基于数字化齿面的准双曲面齿轮主动设计方法及关键技术研究

【作者】 聂立新；

【导师】 苏智剑；

【作者基本信息】 郑州大学 ， 机械设计及理论， 2004， 硕士

【摘要】 准双曲面齿轮是一种特殊的锥齿轮，它在航空、汽车、拖拉机等工业中得到了较为广泛的应用。与普通锥齿轮相比，准双曲面齿轮重迭系数较大、齿面比压较低，具有传动平稳、冲击和噪音比较小、承载能力高和寿命长等优点。但对传统的准双曲面齿轮来讲，其齿面只能在有限的几种模式中作出选择，并不能够根据实际功能需求，在设计时对整个接触传动过程中齿面啮合性能进行有效控制。同时依据目前的准双曲面齿轮加工方法，共轭齿面的加工是在反复试切中完成的，机床调整周期长，并且难以保证加工质量。 如果能突破齿面设计、加工的局限性和复杂性的限制，准双曲面齿轮的设计制造水平必将得到大幅度的提高。准双曲面齿轮齿面主动设计技术为准双曲面齿轮副的设计提供了一种全新的思路。该设计方法从实际的功能需求出发（如可靠、平稳、耐久地传递需要的运动和动力等），根据已知齿面∑^（1）（常为大轮齿面）的特征参数（齿面参数方程、接触点迹线等）和具体传动要求（如瞬时传动比），设计出符合要求的啮合齿面∑^（2）。齿面的数字化是准双曲面齿轮设计、制造和测量技术发展的必然要求，面向设计、制造和测量的统一齿面数学模型是实现准双曲面齿轮设计、制造、测量一体化的重要技术基础。 本文首先讨论了准双曲面齿轮齿面离散点的获得方法，编制了齿轮加工仿真程序，获得了准确的齿面离散点数据，并在此基础上实现了准双曲面齿轮齿面的NURBS表示。所研究的以齿面离散点为基础，构建齿面的NURBS模型的方法适用于准双曲面齿轮的设计、制造以及测量过程，是一种具有广泛适用性的方法。依据该方法，可在已知来自设计、制造或测量数据的基础上，构造齿面的NURBS模型，实现了准双曲面齿轮齿面数学模型的统一。 其次，在实现了准双曲面齿轮齿面NURBS表示的基础上，本文依据主动设计思想，针对齿面NURBS表示后出现的特殊情况，推导了实现数字化齿面主动设计所需的全部公式，同时精心设计了求解过程，并通过实例计算验证了所提出理论及方法的正确性。 论文研究了构建面向设计、制造及测量过程的准双曲面齿轮齿面数学模型的郑州大学工学硕士论文方法，采用了NURJ3S表示，实现了齿面模型的统一。完成了齿面NURBS表示情况下的数字化共扼齿面的主动设计方法研究，为准双曲面齿轮的齿面表示及设计提供了新途径。此外，论文研制的仿真加工程序可方便、快速地利用计算机模拟分析准双曲面齿轮的加工过程，省去了传统的试切、反复滚检和修正过程，既降低了设计的难度，又减小了加工废品率，具有很高的实用性。更多还原

【Abstract】 The hypoid gear is one sort of the special bevel gears. It gets comparatively extensive application in aircraft industry, automotive industry and tractor industry. Compared with the ordinary bevel gear, its overlapping coefficient is bigger, specific pressure of the tooth face is lower. Therefore, the hypoid gear has advantage of stability at transmission, lower impact and noise, higher carrying capacity and longer life. But the tooth face of traditional hypoid gear can only have the several kinds of finite modes of tooth face, and can’t be to carrying on valid control in the whole meshing performance which is exposed to the course of the transmission according to the practical function demand. At the same time, according as current maufacture method of the hypoid gear, the maufacture of conjugate tooth profiles need repeated revision the tooth, the cycle of adjusting machine tool is longer, and it is very difficult to assure manufacture quality.If the limit of the complexity and limitation of the hypoid gear design and manufacture is broken through, the design & manufacture level must be rapidly hightened. The active design technique of hypoid gear tooth face provides a kind of fresh method of the hypoid gear design. The active design method startes from real function demand (such as being reliable, steady and durable drive that be required, etc.), according to the known tooth face ∑(1) (that is the bigger gear tooth face) characteristic parameter (parametric equation of tooth face, trajectory of contact point, etc.) and concrete require at transmission (such as instantaneous transmitting ratio), designs the qualified meshing tooth face ∑(2). The Digitization of the Tooth face is an inevitable demand of design, manufacture, and measureing technology of the hypoid gear, the uniform mathematical model that oriented deisgn, manufacture and measuring of tooth face is an important technical basis of hypoid gear’s study.In the thesis, the way of obtaining disperse points of tooth face is discussed, a program of emulation of tooth face’s manufacture is compiled, a series of accurate disperse points of tooth face are gained, and the hypoid gear tooth face is figured byNURBS method. The method of constructing NURBS model of tooth face based on disperse points of tooth face is the same with the process of design, manufactue and measureing of the hypoid gear. It is a kind of method that has broad applicability. Depended on the above method, it can be constructed that NURBS model of tooth face at the basis of known data come from design, manufacture and measureing, so that it is realized that unification of mathematical model of the hypoid gear.Secondly, at the basis of realizing the hypoid gear tooth face’s NURBS expression, according to the active design method, faced special circs of tooth face’s NURBS expression, it is deduced that all equations that must be required when realized the actice design of digitization tooth face. At the same time, it is detailedly designed that program of solution, and the above theory and method is validated by real example.In conclusion, it is studied that method of contructing mathematical model of the hypoid gear oriented design, manufacture and measuring process. It is realized that unification of tooth face model by NURBS expression. It is completed that the study of the active design method of NURBS tooth face, the way of tooth face expression and design is provided. Besides, the designed emulation manufacture program can expediently and rapidly analyze manufacture process of the hypoid gear through computer simulation, passes over traditional process of trial cutting, repeat rolling test and modifying, not only reduces the design difficulty, but also decreases the rejection ratio of manufacture. Therefore, the above method has very good favorable practicability.更多还原