双圆弧弧齿锥齿轮传动的三维建模及切齿啮合模拟与分析

【作者】 姚俊红；

【导师】 武宝林；

【作者基本信息】 天津工业大学 ， 机械设计及理论， 2003， 硕士

【摘要】 作为一种新型齿轮传动方式，双圆弧弧齿锥齿轮传动不论在齿线方向、还是在齿高方向，均为凸、凹齿廓相啮合，因而它比一般的弧齿锥齿轮传动的承载能力高，使用寿命长；并且在啮合过程中两齿面间容易形成润滑油膜，具有良好的跑合性能，所以对它的应用和研究日益受到人们的重视。 本论文首先根据双圆弧齿轮传动的啮合理论，结合其齿形特点和弧齿锥齿轮的加工原理，进行了双圆弧弧齿锥齿轮的切齿啮合分析，得到了切齿啮合过程中的啮合方程、产形轮齿面方程以及双圆弧弧齿锥齿轮的通用齿面方程，为下一步生成双圆弧弧齿锥齿轮的三维模型打下了基础。 在上述工作的基础上，综合应用计算机图形学理论、C语言、VC++语言、AUTOLISP编程以及CAD技术，编制了一交互式图形系统和双圆弧弧齿锥齿轮的三维建模软件。其中，C语言是计算部分，AUTOLISP语言是模型建立部分，VC++语言完成程序界面的生成。在参数界面中，不但有各个参数的编辑框，而且还有锥齿轮的结构图和双圆弧齿轮的基本齿形图，这样可以一边参照图形一边进行设计，从而大大提高了设计效率；另一方面，点击相应按扭后，可以马上得到这种双圆弧弧齿锥齿轮的三维模型。同时也可直接输入齿轮参数和齿形参数，来生成相应齿轮的三维模型，从而证明了前面推导的双圆弧弧齿锥齿轮通用齿面方程式的正确性。 在实体建模程序中，以双圆弧弧齿锥齿轮的加工原理为基础，借助绘图软件AutoCAD，模拟了双圆弧弧齿锥齿轮铣刀盘刀齿形状、轮齿毛坯形状等，进而根据产形轮与被加工齿坯之间的共轭啮合关系，进行了双圆弧弧齿锥齿轮的实体建模及加工过程模拟，在屏幕上动态显示刀具及被加工齿轮的相对位置及其加工时的运动轨迹和规律。 最后，通过比较双圆弧弧齿锥齿轮齿面理论方程与加入刀位及刀位角误差后的齿面方程，应用上述软件和通过进一步的数值计算，进行了无误差的理论齿形与加入刀位及刀位角误差后所得到的实际齿形之间的定量分析，比较直观、方便、准确地对刀位及刀位角误差对双圆弧弧齿锥齿轮的齿形以及传动的影响进行了初步研究。更多还原

【Abstract】 As a new type gear transmission, double circular arc profile bevel gearing carries out its transmission by means of meshing between convex-concave tooth profile in both of the direction of tooth trace and the direction of tooth depth, so it has advantage of high load capacity, long service life, easy forming hydrodynamic oil film between teeth as well as high quality of running-in etc. Therefore, more attention has been paid to its application and research in recent years.In this dissertation, first, based on the theory of W-N gearing, characteristic of tooth profile as well as the processing principle of helical bevel gear, a cutting meshing analysis about double circular arc profile bevel gear was carried out, the equation of meshing in the process of cutting tooth, the surface equation of generating gear as well as the general tooth surface equation of double circular arc profile bevel gear were obtained. Which established a foundation for building three-dimensional model of double circular arc profile bevel gear.Second, based on works mentioned above, an interactive graphic system, i.e. an interactive parametric three-dimensional model-building software about double circular arc profile bevel gear were established according to computer graphics, C language, VC++ language, AUTOLISP programmed and CAD technology, in which, language C completed complicated calculation, AUTOLISP language finished model-building, VC++ language accomplished the generation of program interface. In parametric interface of this software, there is not only the editor frame of every parameter but also the standard schemes of double circular arc profile and the structural scheme of bevel gear .We can design the gearing according to the schemes efficiently. On the other hand, after clicking corresponding button, we can get the three-dimensional model at once. Simultaneity it can generate the three-dimensional model of corresponding gear in a minute after by directly inputting gear parameters and the parameters of tooth form, which could prove that the general tooth surface equation of double circular arc profile bevel gear obtained above was correct.In the solid model building program, based on the cutting tooth theory of double circular arc profile spiral bevel gear and AutoCAD software, a series of computer simulations about solid model building and cutting tooth process of the gear were curried out. The cutter’s tooth shape, the processed gear blank shape and its conjugated tooth profile shape as well as visual movement relationship between generating gear and processed gear blank etc. were obtained. The relative position of cutter and processed gear as well as the movement trace and rule in the cutting process can be showed dynamically on screen.Finally, by means of comparing the theoretical tooth surface equation with the tooth surface equation included errors of cutter position and cutter position angle, the quantitative analysis of the theoretical tooth shape and the tooth shape considering the errors of cutter position and cutter position angle was curried out based on the software above. From which, the effect of errors of cutter position as well as cutter position angle on the processed tooth shape and transmitting behavior of this kind of gearing was studied.更多还原