Pitch deviation measurement of an involute spur gear by a rotary profiling system

This paper presents surface-profiling based gear pitch deviation measurement for an involute spur gear. A rotary profiling system, which consists of an air-bearing spindle and a displacement sensor with a diamond stylus, is employed to measure gear pitch deviation. In measurement of gear pitch deviation, an eccentric error between a gear axis and a motion axis of the rotary stage in the profiling system would affect accuracy of gear profile measurement. In this paper, at first, the influence of the eccentric error on measurement of gear pitch deviation is estimated in computer simulation based on a geometric model of the profiling system. After that, a new scanning method named “opposite-direction dual scanning method” is proposed so that a steep profile of gear flank surface with a local slope of up to 90° can be measured by the developed rotary profiling system. For compensating distortions in the measured gear tooth profile, which are induced not only by the eccentric error but also by a probe offset introduced by the proposed scanning method, a self-calibration and compensation method is applied. To verify the feasibility of the proposed method, measurement of gear pitch deviation of a master involute spur gear with a certificate data is carried out. Measurement uncertainty of the proposed method is also analyzed.     

基于全齿廓信息的齿距偏差快速测量方法

齿距偏差直接影响齿轮传动的性能,一直是最受重视的齿轮精度指标之一。如何快速、准确地获取中等精度齿轮的齿距偏差是汽车齿轮行业亟待解决的关键问题,但传统方法存在测量效率低、重复性差等不足。所提方法采用齿廓偏差曲线的全部信息作为齿距偏差的评价依据,采用统计分析方法定义和计算齿距评价新指标,克服了传统方法使用小样本和极值法进行齿距偏差评价的不足。所提方法可充分利用齿轮测量数据,具有评价指标值对随机误差不敏感、重复测量结果一致性好、评价结果与齿轮实际使用性能之间相关性更加紧密的特点。在汽车齿轮快速测量机上通过实际测量实验验证了新方法的使用效果,齿距测量速度高达0.3 s/齿面时仍具有很高的重复测量精度。     

齿廓偏差测量起始点的确定方法

齿轮测量中心作为齿轮测量技术的先进发展方向,正成为目前多数齿轮厂家检测齿轮的首选检测产品.基于电子展成原理的齿轮测量中心能测量渐开线圆柱齿轮的齿距偏差、齿廓偏差和螺旋线偏差.根据国家标准GB/T 10095.1-2001<渐开线圆柱齿轮精度>和GB/T 13924-2008<渐开线圆柱齿轮精度检验细则>中齿廓偏差的定义和测量规范,给出渐开线圆柱齿轮齿廓偏差测量起始点和终止点的计算方法和公式,并通过一实例加以说明.该计算方法适用于齿轮偏差测量仪器的软件开发.     

DESIGN OF NONCIRCULAR GEARS WITH DISCONTINUOUS PITCH CURVE

When the noncircular gear pair is applied to the continuously variable transmission (CVT) with gear, the transmission ratio function is discontinuous. In accordance with this unique characteristic, a new approach to design and analyze noncircular gears with discontinuous pitch curve is proposed. The design courses of various noncircular gear pairs with discontinuous pitch curve are unified based on the numerical algorithm of spline fitting and "fairing boundary condition". According to the particularity of discontinuous pitch curve, the rules and procedures for teeth distribution are recommended. It is explained in detail why the undercut is formed and how to manage the undercut based on meshing principle. In addition, the calculation formulas for each tooth profile segment are also derived. If the tooth profile data are calculated, the measurement and the incision process for noncircular gear can be conducted and the CAD simulation can be achieved easily. To ensure the continuity of the transmission, the transmission interference of the tooth which is located at the pitch curve joint point is managed by utilizing Bezier curve with CAD software. And the contact ratio of gear pair is obtained. The case study shows that this approach is successful and opens up a new way for the design of noncircular gear.     

