CN113857266B - Method for formulating rolling schedule of single-stand reversible cold rolling mill through multi-objective optimization - Google Patents

Method for formulating rolling schedule of single-stand reversible cold rolling mill through multi-objective optimization Download PDF

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CN113857266B
CN113857266B CN202111088692.6A CN202111088692A CN113857266B CN 113857266 B CN113857266 B CN 113857266B CN 202111088692 A CN202111088692 A CN 202111088692A CN 113857266 B CN113857266 B CN 113857266B
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CN113857266A (en
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陈树宗
白佳丽
华长春
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Yanshan University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/48—Tension control; Compression control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/16—Control of thickness, width, diameter or other transverse dimensions
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/46—Roll speed or drive motor control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/58—Roll-force control; Roll-gap control
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P70/00—Climate change mitigation technologies in the production process for final industrial or consumer products
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Abstract

The invention discloses a method for formulating a rolling schedule of a single-stand reversible cold rolling mill by multi-objective optimization, which comprises the following steps: acquiring strip steel PDI parameters, rolling mill equipment parameters and rolling process parameters; determining the minimum pass number required by rolling as the initial pass number according to the strip steel PDI parameter and the maximum reduction rate of each pass; obtaining the outlet thickness and outlet unit tension of each pass when the multi-objective function value of the rolling procedure is minimum; if the number of times of the rolling pass exceeds the maximum number of times, determining an optimal rolling schedule, otherwise, re-solving the exit thickness and the exit unit tension of each pass when the multi-objective function value of the rolling schedule is minimum, comprehensively considering the production efficiency and the product quality, establishing single objective functions such as rolling force, plate shape, motor power, reduction rate, tension and the like, establishing a multi-objective function based on a penalty function, and solving the objective function by adopting a simplex algorithm to obtain the exit thickness and the tension of each pass; the equipment capacity is fully exerted to achieve the aims of improving the production efficiency and the product quality.

Description

Method for formulating rolling schedule of single-stand reversible cold rolling mill through multi-objective optimization
Technical Field
The invention relates to a method for establishing a rolling schedule of a single-stand reversible cold rolling mill by multi-objective optimization, belonging to the technical field of strip rolling.
Background
The establishment of the rolling regulation is an important content of cold rolling process research, which directly relates to the yield, the production cost and the product quality of a rolling mill, and the reasonable rolling regulation is the first problem of the standardization and the scientization of the steel rolling production and is also one of the problems of long-term research and exploration of steel rolling workers. The reasonable rolling schedule is formulated, so that the potential of equipment is fully excavated, the yield is improved, the production cost is reduced, the long-term reliable and stable operation of the equipment is ensured, and the shape quality and the plate thickness precision of products are improved. Generally speaking, reasonable rolling schedule enables high rolling mill output, good product quality, and low energy consumption (including power consumption, medium consumption, roll consumption, etc.). On the contrary, if the rolling schedule is not reasonable, the production process is not smooth, the yield of the rolling mill and the quality of products are affected, and even the normal production cannot be realized. Therefore, the research on the optimization method of the rolling schedule suitable for online use has important practical significance.
For a single stand reversible cold mill, the rolling schedule includes: and (4) determining rolling passes, pass reduction, front and back tension and rolling speed. At present, the single-stand reversible cold rolling procedure is mainly established by an empirical method or a load proportion distribution coefficient method. The method for determining load distribution in proportion to load requires a set of load distribution coefficients which are divided according to the specification levels of steel grades and strip steels, the coefficients are empirical values obtained in mass production practice, and the process of determining and optimizing the load distribution coefficients is a long-term process. Meanwhile, once the load distribution data is determined, for each steel type and specification, the tension schedule, the thickness distribution, the rolling force distribution, the moment distribution, the speed distribution and the motor power distribution are also determined, so that the online optimization of the rolling schedule cannot be realized.
Compared with the cold tandem mill, researchers have obviously insufficient attention to research and engineering practice of the optimization of the rolling schedule of the single-stand reversible cold rolling mill. In recent years, scholars at home and abroad propose a single-stand rolling schedule optimization method based on a correlation algorithm, such as an energy consumption minimum target method, a relative equal-load rolling target, a comprehensive equal-load function target, an optimal plate shape target method, a slippage prevention target and the like. However, most of the methods only consider the problem of thickness distribution, the rolling passes are fixed during optimization, and the optimization of a speed system and a tension system is not considered; meanwhile, the adopted optimization algorithm has longer calculation time and is not suitable for online use.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for formulating the rolling schedule of a single-stand reversible cold rolling mill through multi-objective optimization.
