运动纱线的动力学行为与控制
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摘要
运动纱线在纺织工业的生产实践中大量存在，随着纺织设备的高速化，其动力学特性对实际生产及产品质量的影响愈加明显。由于实际工程系统在高速运行时对外界因素的干扰比较敏感，任何外部扰动都可引起参数变化而导致参数振动。本文以纺织生产过程中的运动纱线作为工程背景，将其模型化为轴向运动弦线，应用理论建模、数值分析和实验验证相结合的手段，对其参激共振的稳定性及控制进行了较系统的研究。具体内容包括以下几个方面：
1.采用Kelvin模型描述粘弹性纱线的本构关系，对多种纱线进行拉伸试验和蠕变试验，得到蠕变回归方程，验证了模型的合理性，并由此得到运动纱线动力学模型中的相关粘弹性参数。在此基础上，得到实际生产过程中运动纱线的粘弹性参数。
2.利用广义Hamilton原理建立轴向变速运动粘弹性纱线横向振动的非线性动力学方程，将Galerkin离散法和多尺度法相结合，获得轴向运动粘弹性纱线在速度参数激励下发生共振的条件。分析了系统参数对参激共振幅值和幅频特性曲线的影响，数值模拟了主参激共振时的时间响应曲线和相轨迹。研究了纺丝和织前准备过程中可能发生的参激共振现象。
3.作为Kelvin模型的退化，分析了运动均质纱线线性参激共振的不稳定区间。设计速度反馈控制来抑制纱线的横向振动，从幅频特性曲线和时域响应曲线上对系统控制效果进行仿真分析，证实了控制策略的可行性。通过滑模控制和参数控制相结合，利用所构造的Lyapunov函数设计张力的变化规律达到控制纱线振动的目的，用有限差分法对纱线共振状态和控制效果进行了数值模拟。为了有效地消除滑模控制中控制力的抖振，设计模糊滑模控制器对粘弹性纱线的横向振动进行控制，通过Matlab仿真分析证明了系统的渐进稳定性和控制规律的鲁棒性。
4.搭建实验平台，通过实验研究轴向运动纱线的参激共振与控制。为了便于信号的检测与控制，以不锈钢箔带替代纱线作为运动介质。实验装置由机械部分、测量部分和控制部分组成。设计以微控制器LPC1768为核心的三相无刷直流电机转速控制系统，实现运行速度的近似简谐规律变化特性。设计运动带的横向振动控制系统，以数字信号控制器TMS320F28335为基础实现了模糊滑模算法。
5.在所设计的轴向运动带的实验装置上，利用虚拟仪器LabVIEW设计的检测分析系统完成对电机转速信号和运动带横向振动信号的实时检测与分析，对轴向运动带的参激共振现象及其控制进行了实验研究。分别研究了当系统固有频率为1Hz和2Hz时系统发生的参激共振现象，并在共振状态下利用所设计的振动控制器对其横向振动施加控制，实验结果验证了参数激励对横向振动的影响以及所设计的控制方案的有效性。
There commonly exist the moving yarns in the production process of textile industry.With the high-speed of textile equipment, the effect on the practical production and productquality becomes more obvious for the dynamic behaviors of moving yarns. The highlyrunning engineering system is very sensitive to foreign interferences, any of which willcause parametrical excitation and consequent parametric vibration. In the engineeringscenario, the moving yarn in the textile production process is modeled as an axiallymoving string. This dissertation focuses on the systematic and intensive research on thestability and control of the parametric resonant with the combination of theoreticalmodeling, numeric analysis and experiment verification. The main respects of the researchare listed as follows:
1. The dynamic behaviors of the moving yarn are discussed and the Kelvin model isused to describe the constitutive relation of the viscoelastic yarn. Tensile tests and creeptests are conducted on various yarns. The regression equation of yarn creep is establishedand the model’s rationality is verified. The corresponding viscoelastic parameters areobtained for the dynamic model of moving yarn，and so are viscoelastic parameters ofyarns in the production process.
