基于梁理论的龙门起重机动力学研究
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摘要
起重机在工作过程中的动力学响应问题是起重机动力学研究的一项重要课题。随着机械工程的迅速发展,龙门起重机的需求不断增长,其在工作过程中产生的振动问题成为一个不容忽视的问题。国内外关于龙门起重机动力学问题方面的研究虽然已经做了很多工作,但是结合梁理论进行起重机动力学方面的研究较少,在这些方面还有很多问题亟待进一步研究。
本文以龙门起重机为研究对象,分别基于Euler-Bernoulli梁理论和Timoshenko粱理论,结合结构振动力学、数值分析方法及有限元法等相关理论,系统地研究了主梁-小车耦合振动系统以及门架-小车-吊重耦合振动系统的振动特性。同时,借助于动力学仿真软件,对起重机进行了动力学仿真分析。研究的主要内容包括：
(1)基于Euler-Bernoulli梁理论,忽略梁的横向剪切变形,建立龙门起重机主梁-小车的耦合系统振动模型,并推导出系统的耦合振动微分方程,利用数值方法进行求解,并得出了主梁与小车耦合系统的固有频率随小车在主梁上的相对位置改变的变化规律。
(2)根据Lagrange方程建立了小车吊重系统的动力学方程,对影响吊重偏摆的因素进行了分析。根据龙门起重机实际工作情况建立了龙门起重机门架-小车-吊重系统的耦合振动模型。考虑梁的剪切变形和转动效应,基于Timoshenko梁理论建立耦合振动系统微分方程。通过有限元法得到龙门起重机结构所需的各阶模态,并将其代入系统的耦合振动方程,并运用数值方法得到耦合系统振动微分方程的数值解,并分析了耦合振动系统的振动特性。
(3)运用CAD软件SolidWorks建立龙门起重机的三维实体模型,并通过导入有限元分析软件ALGOR,对龙门起重机作了动力学仿真分析,得到了小车处于主梁不同的位置时整个结构的固有频率和振型,并对结果进行了分析。同时,将实体建模与梁单元建模的结果进行了对比分析。通过ALGOR非线性材料运动仿真分析,进行了龙门起重机的刚柔耦合运动仿真分析,得出了小车运动时主梁的响应。
The dynamic response in the work process of crane is an important subject in crane dynamic study. With the rapid development of mechanical engineering, the demand of gantry crane is constantly increasing, vibration problem cannot be ignored in the course of its work. Though there have been a lot of research about gantry crane dynamics, these researches rarely combined with beam theory, and there are still many problems to be studied further in these aspects.
This paper use gantry crane as the research object, respectively based on Euler-Bernoulli beam theory and Timoshenko beam theory, combined with the structure dynamics, numerical analysis method, the finite element method and some other related theory, the main girder structure-trolley coupling vibration model and structure-trolley-load coupling vibration model are established to study its vibration characteristics. At the same time, with the dynamic simulation software, the dynamic simulation of the crane is analyzed. The main contents include:
First, Based on Euler-Bernoulli beam theory, ignored the transverse shear deformation, the crane girder structure and trolley coupling vibration model is established, and the coupling vibration system differential equation is deduced. With the numerical analysis method, the equations are well solved. With the further research, the change rule of the system's natural frequency according to the position change of the car is given.
Second, using Lagrange equation, the trolley and load system dynamics equation is established, the factors which lead to load swing are analyzed. Gantry crane structure-trolley-load coupling vibration model is established according to practical work process. Considered with the effect of the rotating and shearing deformation on the beam, based on Timoshenko beam theory, the differential equations of coupling vibration system is established. Through the finite element method, the gantry crane structure modal is got, this parameter is substituted in the coupling vibration system equation, and finally the numerical solution of the vibration differential equation is got by the numerical analysis method, then the coupling vibration system vibration characteristics are analyzed.
