直齿圆柱齿轮渐开线齿廓的结构光视觉测量技术
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摘要
结构光视觉技术以光学和电学中的物理现象为基础，获取并处理被测物体表面与结构光相接处的图像来重构被测物体的三维几何信息，可主要用于复杂曲面或自由曲面的三维测量。将结构光视觉技术应用于机械工业中的零件尺寸测量，具有非接触、速度快、自动化程度高等优点，因此结构光视觉技术在机械工业领域中的应用越来越受到人们的关注。
齿轮是机械工业中一种重要的传动零件，直齿圆柱齿轮的应用尤为广泛，随着对齿轮质量的要求越来越高，对齿轮的测量也提出了更加严格的要求。测量精度的发展影响着制造技术的提高，因此研究更加先进的齿轮测量技术对齿轮制造技术的整体提高有着非常重要的推动作用。
当齿轮存在较大的齿形误差时，工作齿形已不是正确的渐开线齿形，其啮合点的运动理论上已经不再符合齿轮基本定律，导致瞬时传动比发生变化，影响齿轮传动的工作平稳性。因此，齿轮齿形误差的测量在齿轮各项参数的测量中尤为重要。本文建立以CCD摄像机、光学镜头、半导体激光器以及计算机为主要组成部分的结构光视觉测量系统，利用直齿圆柱齿轮的几何特征，提出了一种基于结构光视觉技术的齿轮渐开线齿形误差的测量方法。
首先，本文分析了结构光视觉模型，该模型分为两部分：对于CCD摄像机的成像模型，基于小孔成像原理的假设，建立非线性的坐标转换关系，并利用经典的两步标定法对模型中各参数进行标定；对于结构光光平面的参数模型，在分析了传统标定法的基础上，提出了基于全局参数的改进标定法，优化了整个系统的参数变量，有效的提高了结构光视觉系统的标定精度。最后，结构光系统标定实验表明，采用6幅共面标靶图像，将光条宽度控制在5个像素左右可以得到最佳的标定结果。
其次，本文根据被测直齿圆柱齿轮的几何特征，建立了渐开线齿廓的测量模型。针对测量时结构光光平面与齿轮回转轴线不垂直的问题，建立了基于回转轴线方向的伪光平面，并将通过结构光视觉系统重构的目标点投影到这个平面上，在垂直于回转轴线的方向上形成一条渐开线。为了简化齿形误差的计算，本文在伪光平面上建立局部坐标系，将被测点的三维坐标转换成光平面上的二维坐标，并在此二维直角坐标系下，按坐标法给出了基圆半径和渐开线齿形误差的计算方法。
为了提高结构光视觉系统测量的分辨率，从图像中获取光条中心点的亚像素位置是必要的。本文分析了几种亚像素光条中心点检测方法。针对经典的Steger光条中心点检测方法，讨论了各参数的最优值选择。针对传统评价方法的不足，本文提出了一种基于量块尺寸的精度评价方法，将实际尺寸测量误差作为精度评价准则，更符合测量的实际要求。
最后，通过测量实验验证了本文提出的直齿圆柱齿轮渐开线齿形误差的结构光视觉测量方法的精度。实验分为测量基圆误差和测量渐开线齿形误差两部分。实验结果表明，结构光视觉测量系统平台的安装位置、齿轮的齿数、结构光光平面与齿轮横截面的夹角对测量精度无明显影响。齿轮的模数越大，本文的测量方法的测量精度也越高。
本文的研究工作对发展结构光视觉测量技术的工程应用具有一定的意义。
Based on light and electricity physical phenomena, structured light vision technologyobtain and process the image of the structured light on the measured object to reconstruct thethree-dimensional geometry. It can be mainly used for the measurements of complex surfaceor freedom three-dimensional surface. The structured light vision technology is used inmechanical industry, which has the outstanding advantages of non-contact, high speed, highdegree of automation. Thus, more and more people pay attention to the use of structuredlight vision technology in the machinery industry.
Gear is an important part of the transmission. The application of spur gear is particularlywidespread. With the increasingly high quality requirements of the gear, measuring gear isalso stricter. The development of measurement precision has an influence on theimprovement of manufacturing technology. As a result, the research of more advanced gearmeasuring technology has a very important role on the overall improvement of the gearmanufacturing technology.
