面阵传感圆柱度非接触测量方法及评定技术研究
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摘要
圆柱度误差是精密轴系零件重要的精度指标之一。精确地测量和评定圆柱度误差不仅为轴类零件的验收提供依据,而且为轴类零件加工精度和装配精度的提高提供可靠的保证。现有的圆柱度误差测量方法中存在随意性大、轴向采样不足、认证不规范等问题。因此,亟需研究高效的、高精度的、符合新一代产品几何技术规范(简称GPS)的测量方法和评定技术。
本文利用面阵传感方式结合多孔径拼接技术实现圆柱度误差的非接触测量,并基于GPS操作技术实现圆柱度误差的规范化评定。构建相应的测量系统及开发数字化评定软件,为圆柱度误差的测量和评定提供了一个有效、可行的新方法。本文对相关技术进行了深入研究,在以下几个方面取得了有价值的研究成果。
1、现行圆柱度误差测量方法分析及其问题
在对ISO/GPS采样规范分析的基础上,通过采用典型圆柱度测量仪器对零件圆柱度进行实测,探讨了现行圆柱度测量方法中存在的局限性和问题。指出现行测量方案多采用圆周轮廓法进行采样,其实质是基于圆度误差测量原理的近似测量。由于受测量仪器自身接触式点位传感方式的限制,在实际测量中,截面个数过少导致轴向信息采样明显不足,从而引起评定结果的不可靠性和不确定性,易导致零件检验的误判。本文依据实测结果和对ISO/TS12180-2规范的深入研究,提出了圆柱度测量采样面密度和采样频率的概念,计算机模拟分析表明实现圆柱度精确测量和评定的关键是提高轴向采样频率。为此,需要探寻新的测量方法和应用技术以实现圆柱度的精密测量。
2、提出面阵传感圆柱度测量新方法,构建新型圆柱度测量系统
该圆柱度测量新方法采用多孔径重叠扫描原理,以数字光栅条纹投射技术作为面阵传感方式,获取各个单视角面形的精确数据,利用多孔径拼接信息融合技术,将各个单视角面形统一于同一坐标系下,从而实现完整柱面的面形测量。新的测量方法具有高精度、非接触、全场的优点。相对现有测量方法,新方法在很大程度上提高了测量的采样面密度和轴向采样频率,从而为圆柱度评定提供完整的、丰富的面形数据。本文选择DLP数字投影机作为光栅投射设备,面阵CCD作为数字图像记录设备,构建了以数字光栅条纹投射技术为原理的多视角测量装置,同时开发相应的配套测量软件,从而为圆柱度测量提供了一套较为完备的新型测量系统。
3、提出系统标定新策略及误差校正新技术
数字光栅条纹投射技术中,系统标定是实现精确测量的关键。本文深入分析了测量系统的结构及几何关系,建立了标定映射关系的精确表达式,通过对参考平面的测量,同时实现相位/深度的纵向标定和横向标定,从而获取系统标定特征参量。在标定过程中,本文提出了改进的Harris角点提取方法,以获取标定平板特征角点的亚像素级图像坐标值;针对CCD的成像畸变,本文提出采用基于BP神经网络的修正法对参考平面的横向坐标进行误差补偿。测量系统的误差分析是保证测量精度的前提。本文提出了一种投射系统非线性自适应校正方法,利用N阶多项式拟合代替传统的单一伽玛参数表示系统的非线性关系,实现了系统非线性影响的有效抑制。为进一步提高测量系统的精度,本文提出了标准平面实测法分析系统误差,并构建了系统误差校正数学模型,实现了系统误差的有效补偿。
4、基于四元数法实现多孔径拼接技术
多孔径拼接技术的基本思想是利用相邻视角重叠区域面形信息建立相对空间位置关系,并利用坐标变换将多视角面形统一于同一坐标系下。因此,坐标变换是实现拼接的关键环节。原有多孔径拼接算法在求解过程中采用传统矩阵法进行坐标变换,并且拼接模型和坐标变换操作分别建立在圆柱坐标系和笛卡尔坐标系下,导致计算较为繁琐。为改善原有拼接算法的可计算性以满足圆柱度测量精度和效率的要求,本文在原有拼接算法的基础上,提出了基于四元数法的拼接方法。该方法采用四元数法代替传统矩阵法进行坐标变换,并将拼接模型和坐标变换操作均统一在笛卡尔坐标系下。在此基础上,利用改进的迭代算法交替进行误差运动求解和坐标变换操作,从而在保证精确求解误差运动的前提下实现拼接。
5、基于GPS规范提出面阵传感测量的圆柱度评定技术
本文基于新一代GPS操作算子技术,结合面阵传感圆柱度拼接测量方法,构建了圆柱度检验算子的具体应用实施步骤,包括分离、提取、滤波、拟合和评估操作。其中,针对滤波操作,本文提出了一种基于三次曲面拟合的非均匀采样加权平均滤波器,可以在进行滤波操作的基础上实现数据的均匀提取。基于以上操作过程的规范和优化,有效地确保了圆柱度误差评定的精确性和可靠性。针对面阵传感测量的面形数据特点,本文提出了圆柱度评定的面形误差等高图C-map、PV值、RMS值三个新参量。新参量的提出和应用有助于分析和改善加工工艺,是对现有圆柱度评定指标的有益补充。同时,本文依据测量不确定度理论和GPS不确定度判定准则,推导出了圆柱度测量不确定度的估计公式,实例应用表明,提出的圆柱度测量不确定度估计,保证了圆柱度评定结果的完整性和有效性。
Cylindricity error is one of the important precision indexes of shaft parts. Accurate measurement and evaluation of cylindricity error can not only provide the basis for parts acceptance, but also guarantee the precision of parts processing and assembly. There exist some disadvantages in current cylindricity measurement methods, such as randomness, insufficient sampling and non-standard verification. Therefore, it needs urgently to research efficient and precision measurement method and evaluation technique which meet the requirement of GPS standard.
Non-contact measurement of cylindricity error is carried out based on area-array sensing technique and multi-aperture connection technique. Moreover, standard evaluation is realized using GPS operator technique. A new measurement system and digital evaluation software are developed, and an efficient and feasible method is presented for cylindricity measurement & evaluation. We have paid more attention to the research of relative fields, and some results are shown as follows:
1. Analysis of current cylindricity measurement methods and their problems
