CN109711101B - Method for solving mechanical energy parameters of same-speed different-diameter snake-shaped rolling of thick steel plate - Google Patents
Method for solving mechanical energy parameters of same-speed different-diameter snake-shaped rolling of thick steel plate Download PDFInfo
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Abstract
The invention provides a method for solving the force energy parameter of the same-speed reducing snake-shaped rolling of a thick steel plate, belonging to the technical field of thick steel plate plastic forming; the method is characterized in that the deformation zone is divided into four parts, namely a rear sliding zone I, a rolling zone II, a front sliding zone III and a recurved zone IV according to the direction of the friction force of the contact surface of the snake-shaped rolling deformation zone; the four areas do not necessarily exist at the same time, and the composition state of the deformation area is preliminarily determined according to the position state of the neutral point; determining a solving model of rolling force and rolling moment according to the composition state, the initial condition and the boundary condition of the deformation area; the invention can accurately predict the rolling force and the rolling moment and provides a theoretical basis for the snake-shaped rolling process design and the rolling mill structure design.
Description
Technical Field
The invention belongs to the technical field of thick steel plate plastic forming, and particularly relates to a method for solving the mechanical energy parameters of the same-speed different-diameter snake-shaped rolling of a thick steel plate.
Background
The high-performance thick steel plate is widely applied to the field of high-end technical equipment such as national defense military equipment, ships, nuclear power, ocean platforms, pressure vessels, heavy machinery and the like, and is an important structural material. In the rolling production process of thick steel plates, as the core part is insufficiently deformed, an as-cast structure exists, and the mechanical property is low. The mechanical property of the core is generally improved by increasing the total compression ratio, but the total compression ratio is generally difficult to meet the process requirements due to the limitations of the production capacity of a continuous casting machine, the opening degree of a rolling mill and the like, and a thick steel plate with good core structure property cannot be obtained.
The structural property inspection in the production of the thin strip steel shows that the asynchronous rolling can refine grains and has the function of improving the deformation of the center of the strip steel compared with the synchronous rolling. However, for the asynchronous rolling of thick steel plates, the linear speeds of the upper working roll and the lower working roll are inconsistent, so that the steel plates are bent after being rolled, and the subsequent steel rotation and the biting of the next pass are influenced. In order to solve the bending problem of thick steel plates, a slow working roll is moved for a certain distance along the rolling direction on the basis of traditional asynchronous rolling, and a front sliding area, a rolling area, a rear sliding area and a reverse bending area are formed in a deformation area. Wherein, the recurved zone can play the role of restraining the steel plate from bending.
The adoption of the snake-shaped rolling mode can lead the plate to generate the action of shearing stress in a deformation area, lead the deformation of the core structure to be more sufficient and achieve the purpose of refining grains. In order to guide production, the mechanical parameter modeling of the snake-shaped rolling method needs to be deeply researched. The force and energy parameters are not only important basis for the design of the rolling process, but also are the precondition for ensuring the safe operation of the rolling mill and the main motor. In order to enable the rolling mill to produce the thick steel plate with good performance, a method for solving the force and energy parameters of the same-speed different-diameter snake-shaped rolling of the thick steel plate is needed.
