Current Research

Fluid film bearings serve a crucial role in many rotordynamic systems, contributing both supporting stiffness and the majority of the system damping. Being able to understand and successfully capture the behavior of these bearings is vital to ensuring machine reliability and improving rotordynamic performance. Irregularities on the bearing surface can have a noticeable effect on bearing operation. These surface irregularities can be either intentional, such as lift pockets, or accidental, such as scratches. CFD will be utilized in order to better understand the effects that these can have on bearing operation. Models of both scratches and lift pockets will be generated and compared to cases without such features. Using the CFD results, a simplified model will be generated in order to couple it with more simplified Reynolds equation solvers. A new 3d Reynolds equation solver will be written and distributed to ROMAC members.

The effects of a lift pocket and circumferential scratch on pressure profiles.

The ability to accurately predict rotating machine resonant frequencies and to assess their stability and response to external forces is crucial from a reliability and preventative maintenance perspective. ROMAC has multiple tools to assist with this prediction ranging from critical speed maps to forced response analyses in lateral, torsional, and axial degrees-of-freedom. RotorSol was developed to combine these tools into one comprehensive package. RotorSol uses a finite element model composed of 12 degree-of-freedom beam elements coupling lateral, torsional, and axial degrees-of-freedom together. RotorSol is currently being linked with RotorLab+, ROMAC’s latest software platform. Tilting pad bearings with full coefficients, aerodynamic cross-coupling, thrust bearings, flexible couplings, flexible supports, and disk stiffness properties are all new components which have been added to RotorSol’s capabilities. Considerable work has also been put into improving the efficiency and reducing the run time of RotorSol. Future work for this project includes: i) adding new components such as gears; ii) new forces such as shaft bow and nonsynchronous forces; iii) new element capabilities such as internal damping, tapered elements, and distributed mass; iv) new analytical tools such as critical speed maps and Campbell diagrams; and v) new options such as inclusion of user-specified matrices for modeling support structures.

Bearings provide a critical supportive function in rotating machinery and are thus commonly designed to operate within a set of design constrictions. This makes optimization a powerful tool for use in bearing design. Design of experiments is a useful method which enables intelligent data point selection in order to create simplified models using a minimum number of data points. This project uses design of experiments coupled with MAXBRG to generate simplified bearing models. The optimization of these simplified models enables the minimization of various bearing operation parameters while maintaining others. In phase I one of this project, tilting pad bearings from an eight-stage centrifugal compressor are examined individually. The bearing power loss and maximum pad temperature are minimized while maintaining a minimum film thickness to ensure film integrity and a maximum film pressure to prevent damage to the bearing structure. The optimization will be performed with varying weights on the maximum pad temperature and power loss to examine the tradeoffs that one can achieve. In phase II of the project the bearing model will be coupled to the compressor model and a similar design of experiments will be performed. The design will be performed in order to generate simplified models for both the bearings individually, as well as for the full rotor/bearing system. In this phase, the optimization will be performed in order to minimize key bearing parameters while maintaining safe rotor and bearing operating conditions.

Bearing design variables include pad arc length, radial clearance, preload, offset, and others.

Model response surface of maximum pad temperature to changes in radial clearance and lubricant viscosity.

The focus of this project is on developing a new fluid film thrust bearing code that performs comprehensive thermoelastohydrodynamic (TEHD) analysis. Like the current ROMAC code for thrust bearings (THRUST), the lubricant would be incompressible and the operation would be steady state. However, this new code would address the weaknesses of THRUST in areas including turbulence modeling and numerical robustness. It would also expand the capabilities to model some geometries that cannot be modeled by THRUST. Moreover, this new code would be flexible enough to allow future improvement of various theoretical models, for example, groove mixing and direct lubrication. To achieve all these goals, modifying the existing THRUST code would not be cost effective because some equations must be reformulated and various iteration loops must be restructured. A better approach is to develop a new analytical software tool utilizing advanced techniques only available in recent years.

High speed rotating machines are subject to unbalance forces caused by residue weight. When the rotor’s axis of geometry and its principal axis of inertia are not aligned, unbalance forces synchronous to the rotational speed cause the rotor to deflect from the geometric center and enter a whirling motion. To reduce the effects that the rotor unbalance has on high speed machineries supported by AMBs, the conventional approach has been to either generate counteracting bearing forces or to shift the rotating axis in such a way that the shaft is rotating force-free or performing auto-balancing.