Based on the analysis of the standard sampling specification of ISO/GPS, the experimental measurements of cylindricity with the existing instrument are carried out. Then, the disadvantages and problems of current methods are discussed. Circumferential section method is used as the main type of sampling in current measurement program. In fact, it is an approximate measurement based on the theory of roundness measurement. Because of the point-contact sensing type of the instrument, too few numbers of the measuring section will cause under-sampling of axial information, and will lead to the instability and unreliability of the evaluation results. The concepts of sampling density and frequency are proposed based on the analysis of the measured results and ISO/TS12180-2. Computer simulation results show that the axial sampling frequency is the key factor to realize precise evaluation of cylindricity. Therefore, we need to find new technique for precision measurement of cylindricity.
2. Novel method and new system for cylindricity measurement
The novel method is based on the theory of multi-aperture overlap scanning technique (MAOST), and digital grating projection technique is employed to capture the profile of part. Firstly each 3D profiles of part from different views can be measured, and then all profiles are transformed into the global coordinate by multi-aperture connection technique. The method has some advantages such as no-contact, high efficiency and whole-field information. Compared with current measurement method, the new method can significantly increase the sampling density and axial sampling frequency, and the abundant data of surface are obtained for cylindricity evaluation. A DLP projector is used to project digital fringe patterns onto the object; and a CCD camera is employed to capture the deformed fringe patterns. A multi-view measurement device is constructed based on digital grating projection technique, and attached software is developed. As a result, a complete system is established for cylindricity measurement.
3. Novel strategy of system calibration and error-correction technique
In digital grating projection technique, system calibration is a critical step to carry out precision measurement. After comprehensive analysis of the geometry of measurement system, the accurate mathematical expressions of the mapping relationship of calibration are set up. The reference plane is measured, and the phase-to-depth and pixel to lateral coordinate mapping relationship are simultaneously calibrated. Then, the characteristic parameters of system calibration are determined. In the calibration process, an improved Harris corner extracting method is proposed, and characteristic corners of the calibration gauge in the image can be extracted with sub-pixel accuracy. Moreover, the neural networks are built to correct the error terms of the lateral coordinates of the reference plane by considering the aberration of CCD. Error analysis is the precondition to ensure the measuring precision. A novel nonlinearity correction method is proposed for fringe projection profilometry. In order to describe the nonlinearity of system, polynomial fitting is introduced instead of the single gamma parameter. Using the suggested method, the influence of nonlinear system is suppressed. Next, in order to improve the precision of measurement, the system error is analyzed by use of standard plane measuring method. The mathematic model of error correction is founded, and the system error can be compensated effectively.
