关节臂式坐标测量机自标定方法与误差补偿研究
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摘要
关节臂式坐标测量机是一种多自由度、非笛卡尔系坐标测量设备,具有体积小、重量轻、运动灵活、方便工业现场测量等特点,具有广泛的应用前景。本学位论文结合杭州市科技计划项目“基于嵌入式系统的柔性臂测量机系统研制”,采用理论分析、计算机仿真和实验研究相结合的方法,系统、深入地开展了关节臂式坐标测量机理论基础和关键技术的研究,研制出六自由度关节臂式坐标测量机样机,并开发了标定和误差补偿系统。
论文的主要研究内容包括：
第一章,阐述本学位论文的研究背景与意义,详细论述关节臂式坐标测量机国内外研究现状,明确关节臂式坐标测量机的关键技术和发展方向。在此基础上,提出论文的主要研究内容。
第二章,建立关节臂式坐标测量机的运动学模型,通过数值计算和图形仿真相结合的方法进行运动学分析。对关节臂式坐标测量机的误差来源进行了全面的分析,建立误差模型,并绘制关节转角、关节扭转角、关节长度、杆长和测头偏置等参量的关节空间误差分布图,通过误差分布图分析结构参数和测量位姿对测量机精度的影响规律,为关节臂式坐标测量机的结构设计、元器件选型及测量区域选择提供理论依据。
第三章,在第二章理论研究的基础上,进行关节臂式坐标测量机的机械结构设计,并对测量机的测量空间进行仿真分析,得到测量空间的形状和大小。运用有限元软件ANSYS分析薄弱环节零件的强度及整机在重力和测量力作用下的变形情况。建立数据采集系统的软硬件平台,实现关节转角、触发按钮等信号的实时采集。研究常用几何元素的拟合及误差评定方法,开发基于Open Cascade CAD平台和多线程技术的坐标测量软件,用于关节臂式坐标测量机的测量和扫描操作。
第四章,研究径向圆光栅角度传感器的组成和工作原理,并分析安装偏心和倾斜对其测量精度的影响规律。分别利用精密三坐标测量机和光电自准直仪对角度传感器的测量误差进行标定,研究测量误差的分布规律,提出两种不同形式的误差补偿方法：第一种方法采用RBF神经网络对角度测量误差进行预测和补偿；第二种方法根据角度测量误差信号的频谱分析结果,推导出一种基于正弦函数的误差补偿模型,并采用自适应粒子群算法对误差补偿模型的参数进行辨识,以克服最小二乘法等传统算法在辨识过程中无法收敛的问题。
第五章,为解决关节臂式坐标测量机现场标定的难题,提出一种基于改进模拟退火算法的自标定方法。为弥补模拟退火算法遗失中间最优解的缺陷,并提高算法搜索效率和最终解质量,提出一种改进模拟退火算法,在算法搜索过程中保留中间最优解,并及时更新,当算法接近最优解时自动减小搜索范围。研究关节臂式坐标测量机自标定的原理及其实现方法,利用一个简单的锥形孔采集单点数据,根据单点数据建立以关节结构参数为未知量的超定方程组,并用改进模拟退火算法求超定方程组的最优解,从而实现关节结构参数的自动标定。
第六章,对研制的关节臂式坐标测量机进行自标定及误差补偿实验研究,实验结果显示经过误差补偿后,各关节转角误差均控制在0.002°以内。经过自标定之后,关节臂式坐标测量机的长度测量精度达到±0.06mm,单点重复测量精度达到±0.05mm。
第七章,对论文的主要研究工作和创新点做了总结,并对未来的研究工作进行展望。
The Articulated Arm Coordinate Measuring Machine (AACMM) is a kind of multi-degree-of-freedom, non-Cartesian coordinate measuring instrument, with features of small size, light weight, flexibility and convenience to be applied in industrial field. Sopported by the Technologies R&D Program of Hangzhou Municipality "Development of flexible arm measuring machine based on embedded system", a six degree-of-freedom AACMM with its calibration and error compensation systems were developed. The rearsearch work of this dissertation was carried out through the methods of theoretical analysis, numerical simulation with experimental verification.
In chapter 1, the background and significance of the research were introduced, the current research situations, key technologies and development trend of the AACMM were expatiated in detail, and then the research contents of this dissertation were proposed.
