CN109201752B - Cold rolling spraying device and method - Google Patents

Cold rolling spraying device and method Download PDF

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Publication number
CN109201752B
CN109201752B CN201710516453.3A CN201710516453A CN109201752B CN 109201752 B CN109201752 B CN 109201752B CN 201710516453 A CN201710516453 A CN 201710516453A CN 109201752 B CN109201752 B CN 109201752B
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emulsion
strip steel
concentration
storage tank
sprayed
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CN109201752A (en
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李秀军
王康健
瞿培磊
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Baoshan Iron and Steel Co Ltd
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B21MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21BROLLING OF METAL
    • B21B45/00Devices for surface or other treatment of work, specially combined with or arranged in, or specially adapted for use in connection with, metal-rolling mills
    • B21B45/02Devices for surface or other treatment of work, specially combined with or arranged in, or specially adapted for use in connection with, metal-rolling mills for lubricating, cooling, or cleaning
    • B21B45/0203Cooling
    • B21B45/0209Cooling devices, e.g. using gaseous coolants
    • B21B45/0215Cooling devices, e.g. using gaseous coolants using liquid coolants, e.g. for sections, for tubes
    • B21B45/0218Cooling devices, e.g. using gaseous coolants using liquid coolants, e.g. for sections, for tubes for strips, sheets, or plates

Abstract

The invention discloses a cold rolling spraying device which is used for spraying emulsion on the surface of strip steel, and comprises a first storage tank for storing the emulsion with first concentration, a second storage tank for storing the emulsion with second concentration, an upper spraying beam arranged above the strip steel and a lower spraying beam arranged below the strip steel, wherein a first booster pump is arranged between the first storage tank and the upper spraying beam, a second booster pump is arranged between the second storage tank and the lower spraying beam, a plurality of upper nozzles capable of spraying the emulsion on the upper surface of the strip steel are arranged on the upper spraying beam, and a plurality of lower nozzles capable of spraying the emulsion on the lower surface of the strip steel are arranged on the lower spraying beam. The invention also discloses a cold rolling spraying method by utilizing the cold rolling spraying device. The cold rolling spraying device and the method can realize the minimum thickness difference of oil films formed on the upper surface and the lower surface of the strip steel, and ensure the quality and the high-speed and stable production of cold rolling strip steel products.

Description

Cold rolling spraying device and method
Technical Field
The invention relates to the field of cold rolling, in particular to a cold rolling spraying device and a cold rolling spraying method.
Background
At present, emulsion is generally adopted in the cold rolling production process for process lubrication so as to reduce the friction coefficient of a rolling deformation area, reduce the rolling pressure and the rolling power and slow down the abrasion of a roller. The emulsion is a solution in which rolling oil is uniformly dispersed in water at a constant concentration as a dispersed phase. The emulsion can be sprayed on the surface of the strip steel through a cold rolling spraying device, and an oil film can be gradually separated from the surface of the strip steel to finish the lubrication of the surface of the strip steel.
In the existing cold rolling spray device, emulsion is respectively sprayed on the upper and lower surfaces of strip steel by a nozzle with a certain concentration. However, due to the action of gravity, only a part of the emulsion sprayed on the lower surface of the strip steel is adsorbed on the lower surface of the strip steel and gradually precipitates an oil film on the lower surface, and the other part of the emulsion is dropped and lost, so that the thickness of the oil film formed on the lower surface of the strip steel is smaller than that of the oil film formed on the upper surface of the strip steel, the friction coefficient of the lower surface of the strip steel is larger than that of the upper surface of the strip steel, and further the uneven extension of the upper surface and the lower surface of the strip steel in a rolling deformation area is caused, so that the stability of the high-speed rolling process of the strip steel is influenced.
Aiming at the problems in the prior art, the cold rolling spraying device and the cold rolling spraying method have important significance.
Disclosure of Invention
In order to solve the problems, the invention provides a cold rolling spraying device and a cold rolling spraying method, which can realize the minimum thickness difference of oil films formed on the upper surface and the lower surface of a strip steel, and ensure the quality of a cold rolling strip steel product and high-speed and stable production.