When there is a large gear profile error, the work profile is not the correct tooth profile.The trajectory of the engagement point theoretically no longer meets the basic laws of gear,resulting the occurrence of the change of instantaneous transmission ratio. It will have animpact on the stability of gear transmission job. Therefore, the measurement of the geartooth error is particularly important in measuring the parameters of the gear. This paperestablishes structured light vision measurement system with CCD camera, optical lenses,semiconductor lasers and computers. Based on the geometric characteristics of the spur gear,a measurement method of gear profile error based on structured light vision technology ispresented.
Firstly, this paper analyzes the model of structure light vision, which is divided into twoparts: For the imaging model of the CCD camera, based on the assumption of pinhole imaging principle, a non-linear relationship of the coordinate transformation is established.Using the classic two-step calibration method, the parameters in the model is calculated; Forthe parameter model of structured light plane, based on the analysis of the traditionalcalibration method, an improved calibration method based on global parameter is proposed.The parameters variables of the system are optimized. The calibration accuracy of thestructure light system is effectively improved. At last, the experiments of calibratingstructured light system showed that the best calibration results can be got by6images ofcoplanar target and the stripe width of5pixel.
Secondly, according to the geometric characteristics of the measured spur gear, a toothprofile measurement model is established. As the structured light measurement plane is notperpendicular to the rotation axis of the measured gear, a pseudo structured light plane basedon the rotation axis is established. The target point which is reconstructed by the structuredlight vision imaging system will project onto the pseudo structured light plane. Ten, aninvolute is formed on the direction of the rotation axis. To simplify the calculation of profileerror, this paper establishes a local coordinate system on the pseudo structured light plane,the three-dimensional coordinates of the measured points are transformed to thetwo-dimensional coordinate plane. In this two-dimensional coordinate system, according tocoordinate method, the radius of the base circle and profile errors is calculated.
To improve resolution of structure light vision system, obtaining a sub-pixel position ofthe light center from the image is essential. This paper analyses several of sub-pixeldetection method of the light center. Based on the classical detection method proposed bySteger, the optimal choose of each parameter is discussed. For the lack of traditionalevaluation methods, this paper presents an accuracy evaluation method based on the blocksize, taking actual measurement error as criterion of accuracy evaluation, which conforms torequirements of actual measurement.
Finally, the experiments verify the accuracy of the proposed measurement method basedon structured light vision. Experiments were divided into two parts: measurements of thebase circle and measurement of profile error. Experimental results show that the installationlocation of the structured light vision measurement system platform, the number of gear teeth and the angle between the plane of structured light and the cross-section plane of gearhave no significant effect on the measurement accuracy. The greater the gear modulus is, thehigher the accuracy of the measurement method is.
The work and research in this article has certain significance for applying structuredlight vision measurement technology in engineering.
齿轮是机械工业中一种重要的传动零件，直齿圆柱齿轮的应用尤为广泛，随着对齿轮质量的要求越来越高，对齿轮的测量也提出了更加严格的要求。测量精度的发展影响着制造技术的提高，因此研究更加先进的齿轮测量技术对齿轮制造技术的整体提高有着非常重要的推动作用。
当齿轮存在较大的齿形误差时，工作齿形已不是正确的渐开线齿形，其啮合点的运动理论上已经不再符合齿轮基本定律，导致瞬时传动比发生变化，影响齿轮传动的工作平稳性。因此，齿轮齿形误差的测量在齿轮各项参数的测量中尤为重要。本文建立以CCD摄像机、光学镜头、半导体激光器以及计算机为主要组成部分的结构光视觉测量系统，利用直齿圆柱齿轮的几何特征，提出了一种基于结构光视觉技术的齿轮渐开线齿形误差的测量方法。
首先，本文分析了结构光视觉模型，该模型分为两部分：对于CCD摄像机的成像模型，基于小孔成像原理的假设，建立非线性的坐标转换关系，并利用经典的两步标定法对模型中各参数进行标定；对于结构光光平面的参数模型，在分析了传统标定法的基础上，提出了基于全局参数的改进标定法，优化了整个系统的参数变量，有效的提高了结构光视觉系统的标定精度。最后，结构光系统标定实验表明，采用6幅共面标靶图像，将光条宽度控制在5个像素左右可以得到最佳的标定结果。
其次，本文根据被测直齿圆柱齿轮的几何特征，建立了渐开线齿廓的测量模型。针对测量时结构光光平面与齿轮回转轴线不垂直的问题，建立了基于回转轴线方向的伪光平面，并将通过结构光视觉系统重构的目标点投影到这个平面上，在垂直于回转轴线的方向上形成一条渐开线。为了简化齿形误差的计算，本文在伪光平面上建立局部坐标系，将被测点的三维坐标转换成光平面上的二维坐标，并在此二维直角坐标系下，按坐标法给出了基圆半径和渐开线齿形误差的计算方法。
为了提高结构光视觉系统测量的分辨率，从图像中获取光条中心点的亚像素位置是必要的。本文分析了几种亚像素光条中心点检测方法。针对经典的Steger光条中心点检测方法，讨论了各参数的最优值选择。针对传统评价方法的不足，本文提出了一种基于量块尺寸的精度评价方法，将实际尺寸测量误差作为精度评价准则，更符合测量的实际要求。
最后，通过测量实验验证了本文提出的直齿圆柱齿轮渐开线齿形误差的结构光视觉测量方法的精度。实验分为测量基圆误差和测量渐开线齿形误差两部分。实验结果表明，结构光视觉测量系统平台的安装位置、齿轮的齿数、结构光光平面与齿轮横截面的夹角对测量精度无明显影响。齿轮的模数越大，本文的测量方法的测量精度也越高。
本文的研究工作对发展结构光视觉测量技术的工程应用具有一定的意义。
