操作机构尺寸与变形误差传递的统一建模方法研究
发布时间：2018-09-16 20:49
【摘要】：机构的误差传递建模是贯穿操作装备设计、制造以及服役的一个关键问题,对于预测装备的定位精度、实现误差参数标定与补偿等均具有至关重要的作用。因此,建立准确、高效的误差传递模型是实现操作装备高精度作业的基础。构件的尺寸和变形误差是影响操作机构末端定位精度的主要因素。它们分别由零部件的制造及装配误差和外载作用下的结构变形所导致,因此现有精度分析方法分别将其归结为机构的尺寸误差分析和结构变形计算两个独立的范畴,通过尺寸误差和结构变形的线性叠加获得操作机构的末端位姿误差。然而,当具有闭环拓扑构型的操作机构中存在过约束时,不满足公共约束的尺寸误差需要通过构件结构变形进行协调,即构件结构变形与尺寸误差之间存在耦合关系。因此,将尺寸误差和结构变形相分离的误差建模方法无法准确反映过约束机构的误差传递规律,需要综合考虑上述两类误差因素,建立同时适用于开链机构、闭环机构以及并联过约束机构的统一误差传递建模方法。针对上述问题,本文基于局部指数映射,分别将尺寸误差和结构变形转化为等效关节的位置误差和变形误差,建立了操作机构的尺寸和变形误差到末端位姿误差的传递模型,实现了尺寸和变形误差的统一建模。在此基础上建立了尺寸误差参数的独立性判别准则和解析分离算子,以及过约束误差子空间的判别与分离方法,为操作机构的误差建模与分析、尺寸参数标定与补偿以及精度设计提供了理论基础。全文的理论和应用研究成果归纳如下:□构件尺寸误差在开链机构中的传递规律研究基于机器人运动学建模的局部指数积公式,建立了满足完备性和连续性要求的开链机构尺寸误差到末端位姿误差的误差映射模型,推导了构件尺寸误差的独立性判别准则,提出了误差参数独立分量和冗余分量的解析分离算法,得到了仅含有独立参数的最小误差映射模型,揭示了构件尺寸参数误差在开链机构中的传递规律,为尺寸和变形误差的统一建模提供了基础。与现有方法相比,本文所建立的尺寸误差建模方法具有更好的通用性,适用于相邻关节轴线存在平行、垂直等特殊关系的开链机构。另外,能够通过解析方式消除模型中的冗余误差分量,得到具有最小误差参数的系统误差传递模型。研究结果表明,开链机构具有确定的独立误差参数,与具体的建模方法无关。□构件结构变形的关节运动误差等效方法研究借鉴机器人末端刚度矩阵综合的思想,进行了构件结构刚度矩阵的中心主轴分解,提出了构件结构变形的关节运动误差等效方法,将构件的结构变形误差转化为等效关节的运动误差,实现了操作机构中构件结构刚度和变形误差的解析建模,为构件尺寸误差与结构变形的统一表征提供了有效的描述方式。采用关节运动误差等效的方式表征构件的结构变形,可以建立各等效关节运动误差与构件尺寸误差之间的映射关系,从而为实现与过约束尺寸误差相耦合的变形误差分离提供了可能。□操作机构尺寸与变形误差传递的统一建模方法借助构件结构刚度的关节等效模型,分别将尺寸误差和结构变形转化为等效关节的位置误差和变形误差,采用关节误差传递的方式建立构件尺寸和变形误差统一表征,实现了操作机构尺寸和变形误差传递的统一建模。研究表明,对于开链机构和非过约束闭环机构,构件尺寸误差和结构变形相互独立,其末端位姿误差可通过两者线性叠加得到。对于过约束操作机构,其构件尺寸误差和结构变形之间存在耦合关系,位于过约束误差子空间上的不相容尺寸误差需要通过构件的结构变形进行协调。与现有方法相比,论文所建立的操作机构尺寸和变形误差统一传递模型具有通用性,同时适用于开链、闭环非过约束和闭环过约束机构。特别地,对于过约束操作机构,能够分离得到系统的过约束误差子空间,并通过内力平衡方程和变形协调条件,最终确定由协调变形所引起的末端位姿误差。□操作机构误差传递模型的区域映射求解算法根据误差因素的有界不确定特性,提出了由输入误差区域到输出误差区域传递的机构区域误差映射模型,借助独立误差约束集形态和的闵可夫斯基法则,建立了基于运动几何包络理论的输出误差区域边界推进求解算法,得到了操作机构末端误差区域的确切边界,以输出误差区域的形式更加准确地描述了操作机构的末端定位精度特性。□操作机构误差建模与分析的应用研究应用论文的理论研究成果,得到了一般串联工业机器人尺寸误差传递的最小参数模型,实现了支线客机前起落架执行机构末端误差区域的准确预测,解决了六自由度并联调姿平台尺寸误差参数的标定与补偿,实现了空间三自由度过约束并联旋压机构尺寸与变形耦合误差的分离计算,验证了论文所建立的误差传递建模方法的通用性和有效性。
[Abstract]:Error transfer modeling of mechanism is a key problem throughout the design, manufacture and service of operational equipment. It plays an important role in predicting the positioning accuracy of equipment and realizing the calibration and compensation of error parameters. Dimension and deformation errors are the main factors affecting the positioning accuracy of the end of the manipulator. They are caused by the manufacturing and assembling errors of the parts and the structural deformation under the action of external loads. Therefore, the existing accuracy analysis methods can be divided into two separate categories: the dimension error analysis of the mechanism and the structural deformation calculation. However, when there are over-constraints in the operating mechanism with closed-loop topology, the dimension errors which do not satisfy the common constraints need to be coordinated by the structural deformation of the component, that is, there is a coupling relationship between the structural deformation and the dimensional error. The error modeling method of separating dimension error and structural deformation can not accurately reflect the error transfer law of over-constrained mechanism. It is necessary to consider the above two error factors comprehensively and establish a unified error transfer modeling method for both open-chain mechanism, closed-loop mechanism and parallel over-constrained mechanism. Dimensional error and structural deformation are transformed into position error and deformation error of equivalent joint respectively by partial exponential mapping. The transfer model from dimension and deformation error of manipulator to position error of end is established, and the unified modeling of dimension and deformation error is realized. The separation operator and the method of distinguishing and separating over-constrained error subspace are analyzed, which provide theoretical basis for error modeling and analysis, dimension parameter calibration and compensation, and precision design. The local exponential product formula of robot kinematics modeling is established. The error mapping model from the dimension error to the position error of the end of the open-chain mechanism satisfying the requirements of completeness and continuity is established. The independence criterion of the dimension error of the component is deduced. The analytical separation algorithm of the independent component of the error parameter and