CN107832535A - A kind of method of cut deal flat shape intelligent predicting - Google Patents
A kind of method of cut deal flat shape intelligent predicting Download PDFInfo
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Abstract
A kind of cut deal flat shape intelligent Forecasting of the application, comprises the following steps：The three-dimensional finite element Explicit Dynamics model established during billet rolling, rolling condition is set, simulate billet rolling process, extraction analog result rolled piece edge node coordinate；According to metal flow curve corresponding to described edge node coordinate fitting generation present day analog process；Said process is repeated, obtains a plurality of metal flow curve corresponding to different steel billets and the corresponding different rolling condition operations of rolling；Rolled piece inlet thickness H, width W, reduction ratio ε are selected as input parameter；Output of the key point as artificial neural network on the described a plurality of metal flow curve of selection, trains described artificial neural network；Current steel billet parameter to be predicted and rolling condition input are completed to the artificial neural network of training, generate prediction result, completes shaping prediction.
Description
Technical field
The invention belongs to roll field, more particularly to a kind of method of cut deal flat shape intelligent predicting.Relate generally to
Patent classificating number G06 is calculated；Calculate；Count numbers of the G06F electricity Digital data processing G06F17/00 especially suitable for specific function
Word computing device or data processing equipment or data processing method G06F17/50 CADs.
Background technology
Cut deal is during multi- pass rolling because the free-flowing of metal under 3 D deformation can cause final products
Flat shape deviates rectangle, as shown in figure 1, causing the increase that damage amount is cut in follow-up shear history, this is to influence lumber recovery
One of key factor.Control device common at present is to carry out band load by hydraulic system in shaping extreme trace time or broadening extreme trace time
Plan view control is depressed, the volume of defect part is converted to the respective change of the thickness of slab cross-section, so that final steel
Plate flat shape farthest reduces steel plate and cuts damage with side end to end close to rectangle.
The control accuracy of flat shape is decided by under different technology conditions to the precision of prediction of the final flat shape of steel plate, often
The flat shape Forecasting Methodology seen is by experimental simulation, is returned to obtain mathematical modeling according to measured data.
Because regression model is simple, actual production conditions are complicated, and the flat shape prediction curve established under experiment condition is difficult
In adapting to actual production, precision of prediction is not high, and flat shape application on site effect can not meet that optimal lumber recovery control requires.
The content of the invention
For traditional flat shape forecast model is simple, low precision, it is difficult to the problem of realizing online high precision computation, this
Invention proposes a kind of cut deal flat shape intelligent Forecasting, based on artificial neural network to finite element software numerical simulation
As a result it is trained, obtains the curve output of operation of rolling 3 D deformation, it is more with reference to flat shape as the flowing law of metal
The normal extension of point setup parameter and operation of rolling steel billet, it is pre- to the Head and Tail Shape progress intelligence of multi- pass rolling technique lower steel plate
Survey, obtain the evaluating of high precision plane shape control, mainly comprise the following steps
- three-dimensional finite element Explicit Dynamics the model established during billet rolling, rolling condition is set, simulate steel billet
The operation of rolling, extraction analog result rolled piece edge node coordinate；
- according to corresponding to described edge node coordinate fitting generation present day analog process metal flow curve；
- said process is repeated, obtain a plurality of metal stream corresponding to different steel billets and the corresponding different rolling condition operations of rolling
Moving curve；
- selection rolled piece inlet thickness H, width W, reduction ratio ε are as input parameter；The described a plurality of metal flow of selection
Output of the key point as artificial neural network on curve, trains described artificial neural network；
- the artificial neural network for completing to train by current steel billet parameter to be predicted and rolling condition input, generation prediction
As a result, shaping prediction is completed.
