Method for calculating bending deformation of thick plate during open V groove cutting

Abstract

This invention provides a method for calculating the side bending deformation of thick plates with large bevels. Based on the principle of thermo-mechanical coupling, this method first derives the deformation curve using a temperature field distribution formula. Then, iterative calculations are performed using an assumed initial deformation, and the results are verified through the balance of internal forces and moments to ultimately obtain the deformation curvature. This method incorporates heat input, material properties, and structural constraints into the calculation system, enabling quantitative analysis of side bending deformation. This calculation method provides a theoretical basis, overcoming the limitations of traditional methods that rely on experience and cannot accurately predict deformation. Iterative verification improves calculation accuracy, ensuring that the deformation results meet mechanical equilibrium. The obtained deformation curvature data can be directly used to guide bevel design and process optimization, helping to predict and control side bending deformation before actual construction, improving shipbuilding precision and quality, and reducing rework and adjustment costs.

Description

Technical Field

[0001] This invention relates to the field of machining technology, and in particular to a method for calculating the side bending deformation during the cutting of thick plates with large bevels. Background Technology

[0002] In the shipbuilding industry, the main engine base panel, as a key structural component supporting the main engine, is usually made of thick plates with a thickness between 65-75mm. When splicing these thick plates, in order to ensure the continuity and smoothness of stress transfer between the plates and reduce stress concentration caused by abrupt changes in cross-section, it is often necessary to open large-sized transition bevels at the edges of the thick panels to achieve a smooth connection with adjacent plates.

[0003] However, due to the thickness of the base panel, the required transition bevel size is often large. During the cutting of such large bevels on one side, localized high-temperature heat input causes uneven thermal expansion and contraction of the metal near the bevel, resulting in significant residual stress within the plate. This asymmetrical stress distribution easily causes lateral bending deformation of the plate along its length, such as... Figure 1 As shown. If this deformation is not controlled and compensated, it will directly affect the installation accuracy of the main engine base and the alignment quality of the overall structure, thereby adversely affecting the ship's construction accuracy and structural safety.

[0004] Currently, there is a lack of systematic and reliable theoretical or empirical methods for predicting and calculating this side-bending deformation value in engineering practice. The difficulty stems primarily from the coupled effects of multiple factors, including the specific thickness difference of the plate material, the bevel type and dimensions, cutting process parameters (such as cutting speed and heat input), the thermophysical properties of the material, and the structural restraint conditions. Existing research mainly focuses on the deformation analysis of general thin or medium-thick plates. However, for the specific side-bending deformation caused by a large bevel on one side of such extra-thick plates, no widely accepted calculation model or standardized formula has yet been developed. This increases the difficulty of pre-controlling the process and correcting deformation, and has become a pressing technical problem to be solved in shipbuilding precision management. Summary of the Invention

[0005] In view of the shortcomings of the prior art described above, the present invention provides a method for calculating the side bending deformation of thick plates with large bevel cutting, comprising the following steps:

[0006] S1: Set basic parameters, including the length of the calculated plate thickness. Width h, thickness Coefficient of thermal expansion Cutting heat power q, thermal conductivity λ1, cutting heat utilization coefficient Cutting speed v, material yield strength Temperature conductivity coefficient a, heat dissipation coefficient ;

[0007] S2: Calculate the temperature curve T. The temperature curve T is calculated based on the parameters in S1. When cutting a large bevel at the edge of the slat, the temperature distribution along the y-direction perpendicular to the flame cutting direction within the x-section where the flame is located is as follows:

[0008]

[0009] The imaginary argument is a zeroth-order Bessel function of the second kind;

[0010] S3: Find the deformation curve λ, based on...

[0011]

[0012] Obtain the expression for λ(y); based on the expression for λ(y), plot the relationship curve between y and λ(y) in a rectangular coordinate system to obtain the curve λ. The horizontal axis of the rectangular coordinate system is y, and the vertical axis is λ(y). This relationship curve forms a fourth intersection point with the horizontal axis, and the y value of the fourth intersection point is y4.

[0013] Optionally, the following steps may also be included:

[0014] S4: Assume a value for Δ0, and based on the assumed value of Δ0, take a numerical point on the vertical axis for subsequent calculations;

[0015] S5: Find the line Δ. Connect the point where Δ0 is located and the fourth intersection point to obtain the line Δ. The expression of the line Δ is Δ(y).