In order to achieve the purpose, the cold rolling spraying device is used for spraying emulsion to the surface of the strip steel and comprises a first storage tank for storing the emulsion with first concentration, a second storage tank for storing the emulsion with second concentration, an upper spraying beam arranged above the strip steel and a lower spraying beam arranged below the strip steel, wherein a first booster pump is arranged between the first storage tank and the upper spraying beam, a second booster pump is arranged between the second storage tank and the lower spraying beam, a plurality of upper nozzles capable of spraying the emulsion to the upper surface of the strip steel are arranged on the upper spraying beam, and a plurality of lower nozzles capable of spraying the emulsion to the lower surface of the strip steel are arranged on the lower spraying beam.
Preferably, a first flow meter is arranged between the first booster pump and the upper spray beam, and a second flow meter is arranged between the second booster pump and the lower spray beam.
Preferably, a first three-way valve is arranged between the first booster pump and the upper spray beam and communicated with the first storage tank; and a second three-way valve is arranged between the second booster pump and the lower spray beam and communicated with the second storage tank.
The method for cold rolling spraying by using the cold rolling spraying device comprises the following steps:
step one, preparing emulsion with first concentration in the first storage tank, and preparing emulsion with second concentration in the second storage tank;
and step two, conveying the emulsion with the first concentration in the first storage tank to the upper spray beam through the first booster pump, spraying the emulsion to the upper surface of the strip steel through the upper nozzle, conveying the emulsion with the second concentration in the second storage tank to the lower spray beam through the second booster pump, and spraying the emulsion to the lower surface of the strip steel through the lower nozzle.
Preferably, the second storage tank has an optimal value of the concentration of the emulsion of the second concentration, and the calculating step includes:
step A, defining a concentration optimization parameter i, i-1, 2, … …, n of the emulsion with a second concentration in the second storage tank, and giving an initial value i-1 to i;
b, defining the optimal value of the ratio of the thickness difference of the oil films formed on the upper surface and the lower surface of the strip steel to the thickness of the oil film formed on the upper surface of the strip steel as FyAnd is given FyInitial value Fy=10000;
Step C, calculating the concentration of the emulsion with the second concentration in the second storage tank:
Figure BDA0001336756150000031
in the formula, CxminA minimum concentration value allowed for an emulsion having a second concentration in the second storage tank; cxmaxThe second storage tank is provided with a maximum concentration value allowed by the emulsion with a second concentration;
step D, calculating the precipitation efficiency of the emulsion sprayed on the upper surface and the lower surface of the strip steel:
Figure BDA0001336756150000032
Figure BDA0001336756150000033
in the formula, αsThe precipitation efficiency of the emulsion sprayed on the upper surface of the strip steel is shown; lambda [ alpha ]sIs the precipitation efficiency coefficient of the emulsion sprayed on the upper surface of the strip steel; l issThe distance from the upper nozzle to the central line of the rolling mill; v is as followsRolling speed of strip steel αxThe precipitation efficiency of the emulsion sprayed to the lower surface of the strip steel is shown; lambda [ alpha ]xThe precipitation efficiency coefficient of the emulsion sprayed to the lower surface of the strip steel is shown; l isxThe distance from the lower nozzle to the central line of the rolling mill;
step E, calculating the residual rate of the emulsion sprayed to the upper surface and the lower surface of the strip steel:
Figure BDA0001336756150000041
Figure BDA0001336756150000042
in the formula, βsThe residual rate of the emulsion sprayed on the upper surface of the strip steel is shown;sthe residual rate coefficient of the emulsion sprayed on the upper surface of the strip steel is shown; qsThe spraying flow rate of the emulsion on the upper surface of the strip steel, B is the width of the strip steel, βxThe residual rate of the emulsion sprayed to the lower surface of the strip steel is shown;xthe residual rate coefficient of the emulsion sprayed to the lower surface of the strip steel is shown; qxThe spraying flow rate of the emulsion on the lower surface of the strip steel is determined;
step F, calculating the thickness of an oil film separated out from the emulsion sprayed on the upper surface of the strip steel:
Figure BDA0001336756150000043
in the formula, CsThe concentration of the emulsion with the first concentration in the first storage tank;
step G, calculating the thickness of an oil film separated out from the emulsion sprayed on the lower surface of the strip steel:
Figure BDA0001336756150000051
step H, calculating the ratio of the thickness difference of the oil films formed on the upper surface and the lower surface of the strip steel to the thickness of the oil film formed on the upper surface of the strip steel:
Figure BDA0001336756150000052
step I, judging Fi<FyIf true, let Fy=FiThe second storage tank has an optimum value C of the concentration of the emulsion of the second concentrationxy=CxiThen, turning to step J; if not, directly switching to the step J;
step J, judging whether i is equal to n, if so, switching to step K; if the information is not satisfied, making i equal to i +1, and then switching to the step C;
step K of outputting an optimal value C of the concentration of the emulsion having the second concentration in the second storage tankxy
According to the cold rolling spraying device and the cold rolling spraying method, the emulsions with different concentrations are respectively sprayed to the upper surface and the lower surface of the strip steel, and the optimal value of the required second concentration of the emulsion sprayed to the lower surface of the strip steel can be calculated, so that the minimum thickness difference of oil films formed on the upper surface and the lower surface of the strip steel can be realized, and the quality and high-speed stable production of cold rolling strip steel products are ensured.