As preferred embodiment, predicted for the flat shape under horizontal-vertical rolling mode of cut deal, multi-pass is rolled
System is divided into steel billet broadening stage, axial rolling the first passage stage and axial rolling residue passes stage；
- broadening stage, the neural network prediction each broadening stage completed based on the training correspond to rolling pass
Side edge shape, generate prediction result corresponding with passage；After completing whole broadening stage rolling passages, it is superimposed corresponding per a time
The sub- result of prediction, obtain broadening stage most end passage side prediction result；
- axial rolling the first passage stage：Rolled piece is rotated by 90 ° after broadening rolls carries out longitudinal rolling, and by described broadening
Initial value of the stage most end passage side prediction result as axial rolling the first passage Head and Tail Shape；Rolling mill strip load pressure is calculated to be abided by
Head and tail shape caused by the setting for the flat shape parameter of curve followed changes；
Calculate rolling mill strip and carry head and tail shape change caused by the setting for depressing followed flat shape parameter of curve；
The artificial neural network completed by the training directly predicts the passage of axial rolling first, the Head and Tail Shape predicted
Change；
Above-mentioned change in shape is superimposed, obtains axial rolling the first passage stage head and tail shape prediction result；
- axial rolling residue passes the stage：
Head and Tail Shape change, the axial rolling passage tried to achieve based on neural network prediction caused by the normal extension in superposition longitudinal direction
Head and Tail Shape changes, as final Head and Tail Shape, i.e., final prediction result.
Further, rolled caused by the setting for calculating the followed flat shape parameter of curve of rolling mill strip load pressure
Part Head and Tail Shape change detailed process is as follows：
- setting rolling mill strip carries the control parameter that pressure follows curve：Stable segment length is L1, band carry pressure segment length
For L2, to carry drafts be Δ h and center shape compensation amount is d to band；Steel plate width is L, initially sets exit thickness as h；7 points are put down
Face Shape Control Point coordinate is respectively (0, h-a+ Δ h), (L1, h-a+ Δs h), (L1+L2, h-a), (h-a-d),(L-L1-L2, h-a), (L-L1, h-a+ Δ h), (L, h-a+ Δ h)；Corresponding thickness
Thk1=h-a-d, thk2=h-a, thk3=h-a+ Δ h；
- be calculated by equation below under plan view control and ensure that shutting out length keeps constant intermediate variable a：
When not putting into plan view control, transverse rolling extreme trace time steel plate rolls into thickness h by thickness H；And in input planar shaped
When shape controls, transverse rolling extreme trace is plan view control passage, and now steel plate is rolled into by the thickening of 7 point curves setting by thickness H
Shape is spent, the length shut out during for the length that ensures to shut out with not putting into flat shape is consistent, according to constancy of volume original
Then with flat shape setup parameter, intermediate variable a value is calculated.
Further, in the calculating process in the axial rolling residue passes stage, inlet thickness section configuration is assumed
For rectangular cross section；
Assuming that axial rolling process, without spreading, the normal extensible extent in longitudinal direction calculates according to constant-volume principle；
Multiple trace points are set in rolled piece half width direction according to flat shape setup parameter, rolled for axial rolling per a time
System, corresponding normal development length is calculated according to trace point position, is superimposed, that is, obtains with the Head and Tail Shape of artificial neural network output
The Head and Tail Shape that this passes terminates.
As preferred embodiment, it is fitted using 4 curves, 4 times curve form is as follows：
Y=A2x2+A3x3+A4x4
Wherein, x is that node normalizes transverse axis coordinate, x=node transverse axis coordinate/1000, is rolled for broadening, X direction
It is width for longitudinal direction rolling X direction for rolling direction；Y exports for matched curve shape；A2、A3And A4For curve
Fitting parameter.
Brief description of the drawings
, below will be to embodiment or existing for clearer explanation embodiments of the invention or the technical scheme of prior art
There is the required accompanying drawing used in technology description to do one and simply introduce, it should be apparent that, drawings in the following description are only
Some embodiments of the present invention, for those of ordinary skill in the art, on the premise of not paying creative work, may be used also
To obtain other accompanying drawings according to these accompanying drawings.
