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.     

DELIBERATlON TO THE DEFINITION OF TOOTH THICKNESS FOR INVOLUTE HELICAL GEAR IN INTERNATIONAL STANDARD ISO1122／1

ＤＥＬＩＢＥＲＡＴｌＯＮＴＯＴＨＥＤＥＦＩＮＩＴＩＯＮＯＦＴＯＯＴＨＴＨＩＣＫＮＥＳＳＦＯＲＩＮＶＯＬＵＴＥＨＥＬＩＣＡＬＧＥＡＲＩＮＩＮＴＥＲＮＡＴＩＯＮＡＬＳＴＡＮＤＡＲＤＩＳＯ１１２２／１ＤＥＬＩＢＥＲＡＴＩＯＮＴＯＴＨＥＤＥＦＩＮＩＴＩＯＮＯ...     

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.     

Investigation on sampling size optimisation in gear tooth surface measurement using a CMM

Coordinate measuring machines (CMMs) are widely used in the gear manufacturing industry. One of the main issues for contact inspection using a CMM is the sampling technique. In this paper the gear tooth surfaces are expressed by series of parameters and inspection error compensation and initial value optimisation method are presented. The minimum number of measurement points for 3D tooth surfaces are derived. If high precision is required, more points need to be inspected. The sampling size optimisation is obtained from the criterion equation. The surface form deviation and initial values are optimised using the minimum zone method and genetic algorithms. A feature-based inspection system for spur/helical gears is developed and trials and simulations demonstrate that the method developed is suitable and very effective. This revised version was published online in October 2004 with a correction to the issue number.     

Algorithm for measuring gears implemented with general-purpose spreadsheet software

Conventional methods to verify gears are based on manual measurement instruments, such as vernier caliper gauges, gear pitch micrometers, profilometers, among others. The use of these instruments is widely described in technical literature, while in the actual industrial arena the coordinate measurement machines (CMM) are commonly used to obtain, with the appropriate software, all the parameters including the tooth profile.Commercial software for measuring gears with a CMM is usually based on continuous touch of teeth’s flanks. In the educational centres is still common to find single-point probing point to point touch machines. To transform them into continuous touch machines, new software and accessories are required and costs can be excessive for instructional purposes.This paper presents the geometrical and mathematical principles to develop a software application for measuring gears and describes its implementation using general-purpose spreadsheet software. For this purpose, the conventionally used software of the CMM is supported by a spreadsheet that calculates the probe positions and direction of measurement. The communication between the spreadsheet and the CMM software is established by ASCII files. At the end of this process, the spreadsheet displays the measurement results, thanks to its graphical and computing power, making possible to improve the learning process of students or training professionals.     

圆柱齿轮剐齿技术发展

剐齿技术是针对现有齿轮加工的局限而发展起来的新型圆柱齿轮加工技术,在小模数非贯通内齿轮的加工方面有明显优势。与传统的滚齿和插齿齿轮加工方法相比,剐齿技术采用干式、断续和微量切削,具有高速、高效、高精度及更环保等优点。本文详细介绍了剐齿概念、剐齿加工运动模型及国内外研究现状,指出了剐齿技术的发展方向。     

Approach for uncertainty analysis and error evaluation of four-axis co-ordinate measuring machines

In the present investigation, a new form of space frame for error evaluation and uncertainty analysis of four-axis co-ordinate measuring machines (CMMs) is proposed and applied. The novel space frame comprises a ball plate that incorporates seven high accuracy spheres. The volumetric error data obtained when a CMM measures the space frame, in different angular locations, can be used to verify whether a CMM maintains the manufacturer specifications. The experimental results have demonstrated that this space frame provides a practical and cost effective mechanical artifact to assessing the volumetric performance of four-axis CMMs. The developed technique can be applied for verification, periodic re-verification and acceptance test of any type of four-axis CMMs.     

Integrated wear prediction model for cylindrical gear with variable hyperbolic circular arc tooth trace under mixed elastohydrodynamic lubrication