In this research, a differential regulator based output regulation approach is presented to addressing the autobalancing problem of AMB systems for varying rotational speeds. The problem of output regulation is to design a controller for disturbance rejection and/or reference tracking, while the disturbance or reference signal is generated by a known dynamic system called exosystem. After formulating the output regulation problem based on a time-varying exosystem, it is observed that the compensator gains can be obtained based on the solution of a differential regulator equation (DRE). Since AMB systems are of non-minimum phase, to ensure the boundedness of the compensator gains, the original normal form is reformulated and a unified gradient method is adopted to guarantee the residue error in the output regulation is minimized. Then the compensator gains are continuously generated to closely approach the output regulation objective with a small error in the regulated output. To apply output regulation to AMB systems for autobalancing, the unbalance force is modeled by the exosystem and the AMB force defines the error to be regulated. When the rotational speed varies, the exosystem becomes time-varying, and the proposed differential regulator based output regulation approach is adopted to generate the desired bounded compensator gains that minimize the AMB control force to achieve autobalancing.

The proposed method is verified in simulation for autobalancing with both varying and constant rotational speeds on a flexible rotor AMB test rig. The vibration levels under both cases are similar while the control voltage is significantly reduced with the differential regulator.

Simulated control voltages and rotor displacements with differential regulator off/on.

Fluid-film bearing applications continue to push the envelope on operating speed, specific load, and performance, requiring bearing technologies to keep pace. Modern applications commonly involve bearing operation in the transition and turbulent flow regions. Little data is available on the dynamic properties of bearings in this range. The Fluid Film Bearing Test Rig (FFBTR) aims to make these measurements possible.

Additionally, the FFBTR will provide additional validation of ROMAC codes including THPAD and MAXBRG. The development of an improved test rig with higher performance capability will lead to continued development and refinement of ROMAC bearing analysis tools for years to come.

Recently a comprehensive analysis of predicted uncertainty in measured dynamic coefficients was completed and the results indicated that the original design of the test rig needed to be modified. To minimize the final measurement uncertainty new technologies such as the “Active Load Cell” concept are being evaluated.

An “Active Load Cell” test bed is being developed in parallel with the FFBTR to validate the concept and ensure the best accuracy possible for bearing force measurements. This piece of equipment will utilize electrodynamic shakers and a control algorithm to accurately identify fluid-film bearing forces. The determination of these forces are critical to understanding the stiffness and damping coefficients of a fluid-film bearing, particularly at high frequencies.

All possible design changes are simulated in a high-fidelity Simulink model in an attempt to fully understand the dynamics of the system and make sure significant factors are not overlooked. In spring 2016 a great deal of progress made in the development of the high-fidelity simulation. Some preliminary results were presented in the summer at the annual meeting. The high-fidelity simulations are currently being finalized.

The objective of this research project is to develop new software and new analysis methods for annular seals of both traditional and non-traditional geometries. In traditional analysis methods such as the analytical perturbation approach known as bulk flow analysis, these expansion and recirculation grooves are commonly rectangular or semi-circular because it simplifies the analytical analysis. Recently, computational fluid dynamics (CFD) work has been performed on the geometric optimization of these groove shapes to minimize leakage through example seals. This work has conclusively demonstrated that non-traditional groove shapes can improve leakage response in the simulated seals. Unfortunately, CFD simulations require increased engineer and computational time in comparison to traditional bulk flow methods.

Semicircular groove flow vs. high aspect ratio trapezoidal groove flow.

A numerical analysis technique is under development to apply alternative numerical techniques to a set of simplified Navier-Stokes Equations representing a steady viscous potential flow. These assumptions are less strict than those of bulk flow and will allow for detailed flow characterization throughout the annular seal. The flow will be modeled with the vortex formulations of the Navier-Stokes equations and solved numerically by boundary element methods. Boundary element methods reduce the dimensionality of a full 3D seal to 2D, significantly reducing mesh sizes and increasing solution speed. The method will be developed for use with generalized, parameterized grooves first, with geometry import and a similar method using the Euler equations for gases for future development steps.

The developed analysis method aims to fully characterize the seal flow and rotordynamic response with solution times at least one order of magnitude faster than a commercial CFD package for a full 3D seal analysis. This will offer more accurate solutions than traditional bulk flow methods for novel annular seal geometries at reasonable computational cost. Accurate and computationally inexpensive modeling tools that allow for large seal geometry variation will prove invaluable to design optimization of turbomachinery flow paths.

Two studies are in progress to investigate new parameterizations for labyrinth seal geometries. These studies are investigating the effects of groove shape and the effects of non-uniform grooves of patterned size and shape on labyrinth seal flow and rotordynamic characterization.

The first study continues previous work by investigating a repeated pentagonal groove shape applied to a full 3D CFD model of a 20-groove balance drum labyrinth seal with a working fluid of water. The grooves are parameterized by inlet and exit angle, front depth, back depth, and the x and y location of a vertex inside the groove. This allows for concave and convex pentagonal groove shapes that manipulate the anchoring and size of the in-groove vortices generated by the pressure and shear-driven flow. These vortices have a significant impact on seal leakage and rotordynamic performance.

Pentagonal groove flow examples.

