刚柔耦合系统的动力学建模与响应分析
发布时间：2018-08-13 13:42
【摘要】：在航空航天、旋转机械、车辆工程、军工器械、机器人以及微机电系统(MEMS)领域中,这类工程中系统的各个柔性部件存在大范围的刚体运动,同时其自身发生弹性变形,这就涉及结构部件的刚体运动与弹性变形相互耦合的问题。运动与变形耦合动力学系统涉及到刚体动力学与变形体力学之间的统一,柔性体在作大范围运动时呈现出的动力过程非常复杂。随着刚柔耦合系统规模越来越庞大,结构越来越复杂,及其运行速度要求不断加快,对系统在不同的约束、不同的受力与控制环节等工况下的运行过程的精确掌握,这些都成为工程预研与设计的重大难题。目前对刚柔耦合系统动力学的研究主要集中在力学建模、计算求解、柔性多体系统的接触与碰撞问题和多物理场下的运动与变形耦合效应等方面,然而对刚柔耦合系统的动力学建模尤为关键,要求所建模型既能反映系统的耦合效应,同时能够在无刚体运动时退化为经典弹性力学,而在不考虑弹性体变形时能够退化成刚体动力学。对于刚柔耦合系统动力学中存在动力刚化效应的机理,目前存在较大争议,其中涉及到几何非线性、运动非线性以及材料非线性等大变形理论,这些问题的探讨仍是研究的重点。随着含偶应力线弹性理论的不断完善,将物质点的旋转变形考虑于弹性体的变形,并计及其产生的偶应力对弹性体的影响,以含偶应力线弹性理论为基础,研究弹性体的刚柔耦合动力学过程,对于这方面的研究受到越来越多的关注,为微观尺寸下柔性体的动力学研究带来较大突破。首先,本文对质量弹簧离心振动系统的刚柔耦合动力学建模、数值求解及其动力学响应分析等作了重点阐述,解析了耦合系统的动力学本质、惯性效应及其动力学特性,并研制出离心振动复合实验装置来验证该理论模型;其次,考虑弹性体的平动变形和旋转变形,将偶应力理论应用于刚柔耦合动力学模型中,建立了广义弹性体作定轴刚体转动的刚柔耦合动力学模型,并开发了相应的有限元计算程序;最后,基于广义弹性体的刚柔耦合动力学模型,对旋转悬臂梁、中心刚体-柔性梁系统、风轮叶片以及超大吨位起重机臂架系统的动力学过程作了深入研究。论文的主要工作和结论如下:(1)针对单质点双自由度的质量弹簧离心振动系统的刚柔耦合动力学过程进行重点研究,建立了已知刚体转动情况时质量弹簧系统的动力学方程,对其进行计算求解,并对其解析解进行详细、系统地研究和分析,尤其针对其动力学特性和动力学响应作了专门研究,为探究刚柔耦合系统动力学耦合的本质,对各种惯性力随时间的变化过程进行了相关研究。为验证刚柔耦合系统中质点出现花瓣形状的运动轨迹,设计并研制出离心振动复合实验装置,通过对比分析得到刚柔耦合系统模型的合理性。(2)以Mindlin线弹性偶应力理论为基础,创建了含三个材料参数的广义弹性理论,并结合质量弹簧系统的动力学建模方法,通过哈密尔顿原理推导出作定轴刚体转动的广义弹性体的刚柔耦合动力学模型,该模型计及了相对惯性力、离心力、科氏力和切向惯性力。考虑以弹性体的位移和变形转角为独立变量,利用约束变分原理建立了广义弹性体作定轴刚体转动的有限元控制方程,其中单元离散采用8个节点48个自由度的三维六面体实体等参元或4个节点24个自由度的三维四面体单元。对广义弹性体的有限元分析可以考虑各种惯性力因素对其内力分布造成的影响,也能够给出其动力特性的变化规律,还可以考虑结构的尺寸效应。(3)数值分析旋转悬臂梁的动力学特性和动力学响应,得到旋转悬臂梁在不同恒定转速下动频的变化规律,对比分析不同旋转姿态、不同恒定转速等工况时悬臂梁的等效应力、等效偶应力及其位移等动力学响应。特别指出了花瓣形状的质点运动轨迹和旋转系统最大转速概念等新的结论。进一步对旋转微梁进行动力学特性和动力学响应分析,突出旋转变形对整个计算结果的影响,体现出广义弹性理论的刚柔耦合动力学模型对微观结构部件进行动力分析时的合理性和精确性。(4)计算选取中心刚体-柔性梁的刚柔耦合系统,对系统最大转速问题展开深入研究,从而为结构的控制提供新的途径。考虑刚柔耦合系统中柔性梁受到不同外力载荷作用时,柔性梁在整个旋转过程中的动力学响应,更加准确和合理地模拟出柔性梁的动力学过程,精确解析了系统结构部件在离心场中的刚柔耦合机理,为更好地数值仿真工程实际结构的运转过程及控制旋转系统结构部件的位移值和应力值提供理论依据和技术指导。(5)建立风轮叶片的力学模型,采用广义弹性体作定轴刚体转动的刚柔耦合动力学模型,数值模拟了风轮叶片从启动加速阶段至额定转速工作阶段的动力学过程。计算还考虑了不同载荷作用时风轮叶片的动力学响应存在的差异,为更精确和合理地仿真风轮叶片的动力学过程提供重要的参考价值。(6)用经典弹性理论以及传统梁,杆单元去仿真求解刚体-柔性多体系统的动力学过程,以超大吨位轮式起重机臂架作大范围回转运动的刚柔耦合动力学过程作为依托,建立其柔性多体动力学模型,并编写相关程序对其进行计算求解,仿真了轮式起重机通过钢丝绳提起吊物,然后回转吊臂使得吊物在空中摆动的整个过程,计算得出吊物的偏摆角和吊臂不同位置的等效应力值随时间的变化曲线,并将仿真结果与试验测量结果进行对比分析,进一步验证了本文模型在建模思想和方法上的合理性。
[Abstract]:In the fields of aerospace, rotating machinery, vehicle engineering, military equipment, robots and micro-electro-mechanical systems (MEMS), the flexible components of such engineering systems have a large range of rigid body motion, while their own elastic deformation occurs, which involves the coupling of rigid body motion and elastic deformation of structural components. Coupled dynamics system involves the unification between rigid body dynamics and deformable body mechanics. The dynamic process of flexible body in large-scale motion is very complex. With the increasing size of rigid-flexible coupling system, the structure is becoming more and more complex, and its speed requirements are accelerating, the system under different constraints, different forces. At present, the study on dynamics of rigid-flexible coupling systems mainly focuses on mechanical modeling, calculation and solution, contact and collision problems of flexible multi-body systems and coupling effects of motion and deformation in multi-physical fields. For the rigid-flexible coupling system, the dynamic modeling is especially important. It requires that the model can reflect the coupling effect of the system and degenerate into classical elasticity when the rigid body is moving, but degenerate into rigid body dynamics when the deformation of the elastic body is not considered. With the development of linear elasticity theory with couple stresses, the rotational deformation of a material point is considered as the deformation of an elastic body and the couple stresses produced by it are taken into account. Based on the theory of linear elasticity with couple stresses, the rigid-flexible coupling dynamics of elastic body is studied. More and more attention has been paid to this field, which brings about a breakthrough in the dynamics of flexible body in micro-size. Firstly, the rigid-flexible coupling