Cylindrical gear with variable hyperbolic circular arc tooth trace (VH-CATT) is a new type of gear. Sliding wear is the main mode of the surface failure of multiple mechanical parts. Both the lubrication state and contact temperature considerably influence wear characteristics, which may aggravate the transmission performance of gear pairs. Wear, contact temperature, as well as lubrication states are jointly explored. Therefore, an integrated wear prediction model was proposed through taking into account flash contact temperature and surface roughness of VH-CATT cylindrical gears in mixed elastohydrodynamic lubrication. According to the equivalent ellipse contact model of VH-CATT cylindrical gears and tooth surface equation, normal curvature and velocity relations for VH-CATT cylindrical gears were observed, and the normal meshing force was obtained through the consideration of load sharing coefficients and quality grades. Flash contact temperature was estimated by using the literature. This study proposes analytical solutions for investigating how various surface roughness, operation, and geometric parameters affect asperity contact ratio (ACR), asperity contact pressure (ACP), flash contact temperature (FCT), as well as wear depth (WD) related to driving gears. ACR, ACP, FCT, as well as WD initially decrease and then increase from engaging-in to engaging-out processes. The minimum occurs at the pitch point. The WD declines as module, cutter radius, and rotational velocity increase while augmenting when surface roughness and torques increase. The maximum and minimum wear depths in driving gears occur at the dedendum and pitch point, respectively. Its overall wear is reduced by 23.16 % compared to the wear of spur gears. The results are valuable for the studies of tooth pitting, wear resistance, and fatigue life improvement for VH-CATT cylindrical gear. These studies can provide verification data and references required for engineering designs and VH-CATT cylindrical gear operations.

     

三坐标机测量齿轮齿廓的不确定度评价

介绍了坐标测量中几种常用的不确定度评价方法.指出传统的三坐标测量机的测量不确定度评价方法大都不适用于评价坐标测量中面向对象的测量不确定度,并对使用蒙特卡洛方法评价测量不确定度进行了研究.首先,根据三坐标测量机详细标定文件及补偿策略说明建立测量模型.然后,将测量中的采样点通过测量模型生成大量测量结果,并以此评价测量不确定度.在齿廓评价实验中,评定齿廓误差的测量不确定度为0.96 μm时,多次评价结果之间的最大差值不超过0.03 μm,具有可靠的理论依据和较稳定的评定结果.文章指出,目前商用三坐标测量机大都不能为特定的测量对象提供测量不确定度报告,使用蒙特卡洛方法有希望改变此现状.     

加工齿轮滚刀齿形过程中如何提高齿形精度

针对阿基米德滚刀加工渐开线圆柱齿轮,用阿基米德造型的滚刀在刃磨滚刀齿形时,为了提高齿形精度,改变加工工艺和检测工艺,使用先进的"砂轮修正器"和"齿轮测量中心",缩短了设计和加工时间,提高了齿轮滚刀齿形磨制的效率,保证了滚刀加工渐开线圆柱齿轮齿形精度,使大于4模数的阿基米德滚刀齿形(A级﹑AA级)易于保证被加工渐开线圆柱齿轮的齿形精度。     

变位内齿轮齿形系数的研究

对变位内齿轮齿根危险截面上的弯矩及其齿厚进行了分析和计算，给出了内齿轮变位系数及齿数与其齿形系数的关系线图。研究结果表明：ＧＢ３４８０－８３中将内齿轮齿形系数视为常量的作法值得商榷     

基于加工精度的齿轮几何参数的选择

应用网格图法分析研究采用蜗杆砂轮磨齿机加工高精度渐开线圆柱齿轮齿廓时,节点附近出现凹下的齿形误差 现象,得到了避免由于与刀具啮合齿数的变化所引起的齿形误差的齿轮变位系数选择方法,并通过实验进行验证。     

Effects of flank deviation on load distributions for helical gear

Flank deviation is one of the important factors that greatly affect helical gear strength. A qualitative analysis is performed using finite element method (FEM) for the effects of flank deviation on load distributions for helical gear based on ANSI/AGMA ISO 1328-1 (standard for cylindrical gears — ISO System of Accuracy — Part 1: Definitions and Allowable Values of Deviations Relevant to Corresponding Flanks of Gear Teeth). To analyze the effects of flank deviation, tooth contact analysis (TCA) is developed and load distributions of helical gears with flank deviation are presented. Load distributions in contact lines are derived and compared to each other under grade 5 and 7 after taking five types of flank deviation, including single pitch deviation, profile form deviation, profile slope deviation and helix form deviation as well as helix slope deviation, into account. It is found that the effects of individual flank deviation on load distribution have the superposition property. Flank crowning and tip relief corrections must be carefully regarded in the design process because of the effects of flank deviation on load distributions.     

