基于柔性多体动力学的混凝土泵车臂架系统的建模与仿真
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摘要
随着我国经济建设步伐的加快,国内商品混凝土行业和建筑机械业务的快速发展,施工规模以及施工范围的不断扩大,市场对混凝土机械的需求呈猛增势态,带动了混凝土输送机械的高速发展,混凝土泵车的市场空间也得到了进一步扩大。目前混凝土泵车已经成为现代建筑企业中不可缺少的建筑机械,对泵车臂架系统自动控制的研究,可以有效的提高施工质量和泵车的工作效率。泵车的臂架是冗余自由度、强非线性、刚柔耦合的多体系统,它涉及了多体动力学以及控制、运动学逆问题、流体力学等方面的问题。因此,对于泵车臂架系统的研究具有重要的理论价值和实际的工程意义。
本文以混凝土泵车的臂架系统为研究对象,主要研究多体动力学尤其是柔性多体动力学理论在混凝土泵车浇筑自动化领域的应用,重点是进行理论性的分析。对混凝土泵车臂架系统的运动以及控制、仿真方面作了细致的研究工作,具体的研究内容包括以下几个方面：
(1)把混凝土泵车臂架系统看作一个开环的运动链,由一系列连杆通过转动副串联、而成。开链一端固定在基座上,另一端自由,从而完成泵车的浇筑动作。基于多刚体动力学的理论,对臂架和液压缸的运动分别进行分析,结合分析力学的相关理论,建立臂架系统的多刚体动力学方程,求解方程中的相关参数并仿真,研究刚性臂杆转动角度的变化对臂架末端轨迹的影响。
(2)随着浇筑范围的扩大,臂架朝着轻质长臂杆的方向发展,很有必要考虑柔性变形对臂架运动轨迹的影响。基于柔性多体系统动力学的相关理论,假设各臂杆均为等截面欧拉梁,采用形函数的方式描述臂杆上任意点的弹性变形,运用递推列式和拉格朗日方程以及虚功原理,建立臂架系统的柔性多体动力学方程,对方程采用向后扩展的微分求解器求解并仿真,研究柔性变形对泵车臂架末端轨迹的影响。并与刚性臂杆的结论进行对比,分析两种建模方法的优缺点。
(3)对泵车浇筑自动化进行研究。采用轨迹规划和最优控制相结合的方法对臂架系统的末端轨迹进行运动学逆问题的研究,得到臂架末端达到预期浇筑点时的最优路线,作为PD控制方法的控制率期望值,结合前面建立的臂架系统动力学方程,分别建立泵车刚性臂架系统的控制动力学方程和柔性臂架系统的控制动力学方程。采用数值迭代的算法对方程求解并仿真,分析臂架系统PD控制的精度和末端轨迹的变化。此方法是基于系统的精确数学模型,把PD控制率直接加到液压阀上,控制臂杆液压缸的驱动力,对每个臂杆的液压系统进行独立的闭环控制,最后形成臂架以及液压系统整体的开环控制,研究控制的精度和控制的实时性,即建立泵车臂架系统的完备动力学方程。
(4)分析了泵车输料管中混凝土砂浆的流动对泵车臂架的振动影响,由于混凝土砂浆不是单一流质,可以简化为固液两相流问题。通过对输料管道和浆体单元进行受力分析,建立输料管道的运动微分方程,结合固液两相流的质量、流量和压强的相关公式,建立了混凝土砂浆在输料管道中流动的固液两相流动方程。
(5)采用ADAMS软件分别建立泵车臂架系统的刚性仿真模型和柔性仿真模型,刚性模型的建立简化了部分结构,各臂杆以及液压缸部分均采用铰接的方式连接。柔性模型是在刚性模型的基础上建立的,通过离散各臂杆为有限个单元,而各臂杆的连接处和液压缸部分还保留其刚性特性。给定各臂杆的转动角度与前面数值计算的期望角度相同,仿真分析研究臂架的运动情况、末端轨迹的变化以及柔性变形对各臂杆转角变化的影响,检验前面对臂架系统建模控制求解的正确性。
With the development of the economic construct in China, the commercial concrete industry and the construction machinery business step into a new stage, in which the construction scale and scope become boarder and boarder, and the demand of the concrete machine from the market become stronger and stronger, so that the rapid development of the concrete transportation machine expand the market space of the concrete pump truck. Nowadays the concrete pump truck has become the important machine in modern construction industry. Study on the automatic control of the concrete pump truck arm system can effectively enhance the construction quality and the working efficiency of the pump truck. The arm system of the pump truck is a multi-body system with redundant freedom, strong nonlinear, coupled with rigid and flexible characters.The system is related to multi-body dynamics, control theory, kinematic reverse problem and hydrodynamics,etc.So it is of great theoretic value and real engineering significance to study the arm system of the concrete pump truck.
In this article, the arm system of the concrete pump truck is considered as the study object. The application of multi-body dynamics,especially the flexible multi-body dynamics theory in the automatic pouring field of the concrete pump truck is mainly studied, and focus on the theoretic analysis.Much research has been done on the dynamics,control and simulation of the concrete pump truck arm system, and in detail the following contents are included.
