A porosity-based bolt pre-tightening force calculation method

Abstract

This invention discloses a method for calculating bolt preload based on porosity. The invention establishes a formula relating contact resistance and bolt preload based on porosity. The contact resistance can be measured by placing electrodes at both ends of the interface, and the bolt preload can be calculated by combining readily available parameters of the same batch of materials. Compared with existing methods, this method does not require the replacement of a special measuring bolt, simplifies the measurement process, and improves the efficiency of preload calculation.

Description

Technical Field

[0001] This invention belongs to the field of structural component connection technology, specifically a method for calculating bolt preload based on porosity. Background Technology

[0002] Bolts, through the engagement of threads and nuts, securely connect multiple components into a whole, ensuring structural stability and safety. In equipment such as valves and pipelines, bolts, through pre-tightening force, compress the sealing surface to prevent media leakage, and are a key factor in ensuring system sealing. Bolts also need to withstand various loads such as internal pressure, vibration, and temperature changes to ensure long-term stable operation of the equipment.

[0003] The current mainstream methods for calculating and detecting bolt preload include using resistance strain gauges to measure stress. There are currently two main types of measurement methods: force-measuring bolts and ring washers. Force-measuring bolts directly replace existing bolts and are sensors that directly measure the bolt preload. They can accurately measure the magnitude of the bolt preload, down to the kilogram. However, all of these methods require replacing the bolts used, making the measurement process cumbersome. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating bolt preload based on porosity, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for calculating bolt preload based on porosity, characterized by comprising the following steps:

[0006] S1: The following parameters are obtained by measuring the bolt and bolt contact interface using instruments: contact resistance between the bolt and the connector. Minimum effective contact area radius between bolt and connector Maximum effective contact area radius between bolt and connector Initial porosity of the connector interface when it is not under pressure Initial interface layer thickness when the connector interface is not under pressure The initial porosity of the connector interface layer is higher than that of the connector. Porosity characteristic pressure Compression modulus of connector material Electrical conductivity of connector material ;

[0007] S2: Substitute the parameters obtained in step S1 into the bolt preload calculation model to calculate the bolt preload. The bolt preload calculation model is as follows:

[0008] ;

[0009] In the formula, For bolt preload, The thickness of the interface layer after the contact interface is subjected to pressure. Equivalent conductivity This represents the actual contact area. For interface pressure, The coefficient has the following values: , For nominal contact area, through The calculation yields the following result: The effective contact area radius is obtained by measurement based on the location of the contact resistance measuring point.

[0010] Furthermore, by measuring the contact resistance The bolt preload calculated from the effective contact area radius Contact resistance The bolt preload at the measuring point, when it is necessary to measure the overall bolt preload, is related to the contact resistance between the bolt and the connecting parts. The result was obtained using numerical integration, and the calculation steps are as follows:

[0011] S21: Calculate the total electrical conductivity at the interface between the bolt and the connector:

[0012] In the formula, The total electrical conductivity at the interface between the bolt and the connector. Porosity of the connector interface after pressure is applied;

[0013] S22: Because Therefore, the integrand of the total conductance in step S21 is calculated as follows:

[0014] ;

[0015] S23: The total conductance is calculated using the trapezoidal method as follows: In the formula, N is the total number of layers in the integration domain, and i is the layer number. It is the radius of the i-th layer after dividing the effective contact area radius into N layers on average. It is the radius of the (i+1)th layer after dividing the effective contact area radius into N layers. It is the radius interval between adjacent layers after the effective contact area radius is divided into N layers on average, that is, ;

[0016] S24: Calculate the contact resistance using the following formula: .