In chapter 2, the kinematics model of the AACMM was established, and it was analyzed through the method of numerical calculation and graphical simulation. The error model of AACMMs was presented followed a thorough analysis of the error sources of AACMMs. Then the error distribution maps of joint angles, joint torsion angles and other linear parameters were plotted, and the influence of structure parameters on measurement precision was analyzed through the error distribution maps, which provide theoretical foundation for structural design, components selection and measurement area selection of AACMMs.
In chapter 3, mechanical structure design of an AACMM was carried out based on the theoretical analysis in chapter 2, and its measurement space is achieved through simulation analysis. The deformation of the AACMM under the gravity and measuring force were analyzed with the software of ANSYS, and the results show that the strength and deformation meet the design requirements. The data acquisition system was built, which can realize real-time signal acquisition and high-speed transmission. The fit and evaluation methods of common geometric elements were studied, and a coordinate measuring software for AACMMs was developed based on Open Cascade CAD and multi-threading technology.
In chapter 4, the composition and working principle of radial circular grating angle sensors were studied, and the measurement errors which caused by installation were analyzed. Then the angle sensors were calibrated respectively with coordinate measuring machines and autocollimators. From the calibration data the distribution of angle measurement errors was achieved. Afterwards two different forms of error compensation methods were proposed. One method predicts the measurement error of the angle sensors with radial basis function neural network at first, and then compensate the reading of the sensors by the predicting data. The other method is based on the spectrum analysis of the calibrating data. From the analysis result a sine function compensation model was proposed. Furthermore, a particle swarm optimization was used to identify the parameters of the compensation model, which can overcome the non-converge problem of the least-squares method and other traditional algorithms.
In chapter 5, the principle and realization method of self-calibration for AACMMs were studied. A modified simulated annealing algorithm was proposed to identify the structural parameters of the AACMMs with the single point data acquisited from a cone-shape hole. The algorithm can keep the best solution during search, and reduce the search range when the solution approaches the global minimum, which can improve the search efficiency and accuracy.
In chapter 6, the 6-DOF AACMM was used to carry out experimental tests to evaluate the calibration and error compensation methods, the results show that after compensation the measurement accuracy of circular grating sensors reaches 0.002°, and after calibration, length measurement and repeatability accuracy of the AACMM reaches 0.06mm and 0.05mm respectively.
In chapter 7, the main work and innovations of this dissertation were summarized, and the further research subjects were proposed.
论文的主要研究内容包括：
第一章,阐述本学位论文的研究背景与意义,详细论述关节臂式坐标测量机国内外研究现状,明确关节臂式坐标测量机的关键技术和发展方向。在此基础上,提出论文的主要研究内容。
第二章,建立关节臂式坐标测量机的运动学模型,通过数值计算和图形仿真相结合的方法进行运动学分析。对关节臂式坐标测量机的误差来源进行了全面的分析,建立误差模型,并绘制关节转角、关节扭转角、关节长度、杆长和测头偏置等参量的关节空间误差分布图,通过误差分布图分析结构参数和测量位姿对测量机精度的影响规律,为关节臂式坐标测量机的结构设计、元器件选型及测量区域选择提供理论依据。
第三章,在第二章理论研究的基础上,进行关节臂式坐标测量机的机械结构设计,并对测量机的测量空间进行仿真分析,得到测量空间的形状和大小。运用有限元软件ANSYS分析薄弱环节零件的强度及整机在重力和测量力作用下的变形情况。建立数据采集系统的软硬件平台,实现关节转角、触发按钮等信号的实时采集。研究常用几何元素的拟合及误差评定方法,开发基于Open Cascade CAD平台和多线程技术的坐标测量软件,用于关节臂式坐标测量机的测量和扫描操作。
第四章,研究径向圆光栅角度传感器的组成和工作原理,并分析安装偏心和倾斜对其测量精度的影响规律。分别利用精密三坐标测量机和光电自准直仪对角度传感器的测量误差进行标定,研究测量误差的分布规律,提出两种不同形式的误差补偿方法：第一种方法采用RBF神经网络对角度测量误差进行预测和补偿；第二种方法根据角度测量误差信号的频谱分析结果,推导出一种基于正弦函数的误差补偿模型,并采用自适应粒子群算法对误差补偿模型的参数进行辨识,以克服最小二乘法等传统算法在辨识过程中无法收敛的问题。
第五章,为解决关节臂式坐标测量机现场标定的难题,提出一种基于改进模拟退火算法的自标定方法。为弥补模拟退火算法遗失中间最优解的缺陷,并提高算法搜索效率和最终解质量,提出一种改进模拟退火算法,在算法搜索过程中保留中间最优解,并及时更新,当算法接近最优解时自动减小搜索范围。研究关节臂式坐标测量机自标定的原理及其实现方法,利用一个简单的锥形孔采集单点数据,根据单点数据建立以关节结构参数为未知量的超定方程组,并用改进模拟退火算法求超定方程组的最优解,从而实现关节结构参数的自动标定。
第六章,对研制的关节臂式坐标测量机进行自标定及误差补偿实验研究,实验结果显示经过误差补偿后,各关节转角误差均控制在0.002°以内。经过自标定之后,关节臂式坐标测量机的长度测量精度达到±0.06mm,单点重复测量精度达到±0.05mm。
