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Bevel gear of the latest developments in measurement technology 1 Overview
Bevel gear drive mechanism in the car, helicopter, machine tools and electric tools manufacturing industry, has been widely used. The use of different performance of the bevel gears are also different quality requirements, can be summarized including: ① a good contact area, can be a reliable torque transmission power; ② good match geometry, a smooth transfer of the movement, in order to ensure uniform load , transmission smooth, vibration small, noise low. Factories are usually small devices and dual-spot detection of rolling contact tester to control the quality of bevel gear, but in reality it is very difficult to determine accurately the performance of the bevel gear.
Bevel gear and the precision of measurement of cylindrical gears similar, can generally be classified into three types: ① Coordinate Geometry Analysis of measurement type. That is, the bevel gear as a geometric entity, its geometric elements, respectively, the geometric precision of individual measurements; Gear Measuring Center is the main measuring instruments. ② Comprehensive engagement measurement accuracy. That is, the bevel gear transmission as a component, the accuracy of their transmission, contact spots, a comprehensive measurement of the vibration noise. The measuring instruments are mainly one-sided meshing bevel gear tester, bevel gear meshing two-sided bevel gear measuring and inspection machine rolling. Bevel Gear ③ the overall measurement error. It will bevel gear transmission as a function for the realization of the geometric entities, or by coordinate measuring method in accordance with the geometric precision of a single measurement to measure the overall error of bevel gears, bevel gears to achieve a single transmission error and the geometric precision of the intrinsic link between the quality of the analysis; or by mating single measurement, the use of mesh point scan measurement of bevel gears for the overall error of measurement, has been integrated bevel gear movement accuracy, contact spots, as well as the geometric precision of the individual. Therefore, the overall error of measurement of bevel gear is a measurement of the first two methods of integration and development.
With the coordinate measuring technology, computer control and measurement technology, in recent years, the overall error of measurement of bevel gear technology
research development soon. Gear Measuring Center as a result of multi-cylinder coordinates, such as multi-function measurement instrument performance, data-processing capacity, bevel gear-type coordinates of analytic geometry measurement technology, has been the development of a single geometric error of measurement to the overall error of measurement of bevel gear, improved cone gear design, processing, quality testing to determine the accuracy and the use of the forecast performance of the bevel gear, such as the level of manufacturing technology. By China's own development, based on the "control point movement - geometric measurement principle" on one side of the bevel gear meshing point scanning technology and technology development based on the overall error of the bevel gear measuring instrument, it is more towards the production of the first line, so that China Bevel Gear measurement theory, the practical application of measurement technology has been further improved and developed.
2.the main bevel gear precision measurement method and apparatus
2.1 Coordinate-style geometric measurement and analysis equipment Machinery Exhibition into a straight bevel gear-type coordinate measuring instrument there earlier products to represented KP42-type, but the complex structure of high accuracy. Since 1990, both before and after, CNC Gear Measuring Center to the market, coordinates arc bevel gear-type geometry of measurement error is the rapid development and popularization and application. Today's market, Gear Measuring Center from abroad, whether it is Klingberg Germany's P63, or the United States Gleason / mar the GMX275, M & M's Sigma 3, have been measured with the function of bevel gear. These instruments have reached VDI / VDE level provided a space measuring uncertainty for more than 2 microns; bevel gear on the geometric error of a single test, such as pitch deviation (including single pitch deviation, the cumulative pitch deviation , total cumulative pitch deviation), tooth profile deviations (including a total deviation of tooth profile, the shape of tooth profile error, tooth profile tilt deviation) and teeth to the error (including the teeth to the total deviation, deviation of the shape of teeth to the teeth to tilt deviation) and output deviation of three-dimensional shape of tooth surface morphology map.
2.2 Integrated single-sided mesh rolling test measurement method and apparatus
Single-sided bevel gear meshing scroll detection methods have been used in production for many years. N0.513 Gleason in the United States rolling test machine
as an example, in the measured single-sided bevel gear pair meshing, the simulation of its work, and to a certain degree of speed and load, adjust the V / H, for colored contact area (spot ) testing to determine the bevel gear pair under test contact conditions; through the use of acceleration sensors, pickup of vibration and noise measured on the tooth scan frequency harmonic detection. This method is "quasi-dynamic" measurement method, which bevel gear for the accuracy of detection is far from complete or accurate enough. Optical encoder used as the base point of view, to cut bevel gears for the accuracy of detection of the integrated single-sided meshing bevel gear tester, such as Germany's Klingberg PSKE900, because a single test items, in particular, it is difficult for the basis of test results Bevel Gear Machine parameters adjusted to give guidance, to improve processing quality bevel gears. Less cost-effective and therefore not much used in production.
Gleason has introduced in recent years, the Phoenix 500HCT CNC bevel gear inspection machine is rolling with a rolling test at the same time and one-sided mating tester measurement function, measurement of both the tangential bevel gear integrated error, while the number of measuring cone gear contact area, three-dimensional structure of the noise analysis. The advanced models, such products represent the contemporary level of development, although expensive, but there are individual users at home. Klingberg also similar GKC60, such as Orion Hole T50 CNC bevel gear inspection machine.
2.3Measurement error overall and equipment
The overall error of measurement of bevel gear is rotating in the same angle displacement coordinates of the order will be based on the meshing bevel gear tooth surface of the work of the detection point measured by the geometric error of all the individual integrated into a bevel gear overall error map, and on this basis, bevel gears for the completion of a single geometric precision, and accuracy of an integrated campaign bevel gear analysis of contact state deputy measurement, the use of bevel gears to achieve the performance and quality assessment and monitoring. Bevel gear and the overall error of measurement apparatus, the current can be divided into three second-class. A class of analytic geometry for coordinate measurement type, the method is divided into "point-to-point measurement" and "point of scan measurements," equipment used in two ways for CNC Gear Measuring Center, but the allocation package by the measurement different; the other for the mating-type movement measurement geometry (ie, mesh-type scan measurement point, the
method for our first), the apparatus used for single-sided meshing bevel gear tester, equipped with a dedicated measurement bevel gear and measurement software package.
