大惯量进给系统动力学特性及其稳定性研究
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摘要
大惯量滚珠丝杠系统是高速、重载、高精度数控机床进给系统中的关键功能部件,是一个多自由度阻尼系统。由于滚珠丝杠的细长中空杆特殊结构,以及丝杠两端不同的支承形式的影响,高速旋转的大惯量滚珠丝杠系统实际上是一个非线性动力学系统,这一观点已得到很多学者认同。目前主流的滚珠丝杠系统的研究工作大部分均基于线性振动的理论来考查进给系统的纵向、横向及扭转振动,忽略了非线性因素的影响,使得理论研究结果与实验结论相较存在较大偏差。当机床进行强力切削、高速切削、难加工材料切削时,或刀具、夹具、工件结构相对复杂时,都会对系统产生各阶频率的激励,使系统的运动状态发生分岔,有可能进入混沌状态。故本论文将在系统线性振动的基础上主要研究大惯量高转速滚珠丝杠的非线性动力学特性。
论文以数控机床进给系统为对象,采用“理论推导—仿真分析—实验验证”的研究方法,主要研究工作包括以下几方面：
利用拉格朗日方程建立进给系统的线性振动模型,辨识影响系统惯量的四个参数,利用正交试验分析主要部件刚度系数和惯量参数对工作台定位精度的影响程度。
分析了滚珠丝杠的支承方式,考虑滚珠丝杠的振动,建立丝杠在弹性支承条件下振动的频率方程和振型函数。采用Timoshenko梁模型,考虑剪切变形、转动惯量和预拉伸力的影响,以及丝杠大导程、大长径比的结构特征,提出滚珠丝杠副的动态刚度呈非线性特性变化,并在理论推导过程中合理简化,建立丝杠的刚度非线性方程。采用林滋-庞加莱法求解方程的近似解析解,通过数值仿真,研究动力学方程的分岔和混沌特征；并分析非线性系统的运动稳定性,找出进给系统动力学特性与系统参数的关系和匹配规律。
由Stribeck摩擦理论和摩擦模型,对摩擦力的非线性特征进行了研究,提出了非线性摩擦力的变化规律在Stribeck摩擦曲线的四个特性区间内的非线性摩擦力的响应分别遵从不同的规律。建立考虑摩擦非线性因素的动力学方程,对方程进行近似解析解分析,通过数值仿真与参数辨识,对非线性系统进行分岔与混沌特征分析。同时考虑弹簧力和摩擦阻尼的非线性作用,即考虑刚度-摩擦耦合非线性动态特性,建立耦合非线性结构模型。对其响应进行数值仿真分析,通过改变相关参数,研究耦合系统的分岔与混沌特征。
以单轴数控铣床为基础,搭建滚珠丝杠副动态特性测试实验台进行实验研究,对采集的加速度时间序列进行一系列分析,作出进给系统动态特性的非线性判断,从不同角度验证理论分析结论的有效性。在一台卧式加工中心上进行进给系统振动实验,得出惯量参数、丝杠与螺母接触刚度、工作台与导轨接触刚度的变化对滚珠丝杠、工作台上刀具作用点纵、横向及扭转振动的影响趋势,验证理论分析。
根据理论分析和实验研究所得的结果,提出Hopf分岔与混沌运动的控制策略,分析非线性刚度和摩擦因素的影响与抑制措施,从控制策略的优化和机械装置的改进等方面探讨了控制措施的有效性。
The ball screw system of big inertia is the key function components of the feed system of high speed, high precision and heavy CNC machine tools, is a damping system of multiple-degree of freedom. Because of the thin and hollow bar of the ball screw special structure, and the influence of different support form of both ends of a ball screw, the ball screw system in high speed rotating is actually a nonlinear dynamic system, this view has been identified by many scholars. At present the research work of mainstream of the ball screw system are mostly based on the theory of linear vibration to check into the vertical, horizontal and torsional vibration a the system, ignore the nonlinear factors, makes the large deviation compared with the theoretical results and experimental conclusion. When the machine tool put up the strong cutting, and high-speed cutting, cutting difficult-to-machine materials, or the structure of cutting tools, fixture, workpiece are relative complex, it's going to produce the incentive of various order of frequency, make the state of motion of system happen bifurcation, may enter chaos state. So this article will be main research the nonlinear dynamic behavior of the ball screw in big inertia at high speed based on the linear vibration of system.
