The Kaybob compressor failure of 1971 was an excellent historic example of rotordynamic instability and the design factors that affect this phenomenon. In the case of Kaybob, the use of poorly designed bearings produced unstable whirling in both the low and high pressure compressors. This required over five months of vibration troubleshooting and redesign along with over 100 million modern U.S. dollars in total costs and lost revenue. In this paper, the history of the Kaybob compressor failure is discussed in detail including a discussion of the ineffective bearing designs that were considered. Modern bearing and rotordynamic analysis tools are then employed to study both designs that were considered along with new designs for the bearings that could have ultimately restored stability to the machine. These designs include four-pad, load-between-pad bearings and squeeze film dampers with a central groove. Simple relationships based on the physics of the system are also used to show how the bearings could be tuned to produce optimum bearing stiffness and damping of the rotor vibration, producing insights which can inform the designers as they perform more comprehensive analyses of these systems.
The rotordynamic stability of high-speed compressors and turbines has been a critical element of their design for decades. With the ever-increasing demand for greater output through an increased number of stages, higher speeds, and higher pressures, these machines are continuously being pushed to the design limits of the previous generation of machines. As they are being pushed to these new extremes of operation the designs must also adapt to accommodate the consequences of these extremes including increased rotor flexibility and an increased likelihood of subsynchronous whirl. This whirl can be excited by a number of sources in turbomachinery including seals and even the bearings supporting the rotor. The stability of that whirl can then be reduced by destabilizing cross-coupled stiffness forces from the bearings, interstage seals, balance pistons, and Alford-type aerodynamic cross-coupled forces around blades.
The increasing use of tilting pad journal bearings in the 1960s and 70s brought about new opportunities for compressor design as these bearings eliminated the self-exciting oil whirl commonly found in fixed geometry bearings. They also essentially eliminated the destabilizing cross-coupled stiffness forces produced by these bearings. However, despite the fact that a number of important papers were being published on these topics by Lund [
The Kaybob compressor failure of 1971 was a historic case of rotordynamic instability from self-excited, subsynchronous whirl. The many months of troubleshooting that followed this failure served as a valuable lesson to the team involved but even to this day this classic example serves as an important motivator for understanding the underlying principles that govern the design of these machines, many of which that were developed after the incident and troubleshooting took place. With the advent of advanced bearing and rotordynamic analysis tools, designers now have the ability to fine tune their designs to avoid these failures; however it is critically important that the underlying principles and physical insights gained from the analysis of these machines are properly considered as even modern bearing technologies can contribute to stability problems when not implemented correctly.
In this study, modern bearing and rotordynamic analysis tools are applied to the Kaybob compressor instability case to highlight the effects of the design choices made with this machine and how they contributed to its ultimate failure. By combining useful design principles with these analysis tools it also showed not only why the costly solution to this failure worked at the time, but also how a number of alternative and much simpler design changes to the support structure could have restored stability to the machine including the use of properly designed tilting pad journal bearings and squeeze film dampers. It is the goal of this study to provide practical information and design approaches that designers can then use to avoid costly failures like the one experienced in Kaybob.
The case of the Kaybob compressor instability began in November of 1971, a detailed summary of which is provided by Smith of Cooper-Bessemer [
These duplicate trains (Figure
Kaybob compressor train schematic from Smith [
The tilting pad journal bearings were designed as five-pad, load-on-pad bearings, a design that has been commonly employed in compressors over the years. Floating oil film ring seals were employed in both compressor casings. The trains were designed for a rated speed of 10,200 rpm with a maximum continuous operating speed of 11,400 rpm.
As site testing began, a significant vibration problem became apparent in the low pressure compressor. A first train was operated at speeds up to 10,000 rpm with inlet pressures of 700–750 psi and discharge pressures of 1,300–1,500 psi. Under these conditions a significant vibration was present at a frequency of approximately 4,250 cpm, producing 3 to 4 mil peak-to-peak amplitudes in one of the bearings which had a 6 mil clearance.
A second train was then tested to rule out possible unexplained sources of resonance from the first train. This machine was ran up to its maximum speed of 11,440 rpm, followed by increases to the inlet and discharge pressures to 1,120 psi and 3,300 psi.
