面齿轮机构具有独特的结构和性能优势，国外已经用面齿轮机构逐步替代某些锥齿轮机构，这不仅可以简化安装、缩小传动机构体积，而且可以提高传动系统可靠性。为了扩大面齿轮在传动领域的应用优势，本文以斜齿面齿轮为研究对象，建立了斜齿面齿轮齿面数值模型，研究了斜齿面齿轮的插齿加工方法。在对常规斜齿面齿轮齿形曲面研究基础上，提出了一种新的可展直纹面斜齿面齿轮，并研究了锥面刀具线接触加工可展直纹面斜齿面齿轮的方法。本文的主要研究内容与相应结论如下：

(1) 建立螺旋插齿刀齿面方程，结合齿轮啮合原理，完成斜齿面齿轮齿面方程的推导。由斜齿面齿轮轮齿齿根根切、齿顶变尖的限制条件，确定了斜齿面齿轮的工作齿宽，并研究了螺旋角、传动比对斜齿面齿轮齿宽的影响规律，数值算例显示：斜齿面齿轮齿宽随传动比增大而增大，不考虑旋向的情况下，斜齿面齿轮齿宽随螺旋角增大而减小。借助MATLAB将斜齿面齿轮齿面点离散化，完成对斜齿面齿轮齿面的数值建模。

(2) 设计了插齿加工斜齿面齿轮的螺旋刀具，通过分析螺旋刀具加工斜齿面齿轮所需的运动，设计了加工斜齿面齿轮的五轴数控插齿机床模型，建立五轴数控插齿机床的坐标变换系统，推导出螺旋刀具的数控运动规律。在VERICUT中建立插齿加工仿真机床模型，使用不同的刀具分度角、刀具轴向进给步长对斜齿面齿轮进行插齿加工仿真，插齿仿真加工齿面偏差结果显示，斜齿面齿轮插齿仿真加工中刀具分度角越小、刀具轴向进给步长越小，插齿仿真加工齿面偏差越小。

(3) 通过面齿轮齿面齿顶线上的点、面齿轮齿面齿根线上的点和面齿轮齿面脊线上的点，设置特定的约束条件，在斜齿面齿轮齿面上构建了空间直线簇。在对常规斜齿面齿轮齿面分析的基础上，提出了一种新的可展直纹面斜齿面齿轮，并针对可展直纹面提出了修正方法。对可展直纹面与常规斜齿面齿轮齿面进行数值分析，结果显示，二者偏差属于微观量，可以用可展直纹面代替常规斜齿面齿轮齿面。

(4) 根据可展直纹面的特性，设计了线接触加工可展直纹面斜齿面齿轮的锥面刀具几何参数，根据锥面刀具铣削可展直纹面所需运动，设计了五轴数控铣床模型，推导了锥面刀具铣削面齿轮的数控运动规律，使用不同直径的锥面刀具，在VERICUT中完成可展直纹面斜齿面齿轮线接触加工仿真，可展直纹面斜齿面齿轮仿真加工齿面偏差结果显示，锥面刀具直径越小，仿真加工齿面与可展直纹面斜齿面齿轮齿面的偏差越小。

The face gear mechanism has unique structure and performance advantages. Some bevel gear mechanisms have been gradually replaced by face gear mechanisms in foreign countries, which not only can simplify the installation and reduce the volume of the transmission mechanism, but also can improve the reliability of the transmission system. In order to expand the application advantages of face gear in the field of transmission, this paper takes the helical face gear as the research object, establishes a numerical model of the helical face gear tooth surface, and studies the gear shaping method of the helical face gear, based on the research on the tooth profile and surface of conventional helical face gear, a new developable ruled surface helical face gear is proposed, and studies the method of machining the developable ruled surface helical face gear by line contact with a cone face tool. The main research contents and corresponding results of this paper are as follows:

(1) The tooth surface equation of the helical gear shaper is established. Based on combining the principle of gear meshing, the derivation of the helical face gear tooth surface equation is completed. The working tooth width of the helical face gear is determined by the limiting conditions of undercutting the tooth root and sharpening of the tooth tip of the helical face gear tooth, the influence of helical angle and transmission ratio on the tooth width of helical face gear is studied. The numerical example shows that the tooth width of the helical face gear increase with the increase of the transmission ratio; without considering the direction of rotation, the tooth width of the helical face gear decreases with the increase of the helical angle. The helical face gear tooth surface points are discretized by MATLAB, and the numerical modeling of the helical face gear tooth surface is completed.

(2) The helical tool for gear shaping to process helical face gear is designed. By analyzing the motion required by the helical tool to process helical face gear, a five-axis CNC gear shaping machine model for processing helical face gear is designed, and a five-axis CNC gear shaping machine tool is established. The coordinate transformation system is used to deduce the numerical control motion law of the helical tool. A gear shaping simulation machine tool model is established in VERICUT, and different tool indexing angles and tool axial feed step lengths are used to simulate the gear shaping processing of the helical face gear. In the processing of gear shaping simulation, the smaller the tool indexing angle, the smaller the tool axial feed step, and the smaller the tooth surface deviation in gear shaping simulation processing.

(3) By setting specific constraints, the point on the tooth top line of the face gear, on the tooth root line of the face gear and on the ridge line of the face gear, a space line clusters are constructed on the tooth surface of the helical face gear. Based on the analysis of the tooth surface of conventional helical face gear, a new developable ruled helical face gear is proposed, and a correction method is proposed for the developable ruled surface. Numerical analysis of developable ruled surface and conventional helical face gear tooth surface is carried out. The results show that the deviation between the two is a microscopic quantity, and the developable ruled surface can be used to replace the conventional helical face gear tooth surface.

(4) According to the characteristics of the developable ruled surface, the geometric parameters of the tapered tool for line contact machining of the developable ruled surface helical face gear are designed. According to the motion required by the tapered cutter to mill the developable ruled surface, a five-axis CNC milling machine model is designed. The numerical control motion law of conical cutter milling face gear is deduced. Using conical cutters with different diameters, the line contact machining simulation of developable ruled surface helical face gear is completed in VERICUT. The results of the tooth surface deviation of the developable ruled surface helical face gear simulation show that the smaller the diameter of the conical surface tool is, the smaller the deviation between the simulated machining tooth surface and the developable ruled surface helical face gear tooth surface.

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