Design method of four-way valve controlled AGC cylinder for flatness control of plate mill

Abstract

This invention provides a design method for a four-way valve-controlled AGC cylinder for planar shape control in medium-thick plate rolling mills, relating to the fields of hydraulic control and mechanical design technology. The method first calculates the piston diameter of the AGC cylinder based on the maximum rolling force of the mill and the maximum design working pressure of the AGC cylinder. The calculated piston diameter is then rounded upwards to determine the piston diameter D. Next, based on the relationship between the steady-state retraction speed of the AGC cylinder and the piston rod diameter, and the piston diameter D, the piston rod diameter is calculated. A lower limit for the piston rod diameter is calculated based on the strength requirements of the piston rod during rolling. Finally, the final piston rod diameter d is determined by the larger of the calculated piston rod diameter and the lower limit. The AGC cylinder designed based on this invention is beneficial for meeting the process requirements of hot rolling planar shape control and improving production line efficiency.

Description

Technical Field

[0001] This invention relates to the fields of hydraulic control and mechanical design technology, and in particular to a design method for a four-way valve-controlled AGC cylinder for planar shape control in medium and heavy plate rolling mills. Background Technology

[0002] For conventional equal-thickness rolling hydraulic AGC control processes, only the loading and pressing speed of the AGC cylinder is typically considered, and usually... Figure 1 The three-way valve control method is shown. Under this control method, the piston diameter D (mm) of the AGC cylinder is initially calculated based on the maximum rolling force of the mill and the maximum working pressure of the AGC cylinder, and then the calculation result is rounded; there are two ways to take the value of the piston rod diameter d (mm): (1) take DK (100mm≤K≤150mm), generally the larger D is, the larger K is; (2) determine d according to the speed ratio of the cylinder. However, the retraction process of the AGC cylinder controlled by the three-way valve relies on the constant back pressure of the rod chamber, which is significantly different from the flow characteristics of the hydraulic oil entering the rodless chamber during the extension process of the AGC cylinder. Therefore, the actual significance of the speed ratio of the AGC cylinder controlled by the three-way valve is not very obvious.

[0003] The application materials for application number 2023103077451 have already clarified that the retraction speed of the AGC cylinder is relatively slow under the three-way valve control method. Using the four-way valve control method is beneficial to simultaneously achieve the functions of rapid pressing down and rapid retraction of the AGC cylinder. The four-way valve controls the AGC cylinder as follows: Figure 2 As shown in the figure. Research indicates that under four-way valve control, if the piston diameter D of the AGC cylinder and other working conditions (such as oil source pressure, rolling force, etc.) are the same, the size of the piston rod diameter d has a significant impact on the retraction speed and even the dynamic performance of the AGC cylinder. The piston rod diameter d obtained based on the above-mentioned traditional design method is generally large, leaving room for optimization. Therefore, optimizing the size design of the AGC cylinder is of great significance for improving the dynamic response speed of the four-way valve controlled AGC cylinder. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing a design method for a four-way valve-controlled AGC cylinder for planar shape control of medium and heavy plate rolling mills, thereby realizing the design of the dimensions of the rolling mill AGC cylinder under four-way valve control.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a design method for a four-way valve-controlled AGC cylinder for planar shape control in medium and heavy plate rolling mills, comprising the following steps:

[0006] Step 1: Based on the maximum rolling force of the rolling mill and the maximum design working pressure of the AGC cylinder, calculate the piston diameter of the AGC cylinder in advance, as shown in the following formula:

[0007]

[0008] Among them, D1 is the piston diameter of the AGC cylinder obtained by preliminary calculation, with the unit of mm; F max is the maximum rolling force of the rolling mill, with the unit of kN; P max is the maximum designed working pressure of the AGC cylinder, with the unit of MPa;

[0009] Step 2: Round up the piston diameter D1 of the AGC cylinder obtained by preliminary calculation, and determine the piston diameter D of the AGC cylinder according to the rounded-up D1;

