螺旋锥齿轮基于离散点描述齿面接触分析研究

详细讨论了用 B样条函数拟合表示的螺旋锥齿轮轮齿齿面接触分析方法 :1建立了螺旋锥齿轮拟合齿面的接触点求解模型 ,并给出了该模型的求解方法 ;2给出了拟合齿面接触区及传动误差曲线的绘制方法 ,最后给出了一个实例。该方法经适当变化后也可用于其它种类齿轮的齿面接触分析。     

A generating method for digital gear tooth surfaces

Based on the theories of digital conjugate surface and gear meshing, a generating method for digital gear tooth surfaces (DGTS) is demonstrated in this paper. The research focuses on the conjugate motion between the DGTS, represented by discrete points, and the cutter figuration determined by analytic function in the manufacture process. Conjugate points in the cutter section corresponding to the discrete points on the digital surface and conjugate movements are solved. Automated sequence arrangements of the generating movement parameters have been performed and the discrete generating movements are interpolated in a continuous conjugate motion along the order. Strategies of error analysis and error compensation are also discussed in this paper. Computer-simulated examples of the generating machining of involute DGTS and non-standard shaped DGTS, the parameters of machining motions and real tooth surfaces verify the developed method. The research develops a new idea for the machining of DGTS, which breaks the limitations of conventional approaches based on analytic surfaces. It is of important theoretical and practical value to manufacture digital surfaces. Our method is not only be applicable in generating machining of discrete DGTS and analytic gear tooth surfaces with complex geometric design, but also in contributing to the processing of discrete digital cam and other 3-D digital surfaces .     

Control by virtual gauge of skew surfaces for correction process

The automation of production has been considerably developed in recent years in all its phases from design and manufacturing to control. The design and manufacture of free form surfaces are a current practice in the industry; thus, the conformity problem of complex geometry parts is felt more and more. The co-ordinate measurement machine (CMM) has largely reduced the acquisition and processing time in the take up measurement operation, which explains the wide use of the CMM in the mechanical industry over the last decade. The modelling and controlling procedure proposed within this paper enables correction of complex surfaces during the parts manufacturing process. The method is based on real surfaces modeled by finite elements starting from cloud points obtained by a digitalizing procedure in the co-ordinate measurement machine. The procedure was applied on a tooth gear which equips the gear box manufactured in the Algeria Engines and Tractors Factory. A comparison between the real and ideal model has been established showing the defects of form in order to correct the grinding process. This comparison is carried out by associating a surface of perfect geometry to a group of palpated dots. The selected criterion of optimisation is the least squares method.     

Determination of Best Objective Function for Evaluating Geometric Deviations

Laser scanning equipment and coordinate measuring machines are used to sample points from manufactured surfaces for inspection purposes. The sampled points are then used to evaluate the geometric deviations associated with the surface. The evaluation of geometric deviations involves an optimisation step which fits a substitute surface to the measured points, while minimising the error between the substitute surface and the measured points. The geometric deviation is equal to the difference between the maximum and the minimum normal distances between the fitted surface and the measured surface points. The choice of the objective function used in fitting the substitute surface affects the accuracy by which the geometric deviations are estimated. This paper presents a procedure for determining the best fitting function. It considers the trade-off between the accuracy of the estimation and the susceptibility to measurements and sampling errors. The proposed procedure has been verified for a number of geometric deviation types. Those results show that adopting a generic form for the fitting objective function may lead to large estimation errors with some geometric deviations, and that the proposed procedure reduces these errors significantly.     

螺旋渐开线齿轮的齿面生成研究

针对圆柱型螺旋渐开线齿轮不易滚削加工的问题,构造出一种碟形螺旋渐开线齿轮,使其滚削加工成为可能。根据齿轮啮合原理及特殊的加工方法,由产形齿条的齿面方程,推导了碟形螺旋渐开线齿轮的渐开螺旋面、过渡曲面及齿根面的方程。采用MATLAB编程得到碟形螺旋渐开线齿轮齿面的点三维坐标值。由生成的齿面上点的三维坐标值,在Pro/E中构建了碟形螺旋渐开线齿轮精确实体模型,为该齿轮的接触分析与有限元分析奠定了基础。     

考虑边缘接触直齿面齿轮传动轮齿接触分析

主要分析了直齿面齿轮传动在考虑边缘接触条件下的啮合.从理论上推导了求解边缘接触的数学模型及边缘接触点满足的约束条件,利用相邻接触点主曲率方向相似的方法确定了当发生边缘接触时在接触曲面上的主曲率方向.结果显示,边缘接触更容易在刚进入啮合时产生,并且在边缘接触点处几何传动误差不再为O.     

