轧机非线性振动建模及其动力学特性研究
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摘要
轧钢机是现代钢铁工业中关键和核心装备之一。近年来，随着现代钢铁工业向着大型化、高荷载、高速化方向发展，轧制过程中非线性因素日益增多，使得轧机在某种轧制条件或轧制过程参数扰动下，诱发不同程度的非线性振动问题。轧机振动问题一直是困扰钢铁企业的重大技术难题，传动系统和机座系统频繁发生的振动不仅影响轧制生产的稳定运行，降低轧制产品的质量及生产效率，剧烈的振动还会导致轧制设备的瞬时破坏，造成巨大的经济损失。因此为了提高轧制生产率和产品质量、降低轧制成本，亟需对轧机非线性振动的特性及其振动形成机制进行深入理论分析。
本文在国家十一五重大攻关课题“大型冷连轧成套装备关键技术研究与示范应用(批准号：2007BAF02B10)”和河北省自然科学基金“轧机传动系统扭振非线性动力学行为研究(批准号：F2008000882)”的资助下，考虑轧机轧制过程中非线性摩擦阻尼、滞后、分段等非线性因素，采用非线性振动理论研究轧机在非线性因素及外部激励下的动态响应，分析轧机的共振和分岔特性，从系统的内在联系上研究了非线性因素对轧机振动的影响，为进一步揭示轧机非线性振动机理及特性提供理论依据。
基于广义耗散系统Lagrange原理，分别考虑轧机传动系统在轧制过程中轧辊端受到的非线性摩擦阻尼、传动系统中滞后弹性力等非线性因素，建立了轧机传动系统的非线性扭振动力学模型；考虑轧机传动系统的连续分布质量，建立了轧机传动系统的连续扭振动力学模型，并研究了存在间隙时非线性连续扭振模型。
根据轧机的结构及受力特点，以机架中轧辊为研究对象，分别考虑机架与轧辊间分段非线性刚度、含三次项非线性刚度以及非线性阻尼影响，建立了辊系的非线性垂直振动动力学模型，为进一步分析轧机非线性动力学特性提供理论模型。
运用渐近法和平均法求解轧机非线性振动系统在自由振动和受外部周期激励下动态响应的解析近似解。在求解轧机非线性振动系统动态响应解的基础上，构造系统在主共振、超谐共振以及亚谐共振时的幅频特性方程，研究非线性参数对系统共振特性的影响，得到轧机的共振特征及动力学响应规律。
应用奇点稳定性理论研究轧机非线性自治系统在奇点附近的分岔形态，得到系统在不同参数下拓扑结构的变化情况；采用奇异性理论研究轧机非线性非自治系统的分岔形态，得到系统的转迁集及其在不同转迁集上的拓扑结构。同时，采用数值仿真研究轧机的全局分岔情况，获得轧机出现周期运动、倍周期运动以及混沌运动的条件，为避免或抑制轧机非线性振动奠定了基础。
通过对承钢1780精轧机中F_1和F_7轧机传动系统扭转振动和机座系统垂直振动数据进行分析，验证本课题提出的连续扭振模型以及非线性垂直振动相关理论的有效性。
The rolling mill is one of the key and core equipment in modern iron and steel industry.In recent years, as the development of modern steel industry towards to large-scale, highload, high-speed direction, the nonlinear factors of rolling process are progressivelyincreasing, which makes various nonlinear vibrations of rolling mill frequently occurredunder perturbation of rolling conditions or parameters in rolling process. The vibration ofrolling mill is always the major technical problems in steel industry. The vibration ofdrive system and frame system not only affects the stability of rolling process, butreduced the quality of product and productivity of production, especially severevibrations will cause the instantaneous destruction of device and lead to huge economiclosses. Therefore, in order to improve rolling productivity and product quality, reducerolling costs, the analysis on the characteristics and mechanism of rolling mill’s nonlinearvibration have been an increasingly important task.
