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VIBRATION AND ROTOR DYNAMICS OF LARGE HIGH-SPEED MOTORS DRIVING COMPRESSORS IN THE OIL AND GAS INDUSTRY

Copyright Material IEEE Paper No. PCIC-2012-46

Sumit Singhal Member, IEEE SIEMENS AG

Large Drives, Berlin, Germany sumit.singhal@siemens.com

Abstract – All electric drive compressor systems are not only more efficient and reliable, but also help to reduce the CO2 footprint. Another advantage of using fully electric drives instead of gas turbines is that electric motors can start up the process much faster and smoother than gas turbine compressor systems. Besides the mechanical design, rotordynamic design, external factors such as foundation design can affect the vibration of the drive train.

Index Terms — Structural dynamics, Rotor dynamics,

Bearings, High speed, Foundation Design, Electric Motors, Magnetic Bearings.

I. INTRODUCTION

Electric motors for high-speed turbo compressors used in the oil and gas industry are limited by three factors: centrifugal forces, thermal considerations and rotordynamic (shaft vibration). The first fully electric liquefied natural gas (LNG) production was started in autumn 2007 [1] at Hammerfest, Norway. Variable-speed electric motors with power ratings of 16 MW, 32 MW and 65 MW were utilized to drive variable speed refrigerating compressors. Fully electric compression systems are not only more efficient and reliable but they also help to reduce the CO2 footprint. Another advantage of using electric motors instead of gas turbines is that electric motors can start up the process much faster and smoother than compressor systems driven by gas turbines. The decision of an operating company for a fully-electric drive solution is also based on the economic advantages, such as higher drive train availability, very low maintenance costs with long maintenance intervals and operational flexibility. Netherlands has several high-speed electric motor driven turbo compressor drive trains, which are all equipped with magnetic bearings on both the motors and compressors. The variable-speed drive electric motor has a rating of 23 MW at 5400 rpm with a maximum speed of 6300 rpm. Depending on the customer demand, compressor systems do not run at peak power all of the time. The requirement for the compression process is that all 25 compressor systems should run at the same time. Electric motor compressor drive trains have a lower total cost of ownership through higher availability and reliability of the drive trains. Magnetic bearings allow oil-free operation, remote monitoring of vibration behavior as well as a higher degree of reliability. A hermetically sealed raw gas compressor with a rating of 6 MW at 12,200 rpm directly driven by an integrated high-speed induction motor is currently operating in Netherlands [1] on

booster compressor duty. This is a canned motor-compressor with no seals between the process fluid and the external environment, and sealed active magnetic bearings, which provide the basis for future “zero emissions” and subsea compression systems where electric motors are the only choice. This design not only allows the contaminated raw gas to be handled but it also eliminates gas leakages to the environment and permits maintenance work to be carried out on the compression string: It is then possible to handle poisonous sour gas and facilitate intervention-free operation for periods not limited by the rotating equipment; this is a prerequisite for inaccessible subsea installations.

Large high-speed electric motors equipped with active magnetic bearings were also employed in refineries to drive compressor trains for dual catalytic cracking units (CCUs) in a large refinery located close to St. Louis, Missouri. The heavy crude found in the sands takes longer to refine using a cyclic process of heating and cooling to separate its parts for various uses. For a CCU application, it is imperative to have a motor with increased reliability, lower maintenance costs, and what is most important, provide uninterrupted service for at least five years.

Large high-speed special motors are also used in pipeline applications driving high-speed centrifugal compressors. Special motors offer customer-specific power, torque and

Converter Fed Synchronous Motors With Solid Turbo Type Rotor

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Fig. 1. Feasibility chart for Synchronous Motors

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speed levels to modernize the station to increase the volumetric flow of gas. A variable-speed electric motor with a power rating 12 MW

and with a speed range of 4500-9500 rpm will soon be tested in the factory. The technology of the motor is discussed in [2]. Large high-speed electric motors for the oil and gas industry must meet stringent vibration and noise requirements, which are laid down in specifications such as API, IEC and ISO. In

order to meet efficiency, vibration and noise levels, several components have to be optimized. The main focus regarding the motors, is its electrical design, which has a fundamental impact on the functionality and performance. However, with an increasing power and speed range of the motor, the mechanical design becomes more and more important in order to comply with the more stringent demands relating to noise and vibration limits. In order to comply with the customer’s vibration and rotor dynamics requirements for a wide speed range, special design calculations have to be performed. To avoid vibration issues on the test floor or in the field, rotor design, bearing design, dynamics of the interaction between the stator and rotor have to be calculated and optimized. For critical applications, rotor dynamics analysis has to be performed to predict the overall vibration behavior and stability of the complete system including the foundation data when mounted in the field.

