Publications

Curvic couplings are commonly utilized in aircraft engines and large gas turbines for high load capacity, precision centering of stacked components in rotating assemblies. The couplings have non-axisymmetric, complex curved mating contact surfaces, which transmit torque, moment and force. Coupling contact surface roughness, and tooth and ring deformations introduce local lateral flexibilities, compared with a continuous beam model, and consequently affect rotordynamic vibration predictions. A novel approach of modeling the Curvic coupling is proposed which combines a GW contact model with a 3D solid element model of flexible teeth and coupling rings. This improves on similar approaches that assume rigid teeth and rings or omits a surface roughness – asperity model. Comparisons of the various models with experimental measurements of free-free natural frequencies of an axially preloaded shaft, demonstrate a marked improvement in accuracy with the proposed approach. A parametric study is performed which varies tooth contact pattern, tooth number, pressure angle, half pitch number, and tooth rigidity to evaluate their effects on vibration and stress. The proposed approach is also applied to an industrial rotor to illustrate the effect of the new Curvic coupling model on critical speeds. The higher fidelity flexible tooth model presented shows a significant change in critical speed relative to the rigid tooth model from the literature.

 

An improved preloaded Curvic coupling model for rotordynamic analyses

Gas turbine and other machinery rotating assemblies are frequently manufactured as multiple components for cost and component alignment reasons. Butt joint, Hirth, and Curvic coupling are widely used for this purpose. Localized joint flexibility in these preloaded couplings introduce non-beamlike behavior which affects rotordynamic critical speeds, imbalance response and stability, rendering a conventional beam model inadequate. 3D solid finite element models of the couplings with Greenwood Williamson (GW) asperity interface features provide accurate representations of the couplings, however computational costs are impractical for use in an industrial design setting, which are limited to beam element models. A novel modeling approach for the coupling is developed that derives equivalent beam element Young’s modulus and shear form factor properties, that replicate the bending behavior of the high fidelity 3D solid models, including GW based interface asperity stiffness. The equivalent beam models for butt, Hirth and Curvic couplings are validated using measured natural frequencies as a benchmark, for a range of through-bolt preloads. The equivalent beam model and the 3D solid model in this correlation incorporate GW contact models derived with experimentally measured surface roughness parameters. An E_coupling sensitivity study for GW surface roughness parameters was conducted and showed a significant level of sensitivity. The effect of the coupling on an industrial class rotor’s critical speed is included to illustrate usage of the approach.

 

Beam Based Rotordynamics Modelling for Preloaded Hirth, Curvic and Butt Couplings

Measured Head-flow HQ curves for a Fontan cavopulmonary assist device (CPAD) in a mock circulatory loop were compared with CFD model predictions. The tests benchmarked the CFD tools for further CPAD design enhancement. Reynolds-Averaged Navier-Stokes (RANS) CFD approaches recommended for development of conventional ventricular assist devices (VAD) were found to have shortcomings when applied to the Fontan CPAD, designed to neutralize off-condition obstruction risks that could contribute to a major adverse event. The no-obstruction condition is achieved with a von Karman type pump, utilizing large clearances and small blade heights, which challenges conventional VAD RANS-based CFD simulations. Accurate head rise and wall shear stress predictions are imperative for pressure boost, power requirement, hemolysis and thrombosis optimizations. Head and power predictions of various RANS turbulence models are compared with pressure test measurements and Large Eddy Simulation (LES) results. The models include standard k-ϵ, RNG k-ϵ, Realizable k-ϵ, SST k-ω, SST with transitional turbulence, and Generalized k-ϵ (GEKO). For the pressure head predictions, the standard k-ϵ model provided the best agreement with experiment, even slightly outperforming the LES. For torque on the rotor, k-ϵ predictions were 30% lower than LES, while the SST and LES values were near identical. The findings support using LES for final Fontan CPAD design simulations. Less preferred is the k-ω model for head and general flow simulation, and SST for power, wall shear stress, hemolysis and thrombogenicity predictions.

