Investigation of mathematical model for machining of externally meshed noncircular gears and characteristics of their undercut

A mathematical model for gear shaping was presented for machining of externally meshed noncircular gears with shaping procedure in terms of the positional relationship between the tool(cutter) and gear's pitch curve.On the basis of selecting such assignment range of gear module and eccentricity that there would be no undercut for shaping the teeth of noncircular gears,dynamically graphic simulation of the shaping process was conducted on the computer by using the mathematical model developed.According to the simulation result,the characteristics of tooth profile such as undercut and convexity of pitch curve of the machined gears could be analyzed and judged,so that a sort of intuitive judgment method was provided for designing and manufacturing of externally meshed noncircular gears with closed pitch curve.