A method for stress verification of sleeves and mandrels suitable for VC roll manufacturing process

Abstract

This invention discloses a method for stress verification of the sleeve and mandrel in the manufacturing process of VC rolls, comprising the following steps: S1, collecting equipment parameters of the VC mill in its initial state; S2, establishing the deformation geometric relationship between the sleeve and mandrel in the initial state; S3, solving for the interference force p0 under the oil-free state; S4, solving for the interference amount G under the oil-free state; S5, obtaining the relationship between the radial and circumferential stress changes after the sleeve is installed; S6, solving for the plastic yield condition and strength condition of the sleeve; S7, calibrating the strength of the sleeve. This invention addresses the persistent interaction between the sleeve and mandrel by establishing a stress verification method model for the VC roll sleeve and mandrel, and verifies the inter-roll pressure between the sleeve and mandrel.

Description

Technical Field

[0001] This invention relates to VC rolling mill technology, and more specifically, to a method for stress verification of sleeves and mandrels during the manufacturing process of VC rolls. Background Technology

[0002] With the rapid development of the automotive, aerospace, and precision instrument industries, the demand for high-quality steel is increasing, and the requirements are becoming more stringent. In the process of rolling high-quality steel, the main focus is on controlling the straightness and thickness accuracy of the strip. The key lies in correctly compensating for the roll crown generated during rolling. Previously, roll crown was controlled by altering the original roll crown and the thermal crown, but this method has limited effectiveness. Therefore, the problem was addressed by introducing a VC rolling mill and improving its process. The VC roll of the VC rolling mill mainly consists of a sleeve and a mandrel, with hydraulic oil filling the gap to control the roll crown. During the manufacturing process of the VC roll, the thermal expansion and contraction of the VC roll sleeve and mandrel are complex, increasing the difficulty of calculating the actual interference fit and interference force. Under normal circumstances, the difference between the diameter of the VC roll mandrel and the inner diameter of the sleeve at the interference point is called the original interference fit, and the pressure generated by this interference fit is called the original interference force. For the sleeve and mandrel, due to the original interference fit caused by the diameter of the sleeve and mandrel in the original design, there is always an interference force between the sleeve and mandrel. In order to ensure the smooth progress of the VC roll manufacturing process, the interference fit and interference force of the VC roll sleeve and mandrel need to be checked to ensure that they meet the strength requirements of the roll. Summary of the Invention

[0003] To address the shortcomings of existing technologies, the purpose of this invention is to provide a stress verification method for the sleeve and mandrel in the manufacturing process of VC rolls. A stress verification method model for the sleeve and mandrel of VC rolls is established to address the interference force that constantly interacts between the sleeve and mandrel, and to verify the inter-roller pressure between the sleeve and mandrel.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] A method for stress verification of sleeves and mandrels suitable for VC roller manufacturing process includes the following steps:

[0006] S1. Collect the equipment parameters of the VC mill in its original state;

[0007] S2. Establish the deformation geometric relationship between the sleeve and the mandrel under the initial state;

[0008] S3. Solve for the interference force p0 under the condition of no oil pressure;

[0009] S4. Solve for the interference G under the condition of no oil pressure;

[0010] S5. Obtain the relationship between the radial and circumferential stresses after the sleeve is installed;

[0011] S6. Solve for the plastic yield condition and strength condition of the sleeve;

[0012] S7. Perform strength calibration on the sleeve.

[0013] Preferably, the equipment parameters in step S1 include: the inner diameter d1 of the sleeve, the outer diameter d2 of the sleeve, and the diameter d of the mandrel. x Elastic modulus E of the work roll, Poisson's ratio of the work roll The yield strength [σ] of the sleeve.

[0014] Preferably, step S2 further includes:

[0015] Establish an unknown quantity, namely a function of the interference force p0:

[0016]

[0017] In the formula, r1 is half the inner diameter of the VC roller sleeve, r1 = d1 / 2; r2 is half the outer diameter of the VC roller sleeve, r2 = d2 / 2; r x Half the diameter of the mandrel, r x =d x / 2.

