CN105068970B - A kind of interpolation iterative approximation computational methods for determining five Stands Cold Tandem Mill thickness - Google Patents
A kind of interpolation iterative approximation computational methods for determining five Stands Cold Tandem Mill thickness Download PDFInfo
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Abstract
The invention provides a kind of interpolation iterative approximation computational methods for determining five Stands Cold Tandem Mill thickness, comprise the following steps：Provide strip raw material data；Determine the power distribution ratio of each frame and the absolute roll-force of the 5th frame；Calculate the inlet thickness of the 5th frame；The average reduction ratio of each frame is calculated according to the inlet thickness of the 5th frame and the first frame；The exit thickness that distribution ratio depresses each frame is calculated for the first time；Calculate first time iteration constant；Calculate the exit thickness of each power distribution mode frame；Calculate the roll-force and roll torque of each frame；Calculate second of iteration constant；The absolute difference of the exit thickness of last frame of the exit thickness and milling train of the calculating distribution ratio pressure frame of mode the 4th；Loop iteration calculates, and when absolute difference is less than the minimal difference allowed or iterations reaches maximum, exits circulation, THICKNESS CALCULATION terminates.The present invention solves thickness based on interpolation method, simplifies algorithm, obtains high-precision thick angle value.
Description
Technical field
The invention belongs to metallurgical engineering and computer application field, more particularly to a kind of five Stands Cold Tandem Mill thickness of determination
Interpolation iterative approximation computational methods.
Background technology
Rolling schedule calculation in five Stands Cold Tandem Mills is the basis for calculating other setting values, and frame THICKNESS CALCULATION is to roll
The important component that code processed calculates, frame THICKNESS CALCULATION have two ways：Absolute draft mode and distribution ratio pressure mode.
Absolute draft mode is divided into absolute draft rate mode and absolute roll-force mode.Absolute draft rate mode calculated thickness
Method be entrance or exit thickness and known reduction ratio known to, outlet or the entrance of the frame can be directly obtained
Thickness；The method of absolute roll-force mode calculated thickness is thick with known entrance or exit thickness and approximate outlet or entrance
Degree calculates approximate roll-force, if the absolute value of approximate roll-force and the known definitely difference of roll-force is less than some
Threshold value, then the approximate outlet or inlet thickness are required.
Distribution ratio, which is depressed, to be referred between certain several frames of five frames by a certain ratio：Reduction ratio ratio, roll-force ratio
Value and power ratio, to distribute certain reduction ratio, therefore, distribution ratio pressure mode has three kinds of pressure modes：Distribution ratio is depressed
Rate mode, distribution ratio roll-force mode and distribution ratio power mode.
By taking distribution ratio power mode as an example：It is P by the formula of distribution ratio power mode1:P2:…:Pn=α1:α2:…αn, its
Middle n is frame number, P1:P2:…:PnFor the power module calculated value of the n-th frame, α1:α2:…αnFor the power ratio of mill condition
Value.Therefore according to each proportional principle of frame power, each rack outlet thickness is that unknown quantity establishes Nonlinear System of Equations,
Solving this equation group can obtain having very high-precision numerical solution.It is to use to solve this Nonlinear System of Equations mostly
Newton-Raphson methods solve, and thus need to solve partial derivative and Jacobi inverse of a matrix square of the roll-force to thickness
Battle array so that it is big to calculate complicated and operand.
The content of the invention
The technical problem to be solved in the present invention is, for existing for existing five Stands Cold Tandem Mills frame THICKNESS CALCULATION method
Above-mentioned deficiency, there is provided it is a kind of to solve the method that thickness is iterated to calculate in the distribution pressure of five Stands Cold Tandem Mills, by based on interpolation
Method solves Nonlinear System of Equations, simplifies calculating and programming.