Fig. 1 is the Plate Rolling Process change in shape schematic diagram mentioned in background of invention
Fig. 2 is that crucial training points choose schematic diagram in shape of rolling piece matched curve of the present invention
Fig. 3 is artificial neural network's structural representation of the present invention
Fig. 4 is the calculation processes schematic diagram of broadening stage side edge shape of the present invention
Fig. 5 is the corresponding 7 controlling curve schematic diagrames chosen of flat shape of the present invention
Fig. 6 is that operation of rolling rolled piece flat shape of the present invention predicts schematic diagram
Fig. 7 is finite element simulation calculation result schematic diagram of the present invention with width rolled piece, and wherein Fig. 7 a are reduction ratio 20%,
Inlet thickness is 50mm head shape finite element simulation calculation result schematic diagram；Fig. 7 b are reduction ratio 20%, and inlet thickness is
200mm head shape finite element simulation calculation result schematic diagram
Error state schematic diagram when Fig. 8 is neural metwork training 10000 times in the embodiment of the present invention
Fig. 9 is head, the change schematic diagram of tail shape during each axial rolling passes in the embodiment of the present invention, wherein scheming
9a is head change schematic diagram；Fig. 9 b are afterbody change schematic diagram
Embodiment
To make the purpose, technical scheme and advantage of embodiments of the invention clearer, with reference to the embodiment of the present invention
In accompanying drawing, the technical scheme in the embodiment of the present invention is clearly completely described：
As shown in Fig. 1-Fig. 9：Technology path is as follows used by a kind of cut deal flat shape intelligent Forecasting：
1. simulation calculating is carried out to one-pass roller process using finite element software
Billet rolling process three-dimensional finite element Explicit Dynamics model is established,
Roll is set as rigid body, rolled piece is deformable body, to cover the primary condition of production process blank and finished product, including is rolled
Part thickness, width and reduction ratio, in finite element software to rolled piece carry out dividing elements, setting friction condition, apply roll and
Simulated after the parameters such as the initial velocity of rolled piece, in the result extract rolled piece end to end the node coordinate with side edge as metal
The assessment calculation basis of flowing.
Rolled piece initial simulation parameters are as follows：
Broadening stage rolling simulates initial parameter
● width of steel billet：2000mm, 2400mm, 2800mm, 3200mm
● steel billet thickness：150mm, 200mm, 250mm, 300mm
● reduction ratio：5%, 10%, 15%, 20%
Axial rolling stage rolling simulates initial parameter
● width of steel billet：1500mm, 2000mm, 2400mm, 2850mm, 3300mm
● steel billet thickness：10mm, 50mm, 100mm, 150mm, 200mm, 250mm, 300mm
● reduction ratio：5%, 10%, 15%, 20%, 30%
2. establish the metal flow matched curve of the operation of rolling
Calculate to simplify, rolled for broadening, the tracking range side metal flow in 800mm end to end；For longitudinal direction
Rolling, tracks metal flow end to end in the range of the half width of rolled piece.
Node coordinate is obtained in the analog result of finite element software, is fitted after processing using 4 curves, 4 songs
Line uses following form, facilitates parameter fitting.
Y=A2x2+A3x3+A4x4 (1)
Wherein, x is that node normalizes transverse axis coordinate, x=node transverse axis coordinate/1000, is rolled for broadening, X direction
It is width for longitudinal direction rolling X direction for rolling direction；Y exports for matched curve shape；A2、A3And A4For curve
Fitting parameter.
In order to ensure the artificial neural network training precision to matched curve, the present invention equidistantly chooses 4 fittings
3 key point P on curve1、P2And P3Height h1、h2And h3Exported as neutral net,
As shown in Figure 2.Assuming that rolled piece half width is w, then the selection of 3 transverse axis coordinates is respectively：x1=w/3, x2=w*
2/3, x3=w, h1、h2、h3For corresponding height in matched curve.
3. the flowing of single pass three-dimensional rolled metal is trained using artificial neural network
Selection is using rolled piece inlet thickness H, width W, reduction ratio ε as input parameter, with 3 passes selected in matched curve
Key point height h1、h2、h3As output parameter, multigroup result of finite element software three-dimensional simulation is trained, obtains training net
The optimized parameter of network, the metal flow that the neutral net trained can calculate any specification rolled piece one-pass roller process are bent
Line, the structure of neutral net are as shown in Figure 3.
The height h of 3 key points of the artificial neural network's output trained1、h2And h3, bring 4 matched curve public affairs into
Formula (1) can be in the hope of parameter of curve A2、A3And A4。
So matched curve parameter is：
4. multi- pass rolling process head and tail shape is superimposed Forecasting Methodology
(1) broadening stage shape is predicted
Broadening stage, steel billet need to be rotated by 90 ° and is rolled, and originally steel billet is changed into side, spreading process side end to end
Shape can also change, it is necessary to be tracked,
Change in shape of this stage per a time side is predicted based on artificial neural network, finally every to the broadening stage
The change in shape of a time is overlapped processing.
