螺旋锥齿轮齿面扫描式测量法及其应用研究

螺旋锥齿轮的实际齿面形状是影响其动力学性能的一个非常重要的因素。本文介绍了采用虚拟共轭基准面的螺旋锥齿轮齿面的扫描式测量、数据处理及应用方法，即大齿轮的基准面采用的是由机床设定参数计算出的理论齿面，而小齿轮的基准面采用的是与大齿轮共轭的假想小齿轮齿面。由于采用了二维测头进行齿面测量，有效地避免了测头与齿面间摩擦力的影响，既能保持高精度，又能进行快速测量。同时，该种测量采用连续扫描的方法，信息量大、速度快，适合于大批量生产中的螺旋锥齿轮的齿面质量管理与控制。由于扫描式测量采用了虚拟共轭基准齿面，所以从测量数据本身就可以判断齿面的接触斑点位置与形状，因而可以直观、有效地对齿面质量进行管理与控制。     

机床齿轮齿面粗糙度检测方法的研究

研究了机床齿轮齿面粗糙度，渐开线仪器测量法的适用性及轮廓仪测量法的可行性，还提出了齿面粗糙度检测的有关问题。     

Measurement of lubricating film thickness,temperature and pressure in gear contacts with surface topography as a parameter

Thin film transducers, sputtered onto a tooth flank, are used to measure temperature, pressure and oil film thickness profiles in gear contact. The former two are resistance sensors, while the film thickness sensor functions as a capacitive transducer. Experiments were carried out with ground and hobbed gears. The measurements are repeated after the tooth flank has been polished. The differences of the measured values for the ‘rough’ and ‘smooth’ surfaces are used for comparisons between differently machined surfaces. An EHD simulation programme has been developed which calculates film thickness and contact pressure, also taking surface roughness into account.     

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.     

非圆齿轮齿面加工余量匀化工艺研究与实现

针对非圆齿轮加工中,由齿坯节曲线曲率变化所引起的分次进刀过程中齿面加工余量分布不均的问题,提出一种匀化非圆齿轮齿面加工余量的工艺方法。以非圆齿轮插削工艺为研究对象,基于插齿加工原理,对齿面加工余量分布不均的成因进行了分析;在此基础上建立了非圆齿轮匀化工艺插削联动模型,通过实时调整插刀与齿坯的几何位置关系,实现了非圆齿轮齿面加工余量的匀化;开发了非圆齿轮插齿CAM系统,利用CAM系统对齿面加工余量匀化工艺进行了仿真验证,仿真结果表明,所提工艺方法正确、可行;将匀化工艺集成到自主开发的齿轮加工数控系统中,进行了非圆齿轮插削加工试验,试验结果表明,所提工艺方法能够有效匀化齿面加工余量;对加工出的非圆齿轮齿面进行了三维形貌检测,检测结果表明,所提工艺方法能够显著提高非圆齿轮的加工精度与表面质量。     

Antiwear performance of modern industrial gear oils

Thermally refined gears were tested under the effects of various modern industrial gear oils, viscosity 1SO VG 220. The wear of the gears was measured for each oil, including tooth surface roughness and the tooth fillet strain of the pinion. It is concluded that graphite additivated gear oil shows excellent wear resistance and surface roughness over sulphur-phosphorus and organic Mo compound added oils, as well as less iron oxide.     

Effect of tooth profile modification on the scoring resistance of spur gears

Using power-circulating gear test rigs, the scoring resistance of gears with tooth profile modification and gears without tooth profile modification, both of which were subjected to different amounts of addendum modification, was studied. The effect of tooth profile modification on the scoring resistance of gears with a small amount of addendum modification was significantly increased by the tooth profile modification. The critical surface temperature for scoring lies between 443 and 447 K under the conditions of tooth material and lubricant used. The scoring resistance of gears can be accurately estimated by evaluating the critical surface temperature.     

