimize the actuator design so as to yield the necessary force capabi lity in the smallest possible bearing. Of interest to the designer are both the peak specific load capacity, which IS fundamentally constrained by saturation value of magnetic flux density, and the RMS specific load capacity, which is essentially limited by coil thennal behaviour. The RMS specific load capacity is a fUIlction of a number of parameters, most importantly the allowable coil CUITent density and the air gap size. While some improvements to the former can be achieve by effective water cooling of the housing and careful design of the coils so as to enhance conduction to the back iron, minimization of the bearing air gap is the most effective approach to maximizing both RMS and peak specific load capacity. Decreasing clearances from the values typically employed in AMB systems (0.5 - I mm) does not pose any particular concern from an
J\s active devices, magnetic bearings also offer a
number of additional advantages to HSM spindles. Halmonic forces may be applied by the bearings so as to effectively counteract the imbalance of the rotor. This may be done in an adaptive fashion (Hope. et aI., 1998) so as to eliminate the rotor vibration over the entire operating speed. Modelbased control may be used so as to render infinite static stiffness at the tool (Stephens, 1995). With this type of control. the AMBs "lift" the rotor so as to yield zero deflection at the tool in response to a static clltting load. Such control capability may be useful in Improving the aCl:uracy of machined surfaces. While rolling element bearings are very stiff. the damping that they provide to the rotor's modes is rather poor. Provided that their feedback loops have sufficient
8
application viewpoint as we expect that the spindle will be precisely manufactured and that its motion within the clearances will be kept small during operation so as to provide machining accuracy. But, smaller clearances will require tight tolerances on both the joull1al and the stator, significantly increasing actuator cost. Furthermore, special care must be taken in bearing design to consider thermal and centrifugal growth of the joull1al in operation. It has been demonstrated that through careful design the specific load capacity of AMBs can be increased by over 60'}1, without changing ferromagnetic material or coi I control approach. Furthell110re, by employing individual coil control, a doubling of specifiC load capacity is possible (Stephens, 1995). For a cobalt-iron radial AMB, this means that a specific load capacity of 23 Ibf/in) is possible.
Fig. I. Block diagram of the chatter control problem; upper loop is the cutting process dynamics. be examined herein is to minimize the tool dynamic compliance so as to gain stabilize this loop (Fittro, 1998). Such controllers increase the allowable width of cut at all speeds and are tenned here as speedindependent. Another approach is to tailor the tool compliance via the control so that it has a favourable interaction with the cutting process, more akin to phase stabilization of the loop. Controllers of this type, referred to as speed-specified, increase the allowable width of cut at the design speed. For implementation over a range of speeds, such controllers would need to be gain scheduled.
4. THE MACHINING CONTROL PROBLEM From a pelioll1lance viewpoint, the efficacy of the bearing feedback control can be evaluated in terms of the tool compliance. This frequency response dictates the quality of machining in three ways: (I) profiling accuracy of the cutter is determined by the low frequency compliance; (2) surface finish of the workpicce is govell1ed by the high frequency compliance; and (3) the achievable width of chip without chatter (hence MRR) is determined by the compliance over the entire frequency range (Stephens, 1995: Chen and Knospe, 2002).
