To determine the coefficient of friction at the die-work piece interface, a friction model that takes into account of the contact Fig. 2. Bending under tension apparatus. angle and bending force is adopted [21]. The coefficient of friction can be calculated from:
d = 2
F1 −
F2 −
Fb
F1 +
F2
(1)where dis the coefficient of friction at die and prepaint sheetmetal interface, is the wrap angle ( = 90◦in the present case),F1is the pulling force from Load Cell I measurement, F2is the backtension from clamping, and Fbis the bending force. The back tensionis calculated from:
F2 =
bN (2)where bis the coefficient of friction between the clamping plateand the specimen, and N is the clamping load that can be obtainedfrom Load Cell II. Note that the friction bcan be measured using asimple strip drawing test. The bending force can be calculated from[22]:
Fb = yt2W
2r
(3)where yis the yield strength, W is the width, t is the thickness ofthe strip, and r is the die radius.