核电循环泵行星齿轮热弹流润滑研究

核电齿轮箱的良好润滑性能是核电循环泵可靠运行的重要保障,充分考虑齿面形貌和齿廓修形等因素对内/外啮合齿轮副的影响是准确评估其润滑特性的前提。建立典型工况下核电循环泵行星传动系统斜齿轮热弹流润滑模型,首先将斜齿轮副的啮合状态几何等效为圆锥滚子的接触问题,然后考虑斜齿轮接触变形和齿廓偏差,计算得到内/外啮合齿轮副接触区域不同位置的油膜厚度、承载压力、摩擦应力和闪温等参数。考虑齿面磨合作用,采用移动平均滤波方法对未经磨合的初始形貌进行光滑处理,分析了齿面形貌对润滑行为的影响,最后采取齿廓修形改善润滑特性。结果表明：粗糙度和齿廓修形均会对润滑特性产生明显的影响,齿面粗糙形貌会造成油膜厚度减小,进而影响其润滑特性,弱化润滑油膜的承载能力;通过齿廓修形可以改善齿轮啮合边界处的几何过渡,降低该区域的应力集中和表面温度,从而明显改善啮合线终端的润滑状态。     

直齿锥齿轮齿廓圆弧修形

以理论渐开线直齿锥齿轮修形减振为目的,用圆弧曲线对直齿锥齿轮进行齿廓修形,以减小齿轮传动误差和啮合刚度的波动为衡量标准,同时确保载荷变化呈平稳过渡。静态计算结果表明,齿廓圆弧修形齿轮具有较好的减振效果。     

On surface integrity of miniature spur gears manufactured by wire electrical discharge machining

This paper reports about investigations on some important aspects of surface integrity of the miniature spur gears manufactured by wire electrical discharge machining (WEDM) process. The investigations included study of variation of form errors (deviations in profile and lead) and surface roughness with discharge energy parameters, i.e., voltage and/or pulse-on time for the miniature gears. The effect of WEDM process on flank surface topography, bearing length parameters, microstructure, and microhardness for the best quality miniature gear were also studied. The manufactured miniature gears were of external spur type having 9.8 mm as outside diameter, 4.9-mm thickness, 0.7 mm as module, 12 teeth, and were made of brass. It was found that combination of low discharge energy parameters resulted in better form accuracy, surface finish, and microstructure ensuring enhanced service life and better functional characteristics of the WEDMed miniature gears. The best quality miniature gear had form errors (i.e., lead and profile deviations) as low as 5.4 μm, very little variation in the actual surface topography from the theoretical one, an average surface roughness of 1 μm, and maximum surface roughness within the entire evaluation length as 6.4 μm, showed consistent surface finish measured by other surface roughness parameters, good bearing area curve, and crack-free gear tooth surface without significant alteration in microhardness. Results of the present work demonstrate the superiority of the WEDM process over the conventional miniature gear manufacturing processes.     

81型双圆弧齿轮的齿根应力公式

本文用微型电阻应变片在中心距为120mm的封闭功率流齿轮实验台上测得经过充分跑合的JB2940-81型双圆弧齿轮的受拉侧及受压测的齿根应力,测得应力随载荷及螺旋角的变化关系,并将测得的数值分析写成应力公式,可作为该齿型双圆弧齿轮齿根弯曲强度计算的基本公式。还测得双圆弧齿轮在啮合过程中邻齿受载对本齿应力的迭加影响和本齿两个接触迹引起的应力迭加影响,这些规律可作为设计新齿形时选择齿型参数的参考。     

3D measurement of gears based on a line structured light sensor

Gears are core components of transmission systems. The current trend of gear measurements is the rapid and full digitization. To rapidly obtain information on the three-dimensional (3D) shape of the gear tooth flank, a 3D point cloud measurement system based on a line structure light sensor and high precision air floating rotary table is proposed. The system can acquire more than 1.5 million 3D data points on one side of the gear tooth flank within less than 5 s. In this study, the measured 3D point cloud data is used to calculate the profile error, pitch error, then compared to those obtained from traditional contact measurements. In addition, tooth flank error was evaluated. The results show that the 3D point cloud measurement system can perform fast and accurately in 3D measurements of gears and it is a novel system for gear measurement and error calculation.     

