Reveal the unmonitored risks in your rotating equipment—Part 1
On December 15, 2002, an anomalous event occurred in a steam turbine of Unit 2 at the South Texas Project Electric Generating Station, a pressurized water reactor (PWR) nuclear reactor near Bay City, Texas. The ensuing investigation concluded that a blade was ejected from a low-pressure stage, and detailed inspections revealed additional cracked blades in several stages.
On December 15, 2002, an anomalous event occurred in a steam turbine of Unit 2 at the South Texas Project Electric Generating Station, a pressurized water reactor (PWR) nuclear reactor near Bay City, Texas. The ensuing investigation concluded that a blade was ejected from a low-pressure stage, and detailed inspections revealed additional cracked blades in several stages. The root cause was determined to be excessive torsional vibration triggered by torsional excitation in the train. A later industry study of 65 PWRs showed that approximately 10% of the inspected plants had similar events involving turbine blade failures that were suspected to be caused by the same torsional vibration phenomenon.1
In another case, a pipeline gas transmission train experienced three coupling failures over a short duration of time. The investigation revealed that the installation of several pieces of equipment had shifted the expected torsional vibration natural frequencies. As a result, the operating speed of the train exactly matched a torsional vibration resonance.2
During the startup of a train comprising a synchronous motor driving a speed-increasing gear box connected to a centrifugal compressor, the motor speed dropped several times. After 12 sec of operation, the high-speed coupler failed with component ejection. The damaged coupler spacer showed the characteristic 45° angle indicating torsional failure. It was determined that faulty wiring of the motor caused fluctuations that excited the torsional natural frequency.3
Unexpected and unmonitored torsional vibration is at the heart of these recent case studies, resulting in sudden failures, costly downtown and potential safety risk. Part 1 of this article examines the origins of torsional vibration and case histories to drive an understanding of the unmonitored risk existing at many industrial sites.
What is torsional vibration?
All rotating equipment power trains at industrial sites experience vibration, which is usually caused by mechanical imbalance of the rotating system, shaft misalignment or weakness in the bearing support. Characteristic vibration is experienced in one or more of three modes: horizontal or vertical (radial), axial (thrust) and twisting (torsional), as shown in FIG. 1. The authors’ company’s asset protection and condition monitoring products, probes, monitors and condition monitoring softwarea allow for the continuous monitoring of radial and axial vibrations on the rotors and casings.
FIG. 1. Vibration modes.
Changes in the cross-coupling of forces from radial vibration, imbalance, generator load variation or power grid fluctuations cause variations in the rotating speed of a machine and produce torsional vibration. Ultimately, torsional vibration can induce radial or axial vibrations in the rotor and attached components that cause component fatigue, such as the steam turbine blades or the coupler in the case histories mentioned here. Component fatigue may cause component liberation, which leads to greater imbalance and, in a feed-positive manner, will increase torsional vibration issues. Torsional vibration in the rotor creates additional varying stresses and strains that can result in failure without warning by fatiguing the rotor material. This represents a risk factor that, although assessed during machine commissioning, can be altered by future modifications and remain unmonitored for the operational life of the equipment.
Torsional vibration is strongly related to the material composition and dimensions of the rotor and accompanying components. The rotor material will define such parameters as component stiffness and inertia, whereas the length, diameter and coupling of the rotor will define the inertial moments.
Cross-coupling refers to a condition where radial vibration can induce torsional vibration, and likewise in the opposite manner. This was the root cause of the first example provided where torsional vibration caused vibration of the steam turbine blades to the point of failure.
Physics of torsional vibration
Torsional vibration is a result of a cross-coupling of forces from machine train speed variations, lateral vibration, imbalance in the machine, generator load variation or power grid fluctuations that cause a variation in rotating speed during the rotational cycle.
Measurement and analysis of radial vibration present in machinery have led to the diagnostics, treatment and correction of many mechanical issues. Given the economic costs involved with turbomachinery, the earliest possible identification of machine malfunctions is recommended. Possible machinery malfunctions are usually noted by evaluating changes in the radial vibration levels and patterns—the so-called “machine personality”—directly by eddy current proximity probes, accelerometers and velometers. Other sensors indicating rotor speed and bearing temperatures of rotor position may also be used. Changes in forces, such as imbalance caused by material losses or changes in dynamic stiffness of the rotor, will be presented as radial or torsional vibration changes.
For the past 60 yr, the condition monitoring industry has used radial vibration measurements to diagnose imbalance, rotor bow, rubs, misalignments, cracks and many other rotor-related dynamics issues. A thorough discussion of rotor dynamics, physics, analytics and relevant case histories can be found in literature.4
Characteristic vibration is also experienced in one or more of four modes: sideways, horizontal, axial or torsional.
Torsional vibration can induce radial or axial vibrations in the rotor and attached components, causing component fatigue, such as the steam turbine blades in the South Texas Project case discussed here. Component fatigue may cause component liberation, which leads to greater imbalance and, in a feed-positive manner, will increase torsional vibration issues. Torsional vibration in the rotor will create additional varying stresses and strains that can result in without warning failure by fatiguing the rotor material. Many plant operators and insurance companies are choosing to focus on monitoring or mitigating torsional vibration issues.
Torsional vibration is strongly related to the material composition and dimensions of the rotor and accompanying components. The rotor material will define such parameters as component stiffness and inertia, whereas the length, diameter and coupling of the rotor will define the inertial moments.
Rotating machinery transmit power by rotating, utilizing the moment of torque acting along the rotor at the couplings and interfaces.
The moment created by an angular force acting over a distant is known as torque (T).
