Abstract: A method of stationary internal toroidal gear tooth surface modeling based on B-spline
surface is put forward in allusion to the difficulty of ensuring numerical control machining accuracy of
stationary internal toroidal gear tooth surface. The interpolation curved surface is constructed by
B-spline surface based on the theoretic tooth surface of stationary internal toroidal gear and then errors
of theoretic tooth surface and interpolation curved surface are calculated. According to error distribution
characteristics a set of data points can be obtained by error analysis and mesh refinement. The helical
tooth surface model of stationary internal toroidal gear that meets accuracy requirement is obtained by
interpolation reconstruction. In the end the validity of the modeling is verified by numerical control
machining. This method provides a theoretical basis of acquiring high-accuracy stationary internal
toroidal gear model.

Key words: toroidal drive, stationary internal toroidal gear, B-spline surface, interpolation error, mesh
refinement