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THERMAL ROTOR INSTABILITY IN GAS COMPRESSORS

JOHN A. KOCUR AND FRITS M. DE JONGH DEMAG DELAVAL

USA/ The Netherlands

Presented at Venezuelan Gas Processors Association (AVPG)

XIV International Gas Convention May 10-12, 2000

Caracas, Venezuela

ASPECTOS OPERATIVOS Y OPTIMIZACION EN COMPRESION DE GAS

AVPG, XIV Convención de Gas, Caracas, Mayo 10 al 12, 2000. Página 2

TT HH EE RR MM AA LL RR OO TT OO RR II NN SS TT AA BB II LL II TT YY II NN GG AA SS

CC OO MM PP RR EE SS SS OO RR SS By

John A. Kocur, Jr. Manager, Compressor and Test Engineering

Trenton, NJ USA and

Frits M. de Jongh Manager, Research and Development

Hengelo, The Netherlands Demag Delaval Turbomachinery

Abstract

The phenomenon of thermal rotor instability in gas compression equipment is explored. Differential heating of the journal at the radial bearing locations has been identified as the source of the instability. Theoretical investigations have shown that fluid film bearings inherently exhibit a non-uniform temperature differential around the circumference of the bearing journal. This has been confirmed with test data on an instrumented rotor. The differential heating leads to a rotor bow. In combination with the overhung masses of impellers or couplings, an increase in the unbalance of the rotor results and, correspondingly, the synchronous vibration levels. In certain situations, the synchronous vibration can become unbounded, i.e. unstable, and can not be predicted using the “standard” rotordynamic tools.

This paper describes the thermal rotor instability phenomenon referred to as the “Morton Effect”. The experimental efforts to measure the differential heating are described and presented. This work was incorporated into existing rotordynamic analysis methods to obtain a predictive tool. The prediction is based upon unbalance response calculations made in concert with the experimental results from the test rig. As with classical rotor instability calculations associated with subsynchronous vibrations, the susceptibility of the rotor/bearing configuration to the thermal bowing and unbounded growth of the synchronous vibration is calculated.

Gas compression equipment has been shown to be susceptible to this behavior due to the overhung impellers used in pipeline service and the high horsepower rotors used in gas boost service. Two such examples are discussed. The first rotor is a single stage overhung pipeline compressor. In this case, vibration

problems had plagued operation since the train commissioning. Thermal bowing was evident on the impeller end probes as synchronous vibration levels at maximum continuous speed increased independently of speed. Modifications to the impeller to affect the overhung mass were not practical. A journal sleeve was installed to isolate the differential heating from the shaft. A second example of a 30,000 HP gas boost compressor is presented. The high power input into the shaft required a large shaft end and coupling. The greater overhung moment increased the sensitivity of the rotor to thermal rotor instablity. The described analytical method was used to determine the overhung moment acceptable to the rotor/bearing configuration. In both cases, the growth of the synchronous vibration was eliminated.

Introduction

Thermal or synchronous rotor instability due to differential journal heating is not a well-known rotordynamic phenomenon. One of the reasons of this may be the misdiagnosis of the problem. Several more publicized conditions, piping strain and rubbing (Newkirk, 1926), also are connected with changes in synchronous behavior over time. Even if thermal rotor instability is considered as a possible cause, direct measurement of the differential temperature in the journal to identify the source of the vibrations may be difficult if not impossible. In the authors’ opinion, this highlights the need to develop an accurate and reliable prediction tool to assist the designer or troubleshooter in identifying compressors susceptible to this behavior.

It is assumed that a few percent of the newly designed and existing rotating compression equipment are affected by this phenomenon. The extent of the problem may range from higher than desired synchronous levels or vibration magnitudes deemed unsafe for operation. The nature of the problem can be experienced as an increase of synchronous levels over a short period of time or the fluctuation of both the synchronous phase and magnitude. In the worst case, the levels may increase unbounded causing damage or outright failure of the rotating equipment.

