Method and system for determining stress concentration coefficient and fatigue notch coefficient of threaded connection pair bolt

Abstract

The invention relates to a method and system for determining a stress concentration coefficient and a fatigue notch coefficient of a threaded connection pair bolt, and belongs to the technical field of bolt fatigue life analysis. The method comprises the following steps that a bolt axial symmetry finite element model is established through finite element simulation, axial average stress corresponding to nominal stress at a thread notch is loaded at the far end of a bolt, the size of a finite element grid is gradually reduced, and the finite element grid in the area nearby a bolt tooth bottom is encrypted to obtain the stress concentration coefficient of the bolt tooth bottom. According to the method, a bolt axial symmetry finite element model is established by utilizing a finite element simulation technology, axial average stress corresponding to nominal stress at a thread gap is loaded at the far end of a threaded connection pair bolt, the size of a finite element grid is gradually reduced, the finite element grid in an area near a bolt root is encrypted to obtain a stress concentration coefficient, and the stress concentration coefficient is calculated. And when the relative error of the stress concentration coefficient of the current encryption and the stress concentration coefficient of the previous encryption is less than or equal to a set value, considering that the stress concentration coefficient with relatively high precision is obtained.

Description

Technical Field

[0001] The invention relates to a method and a system for determining a stress concentration factor and a fatigue notch factor of a threaded connection pair bolt, and belongs to the technical field of bolt fatigue life analysis. Background Art

[0002] The stress concentration factor (also known as the theoretical stress concentration factor or geometric stress concentration factor) and the fatigue notch factor (also known as the effective stress concentration factor) are the main parameters that characterize the fatigue notch sensitivity of materials. Among them, the fatigue notch factor is an important conversion factor to establish the relationship between the fatigue strength of the standard specimen without a notch and the fatigue strength of the notched specimen. The fatigue notch factor has an important influence on the fatigue analysis of the threaded structure, especially when the local stress-strain method is used to estimate the fatigue crack formation life under complex loads, it is crucial to determine the local stress or strain history of the stress concentration part.

[0003] In view of the shortcomings of the traditional Neuber hyperbola equation in fatigue analysis, the modified Neuber hyperbola form that uses fatigue notch factor instead of theoretical stress concentration factor is more commonly used in engineering. When the modified Neuber hyperbola is used for fatigue life prediction, the predicted results of fatigue life are quite sensitive to the fatigue notch factor. Therefore, determining the accurate fatigue notch factor becomes the key to obtaining a high-precision fatigue life prediction result.

[0004] Among them, the mathematical expressions of the traditional Neuber hyperbola and the modified Neuber hyperbola are as follows:

[0005]

[0006] Where Δσ is the local stress range of the notch, Δε is the local strain range of the notch, and K t is the stress concentration factor, K f is the fatigue notch coefficient, ΔS is the notch nominal stress range, and E is the cyclic elastic modulus.

[0007] When the traditional Neuber method is used to solve the notch local stress and strain, the Neuber hyperbola needs to be combined with the cyclic stress-strain curve, hysteresis loop and fatigue load spectrum to solve the notch local stress and strain; when the modified Neuber method is used to solve the notch local stress and strain, the modified Neuber hyperbola needs to be combined with the cyclic stress-strain curve, hysteresis loop and fatigue load spectrum to solve the notch local stress and strain. The principle of solving the notch local stress and strain is as follows: Figure 1 As shown, Figure 1 The principle of solving the local stress and strain at points A and B by using the Neuber hyperbola combined with the cyclic stress-strain curve, hysteresis loop and fatigue load spectrum is demonstrated.

[0008] The fatigue notch factor mainly depends on the stress concentration factor, but it is also related to material properties, notch type, notch radius and notch depth, and the influence of stress concentration factor is far greater than other factors. The method to determine the accurate fatigue notch factor is through experimental method, but it is time-consuming and expensive to obtain the fatigue notch factor through experimental method (such as fatigue test of V-notch specimen), and the value of the fatigue notch factor obtained in this way is related to the size and material. A large number of experiments have shown that fatigue strength decreases with increasing size. Therefore, the fatigue notch factor obtained by fatigue test of the specimen cannot be directly used to determine the general coefficient of the material, nor can it be used for structural fatigue design without modification. P. Kuhn, H. Neuber, RE Peterson and others proposed many practical empirical or semi-empirical formulas based on point stress or average stress models, but the physical foundation is not strong enough. TH Topper and others established some expressions based on fracture mechanics models. SD Sheppard, Yao Weixing and others studied the fatigue notch factor using the stress field intensity method. However, due to the many factors involved in the fatigue notch factor expression, an economical and reliable way to obtain a fatigue notch factor expression that can adapt to various situations has not yet been found.

[0009] A large number of studies have shown that the stress concentration factor is only related to the geometric shape of the specimen or component and is not affected by the material and other factors. The fatigue notch factor is affected by many factors. In addition to being closely related to the theoretical stress concentration factor, it is also related to material properties, notch type, notch radius, notch depth, etc. Therefore, in order to obtain a more accurate fatigue notch factor, it is first necessary to solve the stress concentration factor with a higher accuracy.