5. CONTROL OF A HIGH SPEED SPINDLE In this paper we will repoli on research conducted on two different test rigs. The first is a 32,000 RPM prototype magnetic bearing spindle, shown in Figure 2, designed and constructed in cooperation with Cincinnati Milaeron (Stephens, 1995; Knospe, et aI., 1997; Fittro, 1998; Fittro, et aI. , 1999; Fittro, et aI., 2003). The rotor is 638 mm (25.1 inch) long with a diameter that varies between 85 mm and 52.8 mm (without journals, motor rotor, and thrust disk) . Inside the rotor shaft is a 14.2 mm (0.56 inch) diameter drawbar. The rotor is supported by 3 radial bearings and a single axial bearing. These are capable of maintaining rotor levitation under cutting loads greater than 4450 N (1000 Ibf) . The radial
Chatter is a self~excited instability resulting from the feedback interaction of the dynamics of the cutting tool (and supporting machine) and the dynamics of the cutting process, see Fig. I. The occurrence of chatter depends on many factors including the structure of the machine and workpiece (stiffness, damping and orientation of modes of vibration) and the cutting conditions (workpiece material, chip Ividth, and rotational speed) (Tlusty, 1984). Key to the onset of chatter is the gain of the cutting process within the feedback loop. This is linearly dependent on the width of cut, which we wish to maximize in order to increase MRR. To achieve high width of cut without the onset of chatter, one approach that will
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9
bearings were constmeted from cobalt-iron laminations with an air gap clearance of 241 mm (0.0095 inch). The journal of the nose bearing, i.e., that closest to the cutting tool, has a diameter of IOX.4 mm and therefore reaches 3.5 million ON at the maximum operating speed. Three radial magnetic bearings were used as analysis during the design ~tage indicated that significant improvements in closed-loop tool dynamic behaviour could be obtained with an additional radial bearing in spite of the increase in rotor length that accompanies its introduction.
locations and the perturbation currents to be applied to generate forces in the x-direction by three actuators. Thus, identical 3-input I 3-output radial control algorithms are applied for the x-plane and yplane of the rotor. Control of the axial direction is established separately by single-input I single output controller. Radial controllers were developed from this plant description using: decentralized PlO design via parameter optimization; complex /1-synthesis via OK iteration; and mixed /1-synthesis via D-G-K iteration. Multivariable controllers typically contained between 100 and 200 states after synthesis. Controller reduction was carried out using a combination of techniques including balance-andtruncate (Fittro. I <')98). Reduction was quite successful with the radial controller for each plane reduced to typically fewer than 22 states.
Occlusion-based optical sensors. consisting of thermally compensated LED/phototransistor pairs operated differentially, measure displacements of the rotor adjacent to the radial bearings. Such sensors allow position measurement with very little noise «0 .5 /1m) induced by AMB fields. Axial displacement is measured in a similar fashion. Eighth order Caucr anti-aliasing filters with a corner frequency of 4.4 kHz are used to minimize the phase lag introduced into the feedback loop below 1000 kHz. The bearings are driven by 150 V switching amplifiers with 30 amp peak current capabilities. This allows force slew rates (when operated about their bias currents) of 8.4 N/ms (1.88 Ibf//1s) for the nose bearing and 5.6 Nlms (1.26 Ibfl/1s) for the middle and tail bearings. The spindle's rotation is driven by a 3-phase AC induction motor rated at 67.1 kW (9() HP). Feedback control algorithms are exec uted on a parallel processing digital controller consisting of four Texas Instnll11ents TMS320C40 DSP chips running at 40 MHz. 14 bit AID converters, and I fi bit D/A converters. Typically, a ~ampling rate of 12 kHz is used (Fittro. 1998).
Several theoretical perfollllance benchmarks were also established via alternative controller design approaches: (I) Hoc design without considering plant uncertainty or any constraint on controller gain/bandwidth ("Hoc"); (11) ~l-synthesis where controller gain/bandwidth is constrained to that practically achievable but no model unceliainty was included ("optimal /1") ; (Ill) /1-synthesis where model unceliainty was included but no constraint was placed on the controller ("high gain /1" ); and (IV) /1-synthesis where both modelling uncertainty and controller limitations were included hut the design controller sampling frequency (i.c .. throughput) was increased to 18 kHz and the antialiasing corner frequency was increased commensurately (" 18 kHz /1"). Table I presents the peak nominal and peak worst-case tool compliances for these designs, as well as experimental results (Fittro, 1998).
