A method for predicting bolt axial force attenuation considering bolt creep

Abstract

The application discloses a bolt axial force attenuation prediction method considering bolt creep, and is characterized by comprising the following steps: 1) obtaining a creep curve of a standard bolt used for connection under a use temperature; 2) determining a function relation between the stiffness of a bolt model in bolt connection and time according to the creep curve; and 3) calculating residual axial force at a selected time according to the function relation between the stiffness of the bolt model and time and a function relation between residual axial force and time, so as to realize the prediction of bolt axial force attenuation. Through the establishment of an equivalent model, the application studies the relation between the change rule of bolt internal stress and strain and external load, thereby summarizing the change rule of pre-tightening force of the bolt in a tightened state due to the creep effect under a medium-high temperature environment, establishing a mathematical function model of bolt pre-tightening force change with time, and predicting the bolt residual axial force and loosening life.

Description

Technical Field

[0001] This invention relates to the field of testing and prediction technology for bolted connections, and more specifically to a method for predicting bolt axial force attenuation that takes into account bolt creep. Background Technology

[0002] The primary function of bolts is to ensure the reliable transmission of force (or movement) between connected structures. When the connected components are pressure vessels or pipelines, threaded connections also need to ensure good sealing of the assembly. Whether achieving fastening, sealing, or transmission, a sufficiently large clamping force between the connected structures is a prerequisite. Strength and life analysis of this component has always been a focus of attention. Bolt loosening is common and difficult to avoid; therefore, it is necessary to predict the bolt axial force decay process before use to guide bolt use and maintenance.

[0003] However, the axial force attenuation process of bolted connections is extremely complex, influenced by numerous factors, and the degree of bolt loosening exhibits a complex nonlinear relationship with these factors. While related technologies have qualitatively summarized the influence patterns of some factors through extensive experimental data, no simple and accurate model exists to predict the residual axial force of bolted connections under different working conditions or to reflect the degree of axial force attenuation. Therefore, the reliability and attenuation characteristics of bolted connections cannot be guaranteed.

[0004] In particular, temperature has a significant impact on bolt axial force attenuation. Existing prediction methods, such as patent applications CN202111375331.X and CN201810578081.1, although they also provide methods for predicting bolt life or bolt preload, do not take temperature as a primary factor. Therefore, they all have obvious limitations in application and accuracy issues. Summary of the Invention

[0005] In view of this, this invention proposes a method for predicting bolt loosening life under medium and high temperatures, based on the phenomenon of bolts loosening due to stress relaxation caused by creep effect in high-temperature working environments. The method establishes an expression for the change of bolt preload over time in the form of a mathematical model, thereby fully considering the influence of temperature, preload, bolt size and other factors on bolt axial force attenuation and bolt life.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for predicting bolt axial force attenuation considering bolt creep, characterized by the following steps:

[0008] 1) Obtain the creep curves of standard bolts used for connection at the operating temperature;

[0009] 2) Determine the functional relationship between the stiffness of the bolt model and time in the bolted connection based on the creep curve;

[0010] 3) Based on the functional relationship between the stiffness and time of the bolt model and the functional relationship between the residual axial force and time, calculate the residual axial force at a selected time to predict the attenuation of the axial force of the connecting bolt.

[0011] The residual axial force is a function of time, as follows: F(t) is the residual axial force at time t, F(0) is the preload of the bolt connection, and J B (t) represents the compliance of the bolt model at time t, J B (0) represents the compliance of the bolt model at t=0, J U To ensure the flexibility of the clamped component, J D The flexibility of the clamped part.

[0012] More preferably, the bolt model is equivalent to three units connected in series. The first unit is a spring with stiffness K1 representing the purely elastic part; the second unit is a spring with stiffness K2 and a damper with damping ratio C2 connected in parallel, representing the elastic-damped part; and the third unit is a damper with damping ratio C1 representing the purely damped part. The stiffness of the bolt model is a function of time, as follows: Where K(t) is the stiffness J of the bolt model at time t. B The reciprocal of (t).

[0013] More preferably, determining the functional relationship between the stiffness of the bolt model and time in the bolted connection based on the creep curve involves selecting four points (t0, t1, t2, and t3) from the creep curve. Here, t0 is the point where time is 0, and it is substituted into the equation relating the stiffness of the bolt model to time to solve for K1. t1 and t2 are points where time is much greater than 0; after solving for K1, these two points are substituted into the equation relating the stiffness of the bolt model to time to solve for K2 and C1. t3 is the point where time approaches 0; after solving for K1, K2, and C1, this point is substituted into the equation relating the stiffness of the bolt model to time to solve for C2, thus finally determining the equation relating the stiffness of the bolt model to time.

