The 12th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery Honolulu, Hawaii, February 17-22, 2008 ISROMAC12-2008-20076 EFFECT OF HYDRODYNAMIC THRUST BEARINGS ON ROTORDYNAMICS Joel V. Madison Chief Executive Officer Ebara International Corporation 350 Salomon Circle, Reno, NV 89434 (775) 356-2796 jmadison@ebaraintl.com ABSTRACT In cryogenic pumps and turbine expanders, the submerged motor or generator is cooled and the bearings lubricated by a predetermined portion of the liquefied gas being pumped or expanded. The cryogenic liquid is routed through a thrust-balancing device to control axial loads on the bearings. The thrust-balancing device is essentially a self-adjusting hydrodynamic thrust bearing with a particular system of flow passages, chambers, labyrinth seals and a stationary thrust plate on the hub side of the impeller or runner. Depending on the tolerance range of the clearances between these passages, the pressure distribution across the thrust balancing device is in some cases not uniform and generates a small asymmetry in the pressure distribution across the thrust-balancing device. This small asymmetry in the pressure distribution is rotating synchronously with the rotor and causes a small bending force on the rotor shaft affecting the dynamic performance of the rotor. The paper presents a detailed analysis of the effect of asymmetric pressure distributions in hydrodynamic thrust bearings on the rotordynamic performance. It is shown, that small tolerances of the clearances have only a minimal effect on the rotordynamics, but with increasing tolerances a resonant effect is observed due to the synchronous rotational speed of the rotor and the asymmetric pressure distribution. INTRODUCTION During the performance testing, an Ebara International Corporation (EIC) high-pressure LNG pump exhibited high vibration levels. After testing, the rotating assembly and clearances of the pump were examined. It was found that the thrust-balancing device was situated at an angle relative to the shaft. The thrust-balancing device discussed in this paper is unique to EIC and is called the Thrust Equalizing Mechanism (TEM). It was theorized that the angle between the TEM impeller and the shaft caused an asymmetric pressure distribution resulting in a bending force on the shaft. Calculations and an analysis were performed to asses whether this unbalanced pressure distribution may affect the rotordynamic performance of the pump. It was found that small moment magnitudes minimally affected the rotordynamic performance, but as the moment magnitudes increased a resonant effect was observed due to the asymmetric pressure distribution and synchronous rotational speed. Sebastian Berger et al (1998, 2001) have studied the nonlinear influence of the thrust bearing on the dynamic behavior of a flexible shaft. Their study considers a perfect thrust bearing and a defected thrust bearing. The coupling between the thrust bearings and the bending vibrations of the shaft is analyzed in their publications and their study is supported by non-linear simulations. In contrast, nonlinear calculations, simulations, and results presented below are supported by performance test data. NOMENCLATURE t M(t) time in seconds Moment as a function of time 1
M ω Magnitude of the moment Pump speed in radians per second TEST RESULTS THRUST-BALANCING DEVICE The TEM is situated on the backside of the first stage impeller and operates by using a small portion of the hydraulic fluid and a two-orifice system that continuously allows for a slight bidirectional axial adjustment of the shaft assembly to balance thrust. The two-orifice system consists of a fixed and a variable orifice; as the system adjusts to balance the thrust, the variable orifice gap either increases or decreases. In Fig. 1 the variable orifice gap is at a maximum causing a low pressure condition in the balance chamber resulting in an upward thrust condition. Figure 2 shows the gap at a minimum which causes a high pressure condition in the balance chamber and a downward thrust condition. Figures 1 and 2 are the two limiting positions of axial shaft movement. At some point between these two limiting positions there is a position at which the sum of all axial forces is zero. It is at this point that the thrust has been balanced. (Weisser, 