dynamics model of mass-spring centrifugal vibration system is established. Value solution and its dynamic response analysis are emphatically expounded. The dynamic essence, inertia effect and dynamic characteristics of the coupled system are analyzed. A centrifugal vibration compound experimental device is developed to verify the theoretical model. Secondly, considering the translational and rotational deformation of elastic body, the couple stress theory is applied to the rigid-flexible coupling dynamics. In the model, the rigid-flexible coupling dynamic model of the generalized elastic body rotating as a fixed-axis rigid body is established, and the corresponding finite element calculation program is developed. Finally, based on the rigid-flexible coupling dynamic model of the generalized elastic body, the dynamic forces of the rotating cantilever beam, the central rigid-flexible beam system, the wind turbine blade and the boom system of the super-tonnage crane are analyzed. The main work and conclusions of this paper are as follows: (1) The rigid-flexible coupling dynamic process of mass spring centrifugal vibration system with single particle and two degrees of freedom is studied emphatically, and the dynamic equation of mass spring system with known rigid body rotation is established, and its analytical solution is obtained. In order to explore the essence of dynamic coupling of rigid-flexible coupling system, the variation process of inertial force with time is studied. In order to verify the motion track of petal shape of particle in rigid-flexible coupling system, the design and research are carried out. (2) Based on Mindlin's linear elastic couple stress theory, a generalized elastic theory with three material parameters is established. Combining with the dynamic modeling method of mass spring system, a rigid body with fixed axis is deduced by Hamilton principle. A rigid-flexible coupling dynamic model of a rotating generalized elastic body is developed, which takes into account the relative inertia force, centrifugal force, Coriolis force and tangential inertia force. Considering the displacement and deformation angle of the elastic body as independent variables, the governing equations of a rotating rigid body with the generalized elastic body as a fixed axis are established by using the constrained variational principle. A 3-D hexahedral solid isoparametric element with 8 nodes and 48 degrees of freedom or a 3-D tetrahedral element with 4 nodes and 24 degrees of freedom are used in the finite element analysis of a generalized elastic body. (3) The dynamic characteristics and dynamic responses of the rotating cantilever beam are analyzed numerically, and the dynamic frequencies of the rotating cantilever beam at different constant rotational speeds are obtained. The equivalent forces, equivalent couple stresses and displacements of the cantilever beam under different rotational postures and rotational speeds are compared and analyzed. Further more, the dynamic characteristics and dynamic response of the rotating micro-beam are analyzed, and the influence of the rotating deformation on the whole calculation result is highlighted. It shows that the rigid-flexible coupling dynamic model of the generalized elastic theory is reasonable for the dynamic analysis of micro-components. (4) Computing and selecting the rigid-flexible coupling system of the center rigid-flexible beam, the maximum speed of the system is studied in depth, which provides a new way to control the structure. The dynamic process of the flexible beam is simulated reasonably, and the rigid-flexible coupling mechanism of the structural components in the centrifugal field is analyzed accurately. The theoretical basis and technical guidance are provided for the better numerical simulation of the actual structure operation process and the control of the displacement and stress values of the structural components of the rotating system. (5) The mechanics of the wind turbine blade is established. A rigid-flexible coupling