At this point the machine became highly unstable, resulting in a violent 5,100 cpm whirl of 9+ mils peak-to-peak amplitude. Figure
(a) Time lapse and (b) orbit of the instability onset. From Smith [
The five months that followed included a thorough investigation into the causes of this instability as well as tests of various potential solutions to the problem including investigations into both seals and journal bearings. The seal investigation involved the consideration of four different seal configurations to determine whether seal lockup or effective damping had any significant effects on the instability. It was concluded, though, that the seals were in fact floating and their configuration overall had little effect on the problem.
A number of design modifications were considered for the tilting pad journal bearings as well. These modifications included increasing the specific load of the bearing, introducing asymmetry to the bearing design, different pad load configurations, offset pads, variable preloads, the introduction of squeeze film dampers, and combinations thereof. Two of the configurations tested are shown in Figure
(a) Asymmetric tilt pad bearing from Smith [
Note that, in Figure
The ultimate solution to this vibration problem was a redesign of the rotor to a shorter, stiffer configuration with increased diameters beneath the impellers. This stiffer shaft would thereby accommodate the stiff bearing designs that were used and that will be demonstrated in Section
Rotor redesign from Smith [
In the original design of the Kaybob rotor, the bearing span was 59.688 inches. A modal analysis of the rotor indicated that the shaft first critical speed modal stiffness was approximately 115,000 lb/in. This fundamental shaft modal stiffness is extremely important for the proper tuning of the bearings to the shaft. From previous research studies of the optimum bearing stiffness, it has been determined that the optimum bearing stiffness is approximately one half the rotor shaft stiffness. When the bearing stiffness greatly exceeds this fundamental design value, the first mode damping is drastically reduced causing the rotor to be very susceptible to self-excited whirl effects.
The fundamental stiffness of a uniform team is given by the following equation:
In the final redesign as shown in the lower rotor of Figure
In revisiting the design and troubleshooting of the Kaybob compressor, the first step was to establish the overall rotordynamic characteristics of the system. A finite element model of the compressor was first developed in the Dyrobes software suite used for this analysis and is presented to scale in Figure
Kaybob compressor model disk properties.
Disk # | Station | Mass (lbm) | Transverse inertia (lbm·in2) | Polar inertia (lbm·in2) | Length (in) | Inner diameter (in) | Outer diameter (in) |
---|---|---|---|---|---|---|---|
1 | 9 | 15 | 760 | 1400 | 1.5 | 4.36 | 15.0 |
2 | 10 | 15 | 760 | 1400 | 1.5 | 4.36 | 14.3 |
3 | 11 | 15 | 760 | 1400 | 1.4 | 4.36 | 14.3 |
4 | 12 | 15 | 760 | 1400 | 1.4 | 4.36 | 14.3 |
5 | 13 | 5 | 760 | 1400 | 1.3 | 4.36 | 13.6 |
6 | 14 | 5 | 400 | 750 | 1.3 | 4.36 | 13.3 |
7 | 15 | 5 | 400 | 750 | 1.3 | 4.36 | 13.1 |
8 | 16 | 5 | 400 | 750 | 1.2 | 4.36 | 13.1 |
9 | 17 | 5 | 400 | 750 | 1.2 | 4.36 | 13.0 |
Kaybob 9-stage compressor model with aerodynamic cross-coupling at stations 13 and 14.
After building the shaft model, the analysis began with an assessment of the rotor critical speeds in the operating range of the compressor (Figure
Compressor critical speed map.
First bending mode of the compressor.
In order to evaluate the stability characteristics of this compressor, a nominal amount of cross-coupled stiffness of 25,000 lb/in was assumed acting at stations 13 and 14. This value was estimated based on experience and the description of the stability characteristics of the machine. These cross-coupling effects are known as the Alford effect [
The shaft modal stresses and stiffness were also assessed for the first bending mode assuming rigid bearings with a stiffness of 108 lb/in (Figure
Shaft modal stresses of the first bending mode.
To further support this important relationship in rotor dynamics, a plot was created showing the amplification factors of the first bending mode under various sets of bearing stiffness and damping (Figure
Amplification factors of the first bending mode.
