工程起重机伸缩臂系统结构稳定性及复合运动动力学研究
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摘要
工程起重机是在一定范围内实现重物水平搬运和垂直提升的多动作起重机械，是各种工程建设中不可或缺的吊装设备。轮式起重机具有机动灵活，稳定性好，效率高，特别适用于狭窄场地作业等优点，被广泛应用于建筑、交通、水电和军工等工程建设中。伸缩臂作为轮式起重机最重要的工作部件，其同时承受较大的轴向载荷和横向载荷，有时还会受到冲击载荷的作用，为保证其安全可靠的工作，不仅需要进行强度和刚度分析，还需进行准确的动静态稳定性和动力学分析。本文以工程起重机伸缩臂系统为主要研究对象，对起重机伸缩臂系统的动静态稳定问题进行研究，并探讨了支撑油缸、伸缩臂间摩擦力和牵绳或拉索等对伸缩臂起升平面外稳定性的影响。同时，在柔性多体系统动力学基础上，建立一种兼顾精度和求解效率的高效运动弹性动力学分析方法，并针对典型工程起重机柔性伸缩臂系统进行弹性动力学分析。
在起重机设计规范GB/T3811-2008中，起重机伸缩臂起升平面外的失稳计算模型为变截面阶梯柱模型，为计算简单起见该模型忽略了内置的支撑油缸和伸缩臂间摩擦力对稳定性的影响。为准确地计入支撑油缸和臂间摩擦力对伸缩臂稳定性的影响，本文在变截面阶梯柱模型的基础上，提出了考虑支撑油缸和同时考虑支撑油缸和臂间摩擦力的两种失稳计算模型。针对不同的失稳计算模型，从精确临界挠曲微分方程出发，分别推导了多节起重机伸缩臂三种失稳计算模型欧拉临界力的递推表达式，并对三种计算模型的欧拉临界力进行了分析比较；此外，还研究了牵绳或拉索等引起的非保向力对伸缩臂起升平面外稳定性的影响。分析结果表明，起重机设计规范中采用变截面阶梯柱模型计算伸缩臂的失稳临界力是偏于安全的，而牵绳或拉索等引起的非保向力能有效地提高伸缩臂起升平面外的抗失稳能力。
针对起重机伸缩臂在小变形情况下的动力稳定性问题，通过非线性有限单元法结合Lagrange方程，建立复杂杆系结构在轴向周期载荷作用下的参数振动方程，推导其动力不稳定边界的临界频率方程。应用该频率方程给出了起重机伸缩臂第一和第二动力不稳定区域，并讨论了阻尼对动力不稳定区域的影响，研究结果表明，应用非线性有限单元法求解结构参数振动问题是有效的和精确的；同时随着阻尼的增大，动力不稳定区域减小，且对第二动力不稳定区域影响更加明显。同时，针对传统两结点梁单元在结构稳定分析中精度不够的问题，依据插值理论构造了计及二阶效应的高精度非线性三结点Euler-Bernoulli梁单元，并将该新型梁单元应用于结构动力稳定分析中。该非线性三结点梁单元的计算精度远高于传统两结点梁单元，新型单元与传统梁单元划分3-4个单元时具有相同的计算精度，从而有效地提高求解效率。
柔性多体系统动力学方程是一组强耦合、强非线性微分-代数方程组，难以求解和工程实际应用。本文从柔性多体系统动力学理论出发，结合KED方法的特点，采用适当的假设建立了柔性梁杆系统的单元运动方程，给出运动方程中各矩阵的显式表达式，并介绍了集中参数在梁杆任意位置时引起的附加矩阵。同时通过整体坐标系和随动坐标系之间的坐标转化关系矩阵，导出空间梁杆系统在整体坐标下的动力学方程。最后，讨论了动力学方程的求解策略和程序组织，编制了相应柔性梁杆系统动力学分析的数值求解程序。对典型的曲柄滑块机构进行了运动弹性动力学分析，证明了本文高效方法具有较高的分析精度，其计算量与KED方法几乎相当，提高了柔性多体系统动力学方程的求解效率。
以QAY500全路面起重机的伸缩臂系统为实例，应用提出的高效柔性系统动力学分析方法，对柔性伸缩臂系统的回转、起升和变幅等复合运动进行动力学分析，考察复合非线性运动过程中柔性伸缩臂系统的动力学响应，给出各关键点或关键构件的变形和内力变化过程，为起重机伸缩臂系统的结构设计分与安全分析提供重要依据。
Construction crane is a kind of hoisting machinery that can lift and move heavy things by multi-action in a specific domain, which play a significant role in all kinds of engineering. Wheel crane has many desirable features such as flexible, stable and efficient, thereby being widely used in structure, transportation, hydroelectric project and military industry. The telescopic boom is the most important working component of the wheel crane because it may bear quite large loads, both axially and transversely, and sometime the impact loads as well. Therefore, the exact analysis of the static and dynamic stability and the motion of the boom are necessary in order to prove that the crane can work in safety. These are also the objects of this thesis. Besides, the effect of the supporting cylinder, friction force between the different sections of the telescopic boom and the pull-rope or drawbar on the out-of-plane stability of the boom. Also, based on the flexible multibody system dynamics, a method that takes both accuracy and efficiency into consideration has been introduced and implemented on the typical flexible boom of the engineering crane in this investigation.
In the crane design role GB/T3811-2008, a multi-stepped column model is used to compute the out-of-plane stability of the telescopic boom, in which the effect of the supporting cylinder and the friction force between the different sections of the boom are omitted. However, these effects should be considered. To this end, two kinds of models are introduced to simulate the instability of the boom. One model only takes the supporting cylinder into consideration, while the other one takes supporting cylinder and the friction force both. Begin with the accurate differential equations of the critical buckling, different recursive