The technical scheme adopted by the invention is as follows:
a method for formulating a rolling schedule of a single-stand reversible cold rolling mill through multi-objective optimization comprises the following steps:
step 1, acquiring strip steel PDI parameters, rolling mill equipment parameters and rolling process parameters;
the strip steel PDI parameters comprise: the steel type of the strip steel, the incoming thickness of the strip steel, the thickness of a finished product of the strip steel and the width of the strip steel;
the parameters of the rolling mill equipment comprise: the roll diameters of the upper and lower working rolls, the rated power of a main motor, the maximum rotating speed of the working rolls and the maximum rolling force;
the rolling process parameters comprise: uncoiling unit tension, coiling unit tension of finished product passes, maximum rolling pass times, maximum reduction rate of each pass, minimum reduction rate of each pass, maximum uncoiling speed and maximum rolling speed of each pass;
step 2, determining the minimum pass number required by rolling as an initial pass number according to the strip steel PDI parameter and the maximum reduction rate of each pass;
step 3, under the given current pass times, adopting a simplex optimization algorithm to obtain the outlet thickness and the outlet unit tension of each pass when the multi-objective function value of the rolling procedure is minimum; the rolling schedule multi-objective function comprehensively considers 5 objective items: the rolling force is balanced and meets the rolling force amplitude limit, the set value of the rolling force can maintain the optimal plate shape, the motor power of each pass is relatively balanced and meets the motor power amplitude limit, the reduction rate of each pass is as close to the given reduction rate as possible and meets the reduction rate amplitude limit, and the set value of the tension of each pass meets the tension amplitude limit;
step 4, judging whether the current pass number exceeds the maximum rolling pass number, if so, executing step 6, otherwise, executing step 5;
step 5, if the single-stand reversible cold rolling mill allows odd-even pass rolling, adding 1 to the current pass number as a new pass number, and returning to the step 3; if the current single-stand reversible cold-rolling mill can only adopt odd-number passes for rolling, adding 2 to the current pass as a new pass number, and returning to the step 3;
and 6, determining an optimal rolling schedule according to the objective function value in the step 3, wherein the number of passes, the outlet thickness of each pass and the outlet unit tension when the objective function value is minimum are the optimal rolling schedule of the single-stand reversible cold rolling mill.
The technical scheme of the invention is further improved as follows: the method for determining the minimum number of rolling passes in the step 2 comprises the following steps: calculating the number of passes N meeting the following formula from the number of passes being 1, namely the minimum number of passes required by rolling:
H 0 (1-r max，1 )(1-r max，2 )…(1-r max，i )…(1-r max，N )≤h，
in the formula, H 0 The thickness of the incoming strip steel is measured; h is the thickness of the finished product of the strip steel; r is max，i The maximum reduction ratio of the ith pass. In this case, the number of passes is the minimum number of passes, and if the single-stand reversible cold rolling mill can only perform odd-numbered passes and N is an even number as determined by the above equation, N is set to N + 1.
The technical scheme of the invention is further improved as follows: the step 3 is specifically carried out according to the following steps:
step 3-1, determining the optimized variables of the rolling procedure objective function as the outlet thickness and the outlet unit tension of each pass except the finished product pass according to the process requirement and equipment limitation of the single-stand reversible cold rolling mill; establishing a rolling schedule multi-objective function, wherein the multi-objective comprehensively considers 5 aspects: the rolling force is balanced and meets the rolling force amplitude limit, the set value of the rolling force can maintain the optimal plate shape, the motor power of each pass is relatively balanced and meets the motor power amplitude limit, the reduction rate of each pass is as close to the given reduction rate as possible and meets the reduction rate amplitude limit, and the set value of the tension of each pass meets the tension amplitude limit;
3-2, determining initial values of optimization variables of the rolling procedure objective function based on the given current pass times, namely determining initial values of outlet thickness and outlet unit tension of each pass except for the finished product pass;
3-3, determining an initial rolling speed set value of each pass according to the motor rotating speed limit and the process limit conditions;
and 3-4, searching each pass outlet thickness and outlet unit tension which enable the total objective function value to be minimum by adopting a Nelder-Mead simplex algorithm.
The technical scheme of the invention is further improved as follows: the step 3-1 is specifically carried out according to the following steps:
3-1-1, establishing a rolling force balance target function, and aiming at keeping the set value of the rolling force of each pass balanced and meeting the rolling force amplitude limit required by rolling mill equipment;
3-1-2, establishing a rolling force objective function considering the plate shape, and aiming at maintaining the optimal plate shape and meeting the rolling force amplitude limit by the set rolling force value of each pass;
3-1-3, establishing a motor power balance target function, and aiming at relatively balancing the motor power of each pass and meeting the motor power amplitude limit;
3-1-4, establishing a reduction rate target function, and taking the reduction setting value of each pass as close to the reduction set by the given reduction rate as possible and meeting the reduction rate limiting as a target;
3-1-5, establishing a tension target function, and taking the tension set value of each pass meeting the tension amplitude limit as a target;
and 3-1-6, on the basis of establishing a rolling force balance objective function, considering a plate shape rolling force objective function, a motor power objective function, a reduction rate objective function and a tension objective function, establishing a rolling procedure multi-objective function by adopting a linear weighting method.
The technical scheme of the invention is further improved as follows: the step 3-1 is specifically carried out according to the following steps:
3-1-1, establishing a rolling force balance target function, and aiming at keeping the set value of the rolling force of each pass balanced and meeting the rolling force amplitude limit required by rolling mill equipment;
3-1-2, establishing a rolling force objective function considering the plate shape, and aiming at maintaining the optimal plate shape and meeting the rolling force amplitude limit by the set rolling force value of each pass;
3-1-3, establishing a motor power balance target function, and aiming at relatively balancing the motor power of each pass and meeting the motor power amplitude limit;
3-1-4, establishing a reduction rate target function, and taking the reduction setting value of each pass as close to the reduction set by the given reduction rate as possible and meeting the reduction rate limiting as a target;
3-1-5, establishing a tension target function, and taking the tension set value of each pass meeting the tension amplitude limit as a target;
and 3-1-6, on the basis of establishing a rolling force balance objective function, considering a plate shape rolling force objective function, a motor power objective function, a reduction rate objective function and a tension objective function, establishing a rolling procedure multi-objective function by adopting a linear weighting method.
