深孔加工中钻杆系统非线性动态行为研究
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摘要
随着冶金、核电和兵器工业对深孔加工高效率、高精度、高可靠性的不懈追求,对深孔加工及其钻杆系统的研究越来越受到重视。然而,由于深孔钻削机理的复杂性及加工条件的多样性,如何在保证非线性分析所需精度的条件下,高效地计算钻杆系统的运动轨迹、切削液流体力等成为深孔加工中的热点和关键问题。人们采用了包括将钻杆系统简化为解析、数值形式的Euler-Bernoulli梁模型求解及经验方程等多种方法,但到目前为止,尚未得到很好的解决。故此,本文在前人工作的基础上,研究深孔加工过程中钻杆系统的非线性动力学行为及其关键技术,为分析解决实际深孔加工钻杆系统中出现的众多动力学行为提供参考,具有重要的理论意义及工程应用价值。
依据实际深孔加工中非线性流体动压力应满足的物理条件,以近似解析解为基础,在研究钻杆转速、涡动速度及钻杆偏心率等因素影响的基础上,建立了有限长钻杆所承受的切削液流体动压模型。针对切削液非线性流体力的分析与计算,阐明了切削液非稳态流体的动压特性,并结合钻杆运动参数与结构设计参数等改变时对非线性切削液流体力分布变化规律的影响,揭示了切削液流体力引起钻杆涡动和失稳的力学机理,得出了对生产实践有指导意义的钻杆间隙系数及其选择准则。
证明了深孔加工切削液流体Reynolds方程的等价变分形式,运用变分约束原理,按照切削液流体的物理特性,形成了修正的Reynolds方程变分形式及其扰动方程。在不增加计算量的情况下,求得了非线性流体力及其Jacobian矩阵,并且使其具有相互协调一致的精度。通过深孔加工钻杆系统切削液非线性流体力解析模型与有限元数值计算模型的对比,获得了现有的非线性切削液流体力解析模型的适用范围和近似程度。
基于传统打靶法的求解思想,设计了一种将周期值作为参数一起参与打靶迭代的算法,通过优化确定迭代过程中的增量值。针对单孔和槽孔两种孔结构形式,将非线性切削液流体力及其Jacobian矩阵联合求解法与改进的打靶法及Floquet理论相结合,得到了不同加工参数条件下钻杆中心的运动轨迹,分析了包括伪周期、倍周期、跳跃等在内的各种复杂现象,从深度和广度两个方面给出了钻杆的运动轨迹特征。以转速为分岔参数,分析了不同转速下钻杆的稳定性、分岔特性及涡动轨迹特征,发现了质量偏心对系统的增稳作用,实验结果验证了上述理论分析方法的正确性和有效性。
依据广义Hamilton原理研究了深孔加工多跨柔性回转钻杆系统横向振动的变分问题,在考虑剪切变形和转动惯量的前提下,建立了基于Timoshenko梁单元模型的多跨柔性回转钻杆横向振动的有限元模型。基于自由界面模态综合技术,提出了一种系统自由度缩减的方法。对实际深孔加工多跨柔性回转钻杆系统的分析结果表明,该降阶方法在保证非线性分析精度的前提下,可缩减钻杆系统大量的自由度数,有效地节约计算资源,可以满足大型复杂深孔加工装备的动力学设计需求,并获得了钻杆设计参数、钻杆长度和辅助支撑位置对钻杆系统固有频率的影响规律,得到了加工单孔和槽孔时不同钻杆转速及切削深度参数空间中钻杆运动的稳定区域、失稳边界和失稳方式。
建立了振动切削深孔加工多跨柔性回转钻杆系统的有限元模型,该模型在普通深孔钻杆模型的基础上,充分考虑了符合振动切削实际特点的钻杆轴向振动、内排屑切削液流体和振动切削力对钻杆的影响。在给定初始偏差量的情况下,分析了孔直线度误差与钻杆长度及辅助支撑位置的关系,获得了孔直线度随加工深度变化的规律,为深孔加工机床的精度设计和加工误差分析提供了依据。
The study on the drilling shaft system is increasingly emphasized due to the increasing demand on high efficiency, high precision and high reliability for metallurgical industry, nuclear power and ordnance industry. However, it is crucial content of nonlinear performance analysis of drilling shaft system to calculate the movement trajectories of the drilling shaft, nonlinear hydrodynamic forces and their Jacobians etc. efficiently without losing dynamic analysis precision due to complexity of the problem. The availability of various approaches such as analytical or numerical Euler-Bernoulli beam equation and empirical equation for solving the dynamic characteristic of drilling shaft just indicate that there is no universally accepted opinion on this point. Based on the relevant mathematical theory and previous research works, some key technologies are presented in this thesis for solving the rich and complex dynamic behaviors of drilling shaft system, the results can make a good reference for the dynamic design of drilling shaft system in practical drilling process and have important significance of the theory and engineering application.
