Vibration Criteria Considered from Case Studies of Active Magnetic Bearing Equipped Rotating Machines

Department of Mechanical Engineering, The National Defense Academy, 1-10-20 Hashirimizu, Yokosuka, Kanagawa, Japan 239," l)Faculty of Mechanical Engineering, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, Japan 812-21, lshikawashima Noise Control Ltd., Ryuseido Okubo Bldg. 1-15-18 Hyakunin-machi, Shinjyuku, Tokyo, Japan 169; ’Compressor Design Department, Tsuchiura works, Hitachi Ltd., 603 Kandatsu-machi, Tsuchiurashi, Japan 300


INTRODUCTION
A few types of active magnetic bearing (AMB) equipped rotating machinery are currently being implemented successfully in the commercial business market since the development phase of the AMB borne rotor was completed.Some successful exam- ples include turbo-molecular pumps, expanders in chemical plants, spindles in machine tools and centrifugal compressors in turbo machinery.The new concept of AMB is indeed welcome, thanks to its features of being contact free, maintenance free and without mechanical losses.
A typical system supported by the AMB is illustrated in Fig. 1.AMBs are located at both ends of the shaft including adjacent placements of displacement sensors and emergency (auxiliary) ball bearings.The control network for driving the AMB device is shown in Fig. 2. As shown in these figures, each displacement sensor detects the shaft position at bearing portions and its signal is fed back to the compensator.The deviation from the bearing center is put into the PID (Proportional, Integral and Differential actions)controller.The controller drives the power amplifiers to sup.ply the coil current and to generate the magnetic force for the levitation and vibration control.Instead of PID, many modern control laws, e.g., LQ and H-infinity, are being investigated for this servo-feedback control design.
The AMB dynamic characteristics is governed by the controller transfer function.An example of the transfer function of a PID controller is illustrated in the Bode diagram of Fig. 3.The phase lead frequency domain of the phase curve, e.g., 0.1-10   ROTOR AMB (non-dimension frequency/the first free-free bending frequency), can provide positive damping to the rotor system, but negative damping in other frequency domains.In this example, the vibrations of the rigid modes and the first bending mode are covered by the positive damping domain.
Compared with conventional oil film lubricated bearings having only positive damping, it can be said that the AMB provides low bearing forces due to limits of the magnetic density.Therefore, concerning bearing support stiffness, the former is strong, and the latter weak.Another opinion might say that the former is too strong, but the latter is preferable.
The main part of turbo machinery is still supported by oil film lubricated bearings.The rotor vibrations can be suppressed within low levels thanks to its stiff support.Vibration evaluations applied to the current type of rotating machines are covered by ISO standards (ISO 7919/1-5) (1996).
These ISO standards consequently require low limits for a permissible vibration level.On the other hand, it is hard to suppress AMB rotor vibrations within such low levels due to the feature of its weak bearing stiffness.Furthermore, the AMB design requires the placement of the AMB at the location of the vibrating portions for effective vibration control.Large vibration magnitude is thus inevi- tably measured in spite of being normal.
This difference between AMB and oil film bearing dynamics induces a potential conflict FIGURE 3 AMB controller transfer function: Note that the positive and negative values of the phase curve correspond to the phase lead and lag, i.e., the positive and negative damping factors, respectively.
between customers and manufacturers.In the case of process compressors equipped with AMBs, a customer requires a manufacturer to comply with the API 617 (1995) regulation which provides for low vibration limits in the same manner as if the compressor were supported by oil film lubricated bearings, though it is actually supported by AMBs.These present limits are too strict for the AMB rotor manufacturing side.
As mentioned above, we need to prepare new ISO standards which will accept the relatively high vibration limits in accordance to the requirement of proper AMB design and operation.This paper proposes new vibration criteria for AMB equipped rotor systems in order to ultimately solve this contradiction.
been recently introduced this type of turbo machinery.The consideration of the differences between the bearing dynamic characteristics of both types, i.e., the strong support of the oil film bearing and the weak support of the AMB, are not considered in these series.So far each vibration criteria prepared in ISO and/or AP! standards govern uniformly oil film bearing equipped turbo machinery.Unfortunately, there are no vibration standards concerning AMB equipped turbo machines.
Because of these concerns, Japanese experts have proposed international standardization for AMB related technology to the ISO TC108/SC2.
The objectives of this standardization are as follows: REQUIREMENTS FOR ISO TC108 ON RELATED VIBRATION REGULATIONS A set of ISO standards on rotor vibration regula- tions for turbo machines is given in ISO 7919 series.ISO 7919: Mechanical vibration of non-recipro- cating machines: measurement on rotating shaft and evaluation criteria Vehicle and Structures)/WG1 (Vibration of Machines) has been developing the ISO 7919 series which specifically covers the vibration of turbo machinery; turbines, generators, compressors, pumps, and so on.When considering centrifugal compressors, these rotors are conventionally supported by oil film bearings, e.g., tilting pad bearings.The AMB has (1) to define AMB terminology for promoting mutual understanding for the relevant people, (2) to resolve conflicts between venders and users with proper designs and operations, (3) to provide vibration criteria to simplify contract concerns, commissions, etc., (4) to promote a design, operation and mainte- nance guides for AMB equipped rotors, (5) to accelerate low cost production and wide- spread applications.
ISO agreed with the necessity of this standardiza- tion and organized a new WG7 on Vibration of Active Magnetic Bearing Equipped Rotating Machines.This paper will be contributed for a working draft of WG7 which covers AMB rigid and flexible rotors.This paper concerns steady state vibrations measured during normal continuous operation, but not resonance vibrations for passing critical speeds.Resonance vibrations are stated in ISO 10814 titled "Mechanical Vibration Susceptibility and Sensitivity of Machines to Unbalance."According to this standard, rotor resonance vibra- tions are evaluated by the modal sensitivity, so called Q-value.This Q-value evaluation was stan- dardized in reference to Balda (1975) and Shiraki and Kanki (1979).