新型高效齿轮测量技术

本文介绍间齿齿轮式啮合分离测试技术和据此开发的新型齿轮测量系统，新技术利用特殊测量齿轮和工件相啮合，可测出齿形、齿向、齿距和切向综合误差等，实验结果表明新技术简单、可行     

运动学法测量齿轮单项误差的发展

介绍了运动学法测量齿轮单项偏差的发展,包括齿轮整体误差测量、基于齿条测头的单项偏差测量、基于齿条测头的左右齿面同时测量。并基于运动学法,设计了同时测左右齿面的测量装置。该装置的设计能实现齿轮单项偏差的测量,为齿轮测量提供了新途径。     

Calibration and uncertainty evaluation of single pitch deviation by multiple-measurement technique

Gears are key elements of power transmission systems, and the inspection of their pitch deviation is one of the most important tests on gears. The specifications of gears are assessed using gear measuring instruments (GMIs) or coordinate measuring machines (CMMs), and the results of the measurements must be validated under an appropriate traceability system. In the traceability system, calibrated gauges whose measuring uncertainties are estimated are necessary. In the case of pitch deviation measurement, special artefacts or gears manufactured with high dimensional accuracy are used as reference gauges. In this paper, authors propose calibration and uncertainty evaluation methods for the single pitch deviation of gears measured using CMMs. First, the evaluation of single pitch deviation using a multiple-measurement technique and the estimation of its uncertainty based on the analysis of variance are formulated. Second, a technique for reducing the measurement trials based on the symmetry of the measurement is discussed. Finally, the proposed calibration method is validated through experiments.     

一种新型齿轮综合偏差测量齿轮及测量原理

传统渐开线齿轮综合偏差的检测常采用齿轮单面啮合法和齿轮双面啮合法。由于2种方法的测量原理及测量参数等不同,需采用齿轮单啮仪和齿轮双啮仪2种仪器分别进行测量,从而分别获得被测齿轮的切向综合偏差和径向综合偏差,2种偏差无法通过一次啮合检测得到。针对传统齿轮综合检测的不足,设计了一种由2个特殊半齿测量齿轮组成的新型测量齿轮,提出了一种新的齿轮综合偏差测量原理,并给出了其综合偏差结果的评定方法。该测量齿轮与被测齿轮通过一次类单面啮合测量,获得产品齿轮两侧齿面的切向综合偏差和径向综合偏差,明显提高了渐开线齿轮综合偏差的检测效率,降低了在测量设备上的投资。     

Calibration method for magnetically self-aligned multiball pitch artifact and accuracy upon reassembly

The vibration/noise of gears is influenced by micrometer-order tooth pitch deviation, and therefore advanced quality control is needed in the gear manufacturing process using measuring instruments. The accuracy of the pitch measuring instrument is verified using a master gear or artifact, but its accuracy is not sufficiently high, and its manufacture is difficult. In our previous report, a novel pitch artifact named the magnetically self-aligned multiball pitch artifact, in which elements with simple geometries are aligned spontaneously by a magnetic force, was proposed for the calibration of pitch measuring instruments. The parts comprising the artifact, which consist of balls, a cylinder, and a plane, have simple geometries and can be manufactured with accuracies on the order of several tens of nanometers. Therefore, this artifact can also have high accuracy. In addition, because it undergoes self-alignment by a magnetic force, it has the advantage of easy assembly. An appropriate calibration method for this artifact using a coordinate measuring machine is proposed, and the accuracy of the artifact is evaluated in this report. The repeatability of pitch measurements when the artifact is disassembled and reassembled is investigated, and the results show high repeatability. A measurement experiment using a pitch measuring instrument is performed. These experiments verified that the calibration and measurement of the proposed pitch artifact are possible with high repeatability.     

锥齿轮齿距及齿形偏差测量与分析方法

研究了基于齿轮测量中心的锥齿轮齿距偏差和齿形偏差测量与分析方法及其实现技术。该方法应用齿轮啮合理论,根据锥齿轮齿面成形方法,建立了齿面几何参数计算模型;在齿面上建立测量网格,控制齿轮测量中心四轴运动使齿面和测头于测量网格点接触,采集实际坐标轴及测头读数;应用B样条法构造实际齿面,计算其齿形偏差。在此基础上,开发了基于哈量集团公司制造的390X系列齿轮测量中心的实现软件系统。30家锥齿轮制造企业实际应用表明,该软件系统为提高锥齿轮精度、减小齿形偏差提供了先进的测量与分析手段。     

