DESCRIPTION

TITLE OF INVENTION: METHOD AND APPARATUS FOR DETERMINING REVOLUTION SPEEDS OF BLOWERS OF COOLING FURNACE

TECHNICAL FIELD

[0001] The present invention relates to a technique for determining revolution speeds of blowers installed in a cooling furnace.

BACKGROUND ART

[0002] In general, in a continuous annealing furnace in a steel strip manufacturing line, various zones are provided along a carrying route of steel strip, such as a heating zone (hereinafter also referred to as a "heating furnace") for heating a cold-rolled steel strip, a soaking zone for retaining a steel strip, which came out of the heating zone, at a predetermined temperature, a cooling zone (hereinafter also referred to as a "cooling furnace") for subsequently cooling the steel strip, and so on.

[0003] In such a continuous annealing furnace, there are performed operations such that respective end portions of steel strips are welded to form a series of continuous steel strip, which is passed continuously through the heating furnace and the cooling furnace. In order to enable continuous annealing, regarding the respective steel strips transferred to the heating furnace and the cooling furnace, the front end of a steel strip to be passed subsequently is welded sequentially to the rearmost end of a steel strip passed upstream of the heating furnace. Thus, in the heating furnace and the cooling furnace, the steel strips are constantly passed through continuously.

[0004] The cooling furnace is divided into plural zones, and the steel strip is cooled by air from respective blowers provided in the zones. Strip temperature control at the delivery of the cooling furnace for steel strip is performed by directly or indirectly varying manipulated variable, which are generally the revolution speeds of the blowers in the cooling furnace. In this case, revolution speed instruction values to the respective blowers of the zones are adjusted in respective revolution speed control equipments provided in the zones, and the control is performed so that the steel strip attain a targeted metallurgical property as a whole.

[0005] The ratio of the revolution speeds (load pattern) of the respective blowers of the zones is determined so that the steel strip attain the targeted metallurgical property at the delivery of the cooling furnace. For example, there are an even load pattern for all zones which distributes the revolution speeds of the blowers so as to perform even cooling in all the zones, a delivery-zone-high load pattern which distributes a high revolution speed to a blower provided in a delivery zone so that the nearer a zone to the cooling furnace delivery, the higher the cooling degree given to the blower installed in this zone, and the like. Then, the respective blower revolution speeds of the zones are determined so that the revolution speed ratio of the respective blowers of the zones becomes the defined ratio while the total cooling performance of all the zones is made to match the required performance.

[0006] When the load pattern is set, it is quite important to determine the revolution speed of each blower in consideration of durability and capability of this blower. When respective manipulated variable are controlled by distributing the load of the determined total manipulated variable to plural actuaters, regardless of upper and lower limit values of manipulated variable settable to the respective actuaters, it is necessary to prevent occurrence of error in the total manipulated variable while appropriately distributing the load of the total manipulated variable to the respective actuaters.

[0007] Patent Document 1 discloses a method for specifically distributing a total manipulated variable to respective heating equipments or respective blowers when the total manipulated variable and the load pattern of a heating furnace or a cooling furnace are determined (load distribution method). In the load distribution method which distributes the load of the determined total manipulated variable to plural actuaters , it is assumed that an manipulated variable calculated for an actuater according to a determined distribution ratio exceeds the range of upper and lower limit values. In this case, the manipulated variable to be distributed to the actuater concerned is set to one of the upper and lower limit values, and the remaining manipulated variable excluding the set manipulated variable is distributed among the remaining actuaters.

CITATION LIST PATENT LITERATURE

[0008] Patent Literature 1: Japanese Laid-open Patent Publication No. 2000-054033

SUMMARY OF INVENTION TECHNICAL PROBLEM

[0009] However, although the method disclosed in Patent Document 1 is able to distribute a ratio of blower revolution speeds (load pattern) determined in advance to blowers installed in respective zones, there arises a problem that there occur cases where it is not possible to supply the blow volume needed in the entire cooling furnace.

[0010] This would not be a problem in the cases where the cooling performances of respective blowers installed in zones are even as in a newly built cooling furnace facility, but such a problem may occur frequently when blowers which differ in cooling performance are installed in the process of updating an aged facility like, for example, a cooling furnace facility that has been used for many years.

[0011] For example, this is a problem that a required blow volume in the cooling furnace cannot always be obtained even when the respective revolution speeds of blowers are determined, due to uneven blow volumes (hereinafter referred to as "cooling performance") obtained at a unit revolution speed of the blowers provided in respective zones of the cooling furnace, or due to that the blow volume obtained at the same revolution speed when a blower is updated is not always the same.

[0012] In other words, when the cooling performance of a blower provided in a first zone and the cooling performance of a blower provided in a second zone are different, or when a blower is updated in a specific zone, a difference is made in the blow volume to be generated even at the same revolution speed. Accordingly, just determining the revolution speed of the blower does not cause the total blow volume of the cooling furnace to be a specified value, and consequently, the cooled steel strip cannot obtain the targeted metallurgical property.

[0013] The present invention has been made in view of the above-described problem, and an object thereof is to enable determination blower revolution speeds by which a blow volume sufficient for appropriately cooling a steel strip can be provided.

SOLUTION TO PROBLEM

[0014] The gist of the present invention is as follows .

(1) A method for determining revolution speeds ri [rpm] of blowers of a cooling furnace when
a desirable ratio of revolution speeds r^ of i-th (i = 1 to k) blowers installed in a cooling furnace is given as
n: r2:r3: . . . : rk = wi: w2: w3 : . . . : wk, maximum values ri max [rpm] of the revolution speeds of the i-th (i = 1 to k) blowers are given as rl max/ ^2 max/ r3 max / • • • i Xk max*
minimum values rx min [rpm] of the revolution speeds of the i-th (i = 1 to k) blowers are given as
^1 min/ ^2 min/ ^3 min/ • • • / ^k min/ and a preferred total blow volume of the entire cooling furnace is given as B [Nm3/hr] , the method having:

obtaining cooling performance coefficients cti [Nm3/hr•rpm] of the i-th (i = 1 to k) blowers;

when the revolution speeds ri of the i-th (i = 1 to k) blowers are determined, calculating a first to a k-th tentative revolution speed rTi [rpm] sequentially as rTi = B X Wi/(wi X a i + W2 X a2 + w3 X a3 + ... + wk X a k) , rT2 = (B - ri X a i) X w2/(w2 X a 2 + w3 X a3 + ... + Wk X a k) ,
rT3 = (B - (ri X a i + r2 X a 2) ) x w3/(w3 X a3 + ... + wk X a k) / and
rTi = (B - (ra X a x + r2 X a 2 + r3 X a3 + ... + ri-i X tti-i)) X Wi/(Wi X a± + ... + wk X a k) , and for each i-th (i = 1 to k) blower, employing the calculated rTi as ri when T ^i max -■* £ i -"* ^i minr employing r± max as ri when rTi ^ ri max, or
employing ri min as r± when ri mm ^ rTi; and when a ratio of the employed blower revolution speeds ri is ri: r2 : r3: . . . : rk = 0.8wi to 1.2w1:0.8w2 to 1.2w2:0.8w3 to 1. 2w3: . . . : 0.8wk to 1.2wk and a total blow volume Tb [Nm3/hr] obtained by Tb = ri X ai + r2 X a 2 + r3 X a3 + ... + rk X a k satisfies
0.99B S Tb ^ 1.01B, determining the employed blower revolution speeds ri as the revolution speeds of the blowers.

(2) A method for determining revolution speeds rA of blowers of a cooling furnace when a desirable ratio of revolution speeds ri [rpm] of i-th (i = 1 to k) blowers installed in a cooling furnace is given as
ri: r2 : r3 : . . . : rk = Wi: w2 : w3 : . . . : wk, maximum values r^ max [rpm] of the revolution speeds of the i-th (i = 1 to k) blowers are given as ^1 maxf r2 max/ ^3 max/ • • • / ^k max, minimum values r± min [rpm] of the revolution speeds of the i-th (i = 1 to k) blowers are given as rl min/ r2 minf r3 min/ • • • t rk minr and a preferred total blow volume of the entire cooling furnace is given as B [Nm3/hr] , the method having:

obtaining cooling performance coefficients ai [NmVhr • rpm] of the i-th (i = 1 to k) blowers;
when the revolution speeds ri [rpm] of the i-th (i = 1 to k) blowers are determined, calculating a k-th to a first tentative revolution speeds rTi [rpm] sequentially as

rTk = B X wic/(wi X a i + w2 X a2 + w3 X a3 + ... + wk X ak) ,
rTk-i = (B - rk X ak) X wk_i/(wi X a 1 + w2 X a2 + w3 X a 3 + ... + wk_i X a k-i) ,

r\-2 = (B - (rk X a k + rk_i X ak-i)) X wk.2/(wi X a 1 + w2 X a 2 + w3 X a 3 +. . . . + wk-2 X ak-2) , and

rTi = (B - (rk X ak + rk_i X a k.x + rk-2 X a k-2 + ... + ri + i X ciiti)) X Wi/(wiOi + ... + wi X a i) , and for each i-th (i = 1 to k) blower, employing the calculated rTi as ri when
ri max ^ r i > Ti min/ employing n max as r± when rTi ^ rx max, or employing rA min as rA when ri mm ^ rTi; and when a ratio of the employed blower revolution speeds ri is ri: r2:r3:. . . : rk

= 0.8wi to 1.2wl:0.8w2 to 1.2w2:0.8w3 to
1. 2w3: . . . : 0 . 8wk to 1.2wic and

a total blow volume Tb [Nm3/hr] obtained by Tb = ri X a i + r2 X a2 + r3 X a3 + . . . + rk X
a k satisfies 0.99B ^ Tb ^ 1.01B, determining the employed blower revolution speeds ri as the revolution speeds of the blowers.