The technical scheme of the invention is further improved as follows: the step 3-2-1 is specifically carried out according to the following steps:
step 3-2-1-1: calculating a beta weight factor beta according to the maximum reduction rate of each pass and the minimum reduction rate of each pass:
Figure BDA0003266722860000051
wherein the content of the first and second substances,
Figure BDA0003266722860000052
Figure BDA0003266722860000053
in the formula, beta is a beta weight factor, and beta is more than or equal to 0 and less than or equal to 1; n is the number of rolling passes; h 0 The thickness of the incoming strip steel is measured; h is the thickness of the finished product of the strip steel; epsilon max,i The maximum value of the true strain of the frame; epsilon min,i Is the minimum value of the true strain of the frame; r is max,i The maximum reduction rate of the ith pass; r is min,i The minimum reduction rate of the ith pass is obtained;
step 3-2-1-2: calculating the true strain of each pass through beta weight factors:
ε i ＝β·ε max,i +(1-β)·ε min,i ，
in the formula, epsilon i True strain for each pass;
step 3-2-1-3: and calculating the reduction rate of each pass according to the relationship between the reduction rate and the true strain:
Figure BDA0003266722860000054
step 3-2-1-4: calculating the initial value of the outlet thickness of each pass outside the finished product pass:
Figure BDA0003266722860000061
in the formula, h ini,i The initial value of the outlet thickness of each pass is obtained.
The technical scheme of the invention is further improved as follows: the steps 3-4 are specifically carried out according to the following steps:
step 3-4-1, taking a vector consisting of the initial value of the outlet thickness and the initial value of the outlet unit tension of each pass as an initial vertex, and increasing each element in the initial vertex by a fixed step length to construct other vertexes of the initial simplex;
3-4-2, calculating the rolling force, the rolling moment and the motor power of each pass according to the outlet thickness and the outlet unit tension of each pass;
3-4-3, adjusting the rolling speed of each pass according to the rated power, the rated rotating speed, the maximum uncoiling speed and the maximum rolling speed of each pass of the motor, and correcting the power of the motor;
3-4-4, substituting the calculated rolling force, motor power and reduction rate of each pass into a multi-objective function for establishing a rolling procedure, and calculating a multi-objective function value for establishing the rolling procedure;
3-4-5, judging whether a convergence condition is met, if the convergence condition is met, obtaining the optimal solution X, otherwise, re-searching through algorithms of simplex reflection, extension, contraction, edge length reduction and the like to obtain the outlet thickness and outlet unit tension of each pass, and repeating the step 3-4-2 to the step 3-4-5;
the convergence conditions are as follows:
Figure BDA0003266722860000062
in the formula
Figure BDA0003266722860000063
Comprises the following steps:
Figure BDA0003266722860000064
wherein ε represents a search termination condition.
Due to the adoption of the technical scheme, the invention has the technical progress that:
the invention provides a method for formulating a rolling schedule of a single-stand reversible cold rolling mill through multi-objective optimization. On the basis of comprehensively considering production efficiency and product quality, single objective functions such as rolling force, plate shape, motor power, reduction rate, tension and the like are established, so that a comprehensive multi-objective function based on a penalty function is established, and a simplex algorithm is developed to solve the objective function to obtain an optimal solution, namely the thickness and the tension of an entrance and an exit of each pass; meanwhile, the optimal rolling pass can be obtained through loop iteration. The method provided by the invention can give full play to the equipment capability, achieve the purposes of improving the production efficiency and improving the product quality, and enable the formulation of the rolling schedule to get rid of the dependence on the load distribution empirical value. The invention has popularization and application value, and can be popularized and applied to the rolling schedule making of multi-frame rolling mills such as cold continuous rolling, hot continuous rolling and the like.
Drawings
FIG. 1 is a layout view of a single stand reversible cold rolling mill installation according to an embodiment of the present invention;
FIG. 2 is a flowchart of a method for scheduling a single stand reversible cold mill rolling by multi-objective optimization in accordance with an embodiment of the present invention;
FIG. 3 is a flow chart of step 3 of an embodiment of the present invention;
FIG. 4 is a flow chart of step 3-1 of an embodiment of the present invention;
FIG. 5 is a flow chart of step 3-2 of an embodiment of the present invention;
FIG. 6 is a flow chart of steps 3-4 of an embodiment of the present invention;
the device comprises an uncoiler 1, a left coiler 2, a left tensiometer 3, a left thickness gauge 4, a left laser velocimeter 5, a right laser velocimeter 6, a right laser velocimeter 7, a right thickness gauge 8, a right tensiometer 9, a plate shape gauge 10, a right coiler 11 and a rack.
Detailed Description
In order to better understand the technical solution of the present invention, the following detailed description of the present invention is made with reference to the accompanying drawings and examples.
The implementation mode is optimized according to the rolling regulation of a 1700mm single-stand reversible cold rolling mill, the equipment layout of the single-stand reversible cold rolling mill is shown in figure 1, and a set of uncoiler 1 is arranged on the leftmost side of a rolling line and used for uncoiling and rolling a steel coil for the first time; the left coiling machine 2 and the right coiling machine 10 on the two sides of the rolling mill can rotate forward and backward, so that reversible rolling is realized; the left tensiometer 3 and the right tensiometer 8 of the rolling mill can measure the strip steel outlet tension and the strip steel inlet tension; a left thickness gauge 4 and a right thickness gauge 7 of the rolling mill are used for measuring the thickness of the strip steel at an outlet and an inlet; a left laser velocimeter 5 and a right laser velocimeter 6 of the rolling mill are used for measuring the speed of strip steel at the outlet and the inlet of the strip steel; the rolling mill 11 is a six-high rolling mill. Since only the right coiling side of the rolling mill is provided with the shape meter 9 and only the side is provided with the coil stripping device, only odd-number passes of rolling can be adopted.