[0010] When the rounded-up D1 ≤ 500 mm, the value of the piston diameter D of the AGC cylinder is referred to the ISO3320 standard; when the rounded-up D1 > 500 mm, the value of the piston diameter D of the AGC cylinder is selected according to the piston seal size series provided by the cylinder seal manufacturer;

[0011] Step 3: According to the relationship between the steady-state retraction speed of the AGC cylinder and the piston rod diameter and the piston diameter D of the AGC cylinder, preliminarily calculate the piston rod diameter size of the AGC cylinder;

[0012] The relationship between the steady-state retraction speed of the AGC cylinder and the piston rod diameter is shown in the following formula:

[0013]

[0014] In the formula, C d is the flow coefficient, ω is the area gradient of the servo valve spool, x v is the spool displacement of the servo valve, P s is the inlet pressure of the servo valve, ρ is the density of the hydraulic oil; F is the load force received by a single AGC cylinder during the rolling process, F ∈ [F1, F2]; F1 is the minimum load force that a single AGC cylinder may receive during the rolling process; F2 is the maximum load force that a single AGC cylinder may receive during the rolling process;

[0015] Let 0 < k < 1, and simplify formula (1) to get:

[0016]

[0017] Let Then after the piston diameter D is determined, at a fixed servo valve opening, the steady-state retraction speed v of the AGC cylinder is proportional to the square of M;

[0018] In formula (1) and formula (2), all variables are in the International System of Units. If P sIf the units are MPa, F is in kN, and D is in mm, then...

[0019]

[0020] When F = F1, find the value of k that makes M reach its maximum value and denote it as k1; when F = F2, find the value of k that makes M reach its maximum value and denote it as k2.

[0021] The preliminary calculated piston rod diameter of the AGC cylinder is shown in the following formula:

[0022]

[0023] In the formula, d1 is the piston rod diameter of the AGC cylinder calculated in advance, in mm; α∈[1.2,1.25] is the compression speed compensation coefficient;

[0024] Step 4: Based on the strength requirements of the piston rod during the rolling process, calculate the lower limit of the piston rod diameter, as shown in the following formula:

[0025]

[0026] In the formula: d min σ1 represents the lower limit of the piston rod diameter in mm; σ1 represents the allowable stress of the piston rod in MPa. n is the safety factor; σ s This represents the yield strength of the piston rod material, in MPa.

[0027] Step 5: Based on the preliminary calculated piston rod diameter d1 and lower limit piston rod dimension d... min The larger of these values ​​determines the final piston rod diameter d;

[0028] Take d1 and d min The larger value is assigned to the intermediate variable d. mid When d mid When the diameter is ≤450mm, the value of the piston rod diameter d should be taken according to ISO 3320 standard; when d mid When the diameter is greater than 450mm, the value of the piston rod diameter d should be selected according to the piston rod seal size series provided by the cylinder seal manufacturer.

[0029] The beneficial effects of adopting the above technical solution are as follows: The present invention provides a design method for a four-way valve-controlled AGC cylinder for planar shape control in medium and heavy plate rolling mills, (1) optimizing the key dimensions of the AGC cylinder operating in four-way valve control mode, which can effectively improve the retraction speed of the AGC cylinder, and the larger the cylinder (i.e., the larger D), the more obvious the improvement effect; (2) during the rolling process, the roll gap of the AGC cylinder continuously increases and the rolling force continuously decreases when it retracts, and the rolling force is the driving force for the retraction action of the AGC cylinder. When the rolling force is small, it is not conducive to achieving rapid retraction of the AGC cylinder. Based on the AGC cylinder designed in this invention, the advantage of retraction speed is more obvious when the rolling force is smaller.

[0030] Planar shape control is mainly applied to medium and heavy plate rolling mills. The AGC cylinders in medium and heavy plate rolling mills are relatively large, and planar shape control primarily occurs in the high-temperature zone of the roughing section, operating mainly with medium to low rolling forces. Therefore, the AGC cylinder designed based on this invention is beneficial for meeting the process requirements of hot rolling planar shape control and improving production line efficiency. Attached Figure Description

[0031] Figure 1 A schematic diagram of the hydraulic circuit for controlling an AGC cylinder with a three-way valve is provided as the background of this invention.