[0014] In a further preferred embodiment, the stiffness-time function curve of the finally determined bolt model is compared with the creep test results. When the deviation between the fitted curve and the creep test results is greater than expected, the selection of t1, t2, and t3 is further adjusted and the calculation and fitting are repeated until the deviation between the fitted curve and the creep test results is less than expected.

[0015] More preferably, the strain of the creep curves at t1 and t2 should be less than 5 × 10⁻⁶.-4 / hour, t3≤20 hours.

[0016] Further preferred, , , Where L is the clamping length of each component, E is the elastic modulus of each component at the operating temperature, and A is the effective stress cross-sectional area of ​​each component, i.e., the bearing area.

[0017] Compared with existing technologies, this invention establishes an equivalent model to study the relationship between the variation law of internal stress and strain of bolts and external loads. This allows for the summarization of the preload variation law of bolts under tightened conditions in medium- and high-temperature environments due to creep effects. A mathematical function model of bolt preload variation over time is established to predict the remaining axial force and loosening life of bolts. Since bolts in actual use under medium- and high-temperature conditions experience changes in material properties due to temperature, leading to bolt preload attenuation, especially the influence of medium- and high-temperature environments on creep, this invention more comprehensively expands the applicable conditions of bolt loosening theory, providing guidance for the safe and efficient design and use of bolts. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0019] Appendix Figure 1 This is a schematic diagram of the stress state and deformation of the equivalent model of the present invention in the initial state (left side) and the stress state (right side);

[0020] Appendix Figure 2 This is a schematic diagram of the creep curve of a standard bolt in an embodiment of the present invention;

[0021] Appendix Figure 3 This is a schematic diagram of the axial deformation of the bolt connection pair after the equivalent model of the present invention. The left side is before installation, the middle side is the pre-tightened installation state, and the right side is the creep state during use.

[0022] Appendix Figure 4 This is a comparison chart of the creep curve obtained by fitting the curve according to the present invention and the actual measured curve. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] This invention mainly considers the influence of medium and high temperature environments on bolt axial force. The most important influence in medium and high temperature environments is the relaxation caused by bolt creep during use. Therefore, an equivalent model of bolt creep in medium and high temperature environments is first established.

[0025] Specifically, such as Figure 1 As shown, the bolt model in a bolted connection is equivalent to three elements connected in series. The first element is a spring with stiffness K1 representing the purely elastic part. The second element is a spring with stiffness K2 and a damper with damping rate C2 connected in parallel, representing the elastic-damped part. The third element is a damper with damping rate C1 representing the purely damped part. First, the elastic component represented by spring K1 deforms by Δ1, and once the load is removed, the elastic component fully recovers. Second, the element composed of K2 and C2 in parallel deforms by Δ2, and if the load is removed, it recovers after a period of time. Therefore, this element is described as a time-dependent, fully recoverable element, which is the first stage of recoverable creep. When subjected to stress at high temperatures for a long time, the plastic element represented by C1 also deforms by Δ3. When the load is removed, it does not recover. Therefore, this element is described as a time-dependent and non-recoverable element, which is the second stage of slow creep.

[0026] In this bolt model, for a given bolt deformation, we have: (1),

[0027] In the formula: F is the external force applied; Δ is the deformation. , These are the rates of change for Δ2 and Δ3, respectively.

[0028] From equation (1), we can obtain: (2),

[0029] Let the total deformation Therefore, the force-deformation compatibility relationship of this bolt model can be determined as follows: (3),

[0030] Therefore, the functional relationship between the stiffness of the bolt model and time can be obtained as follows: (4).

[0031] In the above equation (4), K1, K2, C1, and C2 can all be determined by creep tests on standard bolt materials. For specific creep curves, please refer to [reference needed]. Figure 3 As shown. Specifically, four points, t0, t1, t2, and t3, are selected in the creep curve, where t0 is the point at time 0. Substituting this point into equation (4) yields K1, i.e. ; t1 and t2 are points where the time is much greater than 0. After solving for K1, substitute these two points into equation (4) to solve for K2 and C1, that is... t3 is the point where time approaches 0. After solving for K1, K2, and C1, substitute this point into equation (4) to solve for C2, that is... Thus, the equation relating the stiffness of the bolt model to time was finally determined.

[0032] After determining the functional relationship between the stiffness and time of the bolt model, an axial deformation model for the preloaded and creep states of the bolt connection is then established using this relationship, as follows: Figure 3 As shown, where K B K U K D These represent the equivalent stiffness of the bolt, the upper clamped component, and the lower clamped component, respectively. In this invention, the clamped components are considered as purely elastic elements. Δ X This indicates the amount of deformation caused by the initial preload.

