轧机主传动扭振系统失稳振荡行为与控制方法研究
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摘要
轧机主传动系统是轧钢机的重要组成部分,随着轧制速度的一再提高轧机主传动系统的扭转振动现象日益突出。轧机发生扭振时会影响到产品的质量和产量,严重时甚至会对轧制设备造成破坏性损害,因此轧机主传动系统的扭振问题对于现代钢铁行业具有重要的研究价值。
轧机主传动系统由多个弹性部件构成,轧制能量在轴系的传输过程中由于轧制条件的变化会激发主传动系统的扭转振荡,本文从扭振系统建模、稳定性分析以及扭振控制三个方面对线性、非线性以及耦合非线性扭振系统展开系统研究,用解析的方法给出扭振系统的失稳振荡规律以及控制策略,推动轧机振动理论及工程应用的进一步发展。
基于广义耗散系统Lagrange原理,建立线性扭振系统模型,并考虑传动系统中结构阻尼、扭转刚度以及摩擦阻尼的非线性形式建立非线性和耦合非线性轧机扭振系统动力学方程;针对普遍采用交流电机驱动实际情况,引入交流电机的气隙磁场能,建立高维的机电耦合扭振系统动力学方程,为进一步揭示扭振系统失稳振荡规律以及控制策略的制定提供理论依据。
分析所建立线性扭振系统的稳定性并给出诱发轴系产生扭振的主要原因,运用H∞理论讨论线性扭振系统在外扰作用下和模型参数摄动时的鲁棒稳定性,通过对H∞混合灵敏度函数的研究,给出改进H_∞算法的扭振控制器,避免了权函数选取的繁琐过程。
运用Hopf分岔理论研究已建非线性轧机扭振系统的分岔现象,并给出Hopf分岔发生的代数判据以及扭振系统的失稳振荡振动形式;综合运用多尺度和谐波平衡法对高维机电耦合扭振系统进行降维,研究电气参数扰动下机电扭振系统出现的双Hopf分岔现象及周期运动的稳定性,揭示了轧机扭振系统的失稳条件和振动规律。
为避免破坏性较强的亚临界分岔对扭振系统的危害,研究含非线性摩阻、耦合非线性刚度和机电耦合扭振系统的分岔控制方法,给出非线性状态反馈控制器,用以转移分岔点和控制周期运动的稳定,同时应用规范形理论给出周期运动幅值计算解析式,实现周期运动的幅值控制;研究含非线性刚度和耦合非线性阻尼扭振系统的时滞反馈控制,采用频域分析法明确线性项延迟时间与分岔点的解析关系,并基于中心流形理论研究非线性项延迟时间对周期运动的稳定性影响,控制周期运动的稳定性,以上方法为工程中解决轧机系统的失稳振荡提供有效的解决办法。
设计轧机扭振模拟测试与控制系统,在扭振实验平台上验证文中所述的非线性条件下主传动系统的扭振现象,并通过变频调速方式验证文中所提出扭振控制方法的有效性。
The main drive system is one of the most important parts in rolling mills, and the torsional vibration is more outstanding with the rolling speed improving. The steel products’quality and yield are obviously influenced when the torsional vibration occurred in rolling mills, further more, the rolling equipments can also be destroyed, so the research about the torsional vibration is very significant for modern steel industries.
The main drive system of rolling mill is consists of some elastic units, and the spindles can be induced vibration while the energy of rolling is transferred. The linear model, nonlinear model and coupled nonlinear systems are studied for their model, stability and control in this paper. The rule of unstable vibration and control method are analytically given, and theory of rolling mill’s vibration and its application in engineering are improved.
Nonlinear stiffness, structure damping and friction damping are considered, and the dynamics equations are established according to Lagrange theory. The magnetic energy of air gas in AC motor is included, and high dimensional coupled dynamics equations can be established on the basic of Lagrange-Maxwell principle. Above all these works can provide effective models for the dynamics performance analysis and control methods.
The stability of linear torsional vibration system in rolling mill is analysed according to Lyapunov theory, and it is studied that causes the main spindle vibrate. Robust and robust stability are also studied based on H∞theory, and an improved H∞control method is proposed through the research for H∞mixed sensitivity function and the robust performance.
Using the Hopf theory, the bifurcation is studied for obtained nonlinear torsional vibration systems of rolling mill, and it is given that necessary and sufficient condition of Hopf and the type of unstable vibration. Using multiple time scales and harmonic balance method, the dimension of electromechanical coupling system can be deduced, and double Hopf bifurcation and stability of periodic motion are studied while the system is disturbed by electronic parameters, at the same time the condition of unstable vibration and vibration character can be revealed.
To avoid subcritical bifurcation, the bifurcation control method is studied in some torsional vibration system who has nonlinear damping, coupled nonlinear stiffness or electromechanical coupled parameters, and a nonlinear feedback controller is proposed in order to transfer the bifurcation point and make the periodic motion stable, and the amplitude of periodic motion can also be controlled by obtained normal form; A delay nonlinear control method is studied in some typical systems which include nonlinear stiffness, coupled nonlinear stiffness or coupled nonlinear damping. It is studied how the delay time in linear feedback parameter influence Hopf bifurcation point by frequency-domain analysis, and the stability of periodic motion can be controlled through the research for the relation between stability and nonlinear delay time and these research can provide an effective method against unstable vibration in engineering.