[0010] The existing methods for solving the stress concentration factor of the bolt thread area of ​​threaded connection pairs mostly adopt the finite element numerical simulation method, and a small number of them adopt the experimental measurement method. Most of the bolts used are small in size, generally with a nominal diameter of less than 30 mm, and most of the thread forms are ordinary metric threads. The analysis results of the stress concentration factor of arc threads with a nominal diameter of 36 mm and above have not been reported. Among them, the two-dimensional axisymmetric model and the three-dimensional fine structure model can both achieve relatively satisfactory results when solving the stress concentration factor by finite element numerical simulation; while the experimental measurement method is used to solve the stress concentration factor. The range of experimental techniques that can be used to evaluate the stress concentration at the root of the thread is extremely limited. This is because when the threaded connection pair of the nut and the bolt is tightened in place, the root of the thread is inside the threaded connection pair and cannot directly contact the root area of ​​the thread of the threaded connection pair. This inaccessibility excludes technologies such as strain measurement and reflected photoelasticity. In existing literature reports, photoelastic measurement is generally used to solve the stress concentration factor by experimental measurement methods. However, the stress concentration measurement at the thread requires a series of extremely complex intermediate processes such as epoxy resin curing, nut cutting, and precise measurement. It is time-consuming, costly, and has low resolution, resulting in low accuracy of the thread stress concentration factor obtained by the experimental measurement method. With the development of software technology and the development of finite element analysis technology, researchers currently conducting fatigue analysis almost no longer use this experimental measurement method to analyze the stress concentration factor, but use finite element analysis as the main technical path.

[0011] At present, the finite element analysis method for solving the stress concentration factor is that one part only models a single bolt and uses a three-dimensional bolt model with a single thread; the other part models the threaded connection pair (bolt and nut combination) and uses an axisymmetric model with 2 to 7 threads (generally 3 to 5 threads) or a three-dimensional bolt and nut combination local model with several threads (generally around 4 threads), and it only densifies a small area at the bottom of the thread, resulting in relatively low continuity and smoothness of its stress distribution, and relatively low ability to capture high-precision stress distribution results, so the accuracy of the obtained stress distribution results is relatively low. In addition, the current research status shows that there are still some researchers who have not considered the change of the stress concentration factor of the thread notch caused by the grid, or although they have considered the change of the stress concentration factor caused by the grid change, they often set the relative error of the results after the two grid size changes to 2% to 4%, believing that the final result of the stress concentration factor solved by the finite element method has converged to a stable value, which makes the final result of the stress concentration factor solved low in accuracy.

[0012] The above research status means that there are still some deficiencies in the solution of high-precision stress concentration factor at the thread notch. It is necessary to develop a method and system for solving thread notch stress concentration factor and fatigue notch factor with high solution accuracy to improve the accuracy of bolt fatigue life prediction and to facilitate its application in engineering. Summary of the invention

[0013] The purpose of the present invention is to provide a method and system for determining the stress concentration factor of a threaded connection bolt, so as to solve the problem that the obtained stress concentration factor has a relatively low solution accuracy; and also to provide a method and system for determining the fatigue notch factor of a threaded connection bolt, so as to solve the problem that the obtained fatigue notch factor has a relatively low solution accuracy due to the relatively low stress concentration factor solution accuracy.

[0014] To achieve the above object, the solution of the present invention includes:

[0015] A method for determining a stress concentration factor of a threaded connection pair bolt of the present invention comprises the following steps:

[0016] Finite element simulation technology is used to establish an axisymmetric finite element model of the bolt. An axial average stress corresponding to the nominal stress at the thread notch is loaded on the end face of the threaded connection pair bolt away from the threaded meshing part, and the size of the finite element mesh is gradually reduced. The finite element mesh in the area near the bolt tooth bottom is encrypted to obtain the stress concentration coefficient at the tooth bottom of the threaded connection pair bolt. The condition for stopping the encryption is that the relative error of the stress concentration coefficient obtained by this encryption and the previous encryption solution is less than or equal to the set value.

[0017] Furthermore, encryption adopts the influence sphere method.

[0018] Furthermore, the set value is 0.1%.

[0019] Furthermore, the ratio of the geometric characteristic size of the axisymmetric finite element model of the bolt to the notch characteristic size is not less than 10.

[0020] Furthermore, in the process of gradually reducing the finite element mesh size, the finite element mesh size after each step of reduction is γ times the finite element mesh size before the step of reduction, γ∈[0.3,0.6].