对偶树复小波分析及其在楔横轧轧件缺陷检测中的应用

针对轧件内部微小缺陷可能出现漏检的现象,提出一种基于对偶树复小波变换（DT-CWT）的超声信号检测方法;通过构造新的对偶树复小波,并利用对偶树复小波的平移不变性,改进现有的基于常规离散正交小波变换的超声回波信号处理方法。试验结果证实了该方法的优点和有效性。     

齿轮特征线统一模型及在齿轮三维误差评定中的应用

表征渐开螺旋齿轮的特征线有多种,广为熟知的是几何意义明确的渐开线和螺旋线。其实齿面上还有法向啮合齿形、接触线等工程价值突出的其他特征线。但特征线增多带来了两个问题,一是复杂的特征线方程彼此不关联,数学上缺乏统一性;二是除了渐开线和螺旋线,其他特征线没有测量手段,缺乏可测性。据渐开线齿轮传动的特点,将齿面特征线映射到啮合平面里,发现齿面上各条特征线在啮合平面里都有各自对应的二维直线,以此建立直线模型统一表达了齿面各种特征线;基于齿轮三维误差测量数据和特征线统一模型,提出了各种特征线偏差的提取方法,应用于测量实践,通过与通用齿轮仪器测量的渐开线偏差和螺旋线偏差作比对,证明了特征线统一模型及特征线偏差提取方法的有效性和实用性,解决了齿面复杂特征线的可测性问题。同时,齿轮特征线统一模型在齿轮工艺误差溯源、传动性能预报等方面也有重要应用价值。     

Magnetically self-aligned multiball pitch artifact using geometrically simple features

The vibration/noise of gears is influenced by micrometer-order tooth pitch deviation, and therefore, advanced quality control is needed in the gear manufacturing process using measuring instrument. The accuracy of the pitch measuring instrument is verified using a master gear or artifact, but its accuracy is not sufficiently high, and its manufacturing is not easy. In our previous report, a novel high-precision pitch artifact composed of simple-shape parts (“multiball pitch artifact”) was proposed for the calibration of pitch measuring instruments. Simple-shape parts such as balls, cylinders, and planes can be manufactured with several-ten-nanometer-order accuracy. Therefore, this artifact can also have high accuracy. In this study, a magnetically self-aligned multiball pitch artifact is proposed in which the simple-shape parts are assembled with high precision using magnetic force without any special assembly technique. The artifact is designed and manufactured. A measurement experiment using a pitch measuring instrument is performed, and it is verified that the proposed pitch artifact is fundamentally valid for calibration.     

降低齿轮齿距累积偏差的方法

为了减小齿轮磨削加工中的磨床系统分度误差,提高齿轮加工精度,分析了齿轮磨床分度误差、齿轮安装偏心和齿轮齿距偏差之间的关系,获得了分度误差的计算方法,并计算出了齿轮磨床的分度误差。依据计算得到的分度误差值调整磨床,降低磨床分度误差,减小齿轮齿距累积偏差,提高了齿轮加工精度。以Y7125大平面砂轮磨齿机床为例验证了提出方法的可行性。建立了齿轮安装偏心和齿廓偏差的数学模型,求出了齿轮安装偏心的幅值和相位角,然后由齿轮安装偏心、磨床分度误差和齿轮齿距偏差的关系得到磨床的分度误差值。根据计算得到的分度误差值调整磨床分度盘,使磨床的分度误差从17.7μm减少为3.3μm,被加工齿轮的齿距累积总偏差由46.9μm降低到11.5μm,齿距精度达到三级。验证结果表明,按照这种方法调整磨床可以快速有效地降低磨床的系统分度误差,从而降低齿轮的齿距累积偏差。     

