Active design and manufacture of face-milled spiral bevel gear by completing process method with fixed workpiece axis based on a free-form machine tool

In the design and manufacture of face-milled spiral bevel gear, the completing process method has significant advantages, such as increased efficiency, cost reduction, machining accuracy improvement, and tooth strength enhancement. Since the intrinsic limitations of the cradle-type machine tool, we develop a mathematical model for the completing process method directly based on the free-form machine tool. It is applied directly to the free-form machine tool, eliminating the need for the equivalent conversion of machine settings from the cradle-type machine tool to the free-form machine tool, and taking advantage of the flexibility and freedom offered by the free-form machine tool. Thus, except the first-order and second-order parameters of the mean contact point of each pinion flank controlled by the existing methods, each point of the contact path on the frequently used drive-side flank of pinion can be guaranteed additionally simultaneously by this method. Furthermore, the workpiece axis linkage is dispensed with during the machining process, avoiding the error caused by poor motion accuracy of the workpiece shaft and the difficulty in its manufacture. The target tooth surface and tooth depth can be guaranteed simultaneously. Finally, the method is verified by tooth contact analysis (TCA), grinding test, and rolling test.