Calculation method for critical preload margin of bolts under external load

Abstract

This invention discloses a method for calculating the critical preload margin of bolts under external loads. The method includes establishing a finite element model of an assembly connected by bolts and setting contact relationships and constraints; applying an external load to the finite element model and solving it to obtain the bolt working load; extracting the force values ​​in the x, y, and z directions at the contact position between the bolt head and the clamping element from the bolt working load; and calculating the shear load and axial load of the bolt working load using these force values; and calculating the critical preload margin required to ensure the clamping element does not separate using the shear load and axial load. This invention, through the contact settings used in finite element analysis, can obtain the actual working load borne by the bolt according to different external loads, and then evaluate the minimum bolt preload force required to prevent the clamping element from separating, i.e., the critical preload margin. This critical preload margin can then be used to guide bolt selection, safety assessment, and product optimization design.

Description

Technical Field

[0001] This invention belongs to the technical field of finite element strength analysis methods, specifically relating to a method for calculating the critical preload margin of bolts under external loads. Background Technology

[0002] Bolts are one of the most commonly used fastening methods for structural connections in industrial manufacturing. Their connection strength directly determines the safety performance of products, especially under complex external loads, where engineering algorithms struggle to provide a reasonable analysis of bolt tightening capacity. Current research on bolted connections using the finite element method (FEM) focuses primarily on bolt strength verification and failure analysis. However, there is a lack of assessment of the safety performance of clamping components in complex assemblies subjected to external loads in engineering projects. This makes it difficult to analyze bolt tightening requirements. Furthermore, FEM analysis typically relies on conditions where a known preload is applied to the bolts, failing to determine the critical preload margin required for different external loads. This hinders guidance for bolt selection, safety assessment, and product optimization design. Summary of the Invention

[0003] The purpose of this invention is to provide a method for calculating the critical preload margin of bolts under external loads, which solves the problem that existing technologies cannot determine the critical preload margin required for bolts under different external loads.

[0004] The technical solution adopted in this invention is: a method for calculating the critical preload margin of bolts under external load, comprising the following steps:

[0005] Step 1: Establish a finite element model of the assembly connected by bolts and set the contact relationships and constraints;

[0006] Step 2: Apply an external load to the finite element model obtained in Step 1 and solve it to obtain the bolt working load;

[0007] Step 3: Extract the force values ​​in the x, y, and z directions at the contact position between the bolt head and the clamping part in the bolt working load obtained in Step 2, and calculate the shear load and axial load of the bolt working load using the force values ​​in the three directions respectively.

[0008] Step 4: Calculate the critical preload margin required for the bolt to ensure that the clamping parts do not separate, using the shear load and axial load obtained in Step 3.

[0009] The invention is further characterized in that,

[0010] Step 1 specifically includes the following steps:

[0011] Step 1.1: Define the material parameters involved in the finite element model, including the density, elastic modulus, Poisson's ratio, yield stress, and ultimate strength of the bolt, nut, and clamping material;

[0012] Step 1.2: Create a 3D solid model including bolts, nuts, and clamping parts, and assemble them. The assembly method is as follows: the bolt shank passes through the through holes on the upper and lower clamping parts in sequence from the head end, and then the tail end is connected to the nut. Then, the bolt is cut into two parts at any position below the head bearing surface and above the lower clamping part. The upper part is the bolt head and the lower part is the shank body. The bolt head and the shank body share an edge.

[0013] Step 1.3: Create a bolt-based local coordinate system for the 3D solid model obtained in Step 1.2, making the z-axis of the local coordinate system consistent with the axial direction of the bolt;

[0014] Step 1.4: Mesh the 3D solid model obtained in Step 1.3 using a sweeping method, ensuring that the number of elements in the thickness direction of the clamping part is no less than 3; connect the bolt head and the screw body at the separation point using a common node method to obtain the finite element model;

[0015] Step 1.5: Set the contact relationships for the finite element model obtained in Step 1.4. Set the bolt head and the upper clamping member joint position as a binding connection A, the screw body and the lower clamping member through hole contact position as a binding connection B, the nut and the lower clamping member joint position as a beam element connection, and the nut inner hole and the screw body contact position as a binding connection C, thus obtaining a finite element model containing contacts.