Theoretical investigations have indicated that rotors supported by fluid-film bearings inherently exhibit a non-uniform temperature distribution around the bearing journal circumference (Keogh and Morton, 1993 & 1994). The effect this had on a particular compressor rotor was investigated at the authors’ company including the development of an experimental rotor rig to measure the temperature differential (de Jongh and Morton, 1996). This differential results in rotor bending, which in combination with an overhung mass, can significantly increase the unbalance and thus, synchronous rotor



vibration. In certain circumstances, it can lead to synchronous rotor instability.

Especially susceptible to this phenomenon is high-speed compression equipment with relatively large overhung moments. While the obvious candidates are overhung compressors and expanders, drive-through compressors and high horsepower equipment can also experience thermal rotor instabilities. The phenomenon was also observed on the high-speed pinion of a parallel gear box. The type of equipment afflicted is diverse and not limited to a particular configuration or application.

Faulkner, et al. (1997) describe a case history of a radial inflow turbine exhibiting the described phenomenon. The problem was recognized and resolved by changing the bearing geometry. It was argued that the thermal bowing would be less evident if the bearing would be loaded to a higher eccentricity. Experimental investigation of this hypothesis is underway at the authors’ company. A special bearing test rig has been developed to study the effect of bearing loading on the temperature differential.

Corcoran, et al. (1997) describe an extensive case history involving a compressor rotor with a high overhung moment. While not recognized as such in the paper, the authors believe that the compressor is experiencing a thermal instability problem at the coupling end bearing. It is interesting to see that either decreasing or significantly increasing the coupling weight can solve the problem. This fact is confirmed by the theory under certain circumstances.

Berot, et al. (1999) describe another case history of an overhung centrifugal compressor. At a constant speed of 6536 rpm, the rotor of this compressor clearly showed synchronous spiral vibrations. The problem was successfully solved by reduction of the NDE bearing width.

This paper presents a description of the thermal rotor instability phenomenon, the experimental verification and calculation method developed to predict it. Two case histories are also presented as examples of gas compression equipment with a vibration problem caused by differential heating in the bearing journal. Solely addressing thermal instability as the cause solved both vibration problems.

Phenomenon of Thermal Rotor Instability

The root cause of thermal rotor instability is a temperature effect, which appears in all practical fluid-film bearings. This temperature effect is the result of differential heating of bearing journals. It is normally assumed that a rotating bearing journal has a uniform temperature distribution around the journal circumference. However this assumption does not hold true when a journal is orbiting in its bearing with a whirl

frequency synchronous to the rotor speed (Morton, 1994). In fact, every practical journal will execute a small synchronous orbit due to residual unbalance that exists in the rotor. Any journal that is synchronously orbiting in a fluid-film bearing produces a temperature difference across its diameter. Figure 1) shows a bearing journal, which is rotating with a constant speed, executing a forward circular orbit. One specific point on the journal will always be at the outside of the orbit and will therefore be nearest to the bearing wall. The point opposite of it will always be furthest away from it. Due to differences in the oil-film shearing, different heat input will be generated for these two points resulting in a differential temperature locally across the bearing journal. This will result in a thermal bend. Figure 1) shows this principle and indicates the point on the journal with the smallest distance to the bearing wall as the ‘hot spot’, whereas the point opposite to it is indicated as the ‘cold spot’. The greater the size of the orbit, the larger the differential temperature. In Figure 1), a forward circular orbit is shown, but the same principle applies for a backward orbit when the journal is positioned eccentric in the bearing, although the heat input will be smaller in this case. For an elliptical orbit, the forward and backward thermal effects can be superimposed, since a linear system is assumed.

Figure 1) Differential Heating at Bearing Journal for Synchronous Forward Rotor Whirl



Figure 2) shows the instability principal for a rotor with one overhung end. For simplicity, the concentrated overhung mass, Mc, is located at the rotor end at a length, l, from the bearing. If we consider for this rotor a very small synchronous orbit vector, ε, at the bearing location, a small thermal bend, θ, will be developed, due to differential heating at the bearing journal, and an unbalance vector, U, will result at the overhang. The unbalance vector can be described as:

( )θsin** lMU c= Eq. 1)

This unbalance vector produces a new orbit vector at the bearing. If the resulting orbit is smaller, the process will decay. But if the resulting orbit is greater, this continuous process will grow. In that case the system is unstable and the vibrations will continue to increase. Since the resulting vibrations are being initiated by rotor unbalance, the vibration frequency of the instability is synchronous with the rotor running speed. The vibration amplitudes of an unstable rotor can increase rapidly to unacceptable levels because they are of the self-excited type.