[0016] S6: Find the line Δ1. Translate the line Δ along the longitudinal direction to obtain the line Δ1. Find the expression for line Δ1. Line Δ1 intersects curve λ at the third intersection point, and the y-value of the third intersection point is y3.

[0017] Optionally, the following steps may also be included:

[0018] S7: To find the line Δ2, draw auxiliary lines y=y1 and y=y2, where y1<y2<y3. The auxiliary line y=y1 intersects the line Δ at the first intersection point, and the auxiliary line y=y2 intersects the line Δ1 at the second intersection point. Connect the first intersection point and the second intersection point to obtain the line Δ2.

[0019] S8: Conditional judgment, which refers to whether the sum of the internal forces and moments of the lath is 0, including...

[0020]

[0021]

[0022] If the assumed value of Δ0 satisfies the above two equations, proceed to step S9; otherwise, re-assume the value of Δ0 and perform the calculation until the above two equations are satisfied.

[0023] Optionally, the following steps may also be included:

[0024] S9: To calculate the curvature C, based on the determined values ​​of Δ0 and y4, determine the straight line Δ, and draw an auxiliary line y=h, where h>y4. The coordinates of the intersection point of the auxiliary line y=h and the straight line Δ are (h, Δ(h)). Then, the formula for calculating the curvature C of the thick plate deformation is:

[0025]

[0026] S10: Calculate the lateral bending deformation value f. Based on the obtained curvature C, the lateral bending deformation value... .

[0027] As described above, this invention provides a method for calculating the side bending deformation of thick plates with large bevels. This method is based on the principle of thermo-mechanical coupling. First, the deformation curve is derived using a temperature field distribution formula. Then, iterative calculations are performed using an assumed initial deformation, and the results are verified through the balance of internal forces and moments to finally obtain the deformation curvature. This method incorporates heat input, material properties, and structural constraints into the calculation system, enabling quantitative analysis of side bending deformation. This calculation method provides a theoretical basis, overcoming the limitations of traditional methods that rely on experience and cannot accurately predict deformation. It improves calculation accuracy through iterative verification, ensuring that the deformation results meet mechanical equilibrium. The obtained deformation curvature data can be directly used to guide bevel design and process optimization, helping to predict and control side bending deformation before actual construction, improving shipbuilding precision and quality, and reducing rework and adjustment costs. Attached Figure Description

[0028] Figure 1 The diagram shows the lateral bending deformation value f caused by the large bevel cutting of a thick plate.

[0029] Figure 2 The diagram shown is a flowchart of the calculation method in this invention.

[0030] Figure 3 The diagram shown is a schematic diagram of the thick plate beveling cutting method in this invention.

[0031] Figure 4 The diagram shows the schematic representation of steps S3 to S7 in this invention.

[0032] Figure 5a The diagram shown is a schematic representation of the dimensions of the thick plate strip in Embodiment 1 of the present invention.

[0033] Figure 5b Displayed as Figure 5a Schematic diagram of the large bevel section along the AA direction.

[0034] Figure 6 The temperature curve T is shown in Embodiment 1 of the present invention.

[0035] Figure 7 The diagram shows T, λ, Δ, Δ1, and Δ2 in Embodiment 1 of the present invention. Detailed Implementation

[0036] The following specific examples illustrate the implementation of the present invention. 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 embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0037] In the detailed description of embodiments of the present invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged and not to scale. Furthermore, the schematic diagrams are merely examples and should not limit the scope of protection of the present invention. In actual fabrication, the three-dimensional spatial dimensions of length, width, and depth should be included.

[0038] For ease of description, spatial relation terms such as “below,” “under,” “lower than,” “below,” “above,” and “upper” may be used herein to describe the relationship between one element or feature shown in the accompanying drawings and other elements or features. It will be understood that these spatial relation terms are intended to include directions other than those depicted in the drawings for the device in use or operation. Furthermore, when a layer is referred to as being “between” two layers, it can be the only layer between the two layers, or there may be one or more layers in between. The phrase “between” as used herein includes both endpoint values.

[0039] In the context of this application, the structure described above the first feature may include embodiments in which the first and second features are formed in direct contact, or embodiments in which additional features are formed between the first and second features, such that the first and second features may not be in direct contact.

