Semi-analytical process modelling and simulation of air bending

Mathematical models for a fast semi-analytica simulation of the air bending process of thin as well as of thick sheets have been developed, implemented, and successfully been tested. In contrast to a large number of available approaches in this field that – for reasons of assuming the neutral fibre to coincide with the central fibre and the sheet thickness to remain constant – are limited to thin sheets, in the present work special attention has been paid to the mathematical description of the shift of individual fibres and the changes of thickness. The adequate modelling of these two effects is essential to ensure that the resulting simulation procedure is applicable in the same way to the bending of thin and, in particular, of thick sheets. The realistic mathematical modelling of the forming process, the accuracy of the results, and the very short computation times permission the simulation system to be used in production-related applications, such as CAPP systems, virtual prototyping environments, and machine control systems, in which commercial finite element analysis software can be utilized either not all or only in a limited way.

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