Figure 2) Analytical Thermal Shaft Bow at Bearing

Experimental verification

In order to verify the existence of a non-uniform temperature distribution around the bearing journal circumference, several experiments were executed. The first experiment in the author’s company was executed in 1992. A simple test rotor as shown in Figure 3) was manufactured and prepared for testing. The rotor was supported by two 4-inch tilting-pad journal bearings. In the non-drive end (NDE) bearing journal 4 calibrated temperature sensors were installed at around 1.0 mm below the journal surface, each sensor spaced 90°. Since, according to the theory, the temperature distribution around the journal is sinusoidal; at least 4 temperature sensors were required to establish the magnitude and direction of any differential temperature vector across the journal.

Figure 3) Test Rotor with Measuring Equipment

For this experiment, the rotor was driven by a variable speed electric motor in the manufacturer’s high-speed balancing facility. To transfer the electrical signals from the rotating shaft to the stationary measuring equipment a special slipringless transmitter has been used. The temperature sensors were electrically wired to the transmitter in such a way that both absolute and differential temperature of the journal could be measured. The differential temperatures were measured with a two-channel carrier wave amplifier, each pair of temperature sensors (spaced 180°) being connected to one channel in a half-bridge configuration.

The shaft was accurately balanced according to ISO 1940 / G=1.0. During the run up the absolute journal temperatures increased and when the shaft speed was kept constant at 12,500 rpm they stabilized. Figure 4) shows a cross section of the shaft at the center of the bearing with the four temperature sensors indicated. The measured temperatures for the first run up, which are nearly equal, are given in Figure 5(a). The orbit size at the NDE bearing was established with two vibration displacement probes, spaced 90°, and after subtraction of the slow roll vector, only around 2 microns pk-pk was measured at this speed. The objective of the experiment was to generate a shaft orbit in the NDE bearing and measure the temperature distribution around the bearing journal. To generate a distinct shaft orbit in the bearing, an unbalance weight was applied on the shaft at a defined location of 0°. Figure 5(b) shows the 4 measured temperatures caused by this shaft orbit. After removing the weight, the temperature values shown in Figure 5(a) were reproduced within 0.3 °C. Figure 5(c) shows the measured temperatures of the next run up were the unbalance was applied at the same axial location on the shaft, but now rotated 180°. As can be seen the direction of the differential temperature was also rotated 180°.

Figure 4) Test Rotor with Four Temperature Sensors at NDE Bearing



Figure 5) Sinusoidal Temperature Distribution at the NDE Bearing - Direction and Magnitude of Maximum

Temperature Derived from the Four Temperature Measurements

After this first experiment another test rotor, with a significant overhung weight, was instrumented with temperature sensors. The design of this rotor is described in de Jongh and Morton, (1994). The aim was to drive this rotor unstable and experimentally establish the differential

temperature level at the NDE bearing journal during this process. Figure 6) shows a Bode plot of one of these unstable test runs, whereas Figure 7) shows the corresponding journal differential temperatures of this run. The test rotor was gradually increased in speed to 10,500 rpm. As can be seen in Figures 6&7(a), at this speed the vibration level was around 8% of the bearing clearance with an observed temperature difference across the bearing journal of about 3°C with the rotor-bearing system being completely stable. When the rotor was accelerated to 11,500 rpm, the system became unstable. Vibration levels were increasing at a constant rotor speed. A phase decrease was also observed. For this case, the vibration vector was spiralling in the same direction as the rotation direction. The differential temperatures measured at the NDE journal were continuously growing. When the vibration level reached about 30% of the bearing clearance, the rotor speed was reduced to 10,500 rpm and held constant. After around two minutes, the initial conditions with respect to vibration amplitude, phase and journal differential temperature were reached again.