Figure
For the case of very high stiffness bearing of 500,000 lb/in, it is seen that the optimum bearing damping is over 800 lb-sec/in and the amplification factor is now over eight. Therefore it is very apparent that it is critical to select the bearing stiffness in relationship to the predicted first modal shaft stiffness. This concept will often lead to the requirement of an extended width bearing in order to have a reduced vertical bearing stiffness in order to properly tune the bearings to the fundamental shaft stiffness.
The analysis of the Kaybob compressor continued with the development of various bearing models to better understand how the design of the bearings would impact the stability of the machine. The original design of the compressor bearings was a 5-pad load-on-pad configuration with an
Original compressor bearing design.
The results of this initial bearing analysis are shown in Figure
Original compressor bearing analysis results.
The next step in analyzing the original rotor-bearing system was to perform a stability analysis of the compressor with the original bearings. The results of the damped eigenvalue analysis are presented in Figure
Stability results for the original bearing design.
First mode shaft and bearings energy distribution with the original bearing design.
A second bearing design considered when troubleshooting the Kaybob compressor was an asymmetric bearing. Smith [
The model (Figure
Asymmetric bearing model.
Results for the asymmetric bearing.
A stability analysis of the bearing-rotor system (Figure
Stability results for the asymmetric bearing.
The team at Cooper-Bessemer tried multiple bearing designs that utilized bearing asymmetry, but with such high levels of bearing stiffness and aerodynamic cross-coupling they were unable to achieve any significant increases in modal stability.
Figure
It is seen that, at the operating speed of 11,400 rpm, there now occurs a self-excited whirl component at 3733 cpm. The log decrement shows a value of −0.51 which represents a highly unstable system. Noncontact probes are often placed at the bearings to observe the rotor motion. The motion observed at the bearing locations is often quite small as compared to the large orbital motion occurring at the rotor center due to the added whirl component. This large motion occurring at the center causes extensive rubbing and seals to be extensively damaged.
A design not considered by the team at Cooper-Bessemer was a 4-pad tilting pad bearing. These bearings, particularly when oriented in a load-between-pad position, are known to be beneficial from a rotordynamic standpoint due to their ability to more evenly distribute stiffness forces in the vertical and horizontal directions. To see how this design might impact the Kaybob compressor, an initial 4-pad load-between-pad bearing design was analyzed with other design parameters that were kept constant from the original 5-pad bearing including the axial length, bearing clearance, and preload as shown in Figure
Initial four-pad bearing design.
The results of the bearing analysis (Figure
Results of the four-pad bearing analysis.
A stability analysis (Figure
Stability results for a four-pad bearing design.
The design for the 4-pad bearing is superior to the asymmetric 5-pad bearing in that the log decrement has improved. However the dynamic analysis of the compressor with the 4-pad design as shown in Figure
In order to improve the rotor dynamics with the 4-pad bearings, it will be necessary to further reduce the vertical bearing stiffness in order to bring the values more in line with the fundamental shaft stiffness value. This requires a longer pad with a reduced bearing preload.
The paradox of this type of design is that the noncontact probes monitoring the bearing motion indicate higher amplitudes of motion, although the shaft center motion has been reduced. This phenomenon led one chief engineer of a compressor company to remove the redesigned 4-pad bearings and replace them with the original 5-pad design because of the increased motion observed at the bearings. Total rotor failure occurred shortly after the 5-pad bearings were installed!
In an effort to determine what bearing design choices were necessary in order to restore stability to Kaybob compressor, a number of modifications were made to the previously analyzed 4-pad bearing. Because it has been revealed that all of the designs considered thus far have produced bearings that are overly stiff, a number of design parameters must be considered to reduce the stiffness of the bearing while maintaining damping so that the bearings can better absorb the energy of the first bending mode.
Design parameters including the bearing clearance, pad preload, load orientation, and lubricant properties have all been shown by many authors [
Improved four-pad bearing design.
The results from the bearing analysis show a significant change in bearing performance when compared to the previous designs (Figure
Analysis of the improved four-pad bearing.
Stability analysis of the improved four-pad bearing.
Energy distribution in the shaft and bearings for the improved four-pad bearing design.