A measure and control system is constructed about the rotary machine, and some conclusions are validated under the condition of nonlinear factors considered with the aid of torsional vibration platform, and control method can also be validated through the frequency control.
轧机主传动系统由多个弹性部件构成,轧制能量在轴系的传输过程中由于轧制条件的变化会激发主传动系统的扭转振荡,本文从扭振系统建模、稳定性分析以及扭振控制三个方面对线性、非线性以及耦合非线性扭振系统展开系统研究,用解析的方法给出扭振系统的失稳振荡规律以及控制策略,推动轧机振动理论及工程应用的进一步发展。
基于广义耗散系统Lagrange原理,建立线性扭振系统模型,并考虑传动系统中结构阻尼、扭转刚度以及摩擦阻尼的非线性形式建立非线性和耦合非线性轧机扭振系统动力学方程;针对普遍采用交流电机驱动实际情况,引入交流电机的气隙磁场能,建立高维的机电耦合扭振系统动力学方程,为进一步揭示扭振系统失稳振荡规律以及控制策略的制定提供理论依据。
分析所建立线性扭振系统的稳定性并给出诱发轴系产生扭振的主要原因,运用H∞理论讨论线性扭振系统在外扰作用下和模型参数摄动时的鲁棒稳定性,通过对H∞混合灵敏度函数的研究,给出改进H_∞算法的扭振控制器,避免了权函数选取的繁琐过程。
运用Hopf分岔理论研究已建非线性轧机扭振系统的分岔现象,并给出Hopf分岔发生的代数判据以及扭振系统的失稳振荡振动形式;综合运用多尺度和谐波平衡法对高维机电耦合扭振系统进行降维,研究电气参数扰动下机电扭振系统出现的双Hopf分岔现象及周期运动的稳定性,揭示了轧机扭振系统的失稳条件和振动规律。
为避免破坏性较强的亚临界分岔对扭振系统的危害,研究含非线性摩阻、耦合非线性刚度和机电耦合扭振系统的分岔控制方法,给出非线性状态反馈控制器,用以转移分岔点和控制周期运动的稳定,同时应用规范形理论给出周期运动幅值计算解析式,实现周期运动的幅值控制;研究含非线性刚度和耦合非线性阻尼扭振系统的时滞反馈控制,采用频域分析法明确线性项延迟时间与分岔点的解析关系,并基于中心流形理论研究非线性项延迟时间对周期运动的稳定性影响,控制周期运动的稳定性,以上方法为工程中解决轧机系统的失稳振荡提供有效的解决办法。
设计轧机扭振模拟测试与控制系统,在扭振实验平台上验证文中所述的非线性条件下主传动系统的扭振现象,并通过变频调速方式验证文中所提出扭振控制方法的有效性。
The main drive system is one of the most important parts in rolling mills, and the torsional vibration is more outstanding with the rolling speed improving. The steel products’quality and yield are obviously influenced when the torsional vibration occurred in rolling mills, further more, the rolling equipments can also be destroyed, so the research about the torsional vibration is very significant for modern steel industries.
The main drive system of rolling mill is consists of some elastic units, and the spindles can be induced vibration while the energy of rolling is transferred. The linear model, nonlinear model and coupled nonlinear systems are studied for their model, stability and control in this paper. The rule of unstable vibration and control method are analytically given, and theory of rolling mill’s vibration and its application in engineering are improved.
Nonlinear stiffness, structure damping and friction damping are considered, and the dynamics equations are established according to Lagrange theory. The magnetic energy of air gas in AC motor is included, and high dimensional coupled dynamics equations can be established on the basic of Lagrange-Maxwell principle. Above all these works can provide effective models for the dynamics performance analysis and control methods.
The stability of linear torsional vibration system in rolling mill is analysed according to Lyapunov theory, and it is studied that causes the main spindle vibrate. Robust and robust stability are also studied based on H∞theory, and an improved H∞control method is proposed through the research for H∞mixed sensitivity function and the robust performance.
Using the Hopf theory, the bifurcation is studied for obtained nonlinear torsional vibration systems of rolling mill, and it is given that necessary and sufficient condition of Hopf and the type of unstable vibration. Using multiple time scales and harmonic balance method, the dimension of electromechanical coupling system can be deduced, and double Hopf bifurcation and stability of periodic motion are studied while the system is disturbed by electronic parameters, at the same time the condition of unstable vibration and vibration character can be revealed.
To avoid subcritical bifurcation, the bifurcation control method is studied in some torsional vibration system who has nonlinear damping, coupled nonlinear stiffness or electromechanical coupled parameters, and a nonlinear feedback controller is proposed in order to transfer the bifurcation point and make the periodic motion stable, and the amplitude of periodic motion can also be controlled by obtained normal form; A delay nonlinear control method is studied in some typical systems which include nonlinear stiffness, coupled nonlinear stiffness or coupled nonlinear damping. It is studied how the delay time in linear feedback parameter influence Hopf bifurcation point by frequency-domain analysis, and the stability of periodic motion can be controlled through the research for the relation between stability and nonlinear delay time and these research can provide an effective method against unstable vibration in engineering.
A measure and control system is constructed about the rotary machine, and some conclusions are validated under the condition of nonlinear factors considered with the aid of torsional vibration platform, and control method can also be validated through the frequency control.
引文
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