Figure 6) Synchronous Shaft Vibration at the NDE Bearing

The above mentioned rotor behavior was obtained on a balanced test rotor to which a small unbalance weight was attached at the NDE overhang. This was done to force a defined point on the NDE journal circumference to be at the outside of the orbit, being the point of the thinnest oil-film and so influencing the location of the hot spot. Similar results however were obtained without an additional unbalance weight, where the location of the hot spot was determined by the position of the residual unbalance of the rotor. Rotating the attached unbalance weight over an angle of 180° resulted in a change of the location of the hot spot of about the same angle (See Figure 7(b)). At 11,500 rpm the experiments showed a significant journal differential temperature proportional to the size of the orbit.



Figure 7) Measured ∆ at the NDE Bearing a) Unbalance Weight @ 0°

b) Unbalance Weight @ 180°

Prediction of Thermal Rotor Instability

Based on the theory and the experiments described above, a computer program has been developed in order to predict the onset of thermal rotor instability. Referring to Figure 8), three transfer functions Mc * l , IOB and T(t, Ω) are shown for one overhang end of the rotor. For a practical rotor Mc * l is defined by the overhang geometry, and IOB is the complex rotor response between the overhang and bearing locations. T(t,Ω) is the complex thermal gain and is depending on the bearing assembly and its operating conditions. The scheme of Figure 8) starts with an initial thermal input bend, θi. The overall ‘Gain’ vector, G, of the three transfer functions is defined as the ratio of the output bend, θo, and the input bend, θi. The rotor system is unstable when the real part of the complex vector, G, is greater than unity. Since a practical rotor usually has two overhung ends, the program establishes this gain vector, G, for each overhung end. When establishing the vector for one overhung end, the influence from the other end must also be taken into account.

Figure 8) Schematic of the Thermal Instability Phenomenon

Differential temperatures across a bearing journal were measured on a rotating shaft for various configurations of fluid-film bearings and different orbit sizes. This experimentally obtained bearing data is implemented to quantitatively describe the thermal effect, T(t, Ω). The sequence of the program is as follows. Depending on the overhang geometry, the program first calculates the unbalance for unit bending at the bearing journals respectively. Then, the rotor response at the bearing locations, due to this unbalance, can be calculated using a general rotor response program. This can be done for a defined rotor speed range with small speed increments. From the calculated rotor response, which also includes phase information, the location of the ‘high spot’ of the shaft is established. The experimentally obtained data are implemented here to establish the differential temperature across the shaft. From this differential temperature a resulting output thermal bend, θo, including its angular direction is calculated. The complex gain vector, G, results from the ratio between the output and the input bend.

Figure 9) shows a typical output plot of an example analysis, which shows the real part of the gain vector G versus rotor speed. From this figure it can be seen that the drive end (DE) overhung end is not causing any trouble. However, at a speed of around 10,500 rpm the rotor in this example becomes unstable, because of the NDE overhung end. For this rotor end the real part of the complex gain vector, G, is exceeding unity. Above 13,800 rpm the rotor becomes stable again, due to a phase change in the dynamic system.

Figure 9) Real Part of the Gain Vector vs. Rotor Speed



Case Studies

Gas compression equipment is susceptible to thermal rotor instability due to the overhung impellers used in pipeline service and the high horsepower rotors used in gas boost service. Two examples are presented to illustrate the effectiveness of the theory in identifying an existing field problem and completing the rotordynamic analysis of new designs. Both compressors were designed to and satisfy the API 617 specifications.

Case History #1: Overhung Pipeline Compressor

The case history discussed in this section involves an overhung compressor in pipeline service. The single stage compressor boosts hydrocarbons to the pipeline pressure of 76 bar. This is accomplished with a 490mm diameter impeller rotating at 10,800 rpm, Figure 10). Movement of 8500 ACFM of gas by the impeller requires 9000 HP. The train consists of the overhung compressor coupled to a speed increasing gear driven by an induction motor.

