多轴数控机床精度建模与误差补偿方法研究
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摘要
加工精度是机床最重要的性能指标之一。本课题运用多体系统运动学为核心的精度分析理论体系，对多轴数控机床精度问题进行了系统、全面的分析，并重点在数控机床误差分析、精度建模、误差检定、加工精度预测以及软件误差补偿等领域开展了深入研究，通过机床精度模型，揭示了误差从机床零部件传递到被加工零件的规律，给出了精度预测，并对机床进行了软件误差补偿以提高加工精度。
多体系统理论在充分利用计算机发展成果的今天，焕发出了新的魅力，在研究多体系统的运动学与动力学问题上显示了很好的通用性、系统性和方便性。多体系统运动学理论应用于有误差运动的精度研究，是其应用领域的新拓展，虽然受到重视是近几年的事，但已显示出强大的生命力。本文对多体系统运动学以及基于该理论的机床精度建模、误差辨识、精度预测及误差补偿的方法作了系统、深入的探讨。
多体系统理论的精髓是用拓扑结构对多体系统进行高度概括和提炼，用低序体阵列描述多体系统拓扑结构，用特征矩阵表示多体系统中体间的相对位冒和姿态。本文对多体系统理论的这部分内容进行了详细阐述。它是机床运动学分析和建模的基石，本文依此建立起了多轴机床的通用精度模型，还以三轴、五轴机床为例给出了理想运动模型、有误差运动模型和空间误差模型等的具体表达式。
在建立起机床精度模型之后，开始进行机床误差参数检定。机床误差参数很多，影响加工精度的主要误差参数就有几何误差、热误差、力变形误差等。在系统介绍了已有的误差检定策略之后，为了充分利用激光干涉测量仪检定多轴机床的三个平动轴系统的21项几何误差，本文详细分析了9线辨识法，提出并深入探讨了新的12线辨识法，为了检定回转轴的6项基本误差，详细阐述了基于径向、轴向及回转误差的误差辨识机理，从而很好地解决了多体系统理论应用中的机床误差检定问题。
误差建模和误差检定完成之后，随即进行机床加工精度预测以及误差补偿。本文提出了轮廓加工误差的指标体系，阐述了位置误差至轮廓误差的映射关系，建立起了机床部件误差至加工误差的映射模型，从而可以实现准确的加工精度预测。
软件误差补偿的关键是获取补偿误差所需的数控指令，本文阐述了直接计算法和叠加附加指令法，并着重以三轴机床和五轴机床为例，深入研究了基于直接计算法修正理论数控指令的软件误差补偿。
本文在理论研究的基础上进行了仿真和实验研究，包括机床平动系统误差12线法和9线法检定实验，回转轴6项基本几何误差辨识实验，虚拟加工的加工精度预测仿真，虚拟机床加工软件误差补偿仿真，以及实体机床软件误差补偿实验。
The machining accuracy is one of the most important performance indexes for machine tools. Firstly, this dissertation details the accuracy problems of the multi-axis CNC machine tool based on the precision analysis theory of kinematics for multi-body system(MBS) systemically. Afterward, it lays the strong emphases on the researches of the error analyzing and precision modeling and the studying of the error identifying, machining accuracy predicting, software error compensating and so on. With the precision model of the multi-axis CNC machine tools, their error transferability rules from the parts to the machined workpieces are opened out, their machining accuracy predicted and their errors compensated based on software to increase their machining accuracy.
Due to taking full advantage of the development results of the computers, the MBS theories have coruscated out of new magic power, showed their good universality, systematization and conveniency for the researches of the kinematics and dynamics of MBS. That the MBS kinematics theories are applied to study the accuracy of nonideal kinematics develops a new usage field of them. Though these researches began to be think much of till in the last few years, they have already displayed their mighty vitality. Thus, this paper makes a systematic and in-depth study on the MBS kinematics theory and the methods of precision modeling, error identification, accuracy prediction, and error compensation based on the studied theory.
The kernels of MBS theories are that the number arrays of low-order body are used to describe the topological structures which are taken to generalize and refine MBS, and the characteristic matrixes are employed to represent the relative positions and gestures between any two bodies in MBS. These kernels are the foundation of the kinematics analyzing and modeling for machine tools and have been detailed. This paper has established a kind of universal precision model for all multi-axis CNC machine tool according to the proposed MBS kinematics theory. After that, the paper has given the concrete expressions of ideal kinematic model, nonideal kinematic model and volumetric error model for a three-axis machine tool and a five-axis machine tool taken for examples.
After establishing the precision model of machine tools, the measurement and evaluation of their error parameters have been started. There are many kinds of error parameters in a machine tool to influence its machining accuracy, for example, geometric errors, heat deformation errors and force deformation errors etc.. The recognized strategies
of error measurements and evaluations for machine tools are introduced. After that, this paper has detailed nine-line method, but also proposed and probed into a new method defined as twelve-line method for the sake of the making the most of double-frequency laser interferometries to measure and evaluate 21 geometric errors of three-movement-axis system in a multi-axis machine tool. In order to identify 6-freedom errors of turning-axis, this paper has detailed the identification mechanism of these errors according to radial errors, axile errors and turning errors. Based on these researches, the problems of the error measurement and evaluation of machine tools in the application process of MBS theories are resolved perfectly.
After completed error modeling and error identification, machining accuracy predicting and error compensating can been carried through with that. This paper has put forward of index systems of machining contour errors, expatiated the mapping relation from position errors to contour errors, and established the mapping model from the errors of the components of machine tools to machining errors so that the machining accuracy estimates can be realized accurately.
