偏置正交弧线齿面齿轮齿面设计及根切研究

为拓宽面齿轮的应用空间，结合面齿轮与弧线齿的特点，提出了偏置正交弧线齿面齿轮。根据坐标变换规律及啮合原理推导了全齿面的方程，并在Matlab软件中建立了全齿面模型。结合齿面模型及根切原理,利用Matlab软件编程计算了齿面根切的位置。借助CATIA软件二次开发进行仿真切齿试验，验证了计算的正确性。探究了各参数对最小内半径的影响，结果表明:坐标系距离与最小内半径呈负相关，刀具圆弧半径、偏置距离及模数都与最小内半径呈正相关，其中模数对根切位置影响最大。最后计算了顶尖位置，通过最大外半径与最小内半径之差确定了面齿轮的最大齿宽。 

Tooth surface design and undercutting research of offset orthogonal arc tooth face gear

For the purpose of expanding the application range of face gear，a new design of offset orthogonal arc tooth face gear was proposed by combining the characteristics of both face gear and arc tooth.The equations of full tooth surfaces were derived，and the visualization of tooth surfaces was realized in Matlab.Based on the mathematical model and the undercutting theory，the undercutting location of the gear was calculated.Result was confirmed by the simulation experiment using CATIA secondary development.Several factors influencing with the minimum inner radius were studied.The research showed that:while the positional parameter had a small negative influence on the minimum inner radius，the radius of the gear cutter and the offset distance both had positive influence on it.When the module of gear increased，the inner radius increased greatly.In the end，the location of the tooth tipping point was confirmed and the tooth width of face gear was calculated.