[0033] Depend on Figure 3 It can be seen that the force and deformation coordination relationship between the bolt and the upper and lower clamped parts is as follows: (5)

[0034] Depend on As can be seen from the definition: (6)

[0035] It can then be deduced that: ,

[0036] Combining the above equations and introducing the flexibility J, which is the reciprocal of stiffness (J = 1 / K), we can calculate: (7),

[0037] in, It can be calculated from equation (4) where K1, K2, C1, and C2 are determined. , , (Where, E is the elastic modulus of the material at high temperature in the corresponding service environment, L is the non-original length of the bearing length, and A is the effective stress cross-sectional area of ​​the component, i.e. the bearing area).

[0038] When the materials of the upper and lower clamped parts are the same, then J U =J D , Substituting into equation (7) and further simplifying, we get:

[0039] (8).

[0040] For bolted connections, significant creep and loosening will occur when the operating temperature exceeds 250℃. Therefore, taking a bolted connection without a washer at an operating temperature of 300℃ as an example, the equivalent model described above is used to calculate the bolt axial force reduction process. Specific parameters of the bolted connection are shown in Table 1.

[0041] according to Figure 2 Substitute the bolt creep test results shown into equation (4) to calculate K1, K2, C1, and C2. Among them, the selected time t1=8 hours, t2=60 hours, and t3=180 hours represent three load levels. The calculation results are shown in Table 2.

[0042] Table 1 Specific parameters in the calculation examples

[0043]

[0044] Table 2 Calculation results of stiffness coefficient

[0045]

[0046]

[0047] Substituting the calculated stiffness coefficients from Table 2 into the bolt creep process, the fitted curve is obtained as follows: Figure 4 As shown, the fitting effect is good, proving the accuracy of the calculation results and demonstrating the rationality and accuracy of the model establishment and calculation in this invention. When the deviation between the fitted curve and the actual measurement results of the creep experiment is greater than expected, the selection of the 3 points t1, t2, and t3 can be further adjusted, and the calculation and fitting can be repeated until the deviation between the fitted curve and the actual measurement results of the creep experiment is less than expected. According to the inventors' research, the strain of the creep curve at t1 and t2 should be less than 5 × 10⁻⁶. -4 When the time is 1 / hour and t3 ≤ 20 hours, the calculated results usually match the actual situation well.

[0048] Of course, the prediction method of the present invention is not limited to the prediction of bolt axial force decay at medium and high temperatures. The model and prediction method of the present invention can be applied to any situation in which creep causes axial force decay and relaxation during use.

[0049] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting bolt axial force attenuation considering bolt creep, characterized in that... Includes the following steps: 1) Obtain the creep curves of standard bolts used for connection at the operating temperature; 2) Determine the functional relationship between the stiffness of the bolt model and time in the bolted connection based on the creep curve; 3) Based on the functional relationship between the stiffness and time of the bolt model and the functional relationship between the residual axial force and time, calculate the residual axial force at a selected time to predict the attenuation of the axial force of the connecting bolt. The residual axial force is a function of time, as follows: F(t) is the residual axial force at time t, F(0) is the preload of the bolt connection, and J B (t) represents the compliance of the bolt model at time t, J B (0) represents the compliance of the bolt model at t=0, J U To ensure the flexibility of the clamped component, J D To ensure the flexibility of the clamped component; The bolt model is equivalent to three units connected in series. The first unit is a spring with stiffness K1 representing the purely elastic part. The second unit is a spring with stiffness K2 and a damper with damping ratio C2 connected in parallel, representing the elastic-damped part. The third unit is a damper with damping ratio C1 representing the purely damped part. The stiffness of the bolt model is a function of time. , where K(t) is the reciprocal of the stiffness, i.e. the flexibility, of the bolt model at time t; The function relationship between the stiffness of the bolt model and time in the bolted connection is determined based on the creep curve. This involves selecting four points (t0, t1, t2, t3) on the creep curve. t0 is the point where time is 0. Substituting t0 into the equation relating the stiffness of the bolt model to time yields K1. t1 and t2 are points where time is much greater than 0. After solving for K1, these two points are substituted into the equation relating the stiffness of the bolt model to time to obtain K2 and C1. t3 is the point where time approaches 0. After solving for K1, K2, and C1, this point is substituted into the equation relating the stiffness of the bolt model to time to obtain C2. This process ultimately determines the equation relating the stiffness of the bolt model to time. The strain rates of the creep curves at t1 and t2 should be less than 5 × 10⁻⁶. -4 / hour, t3≤20 hours; in, , , Where L is the effective clamping length of each component, E is the elastic modulus of each component at the operating temperature, and A is the effective stress cross-sectional area of ​​each component.

2. A method for predicting bolt axial force attenuation considering bolt creep according to claim 1, characterized in that, The stiffness-time function curve of the finally determined bolt model is compared with the creep test results. When the deviation between the fitted curve and the creep test results is greater than expected, the selection of t1, t2, and t3 is further adjusted and the calculation and fitting are repeated until the deviation between the fitted curve and the creep test results is less than expected.

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