高阶多段变性椭圆拟合自由节曲线的非圆齿轮制造及适应性设计研究

For the drawback that the pitch curve of non-circular gear is irregular and the gear is hard to be made by applying high-speed manufacturing method, a principle of non-circular gears with free pitch curve fitted into high-order and multi-segment modified elliptic gears is constructed from the viewpoint of manufacture. On the one hand, the interpolation theory of high-order and multi-segment modified pitch curve of elliptic gears will be studied in detail based on high-speed target. In order to test and verify the validity of it, the method of predictor-corrector NURBS interpolation creating free curve of non-circular gears is studied to compare with the interpolation theory presented here. The science questions of manufacturing in this research include: 1) The composition of error model, which includes the fitting error, the manufacturing error of pitch curve, the transient dynamic manufacturing error of pitch curve; 2) The analysis and selection for the processing strategy and model performance of the non-circular gears, which include the number of linkage axis, the form of face hobbing, the way of axial movement and the methods of increment motion; 3) Analyzing the vibratory mechanism during the manufacturing and the forming error in processing as well as the transient dynamic manufacturing error; 4) Research on the mechanisms of vibration control and the control of speed, forward acceleration，backward acceleration and jerk. For the other hand, the theory of non-circular gears is reconstructed, and a design theory adapted to the manufacture high-order multi-segment modified elliptic gear is established, and its standardization maps and system are created then. A new theory of design and manufacture for non-circular gear will be established with greater generality and universality in the industry. It will be useful for designing and manufacturing to the non- circular spiral bevel gears.

针对非圆齿轮节曲线不规则难于高速制造之弊端，从制造角度，建立高阶多段变性椭圆齿轮拟合自由节曲线非圆齿轮原理。一方面，研究基于高速目标的高阶多段变性椭圆节曲线插补理论,为验证其有效性，项目同时研究预估校正的NURBS插补自由节曲线方法，进行比照分析。制造中需解决的科学问题包括：1）综合误差的模型，包括拟合误差、节曲线动态制造误差、节曲线过渡动态制造误差；2）加工策略及实用模型性能分析与遴选，包括联动轴数、端面滚切形式、轴向运动方式、附加运动方法的组合；3）分析制造过程中的振动机理，及过程、过渡动态制造误差；4）研究振动抑制机制及加工过程速度、前加速度、加加速度控制。另一方面，重构非圆齿轮设计理论，研究适应制造的高阶多段变性椭圆齿轮设计理论，进而构建标准图谱及体系。项目在业界构架非圆齿轮设计、制造崭新理论，具有更强的概括性和普适性，对螺旋锥齿轮的设计制造也有借鉴价值。

非圆齿轮综合了圆柱齿轮与凸轮的优点，可根据实际运动需求进行设计以实现变传动比，具有效率高、结构紧凑、工作可靠以及传动比稳定等优点，在农业机械，轻工机械，仪器仪表工业和航空航天工业领域都有广泛应用。针对非圆齿轮形状多变、设计复杂、制造困难等问题，对非圆齿轮的节曲线数学模型建立、适应性设计方法、加工策略分析与遴选、节曲线高效插补理论、柔性电子齿轮箱设计应用、精度控制与偏差测量等相关内容进行了深入研究，较好地系统解决了非圆齿轮设计、制造与检测中的难题。首先，建立了高阶多段变性椭圆精确化数学模型与传动设计方法，开发了高阶多段变性椭圆齿轮以及自由节曲线齿轮CAD/CAM软件，实现了非圆齿轮（副）的快速设计与精确建模；然后，基于展成加工原理建立了非圆齿轮滚齿、插齿加工联动模型，通过仿真对各加工策略进行了分析与遴选，确定了最优加工策略；其次，将最优加工联动模型与柔性电子齿轮箱控制原理相结合，研究了非圆齿轮实时展成加工方法，开发了非圆齿轮数控加工系统，并分别进行了数控插齿、滚齿、剃齿的实际加工；再次，对非圆齿轮展成加工运动进行了精度控制与误差补偿研究，拟定了相应精度标准并建立了非圆齿轮各项偏差的测量模型；最后，根据所研究内容，对多套工业用非圆齿轮传动机构进行了设计，并将非圆齿轮加工控制算法成功嵌入到合肥工业大学CIMS研究所与广州数控公司联合开发的GSK25iG齿轮机床数控系统中，实现了项目成果的应用转化。本项目对非圆齿轮设计、制造及检测均进行了系统研究，研究成果概括性、普适性较强，极大地完善了非圆齿轮理论体系，实现了非圆齿轮的高速高精加工，有效解决了非圆齿轮的精确设计和数控加工难题，拓展了非圆齿轮的应用领域，具有较好的理论价值与工程应用价值。