Generally, transition curve should be designed for gear root, which can reduce stress concentration and improve gear bearing capacity. There are two kinds of tooth root transition curves
(1) The arc transition with radius R is used directly, R ≤ c * Mn;
(2) Draw the root transition roller line.
Use method (2) to design the tooth root transition curve of non-circular gear. As shown in Figure 1, point P is the initial meshing point, points A1 and C1 are the vertices of the profile of the gear shaper cutter, point B1 is the midpoint of a1c1, a1k intersects the pitch circle of the gear shaper cutter at point C, and c1k ‘intersects the pitch circle of the gear shaper cutter at point C’. The pitch circle of the gear shaper cutter rolls clockwise along the pitch curve of the non-circular gear δ When the angle is 1, points A1, B1 and C1 will coincide with A2, B2 and C2 respectively. Taking A2 as the starting point, if the indexing circle of the gear shaper cutter continues to roll clockwise along the pitch curve, the motion trajectory of the tooth profile vertex A1 will outline the left tooth root transition curve; When the rotation angle of gear shaper cutter is equal to δ 1+ δ At 2, point A1 starts to be far away from the machined tooth profile, and the machining of the left tooth root transition curve ends. Similarly, when the rotation angle of gear shaper cutter is equal to δ 1- δ At 3, the trajectory of point C1 will begin to outline the right root transition curve; When the rotation angle of gear shaper cutter is equal to δ At 1, the point C1 starts to be far away from the machined tooth profile, and the machining of the right tooth root transition curve ends.