The process for formulating the rolling schedule of the single-stand reversible cold rolling mill through multi-objective optimization in the embodiment comprises two aspects: firstly, determining the total rolling pass; and secondly, determining the reduction and tension system of each pass. The two problems are closely related and cannot be considered separately, so that the rolling schedule is optimized by adopting a mode of iteration of an inner layer and an outer layer. The outer layer is iteration of the rolling total pass times, and the inner layer adopts a multi-objective optimization algorithm to optimize the rolling reduction and the tension. The method for formulating the rolling schedule of the single-stand reversible cold rolling mill by multi-objective optimization is shown in a flow chart of figure 2 and comprises the following steps:
step 1, acquiring strip steel PDI parameters, rolling mill equipment parameters and rolling process parameters;
the strip steel PDI parameters comprise: the steel type of the strip steel, the incoming thickness of the strip steel, the thickness of a finished product of the strip steel and the width of the strip steel;
the parameters of the rolling mill equipment comprise: the roll diameters of the upper and lower working rolls, the rated power of a main motor, the maximum rotating speed of the working rolls and the maximum rolling force;
the rolling process parameters comprise: uncoiling unit tension, coiling unit tension of finished product passes, maximum rolling pass times, maximum reduction rate of each pass, minimum reduction rate of each pass, maximum uncoiling speed and maximum rolling speed of each pass;
the strip steel PDI parameters are as follows: the thickness of the strip steel CQ, the incoming material thickness of the strip steel is 2.30mm, the thickness of the finished product of the strip steel is 0.39mm, and the width of the strip steel is 1100 mm;
the parameters of the rolling mill are as follows: the roll diameters of the upper and lower working rolls are 420mm, the rated power of a main motor is 6000kW, the maximum rotating speed of the working rolls is 104.1rad/s, and the maximum rolling force is 20000 kN;
the rolling technological parameters are as follows: the uncoiling unit tension is 50MPa, the coiling unit tension of the finished product pass is 50MPa, the maximum rolling pass number is 7, the maximum reduction rate of each pass is 5%, the minimum reduction rate of each pass is 40%, the maximum uncoiling speed is 450m/min, and the maximum strip steel rolling speed is 1200 m/min.
In this embodiment, a rolling strategy parameter is further set, including: weighting coefficient q of each single objective function in multiple objective functions Fb :q Ff :q R :q P :q T 1: 0: 1: 1: 1. the rolling force weighting coefficient related to the pass, the index coefficient of the rolling force balance objective function of each pass, the plate shape rolling force weighting coefficient related to the pass, the index coefficient of the rolling force objective function considering the plate shape of each pass, the motor power weighting coefficient related to the pass, the index coefficient of the motor power balance objective function of each pass, the reduction rate weighting coefficient related to the pass, the index coefficient of the reduction rate objective function of each pass, the tension weighting coefficient related to the pass and the index coefficient of the tension objective function of each pass.
The pass-dependent weighting coefficients and the exponential coefficients in the multi-objective function are shown in table 1.
TABLE 1 weighting and exponential coefficients in the objective function
k Fb n Fb np Fb k Ff n Ff np Ff k P n P np P k R n R np R k T n T np T
Pass 1 1 2 80 0 2 0 1 2 80 0 2 20 0 0 8
Pass 2 1 2 80 0 2 0 1 2 80 0 2 20 0 0 8
Pass 3 1 2 80 0 2 0 1 2 80 0 2 20 0 0 8
Pass 4 1 2 80 0 2 0 1 2 80 0 2 20 0 0 8
Pass 5 1 2 80 0 2 0 1 2 80 0 2 20 0 0 8
Pass 6 1 2 80 0 2 0 1 2 80 0 2 20 0 0 8
Pass 7 1 2 80 0 2 0 1 2 80 0 2 20 0 0 8
Step 2, determining the minimum pass number required by rolling as an initial pass number according to the strip steel PDI parameter and the maximum reduction rate of each pass;
the method for determining the minimum number of rolling passes in the step 2 comprises the following steps: calculating to obtain the number of passes N meeting the following formula from the number of passes being 1, namely the number of the minimum passes required by rolling;
H 0 (1-r max,1 )(1-r max,2 )…(1-r max,N )≤h
in the formula, H 0 The thickness of the incoming material of the strip steel is 2.30 mm; h is the thickness of the finished product of the strip steel, and is 0.39 mm; r is a radical of hydrogen max,i The maximum reduction ratios in the i-th pass were all 40%. In this case, the number of passes is the minimum number of passes, and in this embodiment, the single-stand reversible cold rolling mill can only use odd-numbered passes, and if N + 4 is even as determined by the above formula, N +1 is 4+1 is 5.
Step 3, under the given current pass times, adopting a simplex optimization algorithm to obtain the outlet thickness and outlet unit tension of each pass when the multi-objective function value of the rolling procedure is minimum; the rolling schedule multi-objective function comprehensively considers 5 objective items: the rolling force is balanced and meets the rolling force amplitude limit, the set value of the rolling force can maintain the optimal plate shape, the motor power of each pass is relatively balanced and meets the motor power amplitude limit, the reduction rate of each pass is as close to the given reduction rate as possible and meets the reduction rate amplitude limit, and the set value of the tension of each pass meets the tension amplitude limit;
as shown in fig. 3, the step 3 is specifically performed as follows:
step 3-1, determining the optimized variables of the rolling procedure objective function as the outlet thickness and the outlet unit tension of each pass except the finished product pass according to the process requirement and equipment limitation of the single-stand reversible cold rolling mill; establishing a rolling schedule multi-objective function, wherein the multi-objective comprehensively considers 5 aspects: the rolling force is balanced and meets the rolling force amplitude limit, the set value of the rolling force can maintain the optimal plate shape, the motor power of each pass is relatively balanced and meets the motor power amplitude limit, the reduction rate of each pass is as close to the given reduction rate as possible and meets the reduction rate amplitude limit, and the set value of the tension of each pass meets the tension amplitude limit;
for a single stand reversible cold mill, the 1 st pass entry thickness H 0 And finished pass exit thickness h are known; at the same time, the entrance unit tension t of the 1 st pass is set 0 And the exit unit tension t of the finished product pass N Setting according to an uncoiling process and a coiling process; in addition, the entrance thickness and the unit post tension of the remaining passes except for the 1 st pass are set to the exit thickness and the unit pre tension of the previous pass, respectively. Therefore, the exit thickness and exit unit tension for each pass (excluding the finished pass) were determined as optimization variables. For the rolling schedule of N passes, there are 2(N-1) optimization variables, expressed as:
X＝(h 1 ,h 2 ,h 3 ,…h N-1 ,t 1 ,t 2 ,t 3 ,…t N-1 ) T
in the formula, X is an optimized vector; n is the track number; h is 1 ,h 2 ,h 3 ,…h N-1 The outlet thickness of the corresponding pass; t is t 1 ,t 2 ,t 3 ,…t N-1 The unit tension of the outlet of the corresponding pass.
