Minimum modification coefficient of spiral bevel gear without undercut

Spiral bevel gear is a very important element in drive lines of various machines such as tractors, trucks etc. It is a good method to use non-zero modification to increase tooth strength or to improve gearing properties in design of spiral bevel gears. To avoid undercut is the most basic requirement. Thus the minimum modification coefficient for non-undercut gears must be determined. However there is not a clear and accurate formula for calculating its parameters even in standards of modern industrial countries. In this paper, based on the theory of three dimensional gearing, the δ-θfmax curves without undercut for Gleason type spiral bevel gears are derived by the optimum method of penalty function. The formula for calculating the minimum modification coefficient at the condition of non-undercut is given through the mathematical treatment of the results. It is proved that the results of calculating by the principle of gearing are true and reliable. Owing to their good accuracy, they are useful to both the manual design and CAD and provide a foundation in design of spiral bevel gears without undercut.