一种2UPS-UPR并联机床的设计理论与关键技术研究
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摘要
并联机床作为并联机器人技术和现代数控机床技术结合的产物,是从上个世纪末开始出现的一种新型制造装备。与传统机床相比,并联机床具有刚度重量比大、响应速度快、环境适应性强、技术附加值高、适合复杂曲面加工等特点,因此在制造领域具有很广泛的应用前景。其中,少自由度并联机床以其自身的优点已成为并联加工装备发展的重要趋势。
世界上许多国家已经对并联机床的研究投入了大量的人力物力,也取得了许多的研究成果,但目前对并联机床的研究总体上还是处于研发、试制和试用阶段。我国在并联机床的研究方面也取得了一些阶段性成果,但目前我国已开发的大多数并联机床尚未达到实用产品水平,均存在动态刚度和加工精度低的共同问题。这反映出国内对并联机床理论、设计与应用等方面的关键技术研究与国外相比较仍有较大差距。因此,系统地研究并联机床设计理论,切实解决设计中的关键技术难题,为并联机床设计提供理论基础,对推动我国并联机床的产业化有着及其重要的意义。
本文以一种新型2UPS-UPR并联机床的研制为主要研究内容,围绕并联机床设计基本理论,从运动学设计、动力学设计、刚度设计、结构动力学建模及数字化样机仿真等方面进行了深入的研究,具体包括以下内容：
(1)对2UPS-UPR并联机床运动学设计进行了研究。根据机床的结构,对机床的并联机构和平行约束机构进行了运动学分析,给出了并联机构和平行约束机构的位置正、逆解,机床的雅可比矩阵,平行约束机构各构件的速度。在此基础上,对机床工作空间的影响因素和工作空间的构成进行了分析,最后,分析并得到了机床结构参数和运动参数对工作空间影响的规律以及机床设计变量对尺度综合性能指标影响的变化规律。
(2)对2UPS-UPR并联机床刚体动力学优化设计进行了研究。首先,通过拉格朗日方程建立了机床刚体动力学模型,以此为基础建立了以获得机床3根驱动杆中最大驱动力的最小值为目标的动力学参数优化设计的数学模型,并通过仿真分析得出了机床设计变量对动力学设计指标的影响规律。然后,从更有实际意义的部分平衡角度出发,给出了基于平行约束机构的动力平衡结构,提出了采用线性加权法建立的动力平衡优化数学模型,并利用MATLAB软件进行了优化求解和计算比较,证明了动力平衡结构对平衡平行约束机构的震动力和震动力矩所起到的良好作用。
(3)对2UPS-UPR并联机床静刚度进行了分析与优化设计。在建立机床整机的刚度模型基础上,给出了各轴向静刚度的计算公式并进行了仿真分析与计算,得出了各轴向静刚度在工作空间的分布规律及典型工况下轴向静刚度数值。然后,分别从轴向刚度和并联机床刚度矩阵的条件数这两个方面定义了机床静刚度性能设计指标,通过利用MATLAB软件进行仿真分析,给出了机床设计变量对这两个设计指标的影响规律并经分析证明了这两个设计指标在衡量机床静刚度性能的一致性,完成了静刚度优化设计。
(4)对2UPS-UPR并联机床结构动力学建模和机构固有频率求解进行了研究,建立了机床整体机构的结构动力学方程,给出了子空间迭代法求解机床结构前5阶固有频率的计算步骤并计算出机床在典型位置时一阶固有频率值。
(5)利用2UPS-UPR并联机床数字化样机在ANSYS Workbench Enviroment中对机床进行了静刚度和模态仿真分析,得到了机床在三个典型位置点时的x、y和z三个方向静刚度值并经分析证明了静刚度仿真结果与理论分析结果是一致的。通过模态仿真并分析所得到的机床固有频率和振型,证明了该机床有比较稳定的动态特性。
(6)对机床的驱动杆和主轴部件进行了结构设计,给出了驱动杆部件设计参数的计算过程和主轴部件运动干涉的判别条件,得到了驱动杆和主轴部件的实体模型和装配图,并依此加工制造出相应的零部件。
(7)利用2UPS-UPR并联机床物理样机进行了静刚度实验和模态分析实验研究,得到了该机床在典型位置时的静刚度数值和一阶固有频率,从而验证了机床静刚度理论研究与仿真分析和机床模态仿真分析的正确性。另外,通过与前期研制的3-TPT并联机床进行比较,证明了2UPS-UPR并联机床比3-TPT并联机床有着更加良好的运动性能、刚度性能和精度性能。
本文对2UPS-UPR并联机床运动学设计、动力学设计、静刚度设计等若干问题的研究成果,为该并联机床物理样机的研发提供了基础性的理论依据和数据参考。同时,也为其它构型的并联机床设计提供了借鉴。然而,由于并联机床动态特性设计的复杂性和数字化样机技术的迅速发展,为完善和发展2UPS-UPR并联机床的设计理论,还需在该机床动态特性设计和机床数字化样机参数设计等方面做大量的深入研究工作。
Parallel machine tool is the combination of parallel robot and modern CNC machine tool technology. It is a kind of new type manufacturing equipment emerging from the end of last century. Compared to conventional machine tools, parallel machine tool is characterized by high ratio of stiffness to weight, fast response speed, strong environmental adaptation, high technology added value and suitable for machining complex surfaces and so on. Thus it has wide application prospect in manufacturing filed. Among these, due to its own advantages, No-full DOF Parallel Machine Tool has become a significant tendency in the field of parallel machining equipment's development.
Although many people in the worldwide range have resorted to develop parallel machine tool, and even to achieve a little progress, the current overall focuses of parallel machine tool research are still in research, trial-production and probation stage. In the P.R. China, although domestic scholars and designers have gotten some research fruits, most of he parallel machine tools which we have developed have not yet reached the level of practical products and have common problems of low dynamic stiffness and machining precision. This reflects that there is still a wide gap between the domestic and abroad research on the key technology of the theory, design and application of parallel machine tool. Thus, systematically studying the design theory of parallel machine tool and effectively resolving the key technical problems during the design can provide a theoretical basis for the design of parallel machine tool, which has the important significance in promoting the industrialization of China's parallel machine tool.