CASE STUDIES
Active Magnetic Bearing Applications to Centrifugal Compressor Fukushima et al. (1994) showed that AMB equipped centrifugal compressors were manufactured by Hitachi Ltd., Japan, and installed at a refinery plant in Okinawa Sekiyu Seisei Co., Ltd. as the end user under the project contract of Idemitsu Engineering Co., Ltd. and Chiyoda Corporation.As shown in Fig. 4, this turbo machine is a train system which includes a turbine and high and low pressure com- pressors, noted (HP) and (LP), respectively.These rotors are connected with flexible couplings.These LP and HP compressors are supported by AMBs.This turbine rotor is conventionally supported by oil film bearings.The rotor configurations of the LP and HP compressors are drawn in Fig. 5, includ- ing eigen mode shapes obtained by average values of the AMB supporting stiffness.The LP and HP compressors have 7 and 8 stage impellers with the rotor weight of 780 and 930kg, respectively.As shown in Fig. 5, the control theory demands that the AMB actuator locations should be on such vibrating portion of eigen mode.This demand opposes the desire for low levels of resultant vibrations.
The design specifications for the process compressor is shown in Table I.The rated speed is 10,900 rpm-182 rps with the nominal shaft power 4120kW.The specification with respect to the AMB is shown in Table II.These radial AMBs are specified by L/D:O.98,C/R:6.8/1000 with C-one side clearance=0.5mmper the AMB journal diameter= 147mm.It is noted that the clearance of the auxiliary bearing is set by about half the AMB clearance for protecting emergency contacts of the AMB itself.
Comparison Between Oil Film Bearings and AMBs on Critical Speed Map One of the most important aspects for designing process compressors is the critical speed map.In order to better understand rotordynamics in comparison with oil film.bearings and AMBs, a uniform shaft simplified from actual rotors is selected, having the equivalent diameter of 150mm and the same length of the LP as shown in Fig. 5.The critical speed map is thus calculated for the uniform shaft, as shown on a non-dimen- sional chart of Fig. 6.The vertical axis is the natural frequency normalized by the first free-free bending mode.The horizontal axis indicates the bearing FIGURE 5 Eigen mode shapes of LP and IHP rotors: The operational speed is set between the 3rd and 4th critical speeds.
The AMB locations are avoided to be not node of each eigen mode, because of maintaining enough controllability.A typical critical speed map of a uniform shaft being equivalent to LP rotor: The critical speeds, Nci, are defined by intersections between natural frequency curves and bearing stiffness curves of oil film bearing and AMB.The possible operational speed are set separately from these criti- cal speeds to allow certain margins, as indicated by shaded regions.
stiffness normalized by "corner stiffness" which is identified by a veering point of the first eigen frequency curve.The curve inclines and then holds steady, as the bearing stiffness increases.In other words, the first eigen mode shape changes from the rigid mode to the first pin-pin bending mode.This value will be clear if the map is displayed in the loglog scale.
On the critical speed map, the left and right ends suggest the free-free condition and the pin-pin condition applied to both bearing portions, respec- tively.The oil film lubricated bearing is generally plotted on the right side due to the strong bearing stiffness.On the other hand, because of weak stiffness, the AMB is plotted on the left side.
In the case of the oil film bearing, its predicted stiffness line (dotted line, X and Y directions) is drawn on the map.The first and second critical speeds are thus marked by the intersections between the eigen frequency curves and the oil film bearing stiffness, noted Ncl and Nc2, respectively.The compressor to be designed as a rigid rotor must locate the operational speed under the Nc within a certain margin as indicated by the B1 region.For the super critical compressor categorized in the flexible rotor, the rotational speed is operated in the range between Nc and Nc2 within a certain margin as indicated by the B2 region.
In the case of the AMB, its predicted stiffness is also drawn on the map on the left side, because the stiffness provided by the magnetic force is much weaker compared to the oil film bearing force.Corresponding critical speeds are noted Ncl, Nc2, Nc3 and Nc4.These shaded regions of A1 and A2 become the possible operational regions for so called rigid and flexible rotors, respectively.For instance, turbo-molecular pump, as one of the successful applications of the AMB, is designed to be the rigid rotor so that the rated speed is placed in the A1 region under the first bending critical speed Nc3.Some AMB equipped compressors are also categorized in this region.The super critical compressors employing the AMB are operated in the A2 region between the first and second free-free bending critical speeds of Nc3 and Nc4.As seen in the Hitachi AMB compressors stated above, this type of super critical AMB compressor is focused to the discussion concerning vibration evaluations.
