阿基米德蜗轮齿面建模与计算

Modeling and calculation of Archimedes worm gear tooth surface

本文基于阿基米德蜗轮蜗杆(ZA蜗轮蜗杆)的加工原理及蜗轮蜗杆空间啮合原理,推导出阿基米德蜗轮齿面数学模型及蜗轮蜗杆啮合方程式。在蜗轮轴截面方向进行齿面网格划分,根据蜗轮蜗杆啮合原理以及齿面网格节点空间坐标的数值关系建立非线性方程组。最后通过MATLAB求解出阿基米德蜗轮空间网格点的坐标值及法矢,并在三坐标测量机上验证了算法的可行性。

In this paper, based on the method for processing the Archimedes worm and worm gear（ZA ） , and the transformation of the space meshing coordinates of the worm and worm gear, themathematical model of the tooth surface of ZA worm gear and the meshing equation is derived.Then the mesh of the tooth surface is carried out in the direction of worm gear axis, with the nonlinearequations established according to the meshing principle of the worm and worm gear andthe numerical relationship of the mesh nodes. Finally, the coordinate value and the normal vectorof the ZA worm gear grid points are obtained by M A T L A B , with the feasibility of the algorithmverified on the three coordinate measuring machine.