Forging Analysis - 2. ver. 1. Prof. Ramesh Singh, Notes by Dr. Singh/ Dr. Colton
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1 Foging Analysis - ve. 1 Pof. ames Sing, Notes by D. Sing/ D. Colton 1
2 Slab analysis fictionless wit fiction ectangula Cylindical Oveview Stain adening and ate effects Flas edundant wo Pof. ames Sing, Notes by D. Sing/ D. Colton
3 Foging cylindical at sliding egion Pof. ames Sing, Notes by D. Sing/ D. Colton 3
4 Equilibium in diection df 0 σ θ σ d neglecting HOTs dθ dθ + ( σ + dσ ) ( + d) dθ N.B. dθ dθ sin dθ d d + σ d σ d dσ 0 θ Pof. ames Sing, Notes by D. Sing/ D. Colton 4
5 Axisymmetic and yield Fo axisymmetic d π ε ; εθ ε ε ; σ σ θ θ ( + d) π π d By Tesca σ + σ τ dσ d σ σ / τ Pof. ames Sing, Notes by D. Sing/ D. Colton 5
6 substituting Stess in z diection d + σ d σ d + d 0 o d d eaanging d d Pof. ames Sing, Notes by D. Sing/ D. Colton 6
7 Foging essue - sliding τ d d fo < < τ ex ( ) Pof. ames Sing, Notes by D. Sing/ D. Colton 7
8 Pof. ames Sing, Notes by D. Sing/ D. Colton 8 Aveage foging essue sliding ( ) ( ) ( ) d d ave π τ π τ ex 1 ( ) ave 1 ex ex τ ( ) 1 ex 1 ex ex ave τ
9 Pof. ames Sing, Notes by D. Sing/ D. Colton 9 Aveage foging essue sliding ( ) ( ) ex ave τ
10 Foging foce sliding F foging A π ave ave ( ) F foging ( ) ( ) τ ex π 4 Pof. ames Sing, Notes by D. Sing/ D. Colton 10
11 Aveage foging essue all sliding aoximation ( 0) Taing te fist fou tems of a Taylo s seies exansion fo te exonential about 0 fo x 1 ex yields x x ( x) 1+ x L + τ ave! ! 3 n x n! n 0 x! Pof. ames Sing, Notes by D. Sing/ D. Colton 11
12 Foging foce all sliding aoximation F foging A π ave ave F foging τ 1 + π 3 Pof. ames Sing, Notes by D. Sing/ D. Colton 1
13 Pof. ames Sing, Notes by D. Sing/ D. Colton 13 Tansition sticing / sliding Set τ and solve fo τ ex ex 1 ln 1 ln
14 Foging essue - sticing egion Use te same metod as fo sliding Substitute τ, Assume Tesca yield citeion d d τ d d τ d d Pof. ames Sing, Notes by D. Sing/ D. Colton 14
15 Foging essue - sticing d τ τ egion d ( ) ( ) τ Pof. ames Sing, Notes by D. Sing/ D. Colton 15
16 Foging essue - sticing egion detemined fom sliding equation ex τ ( ) fo 0 < < τ ex ( ) + ( ) Pof. ames Sing, Notes by D. Sing/ D. Colton 16
17 Pof. ames Sing, Notes by D. Sing/ D. Colton 17 Aveage foging essue - sticing ( ) d d ave ex 1 π π τ ( ) d ave ex τ ( ) ave ex + τ
18 Pof. ames Sing, Notes by D. Sing/ D. Colton 18 Aveage foging essue - sticing ( ) + ave 3 ex 3 3 τ ( ) + ave 3 ex τ ( ) ave ex + τ
19 Foging foce sticing egion F foging A π ave ave F foging τ ex π 3 ( ) + Pof. ames Sing, Notes by D. Sing/ D. Colton 19
20 Sticing and sliding If you ave bot sticing and sliding, and you can t aoximate by one o te ote, Ten you need to include bot in you essue and aveage essue calculations. F F + foging sliding F sticing F foging ( ) ( ) ave A sliding + ave A sticing Pof. ames Sing, Notes by D. Sing/ D. Colton 0
21 Stain adening (cold - below ecystallization oint) Tesca τ Y K ε n Pof. ames Sing, Notes by D. Sing/ D. Colton 1
22 Stain ate effect (ot above ecystallization oint) 1 d v ε & dt laten velocity instantaneous eigt Tesca τ Y C( & ε ) m Pof. ames Sing, Notes by D. Sing/ D. Colton
23 Flas fo closed die foging (lane stain) Say we ave a tyical flas wit ticness /0 and lengt w/4 /0 w w/4 Pof. ames Sing, Notes by D. Sing/ D. Colton 3
24 Aveage foging essue in foging (Tesca) w ave τ 1 + in flas (Tesca) ave 5 w τ 1 + Pof. ames Sing, Notes by D. Sing/ D. Colton 4
25 Flas Flas s ig defomation esistance esults in filled mold Pocess wouldn t wo witout fiction Pof. ames Sing, Notes by D. Sing/ D. Colton 5
26 Defomation Wo In geneal, wo done in bul defomation ocesses as tee comonents Total wo, W W ideal + W fiction + W edundant Wo of ideal lastic defomation, W ideal (aea unde tue stess-tue stain cuve)(volume) ε t σ ε t t (volume) ideal 0 n 1 + Fo a tue stess-tue stain cuve : n σ t Kε t t d W Kε n+ 1 ( volume) ( volume) Yf t Y f ε Avg. stess Pof. ames Sing, Notes by D. Sing/ D. Colton 6
27 Defomation Wo Fiction between dies and woiece causes inomogeneous (non-unifom) defomation called baeling Fictional Foces Baeling Effect Pof. ames Sing, Notes by D. Sing/ D. Colton 7