The second study investigates the same nominal full 3D CFD model of a 20-groove balance drum labyrinth seal with a parameterized model consisting of 10-60 traditional rectangular grooves. These grooves vary axially in width and depth according to quadratic functions representing groove aspect ratio and percentage of available width (per groove). This will allow for the investigation of the effects of number of grooves and converging and diverging groove profiles on seal leakage and rotordynamic performance.

Non-uniform groove flow example.

Both studies are performed with experimental design methods to reduce the number of CFD simulations and develop a response surface map of seal design parameters against seal performance responses. A multi-objective optimization will be performed with a range of weighting parameters to obtain seals with minimum leakage and maximum effective damping properties. 

Over the years many control methods have been proposed towards controlling rotating machines such as PID control, state-space control, robust control, and optimal control. These methods have proven their performance when a good mathematical model of the machine is available. However, extracting model information is generally challenging and also involves uncertainties in the identified model. Learning-based techniques come into picture when accurate models are not known in advance.

Reinforcement learning is new in line of modern adaptive control techniques which aims to design control systems that are both adaptive and optimal. These controllers can be considered as direct optimal adaptive controllers in which an optimal controller is designed without heavily relying on system models. The controller interacts with the system and modifies its control policy based on some reinforcement signal. The process involves online iterative approximation of optimal cost function and optimal control.

The theory of reinforcement learning control is however still new, and more results are needed for it to be feasible in practical control applications. In this project, we are investigating some reinforcement learning algorithms and seeking to extend the theory in order for it to be applied in rotating machines. In the future, such advanced control techniques are expected to require more computational capability, therefore we are also considering upgrading our existing control system hardware for our test rigs. High speed control and data acquisition boards comprising of modern embedded systems such as multi-core processors, DSPs or FPGAs are currently in consideration.

Big-Picture Overview of Reinforcement Learning Control

Development of a computational model that better predicts the performance of small, low-speed gas centrifuges based on the Onsager Equation with Carrier-Maslen end conditions. The linearized sixth-order partial differential equation is solved using a finite element algorithm to describe the flow in the centrifuge. The velocity profile described by the flow solution is then used to obtain a numerical solution of the isotopic diffusion to predict the transport of uranium hexafluoride molecules. A centrifuge performance map describing the separative performance over a range of feed and product rates is then generated for use in cascade modeling software packages to more accurately predict the separative performance potential of existing gas centrifuge enrichment plants (GCEP) subjected to traditional and off-normal operating conditions.

This project expands ROMAC’s computational analysis methods to helical groove seals, which are non-contacting annular seals with continuously cut grooves on the surface of the rotor and/or stator. The initial code has been developed as a three control volume bulk flow code for helical groove seals with either grooves on the rotor or grooves on the stator. This code numerically solves the continuity and conservation of momentum equations in each control volume using three key concepts. The first is that the turbulence can be modeled as shear stress momentum loss terms, which is the basis of bulk flow theory. The second is the assumption that the rotor has a small eccentricity with a circular orbit. The final principle used is a Jacobian transformation to the characteristic flow patterns, which are the axial flow and the groove flow.

Currently, this code is being expanded to a six control volume method for helical groove seals with grooves on both the rotor and the stator. Methods of modeling the interactions of the two sets of grooves are being explored.

ANSYS CFX modeling is being used to develop optimized helical groove seal designs for a variety of configurations and operating conditions. The goal of this project is threefold. First, the optimization can be used to explore the performance of helical groove seals. Second, the computational data can be used to calibrate helical groove seal codes currently being developed. Third, comparison of the results to that of the helical groove seal bulk flow codes will allow for error mapping to quantify the accuracy of the computational method throughout the design space.

Pressure Profile for Helical Seal from ANSYS CFX Simulation

 The initial phase of this project has been to optimize high pressure helical groove seals with grooves on the stator for use in an impeller stage. Additional work shows the comparison of the performance for helical groove seals with grooves on the rotor versus helical groove seals with grooves on the stator. The next phase of this project is to perform ANSYS CFX simulations to calculate rotordynamic coefficients and optimize for maximum effective damping. Finally, similar optimization studies will be performed for helical groove seals with grooves on both the rotor and the stator.

A number of ROMAC’s existing labyrinth seal codes are more than twenty years old and were therefore developed in a time where computational resources were much more limiting. This project seeks to expand the capabilities of current labyrinth seal codes to be three control volume methods, which will allow for improved analysis of labyrinth seals. Other improvements being considered are:

1. Allowing the inlet boundary condition used to be chosen between inlet velocity or inlet pressure depending on the application of the user.
2. Increasing the order of the perturbation method to allow for eccentricities greater than 10%.
3. Incorporating multistage seals such as smooth-labyrinth or brush-labyrinth seals.

Additionally, calibration and error analysis of the codes is planned so that quantification of the accuracy of the numerical methods are available in the user manuals.