Side edge shape change is concentrated mainly on close to part end to end in spreading process, and chosen distance of the present invention is end to end
Computer capacity of the 800mm length as side edge shape, as shown in Figure 4.
It is initial end to end as axial rolling by obtaining the net shape of broadening extreme trace time side after multi-pass superposition calculation
Shape.
(2) axial rolling the first passage rolling rolling stock Head and Tail Shape is predicted
Control passage of the broadening stage extreme trace time as flat shape, the hydraulic system of this passage milling train can be bent according to setting
Line carries out band and carries pressure, and the control parameter of common 7 points of setting curves includes：L1、L2, Δ h and d, plan view control schematic diagram
As shown in Figure 5：
In Fig. 5, L1、L2, Δ h and d be plan view control parameter；L is steel plate width；H is inlet set thickness；thk1、
Thk2 and thk3 is thickness corresponding to control point；A be it needs to be determined that intermediate variable.
In broadening stage extreme trace time, i.e. plan view control passage, in order to ensure the final control width of steel plate, according to body
Product principle of invariance determines the relation between the inlet thickness H parameters a of rolled piece：
When not putting into plan view control, transverse rolling extreme trace time steel plate rolls into thickness h by thickness H；And in input planar shaped
When shape controls, transverse rolling extreme trace is plan view control passage, and now steel plate is rolled into by the thickening of 7 point curves setting by thickness H
Shape is spent, the length shut out during for the length that ensures to shut out with not putting into flat shape is consistent, according to constancy of volume original
Then with flat shape setup parameter, intermediate variable a value is calculated.
So the prediction of the shape end to end of the passage of axial rolling first, which calculates, includes three parts superposition：
The broadening stage side change in shape, Head and Tail Shape change caused by flat shape curve setting, based on artificial god
The first passage of the axial rolling Head and Tail Shape change tried to achieve through neural network forecast.
(3) axial rolling residue passage head and tail shape is predicted
Since the passage of axial rolling second, inlet thickness section configuration is assumed to be rectangular cross section, and the change of Head and Tail Shape includes
Two-part superposition below：Head and Tail Shape caused by the normal extension in longitudinal direction is changed, indulged based on what neural network prediction was tried to achieve
Mill train time Head and Tail Shape change.
Assuming that axial rolling process without spreading, then the normal extensible extent in longitudinal direction can calculate according to constant-volume principle.
In order to accurately be calculated Head and Tail Shape, set according to flat shape setup parameter in rolled piece half width direction
Multiple trace points are put, for each passes of axial rolling, corresponding normal development length are calculated according to trace point position, with artificial god
Head and Tail Shape through network output is superimposed, that is, obtains the Head and Tail Shape that this passes terminates.
Initial length using the final development length after each trace point superposition of this passage as lower passage, successively circulation are counted
Calculate, completed until all passages calculate, obtain final Head and Tail Shape.Rolled piece flat shape is predicted according to rolling mill practice code
Schematic diagram is as shown in Figure 6.
Embodiment
The present embodiment carries out flat shape prediction to certain Medium and Heavy Plate Rolling technological procedure, and the technological parameter of rolled products is such as
Under：
● steel grade：Q235
● blank specification：220mm×2000mm×300mm
● trimmed size：55mm×2200mm
● broadening 7 flat shape setup parameters of extreme trace time：L1=150mm, L2=177.57mm, Δ h=3.1mm, d=
1.0mm
Rolling mill practice code and pre-calculated data are as shown in table 1.
The rolling mill practice protocol table of table 1
Rolling procedure has 8 passages altogether, using horizontal-vertical rolling mode, is rolled wherein preceding 2 passage enters line broadening, remaining 6
Secondary carry out axial rolling, broadening extreme trace employ 7 plan view controls.The prediction of the final flat shape of rolled piece end to end considers 3
Some effects factor：During broadening rolling pass when the shape of rolled piece side, flat shape parameter setting, axial rolling passes end to end
Shape.When head-tail Shape Prediction is to roll calculation basis, different elongations warp are used as in extension of the width to diverse location
Cross the net shape end to end that multi-pass superposition can obtain steel plate.
1. the three-dimensional simulation of one-pass roller process finite element calculates metal flow
Initial parameter by setting covering production process blank and finished product carries out the finite element modelling of the operation of rolling in advance
Calculate, the cell node coordinate under corresponding different initial setting conditions is obtained, as the rule for representing metal flow.Fig. 7 is point
Reduction ratio 20%, the finite element simulation calculation result of thickness 50mm, 100mm different in width rolled piece are not corresponded to.