II. CAUSES OF VIBRATION

1) Mechanical unbalance

API 684 [3], chapter 5.2 describes balancing as “A procedure for adjusting the radial mass distribution of a rotor so that the mass centerline (principal inertial axis) approaches or coincides with the rotor’s rotational axis, thus reducing the lateral vibration of the rotor due to unbalanced forces of inertia and forces on the bearings, at once-per-revolution frequency (1X).” API 684 emphasizes that achieving a balanced condition for a rotating assembly is a fundamental element of maximizing machinery reliability. An excess mass on one side of the rotor will cause unbalance.

2) Critical speed resonance A rigid rotor is defined as a rotor that operates far below its

first bending critical speed. The first bending critical speed of a rotor can be calculated based on the bending stiffness of the rotor only, not considering the bearing or support stiffness, and independent of the bearing type used. However, the first critical speed of a rotor-bearing system changes when the rotor is mounted on fluid film bearings. Critical speeds of a rigid rotor – soft bearing system can be predicted by performing a damped critical speed analysis which includes oil film bearing stiffness and damping coefficients besides shaft and support stiffness coefficients.

The combined stiffness of a rotor-bearing system is a function of the shaft and the stiffness of the two bearings as given by equation 1.

systemk1

= shaftk1

+ bearingk1

(1)

Equation 1 indicates that the combined stiffness of a rotor – bearing system will be less than the stiffness of the most flexible element, which is generally the fluid-film stiffness. In the case of sleeve bearing motors: Fluid film stiffness and damping in plain cylindrical sleeve bearings are anisotropic in nature (they have a different stiffness and damping coefficients in different directions), where normally the horizontal spring is softer (weaker) than the vertical spring. Due to this fact, a stiff shaft/soft bearing system will pass through two resonance

Fig. 2. Synchronous turbo-rotor motor with a rating of 65 MW at 3600 rpm to drive a main refrigeration compressor in a fully electric LNG liquefaction plant

Fig. 3. Synchronous 2-pole motor, 23 MW, 6400 rpm with active magnetic bearings

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points, also known as the rigid body mode of vibration [3] before the first bending mode occurs. API 684 defines a critical speed as a shaft rotational speed, which corresponds to a non-critically damped (AF>2.5) rotor system resonance frequency. In order to prevent catastrophic equipment failure and to increase the reliability of mechanical components at continuous operation close to or at the critical speed should be avoided at all cost. API specifications require a minimum 15% separation margin between the critical speed and the operating speed.

2) Self-excited instabilities A) Oil film instability

In rare instances, induction motor sleeve-bearing configurations are susceptible to large-amplitude lateral vibrations due to a “self-excited instability” also known as oil whirl [3]. Oil whirl is completely independent of rotor unbalance or misalignment, and is a self-excited instability caused by the forces generated in the lubricating oil film due to hydrodynamic action. During oil whirl, the rotor orbits in its bearing clearance at a frequency that is approximately less than half the rotor angular speed, and in the same direction of the rotor. If not controlled, this non-synchronous, self-excited orbital motion will continue to grow without any restrictions, which may lead to catastrophic bearing failure and equipment damage. It has been observed that at the onset of oil whirl, rotor behavior is unlike the resonance effect a critical speed, where the amplitude of motion builds up as the rotor reaches its critical speed and then decreases once it has passed through the critical speed. At the inception of non-synchronous whirl, the amplitude of rotor motion continually builds up at a frequency of approximately less than half of that of the rotor speed, and never subsides. Lightly loaded bearing or very large bearing clearances are the most common reasons for oil whirl problems in induction motor. The use of magnetic bearings instead of fluid bearings can be a better solution for motors susceptible to these kinds of instability.