[0016] Step 1.6: Set constraints on the finite element model obtained in Step 1.5, and set fixed constraints on one side of the upper clamping member and one side of the lower clamping member respectively.

[0017] In step 2, the external load on the finite element model is applied by applying a vertically upward pressure to the upper surface of the upper clamping member and a vertically downward pressure to the lower surface of the lower clamping member.

[0018] Step 3: Extract the force values ​​F at the binding connection A in the x, y, and z directions. x F y F z Then the axial load F of the bolt is acial That is, F z The shear load F of the bolt operation s h ear Calculated using formula (1):

[0019]

[0020] The formula for calculating the critical preload margin in step 4 is:

[0021]

[0022] The beneficial effects of the present invention are: the method for calculating the critical preload margin of bolts under external loads of the present invention, through the contact settings used in finite element analysis, can obtain the actual working load borne by the bolt according to different external loads, and then evaluate the minimum bolt preload required to prevent the clamping parts from separating, i.e., the critical preload margin, so as to use the critical preload margin to guide bolt selection, safety assessment and product optimization design. Attached Figure Description

[0023] Figure 1 This is an embodiment of the method for calculating the critical preload margin of bolts under external load of the present invention.

[0024] In the figure, 1. Bolt head, 2. Screw body, 3. Shared edge of upper and lower parts of bolt, 4. Nut, 5. Upper clamping part, 6. Lower clamping part, 7. Binding connection A, 8. Binding connection B, 9. Beam element connection, 10. Binding connection C, 11. Fixed constraint A, 12. Fixed constraint B. Detailed Implementation

[0025] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0026] This invention provides a method for calculating the critical preload margin of bolts under external loads, such as... Figure 1 As shown, finite element analysis was performed using the Ansys Workbench platform:

[0027] 1) Define the material parameters involved in the finite element model. In this embodiment, the bolts, nuts, and clamps are made of structural steel with a density of 7850 kg / m³. 3 The elastic modulus is 200 GPa, the Poisson's ratio is 0.3, the yield stress is 250 MPa, and the ultimate strength is 460 MPa.

[0028] 2) Establish a three-dimensional solid model of the bolt, nut 4 and clamping parts. Divide the bolt into two parts along the head bearing surface below and the lower clamping part 6 above, namely the bolt head 1 and the screw body 2. Set the dividing position to the shared edge 3 of the upper and lower parts of the bolt to ensure that the bolt head 1 and the screw body 2 can be connected in the form of shared nodes during mesh generation.

[0029] 3) Import the 3D solid model into the Static Structure module in Workbench and assign the defined materials to the corresponding solids;

[0030] 4) Establish a local coordinate system based on the bolt, ensuring that the z-axis of the local coordinate system is consistent with the axial direction of the bolt, and name it Bolt Coordinate System;

[0031] 5) The three-dimensional solid model was meshed using the sweeping method. The bolt shank had 26 circumferential elements and 21 axial elements. The bolt shank had 18 circumferential elements through the through holes of the upper and lower clamping parts and 4 elements in the thickness direction of the clamping parts. All of these were hexahedral meshes, resulting in a finite element model with a total mesh count of 197,850.

[0032] 6) Set the contact relationships for the finite element model. The position of the bolt head 1 and the upper clamping member 5 joint is set as a binding connection A7; the contact position of the screw body 2 and the through hole of the lower clamping member 6 is set as a binding connection B8; the contact position of the nut 4 and the lower clamping member 6 is connected by beam elements 9; the contact position of the inner hole of the nut 4 and the screw body 2 is set as a binding connection C10. No contact is set between the upper and lower clamping members, including the contact between the bolt and the through hole and the contact at the clamping member joint position, to ensure that all loads acting on the clamping member joint can be transmitted to the bolt. Thus, a finite element model containing contact is obtained. The above contact relationship settings simulate the ideal working environment in which the clamping members do not separate under the action of external loads, and all external loads on the upper and lower clamping members are transmitted to the bolt. Subsequently, the bolt force is extracted and analyzed to obtain the minimum preload force required by the bolt to achieve the ideal non-separation state of the clamping members.

