Publications

Drillstring–borehole interaction can produce severely damaging vibrations. An example is stick–slip vibration, which negatively affects drilling performance, tool integrity and completion time, and costs. Attempts to mitigate stick–slip vibration typically use passive means and/or change the operation parameters, such as weight on bit and rotational speed. Automating the latter approach, by means of feedback control, holds the promise of quicker and more effective mitigation. The present work presents three separate fractional-order controllers for mitigating drillstring slip–stick vibrations. For the sake of illustration, the drillstring is represented by a torsional vibration lumped parameter model with four degrees of freedom, including parameter uncertainty. The robustness of these fractional-order controllers is compared with traditional proportional-integral-derivative controllers under variation of the weight on bit and the drill bit’s desired rotary speed. The results confirm the proposed controllers effectiveness and feasibility, with rapid time response and less overshoot than conventional proportional-integral-derivative controllers.

 

Fractional Order Controllers for Stick-slip Vibration Mitigation in Oil Well Drill-strings

Nonlinear elements found in fluid film journal bearings and their surrounding structures are known to induce sub- and super-synchronous, chaos and thermally induced instability responses in rotor-bearing systems. The current review summarizes the literature on journal bearing induced nonlinear, rotordynamic forces, and responses. Nonlinear, thermo-elasto-hydrodynamic (TEHD) aspects of journal bearings has become increasingly important in high-performance turbomachines. These have significant influence on bearing dynamic performance and thermally induced, rotordynamic instability problems. Techniques for developing TEHD bearing models are discussed in the second section. Nonlinear solution methodology, including bifurcation determination and time and frequency domain methods such as harmonic balance, shooting and continuation, etc., is presented in the third section. Numerical tools to determine nonlinear vibration responses, including chaos, along with examples of bearing induced nonlinear vibrations are presented in the fourth and fifth sections, respectively.

 

A Review of Journal Bearing Induced Nonlinear Rotordynamic Vibrations

This paper presents a novel controller for drill string systems based on a super-twisting sliding mode theory. The aim is to eliminate the stick-slip vibration and maintain a constant drill string velocity at the desired reference value. The proposed controller inherently attenuates the torsional vibration while ensuring the stability and high efficiency of the drill string. A discontinuous lumped-parameter torsional model of vertical drill strings based on four components (rotary table, drill pipes, drill collars, and drill bit) is considered. The Karnopp friction model is adopted to simulate the nonlinear bit-rock interaction phenomena. In order to provide a more accurate evaluation, the proposed drill string controller is implemented with the induction motor, a variable frequency drive, and a gearbox to closely mirror the real environment of oil well drill strings. The increasing demand for prototyping and testing high-power plants in realistic and safe environments has led to the advancement of new types of experimental investigations without hurting the real system or building a small-scale prototype for testing. The dynamic performance of the proposed controller has been investigated with matlab software and in a novel hardware-in-the-loop (HIL) testing platform. A power plant is modeled and implemented in the real-time simulator OPAL-RT 5600, whereas the controllers are implemented in the dSPACE 1103 control board. The results obtained through simulatiosn and HIL testing demonstrate the feasibility and high performance of the proposed controller.

 

Design and Hardware in-the-Loop Validation of an Effective Super-Twisting Controller for Stick-Slip Suppression in Drill-String Systems

The Morton effect (ME) is a thermally induced vibration problem observed in a rotor supported by hydrodynamic bearings. The journal’s synchronous orbiting induces nonuniform viscous heating on its circumference, and the ensuing thermal bow often causes unacceptable vibration levels in the rotor. This paper investigates the influence of the tilting pad journal bearing (TPJB)’s pivot design on the severity and instability speed range of ME vibration. Simulations are conducted with two different types of pivots: cylindrical (CYL) and spherical (SPH), which produce different pad degrees-of-freedom and nonlinear pivot stiffness due to their geometries. The friction between pad and pivot, which only exists with the spherical pivot, is modeled, and its impact on the ME is evaluated. The example rotor model, as obtained from the literature, is single overhung, with experimentally measured excessive vibration and large journal temperature differentials, near 8000 rpm. The bearing and journal are modeled with three-dimensional (3D) finite elements, and the shaft with flexible beam elements for ME simulation. Nonlinear transient simulations are carried out for a wide operating speed range with varying pivot design parameters. Simulation results indicate that the predicted ME instability is sensitive to the pivot shape, pivot flexibility, and pad-pivot friction.

Tilting Pad Bearing Pivot Friction and Design Effects on Thermal Bow-Induced Rotor Vibration

This study presents an advanced theoretical modeling methodology and simulation procedure to evaluate the performance of granular lubrication. The computational approach utilizes the Euler-Eulerian multiphase flow model based on the solid kinetic theory in a 3D Computational Fluid Dynamics (CFD) framework. The predictions of the CFD model are verified by available experimental data, and a parametric study is presented to assess the influence of critical input parameters. The parametric study provides valuable information for a suitable and efficient granular lubricating system design.

 

CFD Investigation of Oil Free Granular Lubrication

Couplings connect the spinning shafts of driving and driven machines in the industry. A coupling guard encloses the coupling to protect personnel from the high-speed rotating coupling. The American Petroleum Institute API publishes standards that restrict the overheating of the coupling guards due to windage caused by the spinning shaft. Based on the most recent version of API 671, the peak temperature for the coupling guard should not exceed 60 °C. This paper proposes a machine learning (ML) model and an empirical formula to predict the maximum guard temperature and power loss. The ML models use a database obtained from simulated computational fluid dynamics (CFD) cases for different coupling guards under various conditions. Also, the paper provides validation for the CFD models with experimental tests for different cases. The proposed ML model uses eight different input parameters to predict temperature and power loss. The model shows an accurate prediction for a varied number of CFD cases. The performance of the generated model has been verified with the experimental results. Also, an empirical formula has been created using the same database from CFD results. The results show that the ML model has better prediction accuracy than the empirical formula for predicting peak temperature and power loss for all cases.