第七章,对论文的主要研究工作和创新点做了总结,并对未来的研究工作进行展望。
The Articulated Arm Coordinate Measuring Machine (AACMM) is a kind of multi-degree-of-freedom, non-Cartesian coordinate measuring instrument, with features of small size, light weight, flexibility and convenience to be applied in industrial field. Sopported by the Technologies R&D Program of Hangzhou Municipality "Development of flexible arm measuring machine based on embedded system", a six degree-of-freedom AACMM with its calibration and error compensation systems were developed. The rearsearch work of this dissertation was carried out through the methods of theoretical analysis, numerical simulation with experimental verification.
In chapter 1, the background and significance of the research were introduced, the current research situations, key technologies and development trend of the AACMM were expatiated in detail, and then the research contents of this dissertation were proposed.
In chapter 2, the kinematics model of the AACMM was established, and it was analyzed through the method of numerical calculation and graphical simulation. The error model of AACMMs was presented followed a thorough analysis of the error sources of AACMMs. Then the error distribution maps of joint angles, joint torsion angles and other linear parameters were plotted, and the influence of structure parameters on measurement precision was analyzed through the error distribution maps, which provide theoretical foundation for structural design, components selection and measurement area selection of AACMMs.
In chapter 3, mechanical structure design of an AACMM was carried out based on the theoretical analysis in chapter 2, and its measurement space is achieved through simulation analysis. The deformation of the AACMM under the gravity and measuring force were analyzed with the software of ANSYS, and the results show that the strength and deformation meet the design requirements. The data acquisition system was built, which can realize real-time signal acquisition and high-speed transmission. The fit and evaluation methods of common geometric elements were studied, and a coordinate measuring software for AACMMs was developed based on Open Cascade CAD and multi-threading technology.
In chapter 4, the composition and working principle of radial circular grating angle sensors were studied, and the measurement errors which caused by installation were analyzed. Then the angle sensors were calibrated respectively with coordinate measuring machines and autocollimators. From the calibration data the distribution of angle measurement errors was achieved. Afterwards two different forms of error compensation methods were proposed. One method predicts the measurement error of the angle sensors with radial basis function neural network at first, and then compensate the reading of the sensors by the predicting data. The other method is based on the spectrum analysis of the calibrating data. From the analysis result a sine function compensation model was proposed. Furthermore, a particle swarm optimization was used to identify the parameters of the compensation model, which can overcome the non-converge problem of the least-squares method and other traditional algorithms.
In chapter 5, the principle and realization method of self-calibration for AACMMs were studied. A modified simulated annealing algorithm was proposed to identify the structural parameters of the AACMMs with the single point data acquisited from a cone-shape hole. The algorithm can keep the best solution during search, and reduce the search range when the solution approaches the global minimum, which can improve the search efficiency and accuracy.
In chapter 6, the 6-DOF AACMM was used to carry out experimental tests to evaluate the calibration and error compensation methods, the results show that after compensation the measurement accuracy of circular grating sensors reaches 0.002°, and after calibration, length measurement and repeatability accuracy of the AACMM reaches 0.06mm and 0.05mm respectively.
In chapter 7, the main work and innovations of this dissertation were summarized, and the further research subjects were proposed.
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