[0021] A method for determining a fatigue notch coefficient of a threaded connection pair bolt of the present invention comprises the following steps:

[0022] The fatigue notch coefficient at the root of the threaded bolt is obtained by using the stress concentration factor at the root of the threaded bolt using the Peterson method based on point stress and sensitivity coefficient, or using the stress concentration factor at the root of the threaded bolt using the Neuber method based on average stress, or using the stress concentration factor at the root of the threaded bolt using the Siebel-Stieler method based on relative stress gradient, or using the stress concentration factor at the root of the threaded bolt using the Zhao Shaobian method based on relative stress gradient;

[0023] The stress concentration factor at the root of the threaded bolt is determined by the following method:

[0024] Finite element simulation technology is used to establish an axisymmetric finite element model of the bolt. An axial average stress corresponding to the nominal stress at the thread notch is loaded on the end face of the threaded connection pair bolt away from the threaded meshing part, and the size of the finite element mesh is gradually reduced. The finite element mesh in the area near the bolt tooth bottom is encrypted to obtain the stress concentration coefficient at the tooth bottom of the threaded connection pair bolt. The condition for stopping the encryption is that the relative error of the stress concentration coefficient obtained by this encryption and the previous encryption solution is less than or equal to the set value.

[0025] Furthermore, encryption adopts the influence sphere method.

[0026] Furthermore, the set value is 0.1%.

[0027] Furthermore, the ratio of the geometric characteristic size of the axisymmetric finite element model of the bolt to the notch characteristic size is not less than 10.

[0028] Furthermore, in the process of gradually reducing the finite element mesh size, the finite element mesh size after each step of reduction is γ times the finite element mesh size before the step of reduction, γ∈[0.3,0.6].

[0029] A system for determining a stress concentration factor of a threaded connection bolt of the present invention comprises a processor, and the processor is used to execute a computer program to implement the steps of the method for determining the stress concentration factor of a threaded connection bolt as described above.

[0030] A system for determining a fatigue notch coefficient of a threaded connection bolt of the present invention comprises a processor, and the processor is used to execute a computer program to implement the steps of the method for determining a fatigue notch coefficient of a threaded connection bolt as described above.

[0031] Beneficial effects of the present invention:

[0032] The present invention is a pioneering invention, which provides a method for determining the stress concentration factor of a threaded connection pair bolt. The finite element simulation technology is used to establish an axisymmetric finite element model of the bolt, and an axial average stress corresponding to the nominal stress at the thread notch is loaded on the end face of the threaded connection pair bolt away from the threaded meshing part, and the size of the finite element grid is gradually reduced. The finite element grid in the area near the bolt tooth bottom is encrypted to obtain the stress concentration factor at the threaded connection pair bolt tooth bottom, until the relative error between the current encrypted stress concentration factor and the previous encrypted stress concentration factor is less than or equal to a set value. At this time, it is considered that the stress concentration factor of the bolt tooth bottom with high accuracy and convergent results is obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is the principle diagram of solving the local stress and strain of the notch by the existing Neuber method and the modified Neuber method;

[0034] Figure 2 It is a schematic diagram of the geometric dimensions of the plane stress model of a flat plate with a central hole;

[0035] Figure 3 It is a schematic diagram reflecting the local mesh encryption of the plane stress model of the central hole plate;

[0036] Figure 4 It is a schematic diagram reflecting the constraints and loading conditions;

[0037] Figure 5 is the stress cloud diagram of the simulation results;

[0038] Figure 6 is a schematic diagram of the selected path;

[0039] Figure 7 is a graph showing the variation of the theoretical stress concentration factor with normalized distance at different size characteristic ratios;

[0040] Figure 8 It is the local situation of the finite element mesh of the axisymmetric single-circle V-notch model;

[0041] Fig. 9 It is the stress cloud diagram of the finite element analysis of the axisymmetric single-circle V-notch model;

[0042] Fig.10 It is a comparison chart of the results of solving the stress concentration factor of a single-circle V-notch specimen using different methods;

[0043] Fig.11 It is a schematic diagram of the finite element mesh encryption part of the arc thread model;

[0044] Fig.12 It is the simulation result of the arc thread model;

[0045] Fig.13It is a schematic diagram of the finite element mesh encryption part of the MJ thread model;

[0046] Fig.14 It is the simulation result of MJ thread model;

[0047] Fig.15 It is a schematic diagram of the finite element mesh encryption part of the common metric thread model;

[0048] Fig.16 This is the simulation result of the common metric thread model;

[0049] Fig.17 It is a schematic diagram of the effect of the local mesh density of the notch of the arc thread model on the convergence of the stress concentration factor;

[0050] Fig.18 It is a schematic diagram of the effect of the notch local mesh density on the convergence of the stress concentration factor of the MJ thread model;

[0051] Fig.19 It is a schematic diagram of the effect of the local mesh density of the notch on the convergence of the stress concentration factor of the common metric thread model;

[0052] Fig. 20 It is a comparison chart between the bolt fatigue life prediction results and fatigue test results;

[0053] Fig.21 It is a flow chart for determining the fatigue notch factor of threaded connection bolts. DETAILED DESCRIPTION

[0054] In order to solve the problem in the background technology, the present invention takes into account the result change of the thread notch stress concentration coefficient caused by the grid change, and sets the relative error of the stress concentration coefficient after the grid size is changed twice to be smaller. It is believed that the finite element results converge at this time, so that the accuracy of the obtained result data is relatively high.

