S. Bashmal

Vibration analysis of drillstrings with string—borehole interaction

Abstract Drillstring vibration is one of the major causes for a deteriorated drilling performance, and if left untreated may result in a complete failure of the drilling process. Although the variations in the drilling load, stick-slip, and whirling are known to be the primary causes of severe vibrations, they often give rise to excessive flexural deformations and subsequent string—borehole interaction. Drillstring contact-impact interaction with borehole results in high-frequency excitations, which further deteriorate the drilling performance, and may cause damage to the bottomhole assembly. Modelling of impact is crucial to understanding the associated dynamic response, and to providing means for controlling the collision phenomenon. A continuous force—displacement law is introduced to model the impulsive force during the short-lived interval of impact, wherein the material compliance and damping coefficients are determined from energy balance relations. The impact model is integrated to the dynamic model of the whole drillstring; including drillpipes and drillcollars. The dynamic model of the rotating drillstring is formulated using a Lagrangean approach in conjunction with the finite-element method. The model accounts for the torsional-bending inertia coupling and the axial-bending geometric non-linear coupling. In addition, the model accounts for the gyroscopic effect and the effect of the gravitational force field. The generalized eigenvalue problem is solved to determine modal transformations, which are invoked to obtain the reduced-order modal form of the dynamic equations. The developed model is integrated into a computational scheme to calculate time-response of the drillstring system in the presence of string—borehole collisions.

Frequency Equations for the In-Plane Vibration of Circular Annular Disks

This paper deals with the in-plane vibration of circular annular disks under combinations of different boundary conditions at the inner and outer edges. The in-plane free vibration of an elastic and isotropic disk is studied on the basis of the two-dimensional linear plane stress theory of elasticity. The exact solution of the in-plane equation of equilibrium of annular disk is attainable, in terms of Bessel functions, for uniform boundary conditions. The frequency equations for different modes can be obtained from the general solutions by applying the appropriate boundary conditions at the inner and outer edges. The presented frequency equations provide the frequency parameters for the required number of modes for a wide range of radius ratios and Poissons ratios of annular disks under clamped, free, or flexible boundary conditions. Simplified forms of frequency equations are presented for solid disks and axisymmetric modes of annular disks. Frequency parameters are computed and compared with those available in literature. The frequency equations can be used as a reference to assess the accuracy of approximate methods.

Effects of radial aerodynamic forces on rotor-bearing dynamics of high-speed turbochargers

This study investigates the radial aerodynamic forces that may develop inside the centrifugal compressor and the turbine volutes due to pressure variation of the circulating gas. The forces are numerically predicted for magnitudes, directions, and locations. The radial aerodynamic forces are numerically simulated as static forces in the turbocharger finite element model with floating ring bearings and solved for nonlinear time-transient response. The numerical predictions of the radial aerodynamic forces are computed with correlation to earlier experimental results of the same turbocharger. The outcomes of the investigation demonstrate a significant influence of the radial aerodynamic loads on the turbocharger dynamic stability and the bearing reaction forces. The numerical predictions are also compared with experimental results for validation.

Effect of Flexible Damped Bearing-Supports on the Dynamic Stability of High-Speed Turbochargers

The aim of this study is to analytically design flexible damped bearing-supports in order to improve the dynamic characteristics of the rotor-bearing system. The finite-element model of the turbocharger rotor with linearized bearing dynamic coefficients is used to solve for the logarithmic decrements and hence the stability map. The design process attempts to find the optimum dynamic characteristics of the flexible damped bearing-support that would give best dynamic stability of the rotor-bearing system. The method is successful in greatly improving the dynamic stability of the turbocharger and may also lead to a total linear stability throughout the entire speed range when used besides the enhanced-performance hydrodynamic bearings.Copyright

Experimental Investigation on the Modal Characteristics of Rolling Thick Disk

Analytical and experimental investigations are carried out to study the combined effect of rotation and support non-uniformity on the modal characteristics of circular thick disks. A three-dimensional model is implemented to study the coupled in-plane and out-of-plane modes of a thick disk and present the variations of the travelling waves with respect to rotating and fixed coordinates. The initial stiffening due to rotation is introduced by developing a non-linear model that permits the coupling between static and dynamic problems. The present formulation is generalized to account for the stiffening effects for disks subject to non-uniform boundary conditions, where the initial displacement cannot be considered as axisymmetric. The general non-linear problem of a rotating annular disk subject to non-uniform boundary conditions is, then, investigated. The laboratory experiments on stationary and rotating circular disks under selected boundary conditions are carried out to demonstrate the validity of the analytical methods in terms of vibration and acoustic emission behaviour. The experimental results examine the combined effect of rotation and point support on the disk. The experimental study confirms the split in natural frequencies of the disk that was observed in the analytical results due to both rotation and support non-uniformity.Copyright

Analysis of In-Plane Modal Characteristics of an Annular Disk With Multiple Point Supports

In-plane free vibrations of an isotropic, elastic annular disk constrained at some points on the inner and outer boundaries are investigated. The presented study is relevant to various practical problems including disks clamped by bolts along the inner and outer edges or the railway wheel vibrations. The boundary characteristic orthogonal polynomials are employed in the Rayleigh-Ritz method to obtain the frequency parameters and the associated mode shapes. The boundary characteristic orthogonal polynomials are generated for the free boundary conditions of the disk while artificial springs are used to realize clamped conditions at discrete points. The frequency parameters for different point constraint conditions are evaluated and compared with those computed from a finite element model to demonstrate the validity of the proposed method. The computed mode shapes are presented for a disk with different point constraints at the inner and outer boundaries to demonstrate the free in-plane vibration behavior of the disk. Results show that addition of point supports causes some of the modes to split into two different frequencies with different mode shapes. The effects of different orientations of multiple point supports on the frequency parameters and mode shapes are also discussed.© 2009 ASME

Coupled Torsional Vibrations in Drilling Systems

The contact between the drilling bit and formation is known to excite severe torsional and axial vibrations in the drillstring. A dynamic model of the drillstring including both drillpipe and drillcollars is formulated. The equation of motion of the rotating drillstring is derived using Lagrangean approach together with the finite element method. The model accounts for the gyroscopic effect, the torsional/bending inertia coupling, the axial/bending geometric nonlinear coupling, and the stiffening effect due to the gravitational force field. Reduced order modal form of the dynamic equations is obtained using complex modal transformation. The developed model is integrated into a computational scheme to calculate time-response of the drillstring due to torsional excitations.Copyright

Modeling of Stick-Slip in Multibody Drilling Systems

Drillstring vibration is one of the major causes for a deteriorated drilling performance. Field experience revealed that it is crucial to understand the complex vibrational mechanisms experienced by a drilling system in order to better control its functional operation and improve its performance. Stick-slip oscillations due to contact between the drilling bit and formation is known to excite severe torsional and axial vibrations in the drillstring. A multibody dynamic model of the drilling system including the drillpipes, drillcollars, and the rotary drive is formulated. The equation of motion of the rotating drillstring is derived using Lagrangean approach in conjunction with the finite element method. The model accounts for the gyroscopic effect, the inertia coupling, the effect of the gravitational force field, and the stick-slip interaction forces. Explicit expressions of the finite element inertia coupling and axial stiffening matrices are derived using a consistent mass formulation. Modal transformations are invoked to obtain a reduced order modal form of the dynamic equations. The developed model is integrated into a computational scheme to calculate time-response of the drillstring system in the presence of stick-slip excitations.Copyright