formulations of the Euler critical force are derived based on three models, which are the conventional model and the two new models introduced in this thesis, respectively. After this, the different Euler critical forces are compared. Finally, the effort of the non-directional force caused by the drawbars on the out-of-plane stability is discussed. The analysis shows that the multi-stepped column model used in the crane design role is more likely to be safe and the non-directional force caused by the pull-ropes or drawbars can improve the out-of-plane stability of the telescopic boom in quite a large extent.
In order to analysis the dynamic stability of the telescopic boom which undergo a small deformation, the finite element method and Lagrange equations are used to build up the parametrical vibration equations of the complex beam-rod structure under a axial periodic load, resulting in the critical frequency equations of the dynamic instability boundary. Using these equations, the first and second dynamic instability regions are obtained. Besides, the effect of the damping on the instability regions is discussed. The results show that the nonlinear finite element method is an efficient and accurate method to solve the parametric vibration problems. The dynamic instability areas become smaller when the damping grows up. What more, the effect on the second area is more significant. After this, because of the low accuracy of the traditional two-node beam element in the stability analysis, a new kind of nonlinear Euler-Bernoulli beam element with three node is created through the interpolation theory, which takes the second order effect into consideration. The successful application of this new element in the structural dynamic stability demonstrates that it has much higher accuracy than the traditional two-node beam element does. Specifically, three or four traditional elements are needed to guarantee the same accuracy as the new one, which means the calculation efficient has been improved.
The kinetic equations of the flexible multibody system are a set of highly coupling and nonlinear differential-algebraic equations which are very difficult to solve. Therefore the application in the engineering is quite inconvenient. Based on the theory of the flexible multibody system dynamics, preserving the features of the KED method and with the use of some suitable assumptions, the kinetic equation of the beam-bar element are built up and the explicit formulation of the coefficient matrixes are given in this thesis. Besides, the additional matrix caused by the lumped parameters has also been taken into consideration. According to the transformation between the nodal position, velocity and acceleration in the floating and the global reference coordinates, the motion equations of the spatial beam-bar system in the global reference coordinates are obtained. Finally, the solving strategy and the organization of the procedure are discussed and the corresponding finite element procedure of the flexible beam-rod system is programmed. The numerical results coming from the flexible dynamic analysis of the typical slider-crank mechanism demonstrate that the high-efficiency method presented in this thesis has quite high accuracy and an appropriate calculation amount which is close to the KED method’s, which means that the solving efficiency of the flexible multibody system dynamics has been improved by this method.