2. The nonlinear dynamic equation is established for the transverse vibration of anaxially moving viscoelastic yarn using the generalized Hamilton principle. By means ofcombining the Galerkin approach and the multi-scale method, the resonant condition forthe axially moving viscoelastic yarn under the speed excitation is found.How systemparameters affect resonant amplitude and the amplitude-frequency characteristic curve isanalyzed. The time response curves and phase trajectories in resonance region arenumerically simulated. Researches are investigated on the parametric resonance whichmay occur during the spinning process and weaving preparation process.
3. As a special case, dynamics of homogeneous yarn is studied. The unstable intervalof linear parametric resonance for moving yarn is analyzed. The transverse vibration is suppressed by the speed feedback, and the control effect is simulated. The feasibility of thecontrol scheme is proved. The vibration of a yarn is controlled by combining sliding-modecontrol and parameter control, and by the tensile force whose change rule is designed byLyapunov function. The vibrating state of the yarn and the control effect are simulated bythe finite difference method. In order to remove effectively the buffet of the controllingforce under the sliding-mode control, a fuzzy sliding-mode controller is designed to controlthe transverse vibration of the viscoelastic yarn. The simulation results demonstrate theasymptotic stability and robustness of the system.
4. The test set-up is designed for signal detection and control, where the stainlesssteel foil is replaced as a moving belt so that the parametric resonance and control of theaxially moving yarn can be experimentally studied. The test system is composed of themechanical, measurement and control components. The speed governing system ofbrushless DC motor uses microcontroller LPC1768as the core and the approximateharmonic speed is produced. The control system of transverse vibration for the moving beltis designed and the fuzzy sliding-mode algorithm is implemented on the digital signalcontroller TMS320F28335.
5. With the help of the designed test set-up, the system based on LabVIEW isdesigned to accomplish the real time detection and analysis for the speed of motor and thetransverse vibration of the moving belt. The parametric resonance and control of theaxially moving belt are tested. The phenomenon of parametric resonance is analyzed whenthe inherent frequency of system is1Hz and2Hz, respectively. The experimental resultsverify the effect of parametric excitation on the transverse vibration and verify the validityof the designed controller.
1.采用Kelvin模型描述粘弹性纱线的本构关系，对多种纱线进行拉伸试验和蠕变试验，得到蠕变回归方程，验证了模型的合理性，并由此得到运动纱线动力学模型中的相关粘弹性参数。在此基础上，得到实际生产过程中运动纱线的粘弹性参数。
2.利用广义Hamilton原理建立轴向变速运动粘弹性纱线横向振动的非线性动力学方程，将Galerkin离散法和多尺度法相结合，获得轴向运动粘弹性纱线在速度参数激励下发生共振的条件。分析了系统参数对参激共振幅值和幅频特性曲线的影响，数值模拟了主参激共振时的时间响应曲线和相轨迹。研究了纺丝和织前准备过程中可能发生的参激共振现象。
3.作为Kelvin模型的退化，分析了运动均质纱线线性参激共振的不稳定区间。设计速度反馈控制来抑制纱线的横向振动，从幅频特性曲线和时域响应曲线上对系统控制效果进行仿真分析，证实了控制策略的可行性。通过滑模控制和参数控制相结合，利用所构造的Lyapunov函数设计张力的变化规律达到控制纱线振动的目的，用有限差分法对纱线共振状态和控制效果进行了数值模拟。为了有效地消除滑模控制中控制力的抖振，设计模糊滑模控制器对粘弹性纱线的横向振动进行控制，通过Matlab仿真分析证明了系统的渐进稳定性和控制规律的鲁棒性。
4.搭建实验平台，通过实验研究轴向运动纱线的参激共振与控制。为了便于信号的检测与控制，以不锈钢箔带替代纱线作为运动介质。实验装置由机械部分、测量部分和控制部分组成。设计以微控制器LPC1768为核心的三相无刷直流电机转速控制系统，实现运行速度的近似简谐规律变化特性。设计运动带的横向振动控制系统，以数字信号控制器TMS320F28335为基础实现了模糊滑模算法。
5.在所设计的轴向运动带的实验装置上，利用虚拟仪器LabVIEW设计的检测分析系统完成对电机转速信号和运动带横向振动信号的实时检测与分析，对轴向运动带的参激共振现象及其控制进行了实验研究。分别研究了当系统固有频率为1Hz和2Hz时系统发生的参激共振现象，并在共振状态下利用所设计的振动控制器对其横向振动施加控制，实验结果验证了参数激励对横向振动的影响以及所设计的控制方案的有效性。