Detailed models of the rotor, actuators. amplifiers. and anti-aliasing filter were developed from lest data and finite element modelling techniques. These along with unceliainty descriptions for each component were assembled to form a complete mockl of the spindle system for robust controller design. This synthesis model incorporates nornlhounded uncertainty blocks. For controller design and evaluation. the performance metric used was the peak dynamic compliance of the tool. This cOITesponds to the Hoc n0I111 of the transfer function bdween cutting force and tool displacement. M inimization of this metric results in both greater accuracy in cutting and a reduction in the tendency to chatter as the cutting process feedback loop resulting from the regeneration of waviness is gain-stabilized (i .e.. this is a speed-independent approach). To ohtain designs suitable for implementation on the available hardware, the controller gain and bandwidth must be restricted in synthesis. This is easily done in the robust control framework via the inclusion of a tictitious uncel1ainty block that feeds the controller output back to its input. In this paper, we will discuss only the results for the radial tool compliance (Fittro, 199R). The multivariable controllers developed for radial control has three inputs and three outputs, corresponding to the displacements in the x-direction at the three sensor ~ensors.
Several conclusions may be developed from this data: ( I) Multivariable controllers developed via ~l synthesis can yield significant improvements in tool compliance over that attainable with conventional magnetic bearing feedback control. Experimental data indicates that a 40'Yc, reduction in compliance is achievable. (2) Elimination of plant model uncel1ainty would in principle result in nearly a 50'% reduction in Table I. Peak Tool Compliance Olinch/lbf) for nominal system model. worst-case svstem model and experiment for a variety of controllers including henchmark desil!ns.
10
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peak tool compliance for multivariable controllers. However, removing the restriction on controller gain/bandwidth would yield a much I,lrger improvement in tool dynamic behaviour. Of course, neither is practically achievable, but thi~ analysis nevertheless indicates the relative benefits of higher accuracy models and higher authority hardware. Cl) ;\ 50'Y<, increase in controller sampling rate (assuming that throughput could be similarly improved) would result in a 15'Yo reduction in peak tool compliance. Fig. 4. Chatter control experiment. Cutting tool and tool platform on tlexures at left AMB and actuator platform (beneath) on right.
rigure :; shows the tool compliance frequency response for both PlO and complex fl-colltrol as nhtained from experiment. It should be noted that the lI -controller has sie-nificantly lower compliance than ~lptimal PlO over ~nost of the frequency range, and that significantly more damping is introduced into the tir~t bending mode (",650 Hz) by the fl-col1troller than by PlO (over 60% reduction in compliance at this frequency).
platform and hence the air gap clearance. This entire assembly is mounted to a lathe such th
h. ACTIVE CONTROL OF CHATTER
The second experiment that will be examined herein, ;Ictive control of chatter in a turning operation. is shown in Fie-ure 4 (Chen and Knospe, 2002; Chen :1I1d Kllospe~ 20(3). This test rig consists of two platfolll1s connected by a leaf spring and constrained to sine-le-axis. rectilinear motion along the feed directi;n bv tlexures. The tool platform holds a cuttine- tool' and the actuator platfolll1 has a journal hearing rigidly mounted upon it. An AM B stator nllJuntcd above the actuator platform can apply a non-c(llltacting force to the journal along the feed direction. thus controlling its motion. The stator used is constructed from cobalt-iron laminations and is of ;1 clln\"cntional radial eight-pole deSign. Two sets of (ni Is nn opposite sides of the stator are wired t()L'ether and each driven by ISO V pulse-widthm;ldulated switching amplifiers. A bias CUITent of I amp is cmployed so as to guarantee sufficient forceslew-rate for the application . The air gap of thc hearing is 250 flm. An eddy current position probe is used to measure the displacement of the actuator
Feedback lineari zation was used (with the amplifiers operated in current mode) to ' render the bearingplatform-sensor system as linear over the entire range of journal travel and perturbation current. For this purpose, more than 600 experimental data points (current/position/force triplets) were experimentally obtained to develop a 5th order static nonlinear model of the actuator. F = ((r.i). This was used to develop a look-up-table that implements the inverse function. i = / - I ( .\" • F ). for execution on the digital controller. Experimental results obtained with this feedback linearization implemented have demonstrated that the variability of plant behaviour across the range of operating points has beell reduced by over 9()'1.1. This allows the use of smaller mCle-nitutles in ullcertainty description for controller synthesis . Thus . higher closed-loop perfOlll1anCe is obtainable over Cl larger range of displacements anti clltting forces.