Drawings
Fig. 1 is a schematic structural diagram of a cold rolling spray device of the invention.
FIG. 2 is a schematic flow diagram of the cold rolling spray method of the present invention.
Detailed Description
The structure, operation, and the like of the present invention will be further described with reference to the accompanying drawings.
Referring to fig. 1, the cold rolling spray apparatus of the present invention sprays emulsion on the surface of a strip 10, which is provided in front of rolling mill rolls 20, comprising a first storage tank 30 for storing emulsion having a first consistency and a second storage tank 40 for storing emulsion having a second consistency, the upper spray beam 34 is arranged above the strip steel 10, the lower spray beam 44 is arranged below the strip steel 10, a first booster pump 31 is arranged between the first storage box 30 and the upper spray beam 34, a second booster pump 41 is arranged between the second storage box 40 and the lower spray beam 44, the upper spray beam 34 and the lower spray beam 44 both extend along the width direction of the strip steel 10, a plurality of upper nozzles 35 capable of spraying emulsion to the upper surface of the strip steel 10 are arranged on the upper spray beam 34, and a plurality of lower nozzles 45 capable of spraying emulsion to the lower surface of the strip steel 10 are arranged on the lower spray beam 44.
In order to monitor the emulsion spraying flow rate of the upper and lower surfaces of the strip steel 10 in real time, a first flow meter 32 may be disposed between the first booster pump 31 and the upper spray beam 34, and a second flow meter 42 may be disposed between the second booster pump 41 and the lower spray beam 44.
Preferably, a first three-way valve 33 may be provided between the first booster pump 31 and the upper shower beam 34, the first three-way valve 33 being in communication with the first storage tank 30; a second three-way valve 43 is provided between the second booster pump 41 and the lower shower beam 44, and the second three-way valve 43 communicates with the second storage tank 40.
When spraying is carried out on the upper surface and the lower surface of the strip steel 10, emulsion with a first concentration in the first storage tank 30 is conveyed to the upper spraying beam 34 through the first booster pump 31 and the first three-way valve 33 in sequence, and emulsion with a second concentration in the second storage tank 40 is conveyed to the lower spraying beam 44 through the second booster pump 41 and the second three-way valve 43 in sequence;
when the shower is finished, the spools of the first and second three- way valves 33 and 43 are operated such that the emulsion having the first concentration is returned to the first storage tank 30 through the first three-way valve 33 and the emulsion having the second concentration is returned to the second storage tank 40 through the second three-way valve 43.
The method for performing cold rolling spraying by using the cold rolling spraying device comprises the following steps:
first, the emulsion having the first concentration is placed in the first storage tank 30, and the emulsion having the second concentration is placed in the second storage tank 40.