Disclosure of Invention
The invention aims to provide a method for solving energy parameters of the same-speed different-diameter snake-shaped rolling force of a thick steel plate, which is used for accurately predicting the rolling force and the rolling moment of a rolling mill. The invention is implemented as follows: the concrete solving steps are as follows:
1) solving the length of the same-speed reducing snake-shaped rolling deformation zone
Neutral point n of upper work roll during serpentine rolling1Moving towards the inlet direction, the neutral point n of the lower working roll2Moving towards the outlet; the position of the neutral point determines the length of a back sliding area I, a rolling area II and a front sliding area III in the snake-shaped rolling deformation area l, and the horizontal dislocation d between the upper working roll and the lower working roll determines the length of a reverse bending area IV; when d is<xn1<l,d<xn2<xn1When in use, the deformation zone consists of a back sliding zone I, a rolling zone II, a front sliding zone III and a reverse bending zone IV; when d is<xn1<l,xn2When d is less than or equal to d, the deformation zone consists of a post-sliding zone I, a rolling zone II and a reverse bending zone IV; when x isn1≥l,xn2When d is less than or equal to d, the deformation zone consists of a rolling zone II and a reverse bending zone IV;
determining the lengths of the deformation zones of the upper and lower working rolls as l and l' respectively according to the geometric relationship of the snake-shaped rolling deformation zone, and solving the formula as follows:
for the upper work roll:
for the lower work roll:
along the vertical direction:
Δh1+Δh2＝H-h0 (3)
in the formula: r1Upper work roll radius, R2Radius of lower working roll, H thickness of steel plate before rolling, H0Thickness of rolled steel sheet, d-offset, Δ h1Reduction of upper work rolls,. DELTA.h2-the reduction of the lower work roll;
the following equations (1) to (3) yield:
in the formula: a. b is the introduction coefficient of the carbon dioxide,
the deformation zone length solving formula:
2) solving yield criterion of rolled piece material
Determining the yield criterion of the rolled piece material according to the Misses yield criterion as follows:
in the formula: sigmax、σy-positive stresses in x, y direction to which the material of the rolled stock is subjected, respectively; sigmaf-the rheological stress of the material of the rolled stock; m-coefficient of friction;
the average shear stress at the top and bottom of the plate is:
wherein c is an introduced coefficient, c is more than or equal to 0 and less than or equal to 1;
by σx＝q，σyObtaining the yield criterion of the top and the bottom of the thick steel plate;
by
And
the following relationships are obtained:
in the formula: q-horizontal normal stress of the deformation zone, p-unit pressure;
the average normal stress in the x direction and the y direction respectively suffered by the upper part and the lower part of the unit body; m-introduction coefficient;
3) unit pressure in plastic deformation zone
Dividing the deformation area into a rear sliding area I, a rolling area II, a front sliding area III and a reverse bending area IV according to the direction of the friction force of the contact surface of the deformation area;
the unit pressure solving models for determining I, II, III and IV in the deformation zone based on the main stress method are respectively as follows:
when xn1When x is not less than l, obtaining:
x whenn2≤x≤xn1Then, the following is obtained:
③ when d is less than or equal to xn2Then, the following is obtained:
when x is more than or equal to 0 and less than or equal to d, obtaining:
in the formula: A. c, D, E, G are the coefficients introduced; i-roll diameter ratio, i ═ R2/R1；
xn1-x coordinate of the neutral point at the upper work roll; x is the number ofn2-x coordinate of neutral point at lower work roll;
4) solving and modeling of rolling force and rolling moment
According to the composition state of the deformation zone, when d<xn1<l,d<xn2<xn1When in use, the deformation zone consists of a back sliding zone I, a rolling zone II, a front sliding zone III and a reverse bending zone IV; when d is<xn1<l,xn2When d is less than or equal to d, the deformation zone consists of a post-sliding zone I, a rolling zone II and a reverse bending zone IV; when x isn1≥l,xn2When d is less than or equal to d, the deformation zone consists of a rolling zone II and a reverse bending zone IV;