This subject adopts the research approaches of "theory derivation-simulation analysis-experiment test" to promote the research for the feeding system of numerical control machine. It mainly includes the following aspects:
First of all, by the use of Lagrange equation to establish linear vibration model of feed system, identificated the four parameters that influent the system inertia, the orthogonal test are used to analysis the influence degree of the stiffness coefficient and inertia parameters to the positioning accuracy of the table.
The study focuses on the nonlinear characteristic of the stiffness based on the ball screw's four supporting scheme, so the dynamic stiffness of ball screw pair is changed with nonlinear characteristics, and make reasonable simplify in the process of theoretical derivation, then identify the stiffness nonlinear dynamics equation of the small errors. The L-P method is used to solve the approximate analytical solution of the equations and compared with the result of numerical simulation with MATLAB; Draw the phase diagram, bifurcation diagram, Poincare section graph, etc, study the chaos characteristics and regularity of the dynamic equation. Focuses on the analysis of the nonlinear systems movement stability and the bifurcation and chaos characteristics of system, and find out the relationship and match rule between the dynamics characteristic and the system parameters of the feeding system.
Then, this paper introduces the Stribeck friction theory and friction model. The nonlinear characteristic of the friction was detailed discussed. It present that the changing law of nonlinear friction in the four characteristics of Stribeck friction curve, the response of nonlinear friction within the range comply with the different laws respectively. The dynamic equation of nonlinear was set up consider friction factors, and was given the analytical solution analysis, numerical simulation and parameter identification. Further through the bifurcation diagram and Poincare section graph, the bifurcation and chaos characteristics were analysised of the nonlinear system.After that, taking into account the nonlinear function of spring force and friction damping in the meantime, that is considering the nonlinear dynamic characteristics of friction coupling stiffness, establish dynamics equation, thus identify coupling nonlinear structure model. The approximate analytical solution of the equation was solved, and the numerical simulation analysis to the response, and programming with the software MAPLE, by changing the related parameters, study the bifurcation and chaos characteristics of the coupled system.
As the foundation of the feeding system of single axis CNC milling machine and horizontal processing center, set up the experiments table for testing the dynamic characteristics of ball screw vice. Make a series of analysis for the collecting the acceleration time series, make the nonlinear judgment of the dynamic property of the system, and checking the effectiveness of the conclusion of the theoretical analysis from different angles. In a horizontal machining center, the vibration experiments were conducted of the feed system. It conclude that the trend that the changes of the inertia parameters, screw and nut contact stiffness, table and rail contact stiffness influence on the longitudinal, transverse and torsional vibration of ball screw and the tool working point. So the theoretical analyse of second chapter were validated.
Finally, according to the results of theory analysis and experimental research, this paper puts forward the control strategy of Hopf bifurcation and chaos movement, and analyze the influence and control measures of nonlinear stiffness and friction factors, and discussed the effectiveness of the control measures from the optimization of the control strategy and improvement of the mechanical device of the CNC machine tools.
论文以数控机床进给系统为对象,采用“理论推导—仿真分析—实验验证”的研究方法,主要研究工作包括以下几方面：
利用拉格朗日方程建立进给系统的线性振动模型,辨识影响系统惯量的四个参数,利用正交试验分析主要部件刚度系数和惯量参数对工作台定位精度的影响程度。
分析了滚珠丝杠的支承方式,考虑滚珠丝杠的振动,建立丝杠在弹性支承条件下振动的频率方程和振型函数。采用Timoshenko梁模型,考虑剪切变形、转动惯量和预拉伸力的影响,以及丝杠大导程、大长径比的结构特征,提出滚珠丝杠副的动态刚度呈非线性特性变化,并在理论推导过程中合理简化,建立丝杠的刚度非线性方程。采用林滋-庞加莱法求解方程的近似解析解,通过数值仿真,研究动力学方程的分岔和混沌特征；并分析非线性系统的运动稳定性,找出进给系统动力学特性与系统参数的关系和匹配规律。
由Stribeck摩擦理论和摩擦模型,对摩擦力的非线性特征进行了研究,提出了非线性摩擦力的变化规律在Stribeck摩擦曲线的四个特性区间内的非线性摩擦力的响应分别遵从不同的规律。建立考虑摩擦非线性因素的动力学方程,对方程进行近似解析解分析,通过数值仿真与参数辨识,对非线性系统进行分岔与混沌特征分析。同时考虑弹簧力和摩擦阻尼的非线性作用,即考虑刚度-摩擦耦合非线性动态特性,建立耦合非线性结构模型。对其响应进行数值仿真分析,通过改变相关参数,研究耦合系统的分岔与混沌特征。
以单轴数控铣床为基础,搭建滚珠丝杠副动态特性测试实验台进行实验研究,对采集的加速度时间序列进行一系列分析,作出进给系统动态特性的非线性判断,从不同角度验证理论分析结论的有效性。在一台卧式加工中心上进行进给系统振动实验,得出惯量参数、丝杠与螺母接触刚度、工作台与导轨接触刚度的变化对滚珠丝杠、工作台上刀具作用点纵、横向及扭转振动的影响趋势,验证理论分析。
根据理论分析和实验研究所得的结果,提出Hopf分岔与混沌运动的控制策略,分析非线性刚度和摩擦因素的影响与抑制措施,从控制策略的优化和机械装置的改进等方面探讨了控制措施的有效性。