[0040] It should be noted that the illustrations provided in this embodiment are only schematic representations of the basic concept of the present invention. Therefore, the illustrations only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0041] like Figure 2 As shown, the present invention provides a method for calculating the side bending deformation of a thick plate with a large bevel, comprising the following steps:

[0042] S1: Set basic parameters. These basic parameters include measuring and calculating fundamental parameters, such as the calculated length of the plate. Width h, thickness Coefficient of thermal expansion Cutting heat power q, thermal conductivity λ1, cutting heat utilization coefficient Cutting speed v, material yield strength Temperature conductivity coefficient a, heat dissipation coefficient For a schematic diagram of the cutting process, please see... Figure 3 .

[0043] S2: Calculate the temperature curve T. The temperature curve T is calculated based on the parameters in S1. When cutting a large bevel at the edge of the slat, the temperature distribution within the x-section where the flame is located, along the width y-direction perpendicular to the flame cutting direction, is as follows:

[0044]

[0045] Here, x1 represents the x-position of the plane where the heat source is located, and its value is 0. Let the imaginary argument be the zeroth-order Bessel function of the second kind (the modified Bessel function of the second kind); set =z, when At that time, K0(z)≈−ln(z / 2)−γ; where γ (Euler's constant) indicates that the temperature at the heat source (y=0) is theoretically infinite; when At that time, K0(z)≈ ;

[0046] The corresponding T value can be obtained based on different y values.

[0047] S3: Find the deformation curve λ. According to...

[0048]

[0049] The expression for λ(y) is obtained. Based on the linear thermal expansion model, assuming that temperature changes cause free expansion of the material, the deformation curve can be determined according to the temperature function, thus obtaining the expression for λ(y). Based on the expression for λ(y), the relationship curve between y and λ(y) is plotted in a rectangular coordinate system to obtain curve λ. The horizontal axis of the rectangular coordinate system is y, and the vertical axis is λ(y). This relationship curve forms a fourth intersection point with the horizontal axis, and the y-value at the fourth intersection point is y4. Figure 4 As shown.

[0050] S4: Assume a value for Δ0. The assumed value for Δ0 refers to taking a numerical point on the vertical axis for subsequent calculations.

[0051] S5: Find the line Δ. To find the line Δ, connect the point where Δ0 is located and the fourth intersection point to obtain the line Δ. The expression for the line Δ is Δ(y).

[0052] S6: Find the line Δ1. Translate the line Δ along the longitudinal direction to obtain the line Δ1. According to... Find the expression for line Δ1. Line Δ1 intersects curve λ at the third intersection point, where the y-value is y3.

[0053] S7: Find the line Δ2. Draw auxiliary lines y=y1 and y=y2, where y1<y2<y3. The auxiliary line y=y1 intersects the line Δ at the first intersection point, and the auxiliary line y=y2 intersects the line Δ1 at the second intersection point. Connect the first intersection point and the second intersection point to obtain the line Δ2.

[0054] S8: Conditional Judgment. The conditional judgment refers to the sum of the internal forces and moments of the lath being 0, i.e.

[0055]

[0056]

[0057] The initial equation needs to be multiplied by Young's modulus on the left side, i.e., deformation × Young's modulus = stress; by dividing both sides of the equation by Young's modulus, we get the two expressions mentioned above.

[0058] If the assumed value of Δ0 satisfies the above two equations, proceed to step S9; otherwise, re-assume the value of Δ0 and perform the calculation until the above two equations are satisfied.

[0059] Specifically, the basic principle of the above calculation process is as follows: temperature changes cause material expansion, i.e., thermal strain. If this strain is suppressed by external or internal constraints, it is transformed into thermal stress (stress = elastic modulus × (total strain − thermal strain)). The iterative format of assuming deformation and checking equilibrium is essentially a numerical method for solving static equilibrium boundary value problems. Each iteration adjusts the internal stress distribution to satisfy the equilibrium condition that the overall resultant force and resultant moment are zero. The deformation curve λ represents the temperature-driven deformation, while Δ represents the actual deformation after the structural response. The difference between the two is caused by stress. When the difference cancels out, internal stress equilibrium is considered to be achieved, and no internal stress drives the lath deformation.

[0060] S9: Calculate the curvature C. Based on the determined values ​​of Δ0 and y4, determine the straight line Δ, and draw an auxiliary line y=h, where h>y4. The coordinates of the intersection point of the auxiliary line y=h and the straight line Δ are (h, Δ(h)). Then, the formula for calculating the curvature C of the thick plate deformation is:

[0061]

[0062] S10: Calculate the lateral bending deformation value f. The calculation of the lateral bending deformation value f is based on the obtained curvature C.