Generally speaking, the configuration of the oil film bearing is determined by LID and C/R-- 0.001.Since the bearing stiffness is so large, the bearing reaction force is very sensitive to resultant vibrations which must be regulated at low limits.
Then, rotors should be well balanced.In the case of AMB, the configuration is mostly seen in about L/ D and C 500 m.Since the stiffness is so weak, the transmission force from the rotor to the floor, i.e., the bearing reaction force, is still at a low level even if the rotor vibrates at a large level.It can be said that the AMB stiffness requires another new vibration regulation for own usages.
A typical unbalance response curve of AMB equipped flexible rotors is illustrated in Fig. 7.The unbalance resonance vibration peaks appear at Ncl, Nc2, Nc3 and Nc4.The first two modes correspond to the rigid mode critical speeds, i.e., parallel and conical modes, which are commonly well damped by PID controls.The third critical speed Nc3 requires fine tuning to provide a sufficient damping effect to pass the resonance.The operational speed is thus set in the range between the third (Nc3) and fourth (Nc4) critical speeds with a large margin under the fourth resonance speed.As shown in this unbalance response curve of Fig. 7, the rated speed, the maximum continuous speed (MCS), the trip speed and the minimum speed (MIN) are determined by referring to the API guidelines.It is noted that the operational speed range of the AMB rotor is set between Nc3 and Nc4 in the A2 region and it will be generally more narrow than the B2 region of the oil film type bearing.The possibility of reduction of the operational speed range for the AMB rotor, compared with the oil film bearing, must be care- fully checked in advance.
Critical Speed Layout of AMB Flexible Rotor The critical speed map of the LP rotor is shown in Fig. 8 on a linear-linear chart.The AMB dynamic characteristics are featured by the transfer function of the controller.The decomposition of the transfer function can provide the spring (K) and damping forces (C) depending upon the rotational speed (f), as separately shown in the figure.The former is determined by the real part of the transfer function and the latter is the imaginary part.So called undamped critical speeds are indicated by the intersections between the natural frequency curves and the spring force curves as indicated by Ncl, Nc2, Nc3 and Nc4.The operational speed range must maintain enough of a margin against the fourth critical speed Nc4.This reveals a typical example of the critical speed layout for the AMB compressor.
In the case of the AMB, modifications of the transfer function are possible by the implementa- tion of control electronics.For instance, one of the modifications is realized by the so called ABS network innovated by Habermann and Brunet  (1985), as shown in Fig. 9.In the figure, the tracking filter including the PLL circuit triggered by the rotational pulse can select only the unbalance vibration which is synchronized with the rotational speed.The substitution in this figure indicates the removal of the filtered unbalance vibration component from the detected displacement signal.The degree of this removal corresponds with the value of this gain Ga.In the case of Ga--1, the absolute removal of the unbalance vibration is achieved.
Half the unbalance vibration is removed if Ga 0.5 is set.The removed signal is then fed to the PID controller.
Consequently, the AMB stiffness is variable by selecting this gain Ga so that the corresponding spring curves are drawn on the critical speed map, as shown in Fig. 8. From the vibration theory point of view, the bearing stiffness for unbalance vibrations is ulti- mately unnecessary at the rated operation because of no resonance.If ultimately Ga is set, the corresponding fourth critical speed is equal to the second free-free bending frequency as indicated by Nc4 t, instead of Nc4 with Ga 0. It is noted that these downward modifications of AMB stiffness induce the reduction of the fourth critical speed which becomes then closer to the operational speed region.In fact, the unbalance response curve sharply increases toward the Nc4' critical speed, as shown in the case of ABS (Ga 1) in Fig. 7.In this way, the rotation under the free-free condition due to the addition of the ABS network becomes dangerous.However, this disadvantage is compen- sated by the trade-off with several merits: lessening the reaction force transmitted from the rotor to the floor and disappearance of the restriction for dynamic current consumption for vibration control.

