Jason C. Wilkes

Tilting Pad Journal Bearings—A Discussion on Stability Calculation, Frequency Dependence, and Pad and Pivot

For several years, researchers have presented predictions showing that using a full tilting-pad journal bearing (TPJB) model (retaining all of the pad degrees of freedom) is necessary to accurately perform stability calculations for a shaft operating on TPJBs. This paper will discuss this issue, discuss the importance of pad and pivot flexibility in predicting impedance coefficients for the tilting-pad journal bearing, present measured changes in bearing clearance with operating temperature, and summarize the differences between measured and predicted frequency dependence of dynamic impedance coefficients. The current work presents recent test data for a 100 mm (4 in.) five-pad TPJB tested in load on pad (LOP) configuration. Measured results include bearing clearance as a function of operating temperature, pad clearance and radial displacement of the loaded pad (the pad having the static load vector directed through its pivot), and frequency-dependent stiffness and damping. Measured hot-bearing clearances are approximately 30% smaller than measured cold-bearing clearances and are inversely proportional to pad surface temperature; predicting bearing impedances with a rigid pad and pivot model using these reduced clearances results in overpredicted stiffness and damping coefficients that are several times larger than previous comparisons. The effect of employing a full bearing model versus a reduced bearing model (where only journal degrees of freedom are retained) in a stability calculation for a realistic rotor-bearing system is assessed. For the bearing tested, the bearing coefficients reduced at the frequency of the unstable eigenvalue (subsynchronously reduced) predicted a destabilizing cross-coupled stiffness coefficient at the onset of instability within 1% of the full model, while synchronously reduced coefficients for the lightly loaded bearing required 25% more destabilizing cross-coupled stiffness than the full model to cause system instability. The same stability calculation was performed using measured stiffness and damping coefficients at synchronous and subsynchronous frequencies. These predictions showed that both the synchronously measured stiffness and damping and predictions using the full bearing model were more conservative than the model using subsynchronously measured stiffness and damping, an outcome that is completely opposite from conclusions reached by comparing different prediction models. This contrasting outcome results from a predicted increase in damping with increasing excitation frequency at all speeds and loads; however, this increase in damping with increasing excitation frequency was only measured at the most heavily loaded conditions.

An Improved Catcher Bearing Model and an Explanation of the Forward Whirl/Whip Phenomenon Observed in Active Magnetic Bearing Transient Drop Experiments

Though many approaches have been proposed in the literature to model the reaction forces in a catcher bearing (CB), there are still phenomena observed in experimental tests that cannot be explained by existing models. The following paper presents a novel approach to model a CB system. Some of the elements in the model have been previously introduced in the literature; however, there are other elements in the proposed model that are new, providing an explanation for the forward whirling phenomena that has been observed repeatedly in the literature. The proposed CB model is implemented in a finite element rotordynamic package, and nonlinear time-transient simulations are performed to predict published experimental results of a high speed vertical sub-scale compressor; with no other forces present in the model, the agreement between simulations and experimental data is favorable.The results presented herein show that friction between the journal and axial face of the catcher bearing results in a forward cross-coupled force that pushes the rotor in the direction of rotation. This force is proportional to the coefficient of friction between the axial face of the rotor and catcher bearing and the axial thrust on the rotor. This force results in synchronous whirl when the running speed is below a combined natural frequency of the rotor-stator system, and constant frequency whip when the speed is above a whip frequency.Copyright

The Numerical and Experimental Characteristics of Multimode Dry-Friction Whip and Whirl

The nature of dry-friction whip and whirl is investigated through experimental and numerical methods. A test rig was designed and constructed to demonstrate and record the character of multi-mode dry-friction whip and whirl. These tests examined steady state whip and whirl characteristics for a variety of rub materials and clearances. A simulation model was constructed using tapered Timoshenko beam finite elements to form multiple-degree-of-freedom rotor and stator models. These models were reduced by component mode synthesis to discard high-frequency modes while retaining physical coordinates at the rub location to model rotor-stator interaction using a nonlinear contact model with Coulomb friction. Simulations were performed for specific test cases and compared against experimental data; these comparisons are favorable. Experimental data analysis showed multiple whirl and whip regions, despite claims of previous investigators that these regions are predicted analytically but not produced in simulations or experiments. Spectral analysis illustrates the presence of harmonic sidebands that accompany the fundamental whirl solution. These sidebands are more evident in whip and can excite higher-frequency whirl solutions.Copyright