[0017] Compared with the prior art, the beneficial effects of the present invention are:

[0018] This invention establishes a formula relating contact resistance and bolt preload based on porosity. The preload of the bolt can be calculated by measuring the contact resistance through electrodes placed at both ends of the interface. Compared with existing methods, it does not require the replacement of a special measuring bolt, simplifying the measurement process and improving the efficiency of preload calculation. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the bolt contact interface provided in an embodiment of the present invention;

[0020] Figure 2 This is a schematic diagram of the pore structure provided in an embodiment of the present invention;

[0021] Figure 3 This is a schematic diagram of the contact area between the bolt and the connector provided in an embodiment of the present invention;

[0022] Figure 4 This is a comparison chart of experimental results provided in the embodiments of the present invention;

[0023] In the diagram, 1-bolt, 2-washer, 3-connector, 4-air pore, 5-effective contact area, 6-ineffective contact area. Detailed Implementation

[0024] 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.

[0025] Example 1: Please refer to Figures 1-3 A method for calculating bolt preload based on porosity:

[0026] 1. Bolt contact interface analysis:

[0027] In this embodiment, the bolt and connector connection structure is as follows: Figure 1 As shown, the assembly includes: bolt 1, washer 2, and connector 3, which have multiple contact interfaces. Pores exist at these contact interfaces. The bolt contact interface is considered a porous composite layer. The electrical conductivity of the contact interface consists of two phases: a metal matrix and air pores 4. The analysis process for calculating the bolt preload using the contact resistance of the contact interface is as follows:

[0028] 2. Porosity calculation:

[0029] First, the relationship between the porosity of the contact interface and the interfacial pressure is expressed by Equation 1:

[0030]

[0031] When the interface is under ultimate pressure, the porosity is 0. At this point, the relationship between the contact interface porosity and the interfacial pressure is:

[0032]

[0033] In the formula, Porosity after compression Porosity after ultimate compression The initial porosity, For interface pressure, The characteristic pressure of porosity is given, thus the relationship between the porosity of the contact interface and the interfacial pressure is obtained.

[0034] 3. Interface layer thickness calculation:

[0035] The entire interface layer is considered as a compressible porous medium, with a total volume of

[0036]

[0037] In the formula, This represents the initial volume of the interface layer. The initial porosity, This represents the initial interface layer thickness (initial height of the micro-protrusion). Nominal contact area

[0038] According to the law of conservation of interface layer volume, the initial volume of the interface layer and the volume of the interface layer after compression are equal, that is, the initial volume minus the initial pore volume equals the initial volume minus the pore volume after compression.

[0039]

[0040] In the formula, To determine the thickness of the interface layer under pressure, divide both sides of equation (4) by... ,have to:

[0041]

[0042] Summarized as follows:

[0043]

[0044] Substituting equation (2) into equation (6), we get:

[0045]

[0046] This allows us to obtain the relationship between the thickness of the interface layer and the interface pressure.

[0047] 4. Calculation of interface layer conductivity:

[0048] 4.1 Calculation of equivalent conductivity:

[0049] According to the effective medium theory, a multi-component medium can be transformed into a macroscopically homogeneous single-phase medium model using mathematical equivalence methods; the formula is as follows:

[0050]

[0051] In the formula, The matrix conductivity, Equivalent conductivity For shape factor, The conductivity refers to the electrical conductivity of the remaining materials embedded in the matrix. In this invention, the pores are filled with air, i.e. Therefore, equation (8) can be rewritten as:

[0052]

[0053] The equivalent conductivity is:

[0054]

[0055] The shape factor is a dimensionless parameter describing the effect of pore geometry on equivalent conductivity, defined as:

[0056]

[0057] In the formula, The depolarization factor is expressed as:

[0058]

[0059] In the formula, the parameter Represented as:

[0060]

[0061] In the formula, The aspect ratio of the pores.

[0062] 4.2 Calculation of Pore Aspect Ratio

[0063] The aspect ratio of a pore is defined as the ratio of the pore width to the pore diameter, such as... Figure 2As shown, the formula for the initial pore aspect ratio can be obtained as follows:

[0064]

[0065] In the formula, The initial void ratio, The initial height of the pores. The initial pore width is determined by the interfacial pressure. Under the influence of the force, the pores mainly undergo compression in the height direction, and the following differential equation can be established:

[0066]

[0067] In the formula, The pore height after compression. Here, c represents the compressive modulus, and c represents the pore height.