The project was supported by the National Major Research Topics for 11~(th)-5-year Planof China (Grant No. 2007BAF02B10) and the Hebei Natural Science Foundation (studyon nonlinear dynamic behaviors of torsional vibration system on rolling mill. Grant No.F2008000882). Considering nonlinear factors in rolling process such as nonlinear friction,hysteresis stiffness and piecewise stiffness and so on, the dynamic response of rollingmill under nonlinear factors and external excitation is analyzed by using the theory ofnonlinear vibration, and the resonance characteristics and bifurcation behaviors of rollingmill are studied from inner relationship of the system. It provide the theoretical basis forfurther revealing the mechanism of nonlinear vibration and characteristic of rolling mill.
Firstly, considering the nonlinear factors such as nonlinear friction of roller surface,hysteresis force of shaft, the nonlinear dynamic models of rolling mill’s torsionalvibration system are modeling by generalized dissipation Lagrange theory; consideringthe continuous distribution of mass and clearance of rolling mill’s drive system, thecontinuous dynamic model of torsional vibration with clearance and no clearance areestablished, respectively.
Secondly, according to the structural and mechanical characteristics of rolling mill, the nonlinear dynamic models of roller system’s vertical vibration are established whichconsidering the effect of piecewise stiffness, nonlinear stiffness with cubic item andnonlinear friction. Based on these models, nonlinear vibration dynamic behavior ofrolling mill can be analyzed further.
Thirdly, the approximate solution of dynamic response of nonlinear vibration modelsunder periodic excitation and no excitation are studied by means of KBM method andaverage method, respectively. On the basis of dynamic response, the amplitude frequencyequation of main resonance, ultraharmonics resonance and subharmonics resonance areobtained, and the influence of resonance characteristics under nonlinear parameters areanalyzed. The dynamic characteristic of resonance and response of rolling mill areobtained.
Fourthly, the stability of nonlinear autonomous system of rolling mill nearby singularpoint are studied by using the stability theory of singular and the topology under differentparameters is obtained. Then the bifurcation characteristics of nonlinear non-autonomoussystem are studied by using singularity theory and the transfer concourse and topology ofbifurcation function are obtained. The global bifurcation is studied by using numericalsimulation and, the conditions of periodic motion, period-doubling motion and chaos areestablished. These theoretical solutions offer base for avoiding or suppressing nonlinearvibration of rolling mill.
Finally, the torsional vibration of drive system and vertical vibration of frame systemin 1780 rolling mill of Chengde Iron and Steel Company are designed and tested. Thefeasibility and effectiveness of studied were verified about mentioned related theoryabove.
本文在国家十一五重大攻关课题“大型冷连轧成套装备关键技术研究与示范应用(批准号：2007BAF02B10)”和河北省自然科学基金“轧机传动系统扭振非线性动力学行为研究(批准号：F2008000882)”的资助下，考虑轧机轧制过程中非线性摩擦阻尼、滞后、分段等非线性因素，采用非线性振动理论研究轧机在非线性因素及外部激励下的动态响应，分析轧机的共振和分岔特性，从系统的内在联系上研究了非线性因素对轧机振动的影响，为进一步揭示轧机非线性振动机理及特性提供理论依据。
基于广义耗散系统Lagrange原理，分别考虑轧机传动系统在轧制过程中轧辊端受到的非线性摩擦阻尼、传动系统中滞后弹性力等非线性因素，建立了轧机传动系统的非线性扭振动力学模型；考虑轧机传动系统的连续分布质量，建立了轧机传动系统的连续扭振动力学模型，并研究了存在间隙时非线性连续扭振模型。
根据轧机的结构及受力特点，以机架中轧辊为研究对象，分别考虑机架与轧辊间分段非线性刚度、含三次项非线性刚度以及非线性阻尼影响，建立了辊系的非线性垂直振动动力学模型，为进一步分析轧机非线性动力学特性提供理论模型。
运用渐近法和平均法求解轧机非线性振动系统在自由振动和受外部周期激励下动态响应的解析近似解。在求解轧机非线性振动系统动态响应解的基础上，构造系统在主共振、超谐共振以及亚谐共振时的幅频特性方程，研究非线性参数对系统共振特性的影响，得到轧机的共振特征及动力学响应规律。
应用奇点稳定性理论研究轧机非线性自治系统在奇点附近的分岔形态，得到系统在不同参数下拓扑结构的变化情况；采用奇异性理论研究轧机非线性非自治系统的分岔形态，得到系统的转迁集及其在不同转迁集上的拓扑结构。同时，采用数值仿真研究轧机的全局分岔情况，获得轧机出现周期运动、倍周期运动以及混沌运动的条件，为避免或抑制轧机非线性振动奠定了基础。
通过对承钢1780精轧机中F_1和F_7轧机传动系统扭转振动和机座系统垂直振动数据进行分析，验证本课题提出的连续扭振模型以及非线性垂直振动相关理论的有效性。