[0055] To facilitate the understanding of the following text, the parameters used in this scheme are explained as follows.

[0056] 1. Stress concentration factor

[0057] The stress concentration factor is a local concept used to express the ratio of the local peak stress of the notch section to the nominal stress. It is a measure of the degree of structural stress concentration. Its expression is:

[0058]

[0059] In the formula, K t is the stress concentration factor, σ max is the maximum local elastic stress at the bottom of the thread, σ n It is the nominal stress (or average stress) at the cross section of the thread bottom.

[0060] The stress concentration factor is only related to the geometric shape of the specimen or part and is not affected by the material and other factors. When the structure is relatively simple, it can be obtained by theoretical calculation, table lookup or experiment. When the structure is complex, it needs to be obtained through numerical simulation methods such as finite element method.

[0061] 2. Fatigue notch coefficient

[0062] The fatigue notch factor is also a local concept. When the load conditions and absolute dimensions are the same, the effective stress concentration factor under cyclic load is equal to the ratio of the fatigue limits of the smooth specimen to the notched specimen. Its expression is:

[0063]

[0064] Among them, K f is the fatigue notch factor, S e is the fatigue strength of the smooth specimen (smooth specimen), S N is the fatigue strength of the notched specimen.

[0065] 3. Fatigue notch sensitivity coefficient

[0066] The fatigue notch coefficient mainly depends on the theoretical stress concentration coefficient. In addition, it is also related to factors such as material properties, notch type, notch radius and notch depth. Experimental research has found that for specimens with the same geometric dimensions but different raw materials, their fatigue notch coefficients are also different. This situation is more complicated. The fundamental reason is that some materials are much more sensitive to notches than others. Therefore, for actual complex situations such as more complex structures and different materials, Petrson introduced the fatigue notch sensitivity coefficient as a measure of the material's sensitivity to stress concentration under cyclic loads. The expression of the fatigue notch sensitivity coefficient is:

[0067]

[0068] Where q is the fatigue notch sensitivity coefficient, K f is the fatigue notch factor, K t is the stress concentration factor.

[0069] By transforming and rearranging the above formula, we can obtain the following solution formula for the fatigue notch factor based on the fatigue notch sensitivity coefficient:

[0070] K f =1+q(K t -1)

[0071] Where q is the fatigue notch sensitivity coefficient, K f is the fatigue notch factor, K t is the stress concentration factor.

[0072] After obtaining the stress concentration factor and fatigue notch sensitivity factor, the fatigue notch factor can be calculated using the above formula. The fatigue notch sensitivity factor first depends on the material properties. Generally, the tensile strength of the material σ b When the fatigue notch sensitivity coefficient increases, the fatigue notch sensitivity coefficient increases, and when the grain size and material property non-uniformity increase, the fatigue notch sensitivity coefficient decreases. In addition to depending on the material properties, the fatigue notch sensitivity coefficient is also related to factors such as stress gradient or notch radius, and its value is not a material constant. Existing literature has disclosed some relationships or curves between fatigue notch sensitivity coefficient and notch radius, but the values ​​of fatigue notch sensitivity coefficients obtained using different notch sensitivity formulas or curves often have large differences, which will directly affect the accuracy of fatigue life prediction results.

[0073] Commonly used fatigue notch sensitivity coefficient formulas are the Neuber formula and the Peterson formula.

[0074] Neuber's formula is:

[0075]

[0076] Where q is the fatigue notch sensitivity coefficient, A is the Neuber parameter, which is generally found from the Neuber parameter diagram, and ρ is the notch radius (mm).

[0077] Peterson's formula is:

[0078]

[0079] Where q is the fatigue notch sensitivity coefficient, α is the Peterson parameter, and ρ is the notch radius (mm).

[0080] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0081] An embodiment of a method for determining a stress concentration factor of a threaded connection pair of bolts:

[0082] A method for determining the stress concentration factor of a threaded connection bolt, referring to Fig.21 , including the following steps:

[0083] Finite element simulation technology is used to establish an axisymmetric finite element model of the bolt. The load conversion is performed through the conversion relationship between the distal load and the nominal stress. The axial average stress corresponding to the nominal stress at the thread notch is loaded at the distal end of the threaded connection pair bolt (i.e., the end face of the threaded connection pair bolt away from the threaded engagement portion). The size of the finite element grid is gradually reduced, and the finite element grid near the bolt tooth bottom is encrypted to obtain the stress concentration coefficient at the tooth bottom of the threaded connection pair bolt. The condition for stopping the encryption is that the relative error of the stress concentration coefficient obtained by the current encryption and the previous encryption solution is less than or equal to the set value.