1997; Finley, 2004) EIC thirteen stage cryogenic high pressure pump, pump model number 4ECC-1513, was tested in LNG with an average LNG temperature of -163 C. The pump exhibited high vibration levels at an operating speed of 50 Hz. Velocity versus frequency response was recorded during the performance testing of the pump by using an accelerometer mounted on the pump motor casing. During testing, velocity response at five different flow rate points was recorded and the maximum velocity of 2.50 mm/sec at 50 Hz was observed regardless of pump flow rate. Figures 5, 6, 7, 8 and 9 are the velocity responses of the pump at five flow points. After the performance testing of the pump, pump running clearances and the rotating assembly were examined in order to investigate the cause of high vibrations at operating speed. It was discovered during the inspection of the TEM impeller that the back shroud was not machined within the allowable tolerance. This caused the TEM impeller to not be perpendicular to the shaft when assembled. Due to this alteration, the TEM impeller back shroud was positioned by a certain angle on the shaft, as shown in Fig. 3, causing an asymmetric pressure distribution and TEM impeller wobble during operation. Stationary Thrust Plate TEM Impeller Non-uniform Pressure Distribution across Fig. 1: TEM and Shaft Assembly at Maximum Variable Orifice Gap Shaft Single Force Distance to Shaft Moment M(t) Fig. 3: Schematic of TEM wobble and applied forces and moments Fig. 2: TEM and Shaft Assembly at Minimum Variable Orifice Gap Per the EIC TEM impeller drawing, it is required to maintain the perpendicularity between the impeller hub and the back shroud within 0.025 mm (0.001 in). Figure 4 illustrates the geometric relation between the impeller hub and the back shroud where the equalizing of the trust takes place. According to the dimensional inspection performed on the TEM impeller, the perpendicularity requirement is not met and the impeller drawing is violated by 0.686 mm (0.027 in), resulting in asymmetry of 0.711 mm (0.028 in) 2
along the impeller back shroud and thrust plate face where the thrust is equalized. -B- Impeller Back Shroud -A- Impeller Hub Fig. 4: Requirement of geometric relation between impeller hub and impeller back shroud. CALCULATIONS & ANALYSIS Maximum allowable perpendicularity tolerance between A and B datum is 0.001" The calculations contained in this section were used to determine the possibility of instability caused by TEM impeller wobble. The calculations are performed for an EIC cryogenic high pressure pump, pump model 4ECC- 1513. The pump is a 13 stage unit and operating conditions are LNG at 423.15 K (-159 o C), with rated flow of 0.0408 m 3 /s (147 m 3 /hr) and rated head of 2185 m. The TEM Impeller has a suction eye diameter of 177.8 mm (7.00 in) and impeller outside diameter of (375 mm) (14.75 in). The hub diameter of the impeller is 76.2 mm (3.00 in). During operation, thrust equalizing takes place between the back shroud area of the TEM impeller and thrust plate front face, which has an outside diameter of 184 mm (7.25 in) and inside diameter of 133 mm (5.25 in). It should be noted that the clearance between the thrust plate and the TEM impeller is the most critical parameter for proper TEM operation, which is 2 mm (0.080 in) during operating condition. For the calculations and analysis, it was assumed that once the TEM impeller was assembled it sat at an angle with respect to the shaft and stationary thrust plate. Since the TEM impeller and the thrust plate are designed to be parallel to each other and the running clearance between the thrust plate and TEM impeller varies across the radial axis, the resulting angle between the pump shaft and the impeller causes an asymmetric pressure distribution as shown in Fig. 10. The non-uniform pressure on the TEM impeller creates an unbalanced force that may cause the shaft to bend depending on the location and magnitude. The maximum thrust (pressure) during operation of the pump was calculated according to EIC TEM analysis and applied to the TEM impeller back shroud as a single force as shown in Fig. 3. The calculations were performed in order to have an idea whether the single force can excite the pump shaft or not. The single force causes a moment, (M(t)) perpendicular to shaft