In this paper, the main research content is to develop a new 2UPS-UPR parallel machine tool. According to the basic design theory of parallel machine tool, it is deeply studied from kinematic design, dynamic design, stiffness design, structural dynamic modeling and digital prototype simulation. It is specifically included as follows:
(1) Kinematic design of 2UPS-UPR parallel machine tool is studied. According to the structure of machine tools, kinematic analysis of parallel mechanism and parallel restriction mechanism of machine tools is conducted, the normal and converse solutions of position analysis of parallel mechanism and parallel restriction mechanism of machine tools, Jacobian matrix and the speeds of the components of parallel restriction mechanism are also given. On this basis, the Influence Factors and the composition of the workspace of machine tools are analyzed. Finally, the law of the influence of structural parameters and motion parameters on the workspace of machine tools and the variation of the influence of design parameters on dimensional synthesis performance index are analyzed and obtained.
(2) Dynamic optimization of rigid body of 2UPS-UPR parallel machine tool is studied. First, rigid body dynamic model of this machine tool is established with Lagrange's equation. On this basis, to obtain the minimum value of the maximum driving force among the three drive rods of this machine tool, mathematical model of optimization design of dynamic parameters is established. Meanwhile, the law of the influence of design parameters on dynamic design index is gained by simulation analysis. Then, from a more meaningful point of view of partial balancing, dynamic equilibrium structure is given based on parallel constraint structure, the establishment of optimization mathematical model of dynamic equilibrium is proposed with a linear weighting method, optimization solution and calculation comparison are conducted with MATLAB software, thus the positive effect which dynamic equilibrium structure has had on shaking force and shaking moment of parallel constraint structure is proved.
(3) Static stiffness of 2UPS-UPR parallel machine tool is analyzed and optimized. On the basis of establishing the stiffness model of machine tool, the formula of axial stiffness is given and simulation analysis and calculation are conducted, thus axial stiffness distribution in the work space and axial stiffness values in typical working conditions are obtained. Then, Static stiffness performance design index is separately defined from axial stiffness and stiffness matrix condition numbers of parallel machine tool. By conducting simulation analysis with MATLAB software, the law of the influence of design parameters of parallel machine tool on the two design indexes is given and the consistency of the two design indexes in measuring stiffness properties is proved. Finally, the static stiffness optimization design is fulfilled.