(3) A method for determining revolution speeds r^ of blowers of a cooling furnace when

a desirable ratio of revolution speeds ri [rpm] of i-th (i = 1 to k) blowers installed in a cooling furnace is given as ri:r2:r3: . . . :rk = wx: w2 : w3 : . . . : wk,

maximum values rA max [rpm] of the revolution speeds of the i-th (i = 1 to k) blowers are given as
^1 max i ^2 max/ ^3 max/ • • • i ^k max/

minimum values ri min [rpm] of the revolution speeds of the i-th (i = 1 to k) blowers are given as
^1 min/ ^2 min/ ^3 rain/ • • ■ / ^k min/ and

a preferred total blow volume of the entire cooling furnace is given as B [Nm3/hr], the method having:
obtaining cooling performance coefficients mi [Nm3/hr•rpm] of the i-th (i = 1 to k) blowers;
calculating revolution speeds rTi [rpm] of the i-th (i = 1 to k) blowers by

rTi = B X Wi/{ £i=1k (Wi X ai)}; and

comparing a number x of blowers in which i that does not satisfy

r- ^ rT> > r-
J-1 max = a. j = i.! mm

exists in a first half from a center of i = 1 to k and a number y of blowers in which i exists in a second half from the center, and

using the method for determining the revolution speed of the blower of the cooling furnace described in above (1) when x ^ y, or

using the method for determining the revolution speed of the blower of the cooling furnace described in above (2) when x < y.

(4) The method for determining the revolution speeds of the blowers of the cooling furnace
described in any one of above (1) to (3), wherein blow volumes bi [Nm3/hr] and the revolution speeds ri of the blowers are measured, and the cooling performance coefficients at of the blowers are obtained by
<*i = bi/ri.

(5) An apparatus for determining revolution speeds ri of blowers of a cooling furnace when
a desirable ratio of revolution speeds ri [rpm] of i-th (i = 1 to k) blowers installed in a cooling furnace is given as ri: r2 : r3: . . . : rk = wi: w2: W3 : . . . : Wt, maximum values rA max [rpm] of the revolution speeds of the i-th (i = 1 to k) blowers are given as ri max; £"2 max/ r3 max r • • • i ?k max r

minimum values ri min [rpm] of the revolution speeds of the i-th (i = 1 to k) blowers are given as
rl mini r2 mint ^3 min/ • • • / ^k min/ ana

a preferred total blow volume of the entire cooling furnace is given as B [NrnVhr], the apparatus having:

a unit calculating by using cooling performance

coefficients aj [Nm3/hr • rpm], when the revolution speeds ri of the i-th (i = 1 to k) blowers are determined, a first to a k-th tentative revolution speed rTi [rpm] sequentially as
rTi = B X wx/(wi X a i + w2 X a 2 + w3 X a3 + ... + wk X ak) ,
rT2 = (B - ri X ai) X w2/(w2 X a 2 + w3 X a3 + ... + wk X a k) ,
rT3 = (B - (ri X ttl + r2 X a2)) X w3/(w3 X a3 + ... + Wjj X a k) , and
rTi = (B - (ri X a i + r2 X a 2 + r3 X a3 + ... + ri-i X ai-i)) X wi/(Wi X ai + ... + wk X ak), and for each i-th (i = 1 to k) blower,
employing the calculated rTi as rA when
ri max -* £ i ^ r^ min/
employing r± max as ri when
T >.
X i = ri max/ Or
employing r± min as r± when
ri min ^ rTi; and
a unit determining, when a ratio of the employed blower revolution speeds ri is ri: r2:r3: . . . : rk

= 0.8wi to 1.2w1:0.8w2 to 1.2w2:0.8w3 to
1.2w3:...:0.8wk to 1.2wk and
a total blow volume Tb [Nm3/hr] obtained by
Tb = r] X a i + r2 X a2 + r3 X a3 + . . . + rk X
a k
satisfies
0.99B ^ Tb ^ 1.01B, the employed blower revolution speeds r± as the revolution speeds of the blowers.
(6) An apparatus for determining revolution speeds ri of blowers of a cooling furnace when
a desirable ratio of revolution speeds ri [rpm] of i-th (i = 1 to k) blowers installed in a cooling furnace is given as
ri: r2: r3: . . . : rk = wi: w2 : w3: . . . : wk,
maximum values ri max [rpm] of the revolution speeds of the i-th (i = 1 to k) blowers are given as
rl max / r2 max/ £3 max/ • • • / rk max/
minimum values ri min [rpm] of the revolution speeds of the i-th (i = 1 to k) blowers are given as
^1 min/ ^2 min/ r3 min/ • • • / rk rttin/ and
a preferred total blow volume of the entire cooling furnace is given as B [Nm3/hr], the apparatus having:
a unit calculating by using cooling performance coefficients a i [NmVhr • rpm], when the revolution speeds r± of the i-th (i = 1 to k) blowers are determined, a k-th to a first tentative revolution speed rTi [rpm] sequentially as

rTk = B X wk/(Wi X a j + w2 X a2 + w3 X 03 + ... + wk X a k) ,
rTk-i = (B - rk X ak) x wk-i/(wx X a 1 + w2 X a 2 + w3 X a 3 + ... + wk-i X ak_i),
rTk.2 = (B - (rk X ak + rk.x X ak-i)) X wk.2/(wx X a 1 + w2 X a 2 + w3 X a3+ ... + wk-2 X ak-2), and
rTi = (B - (rk X ak + rk-i X a k_i + rk.2 X ak-2 + ... + ri+i X ai+i)) X Wi/(wiai + ... + wA X a ±) , and for each i-th (i = 1 to k) blower,
employing the calculated rTi as ri when
T ^i max ^ £ i ■> £± mini
employing r± max as ri when
^ i = ri max/ OJT
employing ri roi„ as ri when
r± min ^ rTi; and
a unit determining, when a ratio of the employed blower revolution speeds ri is
r'i: r2:r3: . . . : rk = 0.8Wi to 1.2wx:0.8w2 to 1.2w2:0.8w3 to 1.2w3:...:0.8wk to 1.2wk and a total blow volume Tb [Nm3/hr] obtained by
Tb = rj. X ai + r2 X a 2 + r3 X a3+ ... +rkX a ic satisfies
0.99B ^ Tb ^ 1.01B, the employed blower revolution speeds r± as the revolution speeds of the blowers.
(7) An apparatus for determining revolution speeds rA of blowers of a cooling furnace when

a desirable ratio of revolution speeds ri [rpm] of i-th (i = 1 to k) blowers installed in a cooling furnace is given as
r1:r2:r3:...:rk.= Wi: w2 : w3: . . . : wk, maximum values rj max [rpm] of the revolution speeds of the i-th (i = 1 to k) blowers are given as
^1 max/ ^2 max / ^-3 max / • • • / ^k max /
minimum values ri min [rpm] of the revolution speeds of the i-th (i = 1 to k) blowers are given as
£l min/ r2 min/ £"3 min/ • • • / r^ min/ and
a preferred total blow volume of the entire cooling furnace is given as B [Nm3/hr] , the apparatus having:
a unit obtaining cooling performance coefficients ai [Nm3/hr • rpm] of the i-,th (i = 1 to k) blowers;
a unit calculating revolution speeds rTi [rpm] of the i-th (i = 1 to k) blowers by
rTi = B X Wi/{Ei=1k(Wi X cti)}; and
a unit comparing a number x of blowers in which i that does not satisfy
r- > rT- ^ r.
J-1 max = J- x — J-i min
exists in a first half from a center of i = 1 to k and a number y of blowers in which i exists in a second half from the center, and
using the apparatus for determining the revolution speed of the blower of the cooling furnace described in above (5) when x ^ y, or
using the apparatus for determining the revolution of the blower of the cooling furnace

described in above (6) when x < y.
ADVANTAGEOUS EFFECTS OF INVENTION [0015] According to the present invention, a significant effect is exhibited such that the revolution speeds of the blowers can be determined by which a blow volume sufficient for appropriately cooling a steel strip can be provided even for, for example, blowers in a cooling furnace facility which has been used for many years.
BRIEF DESCRIPTION OF DRAWINGS
[0016] [Fig. 1] Fig. 1 is a diagram illustrating a structure of an apparatus for determining revolution speeds of blowers according to an embodiment.
[Fig. 2] Fig. 2 is a diagram illustrating an example of a blower cooling furnace.
[Fig. 3] Fig. 3 is a diagram for describing examples.
DESCRIPTION OF EMBODIMENTS
[0017] Hereinafter, preferred embodiments of the present invention will be described with reference to the attached drawings.
(Cooling performance coefficient cti)
The case where a cooling zone is divided into a
first zone to a k-th zone in a cooling furnace will
be described below.
Fig. 2 is an example of a blower cooling furnace.

