基于新一代GPS框架的特征几何变动建模及三维公差转换技术研究

The mathematical modelling of feature geometric variations and three-dimensional (3D) tolerance transfer techniques directly affect integration of product geometric accuracy information and CAX system, which have become the key technologies to be solved urgently in the new generation GPS. The main research contents in this project include: studying the mathematical description methods of the variations of various complex irregular geometric features and kinematic link features within the framework of the new generation GPS, deriving the cumulative functional relationships of geometric variations, establishing the 3D tolerance analysis torsor chain integrated geometry constraint conditions for assembly, and then extending the tolerance analysis model to realize 3D tolerance synthesis, simulating 3D geometric variations based on the manufacturing processes and predicting its defects using the SDT for a manufactured part, revealing the influencing mechanism for different scale of machining errors to quality of mechanical part, and discussing the control and compensation mechanism of machining errors combined with the typical mechanical parts. Finally, the theories and methodologies proposed in this project will be tested on engineering experiments. A prototype system for 3D tolerance transfer based on the 3D CAD software platform is developed. The concept “feature geometric variation” used in this project comes from definition of geometric feature in the new generation GPS, the design ideas used in this project are in line with the new generation GPS standard system. The implementation of this project will have important theoretical and practical significance to promote the integration of 3D CAT technology with CAD/CAPP/CAM and other advanced manufacturing technologies.

特征几何变动的数学建模及三维公差转换技术直接影响产品几何精度信息与CAX系统的集成，是新一代GPS体系亟待解决的关键问题。本项目的主要研究内容包括：在新一代GPS框架下探讨各种复杂非规则几何特征和各种连接特征变动的数学描述方法，推导特征几何变动量的累积函数关系，建立集成几何约束条件的三维装配公差分析旋量链，扩展公差分析模型实现三维公差综合，进行基于零件工序规划的特征几何变动三维模拟并预测其加工缺陷，揭示不同尺度加工误差对零件质量的影响机理并结合典型零件探讨零件加工误差的控制与补偿机制，对提出的理论与方法进行实验验证并开发一套基于三维CAD软件平台的公差转换原型系统。项目所采用的“特征几何变动”的概念源于新一代GPS标准体系中有关几何特征的定义，其设计思想符合新一代GPS标准体系，本项目的实施对促进三维CAT技术与CAD/CAPP/CAM等先进制造技术的集成有着重要的理论和现实意义。

特征几何变动的数学建模及三维公差转换技术的不完善直接影响着计算机辅助公差设计（Computer- Aided Tolerancing, CAT）技术与三维CAD软件系统的有效集成，在一定程度上制约了三维CAT技术在工业生产上的应用。本项目的实施将进一步丰富和发展新一代GPS的公差理论，对于促进三维CAT技术与先进制造技术集成有着重要的理论和现实意义。项目主要研究内容包括：（1）基于新一代GPS几何特征分类法和恒定类的概念，采用小位移旋量（Small Displacement Torsor, SDT）参数描述名义特征和拟合特征之间的几何变动，建立复杂非规则特征变动的定量化数学表达模型。（2）探讨特征几何变动的累积函数关系，将几何参数的公差值或几何约束条件集成于旋量的表达中，提出集成几何约束条件的三维公差分析Jacobian-Torsor模型，并开展了三维装配公差分析的分析线法的研究。（3）对Jacobian-Torsor模型进行扩展研究，以使该确定性公差分析模型实现统计公差分析，进而提出三维统计公差再设计的迭代方法。（4）基于几何公差的数学表达，提出了综合考虑尺寸和几何公差的并行设计和工序公差优化设计模型，模型中几何公差或者转换为等效尺寸公差，或者根据其自身特性仅作为附加的加工约束条件。（5）基于零件加工过程中特征几何变动的累积函数关系，建立每个工序过程的几何变动旋量链，实现零件制造过程的三维模拟，探讨制造公差转换技术。（6）在分析零件加工过程特征和误差源的基础上，探讨零件加工过程的误差传递、累积规律，研究表面形貌对零件耐磨性能的影响机理。（7）以上述研究为理论基础，开发一套三维公差统计分析与再设计软件系统。