at the upper work roll throw-out point O, the boundary conditions are: x is 0 and q is 0, thus obtaining
Substitution of formula (14) to CⅣ；
When d<xn1<l,d<xn2<xn1The boundary conditions for the entry position are: x is equal to l and q is equal to 0, thus obtaining
Substituting it into equation (11) to obtain CI(ii) a Because there is p at x ═ dⅢ(x＝d)＝pⅣ(x ═ d), and C was obtainedⅢ(ii) a Where x is xn1Where is provided with pⅠ(x＝xn1)＝pⅡ(x＝xn1) To find out CII(x＝xn1) Where x is equal to xn2Where is provided with pⅡ(x＝xn2)＝pⅢ(x＝xn2) To find out CII(x＝xn2) (ii) a ByThe unit compression pressure is continuous at the upper and lower work roll neutral points, thus yielding the following equation:
CII(x＝xn1)＝CII(x＝xn2) (15)
during rolling, the volume remains unchanged, thus obtaining the following relationship:
in the formula: v. of1、v2Surface linear velocities, x, of upper and lower work rolls, respectivelyn1、xn2-x coordinates of the neutral points at the upper and lower work rolls, respectively;
x is obtained by combining the vertical type (15) and the formula (16)n1、xn2And CⅡ；
When the rolled piece is in a balanced state in the vertical direction, the rolling forces of the upper and lower working rolls are equal, namely F1＝F2F; and (3) obtaining the same-speed reducing snake-shaped rolling force F by integrating the unit pressure along the contact arc:
in the formula: b, the width of a rolled piece, and l is the length of a deformation area;
obtaining rolling torque T of the upper and lower working rolls by solving the torque along the friction force on the contact arcs of the upper and lower working rolls1、T2：
In the formula:
k is shear deformation resistance;
when d<xn1<l,xn2When d is less than or equal to d, the boundary conditions of the inlet position are as follows: x is l, q is 0,
substituting it into equation (11) to obtain CI(ii) a From pⅡ(x＝d)＝pⅣ(x ═ d), and C was obtainedII(ii) a Because of pⅠ(x＝xn1)＝pⅡ(x＝xn1) So that x is found by equation (11) and equation (12)n1；
And (3) obtaining the same-speed reducing snake-shaped rolling force F by integrating the unit pressure along the contact arc:
obtaining rolling torque T of the upper and lower working rolls by solving the torque along the friction force on the contact arcs of the upper and lower working rolls1、T2：
(x)n1≥l,xn2When d is less than or equal to d, the boundary conditions of the inlet position are as follows: x is l, q is 0,
substituting it into equation (12) to obtain CII；
And (3) obtaining the same-speed reducing snake-shaped rolling force F by integrating the unit pressure along the contact arc:
obtaining rolling torque T of the upper and lower working rolls by solving the torque along the friction force on the contact arcs of the upper and lower working rolls1、T2：
The invention has the advantages and positive effects that: and preliminarily predicting the composition state of the rolling deformation zone according to the position state of the neutral point, and accurately solving the rolling force and the rolling moment according to the composition state, the boundary condition and the initial condition of the deformation zone, so as to provide a theoretical basis for the snake-shaped rolling process design and the rolling mill structure design.
Drawings
FIG. 1 is a schematic view of geometric relationship of a same-speed different-diameter snake-shaped rolling deformation zone;
FIG. 2 is a graph of unit body stress in a deformation zone;
FIG. 3 is a flow chart of deformation region composition solution;
in the figure, R1,R2-radius of upper and lower work rolls; v. of1、v2-surface linear velocities of the upper and lower work rolls, respectively; d is the amount of the offset; Δ h1,Δh2-the reduction of the upper and lower work rolls; l-deformation zone length; h, the thickness of the steel plate before rolling; h is0-thickness of rolled steel sheet; x is the number ofn1、xn2-x coordinates of the neutral points at the upper and lower work rolls, respectively; xOy-coordinate system; o-origin of coordinate system; i, a backward sliding area; II, rolling the area; III-forward slide zone; IV-recurve region; tau is1,τ2-frictional stress of the upper and lower work rolls with the workpiece;