(1)The pump truck arm system is considered as a open-looped movement chain, consists of a series of poles connected with rotation fit. One end of the chain is fixed on the basement, the other end is free, so that the pouring movement is completed. Based on the multi-body rigid dynamic theory, the movement of the arms and the hydraulic cylinders are analyzed respectively, and the multi-body rigid dynamic equation of the arms is built with correlative theory of the analysis mechanics.After solution of the equation and with simulation, the influence to the arm end track from the rotation angles change of the rigid arms is studied.
(2) With the extension of the pouring range, the arms are tending to be longer and lighter, which is necessary to consider the influence to the arm moving track from the flexible distortion. Based on the correlative theory of the flexible multi-body dynamics, all the arms are supposed as the equal-section Euler beams and the elastic distortion of any point on the arm is described by the style function. With the deduce formula, the Lagrange Equation and the virtual work theory, the flexible multi-body dynamic equation is built.And with the MEBFDAE to solute the equation and according to the simulation results, the influence to the arm end track from the flexible distortion is studied.Compared with the conclusion of the rigid arms, the advantages and disadvantages of the two modeling methods are analyzed.
(3)The automation of pouring is studied. With the track programming and the optimization method, the dynamic converse problem of the arm end track is researched, so as to get the optimized rotation angle when the arm end reaches the expected pouring point, and the angle is considered as the expected value of the PD control rate.Combined with foregoing dynamic equation of the arm system, the dynamic control equations of the rigid and flexible arm systems are both built. With the numerical iterative arithmetic solving the equations and with simulation, the precision of the PD control and the change of the end track are both analyzed. This method is based on the accurate mathematic model of the system, in which the PD control rate is applied to the hydraulic driving force of the arms to independently close-loop control the hydraulic cylinder of each arm. And then it is extended to the whole control to the arms and the hydraulic driving system, with the study of the control precision and the real time character, the complete dynamic equation of the pump truck arm system is built.
(4) The libration influence to the arms from the flow of the concrete slurry in the pump truck pipes. Because the concrete slurry is not the unitary fluidity, it can be predigested as the solid-liquid two phases flow. With the force analysis of the transport pipes and the slurry unit, the dynamic differential equation of the transport pipes is built. And with the correlative formulas of the mass, flex and the pressure of the solid-liquid two phases flow, the solid-liquid two phases flow equation of the concrete slurry is built.
(5) With the ADAMS software, the rigid and flexible models of the pump truck arm system are both built. When building the rigid model, the structure segment is predigested and each arm is connected with the hydraulic cylinder by hinges. The flexible model is based on the rigid one.By dispersing the finite element of each arm, remaining the rigid characters at the hydraulic cylinders and the connection of each arm, with the same rotation angles as values in the foregoing numerical calculation, the movement situation of the arms, the change of the arms end track and the influence to the rotation angles from the flexible distortion are simulated and analyzed. The correction of the foregoing calculation is proved.Also the forces on each arm are simulated.
本文以混凝土泵车的臂架系统为研究对象,主要研究多体动力学尤其是柔性多体动力学理论在混凝土泵车浇筑自动化领域的应用,重点是进行理论性的分析。对混凝土泵车臂架系统的运动以及控制、仿真方面作了细致的研究工作,具体的研究内容包括以下几个方面：
(1)把混凝土泵车臂架系统看作一个开环的运动链,由一系列连杆通过转动副串联、而成。开链一端固定在基座上,另一端自由,从而完成泵车的浇筑动作。基于多刚体动力学的理论,对臂架和液压缸的运动分别进行分析,结合分析力学的相关理论,建立臂架系统的多刚体动力学方程,求解方程中的相关参数并仿真,研究刚性臂杆转动角度的变化对臂架末端轨迹的影响。
(2)随着浇筑范围的扩大,臂架朝着轻质长臂杆的方向发展,很有必要考虑柔性变形对臂架运动轨迹的影响。基于柔性多体系统动力学的相关理论,假设各臂杆均为等截面欧拉梁,采用形函数的方式描述臂杆上任意点的弹性变形,运用递推列式和拉格朗日方程以及虚功原理,建立臂架系统的柔性多体动力学方程,对方程采用向后扩展的微分求解器求解并仿真,研究柔性变形对泵车臂架末端轨迹的影响。并与刚性臂杆的结论进行对比,分析两种建模方法的优缺点。
(3)对泵车浇筑自动化进行研究。采用轨迹规划和最优控制相结合的方法对臂架系统的末端轨迹进行运动学逆问题的研究,得到臂架末端达到预期浇筑点时的最优路线,作为PD控制方法的控制率期望值,结合前面建立的臂架系统动力学方程,分别建立泵车刚性臂架系统的控制动力学方程和柔性臂架系统的控制动力学方程。采用数值迭代的算法对方程求解并仿真,分析臂架系统PD控制的精度和末端轨迹的变化。此方法是基于系统的精确数学模型,把PD控制率直接加到液压阀上,控制臂杆液压缸的驱动力,对每个臂杆的液压系统进行独立的闭环控制,最后形成臂架以及液压系统整体的开环控制,研究控制的精度和控制的实时性,即建立泵车臂架系统的完备动力学方程。
(4)分析了泵车输料管中混凝土砂浆的流动对泵车臂架的振动影响,由于混凝土砂浆不是单一流质,可以简化为固液两相流问题。通过对输料管道和浆体单元进行受力分析,建立输料管道的运动微分方程,结合固液两相流的质量、流量和压强的相关公式,建立了混凝土砂浆在输料管道中流动的固液两相流动方程。
(5)采用ADAMS软件分别建立泵车臂架系统的刚性仿真模型和柔性仿真模型,刚性模型的建立简化了部分结构,各臂杆以及液压缸部分均采用铰接的方式连接。柔性模型是在刚性模型的基础上建立的,通过离散各臂杆为有限个单元,而各臂杆的连接处和液压缸部分还保留其刚性特性。给定各臂杆的转动角度与前面数值计算的期望角度相同,仿真分析研究臂架的运动情况、末端轨迹的变化以及柔性变形对各臂杆转角变化的影响,检验前面对臂架系统建模控制求解的正确性。