Rotation Test Results
Each LP and HP compressors must independently satisfy the shop performance test in accordance FIGURE 11 Unbalance response influenced by ABS: Note that the ABS induces the reduction of 4th critical speed and system instability near the 3rd critical speed.
with ASME PTC-10 and the mechanical run test in accordance with API 617.The test results at the final phase of the mechanical run done at the shop are shown in Fig. 10, as unbalance response curves.Owing to the well rotor balancing, the unbalance vibration amplitude is suppressed enough to the low level of about 20 lampp, though the value itself is still larger than the oil film type of compressors.Depending upon the gain Ga of the ABS circuit shown in Fig. 9, the possible upper limit of the operational speed range is restricted by the unbal- ance resonance of the critical speed Nc41 as illu- strated in Fig. 7.This fact is examined through a test by exciting the rotor by harmonic waves at stop.The result is shown in Fig. 11.Instead of a rotational pulse, the excitation harmonic wave signal is con- current with the trigger signal to the PLL function.It is also noted that the decrease of the Nc4 critical speed to the Nc4' is remarkably recognized by the reduction of the AMB stiffness corresponding upon the selection of the gain Ga.Vibration limitation levels which should be satisfied were agreed by this project as shown in Fig. 12.This criterion was determined by calcu- lating non-contact conditions between the rotor and stators within a certain margin.The minimum clearance for the non-contact is determined by considering static deflections, vibrational eigen mode shapes and/or rubbing vibration deforma- tions between rotating and stationary parts, e.g., touch down bearing, sensors, labyrinth seal, balanc- ing piston and other parts.The shop test of Fig. 10 proved that these vibration limit levels agreed with the vender and the user are comparably large with conventional oil film bearing type compressors, but are still within normal limits for the AMB rotor.
Since the machine was installed on site for the commission 5 years ago, continuous operations have been completed including the repeat of maintenance every six months without any major problem, as of this writing.An example of field data measured on site is shown in Fig. 13.Steady state data at normal operations concerning the vibration and the current are 50 lampp and 3 5 % of the current capacity, respectively, as shown in Fig. 13.Both measured values of the vibration and the current are low enough in comparison with each upper limits; about 100 lampp in vibration amplitude and 60 A in current which are indicated on the vertical axes.An example of vibration magnitude measured during a  The difference between these upper and lower coil currents is for the rotor levitation.
certain start-stop test is shown in Fig. 14.These vibration data during MCS and MIN operations reveal base line values ranging between 40 and 60pmpp.These data fall within predetermined limits.
is just beginning.The initial kick-off meeting of WG7 was held during the program of the ISO TC108 annual meeting at DIN, Berlin, in September, 1997.Every expert from each country can be encouraged to join this project.Kamemitsu el al. (1996) proposed a working draft on AMB vocabulary as a Japanese delegate.
Measurement Procedure PROPOSAL DRAFT FOR ISO AMB PROJ.ECT ISO TC108/SC2/WG7: AMB Project ISO TC108/SC2/WG7 has been organized to discuss AMB related technology and the required vibration criteria for the AMB equipped rotating machine.The standardization for the AMB project AMB equipment in rotating machines has its own displacement sensor for detecting shaft motion within the servo-feedback system.The detected value of shaft vibration by the AMB sensor equipment is subject to these guidelines, but no sensor is additionally needed for this purpose.This rotor vibration evaluation excludes the vibration of the stationary parts of the machine.The AMB coil current should be monitored for this evaluation.
Criterion 1" Evaluation Zone Limits One of the features of the AMB is its large AMB clearance.If the rotor does not make contact with the stators, it can be said that even large vibrations are within normal limits.Therefore, based upon the characteristics of AMB, the criteria concerning the vibrations and current are derived from the following parameters: (1) No contact With bearings, adjacent displace- ment sensors, stationary labyrinth seals and auxiliary (emergency, touch down) bearings; (2) Limit of current compared to power amplifier capacity.
The first parameters concerning each clearance indicate the minimum clearance required for avoiding any rotor rub at any portion of the shafting even in a state of emergency.Thus, the minimum clearance, noted Cmin, is commonly defined by the clearance of the auxiliary bearing assuming touch down operations in an emergency.The clearance of the auxiliary bearing is usually determined by half the AMB clearance.The second parameter indicates the current supply capacity, noted Ic, which can provide the maximum current for supplying AMB driving power devices.As an allowable limit for Zone B, it is recommended that the limit values of vibration and current magnitudes be 60% of each possible maximum value, Cmin and Ic, because these limit values should be a design point when considering excess load and/or unex- pected excitation force.The zone table is thus proposed as shown in Table III.The parameters of each zone is described in the guidelines of ISO 7919-1, as follows.Zone A: The vibration of newly commissioned machines would normally fall within this zone.
Zone B: Machines with vibration within this zone are normally considered acceptable for unrestricted long-term operation.Zone C: Machines with vibration within this zone are normally considered unsatisfactory for long-term continuous operation.Generally, the machine may be operated for a limited period in this condition until a suitable opportunity arises for remedial action.
Zone D: Vibration values within this zone are normally considered to be of sufficient severity to cause damage to the machine.
These zone limit values are applied to the measured value of the base line vibration magnitude under steady state operational conditions.According to these criteria, broad-band vibration magnitude less than 100 lampp is thus accepted as Zone A, if Cmin 250 gm of the auxiliary bearing clearance is commonly employed.These values are rather large compared to the present ISO or API 617 criteria, as stated in the following sections.
Criterion 2: Change in Vibration Magnitude This criterion provides an assessment of the change in vibration magnitude from a base line.A sig- nificant change in broad-band vibration magnitude may occur which would require some actions even though Zone C of Criterion has not been reached.Such changes can be progressive with time or virtually instantaneous and may point to incipient damage or some other irregularity.Criterion 2 is specified on the basis of the change in broad-band vibration magnitude occurring under steady-state operating conditions.When Criterion 2 is applied, it is essential that the vibration measurements being compared are taken at the same sensor location and orientation, and under approximately the same machine operating conditions.Significant changes from the normal vibration magnitudes should be regulated to be less than 25% of the upper boundary value of Zone B, as defined in Table III, because a potentially serious fault may be indicated.When change in vibration magnitude exceeds this value, diagnostic investigations should then be initiated to determine the reason for the change and to decide what further action is necessary.

