CN105290116A - Method for controlling transverse rolling width and longitudinal rolling width of moderately-thick plate - Google Patents

Abstract

The invention discloses a method for controlling transverse rolling width and longitudinal rolling width of a moderately-thick plate, and relates to the technical field of pressure processing of metals. The method comprises the following steps: A, setting rolling procedures, wherein the rolling reduction of all passes before the last pass in the transverse rolling stage is set according to the maximum allowable load which can be borne by a rolling machine; B, shooting a shape image of the side surface of a rolling part in front of an inlet of the last pass so as to obtain the ratio of the effective width of the middle part of the rolling part in the image to the thickness of the rolling part in the image, and synchronously measuring the actual thickness of the rolling part at the moment to obtain the width deviation; C, calculating the compensation rolling reduction of the last pass of the rolling part according to the width deviation, summing the compensation rolling reduction and the set rolling reduction of the last pass to obtain the compensated rolling reduction of the last pass, and then adjusting the roll gap value of the last pass or the last two passes according to the compensated rolling reduction, so as to obtain the expected effective width of the middle part of the finished product of the rolling part. Compared with the prior art, the method has the advantage that the width accuracy of the moderately-thick plate in the transverse rolling stage can be effectively improved.

Description

The width control method that cut deal transverse and longitudinal is rolled

Technical field

The present invention relates to metal-pressed machine technical field, the control method of rolling width under especially a kind of rolling mode rolled in transverse and longitudinal for cut deal.

Background technology

In medium-thick plate production process, by the restriction of ingot casting width, often need the mode adopting transverse and longitudinal to roll to produce, be divided into transverse rolling stage and axial rolling stage by the whole operation of rolling, by transverse rolling, sheet material is rolled to the width of expectation, then by axial rolling, sheet material is rolled to the length of expectation.In the transverse rolling stage, prior art is according to rolled piece metal volume principle of invariance, and ignores the natural width spread of trace, suppose that rolled piece is always a standard rectangular body, calculate thickness when rolled piece reaches desired width, utilize milling train that rolled piece is rolled to this thickness, desired width can be obtained.When the thicker ingot casting of rolling, because the distortion of rolled piece upper and lower surface is larger, mid portion distortion is less, the side of rolled piece easily forms bending concave shape as shown in Figure 1, if therefore suppose, rolled piece is always a standard rectangular body, the larger error of calculation will be brought, cause the width error of rolled piece to exceed the scope of permission.

Summary of the invention

The object of this invention is to provide the width control method that a kind of cut deal transverse and longitudinal is rolled, this method can solve existing cut deal transverse and longitudinal and roll and there is the large problem of width error.

In order to solve the problem, the technical solution used in the present invention is: the width control method that this cut deal transverse and longitudinal is rolled, and is provided with the video camera of metal detector and detection rolled piece side view before and after the milling train that transverse rolling stage extreme trace is secondary; Adopt following steps:

A, in rolling procedure, obtain rolled piece complete the exit thickness of all preorder passages, drafts and corresponding width in the transverse rolling stage, and the inlet set thickness of extreme trace time, the outlet setting thickness of extreme trace time, extreme trace time inlet set width and expectation finished product rolled piece in the middle part of effective width, wherein, the maximum permission load that all reductions in pass before transverse rolling stage extreme trace time all can bear according to milling train sets;

B, when metal detector detects that rolled piece enters camera watch region, rolled piece side view image before the lower extreme trace time entrance of video camera shooting, the ratio of the thickness of rolled piece in the middle part effective width of rolled piece in image and image is obtained after image procossing, measured the actual (real) thickness of now rolled piece by calibrator simultaneously, effective width in the middle part of the entrance calculating rolled piece extreme trace time according to the actual (real) thickness of described ratio and rolled piece, can obtain the width difference of effective width in the middle part of the extreme trace time inlet set width of the transverse rolling stage rolled piece entrance secondary with extreme trace thus;

C, calculate the secondary drafts that sets of compensation drafts and the extreme trace of the extreme trace time of rolled piece according to described width difference and to sue for peace the last reduction in pass obtained after compensating, with the gap values between rollers that this regulates extreme trace secondary, thus effective width in the middle part of the finished product rolled piece that rolled piece acquisition is expected; When the last reduction in pass after compensating has exceeded the maximum permission load of milling train, increase a rolling pass, be divided into two passages to be rolled the last reduction in pass after compensating, then regulate the gap values between rollers of last two passages.