-average shear stress of the upper and lower parts of the unit cell; sigmax-positive stress in horizontal direction;p1-upper working roll stress; p is a radical of2-lower work roll compressive stress; theta1,θ2The variable angle of the contact arc with the x-axis.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the technical solution of the present invention will be described in detail below with reference to the accompanying drawings. It should be noted, however, that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Taking a 4200 heavy and medium plate mill as an example, the detailed parameters are shown in table 1. Three groups of different roll diameters are taken for detailed description:
the first set of data: the diameter of the upper working roll is 1095mm, and the diameter of the lower working roll is 1100 mm;
the second set of data: the diameter of the upper working roll is 1080mm, and the diameter of the lower working roll is 1100 mm;
third group of data: the diameter of the upper working roll is 950mm, and the diameter of the lower working roll is 1100 mm;
TABLE 1 Rolling parameters
1. Solving the length of the same-speed reducing snake-shaped rolling deformation zone
According to the calculation formulas (4) and (5) for the rolling reduction of the upper working roll and the lower working roll in the same-speed reducing snake-shaped rolling process:
the first set of data: Δ h1＝21.4345mm，Δh2＝18.5655mm；
The second set of data: Δ h1＝21.5823mm，Δh2＝18.4177mm；
Third group of data: Δ h1＝22.9530mm，Δh2＝17.0470mm；
According to the length calculation formula (6) of the deformation zone, the following results are obtained:
the first set of data: 151.69 mm;
the second set of data: 151.14 mm;
third group of data: 145.87 mm;
2. calculating yield criterion of rolled piece material
According to the rolled piece material yield criterion calculation formula (10), the following results are obtained:
the first set of data:
the second set of data:
third group of data:
3. calculating rolling force and rolling moment
(1) The first set of data: the diameter of the upper working roll is 1095mm, the diameter of the lower working roll is 1100mm, and the assumed deformation zone consists of a back sliding zone I, a rolling zone II, a front sliding zone III and a reverse bending zone IV. At this time, x can be obtained by combining the vertical type (15) and the formula (16)n1＝34.5218mm，xn215.9950 mm. Determining the match d according to FIG. 3<xn1<l,d<xn2<xn1Therefore, the deformation zone is really composed of a back sliding zone I, a rolling zone II, a front sliding zone III and a reverse bending zone IV. At this time, at the upper work roll throw-out point O, the boundary conditions are: x is 0 and q is 0, thus obtaining pⅣ125.0570MPa, substituting formula (14) to obtain CⅣ308.8774 MPa; at the entrance of the deformation zone, the boundary conditions are: x is 151.69mm and q is 0, so p is obtainedⅠC was obtained by substituting formula (11) under 125.0570MPaⅠ317.9013 MPa; because there is p at x ═ dⅢ＝pⅣTo find out CⅢ307.9013 MPa; where x is xn1Where is provided with pⅠ＝pⅡThus obtaining CⅡ(x＝xn1) (ii) a Where x is xn2Where is provided with pⅡ＝pⅢThus obtaining CⅡ(x＝xn2)。
X is obtained by combining vertical type (15) and formula (16)n1＝34.52mm，xn2＝16.00mm，CⅡ＝302.34MPa。
At this time, unknown constants of the unit pressure calculation formulas (11), (12), (13), and (14) are obtained.
Obtaining a rolling force F of 60165.885KN according to the formula (17);
calculating the upper working roll manufacturing moment T according to the equations (18) and (19)12620.84KN m, lower roll rolling moment T2＝4756.71KN·m。
(2) The second set of data: the diameter of the upper working roll is 1080mm, the diameter of the lower working roll is 1100mm, and the assumed deformation zone consists of a rear sliding zone I, a rolling zone II, a front sliding zone III and a recurved zone IV. At this time, x can be obtained by combining the vertical type (15) and the formula (16)n1＝59.3503m-m，xn2-8.9625 mm. Determining the match d according to FIG. 3<xn1<l,xn2D is less than or equal to d. Therefore, the deformation zone is composed of a post-sliding zone I, a rolling zone II and a recurved zone IV. At this time, at the upper work roll throw-out point O, the boundary conditions are: x is 0 and q is 0, thus obtaining pⅣ125.0570MPa, substituting formula (14) to obtain CⅣ310.6024 MPa; at the entrance of the deformation zone, the boundary conditions are: x is 151.14mm and q is 0, so p is obtainedⅠC was obtained by substituting formula (11) under 125.0570MPaⅠ317.1771 MPa; because there is p at x ═ dⅡ＝pⅣTo find out CⅡ299.9410 MPa; where x is xn1Where is provided with pⅠ＝pⅡThus, the neutral point x at the upper work roll is obtainedn1＝45.4582mm。