the redundant component is proposed. The algorithm contains only the error components. The minimal error mapping model with independent parameters reveals the transfer rule of dimension parameter errors in open-chain mechanisms and provides a basis for the unified modeling of dimension and deformation errors. In addition, the redundant error components in the model can be eliminated analytically, and the system error transfer model with minimum error parameters can be obtained. The results show that the open-chain mechanism has definite independent error parameters and is independent of the specific modeling methods. Based on the idea of robot end stiffness matrix synthesis, the central principal axis decomposition of component structure stiffness matrix is carried out, and the joint motion error equivalent method of component structure deformation is proposed. The structural deformation error of component is transformed into the motion error of equivalent joint, and the structural stiffness and change of component in operating mechanism are realized. Analytical modeling of form error provides an effective description for the unified characterization of component dimension error and structural deformation. By using the equivalent method of joint motion error to characterize the structural deformation of components, the mapping relationship between the equivalent joint motion error and component dimension error can be established, thus realizing the phase of over-constrained dimension error. _Unified modeling method of dimension and deformation error transfer of manipulator mechanism transforms dimension error and structure deformation into position error and deformation error of equivalent joint respectively by means of joint equivalent model of structural stiffness of component, and establishes dimension and deformation of component by joint error transfer. The research shows that the dimension error and structure deformation are independent of each other for open-chain mechanism and non-over-constrained closed-loop mechanism, and the end pose error can be obtained by linear superposition of them. Comparing with the existing methods, the unified transfer model of the dimension and deformation errors of the operating mechanism established in this paper is universal and applicable to open-chain, closed-loop non-over-constrained and closed-loop over-constrained systems. In particular, for over-constrained manipulators, the over-constrained error subspace of the system can be separated and the end pose error caused by coordinated deformation can be determined by the internal force balance equation and the deformation coordination condition. The region mapping algorithm for solving the error transfer model of the manipulator is bounded according to the error factors. Based on the Minkowski's law of the sum of independent error constraints, a boundary-propulsion algorithm of output error region based on the envelope theory of kinematic geometry is established, and the accuracy of the error region at the end of the manipulator is obtained. 鍒囪竟鐣，
本文编号：2244744
[Abstract]:Error transfer modeling of mechanism is a key problem throughout the design, manufacture and service of operational equipment. It plays an important role in predicting the positioning accuracy of equipment and realizing the calibration and compensation of error parameters. Dimension and deformation errors are the main factors affecting the positioning accuracy of the end of the manipulator. They are caused by the manufacturing and assembling errors of the parts and the structural deformation under the action of external loads. Therefore, the existing accuracy analysis methods can be divided into two separate categories: the dimension error analysis of the mechanism and the structural deformation calculation. However, when there are over-constraints in the operating mechanism with closed-loop topology, the dimension errors which do not satisfy the common constraints need to be coordinated by the structural deformation of the component, that is, there is a coupling relationship between the structural deformation and the dimensional error. The error modeling method of separating dimension error and structural deformation can not accurately reflect the error transfer law of over-constrained mechanism. It is necessary to consider the above two error factors