4. Multi-aperture connection method based on quaternion
The principle of multi-aperture overlap-scanning technique is to make the adjacent sub-apertures partially overlapped, and then their relative location and orientation can be obtained through the overlapped area. The sub-apertures can be transformed to a global coordinate system. Therefore, coordinate transformation is the key step to realize connection. In the computation process of the original connection algorithm, the traditional matrix method is used to realize coordinates transformation. In addition, connection model and coordinate transformation are established in cylindrical coordinates system and Cartesian coordinates system, respectively. In order to improve calculability of the connection algorithm for the precision requirement of cylindricity measurement, a new connection algorithm method using quaternion method is brought forward according to the original algorithm. The quaternion instead of the traditional matrix is used to realize coordinates transformation, and connection model and coordinate transformation are established in the same Cartesian coordinate system. On these bases, the error movement calculation and coordinates transformation are performed by the improved iterative algorithm. Then, the multi-aperture connection can be realized by means of the high precision error movement calculation.
5. Cylindricity evaluation techniques of area-array sensor measurement based on GPS specification
Based on the GPS operator technology and the new measurement method, a complete verification operator of cylindricity is constructed, which includes partition, extraction, filtration, association and verification. Because the filtration is the critical role of operator, a weighted average filter with nonuniform sampling is proposed on basis of cubic-fit filtering algorithm. The filter can realize filtering and extract uniform data. Based on the standard and optimal operation process, the accuracy and reliability of cylindricity evaluation can be ensured. According to the characteristic of tested data, three new parameters for form errors evaluation are presented, including C-map, PV, RMS. New parameters are useful for analysis and improvement of the processing technology, and they can also supplement the cylindricity evaluation indexes. Moreover, according to the theory of measurement uncertainty and the uncertainty judging principle of GPS, the equation of uncertainty estimation for cylindricity measurement is deduced. The practical application shows that the uncertainty estimation of cylindricity can guarantee the integrality and validity of evaluation results.
本文利用面阵传感方式结合多孔径拼接技术实现圆柱度误差的非接触测量,并基于GPS操作技术实现圆柱度误差的规范化评定。构建相应的测量系统及开发数字化评定软件,为圆柱度误差的测量和评定提供了一个有效、可行的新方法。本文对相关技术进行了深入研究,在以下几个方面取得了有价值的研究成果。
1、现行圆柱度误差测量方法分析及其问题
在对ISO/GPS采样规范分析的基础上,通过采用典型圆柱度测量仪器对零件圆柱度进行实测,探讨了现行圆柱度测量方法中存在的局限性和问题。指出现行测量方案多采用圆周轮廓法进行采样,其实质是基于圆度误差测量原理的近似测量。由于受测量仪器自身接触式点位传感方式的限制,在实际测量中,截面个数过少导致轴向信息采样明显不足,从而引起评定结果的不可靠性和不确定性,易导致零件检验的误判。本文依据实测结果和对ISO/TS12180-2规范的深入研究,提出了圆柱度测量采样面密度和采样频率的概念,计算机模拟分析表明实现圆柱度精确测量和评定的关键是提高轴向采样频率。为此,需要探寻新的测量方法和应用技术以实现圆柱度的精密测量。
2、提出面阵传感圆柱度测量新方法,构建新型圆柱度测量系统
该圆柱度测量新方法采用多孔径重叠扫描原理,以数字光栅条纹投射技术作为面阵传感方式,获取各个单视角面形的精确数据,利用多孔径拼接信息融合技术,将各个单视角面形统一于同一坐标系下,从而实现完整柱面的面形测量。新的测量方法具有高精度、非接触、全场的优点。相对现有测量方法,新方法在很大程度上提高了测量的采样面密度和轴向采样频率,从而为圆柱度评定提供完整的、丰富的面形数据。本文选择DLP数字投影机作为光栅投射设备,面阵CCD作为数字图像记录设备,构建了以数字光栅条纹投射技术为原理的多视角测量装置,同时开发相应的配套测量软件,从而为圆柱度测量提供了一套较为完备的新型测量系统。