The ball screw system of big inertia is the key function components of the feed system of high speed, high precision and heavy CNC machine tools, is a damping system of multiple-degree of freedom. Because of the thin and hollow bar of the ball screw special structure, and the influence of different support form of both ends of a ball screw, the ball screw system in high speed rotating is actually a nonlinear dynamic system, this view has been identified by many scholars. At present the research work of mainstream of the ball screw system are mostly based on the theory of linear vibration to check into the vertical, horizontal and torsional vibration a the system, ignore the nonlinear factors, makes the large deviation compared with the theoretical results and experimental conclusion. When the machine tool put up the strong cutting, and high-speed cutting, cutting difficult-to-machine materials, or the structure of cutting tools, fixture, workpiece are relative complex, it's going to produce the incentive of various order of frequency, make the state of motion of system happen bifurcation, may enter chaos state. So this article will be main research the nonlinear dynamic behavior of the ball screw in big inertia at high speed based on the linear vibration of system.
This subject adopts the research approaches of "theory derivation-simulation analysis-experiment test" to promote the research for the feeding system of numerical control machine. It mainly includes the following aspects:
First of all, by the use of Lagrange equation to establish linear vibration model of feed system, identificated the four parameters that influent the system inertia, the orthogonal test are used to analysis the influence degree of the stiffness coefficient and inertia parameters to the positioning accuracy of the table.
The study focuses on the nonlinear characteristic of the stiffness based on the ball screw's four supporting scheme, so the dynamic stiffness of ball screw pair is changed with nonlinear characteristics, and make reasonable simplify in the process of theoretical derivation, then identify the stiffness nonlinear dynamics equation of the small errors. The L-P method is used to solve the approximate analytical solution of the equations and compared with the result of numerical simulation with MATLAB; Draw the phase diagram, bifurcation diagram, Poincare section graph, etc, study the chaos characteristics and regularity of the dynamic equation. Focuses on the analysis of the nonlinear systems movement stability and the bifurcation and chaos characteristics of system, and find out the relationship and match rule between the dynamics characteristic and the system parameters of the feeding system.
Then, this paper introduces the Stribeck friction theory and friction model. The nonlinear characteristic of the friction was detailed discussed. It present that the changing law of nonlinear friction in the four characteristics of Stribeck friction curve, the response of nonlinear friction within the range comply with the different laws respectively. The dynamic equation of nonlinear was set up consider friction factors, and was given the analytical solution analysis, numerical simulation and parameter identification. Further through the bifurcation diagram and Poincare section graph, the bifurcation and chaos characteristics were analysised of the nonlinear system.After that, taking into account the nonlinear function of spring force and friction damping in the meantime, that is considering the nonlinear dynamic characteristics of friction coupling stiffness, establish dynamics equation, thus identify coupling nonlinear structure model. The approximate analytical solution of the equation was solved, and the numerical simulation analysis to the response, and programming with the software MAPLE, by changing the related parameters, study the bifurcation and chaos characteristics of the coupled system.
As the foundation of the feeding system of single axis CNC milling machine and horizontal processing center, set up the experiments table for testing the dynamic characteristics of ball screw vice. Make a series of analysis for the collecting the acceleration time series, make the nonlinear judgment of the dynamic property of the system, and checking the effectiveness of the conclusion of the theoretical analysis from different angles. In a horizontal machining center, the vibration experiments were conducted of the feed system. It conclude that the trend that the changes of the inertia parameters, screw and nut contact stiffness, table and rail contact stiffness influence on the longitudinal, transverse and torsional vibration of ball screw and the tool working point. So the theoretical analyse of second chapter were validated.
Finally, according to the results of theory analysis and experimental research, this paper puts forward the control strategy of Hopf bifurcation and chaos movement, and analyze the influence and control measures of nonlinear stiffness and friction factors, and discussed the effectiveness of the control measures from the optimization of the control strategy and improvement of the mechanical device of the CNC machine tools.
引文
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