Aim\ To explore the method for describing cutter and workpiece

and the method for recording the shape and parameters of the cutting layer when complex workpiece is processed by using complex cutter

and to establish the mathematical model for thread cutting process. Methods\ The working surface of the complex cutter and the processed surface of the workpiece are discretized to record the shape of the cutter and workpiece

and the shaping of the workpiece. Results and Conclusion\ When the workpiece is of little elastic deformation

the discretization approach as proposed in this paper is applicable not only to the mathematical modeling for thread-cutting process

but to the modeling for processing simple workpiece by using complex cutter

and processing complex workpiece by using simple cutter.