CN115415361A - Straightening machine roller bending force setting method based on particle swarm optimization - Google Patents
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Abstract
Description
技术领域technical field
本发明属于板材矫直技术领域,涉及一种基于粒子群算法的矫直机弯辊力设定方法。The invention belongs to the technical field of plate straightening, and relates to a method for setting the bending force of a straightening machine based on a particle swarm algorithm.
背景技术Background technique
矫直机被普遍应用于热轧、冷轧、热处理等多种带钢生产线中。目前第三代矫直机具有压下机构和弯辊机构,为了充分的发挥设备的能力,对压下和弯辊进行准确的设定很有必要。目前,相对压下而言,弯辊设定较为困难,还没有一套成熟的技术方案。Straightening machines are widely used in various strip steel production lines such as hot rolling, cold rolling, and heat treatment. At present, the third-generation straightening machine has a pressing mechanism and a bending mechanism. In order to fully utilize the capabilities of the equipment, it is necessary to accurately set the pressing and bending. At present, compared with the reduction, the setting of the bending roll is more difficult, and there is no mature technical solution.
发明内容Contents of the invention
有鉴于此,本发明的目的在于提供一种基于粒子群算法的矫直机弯辊力设定方法,对于由弯辊液压缸直接控制的多个支撑辊的矫直机,在已知矫直力的前提下,以矫直辊的挠度最小为目标,计算出所需的弯辊力。In view of this, the object of the present invention is to provide a method for setting the bending force of a straightener based on the particle swarm algorithm. Under the premise of the force, the minimum deflection of the straightening roller is the goal, and the required bending force is calculated.
为达到上述目的,本发明提供如下技术方案:To achieve the above object, the present invention provides the following technical solutions:
一种基于粒子群算法的矫直机弯辊力设定方法,包括以下步骤:A method for setting the bending force of a straightening machine based on particle swarm optimization, comprising the following steps:
S1:根据矫直机设备结构,建立液压缸、矫直辊、支撑辊的几何关系;S1: According to the equipment structure of the straightening machine, establish the geometric relationship of the hydraulic cylinder, straightening roller and support roller;
S2:建立矫直辊挠度关于矫直力、弯辊力的函数模型;S2: Establish a function model of straightening roller deflection with respect to straightening force and bending force;
S3:采用粒子群算法求出矫直辊挠度最小时的正弯力和负弯力;S3: Use the particle swarm algorithm to find the positive bending force and negative bending force when the deflection of the straightening roller is the smallest;
S4:将正弯力和负弯力分配到正弯液压缸和负弯液压缸上;S4: distribute the positive bending force and negative bending force to the positive bending hydraulic cylinder and the negative bending hydraulic cylinder;
S5:对正弯力和负弯力进行修正。S5: Correct the positive bending force and negative bending force.
进一步,所述矫直机包括弯辊盒,以及多个矫直辊、液压缸和支撑辊;所述支撑辊分组设置在弯辊盒内,所述矫直辊设置在弯辊盒下方,所述支撑辊与矫直辊接触并提供弯辊力;所述液压缸位于弯辊盒上端,所述液压缸包括正弯液压缸和负弯液压缸,所述正弯液压缸为支撑辊提供正弯力,所述负弯液压缸为支撑辊提供负弯力。Further, the straightening machine includes a bending roll box, and a plurality of straightening rolls, hydraulic cylinders and support rolls; the support rolls are arranged in groups in the bending roll box, and the straightening rolls are arranged under the bending roll box, so The support roll is in contact with the straightening roll and provides roll bending force; the hydraulic cylinder is located at the upper end of the roll bending box, and the hydraulic cylinder includes a positive bending hydraulic cylinder and a negative bending hydraulic cylinder, and the positive bending hydraulic cylinder provides positive bending force for the support roll. Bending force, the negative bending hydraulic cylinder provides negative bending force for the support roller.