comprehensively and establish a unified error transfer modeling method for both open-chain mechanism, closed-loop mechanism and parallel over-constrained mechanism. Dimensional error and structural deformation are transformed into position error and deformation error of equivalent joint respectively by partial exponential mapping. The transfer model from dimension and deformation error of manipulator to position error of end is established, and the unified modeling of dimension and deformation error is realized. The separation operator and the method of distinguishing and separating over-constrained error subspace are analyzed, which provide theoretical basis for error modeling and analysis, dimension parameter calibration and compensation, and precision design. The local exponential product formula of robot kinematics modeling is established. The error mapping model from the dimension error to the position error of the end of the open-chain mechanism satisfying the requirements of completeness and continuity is established. The independence criterion of the dimension error of the component is deduced. The analytical separation algorithm of the independent component of the error parameter and the redundant component is proposed. The algorithm contains only the error components. The minimal error mapping model with independent parameters reveals the transfer rule of dimension parameter errors in open-chain mechanisms and provides a basis for the unified modeling of dimension and deformation errors. In addition, the redundant error components in the model can be eliminated analytically, and the system error transfer model with minimum error parameters can be obtained. The results show that the open-chain mechanism has definite independent error parameters and is independent of the specific modeling methods. Based on the idea of robot end stiffness matrix synthesis, the central principal axis decomposition of component structure stiffness matrix is carried out, and the joint motion error equivalent method of component structure deformation is proposed. The structural deformation error of component is transformed into the motion error of equivalent joint, and the structural stiffness and change of component in operating mechanism are realized. Analytical modeling of form error provides an effective description for the unified characterization of component dimension error and structural deformation. By using the equivalent method of joint motion error to characterize the structural deformation of components, the mapping relationship between the equivalent joint motion error and component dimension error can be established, thus realizing the phase of over-constrained dimension error. _Unified modeling method of dimension and deformation error transfer of manipulator mechanism transforms dimension error and structure deformation into position error and deformation error of equivalent joint respectively by means of joint equivalent model of structural stiffness of component, and establishes dimension and deformation of component by joint error transfer. The research shows that the dimension error and structure deformation are independent of each other for open-chain mechanism and non-over-constrained closed-loop mechanism, and the end pose error can be obtained by linear superposition of them. Comparing with the existing methods, the unified transfer model of the dimension and deformation errors of the operating mechanism established in this paper is universal and applicable to open-chain, closed-loop non-over-constrained and closed-loop over-constrained systems. In particular, for over-constrained manipulators, the over-constrained error subspace of the system can be separated and the end pose error caused by coordinated deformation can be determined by the internal force balance equation and the deformation coordination condition. The region mapping algorithm for solving the error transfer model of the manipulator is bounded according to the error factors. Based on the Minkowski's law of the sum of independent error constraints, a boundary-propulsion algorithm of output error region based on the envelope theory of kinematic geometry is established, and the accuracy of the error region at the end of the manipulator is obtained. 鍒囪竟鐣，
本文编号：2244744
本文链接：https://www.wllwen.com/kejilunwen/jixiegongcheng/2244744.html