The Morton effect (ME) is a synchronous vibration problem in turbomachinery caused by the nonuniform viscous heating around the journal circumference, and its resultant thermal bow (TB) and ensuing synchronous vibration. This paper treats the unconventional application of the SFD for the mitigation of ME-induced vibration. Installing a properly designed squeeze film damper (SFD) may change the rotor’s critical speed location, damping, and deflection shape, and thereby suppress the vibration caused by the ME. The effectiveness of the SFD on suppressing the ME is tested via linear and nonlinear simulation studies employing a three-dimensional (3D) thermohydrodynamic (THD) tilting pad journal bearing (TJPB), and a flexible, Euler beam rotor model. The example rotor model is for a compressor that experimentally exhibited an unacceptable vibration level along with significant journal differential heating near 8000 rpm. The SFD model includes fluid inertia and is installed on the nondrive end bearing location where the asymmetric viscous heating of the journal is highest. The influence of SFD cage stiffness is evaluated.

 

Squeeze Film Damper Suppression of Thermal Bow Morton Effect

Although rotors are simplified to be axisymmetric in rotordynamic models, many rotors in the industry are actually non-axisymmetric. Several authors have proposed methods using 3D finite element, rotordynamic models, but more efficient approaches for handling a large number of degrees-of-freedom (DOF) are needed. This task becomes particularly acute when considering parametric excitation that results from asymmetry in the rotating frame. This paper presents an efficient rotordynamic stability approach for non-axisymmetric rotor-bearing systems with complex shapes using three-dimensional solid finite elements. The 10-node quadratic tetrahedron element is used for the finite element formulation of the rotor. A rotor-bearing system, matrix differential equation is derived in the rotor-fixed coordinate system. The system matrices are reduced by using Guyan reduction. The current study utilizes the Floquet theory to determine the stability of solutions for parametrically excited rotor-bearing systems. Computational efficiency is improved by discretization and parallelization, taking advantage of the discretized monodromy matrix of Hsu’s method. The method is verified by an analytical model with the Routh–Hurwitz stability criteria, and by direct time-transient, numerical integration for large order models. The proposed and Hill’s methods are compared with respect to accuracy and computational efficiency, and the results indicate the limitations of Hill’s method when applied to 3D solid rotor-bearing systems. A parametric investigation is performed for an asymmetric Root’s blower type shaft, varying bearing asymmetry and bearing damping.

 

Stability of Non-Axisymmetric Rotor and Bearing Systems Modeled with 3D-Solid Finite Elements

This paper presents a novel approach for modeling and analyzing a geared rotor-bearing system including nonlinear forces in the gear set and the supporting fluid film journal bearings. The rotordynamics system model has five degrees of freedom that define the transverse displacements of the shaft-gear centerlines and the relative displacement of the gear tooth contact point. The journal bearing nonlinear forces are obtained via a solution of Reynolds equation for lubricant film pressure utilizing the finite element method. Co-existing, steady-state, autonomous and non-autonomous responses are obtained in an accurate and computationally efficient manner utilizing the multiple shooting and continuation algorithms. This yields the full manifolds of the multiple bifurcation system. Chaos is identified with maximum Lyapunov exponents, frequency spectra, Poincaré attractors, etc. The results reveal a dependence of the gear set contact conditions and system nonlinear response characteristics, i.e. jump, co-existing responses, subharmonic resonances and chaos on the choice of journal bearing parameters. The results also show that Hopf bifurcations, which occur along with oil whirl in a journal bearing system, can be attenuated by increasing the gear torque.

Nonlinear Analysis of a Geared Rotor System Supported by Fluid Film Journal Bearings

 

1/2X forward whirl repeatedly occurred after a test rotor spinning at 5,800 rpm was dropped onto ball bearing type auxiliary bearings AB, utilized as a backup for magnetic bearings. The measured contact forces that occurred between the rotor and the auxiliary bearing during the ½X subsynchronous vibration were about thirteen times larger than the static reaction force. The vibration frequency coincided with the rotor-support system natural frequency with the rotor at rest on the auxiliary bearing AB, an occurred at ½ of the rotor spin speed when dropped. The test rig provided measurements of rotor-bearing contact force, rotor orbit (vibrations), and rotational speed during rotor drop events. A simulation model was also developed and demonstrated that parametric excitation in the form of a Mathieu Hill model replicated the measured 1/2X forward whirl vibrations. The simulation model included a nonlinear, elastic-thermal coupled, ball bearing type auxiliary bearing model. The transient model successfully predicted the 1/2X vibration when the rotor was passing 5800RPM as well, and the simulation results quantitatively agreed well with the test results in the frequency domain. Several approaches for mitigating the 1/2X forward whirl were presented such as adding an elastomer O-ring or waviness spring in the AB support system. Measurements confirmed that adding AB dampers effectively mitigated the ½ subsynchronous forward whirl and significantly reduced the contact forces.

 

Simulation, Test, and Mitigation of 1_2x Forward Whirl Following Rotor Drop onto Auxiliary Bearings