进一步,步骤S1中,所述建立液压缸、矫直辊、支撑辊的几何关系,包括:Further, in step S1, the establishment of the geometric relationship of the hydraulic cylinder, the straightening roller, and the support roller includes:
单个支撑辊提供的正弯力或负弯力为:The positive or negative bending force provided by a single support roller is:
式中,Fz为每根矫直辊上单个支撑辊提供的正弯力或负弯力;Fw为每根矫直辊受到的总的正弯力或负弯力;N为每根矫直辊上提供正弯力或负弯力的支撑辊的个数;In the formula, F z is the positive bending force or negative bending force provided by a single support roll on each straightening roll; F w is the total positive or negative bending force received by each straightening roll; N is the bending force of each straightening roll The number of support rolls providing positive or negative bending force on straight rolls;
单个支撑辊传递给矫直辊的正弯力或负弯力为:The positive or negative bending force transmitted by a single support roll to the straightening roll is:
F=Fz·cosθ (2)F=F z cosθ (2)
式中,F为单个支撑辊传递给矫直辊的正弯力或负弯力;θ为支撑辊和矫直辊的夹角,当支撑辊位于矫直辊的正上方时,θ=0°;In the formula, F is the positive bending force or negative bending force transmitted to the straightening roller by a single supporting roller; θ is the angle between the supporting roller and the straightening roller, when the supporting roller is located directly above the straightening roller, θ=0° ;
矫直机所需的总正弯力或负弯力为:The total positive or negative bending force required for the leveler is:
Fsum=Fw1+Fw2+…+Fwn (3)F sum =F w1 +F w2 +...+F wn (3)
式中,Fsum为矫直机所需的总正弯力或总负弯力;Fw1到Fwn为第1个矫直辊到第n个矫直辊所需的正弯力或负弯力。In the formula, F sum is the total positive or negative bending force required by the straightening machine; F w1 to F wn are the positive or negative bending forces required from the first straightening roll to the nth straightening roll force.
进一步,步骤S2所述矫直辊挠度关于矫直力、弯辊力的函数模型为:Further, the function model of the straightening roll deflection described in step S2 about straightening force and roll bending force is:
f(x)=fj(x)+fw(x) (4) f (x)= fj (x)+fw(x) (4)
式中,f(x)为矫直辊辊身上某一点x处的挠度;fj(x)为矫直力作用下矫直辊辊身上某一点x处的挠度;fw(x)为弯辊力作用下矫直辊辊身上某一点x处的挠度。In the formula, f(x) is the deflection at a point x on the straightening roller body; f j (x) is the deflection at a certain point x on the straightening roller body under the action of straightening force; f w (x) is the bending The deflection at a point x on the straightening roller body under the action of the roller force.
进一步,步骤S3具体包括以下步骤:Further, step S3 specifically includes the following steps:
S31:设置初始正弯力和负弯力的范围为[0,Fji],其中Fji为当前矫直辊的矫直力;S31: Set the range of the initial positive bending force and negative bending force to [0, F ji ], where F ji is the straightening force of the current straightening roller;
S32:设置粒子群算法的超参数,包括种群数ng、自身认知项学习因子c1、群体认知项学习因子c2、每次迭代允许的最大变化量vmax、惯性因子ω;S32: Set the hyperparameters of the particle swarm optimization algorithm, including the population number n g , the self-awareness item learning factor c 1 , the group-awareness item learning factor c 2 , the maximum variation v max allowed for each iteration, and the inertia factor ω;
S33:初始化种群,将初始正弯力和负弯力代入目标函数,计算种群的个体最优值和群体最优值,其中,目标函数为:S33: Initialize the population, substitute the initial positive bending force and negative bending force into the objective function, and calculate the individual optimal value and group optimal value of the population, where the objective function is:
max[φ(Fzi,Ffi)]=max[-|f(x)|] (5)max[φ(F zi ,F fi )]=max[-|f(x)|] (5)
S34:求出第k次迭代时的自变量增量,其中,第k次迭代惯性因子为:S34: Calculate the increment of the independent variable at the kth iteration, where the inertia factor of the kth iteration is:
第k次迭代自变量增量为:The independent variable increment of the kth iteration is:
vk=ωk·vk-1+c1·Ra·(pb-xk-1)+c2·Ra·(gb-xk-1) (7)v k =ω k ·v k-1 +c 1 ·R a ·(p b -x k-1 )+c 2 ·R a ·(g b -x k-1 ) (7)