The rolling mill is one of the key and core equipment in modern iron and steel industry.In recent years, as the development of modern steel industry towards to large-scale, highload, high-speed direction, the nonlinear factors of rolling process are progressivelyincreasing, which makes various nonlinear vibrations of rolling mill frequently occurredunder perturbation of rolling conditions or parameters in rolling process. The vibration ofrolling mill is always the major technical problems in steel industry. The vibration ofdrive system and frame system not only affects the stability of rolling process, butreduced the quality of product and productivity of production, especially severevibrations will cause the instantaneous destruction of device and lead to huge economiclosses. Therefore, in order to improve rolling productivity and product quality, reducerolling costs, the analysis on the characteristics and mechanism of rolling mill’s nonlinearvibration have been an increasingly important task.
The project was supported by the National Major Research Topics for 11~(th)-5-year Planof China (Grant No. 2007BAF02B10) and the Hebei Natural Science Foundation (studyon nonlinear dynamic behaviors of torsional vibration system on rolling mill. Grant No.F2008000882). Considering nonlinear factors in rolling process such as nonlinear friction,hysteresis stiffness and piecewise stiffness and so on, the dynamic response of rollingmill under nonlinear factors and external excitation is analyzed by using the theory ofnonlinear vibration, and the resonance characteristics and bifurcation behaviors of rollingmill are studied from inner relationship of the system. It provide the theoretical basis forfurther revealing the mechanism of nonlinear vibration and characteristic of rolling mill.
Firstly, considering the nonlinear factors such as nonlinear friction of roller surface,hysteresis force of shaft, the nonlinear dynamic models of rolling mill’s torsionalvibration system are modeling by generalized dissipation Lagrange theory; consideringthe continuous distribution of mass and clearance of rolling mill’s drive system, thecontinuous dynamic model of torsional vibration with clearance and no clearance areestablished, respectively.
Secondly, according to the structural and mechanical characteristics of rolling mill, the nonlinear dynamic models of roller system’s vertical vibration are established whichconsidering the effect of piecewise stiffness, nonlinear stiffness with cubic item andnonlinear friction. Based on these models, nonlinear vibration dynamic behavior ofrolling mill can be analyzed further.
Thirdly, the approximate solution of dynamic response of nonlinear vibration modelsunder periodic excitation and no excitation are studied by means of KBM method andaverage method, respectively. On the basis of dynamic response, the amplitude frequencyequation of main resonance, ultraharmonics resonance and subharmonics resonance areobtained, and the influence of resonance characteristics under nonlinear parameters areanalyzed. The dynamic characteristic of resonance and response of rolling mill areobtained.
Fourthly, the stability of nonlinear autonomous system of rolling mill nearby singularpoint are studied by using the stability theory of singular and the topology under differentparameters is obtained. Then the bifurcation characteristics of nonlinear non-autonomoussystem are studied by using singularity theory and the transfer concourse and topology ofbifurcation function are obtained. The global bifurcation is studied by using numericalsimulation and, the conditions of periodic motion, period-doubling motion and chaos areestablished. These theoretical solutions offer base for avoiding or suppressing nonlinearvibration of rolling mill.
Finally, the torsional vibration of drive system and vertical vibration of frame systemin 1780 rolling mill of Chengde Iron and Steel Company are designed and tested. Thefeasibility and effectiveness of studied were verified about mentioned related theoryabove.
引文
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