2. the metal flow curve matching of one-pass roller process
In order to represent the change of Head and Tail Shape with curve form, based on finite element modelling result, carried out with 4 curves
Fitting obtains parameter of curve.Rolled for broadening, only to being fitted close to the side edge shape of 800mm length ranges end to end；It is right
It is fitted in the Head and Tail Shape in longitudinal rolling, double of width range.The one of which initial parameter of finite element simulation calculation：
Inlet thickness is 100mm, and reduction ratio 20%, rolled piece width is 2400mm, carries out the head that finite element rolling simulation obtains and intends
Closing curve is：Y=0.7348x2+0.0516x3+9.67823x4, corresponding 3 key points are highly respectively：0.36863、
4.4609 with 21.216；Afterbody matched curve is：Y=0.8206x2+0.057x3+10.6x4, corresponding 3 key points highly divide
It is not：0.406th, 4.894 and 23.251.
3. training of the artificial neural network to analogue data
Artificial neural network is established, input layer is 3 variables：Inlet thickness, reduction ratio and rolled piece width；Output layer is 3
Individual variable, correspond to the height h of 3 key points selected on metal flow curve1、h2And h3, specific neural network parameter setting
It is as follows：
● neural network structure：3 layers of BP neural network
● input layer unit number 3；Hidden layer unit number 20, output layer unit number 3
● learning rate η takes 0.4
● factor of momentum α takes 0.3
Fig. 8 is the convergence situation of neural network training process error.Finite element modelling result is trained, passed through
32000 training, network output error are less than 1.0 × 10-6, it is met the result of required precision, the nerve net after training
Network can carry out Shape Prediction to the metal flow after any specification rolled piece one-pass roller.
4. intelligent predicting is carried out to rolled piece flat shape according to rolling mill practice code
For 7 plan view controls in process above, the present invention is bent according to the setting of flat shape in half width
Line is divided into 19 shape trace points, and 5 parts are divided wherein in L1 length, 5 parts are divided in L2 length, remainder divides 8 parts.Opening up
In the wide stage, the curve of output of preceding 2 passage side is overlapped, obtains 4 parameters of curve apart from 800mm end to end；Consideration exhibition
The plan view control that wide stage extreme trace time is implemented, consider initial side shape when longitudinally the first passage of rolling predicts mouth-shaped
The metal of normal extension and neutral net output caused by shape, flat shape setting flows freely three influences, and is overlapped；
Since the passage of axial rolling the 2nd, influence the normal extension only comprising every time pressure process of the changing factor of rolled piece flat shape and
Metal end to end flows freely two superpositions.
It is superimposed, is obtained every with normal extension calculated value by flowing freely result to the wide metal end to end to 19 trace points
The head and tail shape that a time rolling terminates.Iterate to calculate according to rolling procedure and completed up to last a time calculates,
Final head and tail shape is obtained, Fig. 9 is the change of head, tail shape during each axial rolling passes.
After multi-pass superposition calculation, in the height of curve result of calculation and actual measured value deviation of the width position of rolled piece half
Less than 5%, due to not considering spreading for rolled piece in calculating process, have one in the Shape Prediction close to rolled piece edge and actual measurement
A little difference, but this has no effect on the evaluation to plan view control parameter.The intelligent Forecasting of exploitation can be used for producing above
Process provides support to the fast prediction of flat shape to the on-line optimization of flat shape parameter.
The foregoing is only a preferred embodiment of the present invention, but protection scope of the present invention be not limited thereto,
Any one skilled in the art the invention discloses technical scope in, technique according to the invention scheme and its
Inventive concept is subject to equivalent substitution or change, should all be included within the scope of the present invention.
Claims (5)
1. a kind of cut deal flat shape intelligent Forecasting, it is characterised in that comprise the following steps：
- three-dimensional finite element Explicit Dynamics the model established during billet rolling, rolling condition is set, simulate billet rolling
Process, extraction analog result rolled piece edge node coordinate；
- according to corresponding to described edge node coordinate fitting generation present day analog process metal flow curve；
- said process is repeated, it is bent to obtain a plurality of metal flow corresponding to different steel billets and the corresponding different rolling condition operations of rolling
Line；
- selection rolled piece inlet thickness H, width W, reduction ratio ε are as input parameter；The described a plurality of metal flow curve of selection
On output of the key point as artificial neural network, train described artificial neural network；
- the artificial neural network for completing to train by current steel billet parameter to be predicted and rolling condition input, generation prediction knot
Fruit, complete shaping prediction.
