Research On The Nonlinear Dynamics Analytic Method Of Beam Element Drill String Based On Domain Decomposition Method

Because of the advantages of high drilling efficiency,low drilling cost and long service life,DTH drilling technology is widely used in drilling operations such as hydrogeology,oil drilling and mineral exploitation,but in practical drilling,the coupling vibration,large deformation buckling and contact of the DTH hammer drill will cause large wear and tear of the drilling tools.Many complex nonlinear dynamic problems are still not well solved.By consulting the data at home and abroad,having detailed understanding the development status of the DTH hammer,the coupling vibration of the drill string system,the large deformation of the drill string and the contact theory of the drill string.Using the Domain Decomposition Method establishes the energy functional of the coupled vibration of the drill string in the space beam element for the first time,carrying out the modal analysis of the coupled vibration of the drill string.Using the nonlinear finite element method establishes the energy functional of the large deformation buckling of the drill string in the space beam element,a theoretical method for studying the large deformation buckling of drill string is preliminarily established.Establishing an innovative elliptic surface Hertz contact model for drill string based on Hertz theory.The details are as follows:The axial impact force and pressure are acted on the top and bottom of the drill string respectively.When impacting the hard rock,the axial force of the drill string is unbalanced,which causes the nonlinear large deformation and buckling of the drill string and collision contact between drill string and wellbore.According to the actual buckling state of collision contact between drill string and wellbore,setting up the two-cylinder bending contact model of drill string lining.Establishing the sine line equation of the outer surface of the bent drill string.Analyzing the contact profile between the bent drill string and the wellbore.Establishing an innovative elliptic surface Hertz contact model for drill string based on Hertz theory,and studying the relationship between immersion depth,drilling parameters and buckling state and contact force.Using the Domain Decomposition Method establishes the energy functional of the coupled vibration of the drill string in the space beam unit for the first time,taking advantage of the displacement polynomial expands the drill string coupled vibration energy function into a dynamic discrete equation.The discrete equation of the coupled vibration of the drill string in the beam element is solved by the direct iterative method.The coupling vibration modal analysis of drill string is carried out and compared with ANSYS simulation results.The results show that when the drilling depth is more than 200m,using beam theory to carry out the coupled vibration modal analysis of the drill string.The frequency error of the first three order and torsional modes of the drill string is 1%,and the error of the first 80 horizontal modal frequencies of the drill string is about 0.1%.With the increase of the drill string length,the longitudinal,transverse,torsion and mode state errors of the drill string gradually decrease.When drilling depth is less than 50m,using shell theory to carry out the coupled vibration modal analysis of the drill string.The error of the longitudinal,transverse and torsional modal frequencies of the drill string is less than 1%compared with the results of the ANSYS simulation.Considering the effect of high order small quantity on the strain energy of the drill string,Using the nonlinear finite element method establishes the energy functional of the large deformation buckling of the drill string in the space beam unit.Taking advantage of the displacement polynomial expands the drill string coupled vibration energy function into a dynamic discrete equation.The discrete equation of the coupled vibration of the drill string in the beam element is solved by the Newton-Raphson method.A theoretical method for studying the large deformation buckling of drill string is preliminarily established.