Third, by the means of CAD software SolidWorks, the three-dimensional entity model of gantry crane is established. By importing the model into finite element analysis software ALGOR, the gantry crane dynamics simulation analysis is done, the different dynamic responses of the crane girder's natural frequency as the movement of the trolley are obtained, such as natural frequency and vibration mode, and the obtained results are further analyzed. Meanwhile, the results which is got by the entity modeling and beam element modeling is compared and analyzed. Through nonlinear material movement simulation analysis in the ALGOR, the rigid-flexible coupling dynamics simulation is done, and the response of the crane girder due to the trolley's movement is also studied in this process.
本文以龙门起重机为研究对象,分别基于Euler-Bernoulli梁理论和Timoshenko粱理论,结合结构振动力学、数值分析方法及有限元法等相关理论,系统地研究了主梁-小车耦合振动系统以及门架-小车-吊重耦合振动系统的振动特性。同时,借助于动力学仿真软件,对起重机进行了动力学仿真分析。研究的主要内容包括：
(1)基于Euler-Bernoulli梁理论,忽略梁的横向剪切变形,建立龙门起重机主梁-小车的耦合系统振动模型,并推导出系统的耦合振动微分方程,利用数值方法进行求解,并得出了主梁与小车耦合系统的固有频率随小车在主梁上的相对位置改变的变化规律。
(2)根据Lagrange方程建立了小车吊重系统的动力学方程,对影响吊重偏摆的因素进行了分析。根据龙门起重机实际工作情况建立了龙门起重机门架-小车-吊重系统的耦合振动模型。考虑梁的剪切变形和转动效应,基于Timoshenko梁理论建立耦合振动系统微分方程。通过有限元法得到龙门起重机结构所需的各阶模态,并将其代入系统的耦合振动方程,并运用数值方法得到耦合系统振动微分方程的数值解,并分析了耦合振动系统的振动特性。
(3)运用CAD软件SolidWorks建立龙门起重机的三维实体模型,并通过导入有限元分析软件ALGOR,对龙门起重机作了动力学仿真分析,得到了小车处于主梁不同的位置时整个结构的固有频率和振型,并对结果进行了分析。同时,将实体建模与梁单元建模的结果进行了对比分析。通过ALGOR非线性材料运动仿真分析,进行了龙门起重机的刚柔耦合运动仿真分析,得出了小车运动时主梁的响应。
The dynamic response in the work process of crane is an important subject in crane dynamic study. With the rapid development of mechanical engineering, the demand of gantry crane is constantly increasing, vibration problem cannot be ignored in the course of its work. Though there have been a lot of research about gantry crane dynamics, these researches rarely combined with beam theory, and there are still many problems to be studied further in these aspects.
This paper use gantry crane as the research object, respectively based on Euler-Bernoulli beam theory and Timoshenko beam theory, combined with the structure dynamics, numerical analysis method, the finite element method and some other related theory, the main girder structure-trolley coupling vibration model and structure-trolley-load coupling vibration model are established to study its vibration characteristics. At the same time, with the dynamic simulation software, the dynamic simulation of the crane is analyzed. The main contents include:
First, Based on Euler-Bernoulli beam theory, ignored the transverse shear deformation, the crane girder structure and trolley coupling vibration model is established, and the coupling vibration system differential equation is deduced. With the numerical analysis method, the equations are well solved. With the further research, the change rule of the system's natural frequency according to the position change of the car is given.
Second, using Lagrange equation, the trolley and load system dynamics equation is established, the factors which lead to load swing are analyzed. Gantry crane structure-trolley-load coupling vibration model is established according to practical work process. Considered with the effect of the rotating and shearing deformation on the beam, based on Timoshenko beam theory, the differential equations of coupling vibration system is established. Through the finite element method, the gantry crane structure modal is got, this parameter is substituted in the coupling vibration system equation, and finally the numerical solution of the vibration differential equation is got by the numerical analysis method, then the coupling vibration system vibration characteristics are analyzed.
Third, by the means of CAD software SolidWorks, the three-dimensional entity model of gantry crane is established. By importing the model into finite element analysis software ALGOR, the gantry crane dynamics simulation analysis is done, the different dynamic responses of the crane girder's natural frequency as the movement of the trolley are obtained, such as natural frequency and vibration mode, and the obtained results are further analyzed. Meanwhile, the results which is got by the entity modeling and beam element modeling is compared and analyzed. Through nonlinear material movement simulation analysis in the ALGOR, the rigid-flexible coupling dynamics simulation is done, and the response of the crane girder due to the trolley's movement is also studied in this process.
