Manufacture of face-hobbed straight bevel gears using a six-axis CNC bevel gear cutting machine

Face hobbing is a continuous indexing and double-flank cutting process whose high productivity and precision has made it one of the leading methods for fabricating spiral bevel and hypoid gears. The current method is inappropriate, however, for cutting straight bevel gears (SBGs) because it generates extended epicycloidal flanks. Nonetheless, a mathematical model of a face-hobbed SBG was successfully established in earlier research that enables straight cutting paths to cut straight tooth spaces based on a hypocycloidal straight-line mechanism in which the rolling circle radius equals half the base circle radius. This mathematical model, however, is based on a virtual universal cradle-type bevel gear cutting machine that has not yet been developed. This paper therefore proposes another mathematical model of face-hobbed SBG based on a modern six-axis computer numerical control (CNC) bevel gear cutting machine. The six-axis nonlinear machine settings are derived through conversion from the cradle-type machine settings. Meanwhile, the usage of electric gearbox (EGB) for bevel gear cutting is not revealed because of commercial consideration. Therefore, we also provide a solution to use EGB of Fanuc 16i CNC controller. A cutting experiment validates the proposed mathematical models using our developed six-axis CNC bevel gear cutting machine to cut the face-hobbed SBGs. Finally, a flank topographic correction is made that, according to postcorrection simulated topographic errors, can effectively reduce manufacturing errors. This paper successfully implements a face-hobbing process for manufacturing SBGs on a modern six-axis CNC bevel gear cutting machine.     

Use of PLC module to control a rotary table to cut spiral bevel gear with three-axis CNC milling

CNC machining nowadays makes more use of "Mechatronics" increasingly. Combining numerical control with mechanic, electric, and data processing systems can lead to new methods of production. In recent years, the development of CNC has made it possible to perform nonlinear correction motions for the cutting of spiral bevel gears. In this paper, we attempt to manufacture the spiral bevel gear using a three-axis CNC milling machine interfaced with an additional PLC module based on traditional discontinuous multicutting method accomplished by using a universal milling machine interfaced with an indexing work head. This research consists of (a) geometric modeling of the spiral bevel gear, (b) simulating the traditional and our new nontraditional method using a CAD/CAE system, (c) process planning for CNC machining and PLC Programming, (d) experimental cuts with a three-axis CNC milling machine were made to discover the validity of the presented method. The results demonstrate that invented experimental cutting method of SBGs not only is less expensive than advanced CNC machining but also produces gears in a shorter time in comparison with the traditional cutting. Thereby, it is an economical method in manufacturing of SBGs.     

Mathematical modeling for finishing tooth surfaces of spiral bevel gears using pulse electrochemical dissolution

Gears with a complex curve tooth, such as spiral bevel and hypoid gears, lack an ideal technique for the final finishing process. Pulse electrochemical finishing (PECF) is considered a promising method for surface finishing due to its micro-removal characteristics. A PECF system for spiral bevel gear (SBG) is established according to the generation of SBG tooth surfaces. An SBG (module, 12?mm; number of teeth, 38) is selected as the processing test piece, and mathematical models are developed for analyzing the characteristics of PECF. The influence of the experimental variables, including applied voltage, interelectrode gap, and finishing time, on the total removal thickness and surface roughness is discussed. The calculated values are found to be approximately consistent with the experimental values. The other parameters, including the concentration of electrolyte, tool rotational speed, flow rate of electrolyte, and pulse period, are also studied. Results show that the roughness of the SBG tooth surface is reduced from Rz 7.13 to 4.32???m. The precision of the SBG is also improved.     

基于空间坐标系的齿轮建模方法与应用研究

给出利用空间坐标系创建齿轮模型的一种方法,即用坐标系方程计算出齿轮轮廓曲面和齿根过渡曲面的三维坐标值,然后利用Pro/E的曲面命令把这些坐标值上的点啮合成轮廓曲面模型,利用曲面模型对齿坯模型进行实体化操作,即可实现齿轮的快速精确建模。通过实验表明,在Pro/E设计环境下,基于空间坐标系的齿轮三维建模方法,建模精度高,速度快,是一种高效的齿轮建模方法。     

螺旋锥齿轮参数化精确建模

以齿轮啮合原理为基础,阐述了球面渐开线螺旋锥齿轮齿廓的形成机理,建立了螺旋锥齿轮齿面点坐标参数方程,构建了格里森制螺旋锥齿轮数学模型.利用基于Pro/E参数化建模方法,创建了螺旋锥齿轮单齿齿形,用阵列操作,建立了完整的螺旋锥齿轮三维实体造型,并通过运动仿真验证了该建模的精确性,为螺旋锥齿轮设计与制造研究提供了一种参数化设计方法.     