(1) coordinate the overall bevel gear-type point-to-point measurement error
Gear Measurement Center in, along with three-dimensional measurement of bevel gear tooth profile and tooth to the two directions, according to a pre-determined interval, the detection of the measured points of the tooth surface (usually the 5 tooth profile, tooth up 9 a total of 45 points) for the geometry error of measurement of 1.1 points. This method can be avoided and the measured three-dimensional probe in the measurement of tooth surface when the impact of friction and the measurement results. The measurement method is based on "direct measurement" principle, concrete steps are: first bevel gear in accordance with the adjustment of machine parameters and tool geometry parameters to be processed by calculating the large and small bevel gear tooth surface ideal geometric processing parameters; the tooth tooth surface as a reference, respectively, and the actual process (or after heat treatment) of large and small gear tooth surface compared to the actual measured tooth surface of the tooth surface with an ideal geometric deviation. MATCH procedures through the use of dedicated, determined corresponding to the actual measured tooth surface machining parameters of the illusion; re-engagement model in accordance with TCA analysis, calculated by the bevel gear pair integrated deviation and tangential contact conditions, test whether or not to meet the requirements. If necessary, the corresponding software will be based on the measurement results, re-calculate and adjust the machining parameters in order to re-try all they can be processed into a more satisfied with the quality of products.
(2) coordinates of point scanning type bevel gear of the overall measurement error
Seiki, Osaka, Japan recently proposed using two-dimensional measurement of bevel gear tooth surface measurement to point scanning method has been satisfactory and reliable results. This method has the following characteristics: the workpiece by controlling the rotation, the parallel displacement of probe movement, to avoid the probe and the tooth surface friction between the adverse effects of measurement; measurement as a result of the use of scanning, surveying the region to cover the entire tooth surface, including Top Gear, as well as close to large and small end of the
region; measurement path can have a wide range of choices, usually tooth number and tooth number of each to the three, a total of six; each sample the number of scanning lines of up to 113 points, as sampling density, to reflect minor tooth surface waviness (which often is not pleasant ripple of the main sources of noise, the conventional point-to-point measurement method difficult to measure). The method used the "conjugation of" principle, the concrete steps are: First of all, the basis of machining parameters and tool parameters to be the ideal gear tooth surface geometry processing parameters, to calculate the conjugate with it, no transmission error of the virtual conjugate of the pinion tooth surface geometry parameters; the actual processing of the large gear tooth surface with the ideal gear tooth surface processing compare measurements to detect gear tooth profile and the relative deviation upward; the actual processing of the pinion tooth surface and calculation of be conjugate Virtual pinion tooth surface compared with measurements, to detect the gear tooth profile and the relative deviation upward. According to the relative deviation of measured, calculated by the deputy of the three-dimensional bevel gear tooth surface morphology of the comprehensive plan deviation, deviation and tangential contact with the integrated form of (including access to the path of contact area shape, size, location, etc.). By physical measurement, than on the authentication, point-to-point and point measurements of the measurement scan measurement results are consistent.
(3) mating-type bevel gear to scan the whole point of the measurement error
Chengdu Tool Research Institute of the bevel gear to mesh-type scan measurement point is one-sided meshing bevel gear tester, the design of the installation location by using a special measuring bevel gear and bevel gear test for measuring the rolling one-sided engagement. This measurement of bevel gear pair "basis" cone measured geometric parameters and the geometric parameters of gear pair are all the same. Measurement methods or the use of corrosion-paste method, in large and small measurement of the gear teeth and white make the necessary gear tooth profile or ridge to the measurement, by measuring the bevel gear or the gear tooth profile and match to the measurement of ridge bevel gear of the measured tooth contact transmission, the meshing of bevel gears to complete scanning the overall error of measurement points. Measurement path and measuring the number of gear teeth, and a total of 3 +3 is generally 6. Mating-type bevel gear to scan the overall error of measurement points used the "relative measurement of the local benchmark" principle.
Measurement of specific steps are as follows: In accordance with the actual bevel gear pair sports / test experiment (or experience), elected by the factory can best meet the needs of the bevel gear use requirements vice as a "benchmark" bevel gear pair (known as the local benchmark), its integrated bias-cut to a cut tooth to the integrated form of bias and the contact area was identified as the assessment of the accuracy of the bevel gear of the main reference Vice indicators. Measurement of Bevel Gear and the local base of meshing bevel gears, bevel gears in mesh single tester measured tooth profile deviation of a consolidated Board - measured (local base bevel gear Deputy - Vice-bevel gear benchmarks, the same below), integrated to the deviation of tooth Board - measuring, cutting to the integrated deviation of the Board - measuring a tooth integrated deviation Board - measuring, shape Council contact area - measured, as well as the integrated deviation of three-dimensional tooth surface morphology of Fig Bureau - measuring and so on, and was recognized as a bulk evaluation of bevel gear testing The accuracy of a single bevel gear indicators mainly refer to baseline data. Measured part bevel gear and bevel gear measuring method according to the same measurement, the deviation of the workpiece has been Bevel Gear - Bevel Gear measurement data; by the computation of the corresponding deviations workers - Bureau data (that is, relative to the workpiece bevel gear partial cone base Gear indicator of the corresponding deviations of the accuracy). And then measured in accordance with the Public Works - Bureau deviation of the accuracy of data and indicators for the development of tolerance, to determine the bevel gear of the level of quality and interchangeability.
Bevel gear overall error measurement method is simple, fast and reliable measurement information-rich, especially for mass production. As a result of measurement must be measured using special gear, so this method should not be used for a single measurement of small quantities. However, since the bevel gear at the same time the overall error of measurement also has a rolling bevel gear tester, so it can be used for single-piece and small-batch precision bevel gear Deputy comprehensive detection and production of the test workpiece and cutting tool debugging.
