受压旋转复合材料钻柱横向振动的格林函数解  

Green's function solution of transverse vibration of rotary composite drill string under pressure

作　　者：常学平[1,2] 陈美 范谨铭 于学会 CHANG Xueping;CHEN Mei;FAN Jinming;YU Xuehui(School of Mechanical&Electrical Engineering,Southwest Petroleum University,610500 Chengdu,China;School of Mechanics&Aeronautics,Southwest Jiaotong University,610031 Chengdu,China)

机构地区：[1]西南石油大学机电工程学院,成都610500 [2]西南交通大学力学与航空航天学院,成都610031

出　　处：《应用力学学报》2025年第2期434-445,共12页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金资助项目(No.51674216,11702230)。

摘　　要：受压旋转钻柱易发生横向振动,引起钻柱失效、井眼扩径等严重事故。采用格林函数法对受压旋转复合材料钻柱系统横向振动响应进行了研究,获得了系统双向耦合振动的响应解析解。以钻柱整体为对象,基于Hamilton原理建立了计入自旋角速度及钻压影响的钻柱双向耦合动力学方程。采用格林函数法,将方程进行分离变量、Laplace变换和Laplace逆变换,获得了受压自旋复合材料钻柱双向耦合振动的格林函数解。在数值分析部分,首先验证本研究方法的可靠性,然后借助系统的格林函数解,分析了纤维铺层角、旋转角速度、钻压、钻井液流速等参数对受压旋转复合材料钻柱系统的横向振动的影响。研究表明,纤维铺层角越大钻柱系统的格林函数响应越大,在一定范围内转速越大对应钻柱的格林函数响应也随之增大;自旋角速度、钻井液流速及纤维铺层角联合效应下,钻柱系统横向耦合振动会产生共振带。据共振带发生的位置可以找出结构因为发生大幅度振动进而导致失稳和破坏的复合材料与旋转角速度的危险取值区间,通过避开危险取值区间从而有效避免结构的失稳和破坏。Transverse vibration of drill string can occur easily,which leads to drill string failure,hole reaming and other serious accidents.In this paper,Green's function method was used to study the lateral vibration response of a rotating composite drill string system under pressure.Based on Hamilton principle,the bidirectional coupling dynamic equation of drill string was established considering the influence of spin angular velocity and bit weight.By using Green's function method,the variables were separated,Laplace transformation and inverse Laplace transformation of the equation were made,and then the Green's function solution of the bidirectional coupling vibration of the spin composite drill string under pressure was obtained.In the numerical analysis part,first,the reliability of the proposed method was verified,and then the effects of fiber layering angle,rotational angular velocity and weight on bit and drilling fluid flow rate on lateral vibration of the rotary composite drill string system were analyzed by means of Green's function solution of the system.The results show that the larger the fiber laying angle is,the larger the green function response of the drill string system is;the larger the rotational speed is within a certain range,the larger the green function basic response of the drill string will be.Under the combined effect of rotation speed,drilling fluid flow rate and fiber layup angle,the lateral coupling vibration of drill string system will produce resonance zone.

关 键 词：格林函数法 LAPLACE变换 复合材料钻柱 旋转角速度 共振带 

分 类 号：O323[理学—一般力学与力学基础] O326[理学—力学]