As shown in fig. 2, preferably, the optimal value of the concentration of the emulsion having the second concentration in the second storage tank 40 is calculated by the steps of:
step a, defining a concentration optimization parameter i, i-1, 2, … …, n of the emulsion with the second concentration in the second storage tank 40, and giving an initial value i-1 to i;
step B, defining the optimal value of the ratio of the thickness difference of the oil films formed on the upper surface and the lower surface of the strip steel 10 to the thickness of the oil film formed on the upper surface 10 of the strip steel as FyAnd is given FyInitial value Fy=10000;
Step C, calculating the concentration of the emulsion having the second concentration in the second storage tank 40:
Figure BDA0001336756150000081
in the formula, CxminThe minimum concentration value allowed for the emulsion having the second concentration in the second storage tank 40, in%; cxmaxThe maximum concentration value allowed for the emulsion having the second concentration in the second storage tank 40, in%;
for example, the minimum concentration C allowed for the emulsion with the second concentration in the second storage tank 40 is selectedxmin1.0%, maximum concentration value C allowedxmax=15.0%;n=141;
When the value of i is 1, the value of i,
Figure BDA0001336756150000082
when the value of i is 2, the ratio of i to i is,
Figure BDA0001336756150000083
and so on until
Figure BDA0001336756150000084
And D, calculating the precipitation efficiency of the emulsion sprayed on the upper surface and the lower surface of the strip steel 10.
The precipitation efficiency of the emulsion is the ratio of the amount of oil film precipitated on the surface of the strip steel 10 sprayed by the emulsion to the amount of oil contained in the emulsion sprayed on the surface of the strip steel 10 by the nozzle, and the precipitation efficiency of the emulsion on the upper surface and the lower surface of the strip steel 10 is calculated according to the following formula:
Figure BDA0001336756150000085
Figure BDA0001336756150000091
in the formula, αsThe precipitation efficiency of the emulsion sprayed on the upper surface of the strip steel 10; lambda [ alpha ]sThe precipitation efficiency coefficient of the emulsion sprayed on the upper surface of the strip steel 10 is in a value range of 0.1-1.0; l issThe distance from the upper nozzle 35 to the central line of the rolling mill is in mm, V is the rolling speed of the strip steel 10 is in m/min, αxThe precipitation efficiency of the emulsion sprayed to the lower surface of the strip steel 10 is shown; lambda [ alpha ]xThe precipitation efficiency coefficient of the emulsion sprayed on the lower surface of the strip steel 10 is in a value range of 0.1-1.0; l isxIs the distance in mm from the lower nozzle 45 to the mill centerline. Wherein λ iss、λxIs empirically derived and is related to the wettability of the rolling oil particles in the emulsion on the surface of the strip 10. The precipitation efficiency coefficient of the rolling oil having good wettability may take a large value within a range.
For example, choose λs=λxWhen the value is 0.6, L is measureds=680mm,Lx575mm and 800m/min, then
Figure BDA0001336756150000092
Figure BDA0001336756150000093
And E, calculating the residual rate of the emulsion sprayed on the upper surface and the lower surface of the strip steel 10.
When the emulsion is sprayed on the surface of the strip steel 10, part of the emulsion on the upper surface of the strip steel 10 splashes to the outer side of the strip steel 10, part of the emulsion on the lower surface of the strip steel 10 splashes to the outer side of the strip steel 10, and part of the emulsion drops due to the action of gravity, so that the residual rate of the emulsion sprayed on the upper surface and the lower surface of the strip steel 10 needs to be calculated. The residual rate of the emulsion is the ratio of the amount of the emulsion adsorbed on the surface of the strip steel 10 after the emulsion is sprayed on the surface of the strip steel 10 to the amount of the emulsion sprayed on the surface of the strip steel 10 by the nozzle, and the calculation formula is as follows:
Figure BDA0001336756150000101
Figure BDA0001336756150000102
in the formula, βsThe residual rate of the emulsion sprayed on the upper surface of the strip steel 10;sthe residual coefficient of the emulsion sprayed on the upper surface of the strip steel 10 is 3000-8000; qsThe spraying flow rate of the emulsion on the upper surface of the strip steel 10 is L/min, B is the width of the strip steel 10 is mm, βxThe residual rate of the emulsion sprayed to the lower surface of the strip steel 10;xthe residual coefficient of the emulsion sprayed on the lower surface of the strip steel 10 is 10000-40000; qxThe spraying flow rate of the emulsion on the lower surface of the strip steel 10 is L/min.
For example, selectings=7500,xAt 35000, Q is measureds=8.24L/min,Qx8.24L/min, B870 mm, then
Figure BDA0001336756150000111
Figure BDA0001336756150000112
Step F, calculating the thickness of an oil film separated out from the emulsion sprayed on the upper surface of the strip steel 10:
Figure BDA0001336756150000113
in the formula, CsIs the concentration in% of the emulsion having the first concentration in the first storage tank 30.