Optimization of single stand rolling schedule is a constrained non-linear problem. Aiming at the problem, a structural form of an augmented objective function is designed, the objective function comprises an objective item and a punishment item, and the multi-objective function constraint solving problem is converted into an unconstrained solving problem through the punishment item introduced into the objective function.
As shown in fig. 4, the step 3-1 is specifically performed as follows:
step 3-1-1, establishing a rolling force balance objective function J Fb (X) the rolling force setting values are kept in balance in each passAnd the rolling force amplitude limit required by the rolling mill equipment is met as a target, and a rolling force balance target function J is obtained Fb (X) is divided into target items Jt Fb (X) and a penalty term Jp Fb (X)；
Figure BDA0003266722860000111
Wherein
Figure BDA0003266722860000112
Figure BDA0003266722860000113
In the formula, X is an optimization vector, namely the outlet thickness and the outlet unit tension of each pass except the 1 st pass; k is a radical of Fb,i Weighting coefficients for rolling forces associated with passes; n is Fb,i 、np Fb,i An exponential coefficient which is a rolling force balance objective function; f min,i 、F max,i The minimum value and the maximum value allowed by the rolling force.
Step 3-1-2, establishing a rolling force objective function J considering the plate shape Ff (X) a rolling force objective function J considering the plate shape is aimed at maintaining the optimum plate shape and satisfying the rolling force limit in each pass Ff (X) divide into target items Jt Ff (X) and a penalty term Jp Ff (X)；
Figure BDA0003266722860000114
In the formula, k Ff,i Weighting coefficients for the strip rolling forces associated with the passes; f flat,i Maintaining the optimal rolling force of the plate shape; n is Ff,i 、np Ff,i The exponential coefficient of the rolling force objective function is taken into account for the slab shape.
3-1-3, establishing a motor power balance objective function J P (X) motor power phase in each passThe aim of balancing and meeting the limit of the motor power is taken as a target, so that the motor capacity of the unit is fully exerted, the rolling speed of the unit is improved, and the motor power is balanced by a target function J P (X) is divided into target items Jt p (X) and a penalty term Jp P (X)；
Figure BDA0003266722860000121
Wherein
Figure BDA0003266722860000122
Figure BDA0003266722860000123
In the formula, k P,i Weighting coefficients of the motor power related to the pass; n is a radical of an alkyl radical P,i 、np P,i An exponential coefficient of a motor power balancing objective function; p max,i Rated power for the motor; p min,i Is the minimum value of the motor power, P min,i ＝0。
3-1-4, establishing a reduction rate objective function J R (X) aiming at setting the rolling reduction value of each pass as close as possible to the rolling reduction value set by the given rolling reduction and satisfying the rolling reduction limiting;
Figure BDA0003266722860000124
wherein
Figure BDA0003266722860000125
Figure BDA0003266722860000126
In the formula, k R,i Is in phase with the pass(ii) a closed reduction rate weighting factor; n is a radical of an alkyl radical R,i 、np R,i Is an exponential coefficient of the reduction rate objective function; r is max,i 、r min,i The maximum and minimum allowable reduction ratios.
Step 3-1-5, establishing a tension objective function J T (X) aiming at the tension set value of each pass to meet the tension limiting limit;
objective function J of tension T (X) is divided into target items Jt T (X) and a penalty term Jp T (X)；
Figure BDA0003266722860000131
Wherein
Figure BDA0003266722860000132
Figure BDA0003266722860000133
In the formula, k T,i Weighting coefficients for tension related to passes; n is a radical of an alkyl radical T,i 、np T,i Is an exponential coefficient of the tension objective function; t is a unit of max,i 、T min,i The maximum and minimum allowable tension values.
3-1-6, on the basis of establishing a rolling force balance objective function, considering a plate shape rolling force objective function, a motor power objective function, a reduction rate objective function and a tension objective function, establishing a rolling procedure multi-objective function J by adopting a linear weighting method total (X)。
Figure BDA0003266722860000134
In the formula, q Fb 、q Ff 、q R 、q P And q is T Respectively the weighting coefficients of each single objective function in the multi-objective function.
3-2, determining initial values of optimization variables of the rolling procedure objective function based on the given current pass times, namely determining initial values of outlet thickness and outlet unit tension of each pass except for the finished product pass;
for the rolling schedule of N passes, there are 2(N-1) optimization variables, expressed as:
X＝(h 1 ,h 2 ,h 3 ,…h N-1 ,t 1 ,t 2 ,t 3 ,…t N-1 ) T
in the formula, X is an optimized vector; n is the track number; h is 1 ,h 2 ,h 3 ,…h N-1 The outlet thickness of the corresponding pass; t is t 1 ,t 2 ,t 3 ,…t N-1 The unit tension of the outlet of the corresponding pass.