In the technical scheme of the width control method that above-mentioned cut deal transverse and longitudinal is rolled, technical scheme can also be more specifically: in steps A, the extreme trace time inlet set width of rolled piece is:

$W_{n-1}=\frac{W\·L\·H}{H_{n-1}\·L}=\frac{W\·H}{H_{n-1}}$

Wherein, W _n-1for the extreme trace time inlet set width of rolled piece, unit is millimeter; W is the width of ingot casting, and L is the length of ingot casting, and H is the thickness of ingot casting, and unit is millimeter; H _n-1for the inlet thickness that rolled piece extreme trace is secondary, unit is millimeter.

Further, in step B, the calculating formula of width difference is:

δ _n-1＝W _n-1-w _n-1

Wherein, δ _n-1for the width difference of effective width in the middle part of the entrance that the extreme trace time inlet set width of transverse rolling stage rolled piece is secondary with extreme trace, unit is millimeter; w _n-1for effective width in the middle part of the entrance that the extreme trace of rolled piece is secondary, unit is millimeter, and it is according to following formulae discovery:

$w_{n-1}=h_{n-1}\·\frac{w_{n-1}^{\′}}{h_{n-1}^{\′}}$

In formula, h _n-1for the actual (real) thickness of the rolled piece before extreme trace time entrance, unit is millimeter; for the ratio of the thickness of rolled piece in the middle part effective width of rolled piece in image and image.

Further, the computational methods of the last reduction in pass in step C after compensating are as follows:

Supposing that the extreme trace of rolled piece sets drafts is Δ h _n, unit is millimeter; Then Δ h _n=H _n-1-H _n, H _nfor the exit thickness that rolled piece extreme trace is secondary, unit is millimeter; The compensation drafts that the extreme trace of rolled piece is secondary is Δ h ' _n, unit is millimeter; Last reduction in pass then after compensating is Δ H _n=Δ h _n+ Δ h ' _n, unit is millimeter; After mill load calculation and check, if this through compensate after last reduction in pass Δ H _nexceed the maximum load that milling train allows, be then divided into two passages to be rolled extreme trace; Δ h ' _nbe made up of two parts, a part is the width compensation drafts before last passes, if it is Δ h ' _n1, unit is millimeter; Another part is the width compensation drafts of last passes, if it is Δ h ' _n2, unit is millimeter;

(1) Δ h ' _n1computational methods

For eliminating the width difference δ before last passes _n-1need allow more height to metal extend to width, namely the secondary drafts of extreme trace is increased, in the actual operation of rolling, have that part is high only to flow on the surface of rolled piece to metal, do not form effective width, need to assess this part metal and account for and be allly out of shape the high ratio to metal, suppose that this ratio is Y, then the calculating formula of Y is:

$Y=\frac{H\·W-w_{n-1}\·h_{n-1}}{(H-h_{n-1})\·W}$

Therefore, when consider high to metal have part rolled piece upper and lower surface distortion time, then the calculating formula compensating drafts is:

${\mathrm{\Δh}}_{n1}^{\′}=\frac{{\mathrm{\δ}}_{n-1}\·h_{n-1}}{{\mathrm{\δ}}_{n-1}+w_{n-1}-Y\·w_{n-1}}$

(2) Δ h ' _n2computational methods

During rolling extreme trace time, still there will be part high to metal only in the phenomenon of rolled piece surface flowing, therefore also need to compensate the drafts of last passes, should at Δ h _n+ Δ h ' _n1basis on compensate, therefore, Δ h ' _n2calculating formula be:

