Fatigue life prediction method and system for common threaded connection pair bolt

Abstract

The invention relates to a fatigue life prediction method and system for a common threaded connection pair bolt, and belongs to the technical field of fatigue life prediction. The method comprises the following steps that a prediction result for predicting the fatigue life of the bolt is obtained by combining a correction fitting relational expression of the total strain amplitude and the fatigue life of the common threaded connection pair bolt with a fatigue load spectrum and a fatigue cumulative damage rule. According to the method, a fitting relational expression of total strain amplitude and stress amplitude, a hysteresis loop curve expression and a modified Neuber hyperbolic expression are combined to obtain local stress-strain response in combination with a fatigue load spectrum and a fatigue notch coefficient at the root of the bolt; the fitting relational expression of the total strain amplitude and the fatigue life is corrected through the Morrow average stress solved through the local stress strain response to obtain a corrected fitting relational expression, and the corrected fitting relational expression is combined with a fatigue load spectrum and a fatigue accumulated damage rule to achieve high-precision prediction of the fatigue life of the bolt of the common threaded connection pair.

Description

Technical Field

[0001] The invention relates to a fatigue life prediction method and system for common threaded connection pair bolts, belonging to the technical field of fatigue life prediction. Background Art

[0002] In actual engineering, fatigue failure of mechanical parts is the most common form of failure, accounting for 50% to 90% of the total failure (total failure) of mechanical parts. Taking the common threaded connection pairs and arc threaded connection pairs commonly used in large wind turbines as an example, the fatigue failure of bolts in the connection pairs accounts for as much as 80.6% of the total failure of bolts. Common threaded connection pairs include metric threaded connection pairs for general purposes and MJ threaded connection pairs for aerospace, among which common threads are also called standard threads.

[0003] The fatigue life of bolts is usually divided into two stages: fatigue crack initiation life and fatigue crack propagation life. Fatigue life is affected by many factors, such as notch effect, average stress, size effect, surface processing method (or thread processing method), surface strengthening and anti-corrosion coating, etc. Generally, the fatigue life of bolts will be shortened in working environments with high stress levels and large stress amplitudes, while the fatigue life of bolts will be relatively long in working environments with low stress levels and small stress amplitudes; under the same working environment, high-strength bolts made of high-toughness and high-strength materials have relatively longer fatigue life.

[0004] The development of fatigue failure is a gradual process in which fatigue damage gradually accumulates. Usually, fatigue failure will occur after the bolt has worked for a period of time, and there will be no obvious signs before failure occurs. Therefore, fatigue failure occurs suddenly.

[0005] The sudden occurrence of fatigue failure makes it difficult to predict the fatigue fracture of the bolted parts of the bolts that have fatigue failure, and the risk is relatively high. Therefore, sufficient attention must be paid to the fatigue resistance design of the bolts. For the bolt structure design of important connection parts of wind power equipment (such as bolting of towers, bolting of blade hubs, bolting of yaw bearings, etc.), first of all, its quality must be guaranteed to be stable and reliable. During the design process, it is also necessary to reasonably predict the fatigue life of the bolts used in the design, and continuously optimize the feasibility of the design scheme to ensure the safety and reliability of the product.

[0006] However, the metric threaded bolts and MJ threaded bolts currently used in wind power equipment design are based on an infinite life design method, and the fatigue life of the bolts is not reliably predicted. Some bolts are designed for fatigue resistance based on the nominal stress method. However, since it ignores the complex situation of the high stress area at the bottom of the tooth, the basic assumptions of the nominal stress method are inconsistent with the fatigue mechanism of fatigue damage in actual bolts, the fatigue characteristics equivalent relationship between the bolt specimen and the standard test piece is difficult to determine, and a large amount of material fatigue performance data (SN curve (stress-life curve) or pSN curve (survival rate-stress-life curve)) is required. As a result, when predicting the fatigue life of bolts based on the nominal stress method, there are generally problems such as low prediction accuracy, unstable prediction results, reliance on experience, high cost and low efficiency. Compared with the test results, the fatigue life prediction results usually differ by more than 3 times, and sometimes by 10 times or even more than 10 times. Therefore, it is urgent to study and develop a new fatigue life prediction method for ordinary threaded bolts to improve the prediction accuracy and efficiency of fatigue life of ordinary threaded bolts and reduce the cost of fatigue life prediction. Summary of the invention

[0007] The purpose of the present invention is to provide a fatigue life prediction method and system for common threaded connection pair bolts, so as to solve the problem that the fatigue life prediction results of common threaded connection pair bolts obtained based on the existing prediction methods are inaccurate.