3 Conclusion
Through the bevel gears in recent years the field of measuring the status of technology research and development, both at home and abroad to highlight the overall error of measurement of bevel gear technology, methods and development of
the corresponding equipment. China's self-developed scanning mating-type bevel gear at the overall error of measurement technology, has been gradually recognized by domestic and foreign counterparts; technology development based on the overall error of the bevel gear measuring instrument is to the production line and continue to improve measurement practice . It is believed that the mesh-style points based on scanning the overall error of measurement of bevel gear technology, the establishment of precision bevel gear bulk products database, it is very possible to adopt in accordance with the use of computer-assisted measurement technique to achieve automatic arc bevel gear pair quickly.
1 概述 锥齿轮测量技术的最新进展
锥齿轮传动机构在汽车、直升飞机、机床及电动工具制造业中，得到了广泛的应用。不同的用途对锥齿轮性能质量的要求也不同，归纳起来包括：①有良好的接触区，能可靠的传递动力扭矩；②有良好匹配的几何形状，能平稳的传递运动，从而保证载荷均匀、传动平稳、振动小、噪音低。工厂通常采用双啮仪及检测接触斑点的滚动检查仪来控制锥齿轮的质量，但实际上很难精确判定锥齿轮的使用性能。
锥齿轮的精度测量方法和圆柱齿轮类同，通常可分为三种：①坐标式几何解析测量法。即把锥齿轮作为一个几何实体，对其几何元素分别进行单项几何精度的测量；齿轮测量中心是其主要测量仪器。②啮合式综合精度测量法。即把锥齿轮作为一个传动元件，对其传动精度、接触斑点、振动噪音进行综合测量。其测量仪器主要有锥齿轮单面啮合检查仪、锥齿轮双面啮合测量仪及锥齿轮滚动检验机。③锥齿轮整体误差测量法。它将锥齿轮作为一个用于实现传动功能的几何实体，或用坐标测量法按单项几何精度测量方式测量出锥齿轮的整体误差，实现锥齿轮单项几何误差和传动精度、质量之间内在联系的分析研究；或按单面啮合测量方式、采用啮合点扫描测量方法，对锥齿轮的整体误差进行测量，得到锥齿轮的综合运动精度、接触斑点以及各单项几何精度。因此，锥齿轮整体误差测量法是前两种测量方法的集成和发展。 随着坐标测量技术、计算机控制与测量技术的发展，近年来对锥齿轮整体误差测量技术的研究得到很快的发展。由于齿轮测量中心等圆柱式多坐标多功能测量仪器的测量性能、数据处理能力的提高，锥齿轮的坐标式几何解析测量技术，已由单项几何误差测量发展到锥齿轮整体误差测量，提高了锥齿轮
设计、加工、精度质量的检测判定以及使用性能的预测等整个锥齿轮制造技术的水平。由我国自行开发、基于“可控点运动—几何测量原理”的锥齿轮单面啮合点扫描测量技术及基于该技术开发的锥齿轮整体误差测量仪，也正在更多地走向生产第一线，使我国锥齿轮测量理论、测量技术的实际应用得到了进一步的提高和发展。
2 锥齿轮精度主要测量方法及仪器
2．1坐标式几何解析测量方法及仪器
机械展成坐标式直锥齿轮测量仪较早就有产品，以瑞士马格KP42型为代表，精度很高但结构复杂。自1990年前后，CNC 齿轮测量中心推向市场，坐标式弧锥齿轮几何形状误差测量方法才有了迅速发展并得到推广应用。现今市场上国外的齿轮测量中心，无论是德国克林伯格的P63，还是美国格里森/马尔的GMX275、M ＆M 的西格马3，都已具备了测量锥齿轮的功能。这些仪器都达到VDI/VDE等级规定的1级，空间测量不确定度在2微米以上；可对锥齿轮的单项几何误差进行检测，如齿距偏差（包括单个齿距偏差、齿距累计偏差、齿距累计总偏差）、齿廓偏差（包括齿廓总偏差、齿廓形状偏差、齿廓倾斜偏差）、齿向偏差（包括齿向总偏差、齿向形状偏差、齿向倾斜偏差）并可输出三维齿面形状偏差形貌图等。
2．2 单面啮合滚动检验综合测量方法及仪器
锥齿轮单面啮合滚动检测方法在生产中已经使用多年。以美国格里森N0.513滚动检验机为例，在被测锥齿轮副单面啮合的情况下，模拟其工作状态，加以一定的速度和载荷，调整V/H，进行着色接触区（斑点）的检测，以判定该被测锥齿轮副的接触状况；借助于加速度传感器、拾音器测量其振动和噪音，对齿频谐波进行扫描检测。这种方法属于“准动态”测量方法，它对于锥齿轮的精度检测是不够完整、不够准确的。而采用光电编码器作为角度基准、用于锥齿轮切向综合精度检测的锥齿轮单面啮合检查仪，如德国克林伯格公司的PSKE900，因其检测项目单一，尤其难以根据检测结果对锥齿轮加工机床参数的调整给以指导、以改进锥齿轮加工质量。性价比较差，故生产中不多采用。
近年来格里森公司推出的凤凰500HCT 数控锥齿轮滚动检验机则同时具备了滚动检验机和单面啮合检查仪的测量功能，既能测量锥齿轮的切向综合误差，又能数字化测量锥齿轮接触区、进行三维结构噪音分析等。该机型功能先进，代表了该类产品当代的发展水平，虽价格昂贵，但在国内已有个别用户。与此类似的还有克林伯格GKC60、奥立孔T50等数控锥齿轮检验机。
2．3 整体误差测量方法及仪器
锥齿轮整体误差测量是在同一个回转角度位移坐标上按啮合顺序将锥齿轮工作齿面上各检测点所测得的所有单项几何误差集成为一个锥齿轮整体误差图，并以此为基础，完成对于锥齿轮单项几何精度、综合运动精度以及锥齿轮副接触状态的分析计量，实现对于锥齿轮使用性能和质量的评估和监控。锥齿轮整体误差测量方法和仪器，目前可分为二类三种。一类为坐标式几何解析测量法，该方法又分为“点到点测量法”和“点扫描测量法”，两种方法采用的仪器都为CNC 齿轮测量中心，但配用的测量软件包有所不同；另一类为啮合式运动几何测量法（即啮合式点扫描测量法，该方法为我国首创），所采用的仪器为锥齿轮单面啮合检查仪，配有专用的测量锥齿轮和测量软件包。