3、提出系统标定新策略及误差校正新技术
数字光栅条纹投射技术中,系统标定是实现精确测量的关键。本文深入分析了测量系统的结构及几何关系,建立了标定映射关系的精确表达式,通过对参考平面的测量,同时实现相位/深度的纵向标定和横向标定,从而获取系统标定特征参量。在标定过程中,本文提出了改进的Harris角点提取方法,以获取标定平板特征角点的亚像素级图像坐标值;针对CCD的成像畸变,本文提出采用基于BP神经网络的修正法对参考平面的横向坐标进行误差补偿。测量系统的误差分析是保证测量精度的前提。本文提出了一种投射系统非线性自适应校正方法,利用N阶多项式拟合代替传统的单一伽玛参数表示系统的非线性关系,实现了系统非线性影响的有效抑制。为进一步提高测量系统的精度,本文提出了标准平面实测法分析系统误差,并构建了系统误差校正数学模型,实现了系统误差的有效补偿。
4、基于四元数法实现多孔径拼接技术
多孔径拼接技术的基本思想是利用相邻视角重叠区域面形信息建立相对空间位置关系,并利用坐标变换将多视角面形统一于同一坐标系下。因此,坐标变换是实现拼接的关键环节。原有多孔径拼接算法在求解过程中采用传统矩阵法进行坐标变换,并且拼接模型和坐标变换操作分别建立在圆柱坐标系和笛卡尔坐标系下,导致计算较为繁琐。为改善原有拼接算法的可计算性以满足圆柱度测量精度和效率的要求,本文在原有拼接算法的基础上,提出了基于四元数法的拼接方法。该方法采用四元数法代替传统矩阵法进行坐标变换,并将拼接模型和坐标变换操作均统一在笛卡尔坐标系下。在此基础上,利用改进的迭代算法交替进行误差运动求解和坐标变换操作,从而在保证精确求解误差运动的前提下实现拼接。
5、基于GPS规范提出面阵传感测量的圆柱度评定技术
本文基于新一代GPS操作算子技术,结合面阵传感圆柱度拼接测量方法,构建了圆柱度检验算子的具体应用实施步骤,包括分离、提取、滤波、拟合和评估操作。其中,针对滤波操作,本文提出了一种基于三次曲面拟合的非均匀采样加权平均滤波器,可以在进行滤波操作的基础上实现数据的均匀提取。基于以上操作过程的规范和优化,有效地确保了圆柱度误差评定的精确性和可靠性。针对面阵传感测量的面形数据特点,本文提出了圆柱度评定的面形误差等高图C-map、PV值、RMS值三个新参量。新参量的提出和应用有助于分析和改善加工工艺,是对现有圆柱度评定指标的有益补充。同时,本文依据测量不确定度理论和GPS不确定度判定准则,推导出了圆柱度测量不确定度的估计公式,实例应用表明,提出的圆柱度测量不确定度估计,保证了圆柱度评定结果的完整性和有效性。
Cylindricity error is one of the important precision indexes of shaft parts. Accurate measurement and evaluation of cylindricity error can not only provide the basis for parts acceptance, but also guarantee the precision of parts processing and assembly. There exist some disadvantages in current cylindricity measurement methods, such as randomness, insufficient sampling and non-standard verification. Therefore, it needs urgently to research efficient and precision measurement method and evaluation technique which meet the requirement of GPS standard.
Non-contact measurement of cylindricity error is carried out based on area-array sensing technique and multi-aperture connection technique. Moreover, standard evaluation is realized using GPS operator technique. A new measurement system and digital evaluation software are developed, and an efficient and feasible method is presented for cylindricity measurement & evaluation. We have paid more attention to the research of relative fields, and some results are shown as follows:
1. Analysis of current cylindricity measurement methods and their problems
Based on the analysis of the standard sampling specification of ISO/GPS, the experimental measurements of cylindricity with the existing instrument are carried out. Then, the disadvantages and problems of current methods are discussed. Circumferential section method is used as the main type of sampling in current measurement program. In fact, it is an approximate measurement based on the theory of roundness measurement. Because of the point-contact sensing type of the instrument, too few numbers of the measuring section will cause under-sampling of axial information, and will lead to the instability and unreliability of the evaluation results. The concepts of sampling density and frequency are proposed based on the analysis of the measured results and ISO/TS12180-2. Computer simulation results show that the axial sampling frequency is the key factor to realize precise evaluation of cylindricity. Therefore, we need to find new technique for precision measurement of cylindricity.