B) Internal damping

According to the vibration theory, damping always reduces the amplitude of vibration and stabilizes the system. This is always true for non-rotating system; but for rotating systems, when the conditions are right, the internal damping arising from the internal friction within the material or structure of a revolving shaft or rotor can cause of vibration to build up and also lead to destabilization of the system. This counter-intuitive phenomenon, that rotational internal damping destabilizes the system was observed and explained in the 1920’s by Kimball and Den Hartog [5, 6]. This is the subsynchronous, self-excited phenomenon, which may be manifested in flexible rotor systems operating well above their first bending frequency. The primary cause of this type of instability has been identified to be internal friction in the shaft material, friction forces due to relative movement between shrunk fitted parts, loose rotating parts or components rubbing against one another. Internal damping within rotating systems cancels the stabilization effects of positive damping provided by external sources such as bearings, aerodynamics and material. The risks of instability caused by internal damping becomes higher in high-speed, flexible rotor systems where

fluid film bearing damping or so called external damping decreases due to higher speed, turbulences within lubricating oil film or location of bending nodes (location of no displacements) close to the bearings. According to author’s knowledge, subsynchronous instability in electric motors has not been reported in published technical literature. Nevertheless, care should be taken during rotor design, rotor dynamics and system design to ensure that all of the eigenfrequencies are adequately and positively dampened.

4) Misalignment The motor should be coupled to the driven equipment so

that the vibration does not increase beyond the vibration limit specified for the coupled assembly. The coupling should not be considered as a vibration damping device, and should be aligned according to the coupling manufacturer’s specification. Proper alignment in the cold and hot condition reduces the load on the shaft and bearings and minimizes vibration. From experience in the field and rotordynamic simulation, it has been observed that a certain degree of misalignment does not influence the rotor vibration much. However, if misalignment is above a certain threshold value, then vibration increases significantly with increasing misalignment. This phenomenon has been observed in the field where drive train vibration levels fluctuate with ambient temperature due to changes in the misalignment dependent on the ambient temperature. This is due to different thermal expansion levels of various mechanical drive components.

5) Electromagnetic excitation

A Unbalanced magnetic pull: An uneven air gap causes electromagnetic excitations due to unbalanced magnetic pull, producing higher magnetic forces in the direction of the minimum air gap. Deviations in part specifications or loose manufacturing tolerances in the stator and rotor components may cause an uneven air gap in the motor due to one or more of the following

1) Out of round stator and rotor bore 2) Out of round bearings housings and frame 3) Bent rotor shaft 4) Tolerance stacking of mechanical components 5) Thermal bow of the rotor

Minimum air gap Maximum radial force

Maximum air gap Minimum radial force

Stator

Rotor

Fig. 4. Schematic of uneven air gap

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A. Twice the line frequency vibration (electrical vibration)

Vibration at twice the line frequency can also be a significant portion of the overall vibration in induction motors. The source of this type of vibration is dependent on various parameters within the motor. The power source is a sinusoidal voltage that varies from positive to negative peak voltage in each cycle. The power supply applied to the stator produces a rotating magnetic field developing an electromagnetic attractive force

between the stator and rotor .This force reaches its maximum magnitude when the magnetizing current flowing in the stator is at a maximum, either positive or negative. As a result, two peak forces exist during each cycle of the voltage or current wave. However, stator and rotor forces go to zero at the point in time when the current and fundamental flux wave pass through zero. This results in a vibration frequency equal to twice the frequency of the power source (twice the line supply frequency). This particular vibration is extremely sensitive to the flatness of the motor mounting feet, frame and base stiffness and the consistency of the air gap between the stator and rotor. It is also very sensitive to the eccentricity of the air gap as shown in Fig. 5. Flux density is computed at the middle of the air gap between the rotor and stator in Fig. 5.

III. ROTOR DESIGN FOR HIGH SPEED

Good rotor design is the fundamental step for designing motors with lower vibrations levels. For a given speed range, the rotor should be designed such that its bending critical frequencies do not fall within the speed range. API specifications require at least 15% separation margin between the critical speed and operational speed range. The rotor bending natural frequencies depend on the bearing span (distance between the bearings) and shaft diameter. Decreasing bearing span or increasing shaft diameters increases the bending natural frequency. For a motor with variable speed and torque, shaft diameters and bearing span are optimized to meet power ratings, speed range, rotor dynamics and cooling airflow. For large, high-speed motors, where the circumferential speed is higher than 180m/s, a solid rotor design as shown in Fig. 6 is required to achieve good rotordynamic and vibration behavior. To achieve a satisfactory electrical performance, a complete copper cage including end rings is then inserted in the rotor body through open, milled slots. The solid shaft with the inserted copper cage after the oven process is shown in Fig. 6. The rotor parts after having been assembled together with the