The hydrodynamic pressure of cutting fluid in deep hole drilling was investigated. According to characteristics of Reynolds equation arising in cutting fluid to satisfy the finite length drilling shaft and taking approximate analytical pressure function as the basic solution, hydrodynamic pressure was modeled. The effects of parameters such as the rotational speed of drilling shaft and its whirling velocity, eccentric velocity etc., can be taken into consideration in the model of hydrodynamic pressure. By using the theoretical analysis and computation for the distribution rules of the hydrodynamic pressure as changing the structural and the moving parameters of drilling shaft, a quantitative elucidation of the dynamic characteristics of hydrodynamic pressure was implemented, and the whirling condition and instability of drilling shaft are discussed. Finally, the rules of selecting drilling shaft parameters are derived, so has significant guidance to the production.
The equivalent variational approach is proved by revising the variational form of Reynolds equation in hydrodynamic forces of cutting fluid with rupture boundary. Then, according to the physical character of cutting fluid, a revise variational form of Reynolds equation and its disturbed equation are formulated by using isoparametric finite element method with 8 nodal points. So, nonlinear hydrodynamic forces of cutting fluid and their Jacobian matrix are obtained simultaneously without increasing the computational costs. The applicable range and the approximate degree of the current model of nonlinear hydrodynamic forces are discussed by comparing the analytical model with finite element model of nonlinear hydrodynamic forces.
Based on the solving thought of traditional shooting method, the generalized shooting procedure is implemented, the period takes part in the iterations of the shooting method as a parameter. The iterations give the periodic orbit and its period simultaneously. The increments of the state variables and period T are selected for iterations using the optimization method, and then the periodic orbit and its period are determined rapidly. For the structural style of round hole and slot hole, the local stability and dynamic behaviors of periodic motion with the change of the drilling shaft design parameters value are obtained by combining the presented method of nonlinear hydrodynamic forces and their Jacobian matrix, improvement shoot method with Floquet theory. The rich and complex dynamic behaviors of the drilling shaft system are presented and further analyzed in depth and scope, such as periodic, quasi-periodic, jumped solution etc. The stability, bifurcation characteristics and whirling motion behaviors of drilling shaft system are analyzed when the rotating speed of drilling shaft is used as the bifurcation parameter. The effect of the increasing stability of eccentricity on the drilling shaft system is discovered Through the combination of theories with experiment, the correctness and effectiveness of the above methods are verified.
Based on the extended Hamilton principle, the variational problem of lateral vibration of drilling shaft system is deduced and the finite element model of lateral vibration of drilling shaft is established using Timoshenko element model. The shear deformation and rotary inertia are taken into account in the model of drilling system. Mode synthesis technique with free-interface is modified to represent a reduced method of degrees-of-freedom. The practical flexible deep-hole drilling shaft system with multi-support is used as subject to test the presented reduced method. The results show that the presented reduced method can reduce a large number of degrees-of-freedom of flexible drilling shaft system, effectively save the computational costs under the condition of maintain nonlinear analysis precision for the system, and may satisfy the dynamic design demand of the large-scale complex deep hole drilling machine. By using the theoretical analysis and computation, the natural frequency influence rules of the drilling shaft system as changing the structural parameters of drilling shaft and the relative distance of intermediate support are discussed. For the structural style of round hole and slot hole, the stable region, unstable boundary and unstable mode of drilling shaft system are analyzed under the different rotating speed and drilling depth parameter in drilling process.