rotating axis. The magnitude of the force is determined by TEM thrust calculation, and the moment, (M(t)) is calculated based on the geometry of the TEM impeller. Since the impeller is a rotating component of the pump, the magnitude and direction of the moment depends on the direction of the rotation and speed. The pump speed is constant and it is 50 Hz. Therefore, the direction of the moment will be opposite for every 1/100 seconds. The moment can be defined as follows, M ( t) = M sin( 2πωt) (1) Where, M is the magnitude of the moment that is equal to the single force times the perpendicular distance to the shaft center and ω is the speed of the pump in rad/sec. The moment is applied to the 69 th element of the pump shaft model where the TEM impeller is located (Fig. 10). TEM thrust calculations indicate that the non-uniform pressure applied on the TEM impeller and thrust plate will cause a single force located at 7.94 cm parallel to the shaft rotating axis with a magnitude of 3692 N [830 lbf]. The rotordynamic behavior of the pump shaft is investigated under 5%, 10%, 20%, 50% and 100% of the thrust, because of the uncertainty of the wobble and magnitude of the force. The transient analyses were performed for duration of 0.1 seconds with increments of 0.001 seconds. The applied moments for all cases are given in Fig. 11. The system is also investigated under zero moment condition. The unbalanced mass of the rotating assembly is also included in the calculations. The transient response of the pump shaft was plotted for all loading cases to investigate the magnitudes of velocity of the shaft as a function of frequency (Fig. 12). The shaft velocity was investigated at the middle location of the hydraulic side of the pump, where the maximum displacement will occur (6 th stage impeller location). As shown in Fig. 12, the transient velocity response under zero moment the maximum velocity is calculated as 0.63 mm/sec at 50 Hz. This is due to unbalanced mass excitation of the system. In addition, the transient velocity response plot under a 5% applied load shows that the velocity of the system increased slightly (Fig. 12). It is observed that the excitation due to the non-uniform pressure distribution has 3
no effect over the unbalanced mass excitation of the rotating assembly. Furthermore, similar behavior was also observed for a 10% applied moment (Fig. 12). There is a slight increase in velocity when 10% of the moment is applied to the system. The velocity response plot for a 20% applied moment indicates that the pump shaft becomes unstable by the application of this moment (Fig. 12). The velocity at operating speed increased by 17% compared to the no moment case. The maximum calculated velocity under this condition is 0.82 mm/sec. Vibration and Acoustics, Vol. 123, Issue 2. April 2001. pp 145-149. Finley, C. Continuously transient operation of two-phase LNG expanders. AIChE Spring National Meeting, LNG IV. April 25-29, 2004. Weisser, L. Hydraulic turbine power generator incorporating axial thrust equalizing means. US Patent No. 5,659,205. 1997. According to Fig. 12, when applying 50% of the moment at the TEM impeller location, the transient velocity response of the system increased by two times when compared to the no moment case. The system has instability at an operating speed of 50 Hz and the vibration level of the equipment is significantly increased by the moment as a result of the asymmetric pressure distribution. Based on results shown in Fig. 12, applying 100% of the moment will increase the velocity of the system by almost 4 times compared to zero the moment case. The maximum velocity is calculated as 2.4 mm/sec at the operating speed of 50 Hz. CONCLUSIONS The rotordynamic response analysis indicates that a small magnitude of moment due to asymmetric clearances between TEM impeller and stationary thrust plate have only a minimal effect on the rotordynamics, but with an increase the magnitude of the loading, a resonant effect is observed due to the synchronous rotational speed of the rotor and the asymmetric pressure distribution. Test results and dimensional inspection of the equipment prove that the non-uniform pressure distribution across the TEM impeller and stationary thrust plate can result in instability of rotating equipment during operation. REFERENCES Berger, s., Bonneau, O., Frene, J. Influence of Axial Thrust Bearing Defects on the Dynamic Behavior of an Elastic Shaft. AUSTRIB 98, Tirbology Conference: Proceedings of the 5 th International Tribology Conference in Australia, Brisbane 6-9 December 1998. Berger, s., Bonneau, O., Frene, J. Influence of Axial Thrust Bearing on the Dynamic Behavior of an Elastic Shaft: Coupling Between the Axial Dynamic Behavior and the Bending Vibrations of a Flexible Shaft. Journal of 4
