Method of equilibrium differential equation for analysis of strength of large deflection drill string

2000 ◽  
Vol 21 (11) ◽  
pp. 1292-1299
Author(s):  
Liu Yan-qiang
Keyword(s):  
Differential Equation ◽  
Large Deflection ◽  
Drill String ◽  
Equilibrium Differential Equation

High Precision Numerical Analysis of Nonlinear Beam Bending Problems under Large Deflection

2014 ◽  
Vol 638-640 ◽  
pp. 1705-1709
Author(s):  
Zhao Qing Wang ◽  
Jian Jiang ◽  
Bing Tao Tang ◽  
Wei Zheng
Keyword(s):  
Differential Equation ◽  
High Precision ◽  
Large Deflection ◽  
Nonlinear Ordinary Differential Equation ◽  
Initial Guess ◽  
Computational Accuracy ◽  
Nonlinear Bending ◽  
Barycentric Interpolation ◽  
Bending Problems ◽  
Linear Differential

The high precision numerical method for solving nonlinear bending problems of large deflection beam is presented. The governing equation of large deflection beam is a strongly nonlinear ordinary differential equation. Using the solution of linear bending beam as an initial guess function, the nonlinear bending equation of beam can be transferred into a linear differential equation. The improvement solution of nonlinear bending beam is obtained by solving the linearized bending equation using barycentric interpolation collocation method. Then, the solution of nonlinear bending beam can be given by iterative method. Some examples demonstrate the validity and computational accuracy of proposed method.

scholarly journals Effect Of Drill String Rotation On The Dynamic Response Of Drilling Risers

2015 ◽  
Vol 20 (3) ◽  
pp. 503-516 ◽  
Author(s):  
I.E. Major ◽  
A. Big-Alabo ◽  
S. Odi-Owei
Keyword(s):  
Differential Equation ◽  
Free Vibration ◽  
Dynamic Response ◽  
Natural Frequency ◽  
First Principles ◽  
Rotational Speed ◽  
Variable Coefficient ◽  
Drill String ◽  
Flexural Response ◽  
Free Vibration Response

Abstract The effect of the rotation of a drill string on the response of a drilling riser has been studied. A governing equation for the flexural response that incorporates the effect of the drill string rotation is developed from first principles, and the resulting differential equation is found to have a variable coefficient, which is a function of the drill string rotational speed. Results simulated for the free vibration response show that the drill string rotation reduces the natural frequency and increases the amplitude of vibration of the drilling riser. The implication of these findings is that neglecting the effect of rotation of the drill string leads to under-estimation of the deflection and over-estimation of the natural frequency. Further analysis reveals that for a drilling riser of given dimensions, a drill string rotational speed exists at which the natural frequency of the drilling riser is theoretical equal to zero, and this rotational speed is the threshold rotational speed.

Large Deflection of Tip Loaded Beam with Differential Transformation Method

2011 ◽  
Vol 250-253 ◽  
pp. 1232-1235 ◽  
Author(s):  
Yi Xiao
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Large Deflection ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Differential Transformation ◽  
The Finite Difference Method ◽  
Large Deflection Problem ◽  
Constant Section

This paper deals with large deflection problem of a cantilever beam with a constant section under the action of a transverse tip load. The differential transformation method (DTM) is used to solve the nonlinear differential equation governing the problem. An approach treats trigonometric nonlinearity is used in DTM. The results obtained from DTM are compared with those results obtained by the finite difference method and they agree well.

scholarly journals Mathematical model of brush seals for gas turbine engines: A nonlinear analytical solution

2021 ◽  
Vol 13 (9) ◽  
pp. 168781402110433
Author(s):  
Amin Changizi ◽  
Ion Stiharu ◽  
Bilal Outirba ◽  
Patrick Hendrick
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Temperature Gradient ◽  
Gas Turbine ◽  
Large Deflection ◽  
Turbine Engines ◽  
Gas Turbine Engines ◽  
Engine Operation ◽  
Curved Bridge ◽  
Brush Seals