Fig. 5. FFT of 3500 Hp 2-pole air gap flux with 10% and 50% air gap eccentricity

Increase at 2x line frequency with 50% eccentricity

Increase at 2x line frequency with 10% eccentricity

Fig. 6. Solid Induction motor rotor with embedded copper

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bearings and the fans before being inserted into the stator is shown in Fig. 7. The solid shaft makes it possible to realize all of the required numbers of balancing planes at the required

positions. In general there are at least three balancing planes available for the balancing and overspeed test in the balancing machine. These balancing planes are located at the end rings and in the middle of the active part, and may be used to balance the rigid modes and, if necessary, the first bending mode. There are also two balancing planes close to each shaft end, which are also accessible when the machine is mounted and can be used to finely balance the rotor if necessary. In electric motors, some amount of thermal energy is generated in the rotor, which is due to electromagnetic and aerodynamic effects. Thermal energy in the rotor can lead to mechanical deformation of the rotor, which in turn, can then cause local unbalance in the rotor that manifests itself as vibration. Therefore, to minimize the effects of thermal energy on rotor vibration, rotors should be well ventilated to minimize thermal distortion. High-speed rotors are equipped with shaft-mounted axial fans to generate the required air flow. Depending on the fan material, these can be attached to the shaft using a shrink fit or special mounting techniques as shown in Fig. 8. Fans made of a fiber composite material are usually used for high circumferential speed rotor designs due to their low weight. Lightweight carbon composite fans do not influence rotor vibration as the degree of unbalance resulting from centrifugal growth is very small, which is not the case with steel fans. Steel fans are usually much heavier than composite material and are shrunk onto the shaft, due to higher centrifugal growth at higher speeds. This growth can change the rotor balance conditions, which means that steel fans influence rotor vibration. Further, there is relative movement between the rotor and fan, which leads to internal friction in the rotor system, which in turn, decreases the rotor stability.

IV. BEARING DESIGN

A. Oil film bearings :

A good rotordynamics design is one of the key elements for reliable and efficient rotating machinery. In order to meet compressor speed requirements, for variable-speed motors operating at high speeds, the rotor bearing may have to be designed so that the system has a safe separation margin from the operating speed – or well damped so that if operated at the eigenmode then the vibration level should not increase. Bearings at the rotor supports play an important role regarding the position of the critical speed and damping of vibration. To meet the stringent noise and vibration requirements for large synchronous two-pole motors, two different motor designs were used depending on the power rating and the operational speed range: a flange-bearing design and a pedestal-bearing design. The pedestal-bearing design is used for very large power ratings, e.g. long and heavy rotors operating at a medium speed. The flange-bearing design is used for smaller rotors and higher speeds. For the upper speed range, the flange bearing design is supported on thick plates with flanges and ribs, which provides the structure with a higher degree of integrity and higher stiffness. However, it has a disadvantage regarding the accessibility to the individual machine parts. The cooling system also has an important impact on the decision regarding the design. Self-cooled rotors with shaft-mounted fans increase the bearing

Fig. 8. Axial fans made of fiber composites

Fig.7 . Assembled rotor with magnetic bearings

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span, which has a decisive impact on the lateral critical speeds of the rotor. For applications with wide speed ranges and certain torque characteristics, shaft-mounted fans are not able to cool the motor in the lower part of the speed range. In such cases, a forced cooling system is required. The next decision that the design engineer has to make is the choice of a two- or three-bearing design. The two bearing design has the advantage of shorter shaft length, but the overhung masses, the coupling at the drive end and the exciter at the NDE, can place restrictions on the second critical speed. Two-bearing designs lead to larger shaft diameters and bearing sizes. A three-bearing design is longer, but the critical speeds of the main rotor and exciter rotor can be individually adjusted. In general, there is no best choice. The decision must be made to achieve the optimum solution for each individual project. In most applications, conventional hydrodynamic fluid film bearings with special geometry – such as two-lobe, three-lobe, four-lobe and tilt-pad bearings – can be optimized to fulfill the rotordynamic criteria for the particular speed range. For the high-speed 16 MW compressor drive with a speed range of 5000–6700 rpm, a block-type design with three flange-mounted tilt-pad bearings was chosen. Because of the wide speed range, it was not practicable to shift all natural modes of the rotor outside the speed range. To move the second critical speed above the separation margin, very tight bearing clearances must be used to obtain a sufficiently stiff oil film. This solution was rejected because this will lead to very sensitive bearings. As an alternative, a bearing design with decreased preload and increased clearance was used. This gives a softer oil film with significantly increased damping for the second critical mode. In another compressor application a variable-speed electric motor with a power rating 12 MW and a speed range of 4500-9500 rpm was used to meet special power and torque requirements. Applications with the best process efficiency require a continuous speed range from 4500 up to 9500 rpm. In order to fulfill API criteria regarding vibration values and the requirement relating to rotordynamics separation margin, an optimized 2-lobe bearing was chosen. The bearings were designed to provide the required stiffness and damping for the rotordynamics separation margin. Special two-lobe bearings with increased preload factor along with tighter bearing clearance, which results in lower cross coupling terms, was designed to stabilize the rotor-bearing system in the higher speed range. B. Magnetic bearings