式中,ωk为第k次迭代时的惯性因子,ωini为初始惯性因子,ωend为最终惯性因子,niter为迭代次数,n为当前迭代次数,n∈[0,niter],xk-1为第k-1次迭代时的自变量,xk=xk-1+vk,Ra为(0,1)之间的随机数,pb为个体最优值,gb为种群最优值;In the formula, ω k is the inertia factor at the kth iteration, ω ini is the initial inertia factor, ω end is the final inertia factor, n iter is the iteration number, n is the current iteration number, n∈[0,n iter ], x k-1 is the independent variable at the k-1th iteration, x k =x k-1 +v k , R a is a random number between (0,1), p b is the individual optimal value, g b is the optimal value of the population;
S35:更新自变量,并求出新的目标函数值;S35: update the independent variable, and obtain a new objective function value;
S36:更新种群的个体最优值和群体最优值;S36: updating the individual optimal value and group optimal value of the population;
S37:重复S34~S36,直到到达迭代次数或达到目标精度;S37: Repeat S34-S36 until the number of iterations is reached or the target accuracy is reached;
S38:重复S31~S37,直到算出所有上矫直辊所需的正弯力和负弯力;S38: Repeat S31-S37 until the positive bending force and negative bending force required by all the upper straightening rollers are calculated;
S39:计算总的正弯力和负弯力,检查是否超限,若超限,则重新设置初始正弯力和负弯力的范围,并重复S31~S38。S39: Calculate the total positive bending force and negative bending force, check whether it exceeds the limit, if it exceeds the limit, reset the range of the initial positive bending force and negative bending force, and repeat S31-S38.
进一步,步骤S4中所述将正弯力和负弯力分配到正弯液压缸和负弯液压缸上,采用平均分配法:Further, as described in step S4, the positive bending force and the negative bending force are distributed to the positive bending hydraulic cylinder and the negative bending hydraulic cylinder, and the average distribution method is adopted:
式中,Fop为每个正弯液压缸或负弯液压缸输出的力;Fsb为计算出的总的正弯辊力或总的负弯辊力;Nop为正弯液压缸或负弯液压缸的个数。In the formula, F op is the force output by each positive bending hydraulic cylinder or negative bending hydraulic cylinder; F sb is the calculated total positive roll bending force or total negative bending roll force; N op is the positive bending hydraulic cylinder or negative bending hydraulic cylinder The number of curved hydraulic cylinders.
进一步,步骤S4中所述将正弯力和负弯力分配到正弯液压缸和负弯液压缸上,采用比例系数分配法:Further, as described in step S4, the positive bending force and the negative bending force are distributed to the positive bending hydraulic cylinder and the negative bending hydraulic cylinder, and the proportional coefficient distribution method is adopted:
假设有m个上矫直辊,带钢入口侧有i个正弯液压缸,主要作用于前n1个上矫直辊,带钢出口侧有j个正弯液压缸,主要作用于第n2个到最后一个上矫直辊,则入口侧单个正弯缸输出的力为:Assuming that there are m upper straightening rollers, there are i positive bending hydraulic cylinders on the strip inlet side, which mainly act on the first n 1 upper straightening rollers, and j positive bending hydraulic cylinders on the strip steel exit side, mainly acting on the nth 2 to the last upper straightening roller, the output force of a single positive bending cylinder on the entrance side is:
式中,Fop2为入口侧单个正弯缸输出的力;Fbp1到Fbpn1为1#矫直辊到n1#矫直辊所需的正弯力,Fbpn2到Fbpm位n2#矫直辊到m#矫直辊所需的正弯力;Fbp为计算出的总的正弯辊力;αp为入口侧正弯辊力比例系数;i为入口侧正弯液压缸的个数;In the formula, F op2 is the output force of a single positive bending cylinder on the entrance side; F bp1 to F bpn1 are the positive bending forces required from 1# straightening roll to n1# straightening roll, F bpn2 to F bpm position n2# straightening The positive bending force required by the roll to the m# straightening roll; F bp is the calculated total positive bending force; α p is the positive bending force proportional coefficient on the entrance side; i is the number of positive bending hydraulic cylinders on the entrance side ;
通过式(9)和(10)计算出每个负弯液压缸输出的力,以及出口侧液压缸输出的力。The output force of each negative bending hydraulic cylinder and the output force of the outlet side hydraulic cylinder are calculated by formulas (9) and (10).