[0032] Figure 2 The hydraulic circuit schematic diagram of the four-way valve controlling the AGC cylinder is provided for the background technology of this invention;

[0033] Figure 3 A flowchart of a four-way valve-controlled AGC cylinder design method for planar shape control of medium and heavy plate rolling mills provided in an embodiment of the present invention;

[0034] Figure 4 The graphs showing the relationship between k and M under different load forces on the hydraulic cylinder provided in the embodiments of the present invention are shown. (a) is the relationship curve when F = 500kN, and (b) is the relationship curve when F = 40000kN.

[0035] In the diagram, Ps represents the oil source pressure of the AGC system; P0 represents the back pressure; and T represents the oil return port of the AGC system. Detailed Implementation

[0036] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0037] This embodiment takes a 3500mm hot rolling mill as an example, and uses the four-way valve controlled AGC cylinder design method for planar shape control of medium and heavy plate rolling mills of the present invention to design the piston diameter D and piston rod diameter d of the AGC cylinder.

[0038] In this embodiment, the hot rolling mill uses a four-way valve to control the operation of the AGC cylinder, requiring a maximum rolling force F. max =80000kN, the minimum load force that a single AGC cylinder may experience during rolling is F1 = 500kN, the maximum load force that a single AGC cylinder may experience during rolling is F2 = 40000kN, and the hydraulic station oil source pressure is P. s =28MPa.

[0039] In this embodiment, the design method of the four-way valve-controlled AGC cylinder for planar shape control of medium and heavy plate rolling mills is as follows: Figure 3 As shown, it includes the following steps:

[0040] Step 1: Based on the maximum rolling force F of the rolling mill max (Unit: kN) and the maximum design working pressure P of the AGC cylinder max (Unit: MPa), the preliminary calculation of the piston diameter D1 of the AGC cylinder (unit: mm) is shown in the following formula:

[0041]

[0042] In this embodiment, the piston diameter D1 of the AGC cylinder was initially calculated to be 1427.3 mm;

[0043] Step 2: Round up the initially calculated piston diameter D1 of the AGC cylinder, and determine the piston diameter D of the AGC cylinder based on the rounded-up D1;

[0044] When the rounded-up D1 ≤ 500mm, the value of the piston diameter D of the AGC cylinder shall be determined in accordance with the ISO3320 standard; when the rounded-up D1 > 500mm, the value of the piston diameter D of the AGC cylinder shall be selected according to the piston seal size series provided by the cylinder seal manufacturer.

[0045] In this embodiment, the piston seal size series provided by a certain cylinder seal manufacturer is shown in Table 1. According to the table, when the initially calculated piston diameter D1 of the AGC cylinder is rounded up to D1 = 1428mm, the final determined piston diameter of the AGC cylinder is D = 1450mm based on the piston seal size series provided by the cylinder seal manufacturer.

[0046] Table 1 Recommended Piston Diameter Series for AGC Hydraulic Cylinders (Unit: mm)

[0047] 520 540 560 600 650 700 710 740 780 800 860 900 920 1000 1050 1065 1070 1200 1225 1250 1450 1500 1580

[0048] Step 3: Based on the relationship between the steady-state retraction speed of the AGC cylinder and the piston rod diameter, and the piston diameter D of the AGC cylinder, preliminarily calculate the piston rod diameter d1 (unit: mm) of the AGC cylinder;

[0049] When the piston diameter is D, the piston rod diameter is d, the piston area of ​​the rodless chamber is A1, and the annular area of ​​the rod chamber is A2, then:

[0050]

[0051] make: m1 = n 2 ,

[0052] During the retraction of the hydraulic cylinder, the flow rate Q2 flowing into the rod chamber of the cylinder through the servo valve is:

[0053]

[0054] In the formula, C d Let ω be the flow coefficient, ω be the area gradient of the servo valve spool, and x be the flow coefficient. v For the servo valve spool displacement, P s P1 is the inlet pressure of the servo valve, P2 is the pressure inside the rod chamber of the cylinder, and ρ is the density of the hydraulic oil.