Magnetic bearings are ideally suited for applications where they provide superior value compared to other types of bearings. Value is a function of the following factors:

• High reliability and uptime • Clean (“Green”) environment • Speed capability • Better position & vibration control • Extreme conditions • Equipment design/development/testing • Machine diagnostics / condition monitoring

Magnetic bearings have some limitations which have to be considered

• Much lower load carrying capacity than oil film • Less tolerant to overload conditions • Requires back up bearings for an emergency landing

(if the magnetic bearings were to fail) The active magnetic bearings (AMB) of the motors levitate the shaft and permit relative motion without friction or wear, unlike traditional oil lubricated or grease lubricated motor bearings. The AMB consists of an electromagnetic assembly, a set of power amplifiers which supply current to the electromagnets, a controller, and gap sensor with associated electronics to provide the feedback required to control the position of the rotor within the gap. Each AMB is equipped with a back-up bearing for emergency coast-down in the event of a power failure to the AMB system. While the electronic sensors of the AMB are located on the shaft at the bearing positions, the back-up bearings are provided directly next to the magnetic bearings just in case the AMB closed-loop control were to unexpectedly fail. These back-up bearings have an air gap of approximately 0.5 mm, while the air gaps of the magnetic bearings and the sensors are about 2 mm. The purpose of the smaller gap in the backup bearings than in the magnetic bearings is to prevent the magnetic bearings from being damaged in case of faults or high vibration levels. Further, the back-up bearings are dry-lubricated, and the sleeve bearing shells are split and have a special material coating.

The following calculations are required to design motors with magnetic bearings: 1) Behavior of the rotor at the stall speed (zero speed), freely suspended in the air without bearing supports. This shows the locations of the nodes in the rotor for various bending mode vibrations. To ensure a rugged design, bearings and sensors should not be located at the nodes. If nodes exist at bearing or sensor locations, then changes should be made to the rotor, bearing or sensor locations so that all modes within the speed range can be observed and controlled. Fig. A-1 shows the example of various rotor modes freely suspended in air. 2) The next step is to see the variation of rotor bending critical speeds when varying the spin speed. At high spin speeds the rotor bending modes split into forward and backward rotation due to gyroscopic effects. This is shown in Fig. A-2. 3) To choose the proper bearing stiffness and damping parameters, the variation of eigenfrequencies with bearing stiffness and damping is observed as shown in Fig. A-3. 4) Based on the vibration and rotordynamic requirements to be fulfilled for operation over a specific speed range, bearing stiffness and damping parameters are chosen for the placement and damping of eigenfrequencies. 5) The controller and filter design strategy can be developed and optimized based on the above information.

The vibration and rotordynamic evaluation of motors

equipped with active magnetic bearings requires a few additional evaluations. In addition to critical speed and vibration amplitudes, as shown in Fig. A-6, actively controlled rotor-bearing is also checked for closed loop system robustness with respect to any external disturbances due to parameter variation. Closed loop design must meet the following requirements:

• Stability of closed loop system up to 2000 Hz • Modal damping of all modes in the speed range to

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be damped by more than 20% • Separation margin requirements according to API

617 or ISO specifications • Modal damping of rigid body modes by a minimum

of 40% • Sensitivity according to ISO Norm 14839/3 (default

<9.5 ) or API 617 Spec [8, 9]. • Unbalance responses for a given unbalance quality

grade are within limits: Bearing capacities that are high enough. Maximum amplitudes according to ISO Norm 14839/2