[0018] Preferably, the interference force p0 under the oil-free state in step S3 is solved as follows:

[0019]

[0020] Preferably, the interference G in step S4 under the condition of no oil pressure is solved as follows:

[0021]

[0022] Preferably, the relationship between the radial and circumferential stresses after the sleeve is installed in step S5 is as follows:

[0023] The expression is obtained based on the generalized Hooke's law in mechanics of materials:

[0024]

[0025] In the formula, σ ρ The radial stress along the sleeve of the VC roller is expressed in MPa. The stress is circumferential along the sleeve of the VC roller, in MPa.

[0026] Preferably, the plastic yield condition and strength condition of the sleeve in step S6 are as follows:

[0027] σ ρ For constant compressive stress, As a constant tensile stress distributed circumferentially along the cylinder wall, σ ρ , Both are principal stresses, which the customer records as σ ρ =σ3;

[0028] According to the maximum shear stress theory, the strength condition of the sleeve is σ1-σ3≤[σ].

[0029] Preferably, the calibration in step S7 is as follows:

[0030] If σ1-σ3≤[σ], then the strength of the sleeve satisfies the strength condition;

[0031] If σ1-σ3>[σ], then the strength of the sleeve does not meet the strength requirements, and it is necessary to increase the thickness of the sleeve or replace it with a material with higher strength.

[0032] This invention provides a stress verification method for sleeves and mandrels suitable for VC roll manufacturing. Combining the parameters of the VC rolling mill equipment under oil-free conditions, the method first calculates the interference force and amount of the VC roll sleeve and mandrel under oil-free conditions. Then, based on the generalized Hooke's law, the radial and circumferential stresses after sleeve installation are determined. Finally, the strength conditions of the sleeve are determined based on the maximum shear stress theory, and a verification method is provided. The verification method proposed in this invention can be used to specifically verify a particular VC roll sleeve, effectively improving the safety of VC roll design and use, and providing a theoretical reference for the verification process of VC roll sleeves. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the radial and circumferential stresses of the sleeve;

[0034] Figure 2 This is a schematic flowchart of the method for stress verification of sleeves and mandrels in the manufacturing process of VC rollers, which is applicable to the present invention. Detailed Implementation

[0035] To better understand the above-mentioned technical solutions of the present invention, the technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0036] Combination Figure 1 and Figure 2 As shown, the present invention provides a method for stress verification of sleeves and mandrels in the manufacturing process of VC rollers, comprising the following steps:

[0037] S1. Collect the equipment parameters of the VC mill in its original state, including the inner diameter d1 of the sleeve, the outer diameter d2 of the sleeve, and the diameter d of the mandrel. xElastic modulus E of the working roll, Poisson's ratio ν of the working roll, and yield strength [σ] of the sleeve;

[0038] S2. Establish the deformation geometry of the sleeve and mandrel under the initial state, and establish an unknown quantity, namely a function of the interference force p0:

[0039]

[0040] In the formula, r1 is half the inner diameter of the VC roller sleeve, r1 = d1 / 2; r2 is half the outer diameter of the VC roller sleeve, r2 = d2 / 2; r x Half the diameter of the mandrel, r x =d x / 2;

[0041] S3. Solve for the interference force p0 under the condition of no oil pressure:

[0042]

[0043] S4. Solve for the interference G under the condition of no oil pressure:

[0044]

[0045] S5. Obtain the relationship between the radial and circumferential stresses after the sleeve is installed, and derive the expression based on the generalized Hooke's law in mechanics of materials:

[0046]

[0047] In the formula, σ ρ The radial stress along the sleeve of the VC roller is expressed in MPa. The stress is circumferential along the sleeve of the VC roller, in MPa.

[0048] S6. As known from the above formula, σ ρ For constant compressive stress, As a constant tensile stress distributed circumferentially along the cylinder wall, σ ρ , Both are principal stresses, which the customer records as σ ρ =σ3;

[0049] According to the maximum shear stress theory, the strength condition of the sleeve is σ1-σ3≤[σ];

[0050] S7. Perform strength calibration on the sleeve:

[0051] If σ1-σ3≤[σ], then the strength of the sleeve satisfies the strength condition;

[0052] If σ1-σ3>[σ], then the strength of the sleeve does not meet the strength requirements, and it is necessary to increase the thickness of the sleeve or replace it with a material with higher strength.