进一步,所述步骤S5中,修正需要以带钢板形平直为目标,根据现场的实际调试结果确定修正系数,假设正弯修正系数为βp,负弯修正系数位βn,则实际所需的正弯力和负弯力为:Further, in the step S5, the correction needs to aim at the flatness of the strip steel plate, and determine the correction coefficient according to the actual commissioning results on site. Assuming that the positive bending correction coefficient is β p and the negative bending correction coefficient is β n , the actual required The positive and negative bending forces of are:
Fap=Fsz·βp (11)F ap = F sz ·β p (11)
Fan=Fsf·βn (12)F an =F sf ·β n (12)
式中,Fap为实际的总正弯力;Fan为实际的总负弯力;Fsz为计算出的总正弯力;Fsf为计算出的总负弯力;βp为正弯修正系数;βn为负弯修正系数。In the formula, F ap is the actual total positive bending force; F an is the actual total negative bending force; F sz is the calculated total positive bending force; F sf is the calculated total negative bending force; β p is the positive bending force Correction coefficient; β n is the negative bending correction coefficient.
本发明的有益效果在于:本发明首先建立液压缸弯辊力和每个支撑辊提供的弯辊力之间的关系,然后以矫直辊的挠度分布为目标函数,进行弯辊力的设定。在已知矫直力的前提下,可以求出需要的弯辊力。The beneficial effect of the present invention is that: the present invention first establishes the relationship between the bending force of the hydraulic cylinder and the bending force provided by each support roll, and then uses the deflection distribution of the straightening roll as the objective function to set the bending force . On the premise of known straightening force, the required bending force can be calculated.
本发明的其他优点、目标和特征在某种程度上将在随后的说明书中进行阐述,并且在某种程度上,基于对下文的考察研究对本领域技术人员而言将是显而易见的,或者可以从本发明的实践中得到教导。本发明的目标和其他优点可以通过下面的说明书来实现和获得。Other advantages, objects and features of the present invention will be set forth in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the investigation and research below, or can be obtained from It is taught in the practice of the present invention. The objects and other advantages of the invention may be realized and attained by the following specification.
附图说明Description of drawings
为了使本发明的目的、技术方案和优点更加清楚,下面将结合附图对本发明作优选的详细描述,其中:In order to make the purpose of the present invention, technical solutions and advantages clearer, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:
图1为本发明所述矫直辊与支撑辊的位置关系;Fig. 1 is the positional relation of straightening roller and support roller of the present invention;
图2为本发明所述矫直机的俯视图;Fig. 2 is the top view of straightener described in the present invention;
图3为本发明实施例中第一次计算时1#辊的辊型曲线;Fig. 3 is the roll profile curve of 1# roll when calculating for the first time in the embodiment of the present invention;
图4为本发明实施例中第二次计算时1#辊的辊型曲线;Fig. 4 is the roll profile curve of 1# roll when calculating for the second time in the embodiment of the present invention;
图5为本发明实施例中第三次计算时1#辊的辊型曲线;Fig. 5 is the roll profile curve of 1# roll when calculating for the third time in the embodiment of the present invention;
图6为本发明实施例中第四次计算时1#辊的辊型曲线;Fig. 6 is the roll profile curve of 1# roll when calculating for the 4th time in the embodiment of the present invention;
图7为本发明实施例中第五次计算时1#辊的辊型曲线。Fig. 7 is the roll shape curve of the 1# roll in the fifth calculation in the embodiment of the present invention.