2. Novel method and new system for cylindricity measurement
The novel method is based on the theory of multi-aperture overlap scanning technique (MAOST), and digital grating projection technique is employed to capture the profile of part. Firstly each 3D profiles of part from different views can be measured, and then all profiles are transformed into the global coordinate by multi-aperture connection technique. The method has some advantages such as no-contact, high efficiency and whole-field information. Compared with current measurement method, the new method can significantly increase the sampling density and axial sampling frequency, and the abundant data of surface are obtained for cylindricity evaluation. A DLP projector is used to project digital fringe patterns onto the object; and a CCD camera is employed to capture the deformed fringe patterns. A multi-view measurement device is constructed based on digital grating projection technique, and attached software is developed. As a result, a complete system is established for cylindricity measurement.
3. Novel strategy of system calibration and error-correction technique
In digital grating projection technique, system calibration is a critical step to carry out precision measurement. After comprehensive analysis of the geometry of measurement system, the accurate mathematical expressions of the mapping relationship of calibration are set up. The reference plane is measured, and the phase-to-depth and pixel to lateral coordinate mapping relationship are simultaneously calibrated. Then, the characteristic parameters of system calibration are determined. In the calibration process, an improved Harris corner extracting method is proposed, and characteristic corners of the calibration gauge in the image can be extracted with sub-pixel accuracy. Moreover, the neural networks are built to correct the error terms of the lateral coordinates of the reference plane by considering the aberration of CCD. Error analysis is the precondition to ensure the measuring precision. A novel nonlinearity correction method is proposed for fringe projection profilometry. In order to describe the nonlinearity of system, polynomial fitting is introduced instead of the single gamma parameter. Using the suggested method, the influence of nonlinear system is suppressed. Next, in order to improve the precision of measurement, the system error is analyzed by use of standard plane measuring method. The mathematic model of error correction is founded, and the system error can be compensated effectively.
4. Multi-aperture connection method based on quaternion
The principle of multi-aperture overlap-scanning technique is to make the adjacent sub-apertures partially overlapped, and then their relative location and orientation can be obtained through the overlapped area. The sub-apertures can be transformed to a global coordinate system. Therefore, coordinate transformation is the key step to realize connection. In the computation process of the original connection algorithm, the traditional matrix method is used to realize coordinates transformation. In addition, connection model and coordinate transformation are established in cylindrical coordinates system and Cartesian coordinates system, respectively. In order to improve calculability of the connection algorithm for the precision requirement of cylindricity measurement, a new connection algorithm method using quaternion method is brought forward according to the original algorithm. The quaternion instead of the traditional matrix is used to realize coordinates transformation, and connection model and coordinate transformation are established in the same Cartesian coordinate system. On these bases, the error movement calculation and coordinates transformation are performed by the improved iterative algorithm. Then, the multi-aperture connection can be realized by means of the high precision error movement calculation.
5. Cylindricity evaluation techniques of area-array sensor measurement based on GPS specification
Based on the GPS operator technology and the new measurement method, a complete verification operator of cylindricity is constructed, which includes partition, extraction, filtration, association and verification. Because the filtration is the critical role of operator, a weighted average filter with nonuniform sampling is proposed on basis of cubic-fit filtering algorithm. The filter can realize filtering and extract uniform data. Based on the standard and optimal operation process, the accuracy and reliability of cylindricity evaluation can be ensured. According to the characteristic of tested data, three new parameters for form errors evaluation are presented, including C-map, PV, RMS. New parameters are useful for analysis and improvement of the processing technology, and they can also supplement the cylindricity evaluation indexes. Moreover, according to the theory of measurement uncertainty and the uncertainty judging principle of GPS, the equation of uncertainty estimation for cylindricity measurement is deduced. The practical application shows that the uncertainty estimation of cylindricity can guarantee the integrality and validity of evaluation results.
引文
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