A study on precision forging of spur gear forms and spline by the upper bound method

Precision forging is an important manufacturing procedure of spline and spur gear forms. It has advantages of improved strength, good tolerance, saving billet material, dispensing with the cutting, etc. In this paper, a mathematical model using an upper bound method is proposed for forging of spur gear forms and spline to investigate the plastic deformation behavior of billet within the die cavity. The material of solid billet was assumed as rigid–plastic and the shape of the tooth profile was accounted for the mathematical modeling of the kinematically admissible velocity field assumed for the plastic zone. The non-uniform velocity was employed for simulating the inhomogeneous deformation and the effect of barreling during the forging. Using the present model, various effects of forming parameter such as the friction factor, reduction, number of teeth, etc. upon the non-dimensional forging pressure, forging force and barreling of the spur gear forms and spline were analyzed systematically and the results compared with those of other researcherʹs analytical and experimental work. It is shown that the present modeling of the process improves knowledge of the process design performance for the precision forging of spur gear form and spline.