Deformation Processing Rolling ver 1 ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 1 Overview Process Equipment Products Mechanical Analysis Defects ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 2 Process ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 3 Process ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 4 Process ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 5 Ring Rolling ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 6 Equipment ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 7 Equipment ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 8 Products ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 9 Products Shapes I beams railroad tracks Sections door frames gutters Flat plates Rings Screws ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 10 Products A greater volume of metal is rolled than processed by any other means ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 11 Model flat sheet zero slip point f a hb sxb vb R vb vR vf vf hf sxf Exit Entrance vR ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 12 Plane strain analysis Entrance f mp Exit f p mp p h dh h dh h sx dsx dx mp p h sx sx dsx dx mp sx p ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 13 Equilibrium top entry bottom exit s x ds x h dh s x h 2 pR df sinf 2mpR df cosf 0 Simplifying and ignoring HOTs d s x h 2 pR sin f m cos f df ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 14 Simplifying Since a 1 then sinf f cosf 1 d s x h 2 pR f m df Plane strain von Mises p s x 1 15 Y flow Y flow ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 15 Differentiating Substituting 2 pR f m h d p Y flow df or p d Y flow 1 h 2 pR f m Y flow df ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 16 Differentiating d d p p h h 2 pR f m Y flow 1 Y flow df Y flow df Y flow rearranging d p df Y flow p Y flow 2R f m h ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 17 Thickness R h h f 2R 1 cosf from the definition of a circular segment f R L hb 2 hb h f hf 2 2 or after using a Taylor s series expansion for small f cosf 1 h h f R f 2 f2 2 f4 4 0 ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 18 Substituting and integrating p d Y flow p Y flow h 2R f R f f m df 2 p h R R 1 ln C ln ln 2m tan f hf Y f R hf ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 19 Eliminating ln h exp mH p C Y flow R R R 1 H 2 tan f hf hf ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 20 Entry region at f a H Hb and p Y flow sxb R C exp mHb hf s xb p Y flow h exp m H b H hb R R 1 Hb 2 tan a hf hf R R 1 H 2 tan f hf hf ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 21 Exit region at f 0 H Hf 0 and p Y flow sxf R C hf h s xf exp mH p Y flow hf R R 1 H 2 tan f hf hf ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 22 Effect of back and front tension maximum pressure pressure Y Y Y s xf Y s xb distance ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 23 Average rolling pressure per unit width pave entry 1 Hb H n 1 Hb Hn Hb Hn 1 Hn H f Hb p entry dH pave exit Hn 1 pentry dH Hb H n Hn Hf pexit dH 1 Hn H f Hb s xb Y flow Hn 1 Hn H f Hf p exit dH Hn h exp m H b H dH hb Hn h s xf exp mH dH Y flow h Hf f ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 24 Average rolling pressure entry pave entry 1 Hb H n Hb h s xb exp m H b H dH Y flow h b Hn Taylor s series expansion 0 2 0 3 n x x x exp x 1 x 2 3 n pave entry s xb Y flow hb H b H n n k 0 xk k Hb h 1 m H b H dH Hn ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 25 Average rolling pressure entry pave entry s xb Y flow hb H b H n Hb h 1 m H b H dH Hn R R 1 H 2 tan f hf hf h h f R f 2 solve numerically ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 26 Average rolling pressure exit 1 pave exit Hn H f Hn s xf Y flow Hf Taylor s series expansion 2 0 h exp mH dH hf 0 3 n x x x exp x 1 x 2 3 n n k 0 xk k s xf Y flow pave exit h 1 mH dH h f H n H f H Hn f ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 27 Average rolling pressure exit s xf Y flow pave exit h 1 mH dH h f H n H f H Hn f R R 1 H 2 tan f hf hf h h f R f 2 solve numerically ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 28 Rolling force F pave entry x Areaentry pave exit x Areaexit ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 29 Force An alternative method a f fn F w pentry R df w pexit R df n 0 again very difficult to do ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 30 Force approximation F roller L w pave L RDh Dh hb hf pave have f L ME 6222 Manufacturing Processes and Systems Prof J S Colton GIT 2010 31 Derivation of L circular segment h h f 2R 1 cosf Taylor s expansion 0 cosf 1 h h f R f f 2 …
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