Obtaining a rolling force F of 62058.3KN according to the formula (20);
calculating the upper working roll manufacturing moment T according to the equations (21) and (22)12169.00KN m, lower roll rolling moment T2＝5176.48KN·m。
(3) The first set of data: the diameter of the upper working roll is 950mm, the diameter of the lower working roll is 1100mm, and the assumed deformation zone consists of a rear sliding zone I, a rolling zone II, a front sliding zone III and a recurved zone IV. At this time, x can be obtained by combining the vertical type (15) and the formula (16)n1＝645.2529mm，xn2-670.7866 mm. Determining the match x according to FIG. 3n1≥l,xn2D is less than or equal to d. Thus, the deformation zone is knownConsists of a rolling area II and a reverse bending area IV. At this time, at the upper work roll throw-out point O, the boundary conditions are: x is 0 and q is 0, thus obtaining pⅣ125.0570MPa, substituting formula (14) to obtain CⅣ326.6415 MPa; at the entrance of the deformation zone, the boundary conditions are: x is 145.87mm and q is 0, so p is obtainedⅡC was obtained by substituting formula (12) under 118.9832MPaⅡ＝275.1103MPa。
Obtaining a rolling force F of 53861.1KN according to the formula (23);
calculating the upper working roll manufacturing moment T according to the equations (24) and (25)1-4620.41KN m, lower roll rolling moment T2＝4983.19KN·m。
Claims (1)
1. A method for solving the mechanical energy parameters of the same-speed different-diameter snakelike rolling of a thick steel plate is characterized by comprising the following steps of: the concrete solving steps are as follows:
1) solving the length of the same-speed reducing snake-shaped rolling deformation zone
Neutral point n of upper work roll during serpentine rolling1Moving towards the inlet direction, the neutral point n of the lower working roll2Moving towards the outlet; the position of the neutral point determines the length of a back sliding area I, a rolling area II and a front sliding area III in the snake-shaped rolling deformation area l, and the horizontal dislocation d between the upper working roll and the lower working roll determines the length of a reverse bending area IV; when d is<xn1<l,d<xn2<xn1When in use, the deformation zone consists of a back sliding zone I, a rolling zone II, a front sliding zone III and a reverse bending zone IV; when d is<xn1<l,xn2When d is less than or equal to d, the deformation zone consists of a post-sliding zone I, a rolling zone II and a reverse bending zone IV; when x isn1≥l,xn2When d is less than or equal to d, the deformation zone consists of a rolling zone II and a reverse bending zone IV;
determining the lengths of the deformation zones of the upper and lower working rolls as l and l' respectively according to the geometric relationship of the snake-shaped rolling deformation zone, and solving the formula as follows:
for the upper work roll:
for the lower work roll:
along the vertical direction:
Δh1+Δh2＝H-h0 (3)
in the formula: r1Upper work roll radius, R2Radius of lower working roll, H thickness of steel plate before rolling, H0Thickness of rolled steel sheet, d-offset, Δ h1Reduction of upper work rolls,. DELTA.h2-the reduction of the lower work roll;
the following equations (1) to (3) yield:
in the formula: a. b is the introduction coefficient of the carbon dioxide,
the deformation zone length solving formula:
2) solving yield criterion of rolled piece material
Determining the yield criterion of the rolled piece material according to the Misses yield criterion as follows:
in the formula：σx、σy-positive stresses in x, y direction to which the material of the rolled stock is subjected, respectively; sigmaf-the rheological stress of the material of the rolled stock; m-coefficient of friction;
the average shear stress at the top and bottom of the plate is:
wherein c is an introduced coefficient, c is more than or equal to 0 and less than or equal to 1;
by σx＝q，σyObtaining the yield criterion of the top and the bottom of the thick steel plate;
by
And
the following relationships are obtained:
in the formula: q-horizontal normal stress of the deformation zone, p-unit pressure;
the average normal stress in the x direction and the y direction respectively suffered by the upper part and the lower part of the unit body; m-introduction coefficient;
3) unit pressure in plastic deformation zone
Dividing the deformation area into a rear sliding area I, a rolling area II, a front sliding area III and a reverse bending area IV according to the direction of the friction force of the contact surface of the deformation area;