The blower cooling furnace 1 has a roll 3, and a steel strip 2 is carried in a carrying direction 8. Further, air cooled in a heat exchanger 7 is sent to a wind box 6 by a blower 4 via a pipe 9, so as to cool the steel strip 2. In the example of Fig. 2, the cooling furnace is divided into four zones, and the steel strip 2 is cooled by air from the blower 4 provided in each zone.
The blow volume b± [Nm3/hr] of each blower 4 can be calculated by inserting an orifice 5 in the middle of the pipe 9 and measuring a pressure loss, as illustrated in Fig. 2. Note that [Nm3/hr] is a flow rate converted into that of a standard condition (1 atm, 0°C). Normally, the orifice 5 is not inserted because it becomes a disturbance. Further, the revolution speed rA [rpm] of a blower can be measured with a not-illustrated revolution counter attached to the blower.
[0018] As a result of intense study and development, the present inventors have found that, for a blower installed in an i-th zone (i = 1 to k), a relation
b± = ri X a i . . . (1) using a cooling performance coefficient a± [Nm3/hr• rpm], which is a fixed value, is established between the revolution speed ri [rpm] and the blow volume bi [Nm3/hr].
[0019] Therefore, the cooling performance coefficient aA can be calculated by
m = bi/r± ... (1)'.

The cooling performance coefficient a± is a value determined in every blower, and is obtained by measuring the air amount bi and the revolution speed ri of the blower as described above. [0020] (Total blow volume B)
When cooling a steel strip, a preferred total blow volume B [Nm3/hr] exists for a total blow volume Tb in the cooling furnace, and it is important to match the total blow volume Tb with the preferred total blow volume B. Here, the total blow volume Tb can be calculated by
Tb = 2i=ikbi = £i=1k(ai X r±) ... (2). When the preferred total blow volume B is determined, the preferred total blow volume B is calculated based on a strip thickness, an entry side target strip temperature, an delivery side target strip temperature, and a line speed actual performance value. In general, the preferred total blow volume B tends to be large when the strip thickness is large, the entry side target strip temperature is high, or the delivery side target strip temperature is low. [0021] (Consideration of a revolution speed ratio of the blowers and upper and lower limit values of revolution speeds ri)
A desirable ratio of the revolution speeds ri of the blowers to be given for the steel strip to exhibit a metallurgical effect is given as
ri: r2 : r3: . . . : rk = wi: W2 : W3 : . . . : w* ... (3). By determining the revolution speeds ri of the blowers

with this ratio, the steel strip can obtain a targeted metallurgical property at the cooling furnace exit. It is possible to give any value that satisfies equation (3) to Wi, which is determined based on usage records and serviceable lives of the blowers. At this time, the revolution speeds ri of the blowers can be calculated using a constant u by
ri = u ' wi . . . (4) . [0022] When there is no limit for the upper and lower limit values for the revolution speeds n of the blowers, equations (1) to (4) are used to formally calculate a preferred revolution speed ri as follows.
B = Tb = 2i=1kbi = 2i=ik(ri X tti) = ^Ei=1k(Wi X
Oi)
H = B/{ 2i=1k(Wi X a±) }
r± = n ' Wi = B • Wi/{ 2i=1k(Wi X ai)} ... (5) bi = tti X ii = B X en X wi/{Ei = 1k(wi X Bl)] [0023] However, when a maximum value (upper limit value) ri max and a minimum value (lower limit value) ri min of the revolution speed exist for each blower, the blower revolution speed rA = bi/oi which gives the blow volume bA formally calculated by equation (5) does not always fall within the range of the upper and lower limit values. When the blower revolution speed ri of each blower is calculated and it exceeds the upper and lower limit values, it is necessary to select one of the upper limit value and the lower limit value that is close to the calculated value. [0024] Thus, as will be described in the following

embodiment, even when the maximum value ri max and the minimum value ri min exist for the revolution speed ri of each blower, the revolution speed ri of each blower is optimized so that the total blow volume Tb of the cooling furnace satisfies the preferred total blow volume B. This will be described in detail below. [0025] [First Embodiment]
A first embodiment is a method for determining revolution speeds ri of k blowers installed in respective zones of the blower cooling furnace. [0026] (Step 1) When the revolution speeds of the blowers are determined, following (a) to (d) are given.
(a) Preferred total blow volume B in the cooling furnace when cooling a steel strip
(b) Desirable ratio of the revolution speeds n of the blowers
ri:r2:r3: .. . :rk = wi:w2:W3 : .. . : wk ... (3)
(c) Maximum value ri max [rpm] of the revolution speeds
of the blowers
ri max 1 r2 max* ^3 max i • • • / rjc max
(d) Minimum value ri min [rpm] of the revolution speeds
of the blowers
ri min, r2 miiw ^3 mint • • • i £]< min
[0027] (Step 2) The cooling performance coefficients cti of the blowers are obtained. As described above, the cooling performance coefficient a± of a blower can be obtained by measuring the blow volume bi and the revolution speed r± of the blower and by equation

(1)'.
[0028] (Step 3) The revolution speeds r± of the blowers are calculated following the procedure below sequentially from the first blower to the k-th blower. In each order, first a tentative revolution speed rT± [rpm] is calculated, and the revolution speed ri is determined by comparison with the maximum value r± max and the minimum value ri min. [0029] First, for i = 1,
rTi = B X wi/(wi X a! + W2 X a2 + W3 X as + ... + wk X a k) ... (6-1) is calculated. Then, ri = rTi is employed when
T rl max > t 1 > ri min/
^i = ri max is employed when
rTi ^ ri max, or ri = ri min is employed when
L 1 mm = L 1 •
[0030] Next, for i = 2, using the revolution speed ri calculated already,
rT2 = (B - rx X ai) X w2/(w2 X a 2 + «3 x «3 + ... + v/k X on) ... (6-2) is calculated. Then, r2 = rT2 is employed when
^2 max > r 2 > ^2 min/
^2 = r2 max is employed when
rT2 ^ r2 max, or r2 = r2 min is employed when
J-2 mm = r 2 •

[0031] Thereafter, for i = 3, using ri and r2 calculated already,
rT3 = (B - (n X ai + r2 X ct2)) X w3/(w3 X a3 + ... + wk X at) ••■ (6-3) is calculated similarly. Then, r3 = rT3 is employed when
T r3 max > T 3 > r3 miiw
r3 = r3 max is employed when
rT3 ^ r3 maxr or r3 = r3 nin is employed when
r- > r-T
-»- 3 min = -I- 3 •
[0032] For an i-th order, using ri to ri-i calculated already,
rTi = (B - (ri X a i + r2 X a2 + r3 X a3 + ... + ri-i X ai-i)) X Wi/(wi X aj + ... + wk X ak) ... (6-i)
is calculated. Then, ri = rTi is employed when
£i max -* ^ i ^ ^i min/
^i = rA max is employed when
rTi ^ ri max, or ^i = ri min is employed when
r- > rT-
[0033] The above calculations are performed for i = 1 to k, and for i = k, when
^l max ■> % k > rk min/
a substitution
T
rk = r k is made, and thereby the revolution speeds rA of all

the blowers of i = 1 to k are determined. By making
the blowers rotate at the respective revolution
speeds ri, the total blow volume Tb becomes a value
equal to the preferred total blow volume B.
[0034] (Correction of displacement from the optimal
solution)
By nature, use of the revolution speeds ri calculated by equation (5) should enable optimal cooling control. However, since the maximum value ri max and the minimum value ri min for the revolution speed exist for each blower, the tentative revolution speed rTi is calculated first for the revolution speed of a blower as described above, and by comparison with the maximum value ri max and the minimum value r± min, a revolution speed rA modified to be within the range of the maximum value ri max and the minimum value ri min is employed. As a result of this, the ratio of the revolution speeds ri deviate from the optimal ratio expected by equation (3).
As a result of intense study and development, the present inventors have found that, when the ratio of the revolution speeds ri of the blowers satisfy
ri: r2:r3: . . . : rk
0.8wi to 1.2wi:0.8w2 to 1.2w2:0.8w3 to 1.2w3: . . . : 0 . 8wk to 1.2wk ... (7),
the blowers can be operated without any problem, and the desirable metallurgical property can be given to the cooled steel strip. Note that in the present invention, for example, the description "0.8wjc to