As shown in fig. 5, the procedure for determining the initial values of the optimization variables of the rolling schedule objective function in step 3-2 will be described with the rolling schedule N being 5:
3-2-1, calculating the reduction rate of each pass by adopting a beta factor theory, and further solving the initial value of the outlet thickness of each pass;
the step 3-2-1 is specifically carried out according to the following steps:
step 3-2-1-1: calculating a beta weight factor beta according to the maximum reduction rate of each pass and the minimum reduction rate of each pass:
Figure BDA0003266722860000141
wherein the content of the first and second substances,
Figure BDA0003266722860000142
Figure BDA0003266722860000143
in the formula, beta is a beta weight factor, and beta is more than or equal to 0 and less than or equal to 1; n is the number of rolling passes; h 0 The thickness of the incoming strip steel is measured; h is the thickness of the finished product of the strip steel; epsilon max,i Is made into a machineMaximum value of the shelf-true strain; epsilon min,i Is the minimum value of the true strain of the frame; r is max,i Is the maximum reduction rate r of the ith pass max,i ＝40％；r min,i Is the minimum reduction ratio of the ith pass, r min,i ＝5％；
Calculating the maximum true strain value of 1-5 passes:
Figure BDA0003266722860000144
calculating the minimum true strain of 1-5 passes:
Figure BDA0003266722860000145
calculating a weight factor:
Figure BDA0003266722860000146
step 3-2-1-2: calculating the true strain of each pass through beta weight factors:
ε i ＝β·ε max,i +(1-β)·ε min,i ＝0.6607×0.5108+(1-0.6607)×0.0513＝0.3549
in the formula, epsilon i True strain for each pass;
step 3-2-1-3: and (3) calculating the reduction rate of each pass according to the relation between the reduction rate and the true strain:
Figure BDA0003266722860000151
step 3-2-1-4: calculating the initial value of the outlet thickness of each pass outside the finished product pass:
Figure BDA0003266722860000152
in the formula, h ini,i The initial value of the outlet thickness of each pass is obtained.
The outlet thickness of the finished product pass is the finished product thickness, and the outlet thicknesses of the other passes are calculated as follows:
the outlet thickness of the 1 st pass:
Figure BDA0003266722860000153
outlet thickness of pass 2:
Figure BDA0003266722860000154
pass 3 outlet thickness:
Figure BDA0003266722860000155
outlet thickness of the 4 th pass:
Figure BDA0003266722860000156
step 3-2-2: and determining the initial value of the outlet unit tension of each pass.
Except for the finished product pass, the initial values of the exit unit tensions of the rest passes are set as the average values of the maximum unit tension and the minimum unit tension, and the specific numerical values are as follows:
initial value of exit unit tension of pass 1:
Figure BDA0003266722860000157
initial value of outlet unit tension of 2 nd pass:
Figure BDA0003266722860000158
initial value of outlet unit tension of pass 3:
Figure BDA0003266722860000159
initial value of exit unit tension of pass 4:
Figure BDA00032667228600001510
3-3, determining an initial rolling speed set value of each pass according to the motor rotating speed limit and the process limit conditions;
Figure BDA00032667228600001511
in the formula, V max,i The initial maximum rolling speed allowed by the i pass;
Figure BDA00032667228600001512
is the rolling speed limited by the maximum process entry for i passes;
Figure BDA0003266722860000161
the maximum rolling speed of an outlet allowed by the i-pass process;
Figure BDA0003266722860000162
the maximum rolling speed limited by the mill drive.
In this example, the maximum unwinding speed is 450m/min, the maximum exit speed for each pass is 1200m/min, and the maximum speed of rotation of the work rolls, limited by the mill drive, is 104.1 rad/s. These factors are combined when calculating the maximum rolling speed for each initial pass.
Taking 5 passes as an example, the initial speed of each pass is calculated:
according to the second flow constant principle, the maximum rolling speed of the 1 st pass limited by the uncoiling speed is calculated as follows:
Figure BDA0003266722860000163
calculating the rolling speed limit according to the maximum rotating speed of the working roll:
Figure BDA0003266722860000164
initial maximum rolling speed of pass 1: v max,1 ＝min{642,1200,1312}＝642m/min
Initial maximum rolling speed of pass 2: v max,2 ＝min{1200,1312}＝1200m/min
Initial maximum rolling speed of pass 3: v max,3 ＝min{1200,1312}＝1200m/min
Initial maximum rolling speed of pass 4: v max,4 ＝min{1200,1312}＝1200m/min
Initial maximum rolling speed of pass 5: v max,5 ＝min{1200,1312}＝1200m/min。
And 3-4, searching each pass outlet thickness and outlet unit tension which enable the total objective function value to be minimum by adopting a Nelder-Mead simplex algorithm.
As shown in fig. 6, the step 3-4 is specifically performed as follows:
step 3-4-1, taking a vector consisting of the initial value of the outlet thickness and the initial value of the outlet unit tension of each pass as an initial vertex, and increasing each element in the initial vertex by a fixed step length to construct other vertexes of the initial simplex;
for 2(N-1) optimization variables, the number of vertices of the initial simplex is 2(N-1) +1, and the formula is:
Figure BDA0003266722860000171
wherein
Figure BDA0003266722860000172
Wherein, X 1 Is an initial vertex; x j The jth vertex of the initial simplex; x 1 [j]Is the jth element in the initial vertex vector.