[0068] Integrating equation (15), we get:

[0069]

[0070] The aspect ratio of the pores at any given time is:

[0071]

[0072] Combining equations (11), (12), (13), and (17), the expression for the shape factor is obtained as follows:

[0073]

[0074] Substituting equations (2) and (18) into equation (10), we can obtain the relationship between the equivalent conductivity and the interfacial pressure:

[0075] .

[0076] 5. Actual contact area of ​​the interface:

[0077] The actual contact area of ​​the interface is:

[0078]

[0079] In the formula, This represents the actual contact area. For coefficients, Substituting equations (2) and (7) into equation (20), we obtain the relationship between the actual contact area and the interfacial pressure:

[0080] .

[0081] 6. Interface pressure calculation:

[0082] 6.1 Gaussian distribution of interfacial pressure:

[0083] like Figure 3 As shown, the area around the bolted connection interface is divided into an effective contact area 5 and an ineffective contact area 6, under interface pressure. Under the influence of [the force], only the effective contact area 5 has interfacial contact force. Considering the interfacial contact force as a Gaussian distribution, the expression for the interfacial pressure is obtained:

[0084]

[0085] In the formula, The effective contact area radius, , For interface pressure, To maximize the pressure on the center of the interface, This is a pressure decay scale.

[0086] 6.2 Calculation of pressure attenuation scale:

[0087] Pressure attenuation scale in engineering The area of ​​the annular contact region is calculated here using the equilibrium condition of force and torque:

[0088]

[0089] In the formula, The area of ​​the annular contact region. This represents the maximum effective contact area radius between the bolt and the connector. This is the minimum effective contact area radius between the bolt and the connector.

[0090] The uniform pressure across the entire interface is:

[0091]

[0092] In the formula, The uniformly distributed pressure on the interface is given by F, where F is the bolt preload. The second moment of the annular contact area is:

[0093]

[0094] The second moment of the Gaussian pressure field is:

[0095]

[0096] Equating equations (25) and (26), we get:

[0097]

[0098] The pressure attenuation scale is as follows:

[0099]

[0100] 6.3 Maximum pressure at the center of the interface;

[0101] From the equilibrium condition of forces, we get:

[0102]

[0103] Integrating equation (29) yields:

[0104]

[0105] The maximum pressure on the center of the interface after sorting is:

[0106]

[0107] Substituting equations (28) and (31) into equation (22), we obtain the expression for the interfacial pressure p as follows:

[0108] .

[0109] 7. Contact resistance calculation:

[0110] Contact resistance is:

[0111]

[0112] Equations (7), (19), and (21) can be combined and written as the following system of equations:

[0113]

[0114] Combining equation (32) with equation (34), we obtain the relationship between interface thickness, equivalent conductivity, and actual contact area as a function of preload:

[0115]

[0116] Substituting the last equation of equation (35) into the first three equations yields the relationships between interface thickness, equivalent conductivity, and actual contact area as a function of preload. Substituting these relationships into equation (33) yields the relationship between contact resistance and preload. Using existing instruments or consulting publicly available materials, the following parameters in the relationship between contact resistance and preload are obtained: contact resistance between the bolt and the connector. Minimum effective contact area radius between bolt and connector Maximum effective contact area radius between bolt and connector Initial porosity of the connector interface when it is not under pressure Initial interface layer thickness when the connector interface is not under pressure The initial porosity of the connector interface layer is higher than that of the connector. Porosity characteristic pressure Compression modulus of connector material Electrical conductivity of connector material The value is obtained by measuring the contact resistance. Calculate the preload F of the bolt.