(4) Study on structural dynamic modeling of 2UPS-UPR parallel machine tool and natural frequency solution of the organization are conducted, the structural dynamic equations of the whole machine tool organization are established, the subspace iteration method is given for solving the former five-order calculation steps of machine structure natural frequency and the value of the first-order natural frequency in the typical location is calculated.
(5) By means of the digital prototype of 2UPS-UPR parallel machine tool, static stiffness and modal simulation analysis of the machine tool is conducted in the ANSYS Workbench Environment, static stiffness values of directions x, y and z in the three typical positions are obtained, The fact that the static stiffness simulation results are consistent with the theoretical analysis results is proved by analysis. With modal simulation analysis of natural frequency and vibration modes of the machine tool, the fact that the machine tool has relatively stable dynamic characteristics is proved.
(6) Drive rods and spindle parts of the machine tool are structurally designed. The calculation process of the design parameters of the drive rod components and the criterion of the movement interference of the spindle components are given. Solid model and assembly drawings of the drive rods and spindle components are gained. According to this, corresponding parts can be manufactured.
(7) By means of the physical prototype of 2UPS-UPR parallel machine tool, static stiffness and modal analysis experiments of the machine tool are conducted, the value of the static stiffness and the first-order natural frequency in the typical location are gained, thus the accuracy of the theoretical study and simulation analysis of machine tool static stiffness and modal simulation analysis of machine tool is verified. Besides, compared with 3-TPT parallel machine tool pre-developed,2UPS-UPR parallel machine tool is proved to have much better sports, stiffness and precision performance.
In this paper, the research results of a number of issues such as kinematic design, dynamic design, static stiffness design provide foundational theoretical basis and data reference for the development of the physical prototype for the parallel machine tool and also provide a reference for parallel machine tool design of other configurations. However, because of the complexity of dynamic characteristic design of parallel machine tool and the rapid development of digital prototyping technology, to improve and develop the design theory of 2UPS-UPR parallel machine tool, a lot more and deeper research work is needed in the dynamic characteristic design and the digital prototype parameters design of the machine tool.
世界上许多国家已经对并联机床的研究投入了大量的人力物力,也取得了许多的研究成果,但目前对并联机床的研究总体上还是处于研发、试制和试用阶段。我国在并联机床的研究方面也取得了一些阶段性成果,但目前我国已开发的大多数并联机床尚未达到实用产品水平,均存在动态刚度和加工精度低的共同问题。这反映出国内对并联机床理论、设计与应用等方面的关键技术研究与国外相比较仍有较大差距。因此,系统地研究并联机床设计理论,切实解决设计中的关键技术难题,为并联机床设计提供理论基础,对推动我国并联机床的产业化有着及其重要的意义。
本文以一种新型2UPS-UPR并联机床的研制为主要研究内容,围绕并联机床设计基本理论,从运动学设计、动力学设计、刚度设计、结构动力学建模及数字化样机仿真等方面进行了深入的研究,具体包括以下内容：
