Research on the Coupled Axial-Transverse Nonlinear Vibration of Sucker Rod String in Deviated Wells

The coupled axial-transverse nonlinear vibration simulation model of sucker rod sting (SRS) in deviated wells is established. Based on the simulation results, the nonlinear vibration phenomenon of SRS is analyzed, and the influence of centralizer arrangement on the nonlinear vibration of SRS is discussed. The mechanical simulation model of the coupled axial-transverse vibration of SRS in deviated wells can be simplified to the coupled axial-transverse vibration model of longitudinal and transverse curved beam with initial bending under borehole constraints. In this paper, when establishing the simulation model of the coupled axial-transverse vibration of SRS, it is proposed that the bending borehole trajectory is a main excitation of the vibration of SRS. Based on the theory of elastic vibration, a nonlinear dynamic simulation model of the coupled axial-transverse vibration of SRS in deviated well is established. Then the fourth-order Runge–Kutta method is used to solve the simulation model. The nonlinear vibration phenomenon of the SRS is studied by example analysis. The simulation results show that: (1) the simulation curve of polished rod dynamometer card is in good agreement with the test curve, and the error value of polished rod maximum load and minimum load is within 5%, which shows that the coupled axial-transverse vibration simulation model of SRS established in this paper has high accuracy. (2) When the centralizer is not arranged, the chaotic motion of SRS mainly occurs in the compression section of SRS, which shows that the instability of SRS is the main reason for the chaotic motion of SRS. (3) The arrangement of centralizer can improve the bending rigidity of SRS, restrain or even eliminate the chaotic motion of SRS.