【作者】 王涛；

【导师】 石照耀；

【作者基本信息】 北京工业大学 ， 机械工程， 2021， 博士

【摘要】 齿轮是广泛应用的关键传动零件,齿轮测量是保证齿轮精度和使用性能的主要措施。随着齿轮产业成为中国机械基础件中规模最大的产业,对大批量成品齿轮进行快速、全面的测量已成齿轮工业亟待解决的问题。齿轮检测按照检测形式分为接触式测量和非接触式测量两大类。目前齿轮接触式测量已达到技术的瓶颈阶段,尤其是测量效率已经很难有显著性提升。作为一种齿轮非接触测量技术,线结构光测量具有测量效率高、点云样本大、齿面信息完整的特点,特别适合于快速、全面的齿轮测量所需,但其三维测量中仍存在一些共性问题没有很好的解决,影响了线结构光测量齿轮的应用与推广。为此,在国家自然基金重点项目、国家重点研发计划项目的资助下,本文通过理论创新,对线结构光下小弧段芯轴标定件的中心确定、齿轮测量系统的线结构光测头姿态以及转台顶尖倾斜的标定、齿轮线结构光偏置捕获完整的三维轮廓、以及全齿面误差评价开展理论及实践研究,最终形成一套线结构光测量齿轮方法。对上述研究点分别进行针对性的实验验证,结果验证了齿轮线结构光测量方法的有效性和准确性。本文主要的研究工作包括:(1)提出基于线结构光的齿轮偏置测量方法。针对齿轮“陡峭”齿面在线结构光测量中阴影效应、样本密度低和可信度低的问题,提出了偏置的最优位姿、量化指标及其计算方法,从齿面模型至偏置测量齿面进行理论推导。为了辨析偏置与非偏置的居中对位,以及接触式测量三种方法本质上的差异,分别进行齿轮线结构光测量实验对比验证。验证结果表明,线结构光偏置测量比线结构光居中对位测量得到的结果可信度和准确性更高,应用本方法所获取的齿面点云更符合最新国际齿轮精度标准要求,且各项评价指标结果与克林贝格P26型齿轮测量中心所测的参照值基本相符。(2)提出确定齿轮测量基准点的新确定方法。针对齿轮测量中基准点确定的基础问题,其小弧段轮廓基准点精确的确定是研究领域的难点和共性问题。通过建立几何圆柱芯轴轮廓的数学模型,引入参数化椭圆轮廓来表征线结构光所捕获的芯轴弧段,构建参数角度与轮廓点的正交距离误差的映射关系,最后Levenberg-Marquardt迭代搜索达到目标函数全局最小值,即轮廓对应求解的最优椭圆满足误差集的平方和最小。所提方法通过仿真和实测实验验证了的鲁棒性、抗噪性和准确性,实验分析表明几何拟合方法可自适应的实现基准点精确获取,即使在线结构光测头有安装误差的情况下,该方法仍能准确计算芯轴的实际基准点及结构光光平面所截取的椭圆参数。几何椭圆拟合适用于齿轮测量基准点获取,满足了线结构光测量齿轮的技术需要。(3)提出线结构光下齿轮测量的坐标关系标定方法。针对传统的球标定时,线结构光在不同曲率上由光场差异所导致的重复性差的问题。新方法提出以圆柱芯轴作为标定件,所捕获的轮廓参数在z轴扫描时曲率相对稳定、计算精度高的特点,保证了标定时校准的重复性和准确性。其次,基于芯轴标定件中心的唯一性,提出了同时标定线结构光系统的外在参数和转台顶尖倾斜的方法。通过两次扫描策略,得到多组非共线校准点,这些生成的非共线点被满足于与相对运动模型的外在参数计算。实验对比验证了所提出新方法应用在集成系统的准确性和有效性。尤其是所提方法标定过程易执行、精度高,适合于对集成了线结构光的CNC测量系统进行快速标定、现场标定等场合。(4)提出基于三维信息的齿轮全齿面误差评价体系。基于齿面误差3D表征的周向、法向和齿向范式的新体系,包括线结构光的(OCPH)全齿面误差数学模型表达,统计新指标的构建,以及精度评价和分析。所提方法避免了误差表征单一化,有效降低了测量随机误差的干扰,并能够直观且具体的获取完整齿轮误差大小、离散程度、分布位置等信息。仿真和实测实验验证了所提评价体系的有效性和实用性,有效的解决了传统小样本测量和评价方法存在的不足,明显优于传统表征和评价方式,以齿轮误差多线集或面集的表征分析,符合大样本量的齿面分析需求,更适合齿轮线结构光测量。(5)开发了齿轮线结构光数据处理软件。在解决基准点计算、系统坐标关系标定、齿面数据获取以及误差三维表征等关键问题的基础上,利用G语言软件labview和matlab联合编程开发了齿轮线结构光数据处理软件。该软件提供了一种非接触齿轮测量数据处理方法,实现了齿面2D和3D的基础参数计算、误差表征和精度评价等功能模块,为齿轮非接触全面的快速测量理论提供了实践验证的计算平台。本文的各种方法通过该软件得到集成,在搭建的齿轮线结构光测量机上得到成功应用。更多还原