2. cut deal flat shape intelligent Forecasting according to claim 1, is further characterized in that：For cut deal
Flat shape prediction under horizontal-vertical rolling mode, steel billet broadening stage, axial rolling the first passage stage are divided into by multi- pass rolling
With the axial rolling residue passes stage；
- broadening stage, the neural network prediction each broadening stage completed based on the training correspond to rolling pass side
Shape, generate prediction result corresponding with passage；After completing whole broadening stage rolling passages, it is superimposed pre- corresponding to per a time
Sub- result is surveyed, obtains broadening stage most end passage side prediction result；
- axial rolling the first passage stage：Rolled piece is rotated by 90 ° after broadening rolls carries out longitudinal rolling, and by the described broadening stage
Initial value of the most end passage side prediction result as axial rolling the first passage Head and Tail Shape；Calculate rolling mill strip and carry what pressure was followed
Head and tail shape caused by the setting of flat shape parameter of curve changes；
The artificial neural network completed by the training directly predicts the passage of axial rolling first, and the Head and Tail Shape predicted becomes
Change；
Above-mentioned change in shape is superimposed, obtains axial rolling the first passage stage head and tail shape prediction result；
- axial rolling residue passes the stage：
Superposition longitudinal direction is normal extend caused by Head and Tail Shape change, the axial rolling passage tried to achieve based on neural network prediction is end to end
Change in shape, as final Head and Tail Shape, i.e., final prediction result.
3. cut deal flat shape intelligent Forecasting according to claim 2, is further characterized in that：The calculating milling train
It is as follows that head and tail shape change detailed process caused by the setting of followed flat shape parameter of curve is pushed with load：
- setting rolling mill strip carries the control parameter that pressure follows curve：Stable segment length is L1, band carry pressure segment length be L2、
Band load drafts is Δ h and center shape compensation amount is d；Steel plate width is L, initially sets exit thickness as h；7 planar shapeds
Shape control point coordinates is respectively (0, h-a+ Δ h), (L1, h-a+ Δs h), (L1+L2, h-a),
(L-L1-L2, h-a), (L-L1, h-a+ Δ h), (L, h-a+ Δ h)；
Corresponding thickness thk1=h-a-d, thk2=h-a, thk3=h-a+ Δs h；
- be calculated by equation below under plan view control and ensure that shutting out length keeps constant intermediate variable a：
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When not putting into plan view control, transverse rolling extreme trace time steel plate rolls into thickness h by thickness H；And in input flat shape control
When processed, transverse rolling extreme trace is plan view control passage, and now steel plate rolls into the Varying-thickness shape set by 7 point curves by thickness H
Shape, the length shut out during for the length that ensures to shut out with not putting into flat shape are consistent, according to constant-volume principle and
Flat shape setup parameter, intermediate variable a value is calculated.
4. cut deal flat shape intelligent Forecasting according to claim 2, is further characterized in that：The axial rolling is remaining
In the calculating process in passes stage, inlet thickness section configuration is assumed to be rectangular cross section；Assuming that axial rolling process is indulged without spreading
Calculated to normal extensible extent according to constant-volume principle；
Multiple trace points are set in rolled piece half width direction according to flat shape setup parameter, for each passes of axial rolling,
Corresponding normal development length is calculated according to trace point position, is superimposed with the Head and Tail Shape of artificial neural network output, that is, obtains this
The Head and Tail Shape that passes terminate.
5. cut deal flat shape intelligent Forecasting according to claim 1, is further characterized in that：Using 4 curves
It is fitted, 4 times curve form is as follows：
Y=A2x2+A3x3+A4x4
Wherein, x is that node normalizes transverse axis coordinate, x=node transverse axis coordinate/1000, is rolled for broadening, X direction is to roll
Direction processed, it is width for longitudinal direction rolling X direction；Y exports for matched curve shape；A2、A3And A4For the plan of curve
Close parameter.
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