(1)对2UPS-UPR并联机床运动学设计进行了研究。根据机床的结构,对机床的并联机构和平行约束机构进行了运动学分析,给出了并联机构和平行约束机构的位置正、逆解,机床的雅可比矩阵,平行约束机构各构件的速度。在此基础上,对机床工作空间的影响因素和工作空间的构成进行了分析,最后,分析并得到了机床结构参数和运动参数对工作空间影响的规律以及机床设计变量对尺度综合性能指标影响的变化规律。
(2)对2UPS-UPR并联机床刚体动力学优化设计进行了研究。首先,通过拉格朗日方程建立了机床刚体动力学模型,以此为基础建立了以获得机床3根驱动杆中最大驱动力的最小值为目标的动力学参数优化设计的数学模型,并通过仿真分析得出了机床设计变量对动力学设计指标的影响规律。然后,从更有实际意义的部分平衡角度出发,给出了基于平行约束机构的动力平衡结构,提出了采用线性加权法建立的动力平衡优化数学模型,并利用MATLAB软件进行了优化求解和计算比较,证明了动力平衡结构对平衡平行约束机构的震动力和震动力矩所起到的良好作用。
(3)对2UPS-UPR并联机床静刚度进行了分析与优化设计。在建立机床整机的刚度模型基础上,给出了各轴向静刚度的计算公式并进行了仿真分析与计算,得出了各轴向静刚度在工作空间的分布规律及典型工况下轴向静刚度数值。然后,分别从轴向刚度和并联机床刚度矩阵的条件数这两个方面定义了机床静刚度性能设计指标,通过利用MATLAB软件进行仿真分析,给出了机床设计变量对这两个设计指标的影响规律并经分析证明了这两个设计指标在衡量机床静刚度性能的一致性,完成了静刚度优化设计。
(4)对2UPS-UPR并联机床结构动力学建模和机构固有频率求解进行了研究,建立了机床整体机构的结构动力学方程,给出了子空间迭代法求解机床结构前5阶固有频率的计算步骤并计算出机床在典型位置时一阶固有频率值。
(5)利用2UPS-UPR并联机床数字化样机在ANSYS Workbench Enviroment中对机床进行了静刚度和模态仿真分析,得到了机床在三个典型位置点时的x、y和z三个方向静刚度值并经分析证明了静刚度仿真结果与理论分析结果是一致的。通过模态仿真并分析所得到的机床固有频率和振型,证明了该机床有比较稳定的动态特性。
(6)对机床的驱动杆和主轴部件进行了结构设计,给出了驱动杆部件设计参数的计算过程和主轴部件运动干涉的判别条件,得到了驱动杆和主轴部件的实体模型和装配图,并依此加工制造出相应的零部件。
(7)利用2UPS-UPR并联机床物理样机进行了静刚度实验和模态分析实验研究,得到了该机床在典型位置时的静刚度数值和一阶固有频率,从而验证了机床静刚度理论研究与仿真分析和机床模态仿真分析的正确性。另外,通过与前期研制的3-TPT并联机床进行比较,证明了2UPS-UPR并联机床比3-TPT并联机床有着更加良好的运动性能、刚度性能和精度性能。
本文对2UPS-UPR并联机床运动学设计、动力学设计、静刚度设计等若干问题的研究成果,为该并联机床物理样机的研发提供了基础性的理论依据和数据参考。同时,也为其它构型的并联机床设计提供了借鉴。然而,由于并联机床动态特性设计的复杂性和数字化样机技术的迅速发展,为完善和发展2UPS-UPR并联机床的设计理论,还需在该机床动态特性设计和机床数字化样机参数设计等方面做大量的深入研究工作。
Parallel machine tool is the combination of parallel robot and modern CNC machine tool technology. It is a kind of new type manufacturing equipment emerging from the end of last century. Compared to conventional machine tools, parallel machine tool is characterized by high ratio of stiffness to weight, fast response speed, strong environmental adaptation, high technology added value and suitable for machining complex surfaces and so on. Thus it has wide application prospect in manufacturing filed. Among these, due to its own advantages, No-full DOF Parallel Machine Tool has become a significant tendency in the field of parallel machining equipment's development.
Although many people in the worldwide range have resorted to develop parallel machine tool, and even to achieve a little progress, the current overall focuses of parallel machine tool research are still in research, trial-production and probation stage. In the P.R. China, although domestic scholars and designers have gotten some research fruits, most of he parallel machine tools which we have developed have not yet reached the level of practical products and have common problems of low dynamic stiffness and machining precision. This reflects that there is still a wide gap between the domestic and abroad research on the key technology of the theory, design and application of parallel machine tool. Thus, systematically studying the design theory of parallel machine tool and effectively resolving the key technical problems during the design can provide a theoretical basis for the design of parallel machine tool, which has the important significance in promoting the industrialization of China's parallel machine tool.