[0053] Example 1

[0054] Combined Figure 1 and Figure 2 As shown in Example 1, the method for stress verification of the sleeve and mandrel in the manufacturing process of VC rollers is as follows:

[0055] S1. Collect the equipment parameters of the VC mill in its original state: VC roll sleeve inner diameter d1 is 945mm, VC roll sleeve outer diameter d2 is 1400mm, and mandrel interference fit diameter d... x The sleeve has a diameter of 946 mm, a yield strength [σ] of 600 MPa, an elastic modulus of 210000 MPa, and a Poisson's ratio of ν = 0.3.

[0056] S2. Establish the deformation geometry of the sleeve and mandrel under the initial state, and establish an unknown quantity, namely a function of the interference force p0:

[0057]

[0058] In the formula, r1 is half the inner diameter of the VC roller sleeve, r1 = d1 / 2; r2 is half the outer diameter of the VC roller sleeve, r2 = d2 / 2; r x Half the diameter of the mandrel, r x =d x / 2;

[0059] S3. Input parameters: VC roller sleeve inner diameter d1 = 945mm, VC roller sleeve outer diameter d2 = 1400mm, mandrel interference fit diameter d x =946mm, elastic modulus of the work roll E = 210000MPa, Poisson's ratio of the work roll ν = 0.3. Using the above formula, solve for the interference force p0 under the condition of no oil pressure:

[0060]

[0061] The solution yields a value of p0 of 64.9 MPa.

[0062] S4. Solve for the interference G under the condition of no oil pressure:

[0063]

[0064] Substituting the inter-roller pressure p0 obtained from the above formula, the value of G is calculated to be 0.4998 mm;

[0065] S5. According to the generalized Hooke's law in mechanics of materials, the radial and circumferential stresses after the sleeve is installed are obtained:

[0066]

[0067] In the formula, σ ρ The radial stress along the sleeve of the VC roller is expressed in MPa. The stress is circumferential along the sleeve of the VC roller, in MPa.

[0068] Substituting the inter-roller pressure p0 into the above equation, the stress σ along the radial direction of the VC roll sleeve is obtained. ρ The stress along the circumferential direction of the VC roller sleeve is -64.9 MPa. It is 173.5 MPa;

[0069] S6. According to the maximum shear stress theory in mechanics of materials, the stress along the radial direction of the VC roller sleeve is denoted as... The stress σ along the circumference of the VC roller sleeve ρ =σ3, the plastic yield condition and strength condition are respectively:

[0070] σ1-σ3≤[σ]

[0071] S7. Finally, the strength of the VC roller sleeve is checked. σ1-σ3=238.4MPa, which is less than the sleeve yield strength of 600MPa; the strength of the sleeve meets the strength requirements.

[0072] Example 2

[0073] Combined Figure 1 and Figure 2 As shown in Example 2, the method for stress verification of the sleeve and mandrel in the manufacturing process of VC rollers is as follows:

[0074] S1. Collect the equipment parameters of the VC mill in its original state: VC roll sleeve inner diameter d1 is 945mm, VC roll sleeve outer diameter d2 is 1400mm, and mandrel interference fit diameter d... x The sleeve has a diameter of 946.5 mm, a yield strength [σ] of 600 MPa, an elastic modulus of 210000 MPa, and a Poisson's ratio of ν = 0.3.

[0075] S2. Establish the deformation geometry of the sleeve and mandrel under the initial state, and establish an unknown quantity, namely a function of the interference force p0:

[0076]

[0077] In the formula, r1 is half the inner diameter of the VC roller sleeve, r1 = d1 / 2; r2 is half the outer diameter of the VC roller sleeve, r2 = d2 / 2; r x Half the diameter of the mandrel, r x =d x / 2;

[0078] S3. Input parameters: VC roller sleeve inner diameter d1 = 945mm, VC roller sleeve outer diameter d2 = 1400mm, mandrel interference fit diameter d x =946.5mm, elastic modulus of the work roll E = 210000MPa, Poisson's ratio of the work roll ν = 0.3. Using the above formula, solve for the interference force p0 under the condition of no oil pressure:

[0079]

[0080] The solution yields a value of p0 of 97.4 MPa.