There commonly exist the moving yarns in the production process of textile industry.With the high-speed of textile equipment, the effect on the practical production and productquality becomes more obvious for the dynamic behaviors of moving yarns. The highlyrunning engineering system is very sensitive to foreign interferences, any of which willcause parametrical excitation and consequent parametric vibration. In the engineeringscenario, the moving yarn in the textile production process is modeled as an axiallymoving string. This dissertation focuses on the systematic and intensive research on thestability and control of the parametric resonant with the combination of theoreticalmodeling, numeric analysis and experiment verification. The main respects of the researchare listed as follows:
1. The dynamic behaviors of the moving yarn are discussed and the Kelvin model isused to describe the constitutive relation of the viscoelastic yarn. Tensile tests and creeptests are conducted on various yarns. The regression equation of yarn creep is establishedand the model’s rationality is verified. The corresponding viscoelastic parameters areobtained for the dynamic model of moving yarn，and so are viscoelastic parameters ofyarns in the production process.
2. The nonlinear dynamic equation is established for the transverse vibration of anaxially moving viscoelastic yarn using the generalized Hamilton principle. By means ofcombining the Galerkin approach and the multi-scale method, the resonant condition forthe axially moving viscoelastic yarn under the speed excitation is found.How systemparameters affect resonant amplitude and the amplitude-frequency characteristic curve isanalyzed. The time response curves and phase trajectories in resonance region arenumerically simulated. Researches are investigated on the parametric resonance whichmay occur during the spinning process and weaving preparation process.
3. As a special case, dynamics of homogeneous yarn is studied. The unstable intervalof linear parametric resonance for moving yarn is analyzed. The transverse vibration is suppressed by the speed feedback, and the control effect is simulated. The feasibility of thecontrol scheme is proved. The vibration of a yarn is controlled by combining sliding-modecontrol and parameter control, and by the tensile force whose change rule is designed byLyapunov function. The vibrating state of the yarn and the control effect are simulated bythe finite difference method. In order to remove effectively the buffet of the controllingforce under the sliding-mode control, a fuzzy sliding-mode controller is designed to controlthe transverse vibration of the viscoelastic yarn. The simulation results demonstrate theasymptotic stability and robustness of the system.
4. The test set-up is designed for signal detection and control, where the stainlesssteel foil is replaced as a moving belt so that the parametric resonance and control of theaxially moving yarn can be experimentally studied. The test system is composed of themechanical, measurement and control components. The speed governing system ofbrushless DC motor uses microcontroller LPC1768as the core and the approximateharmonic speed is produced. The control system of transverse vibration for the moving beltis designed and the fuzzy sliding-mode algorithm is implemented on the digital signalcontroller TMS320F28335.
5. With the help of the designed test set-up, the system based on LabVIEW isdesigned to accomplish the real time detection and analysis for the speed of motor and thetransverse vibration of the moving belt. The parametric resonance and control of theaxially moving belt are tested. The phenomenon of parametric resonance is analyzed whenthe inherent frequency of system is1Hz and2Hz, respectively. The experimental resultsverify the effect of parametric excitation on the transverse vibration and verify the validityof the designed controller.
引文
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