Since commissioning of the unit, high vibration on the impeller end probes was reported. Levels in excess of 50 microns p-p were measured following the start of the train. The vibration was chiefly synchronous in nature. Initial reports from the field indicated a sensitivity to unbalance thought to be caused by a critical speed in close proximity to the operating speed. However, examination of the dynamic behavior of the compressor did not reveal an encroachment on the operating speed by a rotor natural frequency. The undamped critical speed map and mode shapes for the rotor at maximum continuous speed (MCS) are displayed on Figures 11&12). A minimum separation margin of 20% to any mode and greater than 50% to the impeller overhung mode is shown on the map. As expected with this type of machinery, the unbalance response indicated a well-damped machine insensitive to unbalance.

Figure 10) Cross-section of the Overhung Pipeline Compressor

Figure 11) Undamped Critical Speed Map

Several hypotheses were developed to help understand the problem and reduce the vibration levels. These were; 1) a manufacturing defect is preventing the compressor from operating as intended, 2) current balancing techniques are inadequate in reducing residual unbalance to acceptable levels and 3) a phenomenon exists that is not predicted by the “standard” rotordynamic methods. While steps could be clearly defined to address hypotheses 1&2), the final hypothesis is troubling since it infers that a behavior exists for this class of machines that is not predictable at the design stage. (Note: This compressor was designed, tested and shipped years before the “Morton” or thermal rotor instability phenomenon was understood or developed.)

Figure 12) Undamped Rotor Mode Shapes at MCS



At considerable cost to both parties, repeated attempts were made to address points 1&2). These included the complete disassembly of the unit in the field and comparison of the as-built condition to the drawings. While this “blueprinting” of the compressor did turn up some out-of-tolerance dimensions, correcting these did not alter the vibration levels or dynamic behavior of the compressor.

Upon reassembling the compressor, the cold and hot alignment conditions were checked. The train movements were compared against the predicted values. Only minor corrections were needed and did not have a significant impact on the vibration.

Additionally, the balance procedure of the rotor was refined. In this compressor configuration, the impeller is hydraulically mounted on the shaft. While this eliminates the need for heat application, it does prevent the use of axial keys maintaining a fixed circumferential location of the impeller with respect to the shaft. Index balancing of the shaft and impeller was implemented to permit arbitrary placement of the impeller on the shaft. A high-speed check balance was used to monitor the success of the index balancing procedure. All practical efforts were made to reduce the residual unbalance levels in the shop. However, these efforts also failed to reduce the vibration levels in the field.

In an effort to extend the capabilities of the rotordynamic model and analysis, several other factors were investigated for their impact on the analytical predictions. The bearing support stiffness was measured in the field and included in the analysis. Disk attachment flexibility was considered at the impeller to shaft mounting location. These factors, while interesting from an academic viewpoint, did not improve the analysis. Either their impact on the predicted behavior was small and/or their contributions did not explain the vibration signature.

This signature can be seen on Figures 13-15). Figure 13) displays a typical Bode plot of two successive starts of the compressor. The impeller end B probe is plotted. A large hysteresis is evident between the runup (lower curve) and shutdown vibration levels. Both curves are repeatable as seen for the two starts plotted. Figures 14&15) plot the trend data of one start. Notice that maximum speed is reached in seconds. However, the vibration level continues to change over the next several minutes with the compressor in recycle and no significant changes to the operating conditions.

Figure 13) Bode Plot of Successive Starts of the Pipeline

Compressor

Years later, this behavior was associated with the thermal rotor instability described previously in this paper. With the development of the prediction tool for the thermal rotor instability, the pipeline compressor was reanalyzed for its sensitivity to this factor. Figure 16) plots the gain vector against speed for the impeller and coupling shaft ends. The prediction confirmed what was seen in the field; namely that the impeller end of the overhung compressor is susceptible to this instability at speeds greater than 10,000 rpm. At the maximum operating speed of 10,800 rpm, the gain vector or thermal index is 1.15 or barely in the unstable region. This may explain the quasi-stable behavior of the rotor with the vibration rising above 75 microns but reaching a steady state level 7 minutes after the start.