[0081] S4. Solve for the interference G under the condition of no oil pressure:

[0082]

[0083] Substituting the roller pressure p0 obtained from the above formula, the value of G is calculated to be 0.7497 mm;

[0084] S5. According to the generalized Hooke's law in mechanics of materials, the radial and circumferential stresses after the sleeve is installed are obtained:

[0085]

[0086] In the formula, σ ρ The radial stress along the sleeve of the VC roller is expressed in MPa. The stress is circumferential along the sleeve of the VC roller, in MPa.

[0087] Substituting the inter-roller pressure p0 into the above equation, the stress σ along the radial direction of the VC roll sleeve is obtained. ρ The stress along the circumferential direction of the VC roller sleeve is -97.4 MPa. It is 260.3 MPa;

[0088] S6. According to the maximum shear stress theory in mechanics of materials, the stress along the radial direction of the VC roller sleeve is denoted as... The stress σ along the circumference of the VC roller sleeve ρ =σ3, the plastic yield condition and strength condition are respectively:

[0089] σ1-σ3≤[σ]

[0090] S7. Finally, the strength of the VC roller sleeve is checked. σ1-σ3=357.7MPa, which is less than the sleeve yield strength of 600MPa; the strength of the sleeve meets the strength requirements.

[0091] Those skilled in the art should recognize that the above embodiments are merely illustrative of the present invention and are not intended to limit the present invention. Any variations or modifications to the above embodiments that are within the spirit and essence of the present invention will fall within the scope of the claims of the present invention.

Claims

1. A method for stress verification of sleeves and mandrels suitable for VC roller manufacturing process, characterized in that, Includes the following steps: S1. Collect the equipment parameters of the VC rolling mill in its original state. The equipment parameters include: the inner diameter d1 of the sleeve, the outer diameter d2 of the sleeve, and the diameter d of the mandrel. x Elastic modulus E of the working roll, Poisson's ratio ν of the working roll, and yield strength [σ] of the sleeve; S2. Establish the deformation geometric relationship between the sleeve and the mandrel under the initial state; Step S2 further includes: Establish an unknown quantity, namely a function of the interference force p0: In the formula, r1 is half the inner diameter of the VC roller sleeve, r1 = d1 / 2; r2 is half the outer diameter of the VC roller sleeve, r2 = d2 / 2; r x Half the diameter of the mandrel, r x =d x / 2; S3. Solve for the interference force p0 under the condition of no oil pressure; S4. Solve for the interference G under the condition of no oil pressure; S5. Obtain the relationship between the radial and circumferential stresses after the sleeve is installed; S6. Solve for the plastic yield condition and strength condition of the sleeve; S7. Perform strength calibration on the sleeve.

2. The method for stress verification of sleeves and mandrels in the manufacturing process of VC rollers according to claim 1, characterized in that, The solution for the interference force p0 under the oil-free state in step S3 is as follows:

3. The method for stress verification of sleeves and mandrels in the manufacturing process of VC rollers according to claim 2, characterized in that, The interference G under the oil-free state in step S4 is solved as follows:

4. The method for stress verification of sleeves and mandrels in the manufacturing process of VC rollers according to claim 3, characterized in that, The relationship between the radial and circumferential stresses after the sleeve is installed in step S5 is as follows: The expression is obtained based on the generalized Hooke's law in mechanics of materials: In the formula, σ ρ The radial stress along the sleeve of the VC roller is expressed in MPa. The stress is circumferential along the sleeve of the VC roller, in MPa.

5. The method for stress verification of sleeves and mandrels in the manufacturing process of VC rollers according to claim 4, characterized in that, The plastic yield condition and strength condition of the sleeve in step S6 are as follows: σ ρ For constant compressive stress, As a constant tensile stress distributed circumferentially along the cylinder wall, σ ρ , Both are principal stresses, which the customer records as σ ρ =σ3; According to the maximum shear stress theory, the strength condition of the sleeve is σ1-σ3≤[σ].

6. The method for stress verification of sleeves and mandrels in the manufacturing process of VC rollers according to claim 5, characterized in that, The calibration in step S7 is as follows: If σ1-σ3≤[σ], then the strength of the sleeve satisfies the strength condition; If σ1-σ3>[σ], then the strength of the sleeve does not meet the strength requirements, and it is necessary to increase the thickness of the sleeve or replace it with a material with higher strength.

Images