Another solution considered by the team at Cooper-Bessemer was a squeeze film damper. Smith [
To further make this point, the analysis was performed on two damper designs surrounding the original 5-pad bearing (Figure
Nongrooved and grooved squeeze film damper analysis.
With all other inputs equal it can be seen that the groove has a significant effect on the predicted stiffness and damping of the damper. The longer damper design—similar to the one used by Cooper-Bessemer—produces very high levels of stiffness and damping while the grooved design produces much more reasonable values.
Stability analyses of these two support scenarios also reveal the significant effect of the central groove (Figures
Stability analysis of the nongrooved squeeze film damper supported system.
Stability analysis of the grooved squeeze film damper supported system.
The grooved damper, however, provides a substantial increase in the log decrement, resulting in a marginally stable system. Had the team at Cooper-Bessemer considered adding a central groove to their squeeze film damper design they may have actually avoided the costly rotor redesign discussed in Section
To produce a stable operating environment the team at Cooper-Bessemer ultimately had to redesign the rotor. This involved multiple design iterations that resulted in a final shaft design with a bearing span reduced from about 60 inches to approximately 53 inches, modified shrink fits, an integral center seal section, and an increased shaft diameter under the impellers (Figure
To show how these shaft design modifications made such a difference in the performance of the machine a shaft model was developed to analyze with the original bearing design and the original design with a long squeeze film damper (Figure
Reduced bearing span shaft model.
Shaft modal stresses of the first bending mode.
The shaft modal stiffness was calculated to be 201,780 lb/in, a 74% increase when compared to the original rotor. This significant increase in shaft modal stiffness made the new rotor design much more suited to the high stiffness bearings utilized.
A stability analysis of the original bearing design with the new shaft design (Figure
Stability analysis of the new rotor design with the original five-pad LOP bearings.
Since the long squeeze film damper was also considered along with the new rotor design, this case was analyzed for stability as well (Figure
Stability analysis of the new rotor design with the original bearing and a long squeeze film damper.
The Kaybob compressor failure of 1971 was a historic case of rotordynamic instability and has taught us many things about the design of these machines. Tilting pad journal bearings have become a new normal in compressor stabilization due to their innate capacity for avoiding self-excited oil whirl; however great care must be taken in the design of these bearings for both ensuring a stable machine and meeting API specifications. Many have been tempted to try and avoid critical speeds and reduce motion at the bearings by increasing bearing stiffness; however this approach can and has often created a stability disaster as demonstrated by the Kaybob case. By designing for stability, however, these modes can also be eliminated from the operating range to the extent that they are not even detected because they are so well-damped.
In particular the Kaybob case has revealed the importance of designing bearings such that the bearing stiffness is tuned in to be in proper proportion to the shaft modal stiffness. By using this simple relationship and designing for proper damping as well, the bearings can properly absorb shaft vibrational energy and produce highly stable modes. While bearing asymmetry has been shown in past cases to produce some increases in stability—particularly in the presence of internal shaft friction or moderate levels of aerodynamic cross-coupling—the bearing stiffness must still be considered as a primary design variable as asymmetry will not benefit a system with a large bearing to shaft modal stiffness ratio. The presented design cases for 5- and 4-pad bearings demonstrate the importance of these concepts.
Squeeze film dampers have also been a significant source of compressor stabilization in decades past and will continue to do so when properly designed. It was shown in the context of the Kaybob failure that important features such as central grooves can make a large difference in the stiffness and damping characteristics of the damper, which can ultimately have as large an effect on compressor stability as the design of the bearing itself. While the redesign of the compressor rotor also produced a stable machine, this solution was far more costly than the simple use of a properly designed bearing or squeeze film damper. However, the team at Cooper-Bessemer cannot be faulted for these errors as they did not have the luxury of high-speed analysis tools that are available to designers today. Overall, the failure of the Kaybob compressor and their work to investigate the instability has helped create the knowledge and methods necessary to avoid these kinds of failures in the future.
The authors declare that they have no competing interests.
This work was supported by the Rotating Machinery and Controls Laboratory and industrial consortium at the University of Virginia and Rodyn Vibration Analysis, Inc.