The telescopic boom of QAY500all terrain crane is chosen to test the method presented in this thesis. Some multiple working conditions are analyzed such as revolution, lifting and changing amplitude. The main purpose is to obtain the dynamic respond of the flexible telescopic boom in the complex nonlinear motions and the deformation and the changing process of the strain of every key point or structural body, which are important basis of the structural design and analysis of the crane.
在起重机设计规范GB/T3811-2008中，起重机伸缩臂起升平面外的失稳计算模型为变截面阶梯柱模型，为计算简单起见该模型忽略了内置的支撑油缸和伸缩臂间摩擦力对稳定性的影响。为准确地计入支撑油缸和臂间摩擦力对伸缩臂稳定性的影响，本文在变截面阶梯柱模型的基础上，提出了考虑支撑油缸和同时考虑支撑油缸和臂间摩擦力的两种失稳计算模型。针对不同的失稳计算模型，从精确临界挠曲微分方程出发，分别推导了多节起重机伸缩臂三种失稳计算模型欧拉临界力的递推表达式，并对三种计算模型的欧拉临界力进行了分析比较；此外，还研究了牵绳或拉索等引起的非保向力对伸缩臂起升平面外稳定性的影响。分析结果表明，起重机设计规范中采用变截面阶梯柱模型计算伸缩臂的失稳临界力是偏于安全的，而牵绳或拉索等引起的非保向力能有效地提高伸缩臂起升平面外的抗失稳能力。
针对起重机伸缩臂在小变形情况下的动力稳定性问题，通过非线性有限单元法结合Lagrange方程，建立复杂杆系结构在轴向周期载荷作用下的参数振动方程，推导其动力不稳定边界的临界频率方程。应用该频率方程给出了起重机伸缩臂第一和第二动力不稳定区域，并讨论了阻尼对动力不稳定区域的影响，研究结果表明，应用非线性有限单元法求解结构参数振动问题是有效的和精确的；同时随着阻尼的增大，动力不稳定区域减小，且对第二动力不稳定区域影响更加明显。同时，针对传统两结点梁单元在结构稳定分析中精度不够的问题，依据插值理论构造了计及二阶效应的高精度非线性三结点Euler-Bernoulli梁单元，并将该新型梁单元应用于结构动力稳定分析中。该非线性三结点梁单元的计算精度远高于传统两结点梁单元，新型单元与传统梁单元划分3-4个单元时具有相同的计算精度，从而有效地提高求解效率。
柔性多体系统动力学方程是一组强耦合、强非线性微分-代数方程组，难以求解和工程实际应用。本文从柔性多体系统动力学理论出发，结合KED方法的特点，采用适当的假设建立了柔性梁杆系统的单元运动方程，给出运动方程中各矩阵的显式表达式，并介绍了集中参数在梁杆任意位置时引起的附加矩阵。同时通过整体坐标系和随动坐标系之间的坐标转化关系矩阵，导出空间梁杆系统在整体坐标下的动力学方程。最后，讨论了动力学方程的求解策略和程序组织，编制了相应柔性梁杆系统动力学分析的数值求解程序。对典型的曲柄滑块机构进行了运动弹性动力学分析，证明了本文高效方法具有较高的分析精度，其计算量与KED方法几乎相当，提高了柔性多体系统动力学方程的求解效率。
以QAY500全路面起重机的伸缩臂系统为实例，应用提出的高效柔性系统动力学分析方法，对柔性伸缩臂系统的回转、起升和变幅等复合运动进行动力学分析，考察复合非线性运动过程中柔性伸缩臂系统的动力学响应，给出各关键点或关键构件的变形和内力变化过程，为起重机伸缩臂系统的结构设计分与安全分析提供重要依据。
Construction crane is a kind of hoisting machinery that can lift and move heavy things by multi-action in a specific domain, which play a significant role in all kinds of engineering. Wheel crane has many desirable features such as flexible, stable and efficient, thereby being widely used in structure, transportation, hydroelectric project and military industry. The telescopic boom is the most important working component of the wheel crane because it may bear quite large loads, both axially and transversely, and sometime the impact loads as well. Therefore, the exact analysis of the static and dynamic stability and the motion of the boom are necessary in order to prove that the crane can work in safety. These are also the objects of this thesis. Besides, the effect of the supporting cylinder, friction force between the different sections of the telescopic boom and the pull-rope or drawbar on the out-of-plane stability of the boom. Also, based on the flexible multibody system dynamics, a method that takes both accuracy and efficiency into consideration has been introduced and implemented on the typical flexible boom of the engineering crane in this investigation.