（1）坐标式点到点锥齿轮整体误差的测量
在齿轮测量中心上，用三维测头沿锥齿轮的齿廓和齿向两个方向，按预先确定的间距，对被测齿面各检测点（通常为齿廓上5处、齿向上9处，共45点）的几何形状误差进行一点一点的测量。这种方法可以避免三维测头和被测齿面间在测量时产生摩擦力而影响测量结果。该测量方法采用的是“直接测量” 原理，具体步骤为：首先根据锥齿轮加工机床的调整参数和刀具几何参数，通过计算得到被加工大、小锥齿轮理想加工齿面的几何参数；将该齿面作为参照齿面，分别与实际加工（或经热处理后）的大、小齿轮的齿面进行比较，测得实际齿面与理想齿面的几何偏差。借助于专用的MATCH 程序，确定相应于被测实际齿面的假象机床加工参数；再按照啮合模型进行TCA 分析，计算得到锥齿轮副的切向综合偏差和接触状况，检验是否满足要求。如有必要，相应软件将根据测量结果，重新计算并调整机床加工参数，以便再次试切时，能加工出质量更满意的产品。
（2）坐标式点扫描锥齿轮整体误差的测量
日本大阪精机近来提出的、采用二维测头对锥齿轮齿面进行点扫描测量的方法，得到了可靠满意的测量结果。该方法具有以下特点：通过控制工件的回转、测头的平行位移运动，避免了测头与齿面间的摩擦力对测量的不利影响；由于采用扫描测量方式，测量区域可覆盖整个齿面包括齿顶以及接近大、小端的区域；测量路径可有多种选择，通常齿形数及齿向数各为3条，共6条；每条扫描线上的采样数可达113个点，由于采样密度大，能够反映齿面上的微小波纹度（该波纹往往是不悦耳噪音的主要来源，用常规的点到点测量方法难以测量）。该方法采用的是“共轭测量”原理，其具体步骤为：首先根据机床加工参数和刀具参数计算得到大齿轮理想加工齿面的几何参数，计算出与它相共轭、无传动误差的虚拟共轭小齿轮的齿面几何参数；将实际加工的
大齿轮齿面与理想加工大齿轮齿面进行对比测量，检测出齿廓及齿向上的相对偏差；将实际加工的小齿轮齿面与计算得到的虚拟共轭小齿轮齿面进行对比测量，检测出齿廓及齿向上的相对偏差。根据所测得的相对偏差，计算得到该锥齿轮副的三维齿面综合偏差形貌图、切向综合偏差和接触形态（包括接触路径，接触区域形状、大小位置等）。经实物测量、比对验证，点到点测量法和点扫描测量法的测量计算结果是一致的。
（3）啮合式点扫描锥齿轮整体误差的测量
成都工具研究所提出的锥齿轮啮合式点扫描测量法，是在锥齿轮单面啮合检查仪上，按设计安装位置、采用特殊测量锥齿轮与被测锥齿轮进行单面啮合的滚动测量。这种测量锥齿轮副的“基础”几何参数和被测锥齿轮副的几何参数是完全一样的。测量时采用腐蚀方法或粘贴方法，在大、小测量齿轮相间的轮齿上做成所需的齿廓或齿向测量棱线，通过测量锥齿轮的齿廓或齿向测量棱线与相配对的被测锥齿轮齿面接触传动，完成锥齿轮的啮合点扫描整体误差测量。测量路径数与测量齿轮齿数有关，一般为3+3共6条。锥齿轮啮合式点扫描整体误差测量采用的是“局部基准相对测量”原理。具体测量步骤如下：根据锥齿轮副实际跑车/试车实验（或经验），由厂方选出能最佳满足使用要求的锥齿轮副作为“基准”锥齿轮副（称为局部基准），它的切向综合偏差、一齿切向综合偏差及接触区形态被确认为评定该对锥齿轮副精度的主要参照指标。测量锥齿轮和局部基准锥齿轮相啮合，在锥齿轮单面啮合检查仪上测得综合齿廓偏差局—测(局部基准锥齿轮副—测量基准锥齿轮副，下同) 、综合齿向偏差局—测、切向综合偏差局—测、一齿综合偏差局—测、接触区形态局—测以及三维齿面综合偏差形貌图局—测等，并被确认为批量锥齿轮检测时评定该单个锥齿轮主要精度指标的参考基准数据。被测工件锥齿轮和测量锥齿轮按同样方法进行测量，得到各项偏差的工件锥齿轮—测量锥齿轮数据；经运算得到相应各项偏差工—局数据（即工件锥齿轮相对于局部基准锥齿轮的相应各项精度指标的偏差）。然后根据所测得的工—局偏差数据和制定的精度指标公差范围，来判定锥齿轮的质量及可互换性水平。 锥齿轮整体误差测量方法简便，快捷可靠，测量信息丰富，特别适用于大批量生产。由于测量时必须采用特殊测量齿轮，因此这种测量方法不宜用于单件小批量的测量。然而，由于锥齿轮整体误差测量仪同时还具备锥齿轮滚动检查仪的功能，因此它完全可用于单件小批锥齿轮副综合精度检测及批量生产工件的试切及机床调试。
3 结语
通过回顾近年来锥齿轮测量技术研究领域的现状与发展，重点介绍了国内外
锥齿轮整体误差测量技术、方法及开发的相应仪器。我国自行开发的啮合式点扫描锥齿轮整体误差测量技术的不断发展，已逐步得到国内外同行的认可；依据该技术开发的锥齿轮整体误差测量仪正在推向生产一线并在测量实践中继续完善。可以相信，依托啮合式点扫描锥齿轮整体误差测量技术，建立锥齿轮批量产品精度数据库，完全有可能根据使用要求采用计算机辅助测量技术实现弧锥齿轮的自动快速配对。
中文3900字
Bevel gear of the latest developments in measurement technology 1 Overview
Bevel gear drive mechanism in the car, helicopter, machine tools and electric tools manufacturing industry, has been widely used. The use of different performance of the bevel gears are also different quality requirements, can be summarized including: ① a good contact area, can be a reliable torque transmission power; ② good match geometry, a smooth transfer of the movement, in order to ensure uniform load , transmission smooth, vibration small, noise low. Factories are usually small devices and dual-spot detection of rolling contact tester to control the quality of bevel gear, but in reality it is very difficult to determine accurately the performance of the bevel gear.
