考虑耗散力的抽油系统动力学分析及弹性机构振动控制
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摘要
机械系统中的耗散力是引起能量消耗和设备磨损的主要因素,同时耗散力对机械系统的动态性能及运转精度也有重要的影响。在机械系统分析与设计中充分考虑耗散力的影响,对于提高设备运行效率、节约能源、减轻振动、改善性能具有重要的理论与实际意义。本学位论文以定向井有杆抽油系统和平面弹性连杆机构为研究对象,对考虑耗散力的抽油系统动力学及弹性机构振动控制问题进行了深入研究。
由于库仑摩擦力与抽油杆柱弹性变形的耦合,使得现有定向井有杆抽油系统动态参数预测模型是一组非线性偏微分方程,求解复杂。鉴于此,提出了一种新的分析方法。该方法以定向井有杆抽油系统中的抽油杆柱作为研究对象,根据三次样条插值模拟得到的定向井的井眼轨迹,利用静力有限元法计算出了油管对抽油杆柱的支反力,进而得出了杆柱与油管之间的库仑摩擦力。在对杆柱单元受力分析基础上,建立了有限元形式的定向井有杆抽油系统动力学方程,并利用状态空间法进行数值求解,获得了该系统的动态参数及地面功图。将本方法计算结果与实测结果以及采用有限差分法的计算结果进行了对比,表明本文方法简便、正确、有效。
定向井有杆抽油系统动态特性分析过程中,抽油杆柱与油液之间粘性摩擦系数和抽油杆柱与油管之间库仑摩擦系数的确定是一个关键和困难的问题。提出了一种基于特征的方法来识别抽油系统摩擦系数。新方法针对现有的Freeman八方向链码码间距过大、采样必须为方格采样、编码过程需要人工干预的不足,对其进行了改进,并利用改进后的链码方法将封闭曲线链码化。根据封闭曲线的周期性,将其参数方程展成傅里叶级数,导出了傅里叶系数与曲线链码之间的关系式。利用傅里叶系数计算封闭曲线的形状特征,建立了实测与仿真地面功图曲线形状特征间的欧氏距离。以该距离为优化目标函数,寻优得到使目标函数值满足给定误差的仿真地面功图曲线,该功图对应的一组摩擦系数即为相应抽油系统的粘性摩擦系数和库仑摩擦系数。基于该参数的动力学特性预测结果与实际吻合。
采用LuGre摩擦模型来描述有杆抽油系统的非线性摩擦,在此基础上对有杆抽油系统进行动力学分析。对LuGre摩擦模型中的六个参数进行了分析并给出了符合工程应用的参数值。将抽油系统中抽油杆柱的振动视为多级杆的纵向振动,对杆柱单元进行了受力分析,结合有限差分法与有限元法建立了杆柱的载荷和位移递推公式,并给出了杆柱载荷和位移的边界条件以及杆柱运动的初始条件。给出了采用LuGre摩擦模型的定向井仿真实例,并与采用经典库仑+粘性摩擦模型的计算结果进行了对比,结果表明LuGre摩擦模型能较好地反映低速换向时系统摩擦的非线性特性。
提出了一种能够比较精确地确定井下各项耗散力耗能的计算方法。基于已知杆管间库仑摩擦力以及杆柱各节点的弹性运动速度,对抽油系统中库仑摩擦力、粘性摩擦力以及盘根盒摩擦力在一个抽油周期内的耗能进行了分析,导出了相应的耗能计算公式。根据地面功图计算出抽油机悬点载荷在一个抽汲周期所做的功,并对抽油系统井下效率进行了计算。为掌握抽油系统井下各环节的耗能情况提供了参考。对杆柱弹性运动速度引起的粘性摩擦力耗能进行了分析,结果表明杆柱弹性运动速度引起的粘性摩擦力耗能不能忽略。
研究了油井地层供液量与井底流压之间的流入动态关系。系统地分析了抽油系统的抽汲参数和沉没度对泵效的影响。根据油井产供平衡原则,以井下效率为目标函数对抽油系统进行了优化。结果表明,优化可明显提高井下效率,降低生产成本。同时也表明油井沉没度对泵效和井下效率的影响比抽汲参数更为明显。
基于阻尼合金的大阻尼能量耗散特性,将其用作弹性机构系统振动被动控制材料。利用粘弹性五参量本构关系来描述阻尼合金材料的应力应变关系。导出了以五参量表示阻尼和刚度特性的单元运动微分方程。为了便于计算,首先将包含卷积运算的微分方程转换成一个四阶常微分方程,进而装配出系统运动微分方程。利用状态空间法对该高阶时变微分方程组进行了数值求解。给出了含阻尼合金构件平面弹性四连杆机构的动力学响应计算实例,结果表明五参量结构阻尼模型克服了三参量阻尼模型中耗散因子在频域是单峰函数的局限,能够更好地描述阻尼合金的阻尼特性。
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.