MANUFACTURING AND TESTING EXPERIENCE WITH DIRECT METAL LASER SINTERING FOR CLOSED CENTRIFUGAL COMPRESSOR IMPELLERS

Direct Metal Laser Sintering (DMLS) is an additive manufacturing process that utilizes a high-powered laser to build up a metal part by selectively melting thin layers of metal powder. This process is attractive for the manufacturing of parts with complex geometry such as closed centrifugal compressor impellers. DMLS allows closed impellers to be made in a single piece and eliminates the shroud joint that results from two-piece manufacturing processes. Using a monolithic impeller can allow higher tip speeds with improved fatigue characteristics compared with two-piece and three-piece designs. Prototype parts can be made more economically than investment casting when considering the tooling costs. Manufacturing costs for DMLS parts are marginally higher than for two-piece machined impellers, but qualification efforts for the braze/weld joint at the cover are circumvented. The DMLS process introduces several factors that must be considered in the impeller design to achieve a successful build with the proper strength and surface finish. This paper describes the authors’ experience with manufacturing and testing multiple closed impeller designs constructed from Inconel 718, 17-4 PH Stainless Steel, and Titanium 6Al-4V. A detailed discussion of design factors and manufacturing experience with a DMLS vendor is included for the various metals. Dimensional, post-test destructive inspection, and material test results are provided showing that the DMLS process can produce an impeller with good dimensional accuracy, surface finish, and material strength. Finally, overspeed test results up to maximum tip speeds of over 1400 ft/s (425 m/s) and aerodynamic performance test results are presented and discussed.

Improving Tilting-Pad Journal Bearing Predictions—Part II: Comparison of Measured and Predicted Rotor-Pad Transfer Functions for a Rocker-Pivot Tilting-Pad Journal Bearing

Measured and Predicted Rotor-Pad Transfer Functions for a Rocker-Pivot Tilting-Pad Journal Bearing. (December 2011) Jason Christopher Wilkes, B.S., Texas A&M University; M.S., Texas A&M University Chair of Advisory Committee: Dr. Dara W. Childs Many researchers have compared predicted stiffness and damping coefficients for tilting-pad journal bearings (TPJBs) to measurements. Most have found that direct damping is consistently overpredicted. The thrust of this research is to explain the difference between measured and predicted stiffness and damping coefficients for TPJBs, and to provide some confidence to designers that TPJB dynamic coefficients can be accurately predicted. Most analytical models for TPJBs are based on the assumption that explicit dependence on pad motion can be eliminated by assuming harmonic rotor motion such that the amplitude and phase of pad motions resulting from radial and transverse rotor motions are predicted by rotor-pad transfer functions. In short, these transfer functions specify the amplitude and phase of pad motion (angular, radial, translational, etc.) in response to an input rotor motion. A new pad perturbation model is developed including the effects of angular, radial, and circumferential pad motion and changes in pad clearance due to pad bending compliance. Though all of these pad variables have previously been included in different analyses, there are no publications containing perturbations of all four variables. In addition, previous researchers have only perturbed the journal, while both the bearing and journal motions are perturbed in the present analysis, and the applicability of comparing rotor-perturbed bearing impedance predictions to impedances measured on a bearing-perturbed test rig is discussed. This perturbation model was

Mechanical Design Features of a Small Gas Turbine for Power Generation in Unmanned Aerial Vehicles

As part of the Intelligence Advanced Research Projects Activity (iARPA) Great Horned Owl (GHO) program, Southwest Research Institute® (SwRI®) developed and tested a small gas turbine for power generation in Unmanned Aerial Vehicles (UAV). This development program focused on advancing the state of the art in UAV power systems by meeting key metrics in weight, fuel efficiency, and noise generation.Design, assembly, and testing of the gas turbine were completed in-house at SwRI. Fundamental mechanical design features of the gas turbine include an integrated 7 kW motor-generator, minimal oil lubrication system, cantilevered compressor/turbine assembly, and can combustor with air-atomizing fuel nozzles. The compressor/turbine assembly is cantilevered directly off of the motor-generator shaft, which spins on hybrid ceramic bearings. Due to potential rotor natural frequencies in the design operating range, the rotor-dynamic design of this configuration was a special design challenge. The outboard rotor bearing is softly supported on O-rings to provide compliance and drive shaft natural frequencies below the operating range.The lube oil system is another interesting design feature of the GHO gas turbine. It is based on a minimal oil lubrication system previously used at SwRI. The minimal oil lubrication system relies on low oil flow rates and cooling air to pull droplets of oil through the bearing. The oil passes through the machine and is consumed during combustion. This system eliminates traditional oil recirculation hardware for simplicity and weight savings.The can combustor features a modular design and uses additive manufacturing techniques to facilitate easy and cost effective prototyping. All combustor components are manufactured from Inconel 718 using direct metal laser sintering (DMLS) with additional post-machining. These parts are particularly challenging for DMLS because of their thin walls and high aspect ratio. The custom air-atomizing fuel nozzles also highlight one of the exciting advantages of the DMLS process. Each nozzle would be difficult to machine using traditional techniques because of the tight internal flow passages; however, they are simple to construct using additive manufacturing.The GHO turbine developed by SwRI demonstrates interesting design features including a minimal oil lubrication system, a cantilever shaft with softly supported bearing, and combustor components built using additive manufacturing techniques. This design provides a platform for further development, testing, and demonstration of small gas turbine technology for UAV power generation.Copyright

A General Model for Two-Point Contact Dry-Friction Whip and Whirl: Further Advancements and Experimental Test Results