Bevel gear and the precision of measurement of cylindrical gears similar, can generally be classified into three types: ① Coordinate Geometry Analysis of measurement type. That is, the bevel gear as a geometric entity, its geometric elements, respectively, the geometric precision of individual measurements; Gear Measuring Center is the main measuring instruments. ② Comprehensive engagement measurement accuracy. That is, the bevel gear transmission as a component, the accuracy of their transmission, contact spots, a comprehensive measurement of the vibration noise. The measuring instruments are mainly one-sided meshing bevel gear tester, bevel gear meshing two-sided bevel gear measuring and inspection machine rolling. Bevel Gear ③ the overall measurement error. It will bevel gear transmission as a function for the realization of the geometric entities, or by coordinate measuring method in accordance with the geometric precision of a single measurement to measure the overall error of bevel gears, bevel gears to achieve a single transmission error and the geometric precision of the intrinsic link between the quality of the analysis; or by mating single measurement, the use of mesh point scan measurement of bevel gears for the overall error of measurement, has been integrated bevel gear movement accuracy, contact spots, as well as the geometric precision of the individual. Therefore, the overall error of measurement of bevel gear is a measurement of the first two methods of integration and development.
With the coordinate measuring technology, computer control and measurement technology, in recent years, the overall error of measurement of bevel gear technology
research development soon. Gear Measuring Center as a result of multi-cylinder coordinates, such as multi-function measurement instrument performance, data-processing capacity, bevel gear-type coordinates of analytic geometry measurement technology, has been the development of a single geometric error of measurement to the overall error of measurement of bevel gear, improved cone gear design, processing, quality testing to determine the accuracy and the use of the forecast performance of the bevel gear, such as the level of manufacturing technology. By China's own development, based on the "control point movement - geometric measurement principle" on one side of the bevel gear meshing point scanning technology and technology development based on the overall error of the bevel gear measuring instrument, it is more towards the production of the first line, so that China Bevel Gear measurement theory, the practical application of measurement technology has been further improved and developed.
2.the main bevel gear precision measurement method and apparatus
2.1 Coordinate-style geometric measurement and analysis equipment Machinery Exhibition into a straight bevel gear-type coordinate measuring instrument there earlier products to represented KP42-type, but the complex structure of high accuracy. Since 1990, both before and after, CNC Gear Measuring Center to the market, coordinates arc bevel gear-type geometry of measurement error is the rapid development and popularization and application. Today's market, Gear Measuring Center from abroad, whether it is Klingberg Germany's P63, or the United States Gleason / mar the GMX275, M & M's Sigma 3, have been measured with the function of bevel gear. These instruments have reached VDI / VDE level provided a space measuring uncertainty for more than 2 microns; bevel gear on the geometric error of a single test, such as pitch deviation (including single pitch deviation, the cumulative pitch deviation , total cumulative pitch deviation), tooth profile deviations (including a total deviation of tooth profile, the shape of tooth profile error, tooth profile tilt deviation) and teeth to the error (including the teeth to the total deviation, deviation of the shape of teeth to the teeth to tilt deviation) and output deviation of three-dimensional shape of tooth surface morphology map.
2.2 Integrated single-sided mesh rolling test measurement method and apparatus
Single-sided bevel gear meshing scroll detection methods have been used in production for many years. N0.513 Gleason in the United States rolling test machine
as an example, in the measured single-sided bevel gear pair meshing, the simulation of its work, and to a certain degree of speed and load, adjust the V / H, for colored contact area (spot ) testing to determine the bevel gear pair under test contact conditions; through the use of acceleration sensors, pickup of vibration and noise measured on the tooth scan frequency harmonic detection. This method is "quasi-dynamic" measurement method, which bevel gear for the accuracy of detection is far from complete or accurate enough. Optical encoder used as the base point of view, to cut bevel gears for the accuracy of detection of the integrated single-sided meshing bevel gear tester, such as Germany's Klingberg PSKE900, because a single test items, in particular, it is difficult for the basis of test results Bevel Gear Machine parameters adjusted to give guidance, to improve processing quality bevel gears. Less cost-effective and therefore not much used in production.
Gleason has introduced in recent years, the Phoenix 500HCT CNC bevel gear inspection machine is rolling with a rolling test at the same time and one-sided mating tester measurement function, measurement of both the tangential bevel gear integrated error, while the number of measuring cone gear contact area, three-dimensional structure of the noise analysis. The advanced models, such products represent the contemporary level of development, although expensive, but there are individual users at home. Klingberg also similar GKC60, such as Orion Hole T50 CNC bevel gear inspection machine.
2.3Measurement error overall and equipment
The overall error of measurement of bevel gear is rotating in the same angle displacement coordinates of the order will be based on the meshing bevel gear tooth surface of the work of the detection point measured by the geometric error of all the individual integrated into a bevel gear overall error map, and on this basis, bevel gears for the completion of a single geometric precision, and accuracy of an integrated campaign bevel gear analysis of contact state deputy measurement, the use of bevel gears to achieve the performance and quality assessment and monitoring. Bevel gear and the overall error of measurement apparatus, the current can be divided into three second-class. A class of analytic geometry for coordinate measurement type, the method is divided into "point-to-point measurement" and "point of scan measurements," equipment used in two ways for CNC Gear Measuring Center, but the allocation package by the measurement different; the other for the mating-type movement measurement geometry (ie, mesh-type scan measurement point, the
method for our first), the apparatus used for single-sided meshing bevel gear tester, equipped with a dedicated measurement bevel gear and measurement software package.