The present invention is that technical scheme is used by solving above-mentioned technical problem：
A kind of interpolation iterative approximation computational methods for determining five Stands Cold Tandem Mill thickness, comprise the following steps：
S1：Provide strip raw material data, plant data and process data；
S2：The power distribution ratio of first frame to the 4th frame and definitely rolling for the 5th frame are determined according to mill condition
Power processed；
S3：The inlet thickness of the 5th frame, the 5th frame are calculated according to the absolute roll-force of the 5th frame and exit thickness
Inlet thickness be the 4th frame exit thickness；
S4：First frame to the 4th frame is calculated according to the exit thickness of the 4th frame and the inlet thickness of the first frame
Average reduction ratio；
S5：Calculate distribution ratio pressure first for the first time according to the average reduction ratio of the first frame that S4 is obtained to the 4th frame
Exit thickness of the frame to the 4th frame；
S6：First time iteration constant it_M1 is calculated according to power distribution ratio in S2；
S7：The exit thickness of each power distribution mode frame is calculated according to first time iteration constant it_M1；
S8：The roll-force and roll torque of each frame are calculated, if for the frame that roll-force or roll torque transfinite
Number summation is more than maximum frame number, then the roll-force apportioning cost that current mill condition provides is unreasonable, exits pressure distribution, turns
To S13, S9 is otherwise gone to；
S9：The exit thickness h1_M1 of the 4th obtained frames of the first time iteration constant it_M1 and S7 that S6 is obtained is set to
Coordinate M1 (h1_M1, it_M1)；
S10：Calculate second of iteration constant it_M2；
S11：Calculate the outlet of last frame of the exit thickness h1_M1 and milling train of the distribution ratio pressure frame of mode the 4th
The absolute difference delta_h of thickness；
S12：Loop iteration calculates, and is changed when delta_h reaches less than the minimal difference dh_limit or iterations allowed
During the maximum in generation, circulation is exited, goes to S13；
S13：THICKNESS CALCULATION terminates, and obtains entrance, the exit thickness of each frame.
By such scheme, the average reduction ratio ε calculation formula of the first frame to the 4th frame are as follows in the S4：
In above formula, h0For the inlet thickness of the first frame, h4For the exit thickness of the 4th frame.
By such scheme, first time, iteration constant it_M1 calculation formula were as follows in the S6：
In above formula, m is the number that distribution ratio depresses frame, is 4, ε in the embodiment of the present inventioniDepressed for i-th of distribution ratio
The reduction ratio of frame, width are strip width, and M (i) depresses the power distribution ratio of frame, power distribution for i-th of distribution ratio
Ratio is found from mill condition table.
By such scheme, second of iteration constant it_M2 calculation formula is as follows in the S10：
In above formula, h0For the inlet thickness of the first frame, h4For the exit thickness of the 4th frame, h '4For with first time iteration
The exit thickness for the 4th frame that constant calculates.
By such scheme, absolute difference delta_h calculation formula are as follows in the S11：
Delta_h=| h5-h′4|。
In above formula, h5For the exit thickness of last frame of milling train, h '4Going out for the frame of mode the 4th is depressed for distribution ratio
Mouth thickness, i.e. h1_M1.
By such scheme, loop iteration is calculated as follows in the S12：
1. walks：According to second of iteration constant it_M2, all exit thicknesses for distributing frames are calculated；
2. walks：The exit thickness h1_M2 and second of iteration constant it_M2 for the 4th frame for 1. walking calculating using as
Second approximation point M2 (h1_M2, it_M2)；
3. walks：Calculate the absolute value of the exit thickness of the 4th frame and the exit thickness of the the 4th frame 1. walked in S3
Deviation, if deviation is less than limiting value, S13 is gone to, otherwise go to and 4. walk；
4. walks：Second of iteration constant it_M2 is calculated again with the method based on interpolation：
5. walks：Approximate point M1 value is replaced with to M2 value, i.e. M1=M2；
6. walks：Iterations adds 1, if iterations is more than maximum iteration, goes to S13, otherwise goes to
1. walk.