[0008] To achieve the above object, the solution of the present invention includes:

[0009] A fatigue life prediction method for a common threaded connection pair bolt of the present invention comprises the following steps:

[0010] The corrected fitting relationship between the total strain amplitude and fatigue life of ordinary threaded connection bolts based on Morrow mean stress correction is combined with the fatigue load spectrum and fatigue cumulative damage law to obtain the prediction result for predicting the fatigue life of ordinary threaded connection bolts.

[0011] The modified fitting relationship is obtained by correcting the fitting relationship between the total strain amplitude and fatigue life of the ordinary threaded connection auxiliary bolts by using the Morrow mean stress solved by the local stress-strain response at the root of the ordinary threaded connection auxiliary bolts;

[0012] The local stress-strain response is obtained by combining the fitting relationship between the total strain amplitude and the stress amplitude of the ordinary threaded connection bolt, the hysteresis loop curve expression and the modified Neuber hyperbola expression, and then combining the fatigue load spectrum and the fatigue notch coefficient at the tooth bottom of the ordinary threaded connection bolt.

[0013] Furthermore, the fitting relationship between the total strain amplitude and fatigue life of the common threaded connection bolts is obtained by least square method by fitting the total strain amplitude and the corresponding fatigue life of the common threaded connection bolts at each strain level in a double logarithmic coordinate system.

[0014] Furthermore, the fitting relationship between the total strain amplitude and stress amplitude of the common threaded connection bolts is obtained by least square method by fitting the total strain amplitude and stress amplitude of the common threaded connection bolts at each strain level in a Cartesian rectangular coordinate system.

[0015] Furthermore, the fatigue notch coefficient at the tooth bottom of the ordinary threaded connection pair bolt is obtained by using the Peterson method based on point stress and sensitivity coefficient to calculate the stress concentration coefficient at the tooth bottom of the ordinary threaded connection pair bolt, or by using the Neuber method based on average stress to calculate the stress concentration coefficient at the tooth bottom of the ordinary threaded connection pair bolt, or by using the Siebel-Stieler method based on relative stress gradient to calculate the stress concentration coefficient at the tooth bottom of the ordinary threaded connection pair bolt, or by using the Zhao Shaobian method based on relative stress gradient to calculate the stress concentration coefficient at the tooth bottom of the ordinary threaded connection pair bolt.

[0016] Furthermore, the stress concentration coefficient at the root of the common threaded connection bolt is obtained by using finite element simulation technology and an axisymmetric bolt model. The axial average stress corresponding to the nominal stress at the thread notch is loaded on the end face of the common threaded connection bolt away from the thread engagement portion, and the size of the finite element mesh is gradually reduced, and the finite element mesh of the area near the root of the bolt is encrypted; 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 0.1%.

[0017] 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].

[0018] A fatigue life prediction system for common threaded connection pair bolts of the present invention comprises a processor, and the processor is used to execute a computer program to implement the steps of the fatigue life prediction method for common threaded connection pair bolts as described above.

[0019] Beneficial effects of the present invention:

[0020] The present invention is a pioneering invention, which provides a fatigue life prediction method for ordinary threaded connection pair bolts. Specifically, a corrected fitting relationship between the total strain amplitude and fatigue life of the ordinary threaded connection pair bolts based on Morrow mean stress correction is combined with a fatigue load spectrum and a fatigue cumulative damage law to obtain a prediction result for predicting the fatigue life of the ordinary threaded connection pair bolts. The present invention obtains a local stress-strain response that can reflect the complex situation of fatigue strength reduction in the high stress area of ​​the tooth bottom of the ordinary threaded connection pair bolt by combining a fitting relationship between the total strain amplitude and the stress amplitude of the ordinary threaded connection pair bolt, a hysteresis loop curve expression of the ordinary threaded connection pair bolt and a modified Neuber hyperbola expression of the ordinary threaded connection pair bolt, and combines the fatigue load spectrum and the fatigue notch coefficient at the tooth bottom that can reflect the complex situation of fatigue strength reduction in the high stress area of ​​the tooth bottom of the ordinary threaded connection pair bolt. The fitting relationship between the total strain amplitude and the fatigue life of the ordinary threaded connection pair bolt is corrected by the Morrow mean stress solved by the local stress-strain response to obtain a corrected fitting relationship between the total strain amplitude and the fatigue life based on the Morrow mean stress correction. The corrected fitting relationship is combined with the fatigue load spectrum and the fatigue cumulative damage law to achieve high-precision prediction of the fatigue life of the ordinary threaded connection pair bolt, and the fatigue life prediction result obtained is accurate and the prediction accuracy is high. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a fatigue life prediction flow chart for common threaded connection bolts;

[0022] Figure 2 is the fitting curve graph of total strain amplitude and cycle reversal number;

[0023] Figure 3 is a fitted curve diagram of the stress amplitude as the cyclic stress and the total strain amplitude as the cyclic strain;

[0024] Figure 4 It is a schematic diagram reflecting the local mesh encryption in the area near the bottom of the metric threaded connection bolt.

[0025] Figure 5 It is a schematic diagram reflecting the local mesh encryption in the area near the bottom of the MJ threaded connection bolt.

[0026] Figure 6 It is the stress distribution cloud diagram of the area near the root of the finite element simulation of the metric thread connection bolt pair;

[0027] Figure 7 This is the stress distribution cloud diagram of the area near the bottom of the MJ threaded connection bolt finite element simulation;

[0028] Figure 8This is a comparison chart between the fatigue life prediction results and test results of ordinary threaded connection bolts. DETAILED DESCRIPTION

[0029] In order to solve the problems in the background technology, the present invention takes into account the complex situation of the high stress area at the bottom of the threaded bolt of an ordinary threaded connection, utilizes correction measures and appropriate damage parameters (Morrow average stress in this scheme), and based on the local stress-strain method, only one material fatigue performance test is performed on the sample to obtain the corresponding fatigue parameters, so that the fatigue life of the ordinary threaded connection bolt can be predicted with high accuracy. The prediction result obtained by this prediction method is accurate and has high prediction accuracy.

[0030] 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.

[0031] An embodiment of a fatigue life prediction method for common threaded connection bolts:

[0032] A fatigue life prediction method for common threaded connection bolts comprises the following steps:

[0033] Through the fitting relationship between the total strain amplitude and stress amplitude of the common threaded connection auxiliary bolt, the hysteresis loop curve expression of the common threaded connection auxiliary bolt and the modified Neuber hyperbola expression of the common threaded connection auxiliary bolt, the local stress-strain response that can reflect the complex situation of fatigue strength reduction in the high stress area of ​​the tooth bottom of the common threaded connection auxiliary bolt is obtained by combining the fatigue load spectrum and the fatigue notch coefficient at the tooth bottom of the common threaded connection auxiliary bolt that can reflect the complex situation of fatigue strength reduction in the high stress area of ​​the tooth bottom of the common threaded connection auxiliary bolt;

[0034] The Morrow mean stress obtained by solving the local stress-strain response that can reflect the complex situation of fatigue strength reduction in the high stress area at the bottom of the common threaded connection bolt is used to correct the fitting relationship between the total strain amplitude and fatigue life of the common threaded connection bolt by the mean stress, and the total strain amplitude and fatigue life correction fitting relationship based on the Morrow mean stress correction of the common threaded connection bolt is obtained; the Morrow mean stress is half of the sum of the maximum stress and the minimum stress in the stress cycle;

[0035] The modified fitting relationship is combined with the fatigue load spectrum and the fatigue cumulative damage law to obtain a prediction result for predicting the fatigue life of ordinary threaded connection bolts, thereby achieving high-precision prediction of the fatigue life of ordinary threaded connection bolts. The obtained prediction result is accurate and has high prediction accuracy.