${\mathrm{\Δh}}_{n2}^{\′}=\frac{({\mathrm{\Δh}}_n+{\mathrm{\Δh}}_{n1}^{\′})\·w_{n-1}\·L\·Y}{w_{n-1}\·L}=({\mathrm{\Δh}}_n+{\mathrm{\Δh}}_{n1}^{\′})\·Y$

Last reduction in pass after compensating is:

${\mathrm{\ΔH}}_n={\mathrm{\Δh}}_n+{\mathrm{\Δh}}_{n1}^{\′}+{\mathrm{\Δh}}_{n2}^{\′}={\mathrm{\Δh}}_n+\frac{{\mathrm{\δ}}_{n-1}\·h_{n-1}}{{\mathrm{\δ}}_{n-1}+w_{n-1}-Y\·w_{n-1}}+({\mathrm{\Δh}}_n+{\mathrm{\Δh}}_{n1}^{\′})\·Y.$

Principle of the present invention is: the maximum permission load that the reduction in pass of preorder all can bear according to milling train sets, and is improved the control accuracy of width by the drafts that adjustment transverse rolling stage extreme trace is secondary.By the distance of adjustment video camera and roller-way, each installation industrial CCD video camera before and after milling train, ensures that each video camera can both photograph the Head and Tail Shape of rolled piece simultaneously.Before a time of rolling end, by the side view of industrial CCD camera acquisition rolled piece, and then obtain the secondary actual entry width of rolled piece extreme trace, and itself and calculating exit width are compared, according to its deviate, the drafts of last a time and exit thickness are revised, if revised drafts is beyond the maximum permission load of milling train, then increase a rolling pass.

Owing to have employed technique scheme, the present invention compared with prior art has following beneficial effect: the present invention adopts video camera to detect the leading flank shape of rolling that extreme trace is secondary, and according to the exit thickness of side view correction transverse rolling stage Mo a time of reality and drafts, to avoid hypothesis rolled piece to be the error of calculation that a standard rectangular body brings, the width accuracy in cut deal transverse rolling stage effectively can be improved.

Accompanying drawing explanation

Fig. 1 is the transverse rolling stage rolled piece side view schematic diagram of industrial CCD video camera shooting.

Fig. 2 is the installation site schematic diagram of industrial CCD video camera and metal detector.

Detailed description of the invention

Below in conjunction with accompanying drawing embodiment, the invention will be further described:

As shown in Figure 2, the present invention is each before and after milling train 1 installs an industrial CCD video camera 3 and metal detector 4, ensures that each video camera can both photograph the Head and Tail Shape of the rolled piece 5 on roller-way 2 simultaneously by the distance of adjustment video camera and roller-way.

The present invention considers on the basis of existing technology, first conventionally set exit thickness and every time the drafts in transverse rolling stage, the maximum permission load that the reduction in pass of preorder all can bear according to milling train is carried out setting by regulating the drafts of last passage to control width.Suppose that rolled piece is always a standard rectangular body, the exit thickness of all preorder passages, drafts and corresponding width can have been obtained according to rolled piece metal volume invariance principle.By the distance of adjustment video camera and roller-way, each installation industrial CCD video camera before and after milling train, ensures that each video camera can both photograph the Head and Tail Shape of rolled piece simultaneously.Before a time of rolling end, the side view of rolled piece is gathered by industrial camera, and then obtain the secondary actual entry width of rolled piece extreme trace, and the extreme trace of itself and rolled piece time inlet set width is compared, revise according to the drafts of its deviate to last a time, if revised drafts is beyond the maximum permission load of milling train, then increase a rolling pass.