In this paper, the main research content is to develop a new 2UPS-UPR parallel machine tool. According to the basic design theory of parallel machine tool, it is deeply studied from kinematic design, dynamic design, stiffness design, structural dynamic modeling and digital prototype simulation. It is specifically included as follows:
(1) Kinematic design of 2UPS-UPR parallel machine tool is studied. According to the structure of machine tools, kinematic analysis of parallel mechanism and parallel restriction mechanism of machine tools is conducted, the normal and converse solutions of position analysis of parallel mechanism and parallel restriction mechanism of machine tools, Jacobian matrix and the speeds of the components of parallel restriction mechanism are also given. On this basis, the Influence Factors and the composition of the workspace of machine tools are analyzed. Finally, the law of the influence of structural parameters and motion parameters on the workspace of machine tools and the variation of the influence of design parameters on dimensional synthesis performance index are analyzed and obtained.
(2) Dynamic optimization of rigid body of 2UPS-UPR parallel machine tool is studied. First, rigid body dynamic model of this machine tool is established with Lagrange's equation. On this basis, to obtain the minimum value of the maximum driving force among the three drive rods of this machine tool, mathematical model of optimization design of dynamic parameters is established. Meanwhile, the law of the influence of design parameters on dynamic design index is gained by simulation analysis. Then, from a more meaningful point of view of partial balancing, dynamic equilibrium structure is given based on parallel constraint structure, the establishment of optimization mathematical model of dynamic equilibrium is proposed with a linear weighting method, optimization solution and calculation comparison are conducted with MATLAB software, thus the positive effect which dynamic equilibrium structure has had on shaking force and shaking moment of parallel constraint structure is proved.
(3) Static stiffness of 2UPS-UPR parallel machine tool is analyzed and optimized. On the basis of establishing the stiffness model of machine tool, the formula of axial stiffness is given and simulation analysis and calculation are conducted, thus axial stiffness distribution in the work space and axial stiffness values in typical working conditions are obtained. Then, Static stiffness performance design index is separately defined from axial stiffness and stiffness matrix condition numbers of parallel machine tool. By conducting simulation analysis with MATLAB software, the law of the influence of design parameters of parallel machine tool on the two design indexes is given and the consistency of the two design indexes in measuring stiffness properties is proved. Finally, the static stiffness optimization design is fulfilled.
(4) Study on structural dynamic modeling of 2UPS-UPR parallel machine tool and natural frequency solution of the organization are conducted, the structural dynamic equations of the whole machine tool organization are established, the subspace iteration method is given for solving the former five-order calculation steps of machine structure natural frequency and the value of the first-order natural frequency in the typical location is calculated.
(5) By means of the digital prototype of 2UPS-UPR parallel machine tool, static stiffness and modal simulation analysis of the machine tool is conducted in the ANSYS Workbench Environment, static stiffness values of directions x, y and z in the three typical positions are obtained, The fact that the static stiffness simulation results are consistent with the theoretical analysis results is proved by analysis. With modal simulation analysis of natural frequency and vibration modes of the machine tool, the fact that the machine tool has relatively stable dynamic characteristics is proved.
(6) Drive rods and spindle parts of the machine tool are structurally designed. The calculation process of the design parameters of the drive rod components and the criterion of the movement interference of the spindle components are given. Solid model and assembly drawings of the drive rods and spindle components are gained. According to this, corresponding parts can be manufactured.
(7) By means of the physical prototype of 2UPS-UPR parallel machine tool, static stiffness and modal analysis experiments of the machine tool are conducted, the value of the static stiffness and the first-order natural frequency in the typical location are gained, thus the accuracy of the theoretical study and simulation analysis of machine tool static stiffness and modal simulation analysis of machine tool is verified. Besides, compared with 3-TPT parallel machine tool pre-developed,2UPS-UPR parallel machine tool is proved to have much better sports, stiffness and precision performance.
In this paper, the research results of a number of issues such as kinematic design, dynamic design, static stiffness design provide foundational theoretical basis and data reference for the development of the physical prototype for the parallel machine tool and also provide a reference for parallel machine tool design of other configurations. However, because of the complexity of dynamic characteristic design of parallel machine tool and the rapid development of digital prototyping technology, to improve and develop the design theory of 2UPS-UPR parallel machine tool, a lot more and deeper research work is needed in the dynamic characteristic design and the digital prototype parameters design of the machine tool.
引文
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