具体实施方式detailed description
以下通过特定的具体实例说明本发明的实施方式,本领域技术人员可由本说明书所揭露的内容轻易地了解本发明的其他优点与功效。本发明还可以通过另外不同的具体实施方式加以实施或应用,本说明书中的各项细节也可以基于不同观点与应用,在没有背离本发明的精神下进行各种修饰或改变。需要说明的是,以下实施例中所提供的图示仅以示意方式说明本发明的基本构想,在不冲突的情况下,以下实施例及实施例中的特征可以相互组合。Embodiments of the present invention are described below through specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation modes, and various modifications or changes can be made to the details in this specification based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the diagrams provided in the following embodiments are only schematically illustrating the basic concept of the present invention, and the following embodiments and the features in the embodiments can be combined with each other in the case of no conflict.
其中,附图仅用于示例性说明,表示的仅是示意图,而非实物图,不能理解为对本发明的限制;为了更好地说明本发明的实施例,附图某些部件会有省略、放大或缩小,并不代表实际产品的尺寸;对本领域技术人员来说,附图中某些公知结构及其说明可能省略是可以理解的。Wherein, the accompanying drawings are for illustrative purposes only, and represent only schematic diagrams, rather than physical drawings, and should not be construed as limiting the present invention; in order to better illustrate the embodiments of the present invention, some parts of the accompanying drawings may be omitted, Enlargement or reduction does not represent the size of the actual product; for those skilled in the art, it is understandable that certain known structures and their descriptions in the drawings may be omitted.
本发明实施例的附图中相同或相似的标号对应相同或相似的部件;在本发明的描述中,需要理解的是,若有术语“上”、“下”、“左”、“右”、“前”、“后”等指示的方位或位置关系为基于附图所示的方位或位置关系,仅是为了便于描述本发明和简化描述,而不是指示或暗示所指的装置或元件必须具有特定的方位、以特定的方位构造和操作,因此附图中描述位置关系的用语仅用于示例性说明,不能理解为对本发明的限制,对于本领域的普通技术人员而言,可以根据具体情况理解上述术语的具体含义。In the drawings of the embodiments of the present invention, the same or similar symbols correspond to the same or similar components; , "front", "rear" and other indicated orientations or positional relationships are based on the orientations or positional relationships shown in the drawings, which are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the referred devices or elements must It has a specific orientation, is constructed and operated in a specific orientation, so the terms describing the positional relationship in the drawings are for illustrative purposes only, and should not be construed as limiting the present invention. For those of ordinary skill in the art, the understanding of the specific meaning of the above terms.
本发明提出一种基于粒子群算法的矫直机弯辊力设定方法,现有15辊矫直机,其中7个上辊,8个下辊,每个上辊配有12个支撑辊,位于3个弯辊盒中。如图1所示,d为左支点距离辊身的距离,l为矫直辊辊身长度;L为两支点的距离;W为带钢宽度;a1为第一个支撑辊距离左支点的距离;b1为支撑辊辊身长度;c1为第一个支撑辊距离右支点的距离。如图2所示,入口侧为带钢进入的一侧,出口侧为带钢出去的一侧,共有7个上矫直辊,每个上矫直辊上有3个弯辊盒,4个支撑辊在一个弯辊盒内,液压缸位于弯辊盒上,中间有4个正弯液压缸,两侧各两个负弯液压缸。The present invention proposes a method for setting the bending force of straightening machine based on particle swarm algorithm. The existing 15-roll straightening machine includes 7 upper rolls and 8 lower rolls, and each upper roll is equipped with 12 support rolls. Comes in 3 bent roll boxes. As shown in Figure 1, d is the distance from the left fulcrum to the roll body, l is the length of the straightening roll body; L is the distance between the two fulcrums; W is the strip width; a 1 is the distance from the first support roll to the left fulcrum distance; b 1 is the length of the support roll body; c 1 is the distance from the first support roll to the right fulcrum. As shown in Figure 2, the entrance side is the side where the strip steel enters, and the exit side is the side where the strip steel goes out. The support rolls are in a bending box, and the hydraulic cylinders are located on the bending box. There are 4 positive bending hydraulic cylinders in the middle and two negative bending hydraulic cylinders on each side.