Numerous papers have investigated the behavior of dry-friction whip and whirl; most of them consider contact between a rotor and stator at a single location. For rotors running on multiple magnetic bearings, air bearings, or bushings, equipment failure may result in rub at more than one location. For these cases, it is important to have an analytical model that characterizes possible regions of two-point contact dry-friction whip and whirl.The current work presents a general model to predict possible whirl regions for multi-contact dry-friction whip and whirl, allowing for an arbitrary phase between contact locations. In theory this method can be applied to more than two contact locations; however, a two-point contact example case is developed and compared to results from an experimental test rig developed to demonstrate multi-contact dry-friction whip and whirl in the current work.Copyright

Improving Tilting-Pad Journal Bearing Predictions: Part I—Model Development and Impact of Rotor-Excited Versus Bearing-Excited Impedance Coefficients

The floating-bearing-test-rig concept was initially developed by Glienicke in 1966 and has since been used to test many tilting-pad journal bearings (TPJBs). The impedances measured during these tests have been compared to rotor/journal perturbed impedance predictions. Since the inertial acceleration of a pad is different for bearing perturbed and rotor perturbed motions, the bearing’s reaction force components for bearing perturbed and journal perturbed motions will also differ. An understanding of how bearing perturbed and rotor perturbed impedances differ is needed to assess the validity of past, present, and future comparisons between TPJB test data and predictions.A new TPJB perturbation model is developed including the effects of angular, radial, and transverse pad motion and changes in pad clearance due to pad bending compliance. Though all of these pad variables have previously been included in different analyses, there are no publications containing perturbations of all four variables. In addition, previous researchers have only perturbed the rotor, while both the bearing and rotor motions are perturbed in the present analysis. The applicability of comparing rotor-perturbed bearing impedance predictions to impedances measured on a bearing-perturbed test rig is assessed by comparing rotor perturbed and bearing perturbed impedance predictions for an example bearing.Copyright

A General Model for Two-Point Contact Dry-Friction Whip and Whirl

Numerous papers have investigated the behavior of dry-friction whip and whirl; most of them consider contact between a rotor and stator at a single location. For rotors running on multiple magnetic bearings, air bearings, or bushings, equipment failure may result in rub at more than one location. For these cases, it is important to have an analytical model that characterizes possible regions of two-point contact dry-friction whip and whirl.Until a recent publication by Childs and Kumar in 2011, there were no attempts to analytically describe the behavior of dry-friction whip and whirl at more than one location. In their work, they assume that forces at the two rotor/stator contacts are either in-phase, or out-of phase. The current work presents a method that is more general, allowing for an arbitrary phase between contact locations. In theory this method can be applied to more than two contact locations; however, a two-point contact example case is developed and compared to numerical simulations in the current work.Copyright

Tilting Pad Journal Bearings: A Discussion on Stability Calculation, Frequency Dependence, and Pad and Pivot Flexibility

For several years, researchers have presented predictions showing that using a full tilting-pad journal bearing (TPJB) model (retaining all of the pad degrees of freedom) is necessary to accurately perform stability calculations for a shaft operating on TPJBs. This paper will discuss this issue, discuss the importance of pad and pivot flexibility in predicting impedance coefficients for the tilting-pad journal bearing, present measured changes in bearing clearance with operating temperature, and summarize the differences between measured and predicted frequency dependence of dynamic impedance coefficients.The current work presents recent test data for a 100 mm (4 in) five-pad TPJB tested in load on pad (LOP) configuration. Measured results include bearing clearance as a function of operating temperature, pad clearance and radial displacement of the loaded pad (the pad having the static load vector directed through its pivot), and frequency dependent stiffness and damping. Measured hot bearing clearances are approximately 30% smaller than measured cold bearing clearances and are inversely proportional to pad surface temperature; predicting bearing impedances with a rigid pad and pivot model using these reduced clearances results in overpredicted stiffness and damping coefficients that are several times larger than previous comparisons.The effect of employing a full bearing model versus a reduced bearing model (where only journal degrees of freedom are retained) in a stability calculation for a realistic rotor-bearing system is assessed. For the bearing tested, the bearing coefficients reduced at the frequency of the unstable eigenvalue (subsynchronously reduced) predicted a destabilizing cross-coupled stiffness coefficient at the onset of instability within 1% of the full model, while synchronously reduced coefficients for the lightly loaded bearing required 25% more destabilizing cross-coupled stiffness than the full model to cause system instability.The same stability calculation was performed using measured stiffness and damping coefficients at synchronous and subsynchronous frequencies. These predictions showed that both the synchronously measured stiffness and damping and predictions using the full bearing model were more conservative than the model using subsynchronously measured stiffness and damping, an outcome that is completely opposite from conclusions reached by comparing different prediction models. This contrasting outcome results from a predicted increase in damping with increasing excitation frequency at all speeds and loads; however, this increase in damping with increasing excitation frequency was only measured at the most heavily loaded conditions.© 2012 ASME