In the crane design role GB/T3811-2008, a multi-stepped column model is used to compute the out-of-plane stability of the telescopic boom, in which the effect of the supporting cylinder and the friction force between the different sections of the boom are omitted. However, these effects should be considered. To this end, two kinds of models are introduced to simulate the instability of the boom. One model only takes the supporting cylinder into consideration, while the other one takes supporting cylinder and the friction force both. Begin with the accurate differential equations of the critical buckling, different recursive formulations of the Euler critical force are derived based on three models, which are the conventional model and the two new models introduced in this thesis, respectively. After this, the different Euler critical forces are compared. Finally, the effort of the non-directional force caused by the drawbars on the out-of-plane stability is discussed. The analysis shows that the multi-stepped column model used in the crane design role is more likely to be safe and the non-directional force caused by the pull-ropes or drawbars can improve the out-of-plane stability of the telescopic boom in quite a large extent.
In order to analysis the dynamic stability of the telescopic boom which undergo a small deformation, the finite element method and Lagrange equations are used to build up the parametrical vibration equations of the complex beam-rod structure under a axial periodic load, resulting in the critical frequency equations of the dynamic instability boundary. Using these equations, the first and second dynamic instability regions are obtained. Besides, the effect of the damping on the instability regions is discussed. The results show that the nonlinear finite element method is an efficient and accurate method to solve the parametric vibration problems. The dynamic instability areas become smaller when the damping grows up. What more, the effect on the second area is more significant. After this, because of the low accuracy of the traditional two-node beam element in the stability analysis, a new kind of nonlinear Euler-Bernoulli beam element with three node is created through the interpolation theory, which takes the second order effect into consideration. The successful application of this new element in the structural dynamic stability demonstrates that it has much higher accuracy than the traditional two-node beam element does. Specifically, three or four traditional elements are needed to guarantee the same accuracy as the new one, which means the calculation efficient has been improved.
The kinetic equations of the flexible multibody system are a set of highly coupling and nonlinear differential-algebraic equations which are very difficult to solve. Therefore the application in the engineering is quite inconvenient. Based on the theory of the flexible multibody system dynamics, preserving the features of the KED method and with the use of some suitable assumptions, the kinetic equation of the beam-bar element are built up and the explicit formulation of the coefficient matrixes are given in this thesis. Besides, the additional matrix caused by the lumped parameters has also been taken into consideration. According to the transformation between the nodal position, velocity and acceleration in the floating and the global reference coordinates, the motion equations of the spatial beam-bar system in the global reference coordinates are obtained. Finally, the solving strategy and the organization of the procedure are discussed and the corresponding finite element procedure of the flexible beam-rod system is programmed. The numerical results coming from the flexible dynamic analysis of the typical slider-crank mechanism demonstrate that the high-efficiency method presented in this thesis has quite high accuracy and an appropriate calculation amount which is close to the KED method’s, which means that the solving efficiency of the flexible multibody system dynamics has been improved by this method.
The telescopic boom of QAY500all terrain crane is chosen to test the method presented in this thesis. Some multiple working conditions are analyzed such as revolution, lifting and changing amplitude. The main purpose is to obtain the dynamic respond of the flexible telescopic boom in the complex nonlinear motions and the deformation and the changing process of the strain of every key point or structural body, which are important basis of the structural design and analysis of the crane.
引文
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