Comparison with Present Criteria
Assuming that the minimum clearance of Cmin 250 gm is employed in usual AMB turbo compressors, each zone value of our evaluation criteria mentioned in the previous section is proposed as shown in Table IV.According to our proposal, even in Zone A, the large value of 100 lampp is accepted.
According to the API 617-6 standard criteria regarding centrifugal compressors, the following vibration regulations would be: 4 /12,000 aPl 617-6, Lv-25.V)V-cs and Lv < 25.4 tmpp, where NMcs=maximum continuous speed (e.g., Lv=25.4gmpp, if MCSll,445rpm).These values are too severe for the commission to exert AMB rotors.As mentioned in these case studies, these proposed evaluation values seem shockingly large compared to present related criteria.However, these values fall within safe parameters and is our recommendation.

Comparison with Experimental Data
As stated in the literature, Fukushima et al. (1994), a Hitachi AMB centrifugal compressor, as shown in Fig. 1, was installed in a refinery plant.As shown in Fig. 12 which agreed with this vender-customer project, the alarm level at the maximum continuous speed was determined as 158 x 0.8 126 gmpp, i.e., approximately the half of the auxiliary bearing clearance of 230 gm.The corresponding field data indicate the vibration magnitude of about 60 gmpp at maximum which satisfied their own criteria.
On the other hand, because this Hitachi AMB centrifugal compressor employed the auxiliary bearing clearance of Cmi 230 gm, our proposed criteria for ISO standards are provided in Table V in which the limit value of Zone A is recommended by Cmi x 40% =92gmpp.It is found that this machine has been operating under normal working conditions while satisfying the vibration evaluation criterion of Zone A.