[0033] 7) Set constraints for the finite element model. Set fixed constraints for the upper clamping member 5 at fixed constraint A11 and for the lower clamping member 6 at fixed constraint B12.

[0034] 8) Apply load conditions to the finite element model. In order to make this embodiment have a more typical clamping separation environment, apply a vertical upward pressure of 10MPa to the upper surface of the upper clamping member 5 and a vertical downward pressure of 10MPa to the lower surface of the lower clamping member 6.

[0035] 9) In the solution output control, turn on the Nodal Forces switch, submit the solution, and output the actual forces on the bolt and clamping parts A7, B8 and C10 in the x, y and z directions under the action of external load. This solution environment simulates the situation where the upper and lower clamping parts do not separate completely under the action of external load.

[0036] 10) In the post-processing module, the deformation results show that the maximum deformation of the upper and lower clamping parts in the separation direction is 0.15mm, which is 2.5% of the thickness of the clamping parts. This can be considered as the upper and lower clamping parts not separating.

[0037] 11) Insert the force analysis toolkit into the post-processing module and extract the force values ​​of the bonded connection A7 in the x, y, and z directions; use the formula Calculate the shear load on the bolt; in the above formula: F s h ear For the shear load of the bolt, F x F represents the force on the bolt in the x-direction. y Let F be the force on the bolt in the y-direction, and let F be the force on the bolt in the z-direction, which is the axial load. axial The purpose of calculating and analyzing bolt shear load and axial load is to obtain a bolt preload margin sufficient to offset the working load between clamping parts. Shear load describes the tangential static friction force at the clamping part joint under any external load in the finite element model. The bolt preload should be greater than the shear load to ensure that the clamping part joint does not move relative to each other under external load. Axial load describes the force that tends to open along the axial direction of the clamping part under any external load. The bolt preload should be greater than the axial load to ensure that the clamping parts do not separate under external load.

[0038] 12) Substitute into the formula The calculated minimum preload is 31171 N, which is the preload allowance of the bolt when tightening the upper and lower clamping parts. In the above formula: F min It is the minimum preload required to ensure that the clamping parts do not separate. 2.51 is a scaling factor provided according to the German VDI2230 standard for calculating dynamic axial loads. 0.15 is the static friction coefficient between the clamping parts. 0.8 is an amplification factor determined based on engineering practice experience. The purpose is to take into account the expected 20% loosening between the bolt joint and the clamping parts during assembly and operation in the minimum preload, thereby improving the safety performance of the bolt preload margin.

[0039] The minimum preload obtained through the above steps is the minimum preload required to ensure that the clamping parts do not loosen when tightening the bolts. The minimum preload obtained through the evaluation of this invention can be applied to the bolts in the original model, and the reliability of the results can be verified by solving the problem using a finite element tool. The bolt preload margin obtained from the analysis will be used to solve and verify the problem using a finite element tool:

[0040] 1) Set new contact relationships for the element model obtained in step 6) of the embodiment. The position where the bolt head 1 contacts the upper clamping member 5 is connected by beam elements; the surface where the upper clamping member 5 contacts the lower clamping member 6 is set to frictional contact with a friction coefficient of 0.15; the position where the inner hole of the nut 4 contacts the screw body 2 is set to a binding connection; thus, a finite element model with new contacts is obtained.

[0041] 2) Set constraints on the unit model with new contact obtained in verification step 1). Set a fixed constraint on the upper clamping member 5 at fixed constraint A11 and set a fixed constraint on the lower clamping member 6 at fixed constraint B12.

[0042] 3) Apply the same external load as in step 8) of the embodiment to the model obtained in verification step 2), and apply a preload of 31171N to the bolts, and submit the solution;

[0043] 4) This solution environment simulates the situation where the model is subjected to external loads after the bolts provide preload to the upper and lower clamping parts;

[0044] 5) By viewing the deformation results through the post-processing module, the maximum deformation of the upper and lower clamping parts in the separation direction is 0.06mm, which is less than the deformation value of 0.15mm under the ideal environment of absolute non-separation as evaluated by this invention, and the deformation is 1% of the thickness of the clamping parts. This verifies that the evaluation method proposed in this invention can obtain a relatively safe and reliable bolt preload margin.