引文
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[2]Guo,BZ, Wang, IM, Yang,KY. Dynamic Stabilization of an Euler-Bernoulli Beam Under boundary control and Non-collocated Observation. Systems and Control letters.2008,57(9):55-59
[3]D.V. Bambill,D.H.,Felix, R.E. Rossi. Vibration Analysis of Rotating Timoshenko Beams By Means of the Differential Quadrature Method. Structural Engineering and Mechanics. 2010,32(2):21-25
[4]李彬,刘锦阳,洪嘉振.计及剪切变形的Timoshenko梁的刚-柔耦合动力学[J].计算力学学报,2006,23(4)：419-422.
[5]张宁.移动车辆载荷作用下桥梁竖直随机振动分析[D].成都：西南交通大学,2010
[6]刘攀.梁-质量块系统的动力学行为研究[D].武汉：华中科技大学,2008.
[7]王华林.车桥耦合系统时变动力学分析[D].上海：同济大学,2004.
[8]赵晓华,张谢东,陈湛,梅宇.移动车辆载荷作用下简支梁动力特性的数值分析[J].武汉理工大学学报(交通科学与工程版),2011,35(2)：349-352.
[9]杨予,滕念管,黄醒春,滕延锋.承受移动均布质量的简支梁振动反应分析[J].振动与冲击,2005,24(3)：19-22.
[10]陈炎,黄小清,马友发.车桥系统的耦合振动[J].应用数学和力学,2004,25(4)：354-358.
[11]孙守胜.龙门起重机结构有限元分析[J].中国水运,2005,5(12)：190-191.
[12]王述真,胡吉全,张春茂.大型龙门起重机主梁起升动态特性研究[J].港口装卸,2009,1：7-9.
[13]肖博.柔性悬挂对门式起重机动力响应影响的研究[D].武汉：武汉理工大学,2010.
[14]常春影.门式起重机结构动态特性分析[D].大连：大连理工大学,2005.
[15]郭永娟.起重机吊重偏摆系统的动力学仿真与控制研究[D].哈尔滨：东北林业大学,2011.
[16]吴晓,钟斌,张则强.小车吊重系统偏摆振动力学模型及仿真[J].计算机仿真,2004,25(4)：354-358.
[17]梁承姬,王重华,梁岗.港口集装箱起重机虚拟操作训练系统的小车-吊重运动模型研究[J].起重运输机械,2005,(12)：54-56.
[18]孙建悦.基于刚柔耦合模型的门座起重机动力学仿真研究[D].武汉：武汉理工大学, 2010.
[19]张欢.基于虚拟样机的大型船用甲板起重机结构动力学仿真研究[D].武汉：武汉理工大学,2011.
[20]肖建军.基于虚拟样机的门式起重机动力学仿真研究[D].成都：西南交通大学,2008.
[21]师汉民.机械振动系统-分析·测试·建模·对策[M].武汉：华中科技大学出版社,2006：66-67.
[22]程靳.理论力学[M].北京：高等教育出版社,2005：41-42.
[23]张相庭,王志培,黄本才,王国砚.结构振动力学[M].上海：同济大学出版社,2005：137-142.
[24]周纪卿,朱因远.非线性振动[M].西安：西安交通大学出版社,2005：6-8.
[25]游福贺.车-桥耦合系统的振动分析[D].长沙：湖南大学,2010：9-11.
[26]姚伟岸,钟万勰.辛弹性力学[M].北京：高等教育出版社,2002：47-50.
[27]王颖泽,张小兵.变速多移动质量耦合作用下柔性梁系统振动响应分析[J].振动与冲击,2011,30(8)：56-60.
[28]彭献,刘子建,洪家旺.匀变速移动质量与简支梁耦合系统的振动分析[J].工程力学,2006,23(6)：25-29.
[29]赵青,雍晓红.移动车辆载荷作用下梁桥的强迫振动分析[J].合肥工业大学学报,2004,27(10)：1277-1280
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