(1) coordinate the overall bevel gear-type point-to-point measurement error
Gear Measurement Center in, along with three-dimensional measurement of bevel gear tooth profile and tooth to the two directions, according to a pre-determined interval, the detection of the measured points of the tooth surface (usually the 5 tooth profile, tooth up 9 a total of 45 points) for the geometry error of measurement of 1.1 points. This method can be avoided and the measured three-dimensional probe in the measurement of tooth surface when the impact of friction and the measurement results. The measurement method is based on "direct measurement" principle, concrete steps are: first bevel gear in accordance with the adjustment of machine parameters and tool geometry parameters to be processed by calculating the large and small bevel gear tooth surface ideal geometric processing parameters; the tooth tooth surface as a reference, respectively, and the actual process (or after heat treatment) of large and small gear tooth surface compared to the actual measured tooth surface of the tooth surface with an ideal geometric deviation. MATCH procedures through the use of dedicated, determined corresponding to the actual measured tooth surface machining parameters of the illusion; re-engagement model in accordance with TCA analysis, calculated by the bevel gear pair integrated deviation and tangential contact conditions, test whether or not to meet the requirements. If necessary, the corresponding software will be based on the measurement results, re-calculate and adjust the machining parameters in order to re-try all they can be processed into a more satisfied with the quality of products.
(2) coordinates of point scanning type bevel gear of the overall measurement error
Seiki, Osaka, Japan recently proposed using two-dimensional measurement of bevel gear tooth surface measurement to point scanning method has been satisfactory and reliable results. This method has the following characteristics: the workpiece by controlling the rotation, the parallel displacement of probe movement, to avoid the probe and the tooth surface friction between the adverse effects of measurement; measurement as a result of the use of scanning, surveying the region to cover the entire tooth surface, including Top Gear, as well as close to large and small end of the
region; measurement path can have a wide range of choices, usually tooth number and tooth number of each to the three, a total of six; each sample the number of scanning lines of up to 113 points, as sampling density, to reflect minor tooth surface waviness (which often is not pleasant ripple of the main sources of noise, the conventional point-to-point measurement method difficult to measure). The method used the "conjugation of" principle, the concrete steps are: First of all, the basis of machining parameters and tool parameters to be the ideal gear tooth surface geometry processing parameters, to calculate the conjugate with it, no transmission error of the virtual conjugate of the pinion tooth surface geometry parameters; the actual processing of the large gear tooth surface with the ideal gear tooth surface processing compare measurements to detect gear tooth profile and the relative deviation upward; the actual processing of the pinion tooth surface and calculation of be conjugate Virtual pinion tooth surface compared with measurements, to detect the gear tooth profile and the relative deviation upward. According to the relative deviation of measured, calculated by the deputy of the three-dimensional bevel gear tooth surface morphology of the comprehensive plan deviation, deviation and tangential contact with the integrated form of (including access to the path of contact area shape, size, location, etc.). By physical measurement, than on the authentication, point-to-point and point measurements of the measurement scan measurement results are consistent.
(3) mating-type bevel gear to scan the whole point of the measurement error
Chengdu Tool Research Institute of the bevel gear to mesh-type scan measurement point is one-sided meshing bevel gear tester, the design of the installation location by using a special measuring bevel gear and bevel gear test for measuring the rolling one-sided engagement. This measurement of bevel gear pair "basis" cone measured geometric parameters and the geometric parameters of gear pair are all the same. Measurement methods or the use of corrosion-paste method, in large and small measurement of the gear teeth and white make the necessary gear tooth profile or ridge to the measurement, by measuring the bevel gear or the gear tooth profile and match to the measurement of ridge bevel gear of the measured tooth contact transmission, the meshing of bevel gears to complete scanning the overall error of measurement points. Measurement path and measuring the number of gear teeth, and a total of 3 +3 is generally 6. Mating-type bevel gear to scan the overall error of measurement points used the "relative measurement of the local benchmark" principle.
Measurement of specific steps are as follows: In accordance with the actual bevel gear pair sports / test experiment (or experience), elected by the factory can best meet the needs of the bevel gear use requirements vice as a "benchmark" bevel gear pair (known as the local benchmark), its integrated bias-cut to a cut tooth to the integrated form of bias and the contact area was identified as the assessment of the accuracy of the bevel gear of the main reference Vice indicators. Measurement of Bevel Gear and the local base of meshing bevel gears, bevel gears in mesh single tester measured tooth profile deviation of a consolidated Board - measured (local base bevel gear Deputy - Vice-bevel gear benchmarks, the same below), integrated to the deviation of tooth Board - measuring, cutting to the integrated deviation of the Board - measuring a tooth integrated deviation Board - measuring, shape Council contact area - measured, as well as the integrated deviation of three-dimensional tooth surface morphology of Fig Bureau - measuring and so on, and was recognized as a bulk evaluation of bevel gear testing The accuracy of a single bevel gear indicators mainly refer to baseline data. Measured part bevel gear and bevel gear measuring method according to the same measurement, the deviation of the workpiece has been Bevel Gear - Bevel Gear measurement data; by the computation of the corresponding deviations workers - Bureau data (that is, relative to the workpiece bevel gear partial cone base Gear indicator of the corresponding deviations of the accuracy). And then measured in accordance with the Public Works - Bureau deviation of the accuracy of data and indicators for the development of tolerance, to determine the bevel gear of the level of quality and interchangeability.
Bevel gear overall error measurement method is simple, fast and reliable measurement information-rich, especially for mass production. As a result of measurement must be measured using special gear, so this method should not be used for a single measurement of small quantities. However, since the bevel gear at the same time the overall error of measurement also has a rolling bevel gear tester, so it can be used for single-piece and small-batch precision bevel gear Deputy comprehensive detection and production of the test workpiece and cutting tool debugging.