[0117] Example 2:

[0118] In this embodiment, the established model is compared with the experimental results in the literature [Wang Yanwei. Research on contact resistance characteristics of grounding down conductors in substations [D]. North China Electric Power University, 2021. DOI:10.27139 / d.cnki.ghbdu.2021.000743.]. The comparison results are as follows: Figure 4 As shown, the calculated preload force is in good agreement with the measured results, thus verifying the accuracy of the established model.

[0119] In this embodiment, the bolt preload calculation method based on porosity includes the following steps:

[0120] S1: The following parameters are obtained by instrument measurement of the bolt and bolt contact interface: minimum effective contact area radius between the bolt and the fastener. Maximum effective contact area radius between bolt and connector Initial porosity of the connector interface when it is not under pressure Initial interface layer thickness when the connector interface is not under pressure The initial porosity of the connector interface layer is higher than that of the connector. Porosity characteristic pressure Compression modulus of connector material Electrical conductivity of connector material The parameter results are shown in Table 1 below:

[0121] Table 1 Measurement model parameter values

[0122]

[0123] S2: Substitute the parameters obtained in step S1 into the bolt preload calculation model to calculate the bolt preload. The bolt preload calculation model is as follows:

[0124] ;

[0125] In the formula, The thickness of the interface layer after the contact interface is subjected to pressure. Equivalent conductivity This represents the actual contact area. For interface pressure, The coefficient has the following values: , For nominal contact area, through Calculated.

[0126] In this embodiment, the calculation needs to be performed on the overall bolt preload when the bolt contacts the connector. Therefore, the contact resistance between the bolt and the connector is also calculated. The result was obtained using numerical integration, and the calculation steps are as follows:

[0127] S21: Calculate the total electrical conductivity at the interface between the bolt and the connector:

[0128] In the formula, Porosity of the connector interface after pressure is applied;

[0129] S22: Because Therefore, the integrand of the total conductance in step S21 is calculated as follows:

[0130] ;

[0131] S23: The total conductance is calculated using the trapezoidal method as follows: In the formula, N is the total number of layers in the integration domain, and i is the layer number. It is the radius of the i-th layer after dividing the effective contact area radius into N layers on average. It is the radius of the (i+1)th layer after dividing the effective contact area radius into N layers. It is the radius interval between adjacent layers after the effective contact area radius is divided into N layers on average, that is, ;

[0132] S24: Calculate the contact resistance using the following formula: ;

[0133] Finally obtained The relationship between the calculation results and the bolt preload is as follows: Figure 4 The triangle symbol is shown in the middle.

[0134] Measurement parameter description:

[0135] Bolt radius / Minimum effective contact area:

[0136] This data represents the diameter of the bolt used, which can be measured directly using a vernier caliper or obtained by reading the standard bolt markings.

[0137] Maximum effective contact area:

[0138] The contact pressure described in this invention is Gaussian distributed, and the maximum value is considered to be twice the minimum value. That is, a characteristic size order of magnitude is used as an approximation of the contact action area scale, and the main / effective contact pressure is concentrated in this area.

[0139] Early research [Gould HH, Mikic B B. Areas of contact and pressure distribution in bolted joints[J]. 1972.] indicated that the contact area diffuses outward from the bolt hole edge to a certain radius, where the contact pressure attenuates to zero; because this invention uses a Gaussian function to describe the radial pressure attenuation characteristics and selects distribution parameters such that... r =2 R i The pressure amplitude has significantly decreased. Therefore, R 0=2 R i The outer boundary of the equivalent action zone is considered. Based on the obvious localization characteristic of the contact pressure caused by bolt preload, this invention approximates the effective action zone as within one hole radius, starting from the hole edge. R i ≤ r ≤2 R i This simplifies the analysis and ensures the conservatism of the results.