5 Fig. 5: Velocity response at 99.98 m 3 /s flow
6 Fig. 6: Velocity response at 126.76 m 3 /s flow
7 Fig. 7: Velocity response at 142.52 m 3 /s flow
8 Fig. 8: Velocity response at 178.20 m 3 /s flow
Fig. 9: Velocity response at 203.62 m 3 /s flow Fig. 10: Pump shaft model with applied moment 9
Applied Moment at Station # 69 of Shaft Model 400.00 Moment [N.m] 300.00 200.00 100.00 0.00 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-100.00 M(t) 5% [N.m] M(t) 10% [N.m] M(t) 20% [N.m] M(t) 50% [N.m] M(t) 100% [N.m] -200.00-300.00-400.00 Time [sec] Fig. 11: Applied moment at station #69 as a function of time for six cases of applied moment Velocity Transient Response 2.6 Velocity, mm/s 2.4 2.2 2 1.8 1.6 1.4 1.2 1 Applied Moment 100% Applied Moment 50% Applied Moment 20% Applied Moment 10% Applied Moment 5% Applied Moment 0% 0.8 0.6 0.4 0.2 0 0 50 100 150 200 250 300 350 400 450 500 Frequency, Hz Fig. 12: Velocity transient response for six cases of applied moment 10
EFFECT OF HYDRODYNAMIC THRUST BEARINGS ON ROTORDYNAMICS ISROMAC 12 Honolulu, Hawaii February 19, 2008 Joel V. Madison C.E.O. Ebara International Corporation Sparks, NV
Overview Cause for investigation Pump model Thrust balancing device (TEM) Performance testing results Post-testing machine examination TEM Wobble Calculations Results and analysis Additional Analysis Conclusions drawn Questions
Cause for Investigation During performance testing of an Ebara International high pressure pump, the machine exhibited increased vibration levels at 50 Hz Examination of straightness and rotating balances checked and verified to be within design specification Concentricity of casing and close clearances checked and verified to be within design specification
Cause for Investigation Large axial vibration at the operating speed led to examination of the Thrust Equalizing Mechanism (TEM) components Examination of the machine found the TEM impeller situated at an angle to the thrust plate Will the tilt of the TEM affect the rotordynamic performance?
High Pressure Pump EIC model # 4ECC-1513 13 stage high pressure pump Rated Flow: 147 m 3 /hr Rated Head: 2185 m Operating liquid: LNG Operating temperature: -159 o C
Thrust Balancing Device (TEM) TEM and shaft assembly at maximum variable orifice gap TEM and shaft assembly at minimum variable orifice gap
Performance Testing Results High vibration levels at synchronous speed of 50 Hz Velocity vs. frequency response was recorded during testing via accelerometer mounted on motor casing Radial velocity traces recorded at the middle bearing Velocity response recorded for 5 different flow rate points Maximum velocity of 2.5 mm/s at 50 Hz regardless of flow rate
Radial Velocity Response Accelerometer vs. Frequency at a Flow Rate of 99.98 m 3 /s
Radial Velocity Response Accelerometer vs. Frequency at a Flow Rate of 126.76 m 3 /s
Radial Velocity Response Accelerometer vs. Frequency at a Flow Rate of 142.52 m 3 /s
Radial Velocity Response Accelerometer vs. Frequency at a Flow Rate of 178.20 m 3 /s
Radial Velocity Response Accelerometer vs. Frequency at a Flow Rate of 203.62 m 3 /s
Axial Displacement FFT recorded for the TEM probe Found large synchronous vibration at operating speed of 50 Hz
TEM Examination Findings Running clearances and rotating assembly was dismantled and examined During inspection of the TEM impeller it was found that the back shroud was not machined within tolerance TEM impeller back shroud was situated at an angle to the shaft
Required Geometric Relation TEM impeller is required to maintain perpendicularity between hub and back shroud within 0.025 mm Asymmetry of 0.711 mm found along impeller back shroud and thrust plate face
TEM Impeller Wobble An angle between the TEM impeller and the shaft causes an asymmetric pressure distribution resulting in TEM impeller wobble during operation.
