Dynamic Stability of Lateral Vibration of Bottom Hole Assemblies

2008 ◽  
Vol 385-387 ◽  
pp. 809-812 ◽  
Author(s):  
Guang Hui Zhao ◽  
Zheng Liang
Keyword(s):  
Parametric Resonance ◽  
Separation Of Variables ◽  
Mathieu Equation ◽  
Parameter Method ◽  
Lateral Vibration ◽  
Oil Drilling ◽  
Bottom Hole ◽  
Parametric Resonances ◽  
Air Drilling ◽  
Weight On Bit

Bottom hole assemblies (BHA) of oil drilling engineering were simplified as simply supported beam, and parametric resonances of BHA in mud drilling and air drilling were studied. Lateral vibration of BHA, which was induced by bit/formation interaction, was described and reduced into Mathieu equation by means of separation of variables and Galerkin method. Modified strained parameter method was adopted in stability analysis. The parametric resonance zones expressed by weight on bit (WOB) are presented here. It is found that drilling method, speed of rotation (SOR), material properties, and length of compression drillstring all can influence parametric resonance zones. So unstable responses can be avoided by adjusting these parameters.

Lateral vibration analysis of pre-bent pendulum bottom hole assembly used in air drilling

2018 ◽  
Vol 24 (22) ◽  
pp. 5213-5224
Author(s):  
He Zhang ◽  
Qinfeng Di ◽  
Wenchang Wang ◽  
Feng Chen ◽  
Wei Chen
Keyword(s):  
Finite Element ◽  
Dynamic Performance ◽  
Drilling Process ◽  
Lateral Vibration ◽  
Tangent Point ◽  
Critical Speeds ◽  
Weighted Residuals ◽  
Bottom Hole ◽  
Air Drilling ◽  
Bottom Hole Assembly

In the air drilling process, the pre-bent pendulum bottom hole assembly (PBP-BHA) has excellent performance in controlling the well deviation and improving the wellbore quality, but the mechanism that is closely related to the dynamics of the PBP-BHA has not been ascertained. In this paper, an effective technique combining the weighted residuals method with the finite element method is presented to study the PBP-BHA lateral vibration. First, a three-dimensional nonlinear static model of pre-bent BHA is established under small deformation condition and solved by the weighted residuals method and optimization method, so as to define the tangent point according to the deformation characteristics of the PBP-BHA. This tangent point determines the end of the effective PBP-BHA length that starts from the drill bit. Subsequently, the finite element model of PBP-BHA is established to solve the lateral natural frequencies and mode shapes of the PBP-BHA. After considering the borehole wall constraint, the modal superposition technique is used to obtain the steady dynamic responses of the PBP-BHA. Meanwhile, the dynamic performance of the PBP-BHA used in the actual air drilling process is calculated to obtain its critical speeds and working status chart. The critical speeds of the PBP-BHA are 80 r/min and 190 r/min, which are far away from the surface rotary speed in the actual drilling site. Through comparing with the dynamic characteristics of regular BHA with the same structural parameters, it is discovered that the bend angle in the PBP-BHA plays a crucial role in improving the dynamic performance of the PBP-BHA. Moreover, the technique presented in this study can be used to make a reasonable design of BHA configuration and optimize drilling parameters.

Analysis of Parametric Resonances in In-Plane Vibrations of Electrostrictive Hyperelastic Plates

2018 ◽  
Vol 13 (9) ◽  
Author(s):  
Astitva Tripathi ◽  
Anil K. Bajaj
Keyword(s):  
Electric Field ◽  
Parametric Resonance ◽  
Mechanical Response ◽  
Element Model ◽  
Mode Shapes ◽  
Principal Parametric Resonance ◽  
Parametric Resonances ◽  
Second Mode ◽  
Electrostrictive Polymer ◽  
Large Amplitude Vibrations

Electrostriction is a recent actuation mechanism which is being explored for a variety of new micro- and millimeter scale devices along with macroscale applications such as artificial muscles. The general characteristics of these materials and the nature of actuation lend itself to possible production of very rich nonlinear dynamic behavior. In this work, principal parametric resonance of the second mode in in-plane vibrations of appropriately designed electrostrictive plates is investigated. The plates are made of an electrostrictive polymer whose mechanical response can be approximated by Mooney Rivlin model, and the induced strain is assumed to have quadratic dependence on the applied electric field. A finite element model (FEM) formulation is used to develop mode shapes of the linearized structure whose lowest two natural frequencies are designed to be close to be in 1:2 ratio. Using these two structural modes and the complete Lagrangian, a nonlinear two-mode model of the electrostrictive plate structure is developed. Application of a harmonic electric field results in in-plane parametric oscillations. The nonlinear response of the structure is studied using averaging on the two-mode model. The structure exhibits 1:2 internal resonance and large amplitude vibrations through the route of parametric excitation. The principal parametric resonance of the second mode is investigated in detail, and the time response of the averaged system is also computed at few frequencies to demonstrate stability of branches. Some results for the case of principal parametric resonance of the first mode are also presented.