现作出以下假设:Now make the following assumptions:
(1)弯辊液压缸的作用力能够完全传递给支撑辊,作为支撑辊对矫直辊的弯辊力;(1) The force of the roll bending hydraulic cylinder can be completely transmitted to the support roll as the bending force of the support roll to the straightening roll;
(2)中间的正弯力只对某一矫直辊上中间6个支撑辊作用,且作用力平均分配,同理,左边的负弯力只对某一矫直辊上左边3个支撑辊作用,且作用力平均分配,右边的负弯力只对某一矫直辊上右边3个支撑辊作用,且作用力平均分配;(2) The positive bending force in the middle only acts on the middle 6 support rollers on a certain straightening roller, and the force is evenly distributed. Similarly, the negative bending force on the left only acts on the 3 support rollers on the left of a certain straightening roller The negative bending force on the right only acts on the three support rollers on the right side of a straightening roller, and the force is evenly distributed;
(3)支撑辊位于矫直辊正上方。(3) The support roller is located directly above the straightening roller.
(4)作用力对称施加,即左侧的负弯力和右侧的负弯力相等。(4) The force is applied symmetrically, that is, the negative bending force on the left side is equal to the negative bending force on the right side.
根据这样的假设,矫直机弯辊力的设定方法包括以下步骤:According to this assumption, the setting method of the bending force of the straightening machine includes the following steps:
(1)如图1和图2所示,理清液压缸、支撑辊、矫直辊的几何关系;也即矫直机有7个上辊,8个下辊,每个上辊配有12个支撑辊,位于3个弯辊盒中。液压缸位于弯辊盒上,中间有4个正弯液压缸,两侧各两个负弯液压缸。(1) As shown in Figure 1 and Figure 2, clarify the geometric relationship between hydraulic cylinders, support rolls, and straightening rolls; that is, the straightening machine has 7 upper rolls and 8 lower rolls, and each upper roll is equipped with 12 support rolls in 3 bending roll boxes. The hydraulic cylinders are located on the bending roll box, with 4 positive bending hydraulic cylinders in the middle and two negative bending hydraulic cylinders on each side.
可以计算出每一组矫直力下所需的正弯力和负弯力,然后加起来可以得到总正弯力和总负弯力。总正弯力由中间4个正弯液压缸分配,总负弯力由两侧的负弯液压缸分配。The positive bending force and negative bending force required under each set of straightening forces can be calculated, and then added up to obtain the total positive bending force and total negative bending force. The total positive bending force is distributed by the four positive bending hydraulic cylinders in the middle, and the total negative bending force is distributed by the negative bending hydraulic cylinders on both sides.
中间4个正弯液压缸一共可提供最大400吨的正弯力,每侧2个负弯液压缸单侧可提供最大200吨的负弯力。矫直辊的弹性模量为208000MPa,辊身长度为2000mm,矫直辊直径为120mm,两侧支点距离辊身的距离为55mm,支撑辊的几何参数(单位:mm)如下:The 4 positive bending hydraulic cylinders in the middle can provide a maximum positive bending force of 400 tons in total, and the 2 negative bending hydraulic cylinders on each side can provide a maximum negative bending force of 200 tons on one side. The elastic modulus of the straightening roller is 208000MPa, the length of the roller body is 2000mm, the diameter of the straightening roller is 120mm, the distance between the fulcrums on both sides of the roller body is 55mm, and the geometric parameters (unit: mm) of the supporting roller are as follows:
表1Table 1
则单个支撑辊提供的负弯力为:Then the negative bending force provided by a single support roller is:
式中,Fyl为左边液压缸提供给某个矫直辊上的负弯力;Fyr为右边液压缸提供给某个矫直辊上的负弯力;Fyf为某个矫直辊上总的负弯力;Fz1为左右两边单个支撑辊提供的负弯力。In the formula, F yl is the negative bending force provided by the left hydraulic cylinder to a certain straightening roller; F yr is the negative bending force provided by the right hydraulic cylinder to a certain straightening roller; F yf is the negative bending force on a certain straightening roller The total negative bending force; F z1 is the negative bending force provided by the single support rollers on the left and right sides.