Figure 14) Speed vs. Time for One Start

Figure 15) Synchronous Vibration vs. Time for One Start

The root cause of the problem, as described in the previous sections of this paper, is the differential heating of the shaft at the impeller end journal location due to the oil-film shearing. The differential heating can not be eliminated since it is inherent to the journal behavior in

the fluid-film bearing. However, it was argued that the heating effects could be isolated from the shaft by installing a heat barrier sleeve. A typical design of the sleeve is shown on Figure 17). The air gap between the sleeve and shaft under the radial bearing acts as the heat insulator which greatly reduces the differential heating of the shaft. Figures 18&19) illustrate the typical temperature distribution in the shaft with and without the sleeve. Since analytical predictions indicated that the sleeve could greatly reduce the effects of the oil-film heating, the decision to install the sleeve was made. To alleviate concerns of sleeve slippage under the radial bearing, thermal and stress finite element studies of the sleeve were made. The sleeve was designed to remain in contact with the shaft under the most severe temperature conditions expected during operation. Stress levels were kept below high cycle fatigue limits to ensure infinite operating life of the sleeve. A patent of the heat barrier sleeve has been applied for by the author’s company.

Figure 16) Real Part of the Gain Vector for the Pipeline

Compressor

Great care was taken during the manufacturing and assembly of the sleeve on the shaft. Numerous dimensional checks were made to ensure that the sleeve was within the design tolerances. The shaft runout was also monitored to make certain that the addition of the sleeve to the shaft did not significantly alter the concentricity of the journal to the impeller fit.

Impeller End

Coupling End



Figure 17) Typical Shaft Barrier Sleeve

Figure 18) Typical Temperature Distribution Across Journal

Figure 19) Typical Temperature Distribution Across Journal with Barrier

The identical assembly and balancing procedures were followed to isolate the changes to the addition of the sleeve only. The rotor assembly with the sleeve was installed in the compressor train for its only test in the field under normal operating conditions. Figure 20) presents the plot of the compressor start for the impeller end B probe. During the several minutes following the start, the transient vibration rise was basically eliminated with the sleeve. Vibration levels remained below 25 microns even during loading of the compressor 20 minutes later. To date, over 25,000 hours of operation have been logged without a vibration-related incident or trip. Levels have remained below 25 microns, well within the customer specifications.

Sleeve

Figure 20) Synchronous Vibration vs. Time with Barrier Sleeve Installed

Case History #2: Gas Boost Compressor

The second case history involves a 30,000 HP gas boost compressor intended for offshore operation. A discharge pressure of 186 bar is reached at the MCS of 12,700 rpm. Five 400mm diameter impellers were needed to boost the natural gas from the 65.5 bar suction pressure with a gas turbine drive. The high power input to the shaft required a large shaft end coupling and, accordingly, a greater overhang to accommodate the increased size. Figure 21) presents a cross-section of the compressor assembly. The greater overhung moment at the coupling end is evident from the picture.

∆∆∆∆T

∆∆∆∆T



Figure 21) Cross-section of Gas Boost Compressor

Following the development of the thermal rotor instability theory and its successful application in identifying susceptible rotors, the analytical method was added as part of the “standard” rotordynamic calculations. This included an undamped critical speed analysis, an unbalance response calculation and a study of the sensitivity to aerodynamic and seal destabilizing forces. These studies are performed during the initial design stage of the compressor rotor/bearing system to determine its dynamic behavior and acceptability to the job specifications both internal and external.

The thermal rotor stability of the gas boost compressor was calculated using the procedure previously described. A plot of the real and imaginary components of the gain vector for the gas boost compressor is shown on Figure 22). In this view, the unstable region is shown as the crosshatched area. The coupling end of the compressor was predicted to go unstable near the MCS and reached a value of the real component of 1.3 at trip speed. At this point, the gas turbine supplier, the coupling purchaser, was informed that the coupling overhung weight was too high. Discussions with the coupling vendor did not result in sufficient reductions in weight and an alternate vendor was not available. With the lack of options available, an engineering decision was made to proceed with the coupling and rotor design in its original form. The decision was based on the thermal index of rotors currently operating in the field. Several were identified with real parts of the index exceeding 1.3 at MCS. While these compressors did not possess a configuration similar to the gas boost compressor under review and with the perceived lack of alternatives, it was felt they represented a sufficient database to proceed with the design. (An error in judgement in both cases as it turned out.)