Calculations Assumptions: TEM impeller was situated at an angle with respect to shaft and stationary thrust plate Running clearance varied across radial axis between thrust plate and TEM impeller Non-uniform pressure distribution resulted Asymmetric pressure distribution can be modeled as a single un-balanced force acting on the TEM impeller back shroud Un-balanced force causes a bending moment acting on the shaft
Calculations Since the impeller is a rotating component, the moment depends on the rotational direction and speed The pump speed is a constant 50 Hz : the direction of the moment will be opposite every 1/100 seconds M ( t) = M *sin(2πωt) Thrust calculations indicate that the force is 3692 N and 7.94 cm from the rotating axis
Calculations Pump model with applied moment
Calculations The rotordynamic behavior was investigated under 5%, 10%, 20%, 50%, and 100% of the thrust Transient analyses were performed for a duration of 0.1s with increments of 0.001s The system was also investigated under zero moment condition Un-balanced mass was included Transient response was plotted for all cases to investigate the velocity as a function of frequency at the middle location of the hydraulic side of the pump where max displacement will occur
Applied Moment Results Applied Moment at Station # 69 of Shaft Model 400.00 Moment [N.m] 300.00 200.00 100.00 0.00-100.00 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 M(t) 5% [N.m] M(t) 10% [N.m] M(t) 20% [N.m] M(t) 50% [N.m] M(t) 100% [N.m] -200.00-300.00-400.00 Time [sec] Applied moment as a function of time for all cases
Transient Response: Zero Moment Zero Applied Moment: Max velocity 0.63 mm/s at 50 Hz Due to un-balanced mass Velocity Transient Response 0.7 0.6 [No Moment] Velocity, mm/s 0.5 0.4 0.3 0.2 0.1 0 0 100 200 300 400 500 600 Frequency, Hz
Transient Response: 5% & 10% Velocity Transient Response Applied Moment: %5 Velocity, mm/s Velocity, mm/s 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 100 200 300 400 500 600 Frequency, Hz Velocity Transient Response Applied Moment: 10% 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 100 200 300 400 500 600 Frequency, Hz 5% & 10% Applied Moment: Slight increase of system velocity Excitation due to non-uniform pressure has no effect over unbalanced excitation
Transient Response: 20% Moment 20% Applied Moment: Max velocity 0.83 mm/s at 50 Hz Primarily due to un-balanced mass Velocity Transient Response Applied Moment: 20% Velocity,mm/s 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 100 200 300 400 500 600 Frequency, Hz
Transient Response: 50% & 100% 50% Applied Moment Velocity twice the zero moment case System unstable at 50 Hz Vibration level of system significantly increased by the moment Velocity, mm/s Velocity Transient Response Applied Moment: 50% 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 100 200 300 400 500 600 Frequency, Hz 100% Applied Moment Increase system velocity by 4 times the zero moment case Max velocity 2.4 mm/s at 50 Hz Velocity, mm/s Velocity Transient Response Applied Moment: 100% 2.5 2 1.5 1 0.5 0 0 100 200 300 400 500 600 Frequency, Hz
Transient Response Results Velocity Transient Response 2.6 Velocity, mm/s 2.4 2.2 2 1.8 1.6 1.4 1.2 1 Applied Moment 100% Applied Moment 50% Applied Moment 20% Applied Moment 10% Applied Moment 5% Applied Moment 0% 0.8 0.6 0.4 0.2 0 0 50 100 150 200 250 300 350 400 450 500 Frequency, Hz Transient response for all cases
Additional Analysis Shaft Deflected Shape at Operating Speed of 3000 RPM Displacement [mils] 0.500 0.475 0.450 0.425 0.400 0.375 0.350 0.325 0.300 0.275 0.250 0.225 0.200 0.175 0.150 0.125 0.100 0.075 0.050 0.025 Location of the Moment Applied Moment 0% Applied Moment 5% Applied Moment 10% Applied Moment 20% Applied Moment 50% Applied Moment 100% 0.000 0 10 20 30 40 50 60 70 80 90 100 110 120 130 Shaft Axial Location [in] Deflected shape of the shaft at operating speed
Additional Analysis Rotordynamic Response Plot 7.50 7.00 6.50 6.00 5.50 Applied Moment 100% Applied Moment 50% Applied Moment 20% Applied Moment 10% Applied Moment 5% Applied Moment 0% Displacement [mils] 5.00 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Rotor Speed [RPM] Effect of moment on the critical speed
Conclusions A small magnitude of moment due to asymmetric clearances between the TEM impeller and thrust plate have a minimal effect on the rotordynamics Increased magnitude of moment results in a resonant effect due to synchronous rotational speed and asymmetric pressure distribution A non-uniform pressure distribution across the TEM impeller and asymmetric clearances may result in instability of rotating equipment during operation The critical speed is not affected by the moment