FIELD OF INVENTION
This invention relates to pre-matching of pressed 'U' shells with equal or different
included angles and thickness using corrected bow technique. More particularly it
relates to a method of measuring the radii at different points of the formed 'U'
shells to find the minimum ovality which is the criteria for selecting the type of
matching.
BACKGROUND OF THE INVENTION
Boiler drums and cylindrical shells that are manufactured from plates are pressed
according to established procedures and are made into 'U' shells. These V shells
are matched with one another in two longitudinal seams as shown in fig 1. The
seams are welded and the two 'U' shells are formed into a cylindrical shell. The
design requirement of the pressure part governed by IBR 1950 and ASME
standards is that ovality i.e.. out of roundness be limited to 1 % of the nominal
internal diameter. The ovality is the difference between the maximum and
minimum diameter, as shown in fig 2.

Previous method of controlling ovality was by ensuring template profile in the
ends. A template is a relief of the same radius having minimum length equal to
quarter of the diameter, as shown in fig 3. Another control is to check the bow
along various axes longitudinally along the length of the shell. Bow is the bend or
out of linearity observed along a linear reference line. In the pressed 'U' shells
the bow measurement was done by placing two standard blocks of height 'h' at
the two ends that lie in geometrical generator lines in the inside surface of the
'U' shells lengthwise as depicted in fig-4. This method however is found
inadequate in measuring ovality at all points eventually resulting middle portion
remaining unchecked leaving no option for correction before both 'U' shells are
matched. This is raised only when V shells are trial matched in the subsequent
work center and later moved back for correction. There have been attempts to
arrive at methods to predict the ovality and control it as the process can be
controlled if one can measure it exactly. There has been a search for newer
techniques, all in vain, which can address the problem of pre-matching of 'U'
shells with different included angles and thickness.
Accordingly there exists a need to find a method that is enable to measure the
radii at various point of the formed 'U' shell and hence to find the ovality at any
cross section guiding the decision of selecting the ends of the two 'U' shells to be
matched. The prior determination of type of matching is referred as pre-
matching.

OBJECTS OF THE INVENTION
It is therefore an object of the invention to propose a method of pre-matching of
pressed 'U' shells with different included angles and thickness using corrected
bow technique which eliminates the disadvantages of prior art.
Another object of the invention is to propose a method of pre-matching of
pressed V shells with different included angles and thickness using corrected
bow technique which is capable of measuring the radii at various cross-section of
the formed 'U' shell and thus to find the ovality at those points.
A still object of the invention is to propose a method of pre-matching of pressed
'U' shells with different included angles and thickness using corrected bow
technique which provides guidance for the selection of pre-matching.
BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS
Fig-1 : sequence of forming a cylindrical shell with two longitudinal seams from
plate
Fig-2: ovality (Out-of-roundness) in a shell
Fig-3: Template checking for profile departure
Fig-4: bow measurement in a shell
Fig-5: A-A matching and A-B matching
Fig-6a: End radii measurements in corresponding end points of shell-I
Fig-6b: End radii measurements in corresponding end points of shell-II

Fig-7: Radii measurement in two U shells having different included angle and
thickness.
Fig-8: Typical radii matching in A-A matching and A-B matching in two shells
with different included angle and thickness.
DETAILED DESCRIPTION OF THE INVENTION
As shown in fig 6(a) and 6(b), two shells numbered as shell I(S1) and shell II(S2)
are being formed into 'U' shells from two shell plates P1 and P2. After hot forming
them into 'U' shells, the ends are identified as 'A'-end and 'B'-end. The two limbs
of the 'U' shells are referred as left limb and right limb as viewed from 'U'-end.
When the shells are matched to form a cylinder with two 'A'-ends at the same
end, it is referred as A-A matching and when A-end of one shell matches with B-
end of the other, it is referred as A-B matching. This prior determination of which
type of matching is to be considered for forming a cylindrical shell after
longitudinal seam welding, is referred as pre-matching. The present invention is
a method of pre-matching formed 'U' shells of various included angles and
thickness by determining intermediate point radii and diameters by corrected
bow measurements. When the shells are matched in A-A matching or A-B
matching, the different set of values of diameter result in ovality. The detail of
the two case studies is depicted below:
Case I
'U' shells with equal 180° included angles are shown in fig 6(a) and 6(b).