The width control method that this cut deal transverse and longitudinal is rolled specifically adopts following steps:

A, rolling procedure by the second-level model default transverse rolling stage of milling train, in rolling procedure, obtain rolled piece complete the exit thickness of all preorder passages, drafts and corresponding width in the transverse rolling stage, and the inlet set thickness of extreme trace time, the outlet setting thickness of extreme trace time, extreme trace time inlet set width and expectation finished product rolled piece in the middle part of effective width, wherein, the maximum permission load that all reductions in pass before transverse rolling stage extreme trace time all can bear according to milling train sets; Now suppose that rolled piece is always a standard rectangular body, the exit thickness of all preorder passages, drafts and corresponding width can have been obtained according to rolled piece metal volume invariance principle; If the length of ingot casting is L, width is W, and thickness is H, and unit is millimeter; Can be obtained by rolling procedure, total road number of times in transverse rolling stage is n; The inlet set thickness of extreme trace time is H _n-1, unit is millimeter; The outlet setting thickness of extreme trace time is H _n, unit is millimeter; In the middle part of the finished product rolled piece expected, effective width is W _n, unit is millimeter.Suppose that the length L of rolled piece is constant, then the extreme trace time inlet set width W of rolled piece _n-1(unit is millimeter) is:

$W_{n-1}=\frac{W\·L\·H}{H_{n-1}\·L}=\frac{W\·H}{H_{n-1}}$

B, when metal detector successively detects that rolled piece is away from the rising edge signal of milling train one end portion with when the trailing edge of milling train one end portion, illustrate that rolled piece enters camera watch region, now send signal by metal detector to PLC system to show to make a video recording, the image of the side view of the rolled piece before the extreme trace time entrance in industrial CCD video camera shooting transverse rolling stage, and send after image digitazation into computer by high speed image data acquisition card, as the object of workpiece measurement identification, by computer, geometric distortion correction is carried out to the shape image of rolled piece, noise filtering, rim detection, locations of contours, sub-pixel method edge local, the steps such as planar dimension measurements and calculations, similar rolled piece side view as shown in Figure 1 can be obtained after treatment, w ' in Fig. 1 _n-1for the middle part effective width of rolled piece in image, h ' _n-1for the thickness of rolled piece in image, unit is millimeter, h ' _n-1, w ' _n-1value obtain by the tape measure in image, can not be full size, because subsequent calculations only needs the proportionate relationship between three, the actual (real) thickness supposing the rolled piece before the actual (real) thickness of now rolled piece and extreme trace time entrance is h _n-1, unit is millimeter, and this value obtains with chi measurement by calibrator or operator, in the middle part of the entrance of the extreme trace of rolled piece time, effective width is w _n-1, unit is millimeter.Therefore, effective width w in the middle part of the entrance that the extreme trace of known rolled piece is secondary _n-1calculating formula be:

$w_{n-1}=h_{n-1}\·\frac{w_{n-1}^{\′}}{h_{n-1}^{\′}}$

The width difference δ of effective width in the middle part of the extreme trace time inlet set width of the transverse rolling stage rolled piece entrance secondary with extreme trace can be obtained thus _n-1(unit is millimeter) is:

δ _n-1＝W _n-1-w _n-1

Due to W _n-1calculate under hypothesis rolled piece is always the condition of a standard rectangular body, and w _n-1that in the actual operation of rolling, rolled piece exists when upper and lower surface and middle part are out of shape uneven and detects and calculate, therefore W _n-1> w _n-1, therefore, δ _n-1be always on the occasion of.

C, calculate the compensation drafts of the extreme trace time of rolled piece according to described width difference, set drafts with extreme trace and to sue for peace the last reduction in pass obtained after compensating, the computational methods of the last reduction in pass after compensation are as follows:

Supposing that the extreme trace of rolled piece sets drafts is Δ h _n, unit is millimeter; Then Δ h _n=H _n-1-H _n; The compensation drafts that the extreme trace of rolled piece is secondary is Δ h ' _n, unit is millimeter; Last reduction in pass then after compensating is Δ H _n=Δ h _n+ Δ h ' _n, unit is millimeter; After mill load calculation and check, if the drafts Δ H after this compensation _nexceed the maximum load that milling train allows, then increase a rolling pass, be divided into two passages to be rolled extreme trace; Because of the extreme trace time setting drafts Δ h of rolled piece _ncan find in the rolling procedure of second-level model system, below to Δ h ' _ncarry out analytical calculation.Δ h ' _nbe made up of two parts, a part is the width compensation drafts before last passes, if it is Δ h ' _n1, unit is millimeter; Another part is the width compensation drafts of last passes, if it is Δ h ' _n2, unit is millimeter;