Figure 22) Complex Gain Vector for the Gas Boost

Compressor

The gas boost compressor proceeded to the test floor to undergo an API mechanical test. At MCS, proximity probe readings were below the API limit of 25 microns at both ends of the compressor. However, during the excursion to trip speed at 13,300 rpm, high vibration was noted on the coupling end of the rotor. Vibration remained below 25 microns until trip speed was reached. Once there the vibration grew over a several minute time span to 50 microns.

Figure 23) is the Bode plot of the coupling end X probe. Immediate identification of the problem as thermal rotor instability was made upon review of the vibration plot. The classical hysteresis loop in the synchronous vibration is evident in both the amplitude and phase angle. Unfortunately, the shop test verified the analytical prediction that the rotor was sensitive to this phenomenon at trip speed.

Methods to reduce the sensitivity of the compressor to thermal instability with minimal impact to the project were investigated. While Demag Delaval had successfully designed heat barrier sleeves for several rotors at this point, sleeves were not possible due to the high power input to the shaft. In order to transmit the power, a large coupling and shaft end was required. This shaft diameter at the coupling was also selected for the size of the radial bearing. This proved to be the largest practical size of the radial bearing for this application keeping losses and heat production to a minimum. However, the lack of a diameter change between the radial bearing and coupling did not permit the installation of a sleeve that maintained the radial bearing size. Oversized bearing and new housings would be required which would severely impact the schedule of the project.

Thrust End

Coupling End



Figure 23) Coupling End Synchronous Vibration on Test Stand

Bearing clearance changes have also been used by Demag Delaval to reduce the thermal instability of compressor rotors. In its current rotor/bearing configuration, the gas boost compressor had satisfactory safety margin for critical speed separation and dynamic stability of the first lateral mode. Modifications to the bearing clearance needed to improve the thermal rotor stability were found to erode these safety margins to unsatisfactory levels.

A significant factor in determining the thermal rotor stability of the gas boost rotor is the overhung mass of the coupling. With the failure of the mechanical test, more urgent discussions were held with the coupling manufacturer and an alternate supplier was sought. From these discussions, several new options were uncovered. The original coupling (Original) had an overhung moment from the radial bearing centerline of 5415 kg-mm. Early on in the design process, the manufacturer proposed a modification of the original coupling (Mod A). This reduced the overhung moment to 4954 kg-mm or an 8.5% reduction. The manufacturer also proposed a reduced moment coupling (Mod C) which reduced the overhung moment by 29% to 3860 kg-mm. Finally, an alternate selection (Mod B) from a different vendor was obtained that reduced the overhung moment by 22% to 4205 kg-mm. A moment of 3975 kg-mm (Hypothetical) was required by the thermal analysis calculations to meet the internal design requirements of a thermal index of 0.75 at the MCS.

The thermal rotor instability for each rotor/coupling configuration was calculated at MCS and trip speed. Figure 24) presents the results of this study. Since the

rotor behavior with the original coupling at MCS was found to be stable during the mechanical test, this was identified as the stability threshold. The study of the Mod A coupling did not predict both MCS and trip would be on the left side on the threshold. Of the coupling configuration options, only the reduced moment and coupling from the alternate vendor were predicted to be stable at both MCS and trip speed. However, due to the modifications required to the bearing housing and oil guard, the reduced moment coupling was rejected as having too great an impact on the project schedule.

Figure 24) Predicted Gain Vector of Various Coupling Configurations

To minimize the impact of the lead-time necessary for delivery of a new coupling, a test coupling was modified to mimic the overhung mass. This permitted the testing to be carried out with minimal delays. The new coupling would be delivered in time for the string testing with the gas turbine. Figure 25) plots the vibration from minimum to trip speed for the coupling end X-probe. There is no sign of hysteresis or transient vibration. The synchronous levels are now stable through trip speed at levels below 12.5 microns.