the unit pressure solving models for determining I, II, III and IV in the deformation zone based on the main stress method are respectively as follows:
when xn1When x is not less than l, obtaining:
x whenn2≤x≤xn1Then, the following is obtained:
③ when d is less than or equal to xn2Then, the following is obtained:
when x is more than or equal to 0 and less than or equal to d, obtaining:
in the formula: A. c, D, E, G are the coefficients introduced; i-roll diameter ratio, i ═ R2/R1；
xn1-x coordinate of the neutral point at the upper work roll; x is the number ofn2-x coordinate of neutral point at lower work roll;
4) solving and modeling of rolling force and rolling moment
According to the composition state of the deformation zone, when d<xn1<l,d<xn2<xn1When in use, the deformation zone consists of a back sliding zone I, a rolling zone II, a front sliding zone III and a reverse bending zone IV; when d is<xn1<l,xn2When d is less than or equal to d, the deformation zone consists of a post-sliding zone I, a rolling zone II and a reverse bending zone IV; when x isn1≥l,xn2When d is less than or equal to d, the deformation zone consists of a rolling zone II and a reverse bending zone IV;
at the upper work roll throw-out point O, the boundary conditions are: x is 0 and q is 0, thus obtaining
Substitution of formula (14) to CⅣ；
When d<xn1<l,d<xn2<xn1The boundary conditions for the entry position are: x is equal to l and q is equal to 0, thus obtaining
Substituting it into equation (11) to obtain CI(ii) a Because there is p at x ═ dⅢ(x＝d)＝pⅣ(x ═ d), and C was obtainedⅢ(ii) a Where x is xn1Where is provided with pⅠ(x＝xn1)＝pⅡ(x＝xn1) To find out CII(x＝xn1) Where x is equal to xn2Where is provided with pⅡ(x＝xn2)＝pⅢ(x＝xn2) To find out CII(x＝xn2) (ii) a Since the unit compression pressure is continuous at the upper and lower work roll neutral points, the following equation is obtained:
CII(x＝xn1)＝CII(x＝xn2) (15)
during rolling, the volume remains unchanged, thus obtaining the following relationship:
in the formula: v. of1、v2Surface linear velocities, x, of upper and lower work rolls, respectivelyn1、xn2-x coordinates of the neutral points at the upper and lower work rolls, respectively;
x is obtained by combining the vertical type (15) and the formula (16)n1、xn2And CⅡ；
When the rolled piece is in a balanced state in the vertical direction, the rolling forces of the upper and lower working rolls are equal, namely F1＝F2F; and (3) obtaining the same-speed reducing snake-shaped rolling force F by integrating the unit pressure along the contact arc:
in the formula: b, the width of a rolled piece, and l is the length of a deformation area;
obtaining rolling torque T of the upper and lower working rolls by solving the torque along the friction force on the contact arcs of the upper and lower working rolls1、T2：
In the formula:
k is shear deformation resistance;
when d<xn1<l,xn2When d is less than or equal to d, the boundary conditions of the inlet position are as follows: x is l, q is 0,
substituting it into equation (11) to obtain CI(ii) a From pⅡ(x＝d)＝pⅣ(x ═ d), and C was obtainedII(ii) a Because of pⅠ(x＝xn1)＝pⅡ(x＝xn1) So that x is found by equation (11) and equation (12)n1；
And (3) obtaining the same-speed reducing snake-shaped rolling force F by integrating the unit pressure along the contact arc:
obtaining rolling torque T of the upper and lower working rolls by solving the torque along the friction force on the contact arcs of the upper and lower working rolls1、T2：
(x)n1≥l,xn2When d is less than or equal to d, the boundary conditions of the inlet position are as follows: x is l, q is 0,
substituting it into equation (12) to obtain CII；
And (3) obtaining the same-speed reducing snake-shaped rolling force F by integrating the unit pressure along the contact arc:
obtaining rolling torque T of the upper and lower working rolls by solving the torque along the friction force on the contact arcs of the upper and lower working rolls1、T2：
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| CN111241635B (en) * | 2020-01-08 | 2022-05-13 | 太原科技大学 | Model and method for calculating bending curvature of thick plate after same-diameter different-speed snake-shaped rolling |
| CN112906183B (en) * | 2021-01-14 | 2024-04-12 | 太原科技大学 | Method for calculating variable-diameter serpentine differential-temperature rolling force energy parameters of thick plates at same speed |
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