(1) Δ h ' _n1computational methods

For eliminating the width difference δ before last passes _n-1, need to allow more height to metal extend to width, if therefore do not consider the distortion of metal in rolled piece upper and lower surface, namely all height have all flow to the width of rolled piece to metal, then need to compensate the calculating formula of drafts to be:

${\mathrm{\Δh}}_{n1}^{\′}=\frac{{\mathrm{\δ}}_{n-1}\·h_{n-1}}{{\mathrm{\δ}}_{n-1}+w_{n-1}}$

But in the actual operation of rolling, have that part is high only to flow on the surface of rolled piece to metal, do not form effective width, need to assess this part metal and account for and be allly out of shape the high ratio to metal, suppose that this ratio is Y, then the calculating formula of Y is:

$Y=\frac{H\·W-w_{n-1}\·h_{n-1}}{(H-h_{n-1})\·W}$

Therefore, when consider high to metal have part rolled piece upper and lower surface distortion time, then the calculating formula compensating drafts is:

${\mathrm{\Δh}}_{n1}^{\′}=\frac{{\mathrm{\δ}}_{n-1}\·h_{n-1}}{{\mathrm{\δ}}_{n-1}+w_{n-1}-Y\·w_{n-1}}$

(2) Δ h ' _n2computational methods

During rolling extreme trace time, still there will be part high to metal only in the phenomenon of rolled piece surface flowing, therefore also need to compensate the drafts of last passes.Should at Δ h _n+ Δ h ' _n1basis on compensate, therefore, Δ h ' _n2calculating formula be:

${\mathrm{\Δh}}_{n2}^{\′}=\frac{({\mathrm{\Δh}}_n+{\mathrm{\Δh}}_{n1}^{\′})\·w_{n-1}\·L\·Y}{w_{n-1}\·L}=({\mathrm{\Δh}}_n+{\mathrm{\Δh}}_{n1}^{\′})\·Y$

Last reduction in pass after compensating is:

${\mathrm{\ΔH}}_n={\mathrm{\Δh}}_n+{\mathrm{\Δh}}_{n1}^{\′}+{\mathrm{\Δh}}_{n2}^{\′}={\mathrm{\Δh}}_n+\frac{{\mathrm{\δ}}_{n-1}\·h_{n-1}}{{\mathrm{\δ}}_{n-1}+w_{n-1}-Y\·w_{n-1}}+({\mathrm{\Δh}}_n+{\mathrm{\Δh}}_{n1}^{\′})\·Y$

If this value has exceeded the maximum permission load of milling train, then by the last reduction in pass Δ H after compensating _nbe divided into two passages to be rolled, can distribute in any proportion, as long as the load of milling train is no more than maximum permissible value.

When calculating the extreme trace after overcompensation time or last two passages, (a time rolling load is transfinited, during point two passes) after drafts, the extreme trace should put in advance by second-level model default milling train time gap values between rollers or last two passage gap values between rollers, and be sent to PLC system and perform.When rolled piece is rolled by this roll gap, can ensure that the middle part effective width of finished product rolled piece can reach desired value W _n.

If the length L=3000 millimeter of ingot casting, width W=2000 millimeter, thickness H=500 millimeter; Can be obtained by rolling procedure, total road number of times in transverse rolling stage is 4; The inlet thickness H that rolled piece extreme trace is secondary _n-1=455 millimeters; The exit thickness H that rolled piece extreme trace is secondary _n=445 millimeters.Effective width W in the middle part of the rolled piece expected _n=2247.2 millimeters.Suppose that the length of transverse rolling passage rolled piece is constant, then the extreme trace time inlet set width W of rolled piece _n-1(unit is millimeter) is:

The middle part effective width w ' of rolled piece in image is obtained by the tape measure in image _n-1=382 millimeters, in image rolled piece thickness h ' _n-1=80 millimeters.The actual (real) thickness h of the rolled piece before the secondary entrance of now extreme trace is obtained with chi measurement by calibrator or operator _n-1=457 millimeters; Effective width w in the middle part of the entrance that then extreme trace of rolled piece is secondary _n-1for:

The width difference δ of effective width in the middle part of the extreme trace time inlet set width of the transverse rolling stage rolled piece entrance secondary with extreme trace can be obtained thus _n-1for:

δ _n-1=W _n-1-w _n-1=2197.8-2182.18=15.62 millimeter

If the extreme trace of rolled piece time setting drafts is Δ h _n=H _n-1-H _n=10 millimeters; Then Y value is:

$Y=\frac{H\·W-w_{n-1}\·h_{n-1}}{(H-h_{n-1})\·W}=\frac{500\×2000-2182.18\×457}{(500-457)\×2000}=0.0319$

The width compensation drafts that can obtain before last passes is:

The width compensation drafts Δ h ' of end passes _n2for:

Δ h ' _n2=(Δ h _n+ Δ h ' _n1) Y=(10+3.35) × 0.0319=0.43 millimeter

Last reduction in pass after compensating is:

Δ H _n=Δ h _n+ Δ h ' _n1+ Δ h ' _n2=10+3.35+0.43=13.78 millimeter

The drafts secondary when extreme trace is Δ H _nwhen=13.78 millimeters, the middle part effective width of finished product rolled piece can reach desired value W _n=2247.2 millimeters.If this value has exceeded the maximum permission load of milling train, then by drafts Δ H _ntwo passages are divided into be rolled.

Claims (4)

1. the width control method that rolls of cut deal transverse and longitudinal, is characterized in that: before and after the milling train of transverse rolling stage extreme trace time, be provided with metal detector and detect the video camera of rolled piece side view; Adopt following steps:

A, in rolling procedure, obtain rolled piece complete the exit thickness of all preorder passages, drafts and corresponding width in the transverse rolling stage, and the inlet set thickness of extreme trace time, the outlet setting thickness of extreme trace time, extreme trace time inlet set width and expectation finished product rolled piece in the middle part of effective width, wherein, the maximum permission load that all reductions in pass before transverse rolling stage extreme trace time all can bear according to milling train sets;

B, when metal detector detects that rolled piece enters camera watch region, rolled piece side view image before the lower extreme trace time entrance of video camera shooting, the ratio of the thickness of rolled piece in the middle part effective width of rolled piece in image and image is obtained after image procossing, measured the actual (real) thickness of now rolled piece by calibrator simultaneously, effective width in the middle part of the entrance calculating rolled piece extreme trace time according to the actual (real) thickness of described ratio and rolled piece, can obtain the width difference of effective width in the middle part of the extreme trace time inlet set width of the transverse rolling stage rolled piece entrance secondary with extreme trace thus;

C, calculate the secondary drafts that sets of compensation drafts and the extreme trace of the extreme trace time of rolled piece according to described width difference and to sue for peace the last reduction in pass obtained after compensating, with the gap values between rollers that this regulates extreme trace secondary, thus effective width in the middle part of the finished product rolled piece that rolled piece acquisition is expected; When the last reduction in pass after compensating has exceeded the maximum permission load of milling train, increase a rolling pass, be divided into two passages to be rolled the last reduction in pass after compensating, then regulate the gap values between rollers of last two passages.

2. the width control method that rolls of cut deal transverse and longitudinal according to claim 1, is characterized in that: in steps A, the extreme trace time inlet set width of rolled piece is:

$W_{n-1}=\frac{W\·L\·H}{H_{n-1}\·L}=\frac{W\·H}{H_{n-1}}$

Wherein, W _n-1for the extreme trace time inlet set width of rolled piece, unit is millimeter; W is the width of ingot casting, and L is the length of ingot casting, and H is the thickness of ingot casting, and unit is millimeter; H _n-1for the inlet thickness that rolled piece extreme trace is secondary, unit is millimeter.