Mod C

Hypothetical

Mod B

Mod A

Original

-0.85

-0.8

-0.75

-0.7

-0.65

-0.6

-0.55

-0.5

-0.45

-0.4

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

Real Part of Gain

Imag

inar

y Pa

rt o

f Gai

n

MCS

Trip Speed

Observed Stable Point

Observed Unstable Point

Stability Boundary

Stable Unstable



Figure 25) Synchronous Coupling End Vibration with Reduced Coupling Overhung Moment

Conclusion

This paper described the thermal rotor instability phenomenon commonly referred to as the “Morton Effect”. Differential heating of the bearing journals was found to be the root cause of the unstable synchronous vibration behavior. Even for small orbits of the shaft, a significant temperature difference across the bearing journal was measured in the test rig. As a largely unexplored source of a significant number of vibration problems, the approach developed in this paper will bring a better understanding of the rotordynamic behavior of gas compression equipment. Where such problems have occurred in the industry, they have often been resolved pragmatically by changing the overhung mass or altering the bearing geometry. A comprehensive program of theoretical and experimental research was carried out to develop a design method to minimize the thermal rotor instability in gas compression equipment. Further efforts will examine the effect of bearing loading and optimization of the heat barrier sleeve.

References

American Petroleum Institute Standard, 1979, “Centrifugal Compressors for Refinery Service,” API 617, Fifth Edition.

Berot, F. and Dourlens, H., 1999, “On Instability of Overhung Centrifugal Compressors”, International Gas Turbine & Aeroengine Congress, Indianapolis, Indiana. ASME 99-GT-202.

Corcoran, J.P., Rea H., Cornejo, G.A. and Leonhard, M.L., 1997, “Discovering the Hard Way, How a High Performance Coupling Influenced the Critical Speeds and the Bearing Loading of an Overhung Radial Compressor – A Case History,” Proceedings of the 26th Turbomachinery Symposium,” Turbomachinery Laboratory, Texas A&M University, College Station, Texas, pp. 67-78.

de Jongh, F.M. and Morton, P.G., 1996, “The Synchronous Instability of a Compressor Rotor due to Bearing Journal Differential Heating,” ASME Transactions, Journal of Engineering for Gas Turbines and Power, Vol. 118, pp. 816-824.

De Jongh, F.M. and Van der Hoeven, P., 1998, “Application of a Heat Barrier Sleeve to Prevent Synchronous Rotor Instability”, Proceedings of the 27th Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, Texas, pp. 17-26.

Faulkner, H.B., Strong, W.F. and Kirk, R.G., 1997, “Thermally Induced Synchronous Instability of a Radial Inflow Overhung Turbine PART II,” Proceedings of the ASME Design Engineering Technical Conference, Sacramento, California.

Keogh, P.S. and Morton, P.G., 1993, “Journal Bearing Differential Heating Evaluation with Influence on Rotordynamic Behavior,” Proceedings of the Royal Society, London, England, A441, pp. 527-548.

Keogh, P.S. and Morton, P.G., 1994, “The Dynamic Nature of Rotor Thermal Bending Due to Unstable Lubricant Shearing Within a Bearing,” Proceedings of the Royal Society, London, England, A445, pp. 273-290.

Morton, P.G., 1994, “Recent Advances in the Study of Oil Lubricated Journal Bearings,” Proceedings of the Fourth International Conference on Rotordynamics, IFFToMM, Chicago, Illinois, pp. 299-305.

Newkirk, B.L., 1926, “Shaft Rubbing,” Mechanical Engineering, No. 48, pp. 830-832.



Nomenclature

G = Gain vector

I = Influence coefficient

Mc = Concentrated overhung mass

R = Journal radius

T = Thermal gain

U = Unbalance vector

h = Distance between journal and bearing wall

l = Overhang length

t = Time

v = Velocity

ε = Orbit vector

ϕ = Phase angle

θ = Change in shaft slope at bearing journal

Ω = Rotational speed

Subscripts

i = input

o = output

O = Overhang position

B = Bearing position

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