1.2wk" means 0.8wk or more and 1.2wk or less. [0035] Further, for i = k, when
^kmax > r it > rfcmin,
a substitution
rk = rxk is made, and thereby the revolution speeds ri of all the blowers of i = 1 to k are determined. By making the blowers rotate at the respective revolution speeds rir the total blow volume Tb becomes a value equal to the preferred total blow volume B.
However, for i = k, when rTk ^ rkmax or rkmin ^ rTk/ substitution of the revolution speed rk from the tentative revolution speed rTk to the maximum value ricmax or the minimum value rkmin results in a mismatch between the total blow volume Tb of equation (2) and the preferred total blow volume B.
As a result of intense study and development, the present inventors have found that, when the total blow volume Tb satisfies
0.99B ^ Tb ^ 1.01B ... (8) , the blowers can be operated without any problem, and the desirable metallurgical property can be given to the cooled steel strip.
[0036] (Step 4) After step 3 is finished, the following step is performed.
When the ratio of the revolution speeds ri of the blowers employed in step 3 satisfies
ri: r2:r3:. . . : rk = 0.8wi to 1.2wi:0.8w2 to 1.2w2:0.8w3 to

1.2w3: . . . : 0. 8wic to 1.2wk ... (7) and
Tb = 2i=ikbi = Si=1k(ai X ri) ... (2) calculated for the employed revolution speeds ri of the blowers satisfies
0.99B ^ Tb ^ 1.01B ... (8) , the revolution speeds r^ of the blowers employed in step 3 are determined as the revolution speeds of the blowers.
[0037] Here, an example of a step of specifically carrying out the calculation of equation (7) will be described. For each of i = 1 to k, when
0.8 ^ (ri/E1=1kri)/(wi/Si=1kwi) ^ 1.2 ... (9) is satisfied, it can be recognized as satisfying equation (7).
[0038] As a result of step 4, when equation (7) and equation (8) are satisfied, the blowers can be operated without any problem, and the desirable metallurgical property can be given to the cooled steel strip. On the other hand, when one or both of equation (7) and equation (8) is or are not satisfied, for example, another preferred solution can be found by implementing a second embodiment, which will be described later.
[0039] Fig. 1 illustrates a structure of a revolution speed determining apparatus for blowers according to the first embodiment. The revolution speed determining apparatus for blowers is constituted of a computer including a CPU, a ROM, a RAM, and so on.

101 denotes an input unit, with which the desirable ratio of the revolution speed r±, the maximum value ri max, the minimum value r± min# the preferred total blow volume B for an i-th (i = 1 to k) blower installed in the cooling furnace, the separately obtained cooling performance coefficients ai for blowers, and so on are inputted. [0040] 102 denotes an employment revolution speed calculating unit which executes above-described step 3. Specifically, when the revolution speeds ri of the i-th (i = 1 to k) blowers are determined, using the cooling performance coefficients ai for blowers, first, a first to a k-th tentative revolution speed rTi are calculated sequentially as
rTi = B X wi/(Wi X a x + w2 X a 2 + w3 X a3 + ... + wk X ak) ... (6-1) ,
rT2 = (B - ri X a i) X w2/(w2 X a 2 + w3 X a3 + . . . + wk X a k) ... (6-2) ,
rT3 = (B - (ri X ttt + r2 X a2)) X w3/(w3 X a 3 + ... + wk X an) . . . (6-3) , and
rTi = (B - (ri X a x + r2 X a2 + r3 X a3 + ... + n-i X OH)) X Wi/(wi X a± + ... + wk X «k) ... (6-i), and for each i-th (i = 1 to k) blower, the calculated rTi is employed as rA when
rimax > ri > rimin,
r± max is employed as rt when
r i = ri max/ or ri min is employed as ri when
■L i min =s i- I •

[0041] 103 denotes a comparison judging unit which executes above-described step 4. Specifically, when a ratio of the blower revolution speeds ri employed in the employment revolution speed calculating unit 102 is
ri: r2:r3: . . . : rk = 0.8wi to 1.2wi:0.8w2 to 1.2w2:0.8w3 to 1.2w3:...:0.8wk to 1.2wk ... (7) and the total blow volume Tb obtained by
Tb = ri X ai + r2 X a 2 + r3 X a 3 + . . . + rk X
«k • • • (2 ) satisfies
0.99B ^ Tb ^ 1.01B ... (8) , the blower revolution speeds ri employed in the employment revolution speed calculating unit 102 are employed as the revolution speeds of the blowers. [0042] [Second Embodiment]
A second embodiment is a method for determining r revolution speeds rA of k blowers installed in respective zones of the blower cooling furnace. Differences from the first embodiment will be mainly described below, and descriptions of items common to the first embodiment are omitted.
[0043] In the second embodiment, step 1 and step 2 are similar to those in the first embodiment. [0044] In step 3, in the first embodiment, the revolution speeds rA of the first to the k-th blower are obtained sequentially. On the other hand, in the second embodiment, the revolution speeds ri of the k-

th to the first blower are calculated sequentially following the procedure below. In each order, first a tentative revolution speed rTi is calculated, and the revolution speed ri is determined by comparison with the maximum value ri max and the minimum value ri
rain •
[0045] First, for i = k,
rTk = B X wk/(Wi X ai+w2 X 0*2 + w3 X a3+ ... + wk X a ic) ... (6-k) '
is calculated. Then, similarly to the first embodiment, rk = rTk is employed when
^k max -> r k > rk min,
rk = rk max is employed when
rTk ^ rk max, or ^k = rk min is employed when
£"k min = £ k •
[0046] Next, for i = k - 1, using the revolution speed rk calculated already,
rTk-i = (B - rk X a k) X wk-i/(wi X a j. + w2 X a2 + w3 X a3 + ... + wjc-i X ajc-i) ... (6-(k-l))' is calculated. Then, similarly to the first embodiment, r(k-i) = rT(k-i) is employed when
^(k-l) max > r (k-i) > r(k_i) min,
r(k-i) = r(k-i) max is employed when
r (k-i) & r(k_i) max, or r(k-i) = r(k-i, roin is employed when
£(k-l) min = r (k-i) .

[0047] Thereafter, calculations are performed sequentially, and for an i-th order, using rk to ri+i calculated already,
rTi = (B - (rk X ak + rk_i X ak-i + rk-2 x a k-2 + . . . + ri + 1 X ai+i) ) X Wj./ (wi X a i + . . . + Wi X a i) ... (6-i)'
is calculated, and then similarly to the first embodiment, ri = rTi is employed when
T ri max -> E i > £i min r
r± = ri max is employed when
rTi ^ r± max, or ri = r± min is employed when
r' ■ 5: rT-[0048] The above-described calculations are performed for i = k to 1, and for i = 1, when
rl max ^ r i > ri min,
a substitution
T
ri = r'i is made, and thereby the revolution speeds r± of all the blowers of i = k to 1 are determined. By making the blowers rotate at the respective revolution speeds ri; the total blow volume Tb becomes a value equal to the preferred total blow volume B. [0049] In step 4, calculations are performed similarly to step 4 of the first embodiment, and when equation (7) and equation (8) are satisfied, the blowers can be operated without any problem, and the desirable metallurgical property can be given to the

cooled steel strip.
[0050] A difference between the first embodiment and the second embodiment is the order of calculations of the tentative revolution speeds rTi of the i-th (i = 1 to k) blowers.
In the first embodiment, the revolution speeds rj. of the blowers are calculated in the order from the first blower to the k-th blower, but in the second embodiment, it is calculated in the order from the k-th blower to the first blower.
[0051] When the revolution speed ri of an i-th blower is calculated and the calculated value exceeds the maximum value ri max or the minimum value r^ min, the maximum value ri max or the minimum value ri min has to be employed, and in this case, the revolution speeds of other blowers are affected, which may result in that equation (7) as the condition for the ratio of the revolution speeds ri of the blowers i and/or equation (8) as the condition for the total blow volume Tb are/is not satisfied. [0052] In this case, when the calculation is performed in the order from the first blower to the k-th blower, one or both of equation (7) and equation (8) is or are not satisfied, but when the calculation is performed in the order from the k-th blower to the first blower, it is possible that both equation (7) and equation (8) are satisfied. Further, the inverse case is also possible.
Accordingly, for example, determination of the

blower revolution speeds rA is attempted first by the first embodiment, and when it is not determined, the determination is then attempted by the second embodiment. Alternatively, determination of the blower revolution speeds ri is attempted first by the second embodiment, and when it is not determined, the determination is then attempted by the first embodiment.
[0053] Note that when the optimal solution satisfying equation (7) and equation (8) cannot be found either by the first embodiment or the second embodiment, there is a possibility that the revolution speed range of the blower of one of i = 1 to k is too narrow. Thus, the blower concerned may be replaced, and a countermeasure for widening the revolution speed possible range of the blower may be taken. Alternatively, it can also be assumed that there is a problem in equation (3) defined in the cooling design for the product type concerned, and hence the cooling design may be reviewed, and equation (3) may be reviewed in consideration of a revolution speed ratio that does not overload respective blowers. [0054] [Third Embodiment]
A third embodiment is a method for determining revolution speeds ri of blowers by selecting and using one of the first embodiment and the second embodiment. [0055] In the third embodiment, step 1 and step 2 are similar to those of the first embodiment.