[0063] The lateral bending deformation value f is the maximum deflection or maximum displacement of the strip bending perpendicular to the cutting direction during cutting, such as... Figure 1 As shown, if the calculated side bending value exceeds the tolerance, the cutting parameters need to be adjusted to control the amount of deformation.

[0064] Example 1

[0065] According to the present invention, a method for calculating the side bending deformation of a thick plate with a large bevel cutting is provided. Taking a Q235B grade steel strip with a length of 1170mm, a width of 215mm, and a thickness of 65mm as an example, a large bevel cutting is performed on one long side. Figure 5a , Figure 5b As shown, it includes the following steps:

[0066] S1: Set basic parameter values.

[0067] Basic parameter values, including the measurement and calculation of some basic parameters, such as the calculated length of the plate. It measures 117cm in length, with a width h of 21.5cm, and a thickness of [missing information]. 6.5cm, coefficient of thermal expansion The cutting heat power q is 165900 J / cm, and the thermal conductivity λ1 is 0.096. Cutting heat utilization coefficient =0.6, cutting speed v is 0.25cm / s, material yield strength The thermal conductivity coefficient α is 0.00114, the thermal conductivity a is 0.085 cm² / s, and the heat dissipation coefficient is... It is 0.0018272.

[0068] S2: Find the temperature curve T.

[0069] The temperature curve T is calculated based on the parameters of S1. When a large bevel is cut at the edge of the slat, the temperature distribution along the width y direction within the x1=0 section where the flame is located is as follows:

[0070]

[0071] Substitute the values

[0072] Based on different y values, the corresponding T values ​​can be obtained, and curves can be plotted, such as... Figure 6 As shown.

[0073] S3: Determine the deformation curve λ. The determination of the deformation curve λ is based on...

[0074]

[0075] have to: ,

[0076] Based on the expression for λ(y), the curve λ is obtained by plotting the relationship curve between y and λ(y) in a rectangular coordinate system.

[0077] S4: Assume a value for Δ0. The assumed value for Δ0 refers to first estimating a value of Δ0, 0.001, and then performing the calculation.

[0078] S5: Find the line Δ.

[0079] The method for finding the straight line Δ is based on the value of Δ0 (0.001) and the value of y4 (10) (when y4 = 10, the temperature T and deformation λ are 0). Figure 4 (middle line Δ).

[0080]

[0081] S6: Find the line Δ1.

[0082] The method for finding the straight line Δ1 is based on...

[0083]

[0084] Material yield strength It is 0.00114

[0085] have to:

[0086]

[0087] Find the line Δ1.

[0088] S7: Find the line Δ2.

[0089] The calculation of the straight line Δ2 is based on the fact that the internal stress of Q235B grade steel increases linearly from 0 to the yield strength stress when the angle changes from 600° to 500°. According to y2=1.53... =0.0028 and y1=1.44 =0.0017, two points determine a straight line, therefore:

[0090]

[0091] Find the line Δ2. See the diagram for T, λ, Δ, Δ1, and Δ2. Figure 7 .

[0092] S8: Conditional Judgment. The conditional judgment refers to the sum of the internal forces and moments of the lath being 0, i.e.

[0093]

[0094]

[0095] If the assumed value of Δ0 satisfies the above two equations, proceed to step S9; otherwise, re-assume the value of Δ0 (generally increasing or decreasing by 0.0005 in each step; for example, if Δ0 = 0.001 in the first step, increase by 0.0005 in the next step, and take Δ0 = 0.0015; if the signs of internal forces and internal moments change, take the average of the two latest Δ0 values, and approximate it in half; for example, if the sign changes when Δ0 = 0.002, take 0.00175), and perform calculations until the above two equations are satisfied.

[0096] Calculations show that the above two equations are satisfied when Δ0 = 0.00199, and the process proceeds to S9.

[0097] S9: Calculate the curvature C. The curvature C is calculated by determining the value of Δh based on the determined values ​​of Δ0 and y4 (using the equation of line Δ, when y=h=21.5, substituting into the equation of line Δ, we calculate Δh=-0.0023). The curvature C of the thick plate deformation is...