Loop细分曲面的自适应等距面生成算法与实现

提出一种精确快速生成有边界等距 L oop细分曲面的新算法 ,其核心思想是 :从控制网格顶点在 L oop细分曲面上的位置 ,按照给定的等距值 ,沿其法矢正 (反 )向等距 ,通过解线性方程组求出等距后的控制网格 ,然后检测等距误差 ,对部分超过给定等距精度的控制网格进行局部自适应细分 ,重新生成等距面并检测误差 ,直至整个细分等距曲面满足精度要求 ,所生成的等距细分曲面除局部 C1 外其余 C2 连续。实例表明 :本算法高效稳定 ,生成的等距细分曲面已完全满足实际工程需要。     

DESIGN AND MANUFACTURE OF STRAIGHT BEVEL GEAR FOR PRECISION FORGING DIE BY DIRECT MILLING

In the manufacture of straight bevel gears, a precision forging method has been mainly used in recent years and the precision forging die has been usually manufactured using electric discharge machining. However, it is difficult to content the high productivity and low manufacturing cost using electric discharge machining because the gears are produced through a process of several steps. In this article, a design and manufacture of a straight bevel gear for a precision forging die by direct milling is developed in order to improve the productivity and manufacturing cost for the gear production. The tooth profile of a straight bevel gear generated by a quasi-complementary crown gear instead of a usual complementary crown gear is introduced. For this study, first the numerical coordinates on the tooth surface of the straight bevel gear were calculated and the tooth profiles were modeled using a 3D-CAD system. Afterward, the direct milling of the precision forging die of the straight bevel gear in the hardened state was carried out using a CNC milling machine based on a CAM process through the calculated numerical coordinates.     

对数螺旋锥齿轮建模优化与加工检测

为了提高对数螺旋锥齿轮三维精确模型的精确性和准确性,提出了基于MATLAB和Pro/E的对数螺旋锥齿轮离散化建模方法。首先,根据对数锥齿轮的形成原理建立齿面方程;然后,根据齿轮的具体参数计算齿面边界条件;接着利用MATLAB计算出齿面离散坐标点,将这些坐标点导入到三维建模软件Pro/E中,利用其逆向工程模块建立齿面的离散模型。以Pro/E为二次开发平台,运用C语言编程建立只需要输入相应参数即可自动完成锥齿轮创建的程序,为后续锥齿轮的静力学分析、动力学分析和齿面修形奠定了基础。     

3~(1/2)互细分曲面的误差分析

针对细分控制网格与细分极限曲面的逼近度这一问题,基于细分控制网格的拓扑结构和细分模式的几何规则,提出一种3~(1/2)细分曲面的误差估计方法并给出一个误差估计公式。利用该公式,根据给定的精度,可事先知道细分之后控制网格满足该精度的最少细分次数而不需要实际对一个模型细分。结合该误差估计方法,给出一种3~(1/2)细分曲面数控加工刀具轨迹生成方法和一种用于直接在STL文件基础上提高精度的方法。试验结果表明这种误差估计方法的有效性。     

给定精度条件下的Catmull-Clark细分曲面求交研究

细分曲面由于没有整体解析表达式,与参数、隐式曲面相比求交更加困难。针对基于平面四边形网格的Catmull-Clark细分曲面,在给定精度条件下,把对细分曲面的求交转化为对一定细分层次控制网格的求交:首先构造两张控制网格上相交四边形网格带及其1-邻域网格带,然后不断细分相交四边形网格带及其1-邻域网格带,提高求交精度,其次求解出相交四边形网格的交点,并根据拓扑关系将其顺序连接起来既得到两细分曲面之间的相交曲线,实现了细分曲面的求交。     

准双曲面齿轮的仿真加工新方法

以五轴联动CNC(computer numerical control)弧齿锥齿轮加工机床的概念模型为基础,提出了一种新的准双曲面齿轮齿面的加工仿真方法。在仿真过程中,将齿坯离散为一个同心圆族,把将刀具刃锥面简化为一个锥面。并以求解代表齿坯的同心圆和代表刃锥面的圆锥面的交点数值分析方法为核心算法,构建起了整个仿真系统的框架。解决了基于通用CAD(computer aided design)平台开发的切齿仿真系统无法直接获得齿面上指定点数据的弊端,为复杂齿面的仿真加工技术的发展提供了新的思路。     