基于移动最小二乘法的渐开线齿轮齿廓曲线拟合方法

针对现有渐开线齿轮齿廓曲线拟合方法精度不高的缺点,提出了一种用移动最小二乘法(MLS)拟合齿廓曲线的新方法,并通过齿距偏差的计算对该方法进行了实例验证。利用三坐标测量机对某齿轮进行测量,得到齿廓数据点和齿距偏差;根据移动最小二乘法原理和实验数据,用MATLAB编程实现了齿廓曲线的拟合;根据拟合结果,利用图解法计算出了左齿廓齿距偏差。与最小二乘法(LS)的拟合结果的对比表明,用移动最小二乘法拟合齿廓曲线精度更高,误差更小,具有良好的拟合效果。齿距偏差计算结果表明,单个齿距偏差和齿距累积偏差与实测值一致,表明该方法准确、有效。研究结果可为齿廓曲线的拟合和齿距偏差的计算提供参考。     

摆线齿轮精度分析(二)——第II、III公差组的精度指标及测量方法

传动平稳性、承载均匀性及合理的啮合侧隙是摆线针轮减速器的重要性能指标。根据摆线齿轮结构特点 ,第II公差组内规定了一齿切向综合公差fi′、一齿径向综合公差fi″、齿距极限偏差±fpt、齿形公差ff 等精度项目 ;第III公差组内规定了齿向公差Fβ 及齿轮接触斑点。由于摆线针轮传动不能采用基中心距法获得啮合侧隙 ,故应规定齿厚极限偏差Es。除齿形误差ff 外 ,Fp、±fpt、Fβ 及齿厚E均可利用渐开线齿轮测量仪器及测试方法进行测量     

A study on the bending stress of the hollow sun gear in a planetary gear train

Generally, planetary gear type traveling reduction gear is composed of multiple planetary gear stages and has a hollow sun gear in the last stage planetary gear. In designing reduction gear, it is important to evaluate accurately the bending stress at the tooth root of the sun gear as the sun gear is the weakest component in the reduction gear system. Although bending stress can be calculated easily using gear standard codes such as the American Gear Manufacturers Association (AGMA) and International Organization for Standardization (ISO) 6336 for almost all gears, meticulous calculation is needed for the hollow sun gear because of its low backup ratio (rim thickness divided by tooth height) and comparatively large root fillet radius. In this study, a finite element analysis (FEA) is carried out to investigate the effect of rim thickness and root fillet radius on bending stress at the tooth root of the hollow sun gear. In standard codes, bending stress at the tooth root is calculated linearly with a constant slope for the backup ratio below 1.2. However, the effect of the rim thickness on bending stress is more complex in the planetary gear system. Bending stresses calculated by FEA with various backup ratios and root filler radii are compared with the bending stresses calculated by the standard codes.     

锥形摆线啮合副加工方法

为解决锥形摆线啮合副软齿面的切削加工和硬齿面的磨削加工,提出用指锥刀具/磨具直接形成零件轴向锥形,而零件断面摆线或圆弧齿通过展成方式形成的"指锥包络"切削/磨削加工方法.以锥形摆线轮的大端作为基准,推导锥形摆线轮和锥形圆弧内齿轮切削/磨削过程中的刀具/磨具中心轨迹方程.针对理论推导的刀具/磨具中心轨迹方程,运用Pro/Engineer软件,对啮合副零件的切削/磨削加工过程进行了运动仿真,验证理论推导的正确性和加工方法的可行性.在理论推导及加工仿真的基础上,进一步完成样机的试制.在ZC1066H三坐标测量机上,对样机的锥形啮合副零件进行加工精度测量,测得锥形摆线轮断面周节累积误差为0.035 mm,圆弧内齿轮断面周节累积误差为0.014 mm,测量结果表明该加工方法切实可行,且具有较高的精度.     

螺旋锥齿轮点接触齿面生成法

提出一种能直接生成点接触,满足啮合配对要求的齿面方法,该方法利用齿面接触分析设计齿面,为齿轮ＮＣ加工运动计算提供新的途径。     

齿轮传动中磨损问题的研究及修复方法

齿轮传动是机器传递运动和动力的一种主要形式.如何减少齿轮工作中的磨损、延长其使用寿命是工业生产中至关重要的问题.重点总结了齿轮磨损问题的基本类型、研究历程、研究方法以及对失效齿轮的常用修复方法等.     

Relationship between calculated film thickness and wear in elastohydrodynamic contacts of gears

Gear oils are important design elements and it is necessary to establish data relating their performance to operating conditions and gear design. Due to a combination of elastic distortion and increased viscosity due to high pressure, a hydrodynamic film is generated in gear tooth contacts. In this paper the authors consider the use of the Dawson and Higginson equation to relate film thickness to the performance of gears with respect to wear rate and present experimental data obtained using the FZG gear test procedure. Initial results of an experimental programme to determine actual pressure viscosity characteristics within highly loaded contacts are also presented, since the authors consider that it is errors in the pressure viscosity relationship that cause the lack of correlation between theoretical film thickness and experimental data on scuffing.