[0036] Among them, the corrected fitting relationship between the total strain amplitude and fatigue life of ordinary threaded connection bolts based on Morrow mean stress correction is as follows:

[0037]

[0038] In the formula, ε a is the strain amplitude, σ f ′ is the fatigue strength coefficient, σ m is the Morrow mean stress, E is the cyclic elastic modulus, N f is fatigue life (cycle life), ε f ′ is the fatigue ductility coefficient, b is the fatigue strength index, and c is the fatigue ductility index.

[0039] Among them, the Morrow mean stress expression used in the mean stress correction is as follows:

[0040] σ m =(σ max +σ min ) / 2

[0041] In the formula, σ m is the Morrow mean stress, which is half of the sum of the maximum stress and the minimum stress in the stress cycle, σ max is the maximum stress in the stress cycle, σ min is the minimum stress in the stress cycle.

[0042] Specifically, the fitting relationship between the total strain amplitude and fatigue life of the common threaded connection bolts is obtained by least square method by fitting the total strain amplitude and the corresponding fatigue life of the common threaded connection bolts at each strain level in a double logarithmic coordinate system.

[0043] Among them, the fitting relationship between the total strain amplitude and fatigue life of ordinary threaded connection bolts is as follows:

[0044]

[0045] In the formula, Δε t / 2 is the total strain amplitude, σ f ′ is the fitting coefficient (fatigue strength coefficient), E is the cyclic elastic modulus, N f is fatigue life (cycle life), b is fitting index (fatigue strength index), ε f ′ is the fitting coefficient (fatigue ductility coefficient), and c is the fitting index (fatigue ductility index).

[0046] Specifically, the fitting relationship between the total strain amplitude and stress amplitude of the common threaded connection bolts is obtained by least square method by fitting the total strain amplitude and stress amplitude of the common threaded connection bolts at each strain level in a Cartesian rectangular coordinate system (plane rectangular coordinate system).

[0047] Among them, the fitting relationship between the total strain amplitude and stress amplitude of the ordinary threaded connection bolt is as follows:

[0048]

[0049] In the formula, Δε t / 2 is the total strain amplitude, Δσ / 2 is the stress amplitude, E is the cyclic elastic modulus, K′ is the fitting coefficient (cyclic strength coefficient), and n′ is the fitting exponent (cyclic strain hardening exponent).

[0050] Specifically, the fatigue notch coefficient at the tooth bottom of the ordinary threaded connection pair bolt is obtained by using the Peterson method based on point stress and sensitivity coefficient to calculate the stress concentration coefficient at the tooth bottom of the ordinary threaded connection pair bolt, or by using the Neuber method based on average stress to calculate the stress concentration coefficient at the tooth bottom of the ordinary threaded connection pair bolt, or by using the Siebel-Stieler method based on relative stress gradient to calculate the stress concentration coefficient at the tooth bottom of the ordinary threaded connection pair bolt, or by using the Zhao Shaobian method based on relative stress gradient to calculate the stress concentration coefficient at the tooth bottom of the ordinary threaded connection pair bolt.

[0051] Specifically, the stress concentration coefficient at the bottom of the bolt teeth of the ordinary threaded connection pair is obtained by utilizing finite element simulation technology and an axisymmetric bolt model. The load is converted 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 on the end face of the ordinary threaded connection pair bolt away from the thread engagement portion. The size of the finite element mesh is gradually reduced, and the finite element mesh of the area near the bottom of the bolt teeth is gradually encrypted. 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 0.1%.

[0052] The number of times the finite element mesh is encrypted near the bolt tooth bottom varies with the bolt structure. The mesh is encrypted only when the relative error of the stress concentration factor obtained from the two encrypted solutions is ≤0.1%.

[0053] 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].

[0054] Specifically, the local stress-strain response at the root of the bolt of the ordinary threaded connection pair is obtained by the random load treatment method of the bolt, and the number of complete cycles and half cycles in the load spectrum after random load treatment and the corresponding cyclic response characteristics are obtained. The load spectrum after random load treatment is used, and the modified Neuber method is used to combine the cyclic stress-strain curve and the hysteresis loop curve to obtain it.

