Self-excited Torsional Vibrations Research Articles

Design and Investigation of a Nonlinear Damper Based on Energy Dissipation through Shock and Dry Friction to Suppress Critical Self-Excited Vibrations in Drilling Systems

In this paper, a passive damper based on energy dissipation through shock and dry friction (shock-friction damper) is investigated regarding its design and effectiveness for damping self-excited torsional vibrations similar to those occurring in deep drilling. The results are compared to the results of conventional friction dampers. The effectiveness of the damper for different operational drilling parameters that change during the drilling process, such as the weight on the bit and the rotary speed of the bit, is analyzed. Two linear reduced order models of a drill string that are based on a complex finite element model are set up. One is reduced using the component mode synthesis and one is reduced to the identified critical mode. A lumped mass represents the inertia of a forcedly connected nonlinear damper. A combined reduced order model of the complex system and the inertia damper is introduced to investigate its dynamic motion and stability. Particular focus is on the energy flow within the dynamic system and on the change of the dissipation energy in the contact. A semi-analytical solution is derived using the harmonic balance method that is used to investigate the damping effect for various designs and operational parameters. Herein, the modal properties as well as parameters of the damper are examined regarding the damping effect and the stability of the system. Finally, the capability of the mechanism to suppress the self-excitation due to the bit–rock interaction in a drilling system is discussed, and recommendations are made with respect to the design parameters and placement of the damper.

Energy transfer through parametric excitation to reduce self-excited drill string vibrations

Drilling a wellbore can result in several types of vibration that lead to inefficient drilling and premature failure of drill string components. These vibrations are subdivided based on their operating direction into lateral, torsional, and axial vibrations. Especially in hard and dense formations, high-frequency torsional oscillations are found in the bottom-hole assembly (BHA). These critical vibrations are induced by a self-excitation mechanism caused by the bit–rock interaction. Self-excitation mechanisms are regenerative effects, mode coupling, or a velocity-dependent torque characteristic at the drill bit. To increase drilling performance and reduce tool failure due to high-frequency torsional oscillations, the critical vibration amplitudes localized at the bottom-hole assembly need to be minimized. Increasing the damping of self-excited systems to affect the energy output during vibration is a common approach to mitigate self-excited vibrations. In drilling systems, the achievable damping is naturally limited by the small installation space due to the drilled borehole diameter. Therefore, alternative methods to influence vibrations are necessary. Applying parametric excitation in self-excited systems can result in a parametric anti-resonance and therefore in an energy transfer within different modes of the structure. This allows, among other benefits, improved utilization of the structural damping. In this article, the influence of additional stiffness–based parametric excitation on self-excited torsional vibration in downhole drilling systems is investigated. For this purpose, a finite element model of a drill string is reduced using the component mode synthesis and analyzed with the goal to mitigate torsional vibrations. The multiple degree of freedom drill string model is investigated regarding the additional energy transfer due to the parametric excitation. Robustness of various parameters, especially with regard to the positioning within the bottom-hole assembly, is analyzed and discussed. Additionally, the problem of multiple unstable self-excited modes due to the nonlinear velocity-dependent torque characteristic in drilling systems is addressed.

A Method for the Design and Optimization of Nonlinear Tuned Damping Concepts to Mitigate Self-Excited Drill String Vibrations Using Multiple Scales Lindstedt-Poincaré

In downhole drilling systems, self-excited torsional vibrations caused by the bit-rock interactions can affect the drilling process and lead to the premature failure of components. Especially self-excited oscillations of higher-order modes lead to critical dynamic loads. The slim drill string design and the naturally limited drilled borehole diameter limit the installation space, power supply and lead to numerous potentially critical self-excited torsional modes. Consequently, small and robust passive damping concepts are required. The variety of possible downhole boundary conditions and potential damper designs necessitates analytical solutions for effective damper design and optimization. In this paper, two nonlinear passive damper concepts are investigated regarding design and effectiveness to reduce self-excited high-frequency torsional oscillations in drill string dynamics. Based on a finite element model of a drill string, a suitable minimal model based on the identified critical mode is generated and solved analytically using the Multiple Scales Lindstedt-Poincaré (MSLP) method. The advantages of MSLP compared to conventional MS methods are shown for this example. On the basis of the analytical solution, parameter influences are determined, and design equations are derived. The analytical results are transferred to self-excited drill string vibrations and discussed using time domain simulations of the drill string model.