Based on light and electricity physical phenomena, structured light vision technologyobtain and process the image of the structured light on the measured object to reconstruct thethree-dimensional geometry. It can be mainly used for the measurements of complex surfaceor freedom three-dimensional surface. The structured light vision technology is used inmechanical industry, which has the outstanding advantages of non-contact, high speed, highdegree of automation. Thus, more and more people pay attention to the use of structuredlight vision technology in the machinery industry.
Gear is an important part of the transmission. The application of spur gear is particularlywidespread. With the increasingly high quality requirements of the gear, measuring gear isalso stricter. The development of measurement precision has an influence on theimprovement of manufacturing technology. As a result, the research of more advanced gearmeasuring technology has a very important role on the overall improvement of the gearmanufacturing technology.
When there is a large gear profile error, the work profile is not the correct tooth profile.The trajectory of the engagement point theoretically no longer meets the basic laws of gear,resulting the occurrence of the change of instantaneous transmission ratio. It will have animpact on the stability of gear transmission job. Therefore, the measurement of the geartooth error is particularly important in measuring the parameters of the gear. This paperestablishes structured light vision measurement system with CCD camera, optical lenses,semiconductor lasers and computers. Based on the geometric characteristics of the spur gear,a measurement method of gear profile error based on structured light vision technology ispresented.
Firstly, this paper analyzes the model of structure light vision, which is divided into twoparts: For the imaging model of the CCD camera, based on the assumption of pinhole imaging principle, a non-linear relationship of the coordinate transformation is established.Using the classic two-step calibration method, the parameters in the model is calculated; Forthe parameter model of structured light plane, based on the analysis of the traditionalcalibration method, an improved calibration method based on global parameter is proposed.The parameters variables of the system are optimized. The calibration accuracy of thestructure light system is effectively improved. At last, the experiments of calibratingstructured light system showed that the best calibration results can be got by6images ofcoplanar target and the stripe width of5pixel.
Secondly, according to the geometric characteristics of the measured spur gear, a toothprofile measurement model is established. As the structured light measurement plane is notperpendicular to the rotation axis of the measured gear, a pseudo structured light plane basedon the rotation axis is established. The target point which is reconstructed by the structuredlight vision imaging system will project onto the pseudo structured light plane. Ten, aninvolute is formed on the direction of the rotation axis. To simplify the calculation of profileerror, this paper establishes a local coordinate system on the pseudo structured light plane,the three-dimensional coordinates of the measured points are transformed to thetwo-dimensional coordinate plane. In this two-dimensional coordinate system, according tocoordinate method, the radius of the base circle and profile errors is calculated.
To improve resolution of structure light vision system, obtaining a sub-pixel position ofthe light center from the image is essential. This paper analyses several of sub-pixeldetection method of the light center. Based on the classical detection method proposed bySteger, the optimal choose of each parameter is discussed. For the lack of traditionalevaluation methods, this paper presents an accuracy evaluation method based on the blocksize, taking actual measurement error as criterion of accuracy evaluation, which conforms torequirements of actual measurement.
Finally, the experiments verify the accuracy of the proposed measurement method basedon structured light vision. Experiments were divided into two parts: measurements of thebase circle and measurement of profile error. Experimental results show that the installationlocation of the structured light vision measurement system platform, the number of gear teeth and the angle between the plane of structured light and the cross-section plane of gearhave no significant effect on the measurement accuracy. The greater the gear modulus is, thehigher the accuracy of the measurement method is.
The work and research in this article has certain significance for applying structuredlight vision measurement technology in engineering.
引文
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