基于递归分割理论的自由曲面建模技术

为应用递归分割理论增强复杂自由曲面建模能力,通过在递归分割Loop方法中引入节点加权因子,实现了对递归逼近分割曲面形状的有效控制,并可以生成不同的尖锐特征。根据曲面模型各点处的平均曲率,对节点位置进行逐步调整,实现了递归分割曲面模型的光顺处理。论述了通过计算递归分割曲面模型的法向偏置面生成薄壁件表面模型的方法,并给出了所建立的自由曲面模型直接应用于快速原型制造的实例,说明应用该项新技术可以直接建立任意拓扑结构复杂自由曲面模型,为复杂自由曲面的建模提供了新的有效途经。     

二齿差纯滚动活齿内齿圈的数字化设计与加工

针对新型二齿差纯滚动活齿内齿圈轮廓曲线加工精度低,加工难度大的问题,提出了基于UG NX设计平台的三维数字化设计与加工的方法。通过二齿差纯滚动滚柱活齿外端曲线的包络方程,在UG NX设计平台对内齿圈三维建模。对齿形进行了分析并对数字化加工做了详细的说明。借助UG NX设计平台,有效解决了内齿圈加工过程中的难题,降低了产品设计、生产成本,提高了工作效率。通过数控机床的切削仿真,降低了零件加工错误的风险。UG NX设计平台的数字化设计与加工为内齿圈的设计与制造提供了新的方法。     

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.     

基于六轴数控铣齿机的点接触曲线圆柱齿轮加工仿真

点接触曲线圆柱齿轮是一种新型平行轴传动齿轮,用常规的机床和刀具难以完成其齿形的高效加工.利用六轴数控铣齿机和面铣式刀盘完成该齿轮的模拟加工.首先,根据该齿轮的成型原理,推导齿面的数学模型,求解齿面点云数据,基于点云数据在三维建模软件中构建齿轮实体模型;然后,在VERICUT中构建数控铣齿机和刀具,再编写齿轮加工的数控程...     

面向制造的弧齿线圆柱齿轮的建模设计

介绍了一种面向制造的设计方法,根据弧齿线圆柱齿轮的加工原理,提出了基于齿轮齿条原理的弧齿线圆柱齿轮的特征建模方法.采用的齿轮实体建模方法与实际齿轮加工方法相同,为精确造型、正确仿真及有限元分析提供了基础.     

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.     

细分造型技术在CAD系统中的应用研究

在现有CAD系统中通用的NURBS造型对于非规则拓扑关系的曲面的表示存在着拼接、剪裁困难、表达难以准确等缺点,而在实际工程应用中形体轮廓复杂、难以通过基本体素复合且要求光滑的实体又普遍存在.细分造型计算简单,可以表达任意拓扑关系,在图形学中已得到广泛研究.本文阐述了细分造型的原理和方法,提出了在现有CAD系统中应用细分造型的方案,对细分造型中的网格生成、边界限定、法线控制、NURBS补片转换等关键技术进行了研究，初步构造了细分造型的原型系统，可极大地缩短复杂曲面形体的造型时间，取得了良好的实践效果。     

基于逆向工程的蒙皮曲面重构技术研究

针对蒙皮曲面生成时截面线相容性处理所带来的数据量过大问题,提出一种蒙皮曲面重构方法.从三次B样条曲线插值入手,基于垂距对自由曲面自适应数据采样,构建物体外形轮廓曲面.该方法可以有效去除截面线相容性处理所产生的大量的冗余控制顶点,在用户定义的精度内实现数据压缩和光滑的曲面造型.最后,应用该方法给出一个完整的基于逆向工程的蒙皮曲面构造过程.     

Adaptive Gregory Patch Approximation to Z-Map Data

A method is proposed for Gregory surface approximation to 3D array data points. Surface approximation is the process of constructing a compact representation to model an object surface based on a fairly large number of measured 3D data points. Based on an adaptive subdivision technique, the proposed method begins with a rough initialisation of the surface and progressively refines it in successive steps in the regions where the data is poorly approximated. The method has been implemented using piecewise bicubic Gregory patches with G 1 continuity. An advantage of this approach is that the refinement is essentially local, reducing the computational requirements that permit the processing of a large number of data points This method, combined with the inverse offsetting method, can be used to obtain an offset surface without self-interference. The offset surface can be used to generate gouging-free CL tool paths for machining compound surfaces on milling machines.