3-4-2, calculating the rolling force, the rolling moment and the motor power of each pass according to the outlet thickness and the outlet unit tension of each pass;
3-4-3, adjusting the rolling speed of each pass according to the rated power, the rated rotating speed, the maximum uncoiling speed and the maximum rolling speed of each pass of the motor, and correcting the power of the motor;
3-4-4, substituting the calculated rolling force, motor power and reduction rate of each pass into the established rolling procedure multi-objective function, and calculating the established rolling procedure multi-objective function value;
3-4-5, judging whether a convergence condition is met or not according to the formula (1), if the convergence condition is met, obtaining the optimal solution X, otherwise, searching again through algorithms of simplex reflection, extension, contraction, edge length reduction and the like to obtain the outlet thickness and outlet unit tension of each pass, and repeating the steps 3-4-2-3-4-5;
the convergence conditions are as follows:
Figure BDA0003266722860000173
in the formula
Figure BDA0003266722860000174
Comprises the following steps:
Figure BDA0003266722860000175
wherein ε is a search termination condition of 10 -4 。
In the present embodiment, the rolling passes N-5 and N-7 were optimized.
When the rolling pass N is equal to 5, the objective function value J total (X) ═ 0.020319, the optimization variable results are:
X＝(h 1 ,h 2 ,h 3 ,…h 5-1 ,t 1 ,t 2 ,t 3 ,…t 5-1 ) T
＝(1.629,1.063,0.694,0.455,77.1,118.2,165.5,172.7) T
when the rolling pass N is equal to 7, the objective function value J total (X) 0.20622, the optimization variable results are:
X＝(h 1 ,h 2 ,h 3 ,…h 7-1 ,t 1 ,t 2 ,t 3 ,…t 7-1 ) T
＝(1.812,1.328,1.000,0.737,0.551,0.435,69.4,94.6,125.7,156.2,170.1,172.2) T
step 4, judging whether the current pass number exceeds the maximum rolling pass number, if so, executing step 6, otherwise, executing step 5;
step 5, if the single-stand reversible cold rolling mill allows odd-even pass rolling, adding 1 to the current pass number as a new pass number, and returning to the step 3; if the current single-stand reversible cold rolling mill can only adopt odd-number pass rolling, adding 2 to the current pass number as a new pass number, and returning to the step 3;
when performing the gate iteration accumulation, the gate increment Δ N in each iteration needs to be set according to the process and the equipment:
if the single stand rolling mill can adopt odd-even pass rolling, the pass increment delta N is equal to 1.
If the single stand rolling mill can only adopt odd-numbered passes, the pass increment delta N is set to be 2.
And 6, determining an optimal rolling schedule according to the objective function value in the step 3, wherein the number of passes, the outlet thickness of each pass and the outlet unit tension when the objective function value is minimum are the optimal rolling schedule of the single-stand reversible cold rolling mill.
In the present embodiment, the maximum number of rolling passes is 7. In the example, the multi-purpose function of the rolling schedule under 5 passes and 7 passes is optimized, wherein the target function value at 5 passes is optimal.
The optimum single stand reversible cold mill rolling schedule and process parameters are shown in table 2.
TABLE 2 optimal Rolling schedule and Process parameters for Single-Stand reversible Cold Rolling Mills
Figure BDA0003266722860000181
The above embodiments are only for illustrating one embodiment of the present invention, and the purpose is to enable those skilled in the art to understand the content of the present invention and implement the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all equivalent changes made according to the technical solutions disclosed by the present invention are within the protection scope of the present invention.

Claims (1)

1. The method for formulating the rolling schedule of the single-stand reversible cold rolling mill through multi-objective optimization is characterized by comprising the following steps of: the method comprises the following steps:
step 1, acquiring strip steel PDI parameters, rolling mill equipment parameters and rolling process parameters;
the strip steel PDI parameters comprise: the steel type of the strip steel, the incoming thickness of the strip steel, the thickness of a finished product of the strip steel and the width of the strip steel;
the parameters of the rolling mill equipment comprise: the roll diameters of the upper and lower working rolls, the rated power of a main motor, the maximum rotating speed of the working rolls and the maximum rolling force;
the rolling process parameters comprise: uncoiling unit tension, coiling unit tension of finished product passes, maximum rolling pass times, maximum reduction rate of each pass, minimum reduction rate of each pass, maximum uncoiling speed and maximum rolling speed of each pass;
step 2, determining the minimum pass number required by rolling as an initial pass number according to the strip steel PDI parameter and the maximum reduction rate of each pass;
the method for determining the minimum number of rolling passes in the step 2 comprises the following steps: calculating the number of passes N meeting the following formula from the number of passes being 1, namely the minimum number of passes required by rolling:
H 0 (1-r max，1 )(1-r max，2 )…(1-r max，i )…(1-r max，N )≤h,
in the formula, H 0 The thickness of the incoming strip steel is measured; h is the thickness of the finished product of the strip steel; r is max,i The maximum reduction rate of the ith pass is obtained; the number of required passes is the minimum number of passes, and if the single-frame reversible cold rolling mill can only adopt odd-number passes for rolling and N is an even number according to the formula, N is made to be N + 1;
step 3, under the given current pass times, adopting a simplex optimization algorithm to obtain the outlet thickness and the outlet unit tension of each pass when the multi-objective function value of the rolling procedure is minimum; the rolling schedule multi-objective function comprehensively considers 5 objective items: the rolling force is balanced and meets the rolling force amplitude limit, the set value of the rolling force can maintain the optimal plate shape, the motor power of each pass is relatively balanced and meets the motor power amplitude limit, the reduction rate of each pass is as close to the given reduction rate as possible and meets the reduction rate amplitude limit, and the set value of the tension of each pass meets the tension amplitude limit;
the step 3 is specifically carried out according to the following steps:
step 3-1, determining optimization variables of a rolling schedule objective function as the outlet thickness and the outlet unit tension of each pass except the finished product pass according to the process requirements and equipment limitations of the single-stand reversible cold rolling mill; establishing a rolling schedule multi-objective function, wherein the multi-objective comprehensively considers 5 aspects: the rolling force is balanced and meets the rolling force amplitude limit, the set value of the rolling force can maintain the optimal plate shape, the motor power of each pass is relatively balanced and meets the motor power amplitude limit, the reduction rate of each pass is as close to the given reduction rate as possible and meets the reduction rate amplitude limit, and the set value of the tension of each pass meets the tension amplitude limit;
the step 3-1 is specifically carried out according to the following steps:
3-1-1, establishing a rolling force balance target function, and aiming at keeping the set value of the rolling force of each pass balanced and meeting the rolling force amplitude limit required by rolling mill equipment;
3-1-2, establishing a rolling force objective function considering the plate shape, and aiming at maintaining the optimal plate shape and meeting the rolling force amplitude limit by the set rolling force value of each pass;
3-1-3, establishing a motor power balance target function, and taking the motor power of each pass to be relatively balanced and meet the motor power amplitude limit as a target;
3-1-4, establishing a reduction rate target function, and taking the reduction setting value of each pass as close to the reduction set by the given reduction rate as possible and meeting the reduction rate limiting as a target;
3-1-5, establishing a tension target function, and taking the tension set value of each pass meeting the tension amplitude limit as a target;
3-1-6, on the basis of establishing a rolling force balance objective function, considering a plate shape rolling force objective function, a motor power objective function, a reduction rate objective function and a tension objective function, establishing a rolling procedure multi-objective function by adopting a linear weighting method;
3-2, determining initial values of optimization variables of the rolling schedule objective function based on the given current pass times, namely determining initial values of outlet thickness and outlet unit tension of each pass except for the finished product pass;
the step 3-2 is specifically carried out according to the following steps:
3-2-1, calculating the reduction rate of each pass by adopting a beta factor theory, and further solving the initial value of the outlet thickness of each pass;
the step 3-2-1 is specifically carried out according to the following steps:
step 3-2-1-1: calculating a beta weight factor beta according to the maximum reduction rate of each pass and the minimum reduction rate of each pass:
Figure FDA0003761984850000031
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003761984850000032
Figure FDA0003761984850000033
wherein beta is a beta weight factor, and beta is more than or equal to 0 and less than or equal to 1; n is the number of rolling passes; h 0 The thickness of the incoming strip steel is measured; h is the thickness of the finished product of the strip steel; epsilon max,i The maximum value of the true strain of the frame; epsilon min,i Is the minimum value of the true strain of the frame; r is max,i The maximum reduction rate of the ith pass is obtained; r is min,i The minimum reduction rate of the ith pass is obtained;
step 3-2-1-2: calculating the true strain of each pass through beta weight factors:
ε i ＝β·ε max,i +(1-β)·ε min,i ，
in the formula, epsilon i True strain for each pass;
step 3-2-1-3: and (3) calculating the reduction rate of each pass according to the relation between the reduction rate and the true strain:
Figure FDA0003761984850000034
step 3-2-1-4: calculating the initial value of the outlet thickness of each pass outside the finished product pass:
Figure FDA0003761984850000035
in the formula, h ini,i The initial value of the outlet thickness of each pass is obtained;
step 3-2-2: determining an initial value of the outlet unit tension of each pass;
3-3, determining an initial rolling speed set value of each pass according to the motor rotating speed limit and the process limit conditions;
3-4, searching each pass outlet thickness and outlet unit tension which enable the total objective function value to be minimum by adopting a Nelder-Mead simplex algorithm;
the step 3-4 is specifically carried out according to the following steps:
step 3-4-1, taking a vector consisting of the initial value of the outlet thickness and the initial value of the outlet unit tension of each pass as an initial vertex, and increasing each element in the initial vertex by a fixed step length to construct other vertexes of the initial simplex;
3-4-2, calculating the rolling force, the rolling moment and the motor power of each pass according to the outlet thickness and the outlet unit tension of each pass;
3-4-3, adjusting the rolling speed of each pass according to the rated power, the rated rotating speed, the maximum uncoiling speed and the maximum rolling speed of each pass of the motor, and correcting the power of the motor;
3-4-4, substituting the calculated rolling force, motor power and reduction rate of each pass into the established rolling procedure multi-objective function, and calculating the established rolling procedure multi-objective function value;
3-4-5, judging whether a convergence condition is met, and if the convergence condition is met, judging whether the convergence condition is met
Figure FDA0003761984850000044
If not, re-searching by a simplex reflection, extension, contraction and edge length reduction algorithm to obtain the outlet thickness and outlet unit tension of each pass, and repeating the step 3-4-2 to the step 3-4-5;
the convergence conditions are as follows:
Figure FDA0003761984850000041
in the formula
Figure FDA0003761984850000042
Comprises the following steps:
Figure FDA0003761984850000043
in the formula, epsilon is a search termination condition;
step 4, judging whether the current pass number exceeds the maximum rolling pass number, if so, executing step 6, otherwise, executing step 5;
step 5, if the single-stand reversible cold rolling mill allows odd-even pass rolling, adding 1 to the current pass number as a new pass number, and returning to the step 3; if the current single-stand reversible cold rolling mill can only adopt odd-number pass rolling, adding 2 to the current pass number as a new pass number, and returning to the step 3;
and 6, determining an optimal rolling schedule according to the objective function value in the step 3, wherein the number of passes, the outlet thickness of each pass and the outlet unit tension when the objective function value is minimum are the optimal rolling schedule of the single-stand reversible cold rolling mill.
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