[0055] The flow rate Q1 exiting the rodless chamber of the hydraulic cylinder through the servo valve is:

[0056]

[0057] In the formula, P1 is the pressure inside the rodless chamber of the hydraulic cylinder.

[0058] During the steady-state motion of the piston in the hydraulic cylinder, the internal and external leakage of the cylinder can be obtained as follows:

[0059]

[0060] When the piston in the hydraulic cylinder is in steady-state motion, the piston is in a state of force equilibrium. Neglecting the frictional force and viscous damping force on the piston:

[0061] P1A1=P2A2+F (4)

[0062] In the formula, F is the load force on the hydraulic cylinder.

[0063] Combining equations (1) and (2), we get:

[0064]

[0065] Combining equations (3) and (5), we get:

[0066]

[0067] By transforming equation (4), we can obtain:

[0068]

[0069] By combining equations (6) and (7), we can obtain:

[0070]

[0071] Based on the relationship between flow rate and piston speed:

[0072] Q1 = A1·v (9)

[0073] By combining equations (2), (8), and (9), we can obtain:

[0074]

[0075] The relationship between the steady-state retraction speed of the AGC cylinder and the piston rod diameter is then obtained by the following formula:

[0076]

[0077] In the formula, C d Let ω be the flow coefficient, ω be the area gradient of the servo valve spool, and x be the flow coefficient. v For the servo valve spool displacement, P s ρ is the inlet pressure of the servo valve, F is the density of the hydraulic oil, F is the load force on a single AGC cylinder during the rolling process, F∈[F1,F2]; F1 is the minimum load force that a single AGC cylinder may experience during the rolling process; F2 is the maximum load force that a single AGC cylinder may experience during the rolling process.

[0078] make 0 < k < 1, simplifying equation (11) yields:

[0079]

[0080] make Once the piston diameter D is determined, under a fixed servo valve opening, the steady-state retraction speed v of the AGC cylinder is proportional to the square of M.

[0081] In formulas (11) and (12), all variables are in the International System of Units (SI). If P s If the units are MPa, F is in kN, and D is in mm, then...

[0082]

[0083] When F = F1, find the value of k that makes M reach its maximum value and denote it as k1; when F = F2, find the value of k that makes M reach its maximum value and denote it as k2.

[0084] The preliminary calculated piston rod diameter d1 of the AGC cylinder is shown in the following formula:

[0085]

[0086] In the formula, α∈[1.2,1.25] is the compression velocity compensation coefficient;

[0087] In this embodiment, P s =28MPa; F1=500kN; F2=40000kN; k∈(0,1). When F=F1=500kN, the relationship curve between k and M is as follows: Figure 4 As shown in (a), find the value of k1≈0.788 that maximizes M. When F=F2, the relationship between k and M is as follows: Figure 4 As shown in (b), find the value of k2 = 0.524 that makes M reach its maximum value.

[0088] In this embodiment, the compression speed compensation coefficient α is taken as 1.2, so the preliminary calculated piston rod diameter of the AGC cylinder is d1≈1020.5mm.

[0089] Step 4: Calculate the lower limit d of the piston rod diameter based on the strength requirements of the piston rod during the rolling process. min As shown in the formula below:

[0090]

[0091] In the formula: σ1 is the allowable stress of the piston rod, MPa; n is the safety factor, generally n = 5; σ s The value is the yield strength of the piston rod material, in MPa;

[0092] In this embodiment, the piston rod is made of 55# carbon steel, which has undergone tempering and high-frequency quenching treatment, with a yield strength σ s =380MPa, with a safety factor n of 5, then the allowable stress of the piston rod is... The lower limit dimension d of the piston rod diameter min ≈818.6mm.