【Abstract】 Gear is a key transmission part widely used.Gear measurement is the main measure to ensure the accuracy and performance of gear.With the gear industry becoming the largest industry in China’s mechanical basic parts,the rapid and comprehensive measurement of large quantities of finished gears has become an urgent problem for the gear industry.Gear detection can be divided into contact measurement and non-contact measurement.At present,the gear contact measurement technology has reached the bottleneck stage,especially the measurement efficiency has been difficult to improve significantly.However,there are still some common problems in its three-dimensional measurement that are not well solved,which affects the application and popularization of line structured light(abbreviated as LSL)measurement of gears.Therefore,with the support of the national natural science foundation and national key R & D program,through theoretical innovation,this paper carries out theoretical and practical research on the determination of the center of small arc mandrel standard parts under LSL,the calibration of linear structured light probe posture and turntable center of gear measuring system,the capture of complete three-dimensional profile by gear LSL offset,and the evaluation of full tooth surface error.Finally,a method of measuring gear with LSL is formed.The experimental results verify the validity and accuracy of the gear LSL measurement method.The main research work of this paper includes:(1)A method of measuring gear offset by LSL is proposed.Aiming at the problems of shadow effect,low sample density and low reliability in LSL measurement of gear "steep" tooth surface,the optimal position and orientation of offset,quantitative index and its calculation method are proposed,and the theoretical derivation is carried out from tooth surface model to offset measurement tooth surface.In order to distinguish the essential differences between the offset and non-offset alignment and the contact measurement,the gear LSL measurement experiments were carried out respectively.The verification results show that the accuracy and reliability of the offset measurement of LSL is higher than that of the center alignment measurement of LSL.The point cloud of tooth surface obtained by this method is more in line with the requirements of the latest international gear accuracy standards,and the evaluation index results are basically consistent with the reference values measured by klingelnberg P26 gear measurement center.(2)A new determination method for determining the reference point of gear measurement is proposed.Aiming at the basic problem of reference point determination in gear measurement,it is a difficult and common problem in the research field to accurately determine the reference point of small arc profile.The mathematical model of geometric cylindrical mandrel contour is established,and the parametric ellipse contour is introduced to represent the mandrel arc captured by the LSL.The mapping relationship between the parameter angle and the orthogonal distance error of the contour point is constructed.Finally,the Levenberg-Marquardt iterative search achieves the global minimum of the objective function,that is,the optimal ellipse corresponding to the profile satisfies the minimum sum of squares of the error set.The robustness,anti noise and accuracy of the proposed method are verified by simulation and experimental results.The experimental analysis shows that the new method can adaptively achieve the accurate acquisition of the reference point.Even if the LSL sensor has installation error,the method can still accurately calculate the real center feature of the mandrel and the ellipse parameters intercepted by the structured light plane.The new method is suitable for obtaining the datum point of gear measurement and meets the technical needs of gear measurement with LSL.(3)A new calibration method of coordinate relationship for gear measurement under LSL is proposed.Aiming at the problem of poor repeatability caused by the difference of light field in different curvatures of LSL in traditional spherical calibration.In the new method,the cylindrical mandrel is used as the calibration part,and the curvature of the captured contour parameters is relatively stable and the calculation accuracy is high,which ensures the repeatability and accuracy of calibration.Secondly,based on the uniqueness of the mandrel calibration center,a method of simultaneously calibrating the extrinsic parameters of the LSL system and the tilt of the turntable tip is proposed.Multiple groups of non-collinear calibration points are obtained by two scanning strategy.These generated non-collinear calibration points are satisfied with the calculation of extrinsic parameters of relative motion model.Experimental results verify the accuracy and effectiveness of the proposed method in the integrated system.In particular,the calibration process of the proposed method is easy to implement and has high accuracy,which is suitable for fast calibration and field calibration of CNC measurement system integrated with LSL.(4)The error evaluation system of gear full tooth surface based on threedimensional information is proposed.A new system of circumferential,normal and tooth pattern based on 3D representation of tooth surface error is proposed,including the mathematical model expression of OCPH,the construction of new statistical indicators,and the accuracy evaluation and analysis.The method avoids the simplification of error representation,effectively reduces the interference of random error measurement,and can directly and concretely obtain the information of the error size,dispersion degree and distribution position of the complete gear.The simulation and the experimental results verify the effectiveness and practicability of the proposed evaluation system,effectively solve the shortcomings of the traditional small sample measurement and evaluation methods,which is obviously superior to the traditional representation and evaluation methods.The gear error multi line set or surface set representation analysis is in line with the demand of tooth surface analysis with large sample size,and more suitable for the gear line structural light measurement.(5)The data processing software of gear line structured light is developed.On the basis of solving the key problems of datum point calculation,system coordinate relationship calibration,tooth surface data acquisition and error three-dimensional characterization,the gear LSL data processing software is developed by using G language software labview and matlab.The software provides a non-contact gear measurement data processing method,realizes the basic parameter calculation,error characterization and accuracy evaluation of 2D and 3D tooth surface,and provides a practical verification calculation platform for gear non-contact multi-dimensional rapid measurement theory.The various methods and theories of this paper are integrated by the software,and successfully applied in the gear LSL measuring machine.更多还原