 

CFD Turbulence Model and Experimental Study for a Fontan Cavopulmonary Assist Device

The accurate characterization of compressor rotordynamic coefficients during the design phase reduces the risk of subsynchronous vibration problems occurring in the field. Although rotordynamists extensively investigate discrete compressor components (such as seals and front shrouds) to tackle instability issues, integrated or system-level analysis of compressor rotordynamics is very sparse. In reality, the impeller, eye-labyrinth seal, and the front shroud heavily influence one another; and the collective dynamic behavior of the system differs from the sum of the dynamic behavior of isolated components. A computational fluid dynamics (CFD)-based approach is taken to evaluate the dynamic behavior of the system as a whole. The geometry and operating conditions in this work are based on the recent experimental study of Song et al. (2019, “Non-Axisymmetric Flows and Rotordynamic Forces in an Eccentric Shrouded Centrifugal Compressor—Part 1: Measurement,” ASME J. Eng. Gas Turbines Power, 141(11), p. 111014. 10.1115/1.4044874) on centrifugal compressor. The commercial CFD code cfx 19.0 is used to resolve Reynolds-averaged Navier–Stokes equations to quantify the eye-labyrinth seal and front cavity stiffness, damping, and added mass. The entire compressor stage is modeled to uncover the coupled behavior of the components and assess the stability of the whole system instead of just discrete components. In the current work, three CFD approaches, namely quasi-steady, transient static eccentricity, and transient mesh deformation techniques are studied and benchmarked against analytical and experimental results from the literature. Having established the efficacy of the proposed approach, four types of swirl brakes are proposed and analyzed for stability. The novel swirl brakes create negative swirls at the brake cavities and stabilize both the front shroud and the eye-labyrinth seal simultaneously

 

Swirl Brake Design for Improved Rotordynamic Vibration Stability Based on CFD System Level Modeling

The Morton effect (ME) is a thermally induced rotodynamic instability problem frequently reported in the fluid film bearing system. The temperature difference across the journal circumference may cause large spiral, synchronous vibration. Earlier ME modeling approaches rarely focus on the flexure-pivot bearing (FPB), significantly disproportionate to its wide application. Hereby, the transient ME prediction algorithm is proposed based on a high-fidelity thermo-elasto-hydrodynamic FPB model. A hybrid finite element analysis is adopted to evaluate the entire rotor thermal bow profile including the rotor midspan. The algorithm is benchmarked with experiments and applied to a realistic compressor model. Simulations confirm the proneness of the FPB system to the ME instability, and reveal the ME sensitivity to the bearing-rotor configuration and operation conditions.

 

Transient Rotordynamic Thermal Bow (Morton Effect) Modeling in Flexure-Pivot Tilting Pad Bearing Systems

Kinetic/Flywheel energy storage systems (FESS) have re-emerged as a vital technology in many areas such as smart grid, renewable energy, electric vehicle, and high-power applications. FESSs are designed and optimized to have higher energy per mass (specific energy) and volume (energy density). Prior research, such as the use of high-strength materials and the reduction of stress concentration, primarily focused on designing and optimizing the rotor itself. However, a modern FESS includes other indispensable components such as magnetic bearings and a motor/generator that requires a shaft. The shaft significantly impacts the flywheel design. This paper investigates several typical flywheel designs and their stress analysis. A simplified analysis method is given for designing rotor-shaft assembly. It is found that the shaftless flywheel design approach can double the energy density level when compared to typical designs. The shaftless flywheel is further optimized using finite element analysis with the magnetic bearing and motor/generators’ design considerations.