[0093] Step 5: Based on the preliminary calculated piston rod diameter d1 and lower limit piston rod dimension d... min The larger of these values ​​determines the final piston rod diameter d;

[0094] Take d1 and d min The larger value is assigned to the intermediate variable d. mid When d mid When the diameter is ≤450mm, the value of the piston rod diameter d should be taken according to ISO 3320 standard; when d midWhen the diameter is greater than 450mm, the value of the piston rod diameter d should be selected according to the piston rod seal size series provided by the cylinder seal manufacturer.

[0095] In this embodiment, the piston rod sealing size series provided by a certain cylinder seal manufacturer is shown in Table 2. According to the table, when the initially calculated piston rod diameter d1 is 1020.5mm, the lower limit size d of the piston rod is... min It is 818.6mm, therefore, d and d min If the larger value is taken as 1020.5mm, then according to the piston rod sealing size series provided by the cylinder seal manufacturer, the final determined piston rod diameter of the AGC cylinder is d = 1050mm.

[0096] Table 2 Recommended Size Series of AGC Hydraulic Cylinder Piston Rod Diameters (Unit: mm)

[0097] 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 688 690 700 710 740 760 770 800 850 870 900 910 950 960 1000 1050 1100 1160 1200 1300 1450 1500 1535

[0098] This embodiment also compares and simulates the maximum steady-state reduction speed and retraction speed of the AGC cylinder under different rolling forces, obtained based on the traditional design method and the design method of this invention. Planar shape control mainly occurs in the high-temperature zone of the roughing mill. The rolling force for planar shape control in a 3500mm hot rolling mill is generally within 45000kN. The simulation data is shown in Table 2, as follows:

[0099] ① Pressing process: Send 100% of the servo valve's rated signal to the servo valve;

[0100] ② Retreat process: Send -100% of the servo valve's rated signal to the servo valve.

[0101] Table 3. Motion simulation data of AGC cylinders for a 3500mm hot rolling mill under different rolling forces.

[0102]

[0103]

[0104] As can be seen from the data in Table 3, the AGC cylinder designed based on the method of the present invention has two characteristics compared with the traditional design method: (1) the rolling speed is reduced by about 4.62%, but the improvement effect of the retraction speed is more significant; (2) the advantage of improving the retraction speed is more obvious when the rolling force is smaller.

[0105] Planar shape control is a type of symmetrical rolling, requiring the AGC cylinder's pressing and retraction speeds to be essentially equal at a constant rolling speed. Therefore, when performing planar shape control, the horizontal rolling rhythm of the mill is limited by the minimum value v_c of the AGC cylinder's pressing and retraction speeds throughout the entire process. minAs shown in Table 3, when the rolling force varies from 2000kN to 45000kN, the minimum movement speed of the AGC cylinder designed using the traditional method is 13.2735mm / s at a minimum rolling force of 2000kN, while the minimum movement speed of the AGC cylinder designed based on this invention is 19.1278mm / s at a minimum rolling force of 2000kN. Theoretically, v min This represents an improvement of 44.1%. When the rolling force varies from 5000kN to 45000kN, the minimum movement speed of the AGC cylinder designed using the traditional method is a retraction speed of 14.2277mm / s at the minimum rolling force of 5000kN, while the minimum movement speed of the AGC cylinder designed based on this invention is a pressing speed of 19.4353mm / s at the maximum rolling force of 45000kN. Theoretically, v min This represents a 36.6% improvement. Even with a minimum rolling force of 20,000 kN and a maximum rolling force of 45,000 kN, the minimum movement speed of the AGC cylinder designed using traditional methods is a retraction speed of 18.2655 mm / s at a minimum rolling force of 20,000 kN, while the minimum movement speed of the AGC cylinder designed based on this invention is a pressing speed of 19.4353 mm / s at a maximum rolling force of 45,000 kN. Theoretically, v min It also increased by 6.4%. min The improvement not only helps to meet the process requirements of hot rolling plane shape control while ensuring rolling speed and ensuring production line efficiency, but also helps to improve the rectangularity of the plate and increase the yield.

