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A Quasi Thee-Dimensional Upper Bound Solution Considering External End Effect for Flat Tool Forging

Su He, Zhao Zhiye and Lin Zhongsheng  
R. Sagar and B.Juneja had presented their quasi three-dimensional upper bound solution for flat tool forging in the International Journal of Machine Tool Design and Research, Vol. 19, №4, 1979, but no experimental verification gave to it. Experiments we made showed that there is a clear discrepancy between the theoretical consideration as above and the actual test results (cf. Fig.3 and Fig.4) . An attempt has thus been made to deduce anew the equation for the quasi three-dimensional upper bound solution with the external end effect being taken into account, and to compare it experimentally with that by Sagar and Juneja.Summary. Taking into account the influence of external end power consumption on the forging force, new calculation equaton for the quasi three-dimensional upper bound solution for flat tool forging has been derived and so programmed. Comparison between the results calculated by computer using the new equation and those from experiments shows that they are in a good approximation (cf. Fig. 2 and Fig. 4), also nearing the relevant curves presented in the other literatures. The work is meaningful not only for forging, but also for rolling.Fig.1 A quasi three-dimensional model of compression (by Sagar and Juneja) Fig.2 Relation between pm/σ0, m, w/t and b/t (by the authors)pm--av. unit pressure; σ0--yield stress;m--friction factor; w--width of specimen;t--thickness of specimen; 6--breadth of die;△--measured value. Fig.3 Relation between pn/σ0, m, w/t and b/t (by Sagar andJuneja)Fig.4 Experimental results of pm/σ0, w/t and b/t Fig.5 Experimental result of σ0- ε Tab.1 Test result of flat tool forging with end compression asw/t = 3 Tab.2 Test result of flat tool forging with end compression as
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