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本文运用三元方法导出了展成滚刀齿形设计的通用公式,即方程组(4.3)。它对任意直齿的或螺旋齿的、渐开线的或非渐开线的工件都适用。和目前一直沿用的平面啮合方法,即法向齿条方法或者包络作图方法相比,具有精度高、结构参数和安装参数选择合理等优点。为了计算最佳的滚切安装参数(中心距A 和轴错角γ)及滚刀螺旋参数P_2,文中提出了五个通用的初始条件和边界条件,已能够满足各种常用工件的设计计算。这种三元方法对于各种高精度齿轮或高效率的螺杆泵等工件的滚刀设计,尤为合适。
In this paper, we derive the general formula of the hob tooth design using the ternary method, that is, the system of equations (4.3). It is suitable for any spur or helical, involute or non-involute work piece. Compared with the planar meshing method, which is used nowadays, that is, the normal rack method or the envelope mapping method, the method has the advantages of high precision, reasonable selection of structural parameters and installation parameters. In order to calculate the optimal hobbing installation parameters (center distance A and shaft misalignment angle γ) and hob helix parameter P_2, five common initial conditions and boundary conditions are proposed in this paper, which can meet the design and calculation of various commonly used workpieces. This ternary method is particularly suitable for hob design of various high-precision gear or high efficiency screw pump and other workpieces.