[0084] The set value is 0.1%. Of course, it can also be set according to the actual situation. The smaller the set value, the higher the accuracy of the stress concentration factor obtained.

[0085] Specifically, the encryption adopts the influence sphere method. The encryption area of ​​this method is larger. Compared with the encryption of a small area, the continuity and smoothness of the stress distribution can be further improved, and the ability to capture high-precision stress distribution results can also be improved. Therefore, the obtained stress distribution results are smooth and fine, that is, the accuracy of the obtained stress concentration factor can be improved.

[0086] Specifically, in order to eliminate the influence of size effect, the ratio of the geometric characteristic size to the notch characteristic size of the established bolt axisymmetric finite element model is not less than 10.

[0087] Specifically, in the process of gradually reducing the finite element mesh size, the finite element mesh size after each step of reduction is γ times the finite element mesh size before the step of reduction, γ∈[0.3,0.6], so that the efficiency of determining the high-precision stress concentration factor is higher.

[0088] The overall solution idea for the stress concentration factor is: use the finite element simulation analysis method to establish an axisymmetric finite element model of the bolt, use the method of local mesh encryption near the root of the thread to solve the local stress, and encrypt the mesh multiple times. The size of the latter mesh changes to 0.3 to 0.6 times the size of the previous mesh, until the absolute value of the relative error between the two stress concentration factor solution results is less than or equal to 0.1%. At this time, it is considered that the stress concentration coefficient with convergent results at the thread root is obtained.

[0089] The number of times the finite element mesh is encrypted near the bolt tooth bottom varies with the bolt structure. The mesh encryption is stopped when the relative error of the stress concentration factor between the last two encryptions is ≤0.1%.

[0090] In order to eliminate the influence of size effect, the axisymmetric finite element model of the bolt is established. Firstly, the ratio of the geometric characteristic dimension W of the model to the characteristic dimension d of the notch should be at least 10.

[0091] The requirement that the ratio of the geometric characteristic size of the model to the notch characteristic size is not less than 10 comes from an example analysis to establish a plane stress model of a plate with a central opening, such as Figure 2 , Figure 3 , Figure 4 and Figure 5 As shown in the figure, stress analysis is performed under multiple size ranges to obtain the hole edge stress concentration factor. A path is selected along the notch bisector. The path is as follows: Figure 6 As shown, the stress results are mapped to the path, and the obtained stress concentration factor is compared with the analytical solution of elastic theory. The results are shown in Figure 7 When the ratio of the plane stress model geometric characteristic size to the notch characteristic size is greater than or equal to 10, the absolute value of the relative error of the result caused by the geometric size effect will be less than 1.20%, and the relative error of the result caused by the size effect is within the engineering allowable range.

[0092] Furthermore, when the ratio of the geometric characteristic size to the notch characteristic size is greater than or equal to 20, the absolute value of the relative error of the result caused by the geometric size effect is no more than 0.28%, and the relative error of the result caused by the size effect is within a satisfactory error range in engineering.

[0093] At present, the solutions and tests of stress concentration factors of round bar specimens with V-notches at home and abroad are expressed differently in different specifications. The theoretical values, calculated values ​​and test values ​​are all different. The V-notch sizes corresponding to the theoretical stress concentration factors declared in existing literature are also different.

[0094] The formula for calculating the stress concentration factor given in Appendix E of the Chinese national recommended standard GB / T 2039-2012 "Uniaxial Tension Creep Test Method for Metallic Materials" is:

[0095]

[0096] The calculation formula recommended by the German national standard DIN 743-2-2009 and the international standard ISO 204 for calculating the stress concentration factor is:

[0097]

[0098] Among them, r n is the cut radius, d n is the notch bottom diameter, D n is the transition section diameter.

[0099] The finite element method is used to establish an axisymmetric single notch model with a V-shaped notch (opening angle 60°) with a ratio of geometric characteristic size to notch characteristic size of 10 and a notch located at 1 / 2 of the model length, as shown in Figure 8 As shown, theoretical calculation and finite element analysis were performed according to the formula, and the results are shown in Fig. 9 and Fig.10 As shown. Compared with the existing declared stress concentration factor (see Table 1), the stress concentration factor value calculated by GB / T 2039-2012 is higher, and the relative error is larger (between 10.4% and 18.0%). The stress concentration factor values ​​calculated by DIN743-2-2009 and ISO204 are closer to the existing declared values, and the relative error is in the middle (between -3.20% and 4.50%). The stress concentration factor of the finite element simulation result is closest to the existing declared value, and the relative error is the smallest (between -0.400% and 1.35%), indicating that the finite element simulation result has the highest accuracy and high solution accuracy. For the sake of simplicity, when solving high-precision stress concentration factors, the German standard DIN 743-2-2009 and the international standard ISO 204 can be used to estimate the stress concentration factor first, and then the finite element simulation method can be used for accurate calculation and compared with the estimated results to prevent deviations. When large deviations occur, it is necessary to carefully check and verify the simulation analysis steps to prevent stress concentration factor calculation errors caused by unexpected calculation errors.