[0140] Initial porosity:

[0141] Using the Sensofor-neox three-dimensional optical surface tester to measure the contact surface, the rough profile of the contact surface can be obtained. With the rough profile, the parameter data of the rough surface can be obtained, and the porosity can be obtained by (contact volume / total volume).

[0142] Initial interface thickness / initial height of micro-protrusion:

[0143] Using the Sensofor-neox three-dimensional optical surface tester to measure the contact surface, the rough profile of the contact surface can be obtained. With the rough profile, the parameter data on the rough surface can be obtained, and the initial height of the micro-protrusion can be selected as the highest micro-protrusion height on the contact surface.

[0144] Initial porosity:

[0145] Using the Sensofor-neox three-dimensional optical surface tester to measure the contact surface, the rough profile of the contact surface can be obtained. With the rough profile, the parameter data on the rough surface can be obtained, and the initial pore aspect ratio can be obtained by the longitudinal height / transverse width of the pore.

[0146] Porosity characteristic pressure:

[0147] The concept of characteristic pressure of porosity was first proposed in geological engineering. Essentially, this parameter refers to a scale parameter in the porosity decay curve with respect to effective pressure. In the field of geological engineering, Rutter, E., Mecklenburgh, J., & Bashir, Y. (2022). Matrix gas flow through “impermeable” rocks - shales and tight sandstone. Solid Earth, 13, 725-743.] mentions that in low-porosity and low-permeability systems (especially tight / shale / tight sandstone systems), characteristic pressures reaching the hundreds of MPa are not unreasonable. Furthermore, tight / shale / tight sandstone systems can correspond to metallic porous systems characterized by "low porosity, strong framework, and harder pores." The aforementioned literature mentions that an effective pressure cycle of 150 MPa corresponds to a certain proportion of pore space closure; therefore, this invention uses the value of 150 MPa.

[0148] Compression modulus and electrical conductivity are inherent properties of materials and can be obtained by consulting the material parameters.

[0149] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A porosity-based bolt pre-tightening force calculation method, characterized by, Includes the following steps: S1: The following parameters are obtained by measuring or calculating the bolt and bolt contact interface using instruments: contact resistance between the bolt and the connector. Minimum effective contact area radius between bolt and connector Maximum effective contact area radius between bolt and connector Initial porosity of the connector interface when it is not under pressure Initial interface layer thickness when the connector interface is not under pressure The initial porosity of the connector interface layer is higher than that of the connector. Porosity characteristic pressure Compression modulus of connector material Electrical conductivity of connector material ; S2: Substitute the parameters obtained in step S1 into the bolt preload calculation model to calculate the bolt preload. The bolt preload calculation model is as follows: ； In the formula, For bolt preload, The thickness of the interface layer after the contact interface is subjected to pressure. Equivalent conductivity This represents the actual contact area. For interface pressure, The coefficient has the following values: , For nominal contact area, through The calculation yields the following result: The effective contact area radius is obtained by measurement based on the location of the contact resistance measuring point.

2. The bolt preload calculation method based on porosity according to claim 1, characterized in that, By measuring contact resistance and effective contact area radius Calculated bolt preload Contact resistance The calculation steps for the bolt preload at the measuring point, when measuring the overall bolt preload, are as follows: S21: Calculate the total electrical conductivity at the interface between the bolt and the connector: wherein Gtot is the total conductance of the bolt to connection interface, is the porosity of the connection interface after compression, calculated by the following equation: ; S22: As a result is the contact area with radius the integral function of the total conductance calculated in step S21 is: ； S23: The total conductance is calculated using the trapezoidal method as follows: In the formula, N is the total number of layers in the integration domain, and i is the layer number. It is the radius of the i-th layer after dividing the effective contact area radius into N layers on average. It is the radius of the (i+1)th layer after dividing the effective contact area radius into N layers. It is the radius interval between adjacent layers after the effective contact area radius is divided into N layers on average, that is, ; S24: Calculate the contact resistance by the following contact resistance formula : .

Images