Nonlinear integrated dynamic analysis of drill strings under stick-slip vibration

Stick-slip torsional vibration raising from bit-formation contact is a catastrophic dynamic phenomenon occurring in deep-water oil and gas drilling systems. The torsional vibrations can result in premature fatigue failure of drilling equipment and reduce drilling efficiency. Thus, studying the dynamics of the system is a vital key to identify the roots of the vibration and establish appropriate mitigation and remediation methods. In this paper, an efficient approach for finite element (FE) modeling of stick-slip vibrations of the full drill strings was proposed. The model was developed based on a rate-dependent formulation of bit-rock interaction, in which the cutting process was integrated through the frictional contact. The nonlinear effects of the large rotations and the geometrically nonlinear axial-torsional coupling were taken into account. The effect of energy dissipation due to the presence of drill mud along the drill pipes and drill collars was incorporated through Rayleigh viscous damping. Modal analysis was conducted to determine the natural frequencies and the mode shapes of the drill string. Furthermore, a five degree-of-freedom lumped parameter model was developed. The performance of the developed models was verified through comparisons with example stick-slip results from a field test. The study showed that the self-excited torsional vibrations may also occur at fundamental frequencies lower than the first natural torsional frequency of the drill string, depending on operational parameters. The conducted research work resulted in a robust and practical integrated FE model to simulate the entire drill string system dynamics under torsional vibrations.

Self-Excited Torsional Vibration in the Flexible Coupling of a Marine Propulsion Shafting System Employing Cardan Shafts

The reliability of propulsion shafting systems is a major concern for ocean-going vessels because mid-ocean repairs can be time-consuming and spare parts must be available. To address this concern, vibration modeling and experimental measurements were conducted on a propulsion shafting system with a Z-drive propeller, with the objective of identifying the source of failure for the flexible rubber coupling connecting the diesel engine with the intermediate shaft. The torsional fluctuations in the flexible coupling dramatically increased and then abruptly ceased. The modeling results revealed that the frictional losses during power transmission through the universal joints could act as an excitation force for self-excited vibration. The coupling connected to the intermediate shaft did not have sufficient radial flexibility to dampen these vibrations. To avoid the effects of the self-excited torsional vibration, it is recommended that this coupling is replaced with one that is capable of absorbing the radial shaft displacement.

Isolator Tool for High-Frequency Torsional Oscillation Proves Effective

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 193313, “Simulation and Testing of an Isolator Tool for High-Frequency Torsional Oscillation,” by Dennis Heinisch, SPE, Baker Hughes, a GE Company; Vincent Kulke, Braunschweig Technical University; Volker Peters, Andreas Hohl, Cord Schepelmann, and Hanno Reckmann, Baker Hughes, a GE Company; and Georg-Peter Ostermeyer, SPE, Braunschweig Technical University, prepared for the 2018 Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, 12–15 November. The paper has not been peer reviewed. During downhole drilling, severe vibration loads can occur that affect the reliability and durability of tools in bottomhole assemblies (BHAs). Such high-frequency torsional oscillation (HFTO) can cause•premature damage to tools or their subcomponents. This paper presents dynamic simulations, prototype testing, and field-test results of a BHA component that isolates the upper part of the BHA from HFTO. The isolator tool reduced torsional vibrations and improved tool reliability, lifetime, and service delivery, especially while drilling in formations that are liable to excite HFTO. Introduction HFTO is a self-excited torsional vibration of the drillstring caused by the interaction of the drill bit and the rock. The latest downhole measurement devices can measure and record torsional accelerations at frequencies greater than 100 Hz and enable observation of HFTO in the field. Consequently, this phenomenon has been well-described and analyzed. In contrast to stick/slip, which occurs at the first torsional eigenfrequency of the drillstring, HFTO occurs at a higher natural torsional frequency, typically between 50 and 500 Hz. In most cases, the mode exhibiting the highest excitability is the stick/slip mode. However, the mode with the second-highest excitability has a frequency that is typically between 50–500 Hz with modal amplitudes concentrated at the BHA. Whereas the frequency of the stick/slip mode varies with the length of the overall drillstring, the BHA-concentrated HFTO modes remain constant in frequency and amplitude, independent of drillstring length. An HFTO mode and the stick/slip mode can occur simultaneously. Isolation of HFTO Previous laboratory tests have shown that the critical HFTO mode shapes of a BHA predicted by finite-element simulation can be reproduced accurately by torsional harmonic excitation using an electrodynamic shaker. The concept of isolation is based on restricting potential damaging HFTO vibrations to a part of the BHA that is by design strong enough to survive HFTO. On the basis of modeling research and experimental analysis of HFTO, a tool for isolating HFTO has been developed. This new isolator tool is part of the BHA and isolates HFTO from the lower to the upper part of the BHA. By the design of the isolator tool, the torsional dynamics of the BHA are modified so that critical HFTO mode shapes only have significant amplitudes in the section below the isolator tool, where the BHA is designed to cope with HFTO. Above the tool, the amplitudes are comparatively low. This effect significantly improves the performance and reliability of measurement-while-drilling (MWD) and logging-while-drilling (LWD) tools and reduces damages and consequent failures caused by HFTO. In addition, the effect opens design freedom for BHA components no longer subjected to these•vibrations.

