Tooth surface mismatch design of cycloidal bevel gear based on two directions modification of pinion cutter

Aiming at the sensitivity of installation errors caused by the complete conjugated tooth surface of cycloidal bevel gear, a method of tooth surface mismatch design which only modified the pinion cutter along two directions was proposed. Firstly, the cutter head structure of cycloidal bevel gear and the tooth surface forming process of generating gear were analyzed, and the tooth surface equations of cuter and generating gear were deduced, and the complete conjugated principle of tooth surface was analyzed. Secondly, the calculation method of processing parameters for the complete conjugated tooth surface was established, and the pinion cutter parameters along two directions modification were solved, and the equation of cutter blade edge with circular arc modification was derived. Based on the position and motion relationship between the cutter head and workpiece, the basic mathematical model of cycloidal bevel gear by generating method was established, therefore the theoretical tooth surface equation of workpiece was derived. On this basis, the numerical solution of tooth surface was studied, and the flow chart of loaded tooth contact analysis of cycloidal bevel gear with finite element method was established by using the ABAQUS software. Taking a pair of cycloidal bevel gear as an example, the tooth contact analysis and loaded tooth contact analysis were carried out, and the influence laws of installation errors on loaded tooth contact area and loaded transmission error were analyzed. The simulation results showed that after pinion cutter modification there formed the crown mismatch relationship along tooth length and tooth profile direction between the gear and pinion tooth surface, and the shapes of loaded tooth contact area and loaded transmission error curves had only little changes under the installation errors, which indicated that the two directions modification of pinion cutter can reduce the sensitivity of tooth surface meshing performance to the installation errors.