螺旋渐开线齿轮的齿面生成研究

针对圆柱型螺旋渐开线齿轮不易滚削加工的问题,构造出一种碟形螺旋渐开线齿轮,使其滚削加工成为可能。根据齿轮啮合原理及特殊的加工方法,由产形齿条的齿面方程,推导了碟形螺旋渐开线齿轮的渐开螺旋面、过渡曲面及齿根面的方程。采用MATLAB编程得到碟形螺旋渐开线齿轮齿面的点三维坐标值。由生成的齿面上点的三维坐标值,在Pro/E中构建了碟形螺旋渐开线齿轮精确实体模型,为该齿轮的接触分析与有限元分析奠定了基础。     

三维数字化齿面的展成方法研究

利用共轭曲面原理和齿轮啮合原理提出一种对以离散点表达的三维数字化齿面展成加工的方法。应用该方法 ,以三维数字化渐开线齿面的展成加工为实例 ,通过仿真计算 ,获得了实际展成加工中的加工参数 ,以及实际展成加工的齿面。该方法对于完善齿面加工理论 ,并应用于实际的三维齿面的滚齿、插齿、磨齿等加工工艺 ,都具有重要的理论价值和应用价值。     

螺旋锥齿轮齿面近似产成方法研究

介绍了一种在CNC机床上用近似加工产成螺旋锥齿轮小轮齿面的方法,推导了刀具表面和产成表面之间的啮合方程以及产成表面的表达式.此方法能够控制齿面一条参考线上所有点的特征,更好地结合了局部共轭和完全共轭,所加工出的齿面仍采用了齿面修正,而且和完全共轭齿面更加接近.     

An intelligent sampling method for inspecting free-form surfaces

The two most important factors in sampling during coordinate verification of a surface are the number of measuring points that accurately represent the surface and the distribution of those points. Three algorithms are developed in this paper for sampling of free-form surfaces at a patch scale (not the entire surface). The three developed algorithms take each patch on the surface as a separate unit and distribute the points within the patch in two steps, namely, sample the most critical points that depend on maximum and minimum Gaussian curvature of each patch and add more points depending on the overall distribution of the most critical points distributed on the surface. In each step of sampling, the maximum difference between the CAD model and the surface created using those sampled points is obtained, and an optimum number of measuring points is determined. This minimizes sampling effort and (non-value-added) measurement time. A comparison is performed between the three proposed algorithms and two well known sampling techniques: the equiparametric approach and the patch-size-based sampling method. The proposed algorithms distribute the points in each patch based on a specific plan. The results show that the developed algorithms help select an efficient number of sampling points.     

Transition curve of involute gear teeth with asymmetric profiles

Analytical determination of the transition curves at the base of asymmetric gear teeth is considered. In the first stage, by roulette constructions associated with initial gear circumferences that roll over one another, the coordinate points of such transition curves are found as the tooth tips slip over the transition curves at the base. In the second stage, a radial gap is constructed so that its outline facilitates simple tooth manufacture and minimum stress concentration at the tooth root.     

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.     

面齿轮磨削齿面齿形误差修正

以面齿轮齿面的形状误差为研究对象,建立了面齿轮齿面数学方程,通过三坐标测量仪（CMM）对面齿轮齿面进行了误差测量。为提高面齿轮齿面的精度,提高其理论和工程的应用价值,提出了一种基于序列二次规划（SQP）的面齿轮齿面误差评定方法。建立了齿面误差的识别方程,应用序列二次规划算法对机床加工参数进行优化求解,并与最小二乘优化法进行对比,应用修正后的机床调整参数,再次通过三坐标测量仪对修正后的齿面误差进行检测,验证了该方法的可行性。     

渐开线斜齿圆柱齿轮的三维造型

渐开线斜齿圆柱齿轮的三维造型存在两大难点:端面齿廓的绘制和轮齿的生成。利用渐开线的参数方程式并通过AutoLISP编程绘制出端面齿廓一侧的渐开线;在对轮齿端面齿廓进行几何分析与计算的基础上,确定并绘制出其对称线及齿顶圆弧,并利用该对称线获得轮齿端面齿廓另一侧的渐开线;绘制出齿轮轮齿两端的齿廓曲线及通过齿廓曲线两端点的齿根螺旋线后,用AutoCAD的“边界曲面”命令,构造斜齿圆柱齿轮的轮齿表面模型。     

格利森制弧齿锥齿轮的齿面曲率特性研究

根据弧齿锥齿轮加工过程,通过计算机仿真方法编程计算得出格利森制弧齿锥齿轮不同加工方法齿面的精确三维坐标点;对不同齿面坐标点进行NURBS参数化曲面拟合,得到了不同齿面的统一数学表达模型;并据此计算格利森制弧齿锥齿轮齿面的曲率,绘制了不同齿面的等平均曲率线图;并研究了加工参数调整与齿面等平均曲率线图变化之间的联系,证明了依据齿面等曲率图的变化实现对弧齿锥齿轮齿面加工误差调整以及对齿面曲率定量修正的可行性.     