3 Conclusion
Through the bevel gears in recent years the field of measuring the status of technology research and development, both at home and abroad to highlight the overall error of measurement of bevel gear technology, methods and development of
the corresponding equipment. China's self-developed scanning mating-type bevel gear at the overall error of measurement technology, has been gradually recognized by domestic and foreign counterparts; technology development based on the overall error of the bevel gear measuring instrument is to the production line and continue to improve measurement practice . It is believed that the mesh-style points based on scanning the overall error of measurement of bevel gear technology, the establishment of precision bevel gear bulk products database, it is very possible to adopt in accordance with the use of computer-assisted measurement technique to achieve automatic arc bevel gear pair quickly.
1 概述 锥齿轮测量技术的最新进展
锥齿轮传动机构在汽车、直升飞机、机床及电动工具制造业中，得到了广泛的应用。不同的用途对锥齿轮性能质量的要求也不同，归纳起来包括：①有良好的接触区，能可靠的传递动力扭矩；②有良好匹配的几何形状，能平稳的传递运动，从而保证载荷均匀、传动平稳、振动小、噪音低。工厂通常采用双啮仪及检测接触斑点的滚动检查仪来控制锥齿轮的质量，但实际上很难精确判定锥齿轮的使用性能。
锥齿轮的精度测量方法和圆柱齿轮类同，通常可分为三种：①坐标式几何解析测量法。即把锥齿轮作为一个几何实体，对其几何元素分别进行单项几何精度的测量；齿轮测量中心是其主要测量仪器。②啮合式综合精度测量法。即把锥齿轮作为一个传动元件，对其传动精度、接触斑点、振动噪音进行综合测量。其测量仪器主要有锥齿轮单面啮合检查仪、锥齿轮双面啮合测量仪及锥齿轮滚动检验机。③锥齿轮整体误差测量法。它将锥齿轮作为一个用于实现传动功能的几何实体，或用坐标测量法按单项几何精度测量方式测量出锥齿轮的整体误差，实现锥齿轮单项几何误差和传动精度、质量之间内在联系的分析研究；或按单面啮合测量方式、采用啮合点扫描测量方法，对锥齿轮的整体误差进行测量，得到锥齿轮的综合运动精度、接触斑点以及各单项几何精度。因此，锥齿轮整体误差测量法是前两种测量方法的集成和发展。 随着坐标测量技术、计算机控制与测量技术的发展，近年来对锥齿轮整体误差测量技术的研究得到很快的发展。由于齿轮测量中心等圆柱式多坐标多功能测量仪器的测量性能、数据处理能力的提高，锥齿轮的坐标式几何解析测量技术，已由单项几何误差测量发展到锥齿轮整体误差测量，提高了锥齿轮
设计、加工、精度质量的检测判定以及使用性能的预测等整个锥齿轮制造技术的水平。由我国自行开发、基于“可控点运动—几何测量原理”的锥齿轮单面啮合点扫描测量技术及基于该技术开发的锥齿轮整体误差测量仪，也正在更多地走向生产第一线，使我国锥齿轮测量理论、测量技术的实际应用得到了进一步的提高和发展。
2 锥齿轮精度主要测量方法及仪器
2．1坐标式几何解析测量方法及仪器
机械展成坐标式直锥齿轮测量仪较早就有产品，以瑞士马格KP42型为代表，精度很高但结构复杂。自1990年前后，CNC 齿轮测量中心推向市场，坐标式弧锥齿轮几何形状误差测量方法才有了迅速发展并得到推广应用。现今市场上国外的齿轮测量中心，无论是德国克林伯格的P63，还是美国格里森/马尔的GMX275、M ＆M 的西格马3，都已具备了测量锥齿轮的功能。这些仪器都达到VDI/VDE等级规定的1级，空间测量不确定度在2微米以上；可对锥齿轮的单项几何误差进行检测，如齿距偏差（包括单个齿距偏差、齿距累计偏差、齿距累计总偏差）、齿廓偏差（包括齿廓总偏差、齿廓形状偏差、齿廓倾斜偏差）、齿向偏差（包括齿向总偏差、齿向形状偏差、齿向倾斜偏差）并可输出三维齿面形状偏差形貌图等。
2．2 单面啮合滚动检验综合测量方法及仪器
锥齿轮单面啮合滚动检测方法在生产中已经使用多年。以美国格里森N0.513滚动检验机为例，在被测锥齿轮副单面啮合的情况下，模拟其工作状态，加以一定的速度和载荷，调整V/H，进行着色接触区（斑点）的检测，以判定该被测锥齿轮副的接触状况；借助于加速度传感器、拾音器测量其振动和噪音，对齿频谐波进行扫描检测。这种方法属于“准动态”测量方法，它对于锥齿轮的精度检测是不够完整、不够准确的。而采用光电编码器作为角度基准、用于锥齿轮切向综合精度检测的锥齿轮单面啮合检查仪，如德国克林伯格公司的PSKE900，因其检测项目单一，尤其难以根据检测结果对锥齿轮加工机床参数的调整给以指导、以改进锥齿轮加工质量。性价比较差，故生产中不多采用。