The operation principle of the present invention：On the basis of Newton-Raphson methods, existing higher convergence rate is constructed, again
The iterative formula of the inverse matrix of partial derivative and coefficient matrix need not be calculated, iteration constant is calculated with the method based on interpolation, with repeatedly
Approximate exit thickness or inlet thickness are obtained for constant, iteration constant is then iterated to calculate and obtains corresponding approximate outlet thickness
Degree or inlet thickness, until approximate exit thickness or inlet thickness meet minimum exit thickness or inlet thickness or iteration time
Count to when reaching maximum, THICKNESS CALCULATION terminates.
Beneficial effects of the present invention：By solving Nonlinear System of Equations based on interpolation method, simplify calculating and programming,
Obtain high-precision thickness value.
Brief description of the drawings
Fig. 1 is the workflow diagram of THICKNESS CALCULATION method of the present invention.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples
The present invention is further elaborated.
As shown in figure 1, the interpolation iterative approximation computational methods of the present invention for determining five Stands Cold Tandem Mill thickness, tool
Body comprises the following steps：
S1：Provide strip raw material data, plant data and process data；
S2：The power distribution ratio of first frame to the 4th frame and definitely rolling for the 5th frame are determined according to mill condition
Power processed；
S3：The inlet thickness h of the 5th frame is calculated according to the absolute roll-force of the 5th frame and exit thickness4, the 5th machine
The inlet thickness h of frame4The as exit thickness of the 4th frame；
S4：First frame to the 4th frame is calculated according to the exit thickness of the 4th frame and the inlet thickness of the first frame
Average reduction ratio ε：
In above formula, h0For the inlet thickness of the first frame, h4For the exit thickness of the 4th frame；
S5：Calculate distribution ratio pressure for the first time according to the average reduction ratio ε of the first frame that S4 is obtained to the 4th frame
Exit thickness h ' of one frame to the 4th frame1, h '2, h '3, h '4；
S6：First time iteration constant it_M1 is calculated according to power distribution ratio in S2：
In above formula, m is the number that distribution ratio depresses frame, is 4, ε in the embodiment of the present inventioniDepressed for i-th of distribution ratio
The reduction ratio of frame, width are strip width, and M (i) depresses the power distribution ratio of frame, power distribution for i-th of distribution ratio
Ratio is found from mill condition table；
S7：The exit thickness of each power distribution mode frame, i.e. the first machine are calculated according to first time iteration constant it_M1
The exit thickness h ' of frame1, the exit thickness h ' of the second frame2, the exit thickness h ' of the 3rd frame3, the exit thickness of the 4th frame
h′4；
S8：Rolling technological parameter is calculated with technological mathematical model：Roll-force and roll-force of first frame to the 4th frame
Square；Whether all transfinite, perform S13 if all transfiniting, otherwise turn if judging the technological parameter of the first frame to the 4th frame
To S9；
Other models, deformation resistance model, roll flattening model, friction are also related to when calculating roll-force and roll torque
Model, roll-force and rolling power model：
1st, deformation resistance model
In above formula, kf is resistance of deformation, and ms0 is the initial value of material resistance of deformation, ms0=282.96 [N/MM2]；msi
For material resistance of deformation increment size, msi=425.45 [N/MM2]；Mse is material work hardening index mse=0.75；Hm is band
The average thickness of steel；h0For raw thickness；
2nd, coefficient of friction model
In formula, μ is coefficient of friction, μ0For basic coefficient of friction；V_0 is to consider the coefficient that speed influences on coefficient of friction；v
For gantry speed；V_1 is the constant relevant with speed；R is the actual roughness of roll；R_0 is the minimum roughness of roll；r_
1 coefficient influenceed for consideration gloss level of roll on coefficient of friction；W_0, w_1 are to consider what roll wear amount influenceed on coefficient of friction
Constant；W is the actual wear amount of roll；F_0, f_1 are to consider the constant that strip exit thickness influences on coefficient of friction；H is band
The exit thickness of steel；Eps is the actual reduction ratio of strip, and eps_0, eps_1 influence normal for consideration reduction ratio on coefficient of friction
Number；
3rd, roll flattening Radius Model
In formula, rb is roll flattening radius；Crb is roll flattening constant, and R is roller radius, FwFor roll-force, B is band
Steel width, h0For strip inlet thickness, h1For strip exit thickness；
4th, rolling force model
F=Fp+Fe
ξ=α tin+β·tout
In formula, F is roll-force (kN)；FpFor plastic zone roll-force (kN)；FeFor elastic region roll-force (kN)；hinFor entrance
Thickness (mm)；houtFor exit thickness (mm)；W is strip width (mm)；tinFor entrance unit tension force (N/mm2)；toutFor outlet
Unit tension (N/mm2)；Kf is average deformation drag (N/mm2)；μ is coefficient of friction；Rb is roll flattening radius (mm)；QFFor
Roll-force external friction influences coefficient；Eps is reduction ratio；V is Poisson's ratio (=0.3)；E be Young's modulus (=21700 ×
9.80665N/mm2)；α is that entrance tension force influences coefficient；β influences coefficient for outlet tension force.
