【作者】 李小清；

【导师】 周云飞；

【作者基本信息】 华中科技大学 ， 机械制造及自动化， 2004， 博士

【摘要】 螺旋锥齿轮是机械传动的基础元件,其空间形状、啮合和加工技术相当复杂。数控技术的发展,为螺旋锥齿轮柔性加工和简化调整提供了途径。数控化加工可极大地提高加工精度,国外该技术仅为少数公司所拥有,国内尚处于起步阶段。为此,本文根据数控化加工的特点,深入研究了螺旋锥齿轮的加工、数字化处理、检测及误差修正技术。本文的主要内容如下所述。深入研究了格里森齿轮的啮合原理与加工特点,根据局部共轭特点,分析和推导了螺旋锥齿轮格里森加工算法。通过切齿方程,计算出了机床调整参数。此算法是实现螺旋锥齿轮数控化加工的基础。基于格里森加工理论,根据数控运动的任意可控性,提出了刀倾变传动比和刀倾变节点两种新的小轮数控加工算法。计算出了机床调整参数。此算法采用定值刀具加工螺旋锥齿轮,实现了刀具规格的减少和刀具半径误差修正。避免了格里森算法带来的多规格刀具。充分发挥数控机床柔性制造特点,提高了加工效率和精度。为了分析齿面设计和加工质量,根据加工参数,进行了齿面接触分析。推导了齿面方程,并依据大、小轮齿面方程求解了齿面接触区和运动误差曲线。建立和推导了离散齿面接触分析算法,为齿面数字化测量分析提供基础。此算法首先通过齿面离散或测量点,利用微分几何及 Ferguson 样条函数反求构造出螺旋锥齿轮齿面。再根据齿轮安装条件,利用优化求极小值复合形方法和共轭理论,通过变定义域,快速求解齿轮副齿面接触点。并计算绘制出接触迹、接触区图和运动误差曲线图。研究了齿面的数字化测量处理技术,并提出一种误差修正方法。此方法,通过网格化齿面坐标测量,测出实际齿面偏离理想齿面的法向误差。在笛卡儿坐标系下,利用线性超越方程组的最小二乘法,求出机床加工调整参数的修正值,使实际齿面与理想齿面误差达到最小。研究了齿轮运动误差,分析了由失配和失准产生的传动误差的机理。并给出了减少传动误差的方法。提出了运动优化的方法,通过预设传动误差抛物线函数,使齿面啮合时运动误差和不连续性减至最小。给出了一种集螺旋锥齿轮加工和五坐标数控技术于一体的螺旋锥齿轮高精度数控展成运动变换方法。它以 NC 原理上的最小步长直接逼近展成轨迹,可以实现高精度的加工运动。提高了齿面加工精度。基于上述研究,编制了螺旋锥齿轮数控加工处理系统和控制系统软件。在通用五坐标数控铣床上加工了样件。进行了齿面测量,对滚,数字化处理和误差修正等实验。更多还原

【Abstract】 As a foundational component in mechanical transmission, spiral bevel and hypoid gearis characteristic of quite a few complexities in space shape, meshing and machining. As aresult of the developing of Numerical Control technology, the flexible machining andsimplifying adjusting are supplied with a way for spiral bevel and hypoid gear. Themachining accuracy of spiral bevel and hypoid gear will be improved greatly with theapplication of NC technology. At present, in the other country just several company grasp thetechnology, in our country the research is just beginning. Therefore, according to thespeciality of NC machining, deep researches are made on the machining theory, digitalprocessing, measure technology, error correcting method in this thesis, whose primarycontent is as follows. The meshing principle and the machining characteristics of the spiral bevel and hypoidgear has been researched deeply. By its local conjugation characteristic, several GLEASONmachining algorithms have been analyzed and deduced. Furthermore, according to theequations of cutting, the parameters of machine settings are calculated. These algorithms arethe foundation of realizing NC machining for spiral bevel and hypoid gear. Based on GLEASON principle and the flexibility characteristics of NC machine tool,two novel algorithms, “the cutter tilt and variable ratio of roll” and “cutter tilt & displacementof pitch point”, for manufacturing hypoid pinion are proposed. And the parameters ofmachine settings are calculated. Manufacturing the pinion with a prescribed-size cutter onNC machine tool can be realized, which helps to simplify cutter specifications and realizeerror compensation of the cutter size. Moreover the NC machine tool characteristic offlexible manufacturing is exploited to the full, and the machining accuracy and efficiency isimproved. To analyze the design of tooth surface and its machining quality, according to themachine settings, tooth surface contact analyzing is taken, and the equation of tooth surface isderived. And by equation of the gear’s tooth surface and that of the pinion’s, the contactpattern and transmission errors curve are got. The algorithm of disperse tooth surface contact analysis is established and deduced,which lays the foundation for the digital measure and analyzing of tooth surface. Firstly thesampling points of tooth surface measurement, mathematics model for spiral bevel andhypoid gear’s fitting tooth surface is formularized reversedly by applying principle ofdifferential geometry and Ferguson parameter spline function. And then according to thefixing condition and the “BOX” optimization method for finding extremum with a limitedboundary and conjugation theory, quick solving the contacting point of tooth surface can be II<WP=5>realized by changing definition region. An algorithm for finding path of contact, contactpattern and transmission errors is investigated. After the research on the digital measure technology of tooth surface, an errorcompensation method is proposed. In this method, the deviations of a gear’s real toothsurface from the theoretical surface along the normal can be determined by coordinatemeasurements at the grid of the surface. Under the Cartesian coordinates, with the applicationof least-square method for an overdetermined system of linear equations, the machinesettings can be calculated, which minimize deviations of a gear’s real tooth surface from thetheoretical surface. On the study of the gear’s transmission errors, its principle resulted from tooth mismatchand misalignment, is analyzed. And the methods reducing the transmission errors arepresented. The motion optimization method is proposed, by which transmission errors anddiscontinuousness of tooth surface meshing is decreased to minimum. A general NC generating motion transition method was proposed, integrated with themachining technique of spiral bevel a更多还原