Shell I and II (S1,S2) are pressed and formed into 'U' shells (S1 and S2). The ends
are marked as A-end and B-end. The vertical radius of the 'U'-shells at their ends
form the height of the 'U' shells. The measurements are taken keeping the
required height as specified in the manufacturing drawing. In earlier practice, the
end radii were matched and diameters calculated and finally ovality checked. The
ovality of the middle portion could only be checked after the diameters are
physically checked. Typically, in this case, as shown in fig.7, the ovality would be

Where,
'a'- is the actual radius at the measured segment
'b'- is the actual radius at the measured segment
'n'- is the number of cross sections measured, and by default ends up at NB' end
Case-II - B1 - thickness shells with unequal included angle and thickness
The ovality in each case as shown in fig.8 can be derived if they are taken with
respect to a circle when the ovality readings are calculated with respect to the
neutral axes of the shells which are aligned to form a circle. Assuming a
correction notation as
fRc (a11+b11) = a11+b11+T/2 +t/2 where, 'T' is the larger thickness and 'Y' is the
smaller thickness of the two cells.

SO, OValityA-A matching =

Assuming an example of a 'U' shell with 1000 mm ID and 400 mm thickness
matching with a 1100 mm ID and 200 mm thickness with included angle of
thinner 'U' shell as 220°, the matching would be like the one shown in the fig.8.
Firstly we set the height of the thinner and thicker shell as in fig.7 at both the
ends. At A-end and B-end the vertical radius is set to the required radius which is
the height of the *U' shell. The radius measured at both ends of the two 'U'
shells. The radius measured at both ends of the 'U' shells considering seven
points of measurement, shall be,

The vertical elements of the radii in this case a14, a84, b14, b84 would be
1000,1000,1100,1100 respectively. As we set the height to that level, the
standard block which is 100 mm in this example, can be kept at both the ends at
points of measurements of a14, a84 and b14, b84 when a twine is tied to maintain
both end heights as 100 mm. If the other readings are as follows, for example,



Similar to the above matrix of corrected bow measurements for shell I, another
matrix is obtained for corrected bow of shell-II.
The radif of the above bow matrix points are calculated as per equation given
below,
[Radius]m,n = [Bow]m/n - [Standard block height] + Radius of ideal *U' shell
where,
m,n are the column and row of the bow matrix described below.

Radius of the ideal 'U' shell is the radius that is given in the manufacturing
drawing.
This gives us the matrices as given below, considering 8 cross sections and 7
segments.


So, ovality at every cross section 'm'
[Om] = Max[Dm] - Min[Dm] where [D] may be [D]A-A or [D]A-B as the matching
case may be.
The above matrices [D]A.A and [D]A.B does not include the radius taken for
thinner to thinner diameter readings. These readings are shown in fig.7 at A-end
as 'ditt'. To consider this type of shell matching where the thinner to thicker
shells match having different included angles, the diameter is taken as given
below,
Diameter for neutral axis = [(Dm+ T/2 +t/2), Dmtt]
where,
Dm is the diameter of the point in consideration at 'm' th section and
Dmtt is the diameter of the thinner to thinner portion as shown by dm at one end.
The ovality at every such 'm' the cross section forms an ovality matrix like, [0]A.A
and [0] A-B. The decision for the best matching can be made by the matching
matrix which has the least of all the values of ovality at various cross section.
The invented technique is put to use by custom made software through which
results are validated.

WE CLAIM
1. A method of pre-matching of pressed 'U' shells with equal or different
included angles and thickness adapting corrected bow technique
comprising;
measuring the radii at the ends of the shells (S1,S2);
checking the height of at least one standard block whose height can be
varied;
setting the corrected bow to measure the bows at the intermediate points,
constructing bow matrices of both the 'U' shells, the exact radii at the
points of consideration calculated on the basis of these bow matrices;
computing the radii into diameter of the cylindrical formed shell by either
A-A matching or A-B matching ;
deriving the ovality at predetermined cross sections as ovality matrix; and
the appropriate matching for the 'U' shells is determined on the basis of
ovality matrix having the least of all the values of ovality at various cross
section.

A method of pre-matching of pressed 'U' shells with equal or different included angles and thickness adapting corrected bow technique consists of measuring the radii at the ends of the shells when at least one standard block whose height can be varied is being set to check the height. The corrected bow being set to
measure the bows at the intermediate points when bow matrices of both the 'U' shells are constructed to calculate the exact radii at the points of consideration. The radii is computed into diameter of the cylindrical formed shell by either A-A matching or A-B matching. The ovality at predetermined cross sections being derived as ovality matrices when the appropriate matching for the 'U' shells is determined on the basis of this ovality matrices having the least of all the values of ovality at various cross sections.