[0100] Table 1 Comparison of the results of calculating the stress concentration factor of notched specimens using different methods

[0101]

[0102] An axisymmetric single-turn thread model with a ratio of geometric feature size to notch feature size of not less than 10 is established. Taking a thread with a nominal diameter of 36 mm (millimeter) as an example, arc thread, MJ thread and ordinary metric thread are studied respectively. The structure is simulated and analyzed using mesh sizes of 0.8 mm, 0.4 mm, 0.2 mm, 0.1 mm, 0.05 mm, 0.025 mm and 0.0125 mm respectively. The mesh encryption parts and simulation results are shown in Figure 2. Fig.11 , Fig.12 , Fig.13 , Fig.14 , Fig.15 and Fig.16 shown.

[0103] When the error of two consecutive simulation results is no more than 0.1%, it is considered that the simulation results have converged well. The influence of mesh density on the convergence of stress concentration factor solution results is as follows: Fig.17 , Fig.18 and Fig.19 As shown, the horizontal axis is the number of grids per unit length (1mm), and the minimum grid sizes when the stress concentration factor solution results of the axisymmetric finite element models of arc thread, MJ thread and ordinary metric thread converge are 25μm (micrometers), 12.5μm and 12.5μm, respectively, and the finite element converged solutions are 2.95, 4.30 and 4.69, respectively.

[0104] The same method was used to simulate and analyze the arc thread, MJ thread and ordinary metric thread with nominal diameters of 39mm and 42mm respectively, and the corresponding stress concentration coefficients were 3.00, 4.37, 4.78 and 3.05, 4.33, 4.73 respectively. Finally, based on the obtained theoretical stress concentration coefficient, the fatigue notch coefficient was calculated using the Peterson method, Neuber method, Siebel-Stieler method and Zhao Shaobian method.

[0105] An embodiment of a method for determining a fatigue notch coefficient of a threaded connection pair bolt:

[0106] A method for determining the fatigue notch factor of a threaded connection bolt pair, such as Fig.21 As shown, the method comprises the following steps: the fatigue notch coefficient at the tooth bottom of the threaded auxiliary bolt is obtained by using the stress concentration coefficient at the tooth bottom of the threaded auxiliary bolt using the Peterson method based on point stress and sensitivity coefficient, or by using the stress concentration coefficient at the tooth bottom of the threaded auxiliary bolt using the Neuber method based on average stress, or by using the stress concentration coefficient at the tooth bottom of the threaded auxiliary bolt using the Siebel-Stieler method based on relative stress gradient, or by using the stress concentration coefficient at the tooth bottom of the threaded auxiliary bolt using the Zhao Shaobian method based on relative stress gradient.

[0107] Among them, the determination of the stress concentration factor at the root of the threaded connection bolt has been described in detail in an embodiment of a method for determining the stress concentration factor of a threaded connection bolt, and will not be repeated here.

[0108] The fatigue notch factor can be solved in the following way:

[0109] ① Peterson method to solve fatigue notch coefficient

[0110] Fatigue notch factor K at the tooth bottom of arc thread high-strength bolt obtained by Peterson method f The calculation formula is as follows:

[0111]

[0112] In the formula, K f is the fatigue notch factor of the bolt tooth bottom, K t is the stress concentration factor, α is the Peterson parameter of the bolt, and ρ is the bolt tooth bottom radius (in millimeters).

[0113] Among them, the Peterson parameter of tempered steel bolts is 0.0635mm, and the Peterson parameter of normalized steel bolts is 0.254mm.

[0114] For medium and high strength steel (limit stress σ u >560MPa (megapascals) for bolts, the approximate calculation formula for α is as follows:

[0115]

[0116] Where α is the Peterson parameter, σ b For tensile strength.

[0117] ② Neuber method to solve fatigue notch coefficient

[0118] Fatigue notch factor K at the tooth bottom of circular arc thread high-strength bolt obtained by Neuber method f The calculation formula is as follows:

[0119]

[0120] In the formula, K f is the fatigue notch coefficient of the bolt tooth bottom; A is the Neuber parameter, which is a material constant and is related to the strength limit of the bolt material. A=f(σ b );K t is the stress concentration factor, σ b For tensile strength.

[0121] ③ Zhao Shaobian method to solve fatigue notch coefficient

[0122] Fatigue notch factor K at the tooth bottom of arc thread high-strength bolt obtained by Zhao Shaobian method f The calculation formula is as follows:

[0123]

[0124] In the formula, K f is the fatigue notch factor of the bolt tooth bottom, K t is the stress concentration factor, Q is the relative stress gradient (in mm -1 ), A and b are constants related to material heat treatment, etc.

[0125] When the steel is in hot-rolled state and has not been heat-treated, A is taken as 0.336 and b is taken as 0.345. The raw materials used for high-strength bolts are generally quenched and then tempered. At this time, A is taken as 0.290 and b is taken as 0.152; if it is normalized heat treated, A is taken as 0.423 and b is taken as 0.279.