Dynamics of rolling mill drive system considering arc tooth gear dynamic characteristics

The arc tooth gear spindle (ATGS) is the key structure of the drive system of hot finishing rolling mills. To investigate the dynamic characteristics of ATGS of the drive system of hot finishing rolling mills, a dynamic mechanical model of ATGS was established. The influences of dynamic displacement and dynamic torque on dynamic load (meshing force, additional torque and friction torque) were studied during the non-steady-state operation of ATGS. On this basis, a dynamic model of rolling mill drive system was established considering the arc tooth gear dynamic characteristics. The dynamic response of the drive system was simulated and analyzed. The results showed that the nonlinear characteristics of ATGS were obvious; the meshing force (PX and PZ) could restrain the increase in dynamic displacement, which reflected the positive stiffness of ATGS; there was a coupling among the vertical, horizontal and torsional directions in the drive system model considering the dynamic characteristics of the arc tooth gear; the vibration intensity of ATGS in the horizontal direction is greater than that in the vertical direction when the self-excited torsional vibration happens; the greater the axial inclination angle was, the more complex the vibration mode was, and the lower the stability of the drive system was.

An analysis of the self-excited torsional vibration of high-speed train drive system

In this paper, a simplified torsional vibration model of drive system with three degrees of freedom is established, and the elasticity of wheelset is considered. In addition to the same wheel-rail adhesion condition for the two wheels, the different wheel-rail adhesion conditions for the two wheels have been considered for the first time, and the mechanism of the vibration forms is explained from the viewpoint of energy. The nonlinear system is linearized at the origin (equilibrium position), and the critical stability curve of the linearized system is drawn according to the eigenvalues of the linearized system in the state space. The results show that the vibration forms of the system are mainly determined by the relationships between the average creep rate and the critical creep rate of the wheel driven directly by motors. When the resistance moments do positive work on the system, they input energy to the system, and the responses do not tend to the origin and produce self-excited vibration. When the resistance moments do negative work on the system, they dissipate energy to system, and the responses tend to the origin. For the linearized system at the origin, the system is more stable at the origin when following factors occur, a gentler negative slope of the adhesion curve, a faster speed, a lighter wheel load, and a larger the moment of inertia of wheels.

A Novel Backstepping Approach for the Attenuation of Torsional Oscillations in Drill Strings

A common problem in the petroleum drilling process is the torsional oscillation generated by the friction present during the cutting process. Torsional oscillations in drill string are particularly difficult to control because the drill string is an underactuated system, it has a very small diameter to length ratio and it is driven at top end with the cutting process at the other end. These factors make the drill string prone to self-excited torsional vibrations caused by the stick-slip of the cutting bit. The system is modeled as a torsional pendulum with two degrees of freedom, where the upper inertia models the top drive and also part of the drilling pipes. The bottom inertia models the bottom hole assembly (BHA). The drill is considered to be a massless torsional spring-damper. The drill string is subjected to friction, which is formulated using a dry friction model. The friction model takes into account Coulomb friction, stiction and Stribeck effect. The latter friction component is the main nonlinear phenomenon that introduces negative damping at the bit; it leads to self-enforcing stick-slip torsional oscillations.In the approach of this work, for the attenuation of these self-excited oscillations a recursive backstepping control strategy is used and it is carried out in continuous time. The main contribution of this work, which is different from the backstepping approaches reported in the literature, is to use a nonlinear/artificial damping as virtual control input. The stability of the system has been proven in the sense of Lyapunov. The goal of the proposed algorithm is to deal the underactuation of the system and to provide a good response for different operating points. The effectiveness and robustness of the controller has been tested in simulations.

Large-scale and small-scale self-excited torsional vibrations of homogeneous and sectional drill strings

To simulate the self excited torsional vibrations of rotating drill strings (DSs) in vertical bore-holes, the nonlinear wave models of homogeneous and sectional torsional pendulums are formulated. The stated problem is shown to be of singularly perturbed type because the coefficient appearing before the second derivative of the constitutive nonlinear differential equation is small. The diapasons ωb ≤ ω ≤ωl of angular velocity ω of the DS rotation are found, where the torsional auto-oscillations (of limit cycles) of the DS bit are generated. The variation of the limit cycle states, i.e. birth (ω = ωb), evolution (ωb < ω < ωl) and loss (ω = ωl), with the increase in angular velocity ω is analyzed. It is observed that firstly, at birth state of bifurcation of the limit cycle, the auto-oscillation generated proceeds in the regime of fast and slow motions (multiscale motion) with very small amplitude and it has a relaxation mode with nearly discontinuous angular velocities of elastic twisting. The vibration amplitude increases as ω increases, and then it decreases as ω approaches ωl. Sectional drill strings are also considered, and the conditions of the solution at the point of the upper and lower section joints are deduced. Besides, the peculiarities of the auto-oscillations of the sectional DSs are discussed.