V. STRUCTURAL DESIGN

A) Interaction between rotating/non-rotating

structures

Electric motors are a special class of rotating machinery where there is strong interaction between the rotating shaft and non-rotating structures, such as stators and frame due to the presence of electromagnetic forces in the air gap. These act on both the rotor and stator. In order to have low vibration levels, the motor should be free of combined rotor-structural resonance points in the operating speed range. Rotating rotor and non-rotating structures are coupled through oil film forces at the bearing locations and also electromagnetic forces in the rotor-stator air gap. Electromagnetic forces generated in the air gap rotate at the line frequency and twice the line frequency. Forces at twice the line frequency can cause ovalization of the stator and frame, which is manifested as vibration and noise. It is also possible that these 2x deformations are transmitted through the base frame to the pedestal bearings. These then result in axial bearing housing velocities that can exceed the specified limit. These vibrations are related to second-order resonance amplification in the stator structure. To assess the vibration behavior and minimize the risk of vibration problems in the field, in critical drive trains, rotor dynamic calculations should be performed, including the non-rotating structures. Figure 9a & 9b show the pure rotor bending modes that are decoupled from non-rotating structures. Figure 9c shows rotor bending due to a large movement of the stator. This mode of vibration mode does not exist if full modeling of non-rotating structures is excluded from the calculation. Normally, the resonance points of a rotor can be easily identified. This is more complicated for the non-rotating parts because a sheet metal construction has many modes, and it is not so easy to filter out the critical ones. The modal mass is one indication for relevant modes. Only modes with sufficiently high modal mass have to be taken into account for structural vibration purposes. To identify the most critical modes, a forced vibration response calculation is normally required. The most sensitive factor for such types of calculation is the assumption of modal damping factors for the individual modes. Comparison of calculation and measured response values leads to modal damping factors of between 1 and 3%, depending on the participation of bolted connections or other damping elements in the mode shapes. In most cases, a visual estimation by looking at mode shapes (how many joint connections are involved in that mode) will lead to normal damping values. For detailed structural calculations, a

sufficiently accurate knowledge of the foundation is necessary, which is discussed in next section.

Fig. 9a. Pure rotor bending mode shape

Fig. 9b. Pure rotor bending mode shape

Fig. 9c. Rotor bending caused by large movement of non-rotating structure (stator)

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VI. FOUNDATION

High-speed drive trains for turbocompressors are mounted on either concrete or steel foundations. The vibration behavior of the drive train system on a concrete foundation is very different from that on a steel foundation. A concrete foundation has very high stiffness, and if designed correctly does not have much influence on the vibration behavior of shaft and bearing housings. The stiffness of a steel foundation is much lower than that of a concrete foundation, therefore it has a significant influence on the vibration behavior of the drive train system. This means that mass stiffness and damping of the foundation table should be included in the rotordynamic calculations to better predict the vibration behavior in the field. It is not uncommon to have a steel foundation that is much softer than the drive train structure. At the design stage, stiffness parameters of foundations are based on finite element models. Quality and modeling methods influence the derivation of foundation parameters that are used in rotordynamics models. The stiffness of the motors is normally not considered when designing the foundation. The mass and mass moment of inertia, e.g. of the motor, is usually modeled using single mass points. The connection of the mass points can be realized using rigid beams to the foot point of the motors. In an ideal case, the stiffness of turbo machinery foundations should be higher than the stiffness of the machinery oil film and bearing housing stiffness. For large turbo machinery trains this cannot be realized in every case due to arrangement and cost/space restrictions. When the foundation parameters are included in the rotordynamics model, this significantly affects the predicted vibration behavior. For soft foundation designs; rotordynamic behavior and vibration amplitudes predicted based on static foundation stiffness are very different than if the modal mass and the stiffness of the foundation is considered when making the analysis. The differences in the vibration amplitude calculations arises due to fact the system eigenvalues (natural frequency) may be different for these methods. If the system eigenvalue is close to the operating speed range, then this will amplify the vibration amplitudes. Realistic predictions can be made by finite element models of the complete system, i.e. the foundation and machine structure are included in the analysis. Such an analysis of the complete system requires a lot of computing power and expert engineering resources. Figs. 11a and b show examples of such calculations.