[0126] The fatigue notch coefficient and the corresponding stress concentration factor obtained by the above three methods are shown in Table 2 below. Wherein, d / mm is the nominal diameter of the threaded connection bolt, in millimeters; K t is the stress concentration factor, K f is the fatigue notch coefficient of the bolt tooth bottom, and q is the sensitivity coefficient.

[0127] Table 2 Results of stress concentration factor and fatigue notch factor calculation

[0128]

[0129]

[0130] This method obtains a stress concentration factor with high accuracy through finite element simulation technology, and then obtains a fatigue notch factor with high accuracy through different methods. The fatigue life of the bolt is predicted based on the obtained fatigue notch factor. Taking a bolt with a nominal diameter of 36 mm as an example, the simulation result of the fatigue notch factor is used to perform local stress-strain analysis on the tooth bottom based on the modified Neuber method. The Morrow damage parameter is selected, and the same cyclic load (average stress 400 MPa, stress amplitude 100 MPa) is used to predict the fatigue life of the bolt. The results are shown in Table 3 below. It can be seen that the stress concentration factor of the arc thread is low, and its fatigue life prediction result is much higher than that of the MJ thread and the ordinary metric thread. The fatigue life of the MJ thread and the ordinary metric thread bolts is close, but both are much lower than the fatigue life of the arc thread bolt.

[0131] Table 3 Fatigue life prediction example

[0132]

[0133] According to GB / T 13682-92, a large number of bolt fatigue tests under different stress levels and stress amplitudes are carried out, and the fatigue notch coefficient results solved by the method provided by the present invention are used to predict the fatigue life under the same test conditions, and the fatigue life prediction results are compared with a large number of fatigue test results. The comparison results are as follows: Fig. 20 As shown, it can be seen that most of the prediction result data are located in the 2 times life dispersion band, and the fatigue life prediction results have a higher accuracy, which in turn shows that the stress concentration factor and fatigue notch factor obtained according to the method of the present invention have a higher solution accuracy.

[0134] The present invention adopts a single-circle axisymmetric model for modeling, and sets the relative error of the result after the grid size is changed (the grid size is on the order of 10 microns) to 0.1%, and the result convergence is considered to be achieved, which greatly improves the accuracy of the result data. The present invention also uses the sphere of influence method to repeatedly encrypt the grid density in the area near the screw thread. Compared with the method of only encrypting a small area at the bottom of the screw thread, the continuity and smoothness of the stress distribution are further improved, and the ability to capture high-precision stress distribution results is further improved. The obtained stress distribution results are smooth and fine, and the accuracy is improved.

[0135] Among them, the concept of mesh encryption by the influence sphere method comes from the ANSYS Workbench finite element analysis software. It is a method of local mesh optimization provided in the software. By setting an influence sphere for the structure, only the finite element mesh inside the influence sphere area can be locally encrypted and optimized. It can be used to improve the mesh of the local area to be evaluated, and it can also make the mesh transition more uniform and avoid the impact caused by mesh mutation. This method is a public method, and the corresponding parameters can be set directly in the software when solving.

[0136] Secondly, the application objects of the present invention are arc threads, MJ threads and ordinary metric threads with a nominal diameter of 36mm and above, which are relatively large in size and different from the existing metric threads of M30 and below. In addition, the application scenarios of the bolt research objects are also quite different. The application scenarios of the bolts studied in the prior art are mostly steel structures (such as bolt ball node grid structures, lightning rod structures, etc.), while the application scenarios of the present invention's research objects are the root connection parts of blades on large wind turbines, which have quite different load conditions and use environments, and the fatigue failure locations are also quite different.

[0137] In addition, the present invention draws on the research content of the stress concentration factor of the V-notch round bar specimen (used for low-cycle fatigue test or tensile creep test under different stress ratios) in the research. After comparing the calculation results of the stress concentration factor of the V-notch round bar specimen recommended in different standards, the present invention finds that the error of the calculation result of the national recommended standard GB / T 2039-2012 is the largest, which is not suitable as a numerical estimate before the precise calculation of the stress concentration factor at the root of the V-notch. The calculation results of the German standard DIN 743-2-2009 and the international standard ISO 204 are relatively close to the finite element method, and the error is moderate. The error of the finite element method results is the smallest overall, and the consistency of the data results is the best. The conclusion that the finite element method results are the most accurate is obtained. The finite element results can also be curve fitted to further obtain the functional relationship between the stress concentration factor and the notch size, which can be used for parameter estimation before precise calculation.