5th, power of motor model
In formula, P is power of motor；η is electric efficiency；R is roller radius (mm)；vRFor the speed of rolls (m/min)；G is
Roll torque；
S9：By the exit thickness h ' of the 4th obtained frames of S74H1_M1 is set to, h1_M1 and S6 obtained first time are changed
Coordinate M1 (h1_M1, it_M1) is set to for constant it_M1；
S10：Calculate second of iteration constant it_M2：
In above formula, h0For the inlet thickness of the first frame, h4For the exit thickness of the 4th frame, h '4For with first time iteration
The exit thickness for the 4th frame that constant calculates；
S11：Calculate the exit thickness h of last frame of milling train5Frame (last of mode the 4th is depressed with distribution ratio
Frame) exit thickness h '4Absolute difference delta_h：
Delta_h=| h5-h′4|；
S12：Delta_h is calculated with the alternative manner based on interpolation, until delta_h is less than the minimal difference dh_ allowed
Limit, for example during the maximum of value 0.001 or iterations arrival iteration, exit circulation, go to S13, loop iteration calculates
It is as follows：
1. walks：According to second of iteration constant it_M2, all exit thicknesses for distributing frames are calculated；
2. walks：The exit thickness h1_M2 and second of iteration constant it_M2 for the 4th frame for 1. walking calculating using as
Second approximation point M2 (h1_M2, it_M2)；
3. walks：Calculate the absolute value of the exit thickness of the 4th frame and the exit thickness of the the 4th frame 1. walked in S3
Deviation, if deviation is less than limiting value, S13 is gone to, otherwise go to and 4. walk；
4. walks：Second of iteration constant it_M2 is calculated again with the method based on interpolation：
5. walks：Approximate point M1 value is replaced with to M2 value, i.e. M1=M2；
6. walks：Iterations adds 1, if iterations is more than maximum iteration, goes to S13, otherwise goes to
1. walk.
S13：THICKNESS CALCULATION terminates (pressure distribution terminates), obtains entrance, the exit thickness of each frame.
Table 1 below is the result of calculation that this example is implemented, and from following table, mill condition can be met using this method
The power of each frame under obtained distribution ratio power condition, while meet the thickness point of the satisfaction in capacity of equipment allowed band
Match somebody with somebody.Raw thickness [mm]：4.030, finished product thickness [mm]：1.201, strip width [mm]：1225, milling train rated power [KW]：
6750。
The computational methods embodiment result of calculation of the present invention of table 1
Example discussed above is only that the basic embodiment of the present invention is described, and not the scope of the present invention is entered
Row limits, and on the premise of design spirit of the present invention is not departed from, those skilled in the art make to technical scheme
Various conversion and improvement, it all should fall into the protection domain of claims of the present invention determination.