[0056] In a stage prior to execution of step 3,
tentative revolution speeds rTi of the i-th (i = 1 to k) blowers are calculated by
rTi = B X Wi/iZwMwi X oil) ... (5). Then, a number x of blowers in which i that does not satisfy
£i max = r i = r± min
exists in a first half from a center of i = 1 to k and a number y of blowers in which i exists in a second half from the center are compared. Note that when k is an even number, the first half refers to the range of 1 ^ i ^ k/2, and the second half refers to the range of k/2 < i ^ k. Further, when k is an odd number, the center value (for example, 3 when k = 5, or 4 when k = 7) may be treated as being excluded from both the first half and the second half or be treated as being included in both the first half and the second half.
As a result, the method of the first embodiment is used when
x ^ y, or the method of the second embodiment is used when
x < y. [0057] In the third embodiment, when one of the method of the first embodiment and the method of the second embodiment is selected and used, it is judged which of them is suitable to be used.
This is because, when the tentative revolution speed rTi of the i-th (i = 1 to k) blower calculated

by equation (5) exceeds the upper and lower limit values, it has to be fixed to the upper limit value or the lower limit value, and in this case, excess and deficiency of blow volume should be distributed to other blowers, and hence processing in advance one that is more likely to exceed the upper and lower limit values in this manner allows to determine an appropriate revolution speed.
EXAMPLE
[0058] (Example 1)
As example 1, present invention examples 1-1 to 1-5 of applying the first embodiment are illustrated in Fig. 3. [0059] (Present invention example 1-1)
In a facility in which the upper limit values of revolution speeds of blowers of a cooling furnace constituting 4 zones of i = 1 to 4 are all 1800 [rpm], and the lower limit values are all 100 [rpm], it was required that the desirable ratio of the blower revolution speeds be Wi:w2:w3:w4 = 1:1:1:1, and the blower cooling furnace total blow volume B be 6000 [Nm3/hr].
As a result of measurement, it was found that the cooling performance coefficients cti [Nm3/hr•rpm] are a i = 1, o, z - 2, 0:3 = 3, a 4 = 4 .
[0060] When the tentative revolution speeds rTi [rpm] are calculated in accordance with the method described in the first embodiment,

r\ = 6000 X 1/(1 X1+1X2+1X3+1X4) = 600,
rT2 = (6000 - 600 X 1) X 1/(1 X2 + 1X3 + 1X 4) = 600,
rT3 = (6000 - 600 X 1 - 600 X .2) X 1/(1 X 3 + 1 X 4) = 600,
rT4 = (6000 - 600 X 1 - 600 X 2 - 600 X 3) X 1/(1 X 4) = 600,
are calculated, which are all within the range of the upper and lower limit values and thus are employed as the revolution speeds ri of the blowers. [0061] In this case, ri:r2:r3:r4 = 1:1:1:1, and hence there is no problem in the ratio of the revolution speeds.
Further, the respective blow volumes bi [Nm3/hr] of the blowers are calculated by equation (1) as
bx = 600 X 1 = 600,
b2 * 600 X 2 = 1200,
b3 = 600 X 3 = 1800,
b4 = 600 X 4 = 2400, resulting in
Tb = 600 + 1200 + 1800 + 2400 = 6000, and thus
6000 X 0.99 ^ 6000 ^ 6000 X 1.01 is satisfied.
Therefore, the employed revolution speeds x± of the blowers are determined as the blower revolution speeds. [0062] (Present invention example 1-2)

Differences from present invention example 1-1 are that wi:w2:w3:w4 = 2:1:1:1 was given, and as a result of measurement it was found that ai = 2, a2 = 2, aj3 = 3, a 4 = 4.
[0063] When the tentative revolution speeds rTi are calculated in accordance with the method described in the first embodiment, rT! to rT4 are calculated as 923, 462, 462, 462, respectively. All of them are within the range of the upper and lower limit values, and hence they are employed as the revolution speeds n of the blowers.
[0064] In this case, r1:r2:r3:r4 = 2:1:1:1, and hence there is no problem in the ratio of the revolution speeds.
Further, the respective blow volumes bi to b4 of the blowers are calculated as 1846, 924, 1386, 1848, respectively, resulting in
Tb = 1846 + 924 + 1386 + 1848 = 6004, and thus
6000 X 0.99 ^ 6004 ^ 6000 X 1.01 is satisfied.
Therefore, the employed revolution speeds ri of the blowers are determined as the blower revolution speeds. [0065] (Present invention example 1-3)
Differences from present invention example 1-1 are that Wi:w2tw3:w4 = 2:1:1:1 was given, and the blower cooling furnace total blow volume B was given as 13000. Further, as a result of measurement it was

found that ai =2, a2 = 2, aj =3, a4 = 4. [0066] When the tentative revolution speeds rTi are calculated in accordance with the method described in the first embodiment,
rTi = 13000 X 2/(2 X2 + 1X2 + 1X3 + 1X4) = 2000
is calculated, which exceeds the upper limit value 1800, and hence 1800 is employed as the revolution speed ri of the blower.
Further, rT2 = (13000 - 1800 X 2) X 1/(1 X 2 + 1 X 3 + 1 X 4) = 1044,
rT3 = (13000 - 1800 X 2 - 1044 X 2) X 1/(1 X 3 +1X4)= 1044,
rT4 = (13000 - 1800 - 2 X 1044 X 2 - 1044 X 3) X 1/(1 X 4) = 1044
are calculated, which are all within the range of the upper and lower limit values and thus are employed as the revolution speeds rA of the blowers. [0067] In this case, ri:r2:r3:r4 = 1.72:1:1:1, but
r i: r 2 : r 3 : . . . : r ic = 0.8wi to 1.2wi:0.8w2 to 1.2w2:0.8w3 to 1.2w3:...:0.8wk to 1.2wk
is satisfied, and hence there is no problem in the ratio of the revolution speeds.
Further, the respective blow volumes bi of the blowers are calculated by equation (1) as
bi = 1800 X 2 = 3600,
b2 = 1044 X 2 = 2088,
b3 = 1044 X 3 = 3132,

b4 = 1044 X 4 = 4176, resulting in
Tb = 3600 + 2088 + 3132 + 4176 = 12996, and thus
13000 X 0.99 ^ 12996 ^ 13000 X 1.01 is satisfied.
Therefore, the employed revolution speeds ri of the blowers are determined as the blower revolution speeds. [0068] (Present invention example 1-4)
Differences from present invention example 1-1 are that w1:w2:w3:w4 = 2:1:1:1 was given, and the blower cooling furnace total blow volume B was given as 13000. Further, as a result of measurement it was found that ax = 3, a2 = 3, a3 = 2, a 4 - 2. [0069] When the tentative revolution speeds rTi are calculated in accordance with the method described in the first embodiment,
rTi = 13000 X 2/(2 X3 + 1X3 + 1X2 + 1X2) = 2000
is calculated, which exceeds the upper limit value 1800, and hence 1800 is employed as the revolution speed ri of the blower.
Further, rT2 = (13000 - 1800 X 3) X 1/(1 X 3 + 1 X 2 + 1 X 2) = 1086,
rS = (13000 - 1800 X 3 - 1086 X 3) X 1/(1 X 2 +1X2)= 1086,
rT4 = (13000 - 1800 X 3 - 1086 X 3 - 1086 X 2) X 1/ (1 X 2) = 1086

are calculated, which are all within the range of the upper and lower limit values and hence are employed as the revolution speeds ri of the blowers. [0070] In this case, ri: r2 : r3:r4 •= 1.66:1:1:1, but
ri: r2 i r3 : . . . :ric = 0.8wi to 1.2wi:0.8w2 to 1.2w2:0.8w3 to 1.2w3:...:0.8wk to 1.2wk
is satisfied, and hence there is no problem in the ratio of the revolution speeds.
Further, the respective blow volumes bi of the blowers are calculated by equation (1) as
bi = 1800 X 3 = 5400,
b2 = 1086 X 3 = 3258,
b3 = 1086 X 2 = 2172,
b4 = 1086 X 2 = 2172, resulting in
Tb = 5400 + 3258 + 2172 + 2172 = 13002, and thus
13000 X 0.99 ^ 13002 ^ 13000 X 1.01 is satisfied.
Therefore, the employed revolution speeds ri of the blowers are determined as the blower revolution speeds. [0071] (Present invention example 1-5)
Differences from present invention example 1-1 are that Wi.-w2:w3:w4 = 1:1:1:2 was given, and the blower cooling furnace total blow volume B was given as 13000. Further, as a result of measurement it was found that «i = 2, a2 = 2, a3 = 3, a< = 3.