CONCLUSIONS
Japanese experts have prepared a draft proposal for vibration criterion to be applied to industrial turbo machines equipped with AMBs.Prior to In the case of Cmi 230 gm.
determining the zone limit values, the design review of AMB equipped compressors was executed with respect to the relationship between AMB dynamic characteristics and critical speed design of flexible rotors in comparison with the case of oil film bearing type compressor rotors.The vibration limits are proposed through the determination of the minimum possible clearance which avoids all contact and/or rubbing at any location between the rotor and stator sides.The case studies concerning the Hitachi compressors equipped with the AMB are successfully functioning under these criteria.
Since the ISO TC108/SC2/WG7 AMB project was initiated, the committee would like to.solicit the review of this draft for vibration evaluation criteria.Your opinion is welcome to help in this endeavor.

FIGURE
FIGUREActive magnetic bearing equipped rotor system.

Part 1 :
General guidelines, Part 2: Large land-based steam turbine generator sets, Part 3: Coupled industrial machines, Part 4: Gas turbine sets, Part 5: Machine sets in hydraulic power generating and pumping plants.ISO TC 108 (Mechanical Vibration and Shock)/SC2 (Measurement and Evaluation of Mechanical Vibration and Shock as Applied to Machines, FIGURE 4 Train of AMB equipped compressor.
FIGURE 7 A typical unbalance response curve: According to API 617, the separation margins of MIN, MCS and Trip speed are expressed in percent.If the ABS function is switched on at MIN, it works afterward in all of operational speeds.

FIGURE 8
FIGURE 8 Critical speed map of LP rotor: The selection of the ABS gain Ga in (0.0-1.0) varies the reduction of bearing stiffness.

FIGURE 9
FIGURE 9 Network including ABS: Ga=0 indicates PID only without ABS.Ga= creates no control for unbalance vibrations.

FIGURE 14
FIGURE 14 Field data (during start-stop): (1)-(4) indicate shaft lateral vibrations and (5) an axial vibration.The upper chart is for LP and the lower for HP.

FIGURE 13
FIGURE 13 Field data (vibration and current): The power amplifiers work as the A-class specification are providing the constant current of 30 A to upper and lower directional coils.
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TABLE III
*Cmi minimum clearance and Ic current capacity.