Claims (5)
1. a kind of interpolation iterative approximation computational methods for determining five Stands Cold Tandem Mill thickness, it is characterised in that including following step
Suddenly：
S1：Provide strip raw material data, plant data and process data；
S2：Determine the first frame to the power distribution ratio of the 4th frame and the absolute rolling of the 5th frame according to mill condition
Power；
S3：The inlet thickness of the 5th frame is calculated according to the absolute roll-force of the 5th frame and exit thickness, the 5th frame enters
Mouth thickness is the exit thickness of the 4th frame；
S4：First frame being averaged to the 4th frame is calculated according to the exit thickness of the 4th frame and the inlet thickness of the first frame
Reduction ratio；
S5：Calculate distribution ratio for the first time according to the average reduction ratio of the first frame that S4 is obtained to the 4th frame and depress the first frame
To the exit thickness of the 4th frame；
S6：First time iteration constant it_M1 is calculated according to power distribution ratio in S2；
S7：The exit thickness of each power distribution mode frame is calculated according to first time iteration constant it_M1；
S8：The roll-force and roll torque of each frame are calculated, if the number for the frame that roll-force or roll torque transfinite is total
With the frame number more than maximum, then the roll-force apportioning cost that current mill condition provides is unreasonable, exits pressure distribution, goes to
S13, otherwise go to S9；
S9：The exit thickness h1_M1 of the 4th obtained frames of the first time iteration constant it_M1 and S7 that S6 is obtained is set to coordinate
M1 (h1_M1, it_M1)；
S10：Calculate second of iteration constant it_M2；
S11：Calculate the exit thickness of last frame of the exit thickness h1_M1 and milling train of the distribution ratio pressure frame of mode the 4th
Absolute difference delta_h；
S12：Loop iteration calculates, when delta_h reaches iteration less than the minimal difference dh_limit or iterations allowed
During maximum, circulation is exited, goes to S13；
Loop iteration is calculated as follows：
1. walks：According to second of iteration constant it_M2, all exit thicknesses for distributing frames are calculated；
2. walks：The exit thickness h1_M2 and second of iteration constant it_M2 for the 4th frame for 1. walking calculating using are as second
Individual approximation point M2 (h1_M2, it_M2)；
3. walks：It is inclined to calculate the absolute value of the exit thickness of the 4th frame and the exit thickness of the the 4th frame 1. walked in S3
Difference, if deviation is less than limiting value, S13 is gone to, otherwise go to and 4. walk；
4. walks：Second of iteration constant it_M2 is calculated again with the method based on interpolation：
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In above formula, h5For the exit thickness of last frame of milling train；
5. walks：Approximate point M1 value is replaced with to M2 value, i.e. M1=M2；
6. walks：Iterations adds 1, if iterations is more than maximum iteration, goes to S13, otherwise goes to and 1. walks；
S13：THICKNESS CALCULATION terminates, and obtains entrance, the exit thickness of each frame.
2. the interpolation iterative approximation computational methods according to claim 1 for determining five Stands Cold Tandem Mill thickness, its feature
It is, the average reduction ratio ε calculation formula of the first frame to the 4th frame are as follows in the S4：
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In above formula, h0For the inlet thickness of the first frame, h4For the exit thickness of the 4th frame.
3. the interpolation iterative approximation computational methods according to claim 1 for determining five Stands Cold Tandem Mill thickness, its feature
It is, first time, iteration constant it_M1 calculation formula were as follows in the S6：
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In above formula, m depresses the number of frame, ε for distribution ratioiThe reduction ratio of frame is depressed for i-th of distribution ratio, width is strip
Width, M (i) are the power distribution ratio that i-th of distribution ratio depresses frame, and power distribution ratio is found from mill condition table.
4. the interpolation iterative approximation computational methods according to claim 1 for determining five Stands Cold Tandem Mill thickness, its feature
It is, second of iteration constant it_M2 calculation formula is as follows in the S10：
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In above formula, h0For the inlet thickness of the first frame, h4For the exit thickness of the 4th frame, h '4For with first time iteration constant
The exit thickness of the 4th frame calculated.
5. the interpolation iterative approximation computational methods according to claim 1 for determining five Stands Cold Tandem Mill thickness, its feature
It is, absolute difference delta_h calculation formula are as follows in the S11：
Delta_h=| h5-h′4|
In above formula, h '4The exit thickness of the frame of mode the 4th, i.e. h1_M1 are depressed for distribution ratio.
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