Dynamic Analysis Of Sucker-Rod Pumping System And Vibration Control Of Elastic Mechanism Considering Dissipation Force

Dissipation force is the main reason for energy dissipation and equipment wear in mechanical system. In addition, dissipation force also affects the dynamic characteristics and running precision of machine sharply. Considering the dissipation force in design and analysis of mechanical system is beneficial to improve system's running efficiency, save energy, reduce vibration and to optimize system's characteristics, which is significant in theory and practice. The purpose of this dissertation is to study thoroughly the dynamic characteristics of sucker-rod pumping system and vibration passive control of elastic mechanism considering dissipation force.The current prediction model of dynamic characteristics of sucker-rod pumping system in directional well is a nonlinear partial differential equation, whose solution is difficult and complex. A novel analytical method is put forward to simplify this prediction model. First, according to the well trajectory fitted by using the cubic spline interpolation method, the support reaction between rod string and pipe in directional well is calculated by means of finite element method for static load. Second, the Coulomb friction force between rod string and pipe is computed by using the calculated support reaction. Third, the loads analysis of rod element is performed and the system dynamic equation of rod string is derived. Dynamic parameters and surface dynamometer card of sucker-rod pumping system are obtained after the system dynamic equation is solved by means of the state space method. In the end, two prediction examples are given, where a comparison between the predicted and the measured dynamometer cards is made to show that the present analytical method is simple, correct and effective.Viscous and Coulomb friction coefficients of sucker-rod pumping system are important but difficult to select during analysis for system's dynamic characteristics. A new identification method based on characteristic, which overcomes the shortcomings of eight-directional Freeman chain code method, is proposed to obtain system's friction coefficients. According to closed boundary curve's periodicity, its parametric equation is transformed into Fourier series, whose coefficients can be computed by curve's chain codes. Shape characteristics of the closed boundary curve are extracted through these computed Fourier series' coefficients. The Euclidean distance between shape characteristics of measured surface dynamometer card and that of simulated card is established and is employed as objective function for optimization. When the Euclidean distance is less than the given error, the corresponding values of friction coefficients in the simulation program are regarded as real friction coefficients of the sucker-rod pumping system of directional well. Numerical example is provided to show that the final simulated dynamometer card based on the identified friction coefficients fits the measured dynamometer card well.The nonlinear dynamic characteristic of a sucker-rod pumping system of directional well is simulated on the basis of LuGre friction model. First, values of six parameters of LuGre friction model, which satisfy the engineering's needs, are obtained according to handbook and computation. Second, the vibration of the rod of sucker-rod pumping system is regarded as an axial vibration of multi-segment flexible rod. The loads analysis of rod element is accomplished by means of finite element method. Recurrence formulas of load and elastic deformation are derived through finite difference method and finite element method. The boundary conditions of load and elastic deformation and initial condition of rod kinematics are provided. In the end, a numerical example is given, where a comparison between the elastic deformation of pumping piston obtained based on LuGre friction model and that on classical Coulomb plus viscous friction model is made to show that the LuGre friction model describes the friction of sucker-rod pumping system better.A more precise method is proposed to calculate the down-hole energy dissipation of sucker-rod pumping system caused by viscous friction force between rod string and liquid and by Coulomb friction force between rod string and pipe, which is difficult for the existing theory to calculate. The Coulomb friction force and the elastic velocities of the rod nodes are computed. Analysis of energy dissipation in one production period caused by viscous friction force, Coulomb friction force and friction force between rod string and stuffing box are performed. According to the surface dynamometer card, the input down-hole energy in one production period is calculated. And then the down-hole efficiency of the suck-rod pumping system is calculated by the obtained input down-hole energy and energy dissipation, which provides a reference for mastering the energy dissipation of every part. Moreover, an analysis of viscous friction dissipation due to elastic velocity of rod string is accomplished, whose result shows that the energy dissipation caused by the elastic velocity of rod string cannot be ignored.The inflow performance relationship (IPR) between liquid amount of supply and the inflow pressure is studied. Analysis of effects of production parameters and submergence depth upon the pump efficiency is performed. According to the law that the liquid amount of supply must equate that of production, the system efficiency optimization, where the down-hole efficiency is taken as the criteria function, is accomplished. The optimization results indicate that effect of the submergence depth upon pump efficiency and down-hole efficiency is more evident than that of production parameters.Damping alloy is employed to reduce vibration of elastic mechanism because of its excellent dissipation characteristics. The Five parameters viscoelastic constitutive relation is adopted to describe the stress-strain relation of damping alloy. Dynamic equations of beam element are derived with five parameters representing the damping and stiffness characteristics. For the convenience of computation, the established dynamic equations with convolution integration are changed into four-order differential equations. And then the system dynamic equation of the elastic linkage mechanism containing damping alloy parts is assembled. The state space method is employed to solve the established high order differential equations with time-varying coefficients. Numerical example shows that the proposed model overcomes theshortcoming of the three parameters damping model, in which the dissipation factor is amonotonic function in frequency domain, and can describe the damping alloy's characteristicsbetter.