高速动车组斜齿轮的齿根裂纹萌生寿命数值计算

为分析高速动车组斜齿轮的齿根裂纹萌生寿命,采用UG建模软件建立了斜齿轮副的三维模型,并通过ABAQUS软件确定了裂纹萌生位置。基于疲劳损伤累积理论,对试验齿轮分别采用名义应力法和局部应力应变法模拟计算出裂纹萌生寿命;进行了高频疲劳试验,得到了裂纹萌生寿命,通过对比模拟结果与试验结果,确定了最佳损伤模型,计算得出了斜齿轮齿根的裂纹萌生寿命。分析了载荷、表面粗糙度、残余应力、齿顶修缘等因素对裂纹萌生寿命的影响规律。研究结果表明,载荷及表面粗糙度对裂纹萌生寿命的影响比较显著;裂纹萌生寿命随着残余压应力的增大而延长;适当的修形可延长斜齿轮裂纹萌生寿命。     

Tooth flank, undercutting and tooth pointing of spherical gears

By the developed mathematical model of spherical gears from literature [16], conditions of tooth undercutting of spherical gears with convex and concave teeth and tooth pointing conditions of the proposed concave spherical gear are derived. Besides, tooth flank profile deviations, limit curves of tooth undercutting and the beginning points of tooth undercutting and tooth pointing of the proposed spherical gear can be obtained by applying the spherical gear tooth mathematical model and the developed computer simulation programs, as illustrated by five numerical examples.     

Fiber optic displacement sensor for imaging of tooth surface roughness

A simple and inexpensive method using fiber optic displacement sensor is proposed for measurements of tooth surface roughness based on the intensity modulation technique. A light beam was launched onto a tooth surface via a bundled fiber. The reflected light from the surface was collected and measured as a function of lateral distance to estimate the roughness of the surface. The system’s roughness measurement capability was successfully tested on teeth surfaces of varying surface texture. In the measurement, the average surface roughness, R_a for the canine, molar, hybrid composite resin and artificial teeth surfaces were estimated to be approximately 121, 62.6, 39 and 37.6 μm, respectively. The experimental results indicated the capability of implementation of the displacement sensor for the imaging of the tooth surface profile as well as a micron-size roughness estimator with a measurement error of less than 2.35%.     

Deterministic mixed lubrication modelling using roughness measurements in gear applications

The presence of surface roughness on the teeth of hardened and ground power transmission gears is an unavoidable consequence of their manufacture. The paper discusses the effect of surface roughness when the elastohydrodynamic lubricant film thickness developed between the gear tooth surfaces is small compared to the heights of the roughness features. The ratio of these quantities, called the Λ value, may be well below unity in typical applications. For such thin film conditions the moving roughness features cause the elastohydrodynamic contact between the gears to be highly transient in nature. Surface roughness features on the working surfaces of the gears move past each other during meshing and these asperity encounters are associated with extreme pressure perturbations, or with film breakdown and isolated asperity boundary lubrication events. The paper reviews approaches used to study this problem and describes a coupled approach to solving the elastic and hydrodynamic equations. This allows numerical solutions to be obtained for these extreme conditions so that transient contact events associated with mixed lubrication can be predicted in a unified numerical solution scheme. Typical results obtained from such an analysis are presented including surface fatigue modelling and contact strain energy calculations.     

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.     

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。     

Assessing the role of plastic deformation in gear-health monitoring by precision measurement of failed gears

For constant loading and speed conditions, the principal sources of vibration excitation arising from meshing gears, characterised by the “static transmission error” (STE) excitation, are geometric deviations of the working surfaces of the teeth from equi-spaced perfect involute surfaces, and tooth/gear body elastic deformations. Changes in these two sources caused by tooth-bending-fatigue damage on one or a few teeth are manifested primarily in the rotational-harmonic content of the STE of each individual damaged gear of the meshing pair, and are most effectively detected in the time domain. The optimum number of gear rotations to be used in synchronous averaging is specified, along with how such synchronous averaging can be used to eliminate the effects of the mating gear in the case of “hunting tooth” gear pairs, and to minimise these effects otherwise. Precision measurements made on the teeth of a gear failed in a tooth-bending-fatigue test strongly suggest that whole-tooth plastic deformation—i.e. yielding, rather than changes in tooth stiffness caused by tooth-root cracks, is the principal source of detectable damage in the case of tooth bending fatigue. Such plastic deformations are geometric deviation STE contributions. Differences in gear materials, materials processing, and gear operating properties may significantly affect the amounts of such plastic deformations before tooth breakage and the operating duration between initial damage detection and tooth breakage, thereby suggesting the need for testing to determine such dependencies.     

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.