[0098]

[0099] S10: Calculate the lateral bending deformation value f. The lateral bending deformation value f is calculated based on the obtained curvature C.

[0100]

[0101] Based on the specific implementation, on-site tests were conducted. The on-site tests showed that the lateral bending deformation value was 0.35cm, and the theoretical calculation error was 2.29%, which meets the requirements for ship construction. Therefore, this calculation method is reliable.

[0102] In summary, this invention provides a method for calculating the side bending deformation of thick plates with large bevels. Based on the principle of thermo-mechanical coupling, this method first derives the deformation curve using a temperature field distribution formula. Then, iterative calculations are performed using an assumed initial deformation, and the results are verified through the balance of internal forces and moments to ultimately obtain the deformation curvature. This method incorporates heat input, material properties, and structural constraints into the calculation system, enabling quantitative analysis of side bending deformation. This calculation method provides a theoretical basis, overcoming the limitations of traditional methods that rely on experience and cannot accurately predict deformation. Iterative verification improves calculation accuracy, ensuring that the deformation results meet mechanical equilibrium. The obtained deformation curvature data can be directly used to guide bevel design and process optimization, helping to predict and control side bending deformation before actual construction, improving shipbuilding precision and quality, and reducing rework and adjustment costs.

[0103] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in the present invention should still be covered by the claims of the present invention.

Claims

1. A method for calculating the side bending deformation of a thick plate after large bevel cutting, characterized in that, Includes the following steps: S1: Set basic parameters, including the length of the calculated plate thickness. Width h, thickness Coefficient of thermal expansion Cutting heat power q, thermal conductivity λ1, cutting heat utilization coefficient Cutting speed v, material yield strength Temperature conductivity coefficient a, heat dissipation coefficient ; S2: Calculate the temperature curve T. The temperature curve T is calculated based on the parameters in S1. When cutting a large bevel at the edge of the slat, the temperature distribution along the y-direction perpendicular to the flame cutting direction within the x-section where the flame is located is as follows: ； The imaginary argument is a zeroth-order Bessel function of the second kind; S3: Find the deformation curve λ, based on... Obtain the expression for λ(y); Based on the expression of λ(y), the curve λ is obtained by plotting the relationship curve between y and λ(y) in a rectangular coordinate system. The horizontal axis of the rectangular coordinate system is y, and the vertical axis is λ(y). This relationship curve forms a fourth intersection point with the horizontal axis, and the y value of the fourth intersection point is y4.

2. The method for calculating the side bending deformation of thick plate with large bevel cutting according to claim 1, characterized in that, It also includes the following steps: S4: Assume a value for Δ0, and based on the assumed value of Δ0, take a numerical point on the vertical axis for subsequent calculations; S5: Find the line Δ. Connect the point where Δ0 is located and the fourth intersection point to obtain the line Δ. The expression of the line Δ is Δ(y). S6: Find the line Δ1. Translate the line Δ along the longitudinal direction to obtain the line Δ1. Find the expression for line Δ1. Line Δ1 intersects curve λ at the third intersection point, and the y-value of the third intersection point is y3.

3. The method for calculating the side bending deformation of thick plate with large bevel cutting according to claim 2, characterized in that, It also includes the following steps: S7: To find the line Δ2, draw auxiliary lines y=y1 and y=y2, where y1<y2<y3. The auxiliary line y=y1 intersects the line Δ at the first intersection point, and the auxiliary line y=y2 intersects the line Δ1 at the second intersection point. Connect the first intersection point and the second intersection point to obtain the line Δ2. S8: Conditional judgment, which refers to whether the sum of the internal forces and moments of the lath is 0, including... ； ； If the assumed value of Δ0 satisfies the above two equations, proceed to step S9; otherwise, re-assume the value of Δ0 and perform the calculation until the above two equations are satisfied.

4. The method for calculating the side bending deformation of thick plate with large bevel cutting according to claim 3, characterized in that, It also includes the following steps: S9: To calculate the curvature C, based on the determined values ​​of Δ0 and y4, determine the straight line Δ, and draw an auxiliary line y=h, where h>y4. The coordinates of the intersection point of the auxiliary line y=h and the straight line Δ are (h, Δ(h)). Then, the formula for calculating the curvature C of the thick plate deformation is: ； S10: Calculate the lateral bending deformation value f. Based on the obtained curvature C, the lateral bending deformation value... .

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