dynamic model with generalized elastomer as fixed-axis rigid-body rotation was used to simulate the dynamic process of wind turbine blades from start-up acceleration stage to rated speed operation stage. (6) Using classical elastic theory and traditional beam and bar element to simulate the dynamic process of rigid-flexible multi-body system, the flexible multi-body dynamic model is established based on the rigid-flexible coupling dynamic process of large-tonnage wheeled crane boom in large-scale rotation. The whole process of lifting the lifting object through wire rope and swinging the lifting object in the air by swinging the boom is simulated. The swing angle of the lifting object and the curve of the equivalent stress at different positions of the boom with time are calculated, and the simulation results are compared with the experimental results. Comparative analysis further validates the rationality of this model in modeling thought and method.
【学位授予单位】：重庆大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O313.3
，
本文编号：2181163
[Abstract]:In the fields of aerospace, rotating machinery, vehicle engineering, military equipment, robots and micro-electro-mechanical systems (MEMS), the flexible components of such engineering systems have a large range of rigid body motion, while their own elastic deformation occurs, which involves the coupling of rigid body motion and elastic deformation of structural components. Coupled dynamics system involves the unification between rigid body dynamics and deformable body mechanics. The dynamic process of flexible body in large-scale motion is very complex. With the increasing size of rigid-flexible coupling system, the structure is becoming more and more complex, and its speed requirements are accelerating, the system under different constraints, different forces. At present, the study on dynamics of rigid-flexible coupling systems mainly focuses on mechanical modeling, calculation and solution, contact and collision problems of flexible multi-body systems and coupling effects of motion and deformation in multi-physical fields. For the rigid-flexible coupling system, the dynamic modeling is especially important. It requires that the model can reflect the coupling effect of the system and degenerate into classical elasticity when the rigid body is moving, but degenerate into rigid body dynamics when the deformation of the elastic body is not considered. With the development of linear elasticity theory with couple stresses, the rotational deformation of a material point is considered as the deformation of an elastic body and the couple stresses produced by it are taken into account. Based on the theory of linear elasticity with couple stresses, the rigid-flexible coupling dynamics of elastic body is studied. More and more attention has been paid to this field, which brings about a breakthrough in the dynamics of flexible body in micro-size. Firstly, the rigid-flexible coupling dynamics model of mass-spring centrifugal vibration system is established. Value solution and its dynamic response analysis are emphatically expounded. The dynamic essence, inertia effect and dynamic characteristics of the coupled system are analyzed. A centrifugal vibration compound experimental device is developed to verify the theoretical model. Secondly, considering the translational and rotational deformation of elastic body, the couple stress theory is applied to the rigid-flexible coupling dynamics. In the model, the rigid-flexible coupling dynamic model of the generalized elastic body rotating as a fixed-axis rigid body is established, and the corresponding finite element calculation program is developed. Finally, based on the rigid-flexible coupling dynamic model of the generalized elastic body, the dynamic forces of the rotating cantilever beam, the central rigid-flexible beam system, the wind turbine blade and the boom system of the super-tonnage crane are analyzed. The main work and conclusions of this paper are as follows: (1) The rigid-flexible coupling dynamic process