[0045] Through the above method, the bolt critical preload margin calculation method under external load of the present invention has the following advantages:

[0046] (1) By using the contact settings in finite element analysis, the actual working load borne by the bolt can be obtained according to different external loads, and then the minimum bolt preload required to keep the clamping parts from separating, i.e. the critical preload margin, can be used to guide bolt selection, safety assessment and product optimization design.

[0047] (2) For working conditions subjected to various complex loads, the method provided by this invention can be used to compare the load conditions under various load conditions, thereby obtaining the bolt load conditions under the worst working conditions, thus providing the safest bolt preload margin, thereby ensuring the fastening performance of the selected bolt type in the assembly.

[0048] (3) This invention utilizes the finite element method to simulate an ideal environment where the clamping parts do not loosen under external loads, analyzes the stress on the bolts under this environment, and thus obtains the preload required for the bolts to reach this ideal environment. Compared with traditional bolt stress analysis, obtaining stress results using the finite element method is simpler and more efficient; compared with traditional experimental stress measurement, it can save costs, and its reliability can be verified by the finite element method; this invention is more suitable for the research and development design, strength verification, and optimization and modification of complex assemblies, and the calculated bolt preload margin can be used as a reference standard for product evaluation, improving work efficiency.

Claims

1. A method for calculating the critical preload margin of bolts under external load, characterized in that, Includes the following steps: Step 1: Establish a finite element model of the assembly connected by bolts and set contact relationships and constraints; specifically including the following steps: Step 1.1: Define the material parameters involved in the finite element model, including the density, elastic modulus, Poisson's ratio, yield stress, and ultimate strength of the bolt, nut, and clamping material; Step 1.2: Create a 3D solid model including bolts, nuts, and clamping parts, and assemble them. The assembly method is as follows: the bolt shank passes through the through holes on the upper and lower clamping parts in sequence from the head end, and then the tail end is connected to the nut. Then, the bolt is cut into two parts at any position below the head bearing surface and above the lower clamping part. The upper part is the bolt head and the lower part is the shank body. The bolt head and the shank body share an edge. Step 1.3: Create a bolt-based local coordinate system for the 3D solid model obtained in Step 1.2, making the z-axis of the local coordinate system consistent with the axial direction of the bolt; Step 1.4: Mesh the 3D solid model obtained in Step 1.3 using a sweeping method, ensuring that the number of elements in the thickness direction of the clamping part is no less than 3; connect the bolt head and the screw body at the separation point using a common node method to obtain the finite element model; Step 1.5: Set the contact relationships for the finite element model obtained in Step 1.

4. Set the bolt head and the upper clamping member joint position as a binding connection A, the screw body and the lower clamping member through hole contact position as a binding connection B, the nut and the lower clamping member joint position as a beam element connection, and the nut inner hole and the screw body contact position as a binding connection C, thus obtaining a finite element model containing contacts. Step 1.6: Set constraints on the finite element model obtained in Step 1.5, and set fixed constraints on one side of the upper clamping member and one side of the lower clamping member respectively. Step 2: Apply an external load to the finite element model obtained in Step 1 and solve it to obtain the bolt working load; wherein, the external load of the finite element model is applied by applying a vertically upward pressure to the upper surface of the upper clamping member and a vertically downward pressure to the lower surface of the lower clamping member. Step 3: Extract the force values ​​in the x, y, and z directions at the contact point between the bolt head and the clamping part from the bolt working load obtained in Step 2. Calculate the shear load and axial load of the bolt working load using these force values ​​in the three directions; that is, extract the force values ​​in the x, y, and z directions at the binding connection A position. , , The axial load of the bolt during operation That is Shear load of bolt operation Calculated using formula (1): （1） Step 4: Using the shear load and axial load obtained in Step 3, calculate the critical preload margin required for the bolt to ensure that the clamping parts do not separate. The calculation formula is as follows: （2）。

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