[0138] The solution of fatigue notch coefficient depends on the solution of stress concentration coefficient. After the stress concentration coefficient is obtained, the Peterson method is currently used to estimate the fatigue notch coefficient, and there are fewer researchers using the Neuber method and relative stress gradient method. The present invention uses the stress concentration coefficient obtained by the aforementioned method for determining the stress concentration coefficient of the threaded connection bolt, and follows the existing fatigue notch coefficient solution method, listing the Neuber method based on average stress, the Peterson method based on point stress, and the Zhao Shaobian method based on relative stress gradient. In addition, the fitting relationship between the stress concentration coefficient and the fatigue notch coefficient is further given, and a numerical solution method that is different from the traditional method is given.

[0139] In general, solving the high-precision stress concentration factor is a key step of the present invention. Based on the obtained stress concentration factor, the present invention adopts several fatigue notch factor solving methods widely used in engineering, and gives the stress concentration factor and fatigue notch factor of arc threads, MJ threads and ordinary metric threads with a nominal diameter of more than 36 mm. After comparing the fatigue life prediction and test results, most of the results are within the 2 times life dispersion band, indicating that the prediction accuracy is high, and also that the stress concentration factor solution accuracy is high. The verification example given in the article uses the Peterson method to solve the fatigue notch factor. The fatigue notch factor result obtained by this method is relatively high, and the life prediction result is conservative, which is in good agreement with the test results.

[0140] An embodiment of a system for determining a stress concentration factor of a threaded connection pair of bolts:

[0141] A system for determining a stress concentration factor of a threaded connection bolt includes a processor, and the processor is used to execute a computer program to implement the steps of a method for determining a stress concentration factor of a threaded connection bolt. The method for determining a stress concentration factor of a threaded connection bolt has been described in detail in an embodiment of a method for determining a stress concentration factor of a threaded connection bolt, and will not be repeated here.

[0142] An embodiment of a system for determining fatigue notch coefficient of a threaded connection pair bolt:

[0143] A system for determining a fatigue notch coefficient of a threaded connection bolt includes a processor, and the processor is used to execute a computer program to implement the steps of a method for determining a fatigue notch coefficient of a threaded connection bolt. The method for determining a fatigue notch coefficient of a threaded connection bolt has been described in detail in an embodiment of a method for determining a fatigue notch coefficient of a threaded connection bolt, and will not be repeated here.

Claims

1. A method for determining the stress concentration factor of a threaded connection bolt, characterized in that: The steps include: An axisymmetric finite element model of the bolt is established using finite element simulation technology, an axial average stress corresponding to the nominal stress at the thread notch is loaded on the end face of the threaded connection pair bolt away from the threaded engagement portion, the size of the finite element grid is gradually reduced, and the finite element grid in the area near the bolt tooth bottom is encrypted to obtain the stress concentration coefficient at the tooth bottom of the threaded connection pair bolt; the condition for stopping the encryption is that the relative error of the stress concentration coefficient obtained by the current encryption and the previous encryption solution is less than or equal to the set value.

2. The method for determining the stress concentration factor of a threaded connection pair bolt according to claim 1, characterized in that: The encryption adopts the influence sphere method.

3. The method for determining the stress concentration factor of a threaded connection pair bolt according to claim 1, characterized in that: The set value is 0.1%.

4. The method for determining the stress concentration factor of a threaded connection pair bolt according to claim 1, characterized in that: The ratio of the geometric characteristic size of the axisymmetric finite element model of the bolt to the notch characteristic size is not less than 10.

5. The method for determining the stress concentration factor of a threaded connection pair bolt according to claim 1, characterized in that: In the process of gradually reducing the finite element mesh size, the finite element mesh size after each step of reduction is γ times the finite element mesh size before the step of reduction, γ∈[0.3,0.6].

6. A method for determining the fatigue notch coefficient of a threaded connection bolt, characterized in that: The steps include: The fatigue notch coefficient at the tooth bottom of the threaded connection auxiliary bolt is obtained by using the Peterson method based on point stress and sensitivity coefficient for the stress concentration coefficient at the tooth bottom of the threaded connection auxiliary bolt, or by using the Neuber method based on average stress for the stress concentration coefficient at the tooth bottom of the threaded connection auxiliary bolt, or by using the Siebel-Stieler method based on relative stress gradient for the stress concentration coefficient at the tooth bottom of the threaded connection auxiliary bolt, or by using the Zhao Shaobian method based on relative stress gradient for the stress concentration coefficient at the tooth bottom of the threaded connection auxiliary bolt; the stress concentration coefficient at the tooth bottom of the threaded connection auxiliary bolt is determined by the method for determining the stress concentration coefficient of the threaded connection auxiliary bolt as described in any one of claims 1 to 5.

7. A system for determining a stress concentration factor of a threaded connection bolt, comprising a processor, characterized in that: The processor is used to execute a computer program to implement the steps of the method for determining the stress concentration factor of a threaded connection pair bolt as claimed in any one of claims 1 to 5.

8. A system for determining fatigue notch coefficient of a threaded connection bolt, comprising a processor, characterized in that: The processor is used to execute a computer program to implement the steps of the method for determining the fatigue notch factor of a threaded connection pair bolt as claimed in claim 6.

Images