Fig.3*1 Function of Static
Shape
Change
List of principal symbols, abbreviations and notations to be found in this chapter and Appendices 1 to 4
Subscripts (unless otherwise defined) General subscripts used are;-
B Quantity refers to backing bearings
2 Quantity refers to second intermediate rolls 1 Quantity refers to first intermediate rolls W Quantity refers to workrolls
N Used as a count (i.e. N = 1,2,3»^... etc.) Common second subscripts used are: -
L Quantity refers to the Left-hand side or end R Quantity refers to the Right-hand side or end
S Quantity refers to the area over the strip being rolled T Refers to the top half of the roll stack ^ (used B Refers to the bottom half of the roll-stack ) ^j) 0 Indicates mill actuator datum positions (used with
L ^
S1S2 D Drive roll)(used with D_)
)
1 Idler rolljMain Variables and Abbreviations
Motion of upper central backing shafts (roll B) towards centre of upper central second intermediate roll(j) at the saddle from front of mill (i.e. due to motion of the As-U-Roll rack). (m) (close approximation)(positive for roll B moving towards roll J ).
As-U-Roll
General functions defined in beams-on-elastic foundations theory (Appendix l)
B.O.E.F. Beams-on-Elastic Foundations
c Camber off diameter of roll specified by subscript s.
S
(m)
BVN AUR A BA x A xMaximum diameter (including camber) of roll specified by subscripts s (m)
e Base of natural logarithms
eaSesse Eccentricity of As-U-Roll rings, screwdown and side Eccentric Discs respectively (m)
— 2 E Young5 s Modulus for all rolls (Nm ).
ECF Abbreviated form of nend-conditioning-force" E, ) Intermediate values defined in beams-on-elasticIs
,
g ^ foundations theory (Appendix l).2s ^
F Value of concentrated force, subscripted as ap propriate, (N) (positive downwards)•
Values of force defined for roll specified by subscript s in b.o.e.f. theory (N).
F ' 0s p» 0s FOAs FOBs
^ G mill gain matrix (N mm )— 2 P
lN "fch
h^,. Strip input gauge over the centre of the N shape meter rotor covered by the strip, (m)
Strip output gauge corresponding to h^. (m)
h. ) Strip general entry and exit gauges used in rolling
x
h ^ theory (m))
I Second moment of area of roll specified by subscript S s. Roll assumed cylindrical and of diameter Dg (m )4 Jg Number of backing bearings
r\
Yieldstress of strip in roll gap (Nm*" )} v a r i a b l e as k(/0
Foundation modulus defined in b.o.e.f. theory (Appendix l) for roll specified by subscript s_
— 2
resting on roll specified by subscript sQ. (Nm ) Taper off base (i.e. uncambered) diameter of first intermediate rolls. (m)
Length of H R tapered portion (ra) Length of each backing bearing, (m)
Length of tapered section of first intermediate rolls which is slid into the cluster, (m)
Width of each shapemeter rotor, (m) Strip Width, (m)
Total roll length (m). (Length of non-tapered portion of lIRs).
Unsupported length of workroll overhanging each edge of the strip. (m)
Abbreviated form of "left-hand". Note that the "left-hand" end of any roll is at the front of the mill.
Distance between centres of rolls specified by sub scripts s^ and s^ (used in cluster angle and force analysis), (m)
Various values of moment defined in the b.o.e.f. theory (Appendix l) for roll specified by subscript s. (Nm) (Positive when clockwise onthe left of a section - i.e. in the direction of the positive shearing force Q on the left of the section. Thus M is positive for a sagging beam).
As-U-Roll Rack position (operator's units)
(positive downwards) side eccentric position (operator's units)
M s screwdown rack position ( " " )
M Even number of points (symmetrical about the vertical ® 1
centre line of mill and equally spaced) at -which deflection is calculated for roll specified by subscript s^.
Pg Pitch of backing bearings (m) P,p Total Rolling Load (N)
P' Distributed Rolling Load (Nm""’**)
q Value of uniformly-distributed loading, subscr
wards)
subscripted as appropriate, (Nm "**) (positive down-
QA \ Values of shear defined in b.o.e.f0 theory
s
)
Q' ) (Appendix l) for roll specified by subscript s. (N) (Positive when acting upwards on the left of a section) A s
0"As %
s
R Undeformed roll radius (m) R' Deformed roll radius (m)
RH Abbreviated form of "right-hand"
r A,r ,r A* s s p Gain of As-U-Roll, screwdown and side eccentric’ actuators (rad/operator's unit)
— 2
s Normal rolling pressure (Nm ) (Variable as s (/0 ) . T.,T Entry & Exit Tensions (N)i * o *'
T.',T'
i o
" " Tension stresses (Nm-2)t^ Peak value of triangular-distributed loading due to backing bearing N. May be further subscripted
WR Abbreviated form of "workroll” w
N
Strip width (m) used in rolling theory. "fch
Distance of front edge of N backing bearing along second intermediate roll. Measured from
front of mill. (A zero preceding the nNn indicates that the measurement is taken at zero As-U-Roll travel), (m)
Im-1 M Array of distances of the Mg points from the
s front of the mill, (m)
x Distance from front of mill of point of
sFn |n ^ j application of concentrated force
s sF acting on roll specified by subscript s. (m) N Definition of workroll at LH edge of stripdue to N element of array F^(J^p). (m)*t h
Deflection of workroll at RH edge of strip du e to N b JU V/ ill element of array Fw (J^p).X JL b U X U J L Jl U J » y
(m)
xM
M=1,M
Deflection of roll specified by subscript s at the section x.,.M (m)
N A number of algebraic reduction factors used in section 3-9-21, defined as required R
Ah
NN=1, JH
p.u. Reduction of strip gauge due to rolling
Differential elongation (w.r.t. mean) of *th filament of strip corresponding to N
covered shapemeter rotor centre from front of mill. (m)