28 Defomation Wo Intenal seaing of mateial equies edundant wo to be exended Ideal Defomation edundant Defomation Pof. ames Sing, Notes by D. Sing/ D. Colton 8
29 edundant Zone Pof. ames Sing, Notes by D. Sing/ D. Colton 9
30 Closed/Imession Die Foging Analysis moe comlex due to lage vaiation in stains in diffeent ats of woiece Aoximate aoaces Divide foging into simle at saes e.g. cylindes, slabs etc. tat can be analyzed seaately Conside entie foging as a simlified sae Pof. ames Sing, Notes by D. Sing/ D. Colton 30
31 Closed/Imession Die Foging Stes in latte analysis aoac Ste 1: calculate aveage eigt fom volume V and total ojected aea A t of at (including flas aea) Ste : ε ε& avg avg V V avg At Lw i avg.stain ln avg v avg.stain ate avg Pof. ames Sing, Notes by D. Sing/ D. Colton 31
32 Closed/Imession Die Foging Ste 3: calculate stess of mateial Y f fo cold/ot woing Ste 4: Avg.foging load F K avg Y f A t K essue multilying facto 3~5 fo simle saes witout flas 5~8 fo simle saes wit flas 8~1 fo comlex saes wit flas Pof. ames Sing, Notes by D. Sing/ D. Colton 3
33 Ote Analysis Metods Comlex closed die foging simulated using finite element softwae Pof. ames Sing, Notes by D. Sing/ D. Colton Souce: tt://nsmwww.eng.oio-state.edu/tml/f-flaslessfog.tml 33
34 Ue Bound Teoem Any estimate of te collase load of a stuctue made by equating te intenal ate of enegy dissiation to te ate at wic extenal foces do wo in some assumed atten of defomation will be > o to te coect load. Pof. ames Sing, Notes by D. Sing/ D. Colton 34
35 Ue Bound Teoem Assumtions Isotoic and omogeneous Neglect stain adening and stain ate Fictionless o constant sea stess condition exists at tool-wo iece inteface -D, lane stain wit all defomation occuing by sea on a few lanes. Elsewee, mateial is igid. Pof. ames Sing, Notes by D. Sing/ D. Colton 35
36 Ue Bound Teoem dw dt i 1 sea stess S i lengt of sea lane V ι* velocity of sea n S i V i Pof. ames Sing, Notes by D. Sing/ D. Colton 36
37 Ue Bound Teoem Indentation of a late (sli-line analysis) L F w v CA v BC v DC D A A D v v o BA C B C Pof. ames Sing, Notes by D. Sing/ D. Colton 37
38 Wo, seaing foce Wo is done by seaing along AB, BC, AC, and CD. Lengts calculated fom figue at igt. Seaing foce along any bounday, e unit lengt, w, is (sea yield stess) times te lengt of te bounday, L. D C A B A D C Pof. ames Sing, Notes by D. Sing/ D. Colton 38
39 Seaing velocities v BA v o v BC v o v BC v CA v o v CA v BA v DC v o v DC v o Pof. ames Sing, Notes by D. Sing/ D. Colton 39
40 Motions Pof. ames Sing, Notes by D. Sing/ D. Colton 40
41 Total owe deliveed Lv o Lv Lv Lv 0 o o + Lvo + + eac tem as been counted twice due to symmety Simlifying 6 Pof. ames Sing, Notes by D. Sing/ D. Colton 41
42 Total owe deliveed 6 using von Mises ence Y Y Y Y Pof. ames Sing, Notes by D. Sing/ D. Colton 4
43 Exact solution Y Solution above Y so we can see te effect of constaint edundant wo: ige essue Pof. ames Sing, Notes by D. Sing/ D. Colton 43
44 Non-omogeneous defomation and edundant wo If te slab is tic o fiction: non-omogeneous defomation edundant wo If te slab is tin o unconstained: (e.g., oen die foging witout fiction) no edundant wo Pof. ames Sing, Notes by D. Sing/ D. Colton 44
45 Indenting at /L 1 L F v 1 B E A C v o v 1 v 1 v BC v CE v o v o v o F v 1 Pof. ames Sing, Notes by D. Sing/ D. Colton 45
46 Analysis - owe deliveed BC CE BC CE L v v v L v L o o 1.15 Y (lane stain esult) v o v 1 B E A C v o v o v 1 v 1 v BC v CE v 1 v o v o Pof. ames Sing, Notes by D. Sing/ D. Colton 46
47 edundant wo limit ( /L) (lane stain) /L < 1: no edundant wo 1.15 Y 1 < /L < 8.7: some edundant wo 1.15 Y < <.97 Y /L > 8.7: edundant wo same as infinite late.97 Y Pof. ames Sing, Notes by D. Sing/ D. Colton 47
48 edundant wo coection facto (Q ) Can be caacteized by: Q Y o Q /σ y /τ y (by Tesca) wee Q coection facto fo edundant wo Pof. ames Sing, Notes by D. Sing/ D. Colton 48
49 edundant wo facto (Bacofen) (fictionless) Q Pof. ames Sing, Notes by D. Sing/ D. Colton 49
50 edundant wo facto (Kalajian) - (fiction) Pof. ames Sing, Notes by D. Sing/ D. Colton 50
51 Slab analysis fictionless wit fiction ectangula Cylindical Summay Stain adening and ate effects Flas edundant wo Pof. ames Sing, Notes by D. Sing/ D. Colton 51
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