Nonlinear Parametric Resonances in a Stay of the Iroise Cable-Stayed Bridge: Analytical Model and Experiments

2007 ◽  
Author(s):  
Olivier Boujard ◽  
Ste´phane Pernot ◽  
Alain Berlioz ◽  
Claude Lamarque
Keyword(s):  
Spectral Analysis ◽  
Analytical Model ◽  
Parametric Resonance ◽  
Resonance Mechanism ◽  
The Third ◽  
Cable Stayed Bridge ◽  
Parametric Resonances ◽  
Traffic Environment ◽  
Cable Stays ◽  
Bending Modes

Recent experimental campaigns led on the Iroise cable stayed bridge near Brest, France, revealed repeated vibratory events in some cable stays likely to provoke durability problems. A spectral analysis emphasized two regimes in which either the fundamental or the third cable mode were excited. Yet, wavelet scalograms of tests allowed to exhibit a global pylon mode excited by traffic environment through deck-cable-tower interaction and which again excites local cable modes by means of a nonlinear parametric resonance mechanism with vertical bending modes of the girder. Preliminary results are introduced as an attempt to explain such a scenario.

Implementation of a Bottom-Hole Assembly Program

2007 ◽  
Author(s):  
Kenneth Bhalla ◽  
Lixin Gong ◽  
George McKown
Keyword(s):  
Computationally Efficient ◽  
Efficient Tool ◽  
Shock Absorbers ◽  
Bottom Hole ◽  
Size Number ◽  
Weight On Bit ◽  
Bottom Hole Assembly ◽  
Parametric Studies ◽  
Dip Angle ◽  
Drill Collar

A state of the art windows graphical user interface (GUI) program has been developed to predict and design the bottom-hole assembly (BHA) performance for drilling. The techniques and algorithms developed in the program are based upon those developed by Lubinski and Williamson. The BHA program facilitates in conducting parametric studies, and in making field decisions for optimal performance. The input parameters may include: formation class, dip angle, hole size, drill collar size, number of stabilizers, stabilizer spacing. The program takes into consideration bit-formation characteristics and interaction, drill collar sizes, square collars, shock absorbers, MWD tools, reamer tools, directional tools, rotary steerable systems etc. The output may consist of hole curvature (build up or drop rate), hole angle, weight on bit and is presented in drilling semantics. Additionally, the program can perform mechanical analyses and solve for the bending moments and reactions forces. Moreover, the program has the capability to predict the wellpath using a drill ahead algorithm. The program consists of a mathematical model which makes assumptions of 2-D, static, constant hole curvature resulting in a robust computationally efficient tool that produces rapid reliable results in the field.

Parametric resonances: from the Mathieu equation to QASER

2016 ◽  
Vol 91 (7) ◽  
pp. 073004 ◽  
Author(s):  
Goong Chen ◽  
Jing Tian ◽  
Bandar Bin-Mohsin ◽  
Reed Nessler ◽  
Anatoly Svidzinsky ◽  
...  
Keyword(s):  
Mathieu Equation ◽  
Parametric Resonances

Calculation Methods of Orienter Torque and Drag in Coiled Tubing Drilling

2014 ◽  
Vol 1065-1069 ◽  
pp. 2049-2052
Author(s):  
Liang Hu ◽  
De Li Gao
Keyword(s):  
Static Friction ◽  
Maximum Output ◽  
Force Analysis ◽  
Viscous Forces ◽  
Coiled Tubing ◽  
Bottom Hole ◽  
Weight On Bit ◽  
Bottom Hole Assembly ◽  
The Impact ◽  
The Relationship

Hydraulic orienter has been widely used to alter the drilling direction downhole in coiled tubing drilling. A problem is encountered in construction field. When torque and drag of bottom hole assembly (BHA) are over the maximum output torque of orienter, This caused that it difficult to orient. Therefore, we need to calculate the maximum torque and drag in the process of orientation, it can provide a theoretical basis for designing and selecting the hydraulic orienter. Compared with the conventional force analysis, this paper additionally considered the case of zero weight on bit (WOB), the impact of the mud viscous forces and the relationship between dynamic and static friction, so that we can get more precise result of force analysis.