近年来格里森公司推出的凤凰500HCT 数控锥齿轮滚动检验机则同时具备了滚动检验机和单面啮合检查仪的测量功能，既能测量锥齿轮的切向综合误差，又能数字化测量锥齿轮接触区、进行三维结构噪音分析等。该机型功能先进，代表了该类产品当代的发展水平，虽价格昂贵，但在国内已有个别用户。与此类似的还有克林伯格GKC60、奥立孔T50等数控锥齿轮检验机。
2．3 整体误差测量方法及仪器
锥齿轮整体误差测量是在同一个回转角度位移坐标上按啮合顺序将锥齿轮工作齿面上各检测点所测得的所有单项几何误差集成为一个锥齿轮整体误差图，并以此为基础，完成对于锥齿轮单项几何精度、综合运动精度以及锥齿轮副接触状态的分析计量，实现对于锥齿轮使用性能和质量的评估和监控。锥齿轮整体误差测量方法和仪器，目前可分为二类三种。一类为坐标式几何解析测量法，该方法又分为“点到点测量法”和“点扫描测量法”，两种方法采用的仪器都为CNC 齿轮测量中心，但配用的测量软件包有所不同；另一类为啮合式运动几何测量法（即啮合式点扫描测量法，该方法为我国首创），所采用的仪器为锥齿轮单面啮合检查仪，配有专用的测量锥齿轮和测量软件包。
（1）坐标式点到点锥齿轮整体误差的测量
在齿轮测量中心上，用三维测头沿锥齿轮的齿廓和齿向两个方向，按预先确定的间距，对被测齿面各检测点（通常为齿廓上5处、齿向上9处，共45点）的几何形状误差进行一点一点的测量。这种方法可以避免三维测头和被测齿面间在测量时产生摩擦力而影响测量结果。该测量方法采用的是“直接测量” 原理，具体步骤为：首先根据锥齿轮加工机床的调整参数和刀具几何参数，通过计算得到被加工大、小锥齿轮理想加工齿面的几何参数；将该齿面作为参照齿面，分别与实际加工（或经热处理后）的大、小齿轮的齿面进行比较，测得实际齿面与理想齿面的几何偏差。借助于专用的MATCH 程序，确定相应于被测实际齿面的假象机床加工参数；再按照啮合模型进行TCA 分析，计算得到锥齿轮副的切向综合偏差和接触状况，检验是否满足要求。如有必要，相应软件将根据测量结果，重新计算并调整机床加工参数，以便再次试切时，能加工出质量更满意的产品。
（2）坐标式点扫描锥齿轮整体误差的测量
日本大阪精机近来提出的、采用二维测头对锥齿轮齿面进行点扫描测量的方法，得到了可靠满意的测量结果。该方法具有以下特点：通过控制工件的回转、测头的平行位移运动，避免了测头与齿面间的摩擦力对测量的不利影响；由于采用扫描测量方式，测量区域可覆盖整个齿面包括齿顶以及接近大、小端的区域；测量路径可有多种选择，通常齿形数及齿向数各为3条，共6条；每条扫描线上的采样数可达113个点，由于采样密度大，能够反映齿面上的微小波纹度（该波纹往往是不悦耳噪音的主要来源，用常规的点到点测量方法难以测量）。该方法采用的是“共轭测量”原理，其具体步骤为：首先根据机床加工参数和刀具参数计算得到大齿轮理想加工齿面的几何参数，计算出与它相共轭、无传动误差的虚拟共轭小齿轮的齿面几何参数；将实际加工的
大齿轮齿面与理想加工大齿轮齿面进行对比测量，检测出齿廓及齿向上的相对偏差；将实际加工的小齿轮齿面与计算得到的虚拟共轭小齿轮齿面进行对比测量，检测出齿廓及齿向上的相对偏差。根据所测得的相对偏差，计算得到该锥齿轮副的三维齿面综合偏差形貌图、切向综合偏差和接触形态（包括接触路径，接触区域形状、大小位置等）。经实物测量、比对验证，点到点测量法和点扫描测量法的测量计算结果是一致的。
（3）啮合式点扫描锥齿轮整体误差的测量
成都工具研究所提出的锥齿轮啮合式点扫描测量法，是在锥齿轮单面啮合检查仪上，按设计安装位置、采用特殊测量锥齿轮与被测锥齿轮进行单面啮合的滚动测量。这种测量锥齿轮副的“基础”几何参数和被测锥齿轮副的几何参数是完全一样的。测量时采用腐蚀方法或粘贴方法，在大、小测量齿轮相间的轮齿上做成所需的齿廓或齿向测量棱线，通过测量锥齿轮的齿廓或齿向测量棱线与相配对的被测锥齿轮齿面接触传动，完成锥齿轮的啮合点扫描整体误差测量。测量路径数与测量齿轮齿数有关，一般为3+3共6条。锥齿轮啮合式点扫描整体误差测量采用的是“局部基准相对测量”原理。具体测量步骤如下：根据锥齿轮副实际跑车/试车实验（或经验），由厂方选出能最佳满足使用要求的锥齿轮副作为“基准”锥齿轮副（称为局部基准），它的切向综合偏差、一齿切向综合偏差及接触区形态被确认为评定该对锥齿轮副精度的主要参照指标。测量锥齿轮和局部基准锥齿轮相啮合，在锥齿轮单面啮合检查仪上测得综合齿廓偏差局—测(局部基准锥齿轮副—测量基准锥齿轮副，下同) 、综合齿向偏差局—测、切向综合偏差局—测、一齿综合偏差局—测、接触区形态局—测以及三维齿面综合偏差形貌图局—测等，并被确认为批量锥齿轮检测时评定该单个锥齿轮主要精度指标的参考基准数据。被测工件锥齿轮和测量锥齿轮按同样方法进行测量，得到各项偏差的工件锥齿轮—测量锥齿轮数据；经运算得到相应各项偏差工—局数据（即工件锥齿轮相对于局部基准锥齿轮的相应各项精度指标的偏差）。然后根据所测得的工—局偏差数据和制定的精度指标公差范围，来判定锥齿轮的质量及可互换性水平。 锥齿轮整体误差测量方法简便，快捷可靠，测量信息丰富，特别适用于大批量生产。由于测量时必须采用特殊测量齿轮，因此这种测量方法不宜用于单件小批量的测量。然而，由于锥齿轮整体误差测量仪同时还具备锥齿轮滚动检查仪的功能，因此它完全可用于单件小批锥齿轮副综合精度检测及批量生产工件的试切及机床调试。
3 结语
通过回顾近年来锥齿轮测量技术研究领域的现状与发展，重点介绍了国内外
锥齿轮整体误差测量技术、方法及开发的相应仪器。我国自行开发的啮合式点扫描锥齿轮整体误差测量技术的不断发展，已逐步得到国内外同行的认可；依据该技术开发的锥齿轮整体误差测量仪正在推向生产一线并在测量实践中继续完善。可以相信，依托啮合式点扫描锥齿轮整体误差测量技术，建立锥齿轮批量产品精度数据库，完全有可能根据使用要求采用计算机辅助测量技术实现弧锥齿轮的自动快速配对。