由于库仑摩擦力与抽油杆柱弹性变形的耦合,使得现有定向井有杆抽油系统动态参数预测模型是一组非线性偏微分方程,求解复杂。鉴于此,提出了一种新的分析方法。该方法以定向井有杆抽油系统中的抽油杆柱作为研究对象,根据三次样条插值模拟得到的定向井的井眼轨迹,利用静力有限元法计算出了油管对抽油杆柱的支反力,进而得出了杆柱与油管之间的库仑摩擦力。在对杆柱单元受力分析基础上,建立了有限元形式的定向井有杆抽油系统动力学方程,并利用状态空间法进行数值求解,获得了该系统的动态参数及地面功图。将本方法计算结果与实测结果以及采用有限差分法的计算结果进行了对比,表明本文方法简便、正确、有效。
定向井有杆抽油系统动态特性分析过程中,抽油杆柱与油液之间粘性摩擦系数和抽油杆柱与油管之间库仑摩擦系数的确定是一个关键和困难的问题。提出了一种基于特征的方法来识别抽油系统摩擦系数。新方法针对现有的Freeman八方向链码码间距过大、采样必须为方格采样、编码过程需要人工干预的不足,对其进行了改进,并利用改进后的链码方法将封闭曲线链码化。根据封闭曲线的周期性,将其参数方程展成傅里叶级数,导出了傅里叶系数与曲线链码之间的关系式。利用傅里叶系数计算封闭曲线的形状特征,建立了实测与仿真地面功图曲线形状特征间的欧氏距离。以该距离为优化目标函数,寻优得到使目标函数值满足给定误差的仿真地面功图曲线,该功图对应的一组摩擦系数即为相应抽油系统的粘性摩擦系数和库仑摩擦系数。基于该参数的动力学特性预测结果与实际吻合。
采用LuGre摩擦模型来描述有杆抽油系统的非线性摩擦,在此基础上对有杆抽油系统进行动力学分析。对LuGre摩擦模型中的六个参数进行了分析并给出了符合工程应用的参数值。将抽油系统中抽油杆柱的振动视为多级杆的纵向振动,对杆柱单元进行了受力分析,结合有限差分法与有限元法建立了杆柱的载荷和位移递推公式,并给出了杆柱载荷和位移的边界条件以及杆柱运动的初始条件。给出了采用LuGre摩擦模型的定向井仿真实例,并与采用经典库仑+粘性摩擦模型的计算结果进行了对比,结果表明LuGre摩擦模型能较好地反映低速换向时系统摩擦的非线性特性。
提出了一种能够比较精确地确定井下各项耗散力耗能的计算方法。基于已知杆管间库仑摩擦力以及杆柱各节点的弹性运动速度,对抽油系统中库仑摩擦力、粘性摩擦力以及盘根盒摩擦力在一个抽油周期内的耗能进行了分析,导出了相应的耗能计算公式。根据地面功图计算出抽油机悬点载荷在一个抽汲周期所做的功,并对抽油系统井下效率进行了计算。为掌握抽油系统井下各环节的耗能情况提供了参考。对杆柱弹性运动速度引起的粘性摩擦力耗能进行了分析,结果表明杆柱弹性运动速度引起的粘性摩擦力耗能不能忽略。
研究了油井地层供液量与井底流压之间的流入动态关系。系统地分析了抽油系统的抽汲参数和沉没度对泵效的影响。根据油井产供平衡原则,以井下效率为目标函数对抽油系统进行了优化。结果表明,优化可明显提高井下效率,降低生产成本。同时也表明油井沉没度对泵效和井下效率的影响比抽汲参数更为明显。
基于阻尼合金的大阻尼能量耗散特性,将其用作弹性机构系统振动被动控制材料。利用粘弹性五参量本构关系来描述阻尼合金材料的应力应变关系。导出了以五参量表示阻尼和刚度特性的单元运动微分方程。为了便于计算,首先将包含卷积运算的微分方程转换成一个四阶常微分方程,进而装配出系统运动微分方程。利用状态空间法对该高阶时变微分方程组进行了数值求解。给出了含阻尼合金构件平面弹性四连杆机构的动力学响应计算实例,结果表明五参量结构阻尼模型克服了三参量阻尼模型中耗散因子在频域是单峰函数的局限,能够更好地描述阻尼合金的阻尼特性。
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.
引文
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