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提出了以现代计算技术为依托，基于数学规划研究共轭曲面原理的新方法──数字仿真方法．建立了直接描述共轭过程的数学模型．这一模型既便于数字计算又便于理论研究．在连续可微的前提下，对模型中标杆函数的存在性及其最小条件与传统理论中啮合条件之间的联系进行了详细的探讨，并给出此框架下共轭曲面接触点处的几何特征、共轭的界限、诱导曲率以及确定接触域的直接方法．结果表明，数字仿真方法涵盖了传统共轭曲面理论的基本内容，又适于解决干涉、奇异、误差变形以及非连续可微等复杂条件下传统理论不易解决的问题，具有拓宽传统理论内涵的独特优越性．
A new method to study conjugate surface theory based on mathematical programming, which is based on modern computing technology, is proposed. A mathematical model that directly describes the conjugate process is established. This model facilitates both numerical calculations and theoretical studies. Under the premise of continuously differentiable, the connection between the existence of the benchmarking function and the minimum conditions in the model and the meshing conditions in the traditional theory is discussed in detail. The geometry of the contact point of the conjugate surface in this framework Features, limits of conjugation, induced curvatures, and direct methods of determining contact fields. The results show that the digital simulation method covers the basic content of the traditional conjugate surface theory and is also suitable for solving the problems that the traditional theory is not easy to solve under complex conditions such as interference, singularity, error deformation, and discontinuity, and has the unique feature of broadening the traditional theoretical connotation Superiority.