[0055] Among them, the local stress-strain response at the bottom of the bolt teeth of the ordinary threaded connection pair is determined by the following expression:

[0056]

[0057] In the formula, σ i is the local stress response of the notch corresponding to the i-th data point in the load spectrum, ε i is the local strain response of the notch corresponding to the i-th data point in the load spectrum, σ i+1 is the local stress response of the notch corresponding to the i+1th data point in the load spectrum, ε i+1 is the local strain response of the notch corresponding to the i+1th data point in the load spectrum, σ i and ε i is the local response of the notch corresponding to the i-th data point in the load spectrum, σ i+1 and ε i+1 is the local response of the notch corresponding to the i+1th data point in the load spectrum; the local response includes stress and strain.

[0058] Specifically, a strain fatigue test is performed on a smooth small specimen by a strain control method to obtain the total strain amplitude and corresponding fatigue life at each strain level, and the total strain amplitude and stress amplitude at each strain level.

[0059] As another embodiment, a fatigue life prediction method for a common threaded connection bolt pair is provided. Figure 1 , including the following steps:

[0060] (1) Obtain strain data.

[0061] The strain data is obtained through strain fatigue test records. Specifically, the strain fatigue test (axial constant amplitude low cycle fatigue test of metal materials) is carried out on a smooth small specimen through the strain control method. At each strain level (strain level or strain amplitude level), the cycle life (fatigue test life) N corresponding to the strain amplitude is obtained. f Valid data points, at the same time, the corresponding total strain amplitude Δε at each strain amplitude level is also obtained t / 2, plastic strain amplitude Δε p / 2, elastic strain amplitude Δε e / 2 and stress amplitude Δσ / 2.

[0062] The strain data include the corresponding total strain amplitude Δε at different strain levels: t / 2, plastic strain amplitude Δε p / 2, elastic strain amplitude Δε e / 2 and stress amplitude Δσ / 2, and the corresponding cycle life (fatigue test life) N corresponding to the strain amplitude f Valid data points.

[0063] (2) Obtain the fitting relationship between total strain amplitude and fatigue life.

[0064] The total strain amplitude Δε t / 2, elastic strain amplitude Δε e / 2, plastic strain amplitude Δε p / 2 respectively corresponds to the cycle life N f The curve is plotted in a double logarithmic coordinate system to obtain the total strain life curve ( Figure 1 The total strain life curve is shown in the figure), and the total strain life equation (the fitting relationship between the total strain amplitude and the fatigue life) is fitted based on the total strain life curve. Figure 1 is the Manson-Coffin equation).

[0065] Specifically, the least square method is used, and the total strain amplitude Δε at each strain level is taken in the double logarithmic coordinate system. t / 2 and corresponding cycle life N f The effective data points were fitted with a power function in a double logarithmic coordinate system to obtain the fitting relationship between the total strain amplitude and the corresponding cycle life (fatigue life).

[0066] (3) Obtain the fitting relationship between the total strain amplitude and the stress amplitude.

[0067] The least square method is used to calculate the total strain amplitude Δε at each strain level in the Cartesian rectangular coordinate system. t / 2 and the stress amplitude Δσ / 2 are fitted with a power function to obtain the fitting relationship between the total strain amplitude and the stress amplitude.

[0068] (4) Obtain the corrected fitting relationship between total strain amplitude and fatigue life based on Morrow mean stress correction.

[0069] Based on the total strain-life equation, considering the influence of mean stress, the total strain-life equation is corrected by the Morrow mean stress obtained by the local stress-strain response at the tooth bottom, and the mean stress-corrected total strain-life equation is obtained (the corrected fitting relationship between the total strain amplitude and fatigue life based on the Morrow mean stress correction).

[0070] Among them, the Morrow mean stress expression used in the mean stress correction is as follows:

[0071] σ m =(σ max +σ min ) / 2

[0072] In the formula, σ m is the Morrow mean stress, which is half of the sum of the maximum stress and the minimum stress in the stress cycle, σ max is the maximum stress, σmin is the minimum stress.

[0073] The calculation formula of the modified total strain life equation is as follows:

[0074]

[0075] In the formula, ε a is the strain amplitude, σ f ′ is the fatigue strength coefficient, σ m is the average stress, E is the cyclic elastic modulus, N f is fatigue life (cycle life), ε f ′ is the fatigue ductility coefficient, b is the fatigue strength index, and c is the fatigue ductility index.