磨齿机分度误差传递规律

为预测被加工齿轮的齿距加工精度,研究了Y7125型大平面砂轮磨齿机系统分度误差的传递规律。采用全闭环测量法对用作角度测量基准的正36面棱体进行了高精度标定;基于该正36面棱体和相对测量法在机提取机床36个等分点系统分度误差曲线;最后在磨齿机上进行精密磨齿实验,通过比较齿轮试件的齿距累积偏差与机床原始系统分度误差的差异,研究机床分度误差的传递规律,并通过实验得到磨齿机分度误差传递过程中的不确定度。实验结果表明:采用全闭环测量法标定正36面棱体的测量不确定度达到±0.05;磨齿机系统分度误差传递到被加工齿轮后,齿距累积总偏差由2.1m增大到2.6m,相对误差增加了24%;通过磨齿实验得到磨齿机分度误差传递过程中的不确定度为±0.6m。得到的机床分度误差传递规律可用于预测齿轮的齿距累积加工精度,为制定科学的磨齿工艺提供技术支持。     

不同重合度非圆齿轮设计及弯曲应力分析

非圆齿轮传动具有广泛的应用场景。针对非圆齿轮传动,采用齿轮啮合原理和材料力学等原理及方法,提出了大重合度非圆齿轮设计方法。探讨了非圆齿轮传动原理和节曲线构建方法,计算了其节曲线曲率半径和重合度方程。建立了不同重合度非圆齿轮轮齿时变啮合刚度与载荷分配率计算模型,推导了不同重合度非圆齿轮齿根弯曲应力方程。探讨了不同结构参数下非圆齿轮副重合度、时变啮合刚度、时变载荷分配率及齿根弯曲应力变化规律,确定了轮齿所受最大载荷位置。开展了不同重合度非圆齿轮齿根弯曲应力仿真分析和实验测量,与理论计算结果进行了对比分析,最大误差分别约为4.8%和5.9%,验证了理论方法的合理性与正确性,为大重合度非圆齿轮传动的工程应用奠定了基础。     

小模数蜗杆副综合误差测量软件的研制

基于单面啮合原理的小模数蜗杆副综合误差测量仪,可以测量蜗杆副切向综合误差、齿距偏差和侧隙.详细介绍了该仪器的测量流程、软件界面、软件结构、误差提取算法和精度等级评定.该软件具有参数管理、自动测量、误差计算、用户管理、SPC分析、频谱分析、等级评定、结果保存、打印报表等功能,可以应用于小模数蜗杆副的精密检测.     

啮合线齿廓偏差测量方法

介绍了一种应用于齿轮测量中心上复杂齿廓测量的新方法——啮合线齿廓测量法。该方法减小了测头在X轴方向上运动距离,有效地保证了精度范围,同时减小测头重力中心的运动及测量时间,实现了高精度测量。该方法能够有效防止齿廓基圆测量法在进行内齿轮测量时的干涉现象,同时实现小直径内齿轮(外圆直径小于10mm)的一次装卡完成齿形、齿向和齿距误差测量。     

一种新型测量齿轮的设计及其刚度校验

针对齿轮测量技术中的测量齿轮的设计,提出了一种全新的由2个半齿齿轮组合而成的半齿测量齿轮。使用该新型测量齿轮,可以在1次测量过程中,同时得到现有的由单面啮合仪和双面啮合仪测量的切向综合偏差和径向综合偏差,从而明显提高了测量效率,并且应用MSC．Patran＆Nastran软件,对该新型测量齿轮进行了有限元分析,验证了其实用性。     

安装距可调的锥齿轮副传动误差测量

由于在齿轮副的最佳啮合位置处测量齿轮副的单面啮合可精确得到锥齿轮副的传动误差,本文研究了锥齿轮副最佳安装距的调整方法,并开发了相应的传动误差测控软件。介绍了在最佳安装距位置对锥齿轮副进行单面啮合测量的原理,描述了通过传动误差分析、频谱分析和精度等级评定对传动误差进行评定的方法。利用统计过程控制(SPC)法对锥齿轮副的切向综合总偏差和一齿切向综合偏差进行了工艺评定和过程监控。然后,设计了基于最佳安装距的锥齿轮副传动误差测控软件,完成了对传动误差的实时采集、数据处理和曲线显示,最佳安装距的寻优调整以及测量结果的SPC统计分析。给出了测控软件的类图、顺序图、测试用例和软件界面。最后,实验测量了一对齿轮副在安装距寻优调整前后的传动误差。结果显示,提出的方法和传动误差测控软件可应用于锥齿轮副或面齿轮副的测量。