SelectingCsWhen 3%, then
Figure BDA0001336756150000114
Step G, calculating the thickness of an oil film separated out from the emulsion sprayed on the lower surface of the strip steel 10:
Figure BDA0001336756150000115
when the value of i is 1, the value of i,
Figure BDA0001336756150000116
when the value of i is 2, the ratio of i to i is,
Figure BDA0001336756150000117
and so on until
Figure BDA0001336756150000118
Step H, calculating the ratio of the thickness difference of the oil films formed on the upper surface and the lower surface of the strip steel 10 to the thickness of the oil films formed on the upper surface of the strip steel 10:
Figure BDA0001336756150000121
the smaller the above ratio is, the smaller the difference in the thickness of the oil films formed on the upper and lower surfaces of the strip steel 10 is, and when the ratio is the smallest, the concentration of the emulsion having the second concentration in the corresponding second storage tank 40 is the optimum value.
When the value of i is 1, the value of i,
Figure BDA0001336756150000122
when the value of i is 2, the ratio of i to i is,
Figure BDA0001336756150000123
and so on until
Figure BDA0001336756150000124
Step I, judging Fi<FyIf true, let Fy=FiThe optimum value C of the concentration of the emulsion having the second concentration in the second storage tank 40xy=CxiTurning to step J; if not, directly turning to the step J;
step J, judging whether i is equal to n, if so, switching to step K; if the information is not satisfied, making i equal to i +1, and then switching to the step C;
step K of outputting the optimum value C of the concentration of the emulsion having the second concentration in the second storage tank 40xy
E.g. when i is 1, F1=0.7694<10000, then order Fy=F10.7694, the second storage tank 40 has an optimum value C of the concentration of the emulsion of the second concentrationxy=Cx1=1.0%;
When the step I is shifted to the step I, when I is equal to 2, F2=0.7462<0.7694, then let Fy=F20.7462, the second storage tank 40 has an optimum value C of the concentration of the emulsion of the second concentrationxy=Cx2=1.1%;
And analogizing until the cycle is ended, and finally calculating to obtain F when i is equal to n and 141y=F34When the concentration of the emulsion having the second concentration in the second storage tank 40 is 0.0078, the optimum value C of the concentration is outputxy=Cx34=4.3%。
And step two, conveying the emulsion with the first concentration in the first storage tank 30 to an upper spray beam 34 through a first booster pump 31 and spraying the emulsion to the upper surface of the strip steel 10 through an upper nozzle 35, and conveying the emulsion with the second concentration in the second storage tank 40 to a lower spray beam 44 through a second booster pump 41 and spraying the emulsion to the lower surface of the strip steel 10 through a lower nozzle 45.
The foregoing is merely illustrative of the present invention, and it will be appreciated by those skilled in the art that various modifications may be made without departing from the principles of the invention, and the scope of the invention is to be determined accordingly.