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。     

Influence of tooth modifications on tooth contact in face-hobbed spiral bevel gears

In this study the influence of tooth modifications induced by machine tool setting and head-cutter profile variations on tooth contact characteristics in face-hobbed spiral bevel gears is investigated. The concept of face-hobbed spiral bevel gear generation by an imaginary generating crown gear is applied. The modifications of tooth surfaces are introduced into the teeth of both members. The lengthwise crowning of teeth is achieved by applying a slightly bigger radius of lengthwise tooth flank curvature of the crown gear generating the concave side of pinion/gear tooth-surfaces, and by the variation of machine tool settings in the generation of pinion/gear teeth. The ease-off in the tooth height direction of meshing tooth surfaces is achieved by applying a head-cutter whose profile consists of two circular arcs, instead of a straight-line. The method of tooth contact analysis applied determines the path of contact, the potential contact lines, the separations along these lines, and the transmission errors. A computer program implements the method. By using this program the influence of the variation of machine tool settings and of head-cutter geometry on tooth contact is investigated and discussed.     

Localised tooth contact analysis of single envelope worm gears with assembly errors

This paper presents the basis of loaded tooth contact analysis and predicts the influence of assembly errors on localised contact stress distribution in single enveloping (cylindrical) worm gearing during a meshing cycle. A method for loaded tooth contact analysis, geometry and kinematics of such gear pairs is developed. The method accounts for the effects of tooth composite deflection caused by bending, shearing, foundation, tooth contact deformation and initial profile separation due to assembly errors. The method includes the determination of contact lines, load and stress distribution due to assembly errors. Because of the complex geometry of worm gear teeth, the tooth bending stiffness is calculated using the slicing technique developed earlier by the authors. Classical Hertz theory is used for calculating contact stress and deformation. A computer program based on the presented method has been developed and used to study the influence of errors on mating teeth contact. It is shown that the governing factors in loaded gears with assembly error are the mesh stiffness and the amount of error which is linked to load sharing between adjacent tooth pairs. A numerical example is presented to further clarify the outlined method.     

基于多目标遗传算法的弧齿锥齿轮多学科优化设计

针对常规设计中弧齿锥齿轮存在的问题,将多学科优化设计引入到弧齿锥齿轮设计中,改善其不足。以大小弧齿锥齿轮体积之和最小、弧齿锥齿轮齿根弯曲应力最小以及工作噪音最小三个方面为目标函数,以齿数、齿宽中点螺旋角、齿宽和大端模数为设计变量,考虑齿面接触疲劳强度、齿根弯曲疲劳强度、环境保护等8个方面约束,建立弧齿锥齿轮的多学科优化设计数学模型。根据该数学模型,运用多目标遗传算法对文中的实例优化求解,计算结果表明该设计方法是合理的,行之有效的。     

Producing gear teeth with high form accuracy and fine surface finish using water-lubricated chemical reactions

A new method was investigated for high-accuracy fine finishing of gear teeth surfaces using a water-lubricated tribo-chemical technique. A pair of shaved gears with rather low surface roughness was rotated in water lubricant for 30 min so that the gear tooth surface contacting the mating tooth was ‘worn’ to a mirror surface and ideal tooth profile, due to the mechano-chemical mild erosion of the contact area. The wear rate was 2.0 μm per 20,000 meshings, corresponding to a wear of one atomic radius thickness per meshing. Oxidation of the steel surface by water molecules is proposed as the dominant wear process. Operation noise from the gear pair rotation was drastically reduced to lower than about 10–15 dB compared to conventionally machined gear surfaces (30 dB in average), as a result of the wear of the tooth surface to form a best-fit profile. The noise increased with further processing of the gear pair. Thus, there is an appropriate number of rotations for suitable surface wear treatment. This new and simple procedure for surface treatment assures saving in energy, and does not require expensive honing techniques or high-accuracy grinding tools.The wear mechanisms used in this process are discussed along with the application of the technique to other processes for precision finishing.