Parametric and Combination Resonances of a Pipe Conveying Pulsating Fluid

1975 ◽  
Vol 42 (4) ◽  
pp. 780-784 ◽  
Author(s):  
M. P. Paidoussis ◽  
C. Sundararajan
Keyword(s):  
Flow Velocity ◽  
Parametric Resonance ◽  
Mean Value ◽  
Pipe Conveying Fluid ◽  
Combination Resonance ◽  
Load Combination ◽  
Parametric Resonances ◽  
The Difference ◽  
Pulsating Fluid ◽  
Conveying Fluid

In this paper we consider the dynamics of a pipe conveying fluid, when the flow velocity is harmonically perturbed about a mean value. Two methods of analysis are presented; Bolotin’s method, which can only give the boundaries of regions of parametric resonance, and a numerical Floquet analysis, which gives also the boundaries of combination resonance. A number of calculations for cantilevered pipes show that, generally, combination resonance is less important than parametric resonance, except for flow velocities near the critical (where the system loses stability in steady flow); parametric resonances are selectively associated with only some of the modes of the system, and combination resonances involve only the difference of the eigenfrequencies. For pipes clamped at both ends the behavior of the system is similar to that of a column subjected to a pulsating load; combination resonances in this case involve the sum of the eigenfrequencies.

Nonlinear Behavior of a Parametric Resonance-Based Mass Sensor

2002 ◽  
Author(s):  
Wenhua Zhang ◽  
Rajashree Baskaran ◽  
Kimberly L. Turner
Keyword(s):  
Parametric Resonance ◽  
Mathieu Equation ◽  
Nonlinear Behavior ◽  
High Sensitivity ◽  
Small Mass ◽  
Mass Change ◽  
Mass Sensor ◽  
Mass Sensors ◽  
Mems Oscillator ◽  
Harmonic Resonance

The ability to detect mass change of the order of femtograms (10e-15g) opens up implementations of various precise chemical and biological sensors. Micro-scale oscillator based mass sensors are promising due to their small mass and high sensitivity. Many such sensors detect mass change by measuring the shift of natural frequency. We have reported previous work introducing the idea of using parametric resonance to detect mass change. This method utilizes stability behavior with mass variation as the detection criterion and high sensitivity is expected. This paper presents theoretical and experimental research on nonlinearity effects on the dynamic behavior of a MEMS oscillator, which is the prototype of such a mass sensor. A Duffing equation and a nonlinear Mathieu equation are used to model the behavior of nonlinear harmonic resonance and parametric resonance. Experimental results agree with the theoretical analysis very well. Some bulk equivalent parameters, such as Q factor, cubic stiffness and linear electrostatic stiffness can be estimated by studying the nonlinear behavior. The estimation of the parameters is important for design of the optimal mass sensor. The potential effects of nonlinearity on mass sensor application are discussed.

scholarly journals Finite Element Simulation of Dynamic Stability of Plane Free-Surface of a Liquid under Vertical Excitation

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Siva Srinivas Kolukula ◽  
P. Chellapandi
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Parametric Resonance ◽  
Linear Equations ◽  
Parametric Instability ◽  
Initial Perturbation ◽  
Mathieu Equation ◽  
External Excitation ◽  
Nonlinear Potential Theory ◽  
Vertical Excitation

When partially filled liquid containers are excited vertically, the plane free-surface of the liquid can be stable or unstable depending on the amplitude and frequency of the external excitation. For some combinations of amplitude and frequency, the free-surface undergoes unbounded motion leading to instability called parametric instability or parametric resonance, and, for few other combinations, the free-surface undergoes bounded stable motion. In parametric resonance, a small initial perturbation on the free-surface can build up unboundedly even for small external excitation, if the excitation acts on the tank for sufficiently long time. In this paper, the stability of the plane free-surface is investigated by numerical simulation. Stability chart for the governing Mathieu equation is plotted analytically using linear equations. Applying fully nonlinear finite element method based on nonlinear potential theory, the response of the plane free-surface is simulated for various cases.

scholarly journals Modeling processes that provide an avalanche of innovation growth

2021 ◽  
Vol 2131 (4) ◽  
pp. 042001
Author(s):  
S Diakonova ◽  
St Artyshchenko ◽  
N Medvedeva ◽  
M Gusev
Keyword(s):  
Mathematical Modeling ◽  
Parametric Resonance ◽  
Economic Activity ◽  
Mathieu Equation ◽  
Modeling Processes ◽  
Accurate Description ◽  
Growth Stages ◽  
Resonance Model ◽  
Innovation Processes ◽  
Over Time

Abstract This paper proposes an addition to Kondratyev’s theory of the emergence of innovations in long cycles. Regularities of the emergence of crisis phenomena and the concept of “avalanche-like growth of innovations” are considered. The study investigated the innovation peaks occurring in the middle of the depression phase, followed by the growth stages of economic activity after a certain period of time. Research has shown that the active emergence of innovations, which we have called the “snowballing growth of innovations,” falls in the middle of the depression phase. The authors investigated and supplemented the theory of the triggering effect of depression, which is similar to the action of the trigger, which results in an “avalanche-like growth of innovations”. To describe the processes associated with resonance and trigger effects, the authors propose to use the parametric resonance model and the Mathieu equation. With the help of mathematical modeling of innovation processes, a more accurate description of the periodic change in the number of innovations over time is possible, namely, the “avalanche-like growth of innovations”.

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