Scale effect in design of the pre-stressed micro-dies for microforming

Abstract

In dies for cold extrusion permissible internal pressure may be increased by the use of one or two shrink rings. Such design creates tensile stresses in the ring and compressive stresses in the insert. The design essentially boils down to define the diametrical interference of the fit to be attained during the assembly. Interference determines the properties of the die and must be carefully selected. There are basically two methods of design: based on Lame’s solution and FEM. None of these two methods include roughness of interface surfaces of the die and shrink ring. The pre-stressed micro-die shows that interface roughness can’t be skipped and the “classical” design of diameter interference must be corrected. The novel method of determination of the correction value is introduced: TheSemi-Physical Modelling of models representing Interface Roughness, SPMIR method. In this method a set of FEM modelling of models created on the base of Abbot-Firestone curves, determined from the roughness profile, lead to determination of Contact Surface Stiffness Curve of interface surface and further to interference correction. Relative correction of the die diameter interference increases along with the diameter decrease that might be recognized as a pre-stressed micro-die assembling scale effect.For the worked example, the relative interference correction is hyperbolically increasing with decreasing the interface diameter decrease, exceeding 10 % for diameter about 8 mm, 25 % for 3 mm and almost 40% for 2 mm. The proposed method is than recommended for the design of pre-stressed micro dies with interface diameter lower than 8 mm.