207204 一様流中に置かれた平板翼列に発生する自励振動(一般02 機械力学・制御工学9)

When wind flows through slats of a blind at the window, sometimes self-excited torsional vibration occurs with a large noise. This report investigates effects of some parameters on the vibration by using an experimental apparatus consisting of two acrylic plates hung by metal wires. Each plate has two degrees of freedom corresponding to translational and torsional motions. Experimental results show that torsional motion is predominantly observed when self-excited vibration occurs, and that bigger vibration is induced when the two plates are located closer to each other. In addition, we show that vortices leave from the plates by visualizing flow.

Mechanism of self-excited torsional vibration of locomotive driving system

A single wheelset drive model and 2-DOFs torsional vibration model were established to investigate the self-excited torsional vibration of a locomotive driving system. The simulation results indicate that the self-excited torsional vibration occurs when the steady slip velocity is located at the descending slope of the adhesion coefficient curve. The principle of energy conservation was used to analyze the mechanism of the self-excited vibration. The factors affecting on the amplitude of the self-excited vibration are studied.

Analysis of Longitudinal Vibration of Wheel Set during Locomotive Slippage

Roll-slip oscillation in locomotive is an unstable vehicle motion and it turns into strong self-excited torsional vibration of drives and is usually associated with a negative slop of adhesion curve. The periodic variation of adhesion coefficient between wheel and rail arises and it provokes longitudinal vibration of wheel set. A simplified mathematical model of single wheel-set drive system of locomotive whose rotary and longitudinal freedoms are taken into account is established. The phase trajectory of longitudinal vibration of wheel-set is drawn by numerical simulation and frequencies of vibrations are calculated on the condition that the mean creep ratio exceeds critical creep ratio. The formed mechanics of longitudinal vibration makes clear with help of graphical analysis. Results demonstrate that the longitudinal vibration is self-excited vibration during locomotive slippage. The longitudinal vibration frequency is integral multiple of nature frequency of torsion vibration and the amplitude of longitudinal vibration is the biggest when it is two times. Therefore, parameters such as longitudinal locating stiffness of wheel set should be set rationally to avoid strong longitudinal vibration of wheel set during slippage.

Active damping of self-excited torsional vibrations in oil well drillstrings

A drillstring used for the drilling of oil or gas wells behaves as a rotating torsional pendulum. The drillstring is rotated at a constant angular velocity by an electric motor, but exhibits superimposed torsional vibrations caused by a non-linear relationship between torque and angular velocity at the rock-crushing tool. The vibrations are self-excited, and disappear when the mean angular velocity of the pendulum is raised above a threshold value. An active damping system is described that strongly reduces the threshold value by using feedback control, thus extending the working range for vibration-free rotation. It operates at the current and the voltage of the electric motor, and can be implemented with only electrical components. The active damping system is interpreted as an extension of the passive tuned vibration absorber for quenching of self-excited vibrations in the form of a resilient foundation, as described by Tondl (1975 Journal of Sound and Vibration 42(2), 251–260). The concept of quenching self-excited vibrations by modifying the drive system as described in this paper is directly applicable to other engineering systems which are driven by a separately excited DC motor. Furthermore, the concept can be applied to systems driven by a hydraulic motor with a continuously variable flow rate.

Closure to “Discussions of ‘Investigation of Self-Excited Torsional Oscillations and Vibration Damper for Induction-Motor Drives’” (1943, ASME J. Appl. Mech., 10, p. A176)

Closure to “Discussions of ‘Investigation of Self-Excited Torsional Oscillations and Vibration Damper for Induction-Motor Drives’” (1943, ASME J. Appl. Mech., 10, p. A176)

Investigation of Self-Excited Torsional Oscillations and Vibration Damper for Induction-Motor Drives

Abstract An unusual case of torsional oscillation was observed recently on several large induction-motor drives used for tunnel ventilation on the Pennsylvania Turnpike. These drives, which consist essentially of an induction motor driving a heavy centrifugal fan through a speed reducer, showed a severe torsional oscillation (with a double amplitude around 80 deg) at a point between two thirds and full speed during the accelerating period. These vibrations were found to be self-excited, as a consequence of the negative damping inherent in the shape of the speedtorque curve of the normal induction motor. After consideration of various methods for eliminating the trouble, a torsional-vibration damper of relatively simple design was developed. Torsiograph records made on the actual drive showed that the oscillation was reduced to negligible values by the use of this damper. Since induction-motor drives of this general type are used rather widely, it was felt that an account of this investigation, including the methods of calculating damper capacity, the laboratory tests on the damper, and the field tests on the actual drives would be of value to engineers, particularly those interested in vibration.