3. the width control method that rolls of cut deal transverse and longitudinal according to claim 2, is characterized in that: in step B, the calculating formula of width difference is:

δ _n-1＝W _n-1-w _n-1

Wherein, δ _n-1for the width difference of effective width in the middle part of the entrance that the extreme trace time inlet set width of transverse rolling stage rolled piece is secondary with extreme trace, unit is millimeter; w _n-1for effective width in the middle part of the entrance that the extreme trace of rolled piece is secondary, unit is millimeter, and it is according to following formulae discovery:

$w_{n-1}=h_{n-1}\·\frac{w_{n-1}^{\′}}{h_{n-1}^{\′}}$

In formula, h _n-1for the actual (real) thickness of the rolled piece before extreme trace time entrance, unit is millimeter; for the ratio of the thickness of rolled piece in the middle part effective width of rolled piece in image and image.

4. the width control method that rolls of cut deal transverse and longitudinal according to claim 3, is characterized in that: the computational methods of the last reduction in pass in step C after compensating are as follows:

Supposing that the extreme trace of rolled piece sets drafts is Δ h _n, unit is millimeter; Then Δ h _n=H _n-1-H _n, H _nfor the exit thickness that rolled piece extreme trace is secondary, unit is millimeter; The compensation drafts that the extreme trace of rolled piece is secondary is Δ h ' _n, unit is millimeter; Last reduction in pass then after compensating is Δ H _n=Δ h _n+ Δ h ' _n, unit is millimeter; After mill load calculation and check, if this through compensate after last reduction in pass Δ H _nexceed the maximum load that milling train allows, be then divided into two passages to be rolled extreme trace; Δ h ' _nbe made up of two parts, a part is the width compensation drafts before last passes, if it is Δ h ' _n1, unit is millimeter; Another part is the width compensation drafts of last passes, if it is Δ h ' _n2, unit is millimeter;

(1) Δ h ' _n1computational methods

For eliminating the width difference δ before last passes _n-1need allow more height to metal extend to width, namely the secondary drafts of extreme trace is increased, in the actual operation of rolling, have that part is high only to flow on the surface of rolled piece to metal, do not form effective width, need to assess this part metal and account for and be allly out of shape the high ratio to metal, suppose that this ratio is Y, then the calculating formula of Y is:

$Y=\frac{H\·W-w_{n-1}\·h_{n-1}}{(H-h_{n-1})\·W}$

Therefore, when consider high to metal have part rolled piece upper and lower surface distortion time, then the calculating formula compensating drafts is:

${\mathrm{\Δh}}_{n1}^{\′}=\frac{{\mathrm{\δ}}_{n-1}\·h_{n-1}}{{\mathrm{\δ}}_{n-1}+w_{n-1}-Y\·w_{n-1}}$

(2) Δ h ' _n2computational methods

During rolling extreme trace time, still there will be part high to metal only in the phenomenon of rolled piece surface flowing, therefore also need to compensate the drafts of last passes, should at Δ h _n+ Δ h ' _n1basis on compensate, therefore, Δ h ' _n2calculating formula be:

${\mathrm{\Δh}}_{n2}^{\′}=\frac{({\mathrm{\Δh}}_n+{\mathrm{\Δh}}_{n1}^{\′})\·w_{n-1}\·L\·Y}{w_{n-1}\·L}=({\mathrm{\Δh}}_n+{\mathrm{\Δh}}_{n1}^{\′})\·Y$

Last reduction in pass after compensating is:

${\mathrm{\ΔH}}_n={\mathrm{\Δh}}_n+{\mathrm{\Δh}}_{n1}^{\′}+{\mathrm{\Δh}}_{n2}^{\′}={\mathrm{\Δh}}_n+\frac{{\mathrm{\δ}}_{n-1}\·h_{n-1}}{{\mathrm{\δ}}_{n-1}+w_{n-1}-Y\·w_{n-1}}+({\mathrm{\Δh}}_n+{\mathrm{\Δh}}_{n1}^{\′})\·Y.$