An upper-bound analysis for the forging of spur gears

The forging of spur gears has been investigated by means of upper-bound analysis. A kinematically admissible velocity field for the forging of spur gears has been newly proposed; especially, a neutral surface has been introduced into the forging of gears by using hollow billets with a flat punch. The half pitch of the gear has been divided into seven deformation regions. By using the kinematically admissible velocity field, the power requirements and suitable conditions for the forging of spur gears were successfully calculated by a numerical method. As a result, (i) for reducing the forging load, the use of a hollow billet is more effective than a solid billet; (ii) for increasing the dimensional accuracy of forged gears, punch with a mandrel is desirable; (iii) the radius of the neutral surface and the inner radius approach zero as the height reduction increases; (iv) a suitable number of teeth for the forging of a spur gear was found to be between 15 and 20; (v) for the dimensional accuracy of forged gears, it is necessary to determine the elastic deformation of die and workpiece, the clearance between the die and punch, etc.