Effect of cup geometry on ear height and thickening in cylindrical flatbottomed steel cups

Abstract

An investigation of the effect of cup geometry on ear height and wall thickening in cylindrical flat-bottom cups made from various mild steels has been carried out, and empirical relationships relating these factors have been established. The work has shown that, with reasonable accuracy, the ear height E is given by:

E=M_P (B²–P²/P)(B–P/P)^1·5

where B is the blank diameter, P is the punch diameter, and M_P is a dimensionless earing parameter of the steel which may vary substantially between different steels. The mean increase in thickness at the top of the cup is given by:

(T_m–T_o)=K_PT_o (B–P/P)

where T_m is the mean final thickness at the top of the cup, T^o is the starting sheet thickness, and K^P is a parameter which varies from steel to steel. The variation in thickness at the top of a cup due to earing ∆T_e is given by:

∆T_e=2·66 M_PT_o (B²–P²/P²)(B–P/P)^1·5

Equations similar in form were found to hold when P was replaced by the die diameter D and these were about as accurate as those involving P. The empirical relationships established may need modification if results of very high accuracy are required, meanwhile the present equations can give a very useful practical guide to the way in which steels of a given earing quality will perform in cylindrical pressings of differing sizes and proportions.