[0076] (5) The stress concentration factor K at the bottom of the bolt teeth of the common threaded connection pair is obtained through finite element simulation analysis with high solution accuracy and convergence results. t .

[0077] Specifically, through finite element simulation technology, an axisymmetric bolt model is adopted, and 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 ordinary threaded connection pair bolt (that is, the end face of the ordinary threaded connection pair bolt away from the thread engagement part), the finite element grid size is gradually reduced, and the finite element grid near the bolt tooth bottom is encrypted multiple times to obtain a stress concentration factor (stress concentration factor) at the tooth bottom of the ordinary threaded connection pair bolt with high accuracy and convergence.

[0078] Among them, the expression of the stress concentration factor at the bottom of the bolt teeth of the ordinary threaded connection pair is as follows:

[0079]

[0080] In the formula, K t is the stress concentration factor at the bottom of the bolt teeth of the common threaded connection, σ max is the maximum local stress at the thread notch, σ n It is the nominal stress or average stress at the root of the thread notch.

[0081] Among them, the thread gap refers to the area range of the entire space of the screw tooth gap; the thread gap root refers to the vertex of the arc at the bottom of the screw tooth gap, which is a specific position.

[0082] The condition for stopping encryption is that the relative error of the stress concentration factor obtained by the current encryption and the previous encryption is less than or equal to 0.1%.

[0083] 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].

[0084] (6) The fatigue notch factor K at the bottom of the bolt of a common threaded connection pair is obtained by the Neuber method based on average stress, the Peterson method based on point stress and sensitivity method (sensitivity coefficient), the Siebel-Stieler method based on stress gradient, or the Zhao Shaobian method based on relative stress gradient. f (fatigue notch factor).

[0085] (7) Through the random load treatment method of the bolt, the number of complete cycles and half cycles in the load spectrum after random load treatment and the corresponding cyclic response characteristics are obtained. Using the load spectrum after random load treatment, the modified Neuber method is used to combine the cyclic stress-strain curve and the hysteresis loop curve to obtain the local stress-strain response at the root of the ordinary threaded bolt of the ordinary threaded connection pair bolt.

[0086] (8) Finally, the fitting relationship between the total strain amplitude and fatigue life of ordinary threaded connection bolts, the fitting relationship between the total strain amplitude and stress amplitude of ordinary threaded connection bolts, the hysteresis loop curve expression, the modified Neuber hyperbola expression, the fatigue notch coefficient at the tooth root of ordinary threaded connection bolts, the local stress-strain response at the tooth root of ordinary threaded connection bolts and the modified fitting relationship between the total strain amplitude and fatigue life of ordinary threaded connection bolts based on Morrow average stress correction are combined as a nonlinear equation group. The nonlinear equation group is solved and combined with the fatigue load spectrum and the fatigue cumulative damage law to obtain the predicted fatigue life of ordinary threaded connection bolts.

[0087] In step (1), the cycle life of the sample is less than 10 5 The strain control was performed using an extensometer with a test frequency of 0.25 Hz to 2.5 Hz.

[0088] In step (1), during the fatigue test of the sample using the strain control method, 5 to 7 strain levels are selected, and the gradient of adjacent strain levels is 0.01% to 0.3%; the total strain amplitude (total strain amplitude) Δε obtained at each strain level t / 2 and the corresponding cycle life N f The number of valid data points is 2 to 4.

[0089] In step (5), the local mesh size of the area near the bolt tooth bottom in the subsequent simulation is reduced to 0.3 to 0.6 times the mesh size of the previous simulation, until the relative error of the stress concentration factor obtained from the two simulations is no more than 0.1%, and it is considered that a converged solution with high accuracy can be obtained.

[0090] In step (5), the converged stress concentration factor K t The expression is as follows:

[0091]

[0092] In the formula, K t is the stress concentration factor at the bottom of the bolt teeth of the common threaded connection, σ max is the maximum local stress at the thread notch, σ n It is the nominal stress or average stress at the root of the thread notch.

[0093] In step (6), the fatigue notch factