Forw ard rod extrusion

6 Solid forming Forging

6.5 Force and w ork requirement

Det erm in at io n o f t h e fo rce an d wo rk req u irem en t is u sed as a basis fo r select io n o f t h e fo rm in g m ach in e an d t h e st ru ct u ral d esign o f t h e fo rm - in g d ies. In p ract ice, calcu lat io n o f t h ese ch aract erist ics sim u lt an eo u sly p ro d u ces valu es o f p ro cess-relat ed p aram et ers su ch as t h e o verall d egree o f t ru e st rain , flo w st ress, fo rm in g p ressu re, co m p ressive st resses o n t h e in sid e wall o f t h e ext ru sio n co n t ain er, et c. cf. Sect . 2.2 . Th e p ro cess lim it s an d t h e resp ect ive case o f ap p licat io n o f t h e fo rm in g m et h o d m u st also be t aken in t o co n sid erat io n h ere. Th e fo rm u lae p ro vid ed belo w are based o n o n ly o n e m et h o d o f cal- cu lat io n an d m ake n o claim o f co m p let en ess. Th e flo w st ress levels are average valu es o bt ain ed fro m t h e flo w cu rves o f VDI 3200 Sh eet s 2 an d 3. To calcu lat e t h e p ro cess variables co n cern in g m ach in e select io n , t h e u p p er lim it o f a flo w cu rve sh o u ld be select ed . Ho wever, in m akin g cal- cu lat io n s regard in g d ie co n figu rat io n , t h e lo wer lim it o f a flo w cu rve sh o u ld be select ed . Table 6.5.1 p ro vid es an o verall view o f t h e p ro cess lim it s fo r t h e m ain ext ru sio n p ro cesses.

6.5.1 Forw ard rod extrusion

Th e fo rward ro d ext ru sio n m et h o d t ran sfo rm s a billet in t o a so lid p art wit h a red u ced cro ss sect io n cf. Fig. 6.1.1 . Th e d ie o p en in g wh ich d et erm in es t h e sh ap e o f t h e ext ru d ed p art s is fo rm ed so lely by t h e p ress co n t ain er. As a resu lt o f t h e wall frict io n wh ich o ccu rs – also d u rin g t h e eject io n p ro cess – t h e rat io o f h eigh t t o d iam et er o f t h e in it ial billet h d [–] sh o u ld be n o great er t h an 5 t o 10 Fig. 6.5.1 . If t h e req u ired Metal Forming Handbook Schuler c Springer-Verlag Berlin Heidelberg 1998 d im en sion s are greater th an th ese valu es, free or op en d ie extru sion m u st be u sed as a su p p lem en tary extru sion p rocess. In ad d ition , th e ratio h d in th e rem ain in g n on -extru d ed p ortion of th e billet m u st be n o sm aller th an 0.5. Oth erwise, th e so-called “su ck-in ” d efects m ay occu r. Th e m axim u m t ru e st rain ach ievable wit h t h e fo rward ro d ext ru sio n o f st eel is aro u n d w = 1.6 d ep en d in g o n t h e m at erial. In t h e case o f m at erials wit h lo w fo rm abilit y, t h is valu e is as lo w as 0.5 t o 0.9. Th e d ie o p en in g an gles 2 a [°] m u st be wit h in a ran ge o f ap p ro x. 45 an d 130°, wh ich resu lt s in t ap ers o n t h e fo rm ed p art wit h an gles bet ween 22.5 an d 65°. Th e p art vo lu m e is calcu lat ed fro m t h e in d ivid u al vo lu m et ric valu es as illu st rat ed in Fig. 6.5.1 : 470 Solid forming Forging Table 6.5.1: Process limits of the most important extrusion methods taking into account economical die life material Process N F- m at er ia ls st ee ls aluminium e.g. Al99,5, lead, zinc copper E-Cu brass CuZn37 - CuZn28 easy to form e.g. QSt32-3, Cq15 difficult to form e.g. Cq35, 15M nCr5 more difficult to form e.g. Cq45, 42CrM o4 limiting A max A max A min A max max max h d 0 max h d max h d 2 1 max 0.98 0.85 0.75 0.98 0.85 0.75 0.10 0.12 0.15 4 1.9 1.4 4 1.9 1.4 0.98 0.80 0.75 0.75 0.67 0.60 0.75 0.67 0.60 0.15 0.25 0.35 1.4 1.1 0.9 1.4 1.1 0.9 0.75 0.65 0.60 15 12 8 10 6 4 3 2 1.5 6 4 3 Forw ard rod extrusion Forw ard tube extrusion Backw ard cup extrusion d h d 1 d 1 h h 2 s 1 d d h s 1 s value V V V V 1 2 1 = + + , hereby V V V nd V re calculated by means of 1 1 2 , , w a a Metal Forming Handbook Schuler c Springer-Verlag Berlin Heidelberg 1998 In t h is calcu lat io n , it is p o ssible t o u se d 2 d as an ap p ro xim at io n ; t h e h eigh t o f t h e t ru n cat ed co n e h 1 ’ an d t h e fo rm in g st ro ke h are d et er- m in ed by m ean s o f: Th e am o u n t o f d efo rm at io n st rain s can be d et erm in ed fro m t h e d egree o f t ru e st rain w an d t h e sp ecific cro ss sect io n ch an ge « A . Th e lat - t er can be o bt ain ed q u ickly fro m t h e relevan t sq u ares o f t h e d iam et ers in st ead o f u sin g t h e su rfaces: 471 Force and w ork requirement V d h mm V d h mm V h d d d d mm V d h mm 2 3 1 1 2 1 3 1 1 2 2 1 2 2 1 3 2 2 2 2 3 4 4 12 4 = ⋅ ⋅ [ ] = ⋅ ⋅ [ ] = ⋅ ⋅ + + ⋅ [ ] = ⋅ ⋅ [ ] ’ π π π π d d 2 d 1 F h V 2 V 1 ’ h 1 ’ h 2 h 1 V 1 α 2 Fig. 6.5.1 Schematic representation of forw ard rod extrusion h d d h h h mm 1 2 1 2 2 – cot – = = [ ] α ϕ =     ln d d 2 2 1 2 Metal Forming Handbook Schuler c Springer-Verlag Berlin Heidelberg 1998 Th e rat io bet ween billet h eigh t h an d billet d iam et er d an d t h e d ie o p en in g an gle are t aken in t o acco u n t wit h t h e co rrect io n co efficien t s k h an d k 2 a [–] wh en est im at in g t h e sp ecific p u n ch p ressu re an d t h u s also wh en calcu lat in g t h e fo rm in g fo rce. Th e flo w st ress at t h e st art o f t h e fo rm in g p ro cess k f0 [N m m 2 ] an d t o ward s t h e en d o f t h e fo rm in g p ro cess k f1 can be d erived fro m t h e sh eet s o f VDI Gu id elin e 3200 fo r t h e m at erial u sed in each case. Bo t h valu es are u sed t o est im at e t h e sp ecific an d id eal fo rm in g wo rk w id : As t h e act u al fo rm in g fo rce d eviat es fro m t h e t h eo ret ically id eal fo rm - in g fo rce, it is co rrect ed by u sin g t h e effien cy fact o r h F [–]. Th e average fo rm in g p ressu re p St [N m m 2 ] an d t h e fo rm in g fo rce F U [kN] are t h u s est im at ed by u sin g: Th e fo rm in g wo rk W is t h e p ro d u ct o f fo rm in g fo rce an d fo rm in g st ro ke h 472 Solid forming Forging ε ε = ⋅ = ⋅ – – A A A d d d A A 1 2 2 1 2 2 2 100 100 k h d k h = ⋅ + = ⋅ + 0 2 0 8 1 200 2 0 7 2 . . . α α w k k Nmm mm id f o f l →≈ + ⋅     2 3 ϕ η ε F A = ⋅ 0 703125 100 . p w k k N mm F p d kN St id h U St = ⋅ ⋅     = ⋅ ⋅ ⋅ [ ] η π α 2 2 2 2 3 4 10 – W F h J resp Nm U = ⋅ [ ] . Metal Forming Handbook Schuler c Springer-Verlag Berlin Heidelberg 1998 Fo r d ie d esign , t h e p ressu re o n t h e co n t ain er wall p i [N m m 2 ] is d et er- m in ed : Example: Th e sam p le calcu lat io n p ro vid ed h ere is based o n t h e wo rkp iece m at erial 1.0303 Q ST 32-3. Th e st art in g valu es are sp ecified o n t h e left , t h e ch aract erist ic valu es su bseq u en t t o t h e p ressin g o p erat io n o n t h e righ t . d = 75 m m d 1 = 45 m m a = 45° h = 110 m m h 2 = 65 m m d 2 = 75.3 m m = h = 45 m m Th e resu lt in g d efo rm at io n o r id eal effect ive st rain is w = 1.03, wh ich co rre- sp o n d s t o a relat ive cro ss sect io n ch an ge o f « A 64 , an d t h e co rrect io n co ef- ficien t s are k h 1.09 an d k 2 a 1.15: If th e am oun t of deform ation is 1.03, th e resultin g value for k f1 is approx. 740 Nm m 2 , k f0 250 Nm m 2 , m ean in g th at th e specific form in g work is approx. 471 Nm m m m 3 . With an efficien cy of t h e sp ecific d ie lo ad s, fo rce an d wo rk resu lt in : 473 Force and w ork requirement p p k k N mm i St f f = + +     1 2 1 2 ϕ ε α =     = = ⋅ = = ⋅   + ≈ = ⋅ ⋅ + ≈ ln . . . – . . . . . . 75 3 45 1 03 75 3 45 75 3 100 64 0 2 110 75 0 8 1 09 1 200 2 45 0 7 1 15 2 2 2 2 2 2 k k h η F = ⋅ = 0 703125 64 100 0 67 . . p N mm F kN esp N mm St U i = ⋅ ⋅ ≈ [ ] = ⋅ ⋅ ⋅ ≈ [ ] = ≈ [ ] = + + ≈ [ ] ⋅ 510 0 67 1 09 1 15 957 957 75 3 4 10 4 261 4 261 0 045 192 2 957 250 740 974 2 2 3 2 . . . . , , . – π W kJ r . kNm p 1 Metal Forming Handbook Schuler c Springer-Verlag Berlin Heidelberg 1998

6.5.2 Forw ard tube extrusion