of mass spring centrifugal vibration system with single particle and two degrees of freedom is studied emphatically, and the dynamic equation of mass spring system with known rigid body rotation is established, and its analytical solution is obtained. In order to explore the essence of dynamic coupling of rigid-flexible coupling system, the variation process of inertial force with time is studied. In order to verify the motion track of petal shape of particle in rigid-flexible coupling system, the design and research are carried out. (2) Based on Mindlin's linear elastic couple stress theory, a generalized elastic theory with three material parameters is established. Combining with the dynamic modeling method of mass spring system, a rigid body with fixed axis is deduced by Hamilton principle. A rigid-flexible coupling dynamic model of a rotating generalized elastic body is developed, which takes into account the relative inertia force, centrifugal force, Coriolis force and tangential inertia force. Considering the displacement and deformation angle of the elastic body as independent variables, the governing equations of a rotating rigid body with the generalized elastic body as a fixed axis are established by using the constrained variational principle. A 3-D hexahedral solid isoparametric element with 8 nodes and 48 degrees of freedom or a 3-D tetrahedral element with 4 nodes and 24 degrees of freedom are used in the finite element analysis of a generalized elastic body. (3) The dynamic characteristics and dynamic responses of the rotating cantilever beam are analyzed numerically, and the dynamic frequencies of the rotating cantilever beam at different constant rotational speeds are obtained. The equivalent forces, equivalent couple stresses and displacements of the cantilever beam under different rotational postures and rotational speeds are compared and analyzed. Further more, the dynamic characteristics and dynamic response of the rotating micro-beam are analyzed, and the influence of the rotating deformation on the whole calculation result is highlighted. It shows that the rigid-flexible coupling dynamic model of the generalized elastic theory is reasonable for the dynamic analysis of micro-components. (4) Computing and selecting the rigid-flexible coupling system of the center rigid-flexible beam, the maximum speed of the system is studied in depth, which provides a new way to control the structure. The dynamic process of the flexible beam is simulated reasonably, and the rigid-flexible coupling mechanism of the structural components in the centrifugal field is analyzed accurately. The theoretical basis and technical guidance are provided for the better numerical simulation of the actual structure operation process and the control of the displacement and stress values of the structural components of the rotating system. (5) The mechanics of the wind turbine blade is established. A rigid-flexible coupling dynamic model with generalized elastomer as fixed-axis rigid-body rotation was used to simulate the dynamic process of wind turbine blades from start-up acceleration stage to rated speed operation stage. (6) Using classical elastic theory and traditional beam and bar element to simulate the dynamic process of rigid-flexible multi-body system, the flexible multi-body dynamic model is established based on the rigid-flexible coupling dynamic process of large-tonnage wheeled crane boom in large-scale rotation. The whole process of lifting the lifting object through wire rope and swinging the lifting object in the air by swinging the boom is simulated. The swing angle of the lifting object and the curve of the equivalent stress at different positions of the boom with time are calculated, and the simulation results are compared with the experimental results. Comparative analysis further validates the rationality of this model in modeling thought and method.
【学位授予单位】：重庆大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O313.3
，
本文编号：2181163
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