Presented herein is a mathematical model employing differential equations formulation for brush seals used in gas turbine engines. These components are used to seal the bearing chamber from the environment and reduce the loss of lubricant in the atmosphere, ensuring a MTBR long enough to have required the change the seals only during the engine overhaul operation. The model assumes a single curved bristle loop in the form of a curved-bridge beam subjected to the influences of complex external loads (static and dynamic). Further, a model for clustered bristles is proposed. Specifically, the static forces acting on the curved-bridge beam include the weight of the oil capillary attached to the beam, the weight of the beam itself, the capillary force developed between the surfaces of the bristles in the brush and the temperature gradient. The dynamic forces include the leakage oil pressure and the rotation of the shaft. This complex loading induces a nonlinear large deflection on the curved-bridge beam. Also, the temperature gradient present on the bristles during the gas turbine engine operation generates a change in the geometry of the beam and in the magnitude of the forces acting on the bristles modeled as beams. In the present model, the weights are assumed as uniformly distributed forces on the surface of the beam while the capillary forces and the force generated by the rotating shaft are considered to be non-uniform. The equation expressing the curvature of the beam under general loading force is developed and one can choose the appropriate method of solving the generated differential equation after the expression of the general force is defined. Hence, the ordinary differential equation describing the nonlinear large deflection of the curved-bridge beam will be derived using general nonlinear elasticity theory.

scholarly journals Ludwick Cantilever Beam in Large Deflection Under Vertical Constant Load

2016 ◽  
Vol 10 (1) ◽  
pp. 23-37 ◽  
Author(s):  
Alberto Borboni ◽  
Diego De Santis ◽  
Luigi Solazzi ◽  
Jorge Hugo Villafañe ◽  
Rodolfo Faglia
Keyword(s):  
Differential Equation ◽  
Cantilever Beam ◽  
Cross Section ◽  
Large Deflection ◽  
External Action ◽  
Constant Load ◽  
Large Deflections ◽  
Eulerian Method ◽  
Vertical Displacements ◽  
Newton Raphson

The aim of this paper is to calculate the horizontal and vertical displacements of a cantilever beam in large deflections. The proposed structure is composed with Ludwick material exhibiting a different behavior to tensile and compressive actions. The geometry of the cross-section is constant and rectangular, while the external action is a vertical constant load applied at the free end. The problem is nonlinear due to the constitutive model and to the large deflections. The associated computational problem is related to the solution of a set of equation in conjunction with an ODE. An approximated approach is proposed here based on the application Newton-Raphson approach on a custom mesh and in cascade with an Eulerian method for the differential equation.

Observer-Based Boundary Control Design for the Suppression of Stick–Slip Oscillations in Drilling Systems With Only Surface Measurements

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Halil Ibrahim Basturk
Keyword(s):  
Differential Equation ◽  
Angular Velocity ◽  
Linear Time ◽  
Control Design ◽  
Drill String ◽  
Friction Torque ◽  
Distributed Model ◽  
Drilling Process ◽  
Stick Slip ◽  
Surface Measurements

We develop an observer-based boundary controller for the rotary table to suppress stick–slip oscillations and to maintain the angular velocity of the drill string at a desired value during a drilling process despite unknown friction torque and by using only surface measurements. The control design is based on a distributed model of the drill string. The obtained infinite dimensional model is converted to an ordinary differential equation–partial differential equation (ODE–PDE) coupled system. The observer-based controller is designed by reformulating the problem as the stabilization of an linear time-invariant (LTI) system which is affected by a constant unknown disturbance and has simultaneous actuator and sensor delays. The main contribution of the controller is that it requires only surface measurements. We prove that the equilibrium of the closed-loop system is exponentially stable, and that the angular velocity regulation is achieved with the estimations of unknown friction torque and drill bit velocity. The effectiveness of the controller is demonstrated using numerical simulations.

An Accurate Numerical Scheme for Large Deflection Analysis of Non-Prismatic Inextensible Slender Beams Subjected to General Loading and Boundary Conditions

2005 ◽  
Vol 8 (6) ◽  
pp. 585-594 ◽  
Author(s):  
Samir Z. Al-Sadder ◽  
Mohammad H. Dado
Keyword(s):  
Differential Equation ◽  
Power Series ◽  
Boundary Conditions ◽  
Numerical Scheme ◽  
Large Deflection ◽  
Element Analysis ◽  
Numerical Examples ◽  
Deflection Analysis ◽  
Slender Beams ◽  
Angle Of Rotation

This paper studies the large deflection behavior of prismatic and non-prismatic inextensible beams subjected to various types of loading and boundary conditions. The formulation is based on representing the angle of rotation by a power series and substituting it into the derived governing nonlinear differential equation. The coefficients of the power series are obtained by minimizing the integral of the residual error over the deflected beam axis. Several numerical examples are presented covering prismatic and non-prismatic beams subjected to uniform and non-uniform distributed loads. A large displacement finite element analysis using the package MSC/NASTRAN was used to check the accuracy and efficiency of the present numerical method. Excellent agreement was observed between the two numerical schemes.

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