 

Analysis and optimization of a novel energy storage flywheel for improved energy capacity

The Morton effect (ME) occurs when a bearing journal experiences asymmetric heating due to synchronous vibration, resulting in thermal bowing of the shaft and increasing vibration. An accurate prediction of the journal’s asymmetric temperature distribution is critical for reliable ME simulation. This distribution is strongly influenced by the film thermal boundary condition at the pad inlets. Part I utilizes machine learning (ML) to obtain a two-dimensional radial and axial distribution of temperatures over the leading-edge film cross section. The hybrid finite volume method (FVM)—bulk flow method of Part I eliminated film temperature discontinuities and is utilized in Part II for improving accuracy and efficiency of ME simulation.

 

Tilt Pad Bearing Distributed Pad Inlet Temperature With Machine Learning – Part II Morton Effect

Uncertainty in mixing coefficients (MCs) for estimating pad leading-edge film temperature in tilt pad journal bearings reduces the reliability of predicted characteristics. A three-dimensional hybrid between pad (HBP) model, utilizing computational fluid dynamics (CFD) and machine learning (ML), is developed to provide the radial and axial temperature distributions at the leading edge. This provides an ML derived, two-dimensional film temperature distribution in place of a single uniform temperature. This has a significant influence on predicted journal temperature, dynamic coefficients, and Morton effect response. An innovative finite volume method (FVM) solver significantly increases computational speed, while maintaining comparable accuracy with CFD. Part I provides methodology and simulation results for static and dynamic characteristics, while Part II applies this to Morton effect response.

 

Tilt Pad Bearing Distributed Pad Inlet Temperature With Machine Learning – Part I Static and Dynamic Characteristics

The treatment of thermal mixing in inter pad grooves of a fluid film bearing is essential due to its influence on the heat transfer with the rotating shaft and stationary bearing. Lower fidelity models that either neglect or over approximate thermal groove mixing may lead to premature bearing or machinery failure, most commonly from babbitt thermally induced fatigue. Conventional models rely on bulk flow and thermal analyses yielding a single temperature at the groove outlet into the pad inlet. The high uncertainty of this approach carries over into downstream predictions for bearing life, stiffness and damping, and machinery vibration predictions. Contrary to a uniform temperature, CFD-Conjugate heat transfer studies reveal large gradient temperature distributions varying in both the radial and axial directions at the groove outlet, especially with jet lubrication implemented with multiple nozzles. These distributions vary continuously with time as the spinning shaft and bearing pads vibrate. A direct CFD simulation thus becomes computationally prohibitive.

The present work introduces a novel approach which yields highly detailed lubricant temperature distributions at the pad inlets in a computationally economical manner. This is implemented with a surrogate groove model via a deep convolutional autoencoder neural network based on CFD (Computational Fluid Dynamics) data. The trained Convolutional Neural Network (CNN) shows excellent prediction capability for 2D temperature distribution at a circumferential groove outlet. The trained CNN is combined with a rotor-bearing model, and the combined model is verified by full CFD results and experimental data. In addition, this approach is expanded to include various oil injection types, illustrating their detailed heat transfer to the rotating shaft and bearing.

 

Deep convolutional autoencoder augmented CFD thermal analysis of bearings with inter pad groove mixing

The Morton Effect (ME) is a thermal-fluid–structure interaction instability occurring in rotating machinery supported by hydrodynamic journal bearings. The mechanism of ME consists of a bowed rotor or mass imbalance induced shaft synchronous whirl vibration in the bearing, which causes local, asymmetric heating of the journal, which causes shaft bending, potentially leading to increasing vibration. This study presents an original ME simulation approach that includes a CFD (Computational Fluid Dynamics) bearing groove model, embedded in a deep learning algorithm for computational efficiency and non-expert usage. The groove model provides a 2D oil temperature distribution at the leading edge of the bearing pads, yielding a more accurate journal axisymmetric temperature distribution which is the source of the ME. The paper provides validation of the approach by test result correlation, and illustrates the effects of parameter variation and configuration variation, by examining various oil injection types. The approach may be used for correcting ME occurring in existing machinery, or for designing machinery to avoid the ME.

 

Morton Effect Prediction with Validation Using a CFD Based CNN for Pad Inlet Temperatures