则单个支撑辊提供的正弯力为:Then the positive bending force provided by a single support roller is:
式中,Fyz为某个矫直辊上总的正弯力;Fz2为中间6个支撑辊中单个支撑辊提供的正弯力。In the formula, F yz is the total positive bending force on a certain straightening roll; F z2 is the positive bending force provided by a single support roll among the six support rolls in the middle.
则单个支撑辊传递给矫直辊的负弯力为:Then the negative bending force transmitted by a single support roller to the straightening roller is:
F1=Fz1·cosθ (16)F 1 =F z1 ·cosθ (16)
由于支撑辊位于矫直辊正上方,θ=0°,则F1=Fz1。Since the support roller is located directly above the straightening roller, θ=0°, then F 1 =F z1 .
单个支撑辊传递给矫直辊的正弯力为:The positive bending force transmitted by a single support roll to the straightening roll is:
F2=Fz2·cosθ (17)F 2 =F z2 ·cosθ (17)
由于支撑辊位于矫直辊正上方,θ=0°,则F2=Fz2。Since the support roller is directly above the straightening roller, θ=0°, then F 2 =F z2 .
矫直机全部矫直辊的总负弯力为:The total negative bending force of all the straightening rollers of the straightening machine is:
Fsum1=Fyf1+Fyf2+…+Fyf7 (18)F sum1 =F yf1 +F yf2 +...+F yf7 (18)
矫直机全部矫直辊的总正弯力为:The total positive bending force of all the straightening rollers of the straightening machine is:
Fsum2=Fyz1+Fyz2+…+Fyz7 (19)F sum2 =F yz1 +F yz2 +...+F yz7 (19)
(2)建立矫直辊挠度关于矫直力、弯辊力的函数模型,具体来说:(2) Set up the function model of straightening roll deflection about straightening force, bending roll force, specifically:
采用材料力学的方法建立弯辊力和矫直力之间的关系如下:The relationship between bending force and straightening force is established by the method of material mechanics as follows:
当单独受到矫直力作用时:When subjected to straightening force alone:
式中,fj(x)为距左支点距离为x处的挠度,mm;E为矫直辊的弹性模量,MPa;I为圆柱形截面的惯性矩,N·mm;Fj为矫直力,N;l为两支点的距离,mm;w为带钢的宽度,mm。In the formula, f j (x) is the deflection at the distance x from the left fulcrum, mm; E is the elastic modulus of the straightening roller, MPa; I is the moment of inertia of the cylindrical section, N mm; F j is the straightening Straight force, N; l is the distance between two fulcrums, mm; w is the width of the strip steel, mm.
当单独受到弯辊力作用时:When subjected to bending force alone:
式中,fw(x)为距左支点距离为x处的挠度,mm;E为矫直辊的弹性模量,MPa;I为圆柱形截面的惯性矩,N·mm;Fi表示第i个支撑辊的弯辊力,N;ai表示第i个支撑辊距左端部左支点的距离,mm;bi表示第i个支撑辊的辊身长度,mm;ci表示第i个支撑辊右端部距右支点的距离,mm;l表示两支点的距离,mm。In the formula, f w (x) is the deflection at the distance x from the left fulcrum, mm; E is the elastic modulus of the straightening roller, MPa; I is the moment of inertia of the cylindrical section, N mm; F i represents the The bending force of the i support roll, N; a i represents the distance between the i support roll and the left fulcrum at the left end, mm; b i represents the length of the i support roll body, mm; c i represents the i The distance between the right end of the support roller and the right fulcrum, mm; l represents the distance between the two fulcrums, mm.
