A critical note on several comments on analysis of cold strip
rolling
Citation for published version (APA):
Mot, E. (1968). A critical note on several comments on analysis of cold strip rolling. (TH Eindhoven. Afd. Werktuigbouwkunde, Laboratorium voor mechanische technologie en werkplaatstechniek : WT rapporten; Vol. WT0193). Technische Hogeschool Eindhoven.
Document status and date: Published: 01/01/1968 Document Version:
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Journal of Engineering for Industry Transactions of the ASME - Series B.
Letter to the Editor.
A critical note on several comments on analyses of cold strip rolling.
E.
Mot-A number of years ago, Mr.
Avi~ur
published several articles on cold strip rolling [1, 2,3].
These publications caused unusually sharp reactions from some other specialists on the subject, e.g •• , •• ,."Dr. J.M.Alexander wrote to say that he thought the author's whole approach to the problem of cold strip rolling was dangerously misleading" •
(1J
.' ••• "The writers are mistified as to wh1_thes~ effor~s are necessary when an adequate theory for all normal cold rolling problems already exists". (comment of J.M. Alexander and H. Ford),
[3].
As to the second comment, Mr. Avitzur replied" that he had drawn several conclusions that had not been drawn before. All authors concerned, however, have completely overlobked the fact that Mr. AVi\ur's theories could for a great deal also be derived from
the existing theory of D.R. Bland and H. Ford
[41,
so that a further development of the latter theory would irrevocably have led to identical conclusions.In reference
[4J,
the authors use an approximate equilibrium approach and derive the following expression. for the normal pressurecurve-j+
=
kh~
kb (
G'i)
=
iil1-~,.• Department of' Production Engineering,
in which
H • 2
~
arctan(~.
f)
The neutral point ia found by the requirement
e: + ..
-- ' • a n n (4)
I take the liberty to extend this consideration and to introduce a perfectly logical hypothesis:
i1.1 !1a~i!!u!! .!:e~uE.t!o.!!. talEe,! ,El!c,! !f_a!l_f.!:iE.t!o~ tOE-c!. !s_u!,!d_t.2,
l?ull_.t.h.o;,P.ir!p_i~ ~elw!.e~ !h.! roo!l!.!..:. This can be formulated by,
B : I O.
,,.D
Using (5) ahd (3) • ."e derive from (6):
In
~(1
-
~)}
\(h;
1-ki
IA
=t
V -; •
---~--..;.-=--arctan (
~
-1)
If no front or back tensions are applied. we find
(6)
f' •
i
V
~I.
In~h
l'
(8)arctan
(~- ~
This is exactly formula (7) of ref.
[1),
which, however, was derived-from a totally different consideration, viz. an energy approach.For a given value of
1",
.e may also derive maximum and minimum possible reduct~ons from (5) and (6) by successive approximations and find results which are similar to those mentioned in rets.[1] and I2].
If
The theor,. of Bland and Ford is generall,. recognised as a
valuable contribution to the mechanics of metalworking processes and is e.g. q,uoted by Johnson and Mellor
[5J.
Therefore, it seems hardly justifiable to classify a theory which differs in approach but not· in ultimate result as "dangerously mis-leading".The second comment quoted seems correct to this extent that all conclusions ot Avi~ur could have been drawn from earlier theories. It should be added, though, that this has not been done.
Rowever, as for ref.
[3l.
the importance is far beyond the scope of solving a strip rolling problem. It is a demonstration of a technical application of the important lower upper-bound theorem, and up to now onl,. rew scientists have been able to use thistheorem succestifttlly in this field .. In
m:r
opinion. furtherapplication of extremum principles in plasticity mechanics will prove to be very useful and give a better insight in man,. processes which are nowadays considered to be insoluble.
Therefore - as far as I am concerned - Mr. A~ur is oongratulated with his work.
Nomendature (similar to ref.
[4]>
h thickness of stripk maximum shear stress
s normal roll pressure
R' radius of deformed are of contact
Suff:Lzesl
angular oo~ordinate, radians
coefficient of friction between roll surface and material. tensile stress (tront or back pull)
entry (I exit n neutral point + between 0 and n - between nand 1 References:
[1]
B. Av~ur, Maximum reduction in cold strip rollins,Proc.lnst. Meoh. Eagra., Vol.
174
No.32,
1960,
,:865-884.
(2)
B. Avi~ur, Power analysis of cold strip rolling,[J)
B. Avitur, An upper bound approach to cold strip rolling, Jrn. of Eng. for Ind., Trans. ASME-B. Febr. 1964, p~31-46.[4) D.R. Bland
&
H. Ford, The calculation of roll force and torque in cold strip rolling with tensions,Research on the rolling of strip, a symposium of selected papers, 1948-1958; B.I.S.R.A., p.68-77
(5] W. Johnson