[0106] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A design method for a four-way valve-controlled AGC cylinder for planar shape control in medium and heavy plate rolling mills, characterized in that: Includes the following steps: Step 1: Based on the maximum rolling force of the rolling mill and the maximum design working pressure of the AGC cylinder, calculate the piston diameter of the AGC cylinder in advance; Step 2: Round up the initially calculated piston diameter D1 of the AGC cylinder upwards, and determine the piston diameter of the AGC cylinder based on the rounded-up value. Step 3: Based on the relationship between the steady-state retraction speed of the AGC cylinder and the piston rod diameter, as well as the piston diameter of the AGC cylinder, calculate the piston rod diameter of the AGC cylinder in advance; The steady-state retraction speed of the AGC cylinder is related to the piston rod diameter by the following formula: （1）； In the formula, C d For flow coefficient, x represents the area gradient of the servo valve spool. v For the servo valve spool displacement, P s For the servo valve inlet pressure, Where is the density of the hydraulic oil; F is the load force experienced by a single AGC cylinder during the rolling process. F1 is the minimum load force that a single AGC cylinder may experience during the rolling process; F2 is the maximum load force that a single AGC cylinder may experience during the rolling process. Let , where \(0 < k < 1\), simplify Equation (1) to obtain: （2）； make Once the piston diameter D is determined, under a fixed servo valve opening, the steady-state retraction speed of the AGC cylinder is... It is proportional to the square of M; In formulas (1) and (2), all variables are in the International System of Units (SI). If P s If the units are MPa, F is in kN, and D is in mm, then... ； When F=F1, find the value of k that makes M reach its maximum value and denote it as k1; when F=F2, find the value of k that makes M reach its maximum value and denote it as k2. The preliminary calculated piston rod diameter of the AGC cylinder is shown in the following formula: ； In the formula, d1 is the preliminary calculated piston rod diameter of the AGC cylinder, in mm; This is the compression speed compensation coefficient; Step 4: Calculate the lower limit of the piston rod diameter based on the strength requirements of the piston rod during the rolling process; Step 5: Determine the final piston rod diameter based on the larger of the initially calculated piston rod diameter and the lower limit of the piston rod.

2. The design method for a four-way valve-controlled AGC cylinder for planar shape control in medium and heavy plate rolling mills according to claim 1, characterized in that: The piston diameter of the AGC cylinder, initially calculated in step 1, is shown in the following formula: ； in, The piston diameter of the AGC cylinder is calculated in mm; F max P represents the maximum rolling force of the rolling mill, measured in kN. max This is the maximum design working pressure of the AGC cylinder, expressed in MPa.

3. The design method for a four-way valve-controlled AGC cylinder for planar shape control in medium and heavy plate rolling mills according to claim 2, characterized in that: Step 2 determines the piston diameter of the AGC cylinder in the following way: When the rounded-up D1 ≤ 500mm, the value of the piston diameter D of the AGC cylinder shall be determined in accordance with the ISO3320 standard; when the rounded-up D1 > 500mm, the value of the piston diameter D of the AGC cylinder shall be selected according to the piston seal size series provided by the cylinder seal manufacturer.

4. The design method of a four-way valve-controlled AGC cylinder for planar shape control in medium and heavy plate rolling mills according to claim 3, characterized in that: The lower limit of the piston rod diameter mentioned in step 4 is shown in the following formula: ； In the formula: d min This is the lower limit of the piston rod diameter, in mm; This represents the allowable stress of the piston rod, expressed in MPa. where n is the safety factor; This represents the yield strength of the piston rod material, expressed in MPa.

5. The design method for a four-way valve-controlled AGC cylinder for planar shape control in medium and heavy plate rolling mills according to claim 4, characterized in that: The specific method for step 5 is as follows: Take d1 and d min The larger value is assigned to the intermediate variable d. mid When d mid When the diameter is ≤450mm, the value of the piston rod diameter d should be taken according to ISO 3320 standard; when d mid When the diameter is greater than 450mm, the value of the piston rod diameter d should be selected according to the piston rod seal size series provided by the cylinder seal manufacturer.

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