Claims (1)

1. A method for cold rolling spraying by using a cold rolling spraying device, wherein the cold rolling spraying device comprises: a second bin for storing the first bin that has the emulsion of first concentration and being used for storing the emulsion that has the second concentration to and locate the last spray roof beam of belted steel top and locate the lower spray roof beam of belted steel below, first bin and last spray roof beam between be equipped with first booster pump, second bin and spray roof beam down between be equipped with the second booster pump, on spray roof beam on be equipped with a plurality of can to the last nozzle that the belted steel upper surface sprayed the emulsion, be equipped with on the spray roof beam down a plurality of can to the belted steel lower surface sprays the lower nozzle of emulsion, its characterized in that, the method includes:
step one, preparing emulsion with first concentration in the first storage tank, and preparing emulsion with second concentration in the second storage tank;
conveying the emulsion with the first concentration in the first storage tank to the upper spray beam through the first booster pump and spraying the emulsion to the upper surface of the strip steel through the upper nozzle, conveying the emulsion with the second concentration in the second storage tank to the lower spray beam through the second booster pump and spraying the emulsion to the lower surface of the strip steel through the lower nozzle;
the second storage tank has an optimum value of the concentration of the emulsion of the second concentration, and the calculating step includes:
step A, defining a concentration optimization parameter i, i-1, 2, … …, n of the emulsion with a second concentration in the second storage tank, and giving an initial value i-1 to i;
b, defining the optimal value of the ratio of the thickness difference of the oil films formed on the upper surface and the lower surface of the strip steel to the thickness of the oil film formed on the upper surface of the strip steel as FyAnd is given FyInitial value Fy=10000;
Step C, calculating the concentration of the emulsion with the second concentration in the second storage tank:
Figure FDA0002532954840000021
in the formula, CxminA minimum concentration value allowed for an emulsion having a second concentration in the second storage tank; cxmaxThe second storage tank is provided with a maximum concentration value allowed by the emulsion with a second concentration;
step D, calculating the precipitation efficiency of the emulsion sprayed on the upper surface and the lower surface of the strip steel:
Figure FDA0002532954840000022
Figure FDA0002532954840000023
in the formula, αsThe precipitation efficiency of the emulsion sprayed on the upper surface of the strip steel is shown; lambda [ alpha ]sIs the precipitation efficiency coefficient of the emulsion sprayed on the upper surface of the strip steel; l issThe distance from the upper nozzle to the central line of the rolling mill, V is the rolling speed of the strip steel, αxThe precipitation efficiency of the emulsion sprayed to the lower surface of the strip steel is shown; lambda [ alpha ]xThe precipitation efficiency coefficient of the emulsion sprayed to the lower surface of the strip steel is shown; l isxThe distance from the lower nozzle to the central line of the rolling mill;
step E, calculating the residual rate of the emulsion sprayed to the upper surface and the lower surface of the strip steel:
Figure FDA0002532954840000031
Figure FDA0002532954840000032
in the formula, βsThe residual rate of the emulsion sprayed on the upper surface of the strip steel is shown;sthe residual rate of the emulsion sprayed on the upper surface of the strip steel isCounting; qsThe spraying flow rate of the emulsion on the upper surface of the strip steel, B is the width of the strip steel, βxThe residual rate of the emulsion sprayed to the lower surface of the strip steel is shown;xthe residual rate coefficient of the emulsion sprayed to the lower surface of the strip steel is shown; qxThe spraying flow rate of the emulsion on the lower surface of the strip steel is determined;
step F, calculating the thickness of an oil film separated out from the emulsion sprayed on the upper surface of the strip steel:
Figure FDA0002532954840000033
in the formula, CsThe concentration of the emulsion with the first concentration in the first storage tank;
step G, calculating the thickness of an oil film separated out from the emulsion sprayed on the lower surface of the strip steel:
Figure FDA0002532954840000034
step H, calculating the ratio of the thickness difference of the oil films formed on the upper surface and the lower surface of the strip steel to the thickness of the oil film formed on the upper surface of the strip steel:
Figure FDA0002532954840000035
step I, judging Fi<FyIf true, let Fy=FiThe second storage tank has an optimum value C of the concentration of the emulsion of the second concentrationxy=CxiThen, turning to step J; if not, directly switching to the step J;
step J, judging whether i is equal to n, if so, switching to step K; if the information is not satisfied, making i equal to i +1, and then switching to the step C;
step K of outputting an optimal value C of the concentration of the emulsion having the second concentration in the second storage tankxy
CN201710516453.3A 2017-06-29 2017-06-29 Cold rolling spraying device and method Active CN109201752B (en)

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS55130306A (en) * 1979-03-30 1980-10-09 Nippon Steel Corp Top and bottom asymmetrical cold rolling method for strip
DE19805377A1 (en) * 1998-02-11 1999-08-12 Schloemann Siemag Ag Spray beam for hydraulic de-scaling plant
JP2004117117A (en) * 2002-09-25 2004-04-15 Kobe Steel Ltd Estimation method of introduction oil film thickness in metal rolling
CN201455026U (en) * 2009-09-03 2010-05-12 中冶恒通冷轧技术有限公司 Emulsified solution purging device of cold-rolled steel strip
CN202591257U (en) * 2012-04-20 2012-12-12 宝山钢铁股份有限公司 Emulsion injecting beam for cold-rolling mill
CN204657118U (en) * 2015-03-30 2015-09-23 重庆松德再生资源股份有限公司 The emulsion circulatory system

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