Tim Dimond

Identification Methods and Test Results for Tilting Pad and Fixed Geometry Journal Bearing Dynamic Coefficients – A Review

Fluid film journal bearings (FFBs) are used to support high-speed rotors in turbomachinery which often operate above the rotor first bending critical speed. The FFBs provide both lateral support and dynamic coefficients: stiffness, damping, and mass terms, related to machine vibrations. Detailed numerical values of the bearing dynamic characteristics are necessary for proper design and operation of rotating machinery. The methods of the identification of fluid film journal bearing static and dynamic characteristics, particularly the bearing stiffness, damping, and mass coefficients, from measured data, obtained from different measurement systems, is reviewed. Many bearing tests have been performed to validate a number of different theoretical models, including the classical Reynolds isoviscous model. More advanced bearing models include the thermohydrodynamic (THD), and thermoelastohydrodynamic (TEHD) approaches. The advanced models also include turbulence effects which are important as rotor speeds continue to increase. The range of measured bearing data no longer includes current operational conditions. The various approaches to the bearing identification problem are discussed, including the different force excitation methods of incremental loading, sinusoidal, pseudorandom, impulse, known/additional unbalance, and non-contact excitation. Also bearing excitation and rotor excitation approaches are discussed. Data processing methods in the time and frequency domains are presented. Methods of evaluating the effects of measurement uncertainty on overall bearing coefficient confidence levels are reviewed. In this review, the relative strengths and weaknesses of bearing identification methods are presented, and developments and trends in improving bearing measurements are documented. Future trends in journal bearing identification improvement are discussed.

Temporal and Convective Inertia Effects in Plain Journal Bearings With Eccentricity, Velocity and Acceleration

This paper extends the theory originally developed by Tichy (Tichy and Bou-Said, 1991, Hydrodynamic Lubrication and Bearing Behavior With Impulsive Loads,” STLE Tribol. Trans. 34 , pp. 505–512) for impulsive loads to high reduced Reynolds number lubrication. The incompressible continuity equation and Navier-Stokes equations, including inertia terms, are simplified using an averaged velocity approach to obtain an extended form of short bearing Reynolds equation which applies to both laminar and turbulent flows. A full kinematic analysis of the short journal bearing is developed. Pressure profiles and linearized stiffness, damping and mass coefficients are calculated for different operating conditions. A time transient solution is developed. The change in the rotor displacements when subjected to unbalance forces is explored. Several comparisons between conventional Reynolds equation solutions and the extended Reynolds number form with temporal inertia effects are presented and discussed. In the specific cases considered in this paper, the primary conclusion is that the turbulence effects are significantly more important than inertia effects.

Design and Analysis of a Unique Energy Storage Flywheel System—An Integrated Flywheel, Motor/Generator, and Magnetic Bearing Configuration

Energy storage is becoming increasingly important with the rising need to accommodate the energy needs of a greater population. Energy storage is especially important with intermittent sources such as solar and wind. Flywheel energy storage systems store kinetic energy by constantly spinning a compact rotor in a low-friction environment. When short-term back-up power is required as a result of utility power loss or fluctuations, the rotor’s inertia allows it to continue spinning and the resulting kinetic energy is converted to electricity. Unlike fossil-fuel power plants and batteries, the flywheel based energy storage systems do not emit any harmful byproducts during their operation and have attracted interest recently. A typical flywheel system is comprised of an energy storage rotor, a motor-generator system, bearings, power electronics, controls, and a containment housing. Conventional outer flywheel designs have a large diameter energy storage rotor attached to a smaller diameter section which is used as a motor/generator. The cost to build and maintain such a system can be substantial. This paper presents a unique concept design for a 1 kW-h inside-out integrated flywheel energy storage system. The flywheel operates at a nominal speed of 40,000 rpm. This design can potentially scale up for higher energy storage capacity. It uses a single composite rotor to perform the functions of energy storage. The flywheel design incorporates a five-axis active magnetic bearing system. The flywheel is also encased in a double layered housing to ensure safe operation. Insulated-gate bipolar transistor (IBGT) based power electronics are adopted as well. The design targets cost savings from reduced material and manufacturing costs. This paper focuses on the rotor design, the active magnetic bearing design, the associated rotordynamics, and a preliminary closed-loop controller.