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11
transfer function e- T1i • This has been shown not to introduce any conservatism with regard to the speedindependent problem . The pelformance goal of such controllers is to push up the stability lobe curve across all cutting speeds. Speed-specified controllers were developed via )l-synthesis by first replacing the time-delay by a finite dimensional approximation. For accuracy over the frequency range of interest, a 40th order Pacle approximation was used . Of course, to employ thi s approach the delay (hence the wo rk piece speed) must be given. The perfonnance goal of these controllers is to push up the stability lobe curve at the given cutting speed.
7. CONCLUSION Active magnetic bearings hold considerable promise for high speed machining applications. A number of difficult technical challenges need to be tackled to realize this application's potential, including actuator design , sensor noise, and high perfomlance feedback control. Considerable progress has been made on a number of fronts over the last decade, but there will continue to be increasing demand from the application for higher performance in tenns of speed, power, dynamic stiffness, and chatter suppression. 8. ACKNOWLEDGEMENTS
Both speed-independent controller and speedspecified controller were implemented on the test rig. Figure 5 and 6 shows the tool compliance frequency n:sponscs and the stability charts, respectively, for the controlled machine tool. Compared to traditional riD controller that have been tested, these 11controllers achieve significantly better machining performance . As can be seen, the speed-specified controller yields n substantial incrense in allowable cutting stiffness (hence MRR) at the designated speed (here 2800 RPM).
The author gratefully acknowledges the help of many colleagues: Prof. L. Scott Stephens. Dr. Roger Fittro, Mr. Min Chen. Or. Stephen Fedigan. Prof. Marcio deQuieroz, Prof. Eric Maslen, Prof. Ronald Williams, Mr. David Wood. and Mr. Eclwanl Rou sc h. This work was pat1ially supported by Cincinnati Milacron an d the National Science Foundation (Grant DMI-9713488).
REFERENCES Chen, M. and Knospe. C.R. (2002)_ Experiments in Chatter Control with Magnetic Bearings . In: Proceedings of'the 2002 NSF Design. Service. and Manufacturing Grantees and Research Conference, San Juan, Jan. 7-10,1082-1095 . Chen, M_ and Knospe, C.R. (2003). A new approach to the estimation of cutting dynamics using active magnetic bearings, submitted to ASM E Journal of' Manufc/cturing Science (1nd Engineering. Fittro. R.L. (199R). A High Speed Machining Spindle with Active Magnetic Bearings: Control Theorl'. Design. and Application. Doctoral Disscl1ation . University of Virginia . Fittro, R.L. and Knospe, C.R. (1999). i control of a high-speed spindle thrust magnetic bearing. In: Proceedings of' the 1999 IEEE Illternational Conference on Control Applications, 570 - 575. Fittro, R.L., Knospe. CR., and Stephens, L.S ., (2003). Il-synthesis applied to the compliance minimization of an active magnetic bearing HSM spindle's thrust axis. Machining Science and Technology, 7. 19-51 . Hope, R.W .. Tessier, L., Knospe, C.R., and Miyamji. T. (1998). Adaptive vibration control of industrial turbomachinery. In : Proceedings of the ASMEI1GTf Turbo Expo, Stockholm. Sweden. Knospe, C.R .. Fittro, R.L., Stephens. L.S. (1997) Control of a high speed machining spindle via isynthesis. In: Proc. of 1997 IEEE International Conference 011 Con trol Applications, 912 - 917. Schweitzer, G_, Bleuler. H., and Traxler, A. (1994) Active Magnetic Bl!arings. Hochschulverlag AG an der ETH Zurich. Zurich, Switzerland. Stephens. L.S. (1995). Design and COllfrol o(Actil'£, Magnetic Bearings ./f)f- a High Speed Spindle. Doctoral Di ssertation. University of Virginia. Tlusty, J. (1984) . Dynamics of high-speed milling . ASME Produ ction Engineering, 12. 101-127.
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