The finite element model of drilling tool is established as flexible vibratory shaft with multi-support in deep hole drilling process. Considering the machining characteristic in vibrating drilling process, the axial vibration of drilling shaft containing flowing cutting fluid in pipe and vibrating cutting force are taken into account in the model of drilling system. Under the given initial value of pilot bush misalignment and the support misalignment, the relationship between the axial hole straightness deviation and cutting parameters as drilling shaft length and drilling depth is analyzed. Finally, the rules for change of the axial hole straightness deviation are derived with drilling length increasing, so provide a basis for the design of deep hole drilling machine and analysis of the errors of mechanical process.
依据实际深孔加工中非线性流体动压力应满足的物理条件,以近似解析解为基础,在研究钻杆转速、涡动速度及钻杆偏心率等因素影响的基础上,建立了有限长钻杆所承受的切削液流体动压模型。针对切削液非线性流体力的分析与计算,阐明了切削液非稳态流体的动压特性,并结合钻杆运动参数与结构设计参数等改变时对非线性切削液流体力分布变化规律的影响,揭示了切削液流体力引起钻杆涡动和失稳的力学机理,得出了对生产实践有指导意义的钻杆间隙系数及其选择准则。
证明了深孔加工切削液流体Reynolds方程的等价变分形式,运用变分约束原理,按照切削液流体的物理特性,形成了修正的Reynolds方程变分形式及其扰动方程。在不增加计算量的情况下,求得了非线性流体力及其Jacobian矩阵,并且使其具有相互协调一致的精度。通过深孔加工钻杆系统切削液非线性流体力解析模型与有限元数值计算模型的对比,获得了现有的非线性切削液流体力解析模型的适用范围和近似程度。
基于传统打靶法的求解思想,设计了一种将周期值作为参数一起参与打靶迭代的算法,通过优化确定迭代过程中的增量值。针对单孔和槽孔两种孔结构形式,将非线性切削液流体力及其Jacobian矩阵联合求解法与改进的打靶法及Floquet理论相结合,得到了不同加工参数条件下钻杆中心的运动轨迹,分析了包括伪周期、倍周期、跳跃等在内的各种复杂现象,从深度和广度两个方面给出了钻杆的运动轨迹特征。以转速为分岔参数,分析了不同转速下钻杆的稳定性、分岔特性及涡动轨迹特征,发现了质量偏心对系统的增稳作用,实验结果验证了上述理论分析方法的正确性和有效性。
依据广义Hamilton原理研究了深孔加工多跨柔性回转钻杆系统横向振动的变分问题,在考虑剪切变形和转动惯量的前提下,建立了基于Timoshenko梁单元模型的多跨柔性回转钻杆横向振动的有限元模型。基于自由界面模态综合技术,提出了一种系统自由度缩减的方法。对实际深孔加工多跨柔性回转钻杆系统的分析结果表明,该降阶方法在保证非线性分析精度的前提下,可缩减钻杆系统大量的自由度数,有效地节约计算资源,可以满足大型复杂深孔加工装备的动力学设计需求,并获得了钻杆设计参数、钻杆长度和辅助支撑位置对钻杆系统固有频率的影响规律,得到了加工单孔和槽孔时不同钻杆转速及切削深度参数空间中钻杆运动的稳定区域、失稳边界和失稳方式。
建立了振动切削深孔加工多跨柔性回转钻杆系统的有限元模型,该模型在普通深孔钻杆模型的基础上,充分考虑了符合振动切削实际特点的钻杆轴向振动、内排屑切削液流体和振动切削力对钻杆的影响。在给定初始偏差量的情况下,分析了孔直线度误差与钻杆长度及辅助支撑位置的关系,获得了孔直线度随加工深度变化的规律,为深孔加工机床的精度设计和加工误差分析提供了依据。
The study on the drilling shaft system is increasingly emphasized due to the increasing demand on high efficiency, high precision and high reliability for metallurgical industry, nuclear power and ordnance industry. However, it is crucial content of nonlinear performance analysis of drilling shaft system to calculate the movement trajectories of the drilling shaft, nonlinear hydrodynamic forces and their Jacobians etc. efficiently without losing dynamic analysis precision due to complexity of the problem. The availability of various approaches such as analytical or numerical Euler-Bernoulli beam equation and empirical equation for solving the dynamic characteristic of drilling shaft just indicate that there is no universally accepted opinion on this point. Based on the relevant mathematical theory and previous research works, some key technologies are presented in this thesis for solving the rich and complex dynamic behaviors of drilling shaft system, the results can make a good reference for the dynamic design of drilling shaft system in practical drilling process and have important significance of the theory and engineering application.