A New Fluid Film Bearing Test Rig for Oil and Water Bearings

Ever-increasing demands on the turbomachinery industry result in faster, lighter machines with higher rotational speeds and power densities. Modern, well-established thermoelastohydrodynamic (TEHD) analyses predict static and dynamic bearing characteristics in the presence of a turbulent lubricant and reduced lubricant flows. Proper design of tilting-pad journal bearings (TPJB) is required for successful operation of rotating machinery. Bearing static effects include pad temperature, bearing pressure profile, and static operating position. Bearing dynamic effects include stiffness, damping, and added mass coefficients. The current body of experimental data does not include the entire range of speed and load for which TEHD analyses are thought to be valid or where industrial machines operate. Experimental data for both oil-lubricated and water-lubricated bearings is desired. Oil lubricated bearings are used in high-speed turbomachinery. Water bearing data are of interest for applications that use the process fluid as the bearing lubricant. This paper describes a new Fluid Film Bearing Test Rig (FFBTR) which is being designed to experimentally verify the TEHD analyses, both in the laminar and in the turbulent regime, and support industrial needs. Static bearing characteristics will be measured with temperature probes, pressure probes, and displacement measurements. The dynamic bearing coefficients will be identified by rotor perturbation with active magnetic bearing force actuators. The rotational speed range of the FFBTR will be 9000–22000 rpm. The test bearing size is 127 mm, giving a range of surface speeds of 60–146 m/s. The range of bearing length-to-diameter (L/D) ratios that can be tested will be 0.5–0.75. Separate lubrication systems for water-lubricated and oil-lubricated bearings will be provided. Two magnetic bearings will be used as non-contact force actuators for rotorbearing system perturbation. The designed capacity for the magnetic force actuators is 13 kN/exciter, for a total static plus dynamic load of 26 kN that can be applied to the test bearing. The actuators are designed to apply forces to the test rotor at non-synchronous frequencies up to 560 Hz. Bearing static characteristics will be measured. Static measurements will include lubricant pressure profile, lubricant and pad temperatures, and static eccentricity. During dynamic testing, test shaft and bearing tilting pad motion will be measured. Dynamic bearing stiffness, damping, and added mass coefficients will be identified from force and displacement measurements. The frequency dependence in tilting-pad journal bearing coefficients will be investigated. The combination of static and dynamic measurements will be used to validate the TEHD analyses and provide design information to industry.Copyright

Steam Turbine Vibration Caused by Oil Coking Rubs: Case Studies and Numerical Simulation

Rotor-stator rub interactions play an important role in the operation of high performance turbomachinery such as steam turbines, compressors, motors, and generators with small clearances between the rotating and stationary components. It is difficult to diagnose the problem because the vibration characteristics are widely varied and often the same as those resulting from other common causes. Also, rubs can cause secondary effects which can be misdiagnosed as the primary cause of the vibration excursion. The paper investigates one of the rub phenomena — the bearing lubricant (oil) coking in the close clearance regions while the other operational parameters are unchanged. The amplitude of vibration typically increases suddenly and then decreases after a few minutes. An FFT analysis of the vibration spectrum result indicates that most of the vibration energy is distributed to synchronous components or super-synchronous components. Two industrial case studies are presented and the possible factors are reviewed. Simulation results indicate that the model can describe the behavior of the steam turbine under oil coking rotor-stator rub conditions well and help locate the axial position of the oil coking rub. The analysis results of the paper are very useful for transient vibration fault diagnosis.Copyright

Lateral Rotordynamic Analysis of a Large Alternator/Flywheel/Motor Train

A large alternator/flywheel/motor train is employed as part of the power system for the ALCATOR C-MOD experiment at the MIT Plasma Fusion Center. The alternator is used to provide peak pulse power of 100 MW to the magnets employed in the fusion experiment. The flywheel diameter is 3.3m and the alternator is 1.8 m in diameter. After being driven up to full speed over a long period of time by a 1491 kW motor, the alternator is rapidly decelerated from approximately 1800 rpm to 1500 rpm during a 2 second interval. This sequence is repeated about six times per working day on average. A full lateral rotordynamic analysis of the including the rotors, fluid film bearings and unbalanced motor magnetic force was carried to assess the effects of rotor modifications in the alternator shaft bore. This paper provides a more detailed analysis of a complicated rotor train than is often performed for most rotors. Critical speeds, stability and unbalance response were evaluated to determine if lateral critical speeds might exist in the operating speed range in the existing or modified rotor train and if unbalance levels were within acceptable ranges. Critical speeds and rotor damping values determined for the rotor system with the existing and modified rotor. The first critical speed at 1069 rpm is an alternator mode below the operating speed range. The second critical speed is also an alternator mode but, at 1528 rpm, is in the rundown operating speed range. The third critical speed is a flywheel mode at 1538 rpm, also in the rundown operating speed range but well damped. The predicted highest rotor amplitude unbalance response level is at 1633 rpm, again in the operating speed range. Direct comparisons were made with measured bearing temperature values, with good agreement between calculations and measurements. Stress levels in the rotor were evaluated and found to be well below yield stress levels for the material for both original and modified rotors. Comparisons we carried out between standard vibration specifications and measured vibration levels which indicated that the third critical speed amplification factors were much higher than API standards indicate they should have been. Corrective actions to reduce unbalance were taken for the modified rotor.Copyright

Axial Flow Seal/Bearing Efficient Pressure Formulation for a Reynolds Equation Solution

Current fluid film seal/bearing pressure numerical solutions taking into account both circumferential and axial lubricant flows are not in wide spread use. The most common method is to solve a two dimensional finite element method of Reynolds equation. However, this type of solution often leads to a long computer solution times when employed in an advanced seal/bearing code. A new approximate solution of Reynolds equation for oil seal or bearing flows is proposed in this paper which includes the axial flow modeling. The objective is achieved by means of an axial approximation that can be used to develop a one dimensional centerline circumferential pressure finite element solution to Reynolds equation. Optimization of the parameters associated with the approximate solution parameters is shown. Example seal/bearing pressure and load capacity calculations are presented and the solution verified by comparison with a full finite element 2-D solution. Also, the method of calculating the axial and circumferential lubricant flows as well as axial and circumferential power losses are presented and validated.