Bertrand共轭曲面基本原理研究

通过对回转面、可展面、法向圆弧曲面等工程常用曲面“沿母线法线共面”这一共性特征的提炼与升华，提出Bertrand曲面的概念，并研究了其性质．作为在高副传动领域的应用与延伸，研究了Bertrand共轭原理。其基本特征是一对Bertrand曲面在共轭的各瞬时接触线均为母线．将Bertrand共轭按母线分为3种典型类型，分别给出共轭的基本条件．为了研究共轭条件的相客性，给出了反映各类共轭传动形式与准线特征的结构条件，并在此基础上建立共轭的微分关系武．这些研究为Bertrand共轭原理向工程转化奠定了基础．

Study of basic principle of Bertrand conjugate surfaces

The concept of Bertrand surface is presented by abstracting and subliming the common characteristics of the usual surfaces, including rotational surface, developable surface, normal circular-arc surface, etc. , namely, the normals along the generator are coplanar. On the basis of this, its properties are researched. As a kind of application in the field of higher-pair gear transmission, Bertrand conjugate principle is studied and its basic characteristic is that the instantaneous contact line between a pair of Bertrand conjugate surfaces is the generator. It can be divided into three kinds of typical conjugations in terms of the generators, and their basic conjugate conditions are given, respectively. In order to examine the consistency of the conjugate conditions, the structure conditions reflecting transmission forms and the characteristics of the directrix are presented, and the differential expression of Bertrand conjugation is also set up. These researches establish the foundation for transforming the Bertrand conjugate principle to the engineering application.