Fig. 10. Rotordynamic model schematic with foundation representation spring element

Fig. 11b. Foundation bending mode Influencing shaft preparation at the drive end of

th t

Fig. 12. Drive train on a steel foundation

Fig. 11a. Pure rotor bending mode concrete foundation

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In accordance with DIN 4024, there are two kinds of foundations. There are rigid foundations, meaning the first eigenvalues are higher than the operational speed. In most cases, only flexible foundations can be realized, which means the first or several eigenvalues are within the operational speed range. In this case, especially the stiffness of the foundation may influence the rotor dynamic calculation. To avoid vibration caused by the foundation, the first eigenmodes of the foundation should be as a minimum 20 % lower or 25% higher than the operational speed. The higher mode should have a separation margin of more than 10 %. The second design criteria also used for foundation design are effective in maintaining the vibration amplitudes at the machinery bearing housing and/or casing in accordance with DIN ISO 10816. For motor design vibration acceptance criteria, velocity measures in accordance with DIN ISO 10816-3, should not exceed 4.5 mm/s for rigid foundations and 7.1 mm/s for flexible foundations. The values are for Zone B/C, which means during operation. For the response analysis, an imbalance quality of G 6.3 and a structural damping of 2 % in accordance with DIN 4024[10] should be assumed.

VII. CONCLUSIONS

Special considerations have to be applied when designing high-speed electric motor drives in order to meet low vibration requirements. Special design features, optimization of the rotor, correct selection and optimization of fluid bearings and magnetic bearings are required to comply with rotordynamics and vibration limits. The interaction between rotating parts and non-rotating structures has to be considered to identify the effects of the system coupling on rotordynamics and shaft vibration. In addition to the motor design, external influences involving the foundation design can lead to high drive train vibration levels. To avoid vibration problems in the field, a complete system analysis consisting of drive train and foundation may be required.

VIII. REFERENCES

[1] H. Kuemmlee, P. Wearon, F. Kleiner, “Large Electrical Drives – Setting Trends for Oil & Gas Applications,” in IEEE PCIC Conference Record, 2008, PCIC-2008-30.

[2] H.Walter,A.Moehle,M. Bade,”Asynchronous Solid Rotors as High Speed Drives in the Megawatt Range“, IEEE PCIC Conference Record, 2007..

[3] API Std 684: Tutorial on the API Standard Paragraphs Covering Rotor Dynamics and Balancing.

[4] S. Singhal, R. Mistry, “Oil Whirl Rotordynamic Instability Phenomenon-Diagnosis and Cure in Large Induction Motors,” in IEEE PCIC Conference Record, 2009.

[5] A Kimball, “Vibration Prevention in Engineering”, New York, John Wiley & Sons, Inc, 1932.

[6] D. Hartog, “Mechanical Vibration”, New York, McGraw-Hill, 1934.

[7] API 546 – Brushless Synchronous Machines – 500 KVA and Larger.

[8] API 617 – Centrifugal Compressors for Petroleum,

Chemical and Gas Service Industry.

[9] ISO 14839: Mechanical Vibration — Vibration of Rotating Machinery Equipped with Active Magnetic Bearings, 1st Edition, 2004, ISO

[10] DIN 4024 – Machine Foundations: Rigid Foundations for Machinery with Periodic Excitations.

VITA IX.

Sumit Singhal graduated with a BSME degree from Bhilai Institute of Technology, India in 2000 and received a Master of Science degree in Mechanical Engineering from Louisiana State University in 2004. Sumit worked for the Center for Rotating Machinery (CEROM) as Research Assistant where he conducted research in an area of Rotordynamic Instability problems. He was Mechanical Engineer in the Above NEMA motor engineering group at Siemens Energy and Automation from 2004-2010. He is presently working in Siemens Large Drives Factory in Berlin, Germany as a Research Engineer, he is responsible for Rotordynamics design. Sumit is a member of IEEE and ASME. He is a member of the API 684 task force and vice chair of the PCIC Young Engineers Development subcommittee.

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Appendix A

HIGH-SPEED ROTOR ON MAGNETIC BEARINGS

Fig. A-1 Modes of vibration of the rotor for free supports

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Fig. A-2 Critical speed map Fig. A-3 Undamped stiffness variation vs critical speed map

Fig.A -4 Critical Speed Map of Closed Loop

Fig. A-5 Sensitivity plot of closed-loop system

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Fig. A-6 Unbalance response with balance grade ISO 2.67 G

Fig. A-7 Bearing control currents requirements with speed for balance grade ISO 2.67 G