则矫直辊目标挠度函数为:Then the target deflection function of the straightening roller is:
f(x)=fj(x)+fw(x) (26) f (x)= fj (x)+fw(x) (26)
式中,f(x)为矫直辊辊身距左支点距离为x处的挠度。In the formula, f(x) is the deflection at the distance x from the straightening roller body to the left fulcrum.
(3)已知矫直某钢种(宽度1500mm)上矫直辊受到的矫直力为:(3) It is known that the straightening force received by the straightening roller on a certain steel grade (width 1500mm) is:
表2Table 2
1#~7#表示矫直机的7个上辊。1#~7# represent the 7 upper rollers of the straightening machine.
以计算1#辊的正弯力和负弯力为例,关键步骤如下:Taking the calculation of positive bending force and negative bending force of 1# roller as an example, the key steps are as follows:
a)设置1#辊初始正弯力和负弯力的范围为0~206.16kN;a) Set the range of initial positive bending force and negative bending force of 1# roller to 0~206.16kN;
b)设置粒子群算法的超参数如下:b) Set the hyperparameters of the particle swarm optimization algorithm as follows:
表3table 3
在本实施例中,对1#辊计算5次,记录每次1#的计算结果如下:In the present embodiment, calculate 5 times to 1# roller, record the calculation result of each 1# as follows:
表4Table 4
可以看到,采用粒子群算法,每次计算得到的结果均不相同。其中每次计算1#辊的辊型曲线如图3~图6所示。It can be seen that with the particle swarm optimization algorithm, the results of each calculation are different. Among them, the roll profile curve of 1# roll is calculated each time as shown in Figure 3-6.
(4)假设按照第5次的计算结果进行后续的计算。(4) Assume that subsequent calculations are performed according to the calculation results of the fifth time.
计算结果如表5:The calculation results are shown in Table 5:
表5table 5
假设按照平均分配法,可得单个正弯液压缸提供的正弯力为:Assuming that the average distribution method is used, the positive bending force provided by a single positive bending hydraulic cylinder can be obtained as:
单个负弯液压缸提供的负弯力为:The negative bending force provided by a single negative bending hydraulic cylinder is:
假设按照比例系数法,可得入口侧单个正弯液压缸提供的正弯力为:Assuming that the proportional coefficient method is used, the positive bending force provided by a single positive bending hydraulic cylinder on the inlet side can be obtained as:
出口侧单个正弯液压缸提供的正弯力为:The positive bending force provided by a single positive bending hydraulic cylinder on the outlet side is:
入口侧单个负弯液压缸提供的负弯力为:The negative bending force provided by a single negative bending hydraulic cylinder on the inlet side is:
出口侧单个负弯液压缸提供的负弯力为:The negative bending force provided by a single negative bending hydraulic cylinder on the outlet side is:
(5)假设正弯修正系数为0.9,负弯修正系数为0.85,则实际的总正弯力为:(5) Assuming that the positive bending correction coefficient is 0.9 and the negative bending correction coefficient is 0.85, the actual total positive bending force is:
Fpsa=579.78×0.9=521.8kN (35)F psa =579.78×0.9=521.8kN (35)
实际的总负弯力为:The actual total negative bending force is:
Fnsa=495.47×0.85=421.15kN (36) Fnsa =495.47×0.85=421.15kN (36)
液压缸的弯辊力分配也需重新计算。The distribution of the bending force of the hydraulic cylinder also needs to be recalculated.
最后说明的是,以上实施例仅用以说明本发明的技术方案而非限制,尽管参照较佳实施例对本发明进行了详细说明,本领域的普通技术人员应当理解,可以对本发明的技术方案进行修改或者等同替换,而不脱离本技术方案的宗旨和范围,其均应涵盖在本发明的权利要求范围当中。Finally, it is noted that the above embodiments are only used to illustrate the technical solutions of the present invention without limitation. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be carried out Modifications or equivalent replacements, without departing from the spirit and scope of the technical solution, should be included in the scope of the claims of the present invention.
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