A key point of software error compensation is that how to obtain the numerical control instructions to compensate the known errors. This paper has expounded several direct calculation methods and adding additional instruction methods. Taking a three-axis machine tool
多体系统理论在充分利用计算机发展成果的今天，焕发出了新的魅力，在研究多体系统的运动学与动力学问题上显示了很好的通用性、系统性和方便性。多体系统运动学理论应用于有误差运动的精度研究，是其应用领域的新拓展，虽然受到重视是近几年的事，但已显示出强大的生命力。本文对多体系统运动学以及基于该理论的机床精度建模、误差辨识、精度预测及误差补偿的方法作了系统、深入的探讨。
多体系统理论的精髓是用拓扑结构对多体系统进行高度概括和提炼，用低序体阵列描述多体系统拓扑结构，用特征矩阵表示多体系统中体间的相对位冒和姿态。本文对多体系统理论的这部分内容进行了详细阐述。它是机床运动学分析和建模的基石，本文依此建立起了多轴机床的通用精度模型，还以三轴、五轴机床为例给出了理想运动模型、有误差运动模型和空间误差模型等的具体表达式。
在建立起机床精度模型之后，开始进行机床误差参数检定。机床误差参数很多，影响加工精度的主要误差参数就有几何误差、热误差、力变形误差等。在系统介绍了已有的误差检定策略之后，为了充分利用激光干涉测量仪检定多轴机床的三个平动轴系统的21项几何误差，本文详细分析了9线辨识法，提出并深入探讨了新的12线辨识法，为了检定回转轴的6项基本误差，详细阐述了基于径向、轴向及回转误差的误差辨识机理，从而很好地解决了多体系统理论应用中的机床误差检定问题。
误差建模和误差检定完成之后，随即进行机床加工精度预测以及误差补偿。本文提出了轮廓加工误差的指标体系，阐述了位置误差至轮廓误差的映射关系，建立起了机床部件误差至加工误差的映射模型，从而可以实现准确的加工精度预测。
软件误差补偿的关键是获取补偿误差所需的数控指令，本文阐述了直接计算法和叠加附加指令法，并着重以三轴机床和五轴机床为例，深入研究了基于直接计算法修正理论数控指令的软件误差补偿。
本文在理论研究的基础上进行了仿真和实验研究，包括机床平动系统误差12线法和9线法检定实验，回转轴6项基本几何误差辨识实验，虚拟加工的加工精度预测仿真，虚拟机床加工软件误差补偿仿真，以及实体机床软件误差补偿实验。
The machining accuracy is one of the most important performance indexes for machine tools. Firstly, this dissertation details the accuracy problems of the multi-axis CNC machine tool based on the precision analysis theory of kinematics for multi-body system(MBS) systemically. Afterward, it lays the strong emphases on the researches of the error analyzing and precision modeling and the studying of the error identifying, machining accuracy predicting, software error compensating and so on. With the precision model of the multi-axis CNC machine tools, their error transferability rules from the parts to the machined workpieces are opened out, their machining accuracy predicted and their errors compensated based on software to increase their machining accuracy.
Due to taking full advantage of the development results of the computers, the MBS theories have coruscated out of new magic power, showed their good universality, systematization and conveniency for the researches of the kinematics and dynamics of MBS. That the MBS kinematics theories are applied to study the accuracy of nonideal kinematics develops a new usage field of them. Though these researches began to be think much of till in the last few years, they have already displayed their mighty vitality. Thus, this paper makes a systematic and in-depth study on the MBS kinematics theory and the methods of precision modeling, error identification, accuracy prediction, and error compensation based on the studied theory.
The kernels of MBS theories are that the number arrays of low-order body are used to describe the topological structures which are taken to generalize and refine MBS, and the characteristic matrixes are employed to represent the relative positions and gestures between any two bodies in MBS. These kernels are the foundation of the kinematics analyzing and modeling for machine tools and have been detailed. This paper has established a kind of universal precision model for all multi-axis CNC machine tool according to the proposed MBS kinematics theory. After that, the paper has given the concrete expressions of ideal kinematic model, nonideal kinematic model and volumetric error model for a three-axis machine tool and a five-axis machine tool taken for examples.
After establishing the precision model of machine tools, the measurement and evaluation of their error parameters have been started. There are many kinds of error parameters in a machine tool to influence its machining accuracy, for example, geometric errors, heat deformation errors and force deformation errors etc.. The recognized strategies
of error measurements and evaluations for machine tools are introduced. After that, this paper has detailed nine-line method, but also proposed and probed into a new method defined as twelve-line method for the sake of the making the most of double-frequency laser interferometries to measure and evaluate 21 geometric errors of three-movement-axis system in a multi-axis machine tool. In order to identify 6-freedom errors of turning-axis, this paper has detailed the identification mechanism of these errors according to radial errors, axile errors and turning errors. Based on these researches, the problems of the error measurement and evaluation of machine tools in the application process of MBS theories are resolved perfectly.
After completed error modeling and error identification, machining accuracy predicting and error compensating can been carried through with that. This paper has put forward of index systems of machining contour errors, expatiated the mapping relation from position errors to contour errors, and established the mapping model from the errors of the components of machine tools to machining errors so that the machining accuracy estimates can be realized accurately.
A key point of software error compensation is that how to obtain the numerical control instructions to compensate the known errors. This paper has expounded several direct calculation methods and adding additional instruction methods. Taking a three-axis machine tool
引文
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