With the development of the economic construct in China, the commercial concrete industry and the construction machinery business step into a new stage, in which the construction scale and scope become boarder and boarder, and the demand of the concrete machine from the market become stronger and stronger, so that the rapid development of the concrete transportation machine expand the market space of the concrete pump truck. Nowadays the concrete pump truck has become the important machine in modern construction industry. Study on the automatic control of the concrete pump truck arm system can effectively enhance the construction quality and the working efficiency of the pump truck. The arm system of the pump truck is a multi-body system with redundant freedom, strong nonlinear, coupled with rigid and flexible characters.The system is related to multi-body dynamics, control theory, kinematic reverse problem and hydrodynamics,etc.So it is of great theoretic value and real engineering significance to study the arm system of the concrete pump truck.
In this article, the arm system of the concrete pump truck is considered as the study object. The application of multi-body dynamics,especially the flexible multi-body dynamics theory in the automatic pouring field of the concrete pump truck is mainly studied, and focus on the theoretic analysis.Much research has been done on the dynamics,control and simulation of the concrete pump truck arm system, and in detail the following contents are included.
(1)The pump truck arm system is considered as a open-looped movement chain, consists of a series of poles connected with rotation fit. One end of the chain is fixed on the basement, the other end is free, so that the pouring movement is completed. Based on the multi-body rigid dynamic theory, the movement of the arms and the hydraulic cylinders are analyzed respectively, and the multi-body rigid dynamic equation of the arms is built with correlative theory of the analysis mechanics.After solution of the equation and with simulation, the influence to the arm end track from the rotation angles change of the rigid arms is studied.
(2) With the extension of the pouring range, the arms are tending to be longer and lighter, which is necessary to consider the influence to the arm moving track from the flexible distortion. Based on the correlative theory of the flexible multi-body dynamics, all the arms are supposed as the equal-section Euler beams and the elastic distortion of any point on the arm is described by the style function. With the deduce formula, the Lagrange Equation and the virtual work theory, the flexible multi-body dynamic equation is built.And with the MEBFDAE to solute the equation and according to the simulation results, the influence to the arm end track from the flexible distortion is studied.Compared with the conclusion of the rigid arms, the advantages and disadvantages of the two modeling methods are analyzed.
(3)The automation of pouring is studied. With the track programming and the optimization method, the dynamic converse problem of the arm end track is researched, so as to get the optimized rotation angle when the arm end reaches the expected pouring point, and the angle is considered as the expected value of the PD control rate.Combined with foregoing dynamic equation of the arm system, the dynamic control equations of the rigid and flexible arm systems are both built. With the numerical iterative arithmetic solving the equations and with simulation, the precision of the PD control and the change of the end track are both analyzed. This method is based on the accurate mathematic model of the system, in which the PD control rate is applied to the hydraulic driving force of the arms to independently close-loop control the hydraulic cylinder of each arm. And then it is extended to the whole control to the arms and the hydraulic driving system, with the study of the control precision and the real time character, the complete dynamic equation of the pump truck arm system is built.
(4) The libration influence to the arms from the flow of the concrete slurry in the pump truck pipes. Because the concrete slurry is not the unitary fluidity, it can be predigested as the solid-liquid two phases flow. With the force analysis of the transport pipes and the slurry unit, the dynamic differential equation of the transport pipes is built. And with the correlative formulas of the mass, flex and the pressure of the solid-liquid two phases flow, the solid-liquid two phases flow equation of the concrete slurry is built.
(5) With the ADAMS software, the rigid and flexible models of the pump truck arm system are both built. When building the rigid model, the structure segment is predigested and each arm is connected with the hydraulic cylinder by hinges. The flexible model is based on the rigid one.By dispersing the finite element of each arm, remaining the rigid characters at the hydraulic cylinders and the connection of each arm, with the same rotation angles as values in the foregoing numerical calculation, the movement situation of the arms, the change of the arms end track and the influence to the rotation angles from the flexible distortion are simulated and analyzed. The correction of the foregoing calculation is proved.Also the forces on each arm are simulated.
引文
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