The applied moment causes the rotor to twist by a certain angle, and variations in force will cause the vibratory nature around the steady-state value. Torsional stiffness [Kt (Nm/deg)], similar to radial stiffness for a uniform circular shaft, is defined by Eq. 1:
T / Phi = Kt = JG / L (1)
where Phi (degree) is the static angle of twist, L (meter) is the shaft length, G is the shear modulus (Pa) and J is the inertial polar moment (m4). J can be calculated for an open cylinder using Eq. 2:
J = Pi (do4 – di4) / 32 (2)
where di and do are the inner and outer cylinder wall diameters.
The inertial moment for a solid rotor can be calculated by setting di to zero. J is highly dependent on the diameter of the shaft with a fourth power so that larger diameter shafts are stiffer, and uniformity of diameter is a grave matter to prevent variations in J. Most rotor trains are not uniform in shaft diameters, so a wide variation exists in torsional stiffness dependent on shaft location. The fatigue damage to the shaft will depend on the variation of the sheer stress, Tau, experienced by the rotor, and the value is defined by Eq. 3.
Tau = TD / (2J) (3)
The rotor speed will remain constant if the driving torque is oppositely balanced by a loading torque. Torsional vibration will result as the rotor speed varies. Torsional vibration may be caused by excitation from worn gear teeth, rubs and coupling misalignment, or by impulses such as variable electrical loads. As with all things that vibrate, whether radially or torsionally, each component dependent upon its shape, mass and material properties will exhibit a natural frequency at which the amplitude of the vibration is greater enhanced. The torsional natural frequency is defined by Eq. 4:
W(omega) = SQRT(2Kt/I) in Hz (4)
where I is the moment of Inertia (kg.m2) defined as Eq. 5:
I = mL2 (5)
where m is mass in kg and L is the distance in meters from which the mass is located from the axis of rotation.
Sophisticated torsional rotor dynamics will allow the calculation of three important parameters: torsional natural frequency, the associated torsional mode shapes and the response of the rotor. These calculations allow the operator to set margins on the desired operating speeds to avoid torsional resonances and possible failures. Many operators desire a fourth parameter, that of a “rain flow” counter, meaning the combination of frequency of vibration, amplitude of response and stress response calculations that will predict the end of life or remaining life of various rotor components.
Why does torsional vibration matter?
All rotating equipment are expected to experience variations in speed and are subjected to torsional vibration. Effective accurate measurement of torsional vibration allows an operator to evaluate several issues, including torsional natural frequencies, dynamic stresses, torsional modes shape, component fatigue and load vibration. Torsional vibration, in some cases, can be deduced by case accelerometers, but is best detected and monitored directly from the rotor. Data from direct measurements are essential to compare with dynamic model simulations. Monitoring torsional vibration as a regular part of preventive maintenance will reduce maintenance costs and may be useful in decreasing machine operating margins.
Takeaway
Determining the extent of torsional vibration issues can be difficult because incident reporting is usually only found in case studies presented at professional gatherings. A survey of papers presented at the Annual Turbomachinery and Pump Symposia in Houston, Texas reveals that a 35% increase in papers relating to torsional vibration has been experienced over the last decade. This is likely a result of the increasing usage of variable frequency drives (VFDs) coupled to large motors.
All rotating equipment power trains found in a power plant have some amount of vibration, usually caused by mechanical unbalance of the rotating system, shaft misalignment or weakness in the bearing support. Rotating equipment is also expected to experience variations in speed and therefore be subjected to torsional vibration. Effective accurate measurement of torsional vibration allows an operator to evaluate several issues, including torsional natural frequencies, dynamic stresses, torsional modes shape, component fatigue and load vibration. Torsional vibration, in some cases, can be deduced by case accelerometers, but is best detected and monitored directly from the rotor.
At present, torsional vibration is the most difficult of the three vibrations to measure and monitor. As no industrially hardened, non-contacting, continuous torsional vibration monitoring system is widely available, investigation and analysis are usually achieved by using other direct and indirect methods. All plant operators, whether at power generation or oil and gas locations, are at risk of rotating machinery damage or unplanned plant outages due to failures by not continuously monitoring torsional vibration. This is a widespread, unplanned maintenance time bomb; yet, it provides an unparalleled opportunity for innovation.
Part 2
Part 2 of this article will appear in the February issue. HP
NOTES
a Bently Nevada’s System 1 condition monitoring software
REFERENCES
- STP Nuclear Operating Co., South Texas Project, online: https://www.nrc.gov/docs/ML0319/ML031900050.pdf
- Corcoran, J., et al, “Preventing unexpected train torsional oscillations,” 39th Turbomachinery and Pump Symposium, Houston, Texas, 2010.
- McClinton, C., et al, “Coupling failure due to a motor fault,” 43th Turbomachinery and Pump Symposium, Houston, Texas, 2014.
- Bently, D. and C. T. Hatch, Fundamentals of Rotating Machinery Diagnostics, American Society of Mechanical Engineers, 2002.
The Authors
O’Connor, D. - Bently Nevada, a Baker Hughes Business, Minden, Nevada
David O’connor is a Principal Engineer and Mechanical Team Lead at Bently Nevada, a Baker Hughes Business in Minden, Nevada. He has developed products for in-core nuclear power reactors, gas and steam turbines, oil and gas exploration, power plant monitoring and large rotating machinery.
Gutierrez, J. - Bently Nevada, a Baker Hughes Business, Minden, Nevada
Jose A. Guttierrez is the Executive Director of Technology at Bently Nevada, a Baker Hughes Business. He is in charge of setting the innovation strategy to deliver best-in-class industrial assets protection and condition monitoring solutions to the company’s customers. Dr. Gutierrez has a wide range of experience leading technology and innovation strategy and developing products for Fortune 100 companies, spanning residential, commercial and industrial market segments.
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