The hydrodynamic pressure of cutting fluid in deep hole drilling was investigated. According to characteristics of Reynolds equation arising in cutting fluid to satisfy the finite length drilling shaft and taking approximate analytical pressure function as the basic solution, hydrodynamic pressure was modeled. The effects of parameters such as the rotational speed of drilling shaft and its whirling velocity, eccentric velocity etc., can be taken into consideration in the model of hydrodynamic pressure. By using the theoretical analysis and computation for the distribution rules of the hydrodynamic pressure as changing the structural and the moving parameters of drilling shaft, a quantitative elucidation of the dynamic characteristics of hydrodynamic pressure was implemented, and the whirling condition and instability of drilling shaft are discussed. Finally, the rules of selecting drilling shaft parameters are derived, so has significant guidance to the production.
The equivalent variational approach is proved by revising the variational form of Reynolds equation in hydrodynamic forces of cutting fluid with rupture boundary. Then, according to the physical character of cutting fluid, a revise variational form of Reynolds equation and its disturbed equation are formulated by using isoparametric finite element method with 8 nodal points. So, nonlinear hydrodynamic forces of cutting fluid and their Jacobian matrix are obtained simultaneously without increasing the computational costs. The applicable range and the approximate degree of the current model of nonlinear hydrodynamic forces are discussed by comparing the analytical model with finite element model of nonlinear hydrodynamic forces.
Based on the solving thought of traditional shooting method, the generalized shooting procedure is implemented, the period takes part in the iterations of the shooting method as a parameter. The iterations give the periodic orbit and its period simultaneously. The increments of the state variables and period T are selected for iterations using the optimization method, and then the periodic orbit and its period are determined rapidly. For the structural style of round hole and slot hole, the local stability and dynamic behaviors of periodic motion with the change of the drilling shaft design parameters value are obtained by combining the presented method of nonlinear hydrodynamic forces and their Jacobian matrix, improvement shoot method with Floquet theory. The rich and complex dynamic behaviors of the drilling shaft system are presented and further analyzed in depth and scope, such as periodic, quasi-periodic, jumped solution etc. The stability, bifurcation characteristics and whirling motion behaviors of drilling shaft system are analyzed when the rotating speed of drilling shaft is used as the bifurcation parameter. The effect of the increasing stability of eccentricity on the drilling shaft system is discovered Through the combination of theories with experiment, the correctness and effectiveness of the above methods are verified.
Based on the extended Hamilton principle, the variational problem of lateral vibration of drilling shaft system is deduced and the finite element model of lateral vibration of drilling shaft is established using Timoshenko element model. The shear deformation and rotary inertia are taken into account in the model of drilling system. Mode synthesis technique with free-interface is modified to represent a reduced method of degrees-of-freedom. The practical flexible deep-hole drilling shaft system with multi-support is used as subject to test the presented reduced method. The results show that the presented reduced method can reduce a large number of degrees-of-freedom of flexible drilling shaft system, effectively save the computational costs under the condition of maintain nonlinear analysis precision for the system, and may satisfy the dynamic design demand of the large-scale complex deep hole drilling machine. By using the theoretical analysis and computation, the natural frequency influence rules of the drilling shaft system as changing the structural parameters of drilling shaft and the relative distance of intermediate support are discussed. For the structural style of round hole and slot hole, the stable region, unstable boundary and unstable mode of drilling shaft system are analyzed under the different rotating speed and drilling depth parameter in drilling process.
The finite element model of drilling tool is established as flexible vibratory shaft with multi-support in deep hole drilling process. Considering the machining characteristic in vibrating drilling process, the axial vibration of drilling shaft containing flowing cutting fluid in pipe and vibrating cutting force are taken into account in the model of drilling system. Under the given initial value of pilot bush misalignment and the support misalignment, the relationship between the axial hole straightness deviation and cutting parameters as drilling shaft length and drilling depth is analyzed. Finally, the rules for change of the axial hole straightness deviation are derived with drilling length increasing, so provide a basis for the design of deep hole drilling machine and analysis of the errors of mechanical process.
引文
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