[0072] When the tentative revolution speeds rTi are calculated in accordance with the method described in the first embodiment,
rTx = 13000 X 1/(1 X2 + 1X2 + 1X3 + 2X3) = 1000,
rT2 = (13000 - 1000 X 2) X 1/(1 X2 + 1X3 + 2 X 3) = 1000,
rT3 = (13000 - 1000 X 2 - 1000 X 2) X 1/(1 X 3 +2X3)= 1000
are calculated, which are all within the range of the upper and lower limit values and hence are employed as the revolution speeds ri of the blowers.
However,
rT4 = (13000 - 1000 X 2 - 1000 X 2 - 1000 X 3) X 2/(2 X 3) = 2000
is calculated, which exceeds the upper limit value 1800, and hence 1800 is employed as the revolution speed r4 of the blower. [0073] In this case, ri:r2:r3:r4 = 1:1:1:1.80, but
ri: r2: r3: . . . : rk = 0.8w! to 1.2wi:0.8w2 to 1.2w2:0.8w3 to 1.2w3: . . .:0.8wk to 1.2wk
is satisfied, and hence there is no problem in the ratio of the revolution speeds.
However, the respective blow volumes bi of the blowers are calculated as
bx = 1000 X 2 = 2000,
b2 = 1000 X 2 = 2000,
b3 = 1000 X 3 = 3000,

b4 = 1800 X 3 = 5400, resulting in
Tb = 2000 + 2000 + 3000 + 5400 = 12400, and thus
12400 ^ 13000 X 0.99, and 0.99B ^ Tb ^ 1.01B is not satisfied.
Therefore, the blower revolution speed cannot be determined.
[0074] Accordingly, instead of the calculation method according to the first embodiment, the calculation method according to the second embodiment was employed, which enabled to obtain a result that satisfies 0.99B ^ Tb ^ 1.01B (see present invention example 2-3 of example 2). [0075] (Example 2)
As example 2, present invention examples 2-1 to 2-5 of applying the second embodiment are illustrated in Fig. 3. [0076] (Present invention example 2-1)
Respective conditions of present invention example 2-1 are the same as those of present invention example 1-1.
[0077] When the tentative revolution speeds rTi are calculated in accordance with the method described in the second embodiment,
rT4 = 6000 X 1/(1 X1 + 1X2 + 1X3 + 1X4) = 600,
rT3 = (6000 - 600 X 4) X 1/(1 X1 + 1X2 + 1X 3) = 600,

rT2 = (6000 - 600 X 4 - 600 X 3) X 1/(1 X 1 + 1 X 2) = 600,
rT! = (6000 - 600 X 4 - 600 X 3 - 600 X 2) X 1/ (1X1)= 600
are calculated, which are all within the range of the upper and lower limit values and hence are employed as the revolution speeds rA of the blowers. [0078] In this case, ri:r2:r3:r4 = 1:1:1:1, and hence there is no problem in the ratio of the revolution speeds.
Further, the respective blow volumes bi of the blowers are calculated by equation (1) as
bi = 600 X 1 = 600,
b2 = 600 X 2 = 1200,
b3 = 600 X 3 = 1800,
b4 = 600 X 4 = 2400, resulting in
Tb = 600 + 1200 + 1800 + 2400 = 6000, and thus
6000 X 0.99 =^ 6000 ^ 6000 X 1.01 is satisfied.
Therefore, the employed revolution speeds rA of the blowers are determined as the blower revolution speeds. [0079] (Present invention example 2-2)
Differences from present invention example 2-1 are that wi:w2:w3:w4 = 2:1:1:1 was given, and as a result of measurement it was found that ai =2, a2 = 2, a 3 = 3, a 4 = 4 .

[0080] When the tentative revolution speeds rTi are calculated in accordance with the method described in the second embodiment, rT4 to rTi are calculated as 462, 462, 463, 923, respectively. All of them are within the range of the upper and lower limit values, and hence they are employed as the revolution speeds ri of the blowers.
[0081] In this case, ri: r2 : r3: r4 = 2:1:1:1, and hence there is no problem in the ratio of the revolution speeds.
Further, the respective blow volumes bi to b4 of the blowers are calculated as 1846, 924, 1386, 1848, respectively, resulting in
Tb = 1846 + 924 + 1386 + 1848 = 6004, and thus
6000 X 0.99 ^ 6004 ^ 6000 X 1.01 is satisfied.
Therefore, the employed revolution speeds r± of the blowers are determined as the blower revolution speeds. [0082] (Present invention example 2-3)
Differences from present invention example 2-1 are that Wi:w2:w3:w4 = 2:1:1:1 was given, and the blower cooling furnace total blow volume B was given as 13000. Further, as a result of measurement it was
found that ai = 2, a2 = 2, a 3 = 3, a4 = 3. [0083] When the tentative revolution speeds rTi are calculated in accordance with the method described in the second embodiment,

rT4 = 13000 X 2/(1 X2 + 1X2 + 1X3 + 2X3) = 2000
is calculated, which exceeds the upper limit value 1800, and hence 1800 is employed as the revolution speed r4 of the blower.
Further, rT3 = (13000 - 1800 X 3) X 1/(1 X 2 + 1 X2+1X3)=1086,
rT2 = (13000 - 1800 X 3 - 1086 X 3) X 1/(1 X 2 +1X2)= 1086,
rTi = (13000 - 1800 X 3 - 1086 X 3 - 1086 X 2) X 1/(1 X 2) = 1086,
are calculated, which are all within the range of the upper and lower limit values and thus are employed as the revolution speeds ri of the blowers. [0084] In this case, ri:r2:r3:r4 = 1:1:1:1.66, but
ri: r2: r3: . . . : rk = 0.8wi to 1.2wi:0.8w2 to 1.2w2:0.8w3 to 1.2w3:...:0.8wk to 1.2wk
is satisfied, and hence there is no problem in the ratio of the revolution speeds.
Further, the respective blow volumes bi of the blowers are calculated by equation (1) as
bi = 1086 X 2 = 2172,
b2 = 1086 X 2 = 2172,
b3 = 1086 X 3 = 3258,
b4 = 1800 X 3 = 5400, resulting in
Tb = 2172 + 2172 + 3258 + 5400 = 13002, and thus

13000 X 0.99 ^ 13002 ^ 13000 X 1.01 is satisfied.
Therefore, the employed revolution speeds r± of the blowers are determined as the revolution speeds of the blowers. [0085] (Present invention example 2-4)
Differences from present invention example 2-1 are that wi:w2iW3:w4 = 2:1:1:1 was given, and the blower cooling furnace total blow volume B was given as 13000. Further, as a result of measurement it was
found that ai = 2, a 2 = 2, «3 = 3, a 4 = 4. [0086] When the tentative revolution speeds rTi are calculated in accordance with the method described in the second embodiment,
rT4 = 13000 X 1/(2 X2 + 1X2 + 1X3 + 1X4) = 1000,
rT3 = (13000 - 1000 X 4) X 1/(2 X2 + 1X2 + 1 X 3) = 1000,
rT2 = (13000 - 1000 X 4 - 1000 X 3) X 1/(2 X 2 +1X2)= 1000
are calculated, which are all within the range of the upper and lower limit values and hence are employed as the revolution speeds rA of the blowers.
However,
rTi = (13000 - 1000 X 4 - 1000 X 3 - 1000 X 2) X 2/ (2 X 2) = 2000,
is calculated, which exceeds the upper limit value 1800, and hence 1800 is employed as the revolution speed ri of the blower.

[0087] In this case, ri:r2:r3:r4 = 1.80:1:1:1, but
ri: r2: r3: . . . : rk = 0.8wi to 1.2wi:0.8w2 to 1.2w2:0.8w3 to 1.2w3:...:0.8wk to 1.2wk
is satisfied, and hence there is no problem in the ratio of the revolution speeds.
However, the respective blow volumes bi of the blowers are calculated by equation (1) as
bi = 1800 X 2 = 3600,
b2 = 1000 X 2 = 2000,
b3 = 1000 X 3 = 3000,
b4 = 1000 X 4 = 4000, resulting in
Tb = 3600 + 2000 + 3000 + 4000 = 12600, and thus
12600 ^ 13000 X 0.99, and 0.99B ^ Tb S 1.01B is not satisfied.
Therefore, the blower revolution speed cannot be determined.
[0088] Accordingly, instead of the calculation method according to the second embodiment, the calculation method according to the first embodiment was employed, which enabled to obtain a result that satisfies 0.99B ^ Tb ^ 1.01B (see present invention example 1-3 of example 1) . [0089] (Present invention example 2-5)
Differences from present invention example 2-1 are that Wi:w2:w3:w4 = 2:1:1:1 was given, and the blower cooling furnace total blow volume B was given

as 13000. Further, as a result of measurement it was found that oi = 3, a2 - 3, 03 = 2, a4 = 2. [0090] When the tentative revolution speeds rTi are calculated in accordance with the method described in the second embodiment,
rT4 = 13000 X 1/(2 X 3 + 1 X 3 + IX 2 + 1X2) = 1000,
rT3 = (13000 - 1000 X 2) X 1/(2 X3 + 1X3 + 1 X 2) = 1000,
rT2 = (13000 - 1000 X 2 - 1000 X 2) X 1/(2 X 3 +1X3)= 1000
are calculated, which are all within the range of the upper and lower limit values and hence are employed as the revolution speeds r± of the blowers.
However,
rT! = (13000 - 1000 X 2 - 1000 X 2 - 1000 X 3) X 2/ (2 X 3) = 2000,
is calculated, which exceeds the upper limit value 1800, and hence 1800 is employed as the revolution speed ri of the blower. [0091] In this case, ri:r2:r3:r4 = 1.8:1:1:1, but
rx: r2:r3: . . . : rk = 0.8wi to 1.2wi:0.8w2 to 1.2w2:0.8w3 to 1.2w3:...:0.8wk to 1.2wk
is satisfied, and hence there is no problem in the ratio of the revolution speeds.
However, the respective blow volumes bi of the blowers are calculated by equation (1) as
bi = 1800 X 3 = 5400,

b2 = 1000 X 3 = 3000,
b3 = 1000 X 2 = 2000,
b4 = 1000 X 2 = 2000, resulting in
Tb = 5400 + 3000 + 2000 + 2000 = 12400, and thus
12400 ^ 13000 X 0.99, and 0.99B ^ Tb ^ 1.01B is not satisfied.
Therefore, the blower revolution speed cannot be determined.
[0092] Accordingly, instead of the calculation method according to the second embodiment, the calculation method according to the first embodiment was employed, which enabled to obtain a result that satisfies 0.99B S Tb ^ 1.01B (see present invention example 1-4 of example 1). [0093] (Example 3)
As example 3, present invention examples 3-1 to 3-3 of applying the third embodiment are illustrated in Fig. 3. [0094] (Present invention example 3-1)
Differences from present invention example 1-1 are that w1:w2:w3:w4 = 1:1:1:2 was given, and the blower cooling furnace total blow volume B was given as 13000. Further, as a result of measurement it was
found that ai =2, a2 = 2, a$ =3, CM = 3.
[0095] When the tentative revolution speeds rTi are
calculated based on
rTi = B X Wi/{Zi-ik(Wi X at)} ... (5),

they become
r\ = 13000 X 1/(1 X 2 + 1X2 + 1X3 + 2X3) = 1000,
rT2 = 13000 X 1/(1 X2 + 1X2 + 1X3 + 2X3) = 1000,
rT3 = 13000 X 1/(1 X2 + 1X2 + 1X3 + 2X3) = 1000,
rT4 = 13000 X 2/(1 X2 + 1X2 + 1X3 + 2X3) = 2000,
where rT4 exceeds the upper limit value 1800. [0096] Since k = 4, when it is divided in two of a first half of 1 to 2 and a second half of 3 to 4 based on 2 resulted from dividing k by 2, none exceeds the upper and lower limit values in the first half, and one exceeds the upper and lower limit values in the second half. Therefore, the calculation is performed by the method of the second embodiment, which is already described in present invention example 2-3. [0097] (Present invention example 3-2)
Respective conditions of present invention example 3-2 are the same as those of present invention example 2-5.
[0098] When the tentative revolution speeds rTi are calculated based on
rTi = B X Wi/{ Zi-i'Mwi X aiM ... (5), they become
rTx = 13000 X 2/(2 X3 + 1X3 + 1X2 + 1X2) = 2000,

rT2 = 13000 X 1/(2 X3 + 1X3 + 1X2 + 1X2) = 1000,
rT3 = 13000 X 1/(2 X3 + 1X3 + 1X2 + 1X2) = 1000,
rT4 = 13000 X 1/(2 X3 + 1X3 + 1X2 + 1X2) = 1000,
where rT! exceeds the upper limit value 1800. [0099] Since k = 4, when it is divided in two of a first half of 1 to 2 and a second half of 3 to 4 based on 2 resulted from dividing k by 2, one exceeds the upper and lower limit values in the first half, and none exceeds the upper and lower limit values in the second half. Therefore, the calculation is performed by the method of the first embodiment, which is already described in present invention example 1-4. [0100] (Present invention example 3-3)
Respective conditions of present invention example 3-3 are the same as those of present invention example 2-4.

[0101] When the tentative revolution speeds rTi are calculated based on

rTi = B X Wi/{ 2i.1k(wi X oi)} ... (5), they become
rTi = 13000 X 2/(2 X3 + 1X3 + 1X2 + 1X2) = 2000,
rT2 = 13000 X 1/(2 X 3 + 1 X 3 + 1 X 2 + 1 X 2) = 1000,
rT3 = .1300 0 X 1/(2 X 3 + 1 X 3 + 1 X 2 + 1 X 2)

= 1000,
rT4 = 13000 X 1/(2 X3 + 1X3 + 1X2 + 1X2) = 1000,
where rTi exceeds the upper limit value 1800. [0102] Since k = 4, when it is divided in two of a first half of 1 to 2 and a second half of 3 to 4 based on 2 resulted from dividing k by 2, one exceeds the upper and lower limit values in the first half, and none exceeds the upper and lower limit values in the second half. Therefore, the calculation is performed by the method of the first embodiment, which is already described in present invention example 1-3.

[0103] In the foregoing, the present invention has been described with various embodiments. However, the present invention is not limited to these embodiments, and any modification and the like are possible within the range of the present invention.

INDUSTRIAL APPLICABILITY

[0104] The present invention can be used for determining the revolution speeds of blowers installed in, for example, a cooling furnace of a continuous annealing furnace.

CLAIMS

[Claim 1] A method for determining revolution speeds ri of blowers of a cooling furnace when
a desirable ratio of revolution speeds rx of i-th (i = 1 to k) blowers installed in a cooling furnace is given as
rx:r2:r3: . . .:rk = wx:w2: w3: . . . : wk,

maximum values ri max of the revolution speeds of the i-th (i = 1 to k) blowers are given as
El max/ ^2 max/ r3 max/ • • • / I"k max/

minimum values r± min of the revolution speeds of the i-th (i = 1 to k) blowers are given as
^-1 min/ ^2 min/ r3 min/ • • • / ^k min/ ana

a preferred total blow volume of the entire cooling furnace is given as B, the method comprising:
obtaining cooling performance coefficients a± of the i-th (i = 1 to k) blowers;

when the revolution speeds ri of the i-th (i = 1 to k) blowers are determined, calculating a first to a k-th tentative revolution speed rTi sequentially as

rTi = B X Wi/ (wx X a i + W2 X a 2 + w3 X a3 + ... + wk X a k) ,
rT2 = (B - ri X BJ) X w2/(w2 X a 2 + w3 X a3 + ... + wk X a k) ,
rT3 = (B - (ri X a ! + r2 X a 2) ) X w3/(w3 X a 3 + ... + wk X a k) , and
rTi = (B - (ri X a i + r2 X a 2 + r3 X a 3 + ... + r±-i X ai-i)) X Wi/(wi X Oi + ... + wk X ak), and for each i-th (i = 1 to k) blower,

employing the calculated rTi as r± when
ri max ^ r i ^ ri liiif

employing ri max as ri when
rT± ri max, or employing ri min as ri when
ri min = rTi,- and

when a ratio of the employed blower revolution speeds ri is
ri: r2:r3: . . . : rk = 0.8wi to 1.2wi:0.8w2 to 1.2w2:0.8w3 to 1.2w3:...:0.8wk to 1.2wk and a total blow volume Tb obtained by

Tb = ri X a i + r2 X a2 + r3 X a3 + . . . + rk X
a k satisfies

0.99B ^ Tb ^ 1.01B, determining the employed blower revolution speeds rx as the revolution speeds of the blowers.

[Claim 2]

A method for determining revolution speeds ri of blowers of a cooling furnace when

a desirable ratio of revolution speeds ri of i-th (i = 1 to k) blowers installed in a cooling furnace is given as
ri: r2 : r3: . . . : rjc = Wi: w2 : w3 : . . . : wk, maximum values ri max of the revolution speeds of the i-th (i = 1 to k) blowers are given as 1-1 max/ *-2 max / ^3 max/ • • • / £k max/
minimum values ri min of the revolution speeds of the i-th (i = 1 to k) blowers are given as

^1 min r %2 mini ^3 min* • ■ • / ^k ninr 311(1
a preferred total blow volume of the entire cooling furnace is given as B, the method comprising:
obtaining cooling performance coefficients a± of the i-th (i = 1 to k) blowers;

when the revolution speeds rA of the i-th (i = 1 to k) blowers are determined, calculating a k-th to a first tentative revolution speed rTi sequentially as

rTk = B X wk/(wi X a 1 + w2 X a2 + W3 X 03 + ... + wk X ak) ,
rVi = (B - rk X ok) X wk-i/(wi X a 1 + w2 X a2 + w3 X a 3 + ... + wk-i X a k_i) ,
rTk-2 = (B - (rk X ak + rk-i X ak_i)) X wk_2/(wi X ai + w2 X a2 + w3 X a3 + ... + wk-2 X ak-2), and
rTi = (B - (rk X ak + rk_x X a k_i + rk-2 X a k_2 + ... + ri+i X Biti)) X Wi/(wiai + ... + wi X a i) , and for each i-th (i = 1 to k) blower, employing the calculated rTi as r± when T ^i max ^ r i > ri min/ employing r± max as rA when
^ i = I"i max t Or employing r± min as r± when r± mm ^ rT±; and

when a ratio of the employed blower revolution speeds ri is rj.:r2: r3: . . . : rk = 0.8wi to 1.2wi:0.8w2 to 1.2w2:0.8w3 to 1.2w3: . . . :0.8wk to 1.2wk and a total blow volume Tb obtained by Tb = ri X a i + r2 X a2 + r3 X a3 + ... + rk X a k satisfies 0.99B ^ Tb ^ 1.01B, determining the employed blower revolution speeds r± as the revolution speeds of the blowers.

[Claim 3] A method for determining revolution speeds ri of blowers of a cooling furnace when a desirable ratio of revolution speeds ri of i-th (i = 1 to k) blowers installed in a cooling furnace is given as ri: r2: r3: . . . : rk = Wi: w2:w3:. . . : wk, maximum values ri max of the revolution speeds of the i-th (i = 1 to k) blowers are given as £l max r ^2 max/ ^3 max/ • • • r £ k max/ minimum values ri min of the revolution speeds of the i-th (i = 1 to k) blowers are given as rl min/ r2 min/ r3 min/ • ■ • / £k min/ and a preferred total blow volume of the entire cooling furnace is given as B, the method comprising:
obtaining cooling performance coefficients a± of the i-th (i = 1 to k) blowers;

calculating revolution speeds rTi of the i-th (i = 1 to k) blowers by rTi = B X Wi/{ 2i=1lc(wi X cti)}; and
comparing a number x of blowers in which i that does not satisfy exists in a first half from a center of i = 1 to k and a number y of blowers in which i exists in a second half from the center, and

using the method for determining the revolution speed of the blower of the cooling furnace according
to claim 1 when x ^ y, or using the method for determining the revolution speed of the blower of the cooling furnace according to claim 2 when x < y.

[Claim 4]

The method for determining the revolution speeds of the blowers of the cooling furnace according to any one of claims 1 to 3,

wherein blow volumes bi and the revolution speeds ri of the blowers are measured, and the cooling performance coefficients a± of the blowers are obtained by cti = bi/ri.

[Claim 5]

An apparatus for determining revolution speeds ri of blowers of a cooling furnace when

a desirable ratio of revolution speeds r± of i-th (i = 1 to k) blowers installed in a cooling furnace is given as
ri : r2: r3 : . . . : rk = Wi: w2 : w3 : . . . : wk,

maximum values r± max of the revolution speeds of the i-th (i = 1 to k) blowers are given as
1 max; r2 max/ ^3 max r • • • r rjc max;

minimum values r± m±n of the revolution speeds of the i-th (i = 1 to k) blowers are given as
^"l minf ^2 min/ ^3 min; • • • 1 ric min; and

a preferred total blow volume of the entire cooling furnace is given as B, the apparatus comprising:

a unit calculating by using cooling performance coefficients a, when the revolution speeds ri of the i-th (i = 1 to k) blowers are determined, a first to a k-th tentative revolution speeds rTi sequentially as

rTi = B X wx/(wi X a! + w2 X a 2 + w3 X a3 + ... + wk X ak) ,
rT2 = (B - ri X ai) X W2/(W2 X a 2 + w3 X a3 + ... + wk X a k) ,
rT3 = (B - (n X 01 + r2 X o2)) x w3/(w3 X a3 + ... + wk X a k) , and
rTi = (B - (ri X a 1 + r2 X a 2 + r3 X a3 + ... + ri-i X a±-i)) X wi/(Wi X ai + ... + wk X ak), and for each i-th (i = 1 to k) blower, employing the calculated rTi as ri when
ri max ^ r i > Ti min/ employing n max as rA when
^ i = ^i max/ Or

employing ri min as r± when
r± min ^ rTi/ and

a unit determining, when a ratio of the employed blower revolution speeds ri is
rx: r2:r3: . . . : rk = 0.8wi to 1.2wi:0.8w2 to 1.2w2:0.8w3 to 1 . 2w3 : . . . : 0 . 8wk to 1 . 2wk and a total blow volume Tb obtained by

Tb = r! X ai + r2 X a 2 + r3 X a3 + ... + rk X ak

satisfies
0.99B ^ Tb ^ 1.01B, the employed blower revolution speeds ri as the revolution speeds of the blowers.

[Claim 6]

An apparatus for determining revolution speeds ri of blowers of a cooling furnace when
a desirable ratio of revolution speeds ri of i-th (i = 1 to k) blowers installed in a cooling furnace is given as
ri: r2:r3: . . . : rk = wi:w2: w3: . . . : wk, maximum values r± max of the revolution speeds of the i-th (i = 1 to k) blowers are given as ^"l max/ ^2 max/ ^3 max/ • • • / ^k max/

minimum values ri min of the revolution speeds of the i-th (i = 1 to k) blowers are given as
£l min/ ^2 min/ ^3 min/ • • • / ^k min/ and

a preferred total blow volume of the entire cooling furnace is given as B, the apparatus comprising:
a unit calculating by using cooling performance coefficients alf when the revolution speeds ri of the i-th (i = 1 to k) blowers are determined, a k-th to a first tentative revolution speed rTi sequentially as

rTk = B X wk/(wi X a 1 + w2 X a 2 + w3 X a3 + ... + wk X ak) ,
rTk_i = (B - rk X ak) X wk_i/(wi X a 1 + w2 X a2 + w3 X a3 + ... + wjc-i X ak_i),
rTk-2 = (B - (rk X a k + rk-i X ak_i)) X wk-2/(wi X ai + w2 X a2 + w3 X a3+ ... + wk-2 X ak-2) , and
rTi = (B - (rk X ak + rk-i X ak-i + rk-2 X a k-2 + ... + ri + i X Oiti)) X Wi/(wi(«i + ... + Wi X ai), and for each i-th (i = 1 to k) blower, employing the calculated rTi as ri when ri max -* r i > r^ mj.n , employing rA max as n when rTi ^ ri max, or employing ri min as ri when r± min ^ rTi; and

a unit determining, when a ratio of the employed blower revolution speeds ri is ri:r2:r3:.. . : rk = 0.8wi to 1.2wi:0.8w2 to 1.2w2:0.8w3 to 1.2w3:...:0.8wk to 1.2wk and a total blow volume Tb obtained by
Tb = n X ai + r2 X a 2 + r3 X a3+ ... +rkX a k satisfies 0.99B ^ Tb ^ 1.01B, the employed blower revolution speeds ri as the revolution speeds of the blowers.

[Claim 7]

An apparatus for determining revolution speeds of blowers of a cooling furnace when
a desirable ratio of revolution speeds ri of i-th (i = 1 to k) blowers installed in a cooling furnace is given as
ri: r2 : r3: . . . : rk = Wi: w2 : w3: . . . : wk, maximum values ri max of the revolution speeds of the i-th (i = 1 to k) blowers are given as E\ max/ £2 max/ £3 max/ tk max/ minimum values rA min of the revolution speeds of the i-th (i = 1 to k) blowers are given as El min/ E2 min/ ^"3 min/ • • • / £"k min/ and a preferred total blow volume of the entire cooling furnace is given as B, the apparatus comprising:

a unit obtaining cooling performance coefficients ai of the i-th (i = 1 to k) blowers;

a unit calculating revolution speeds rTi of the i-th (i = 1 to k) blowers by

rTi = B X Wi/{ Zi=1k(Wi X ai)}; and

a unit comparing a number x of blowers in which i that does not satisfy Ei max r= r i = ri mj.n
exists in a first half from a center of i = 1 to k and a number y of blowers in which i exists in a second half from the center, and

using the apparatus for determining the revolution speed of the blower of the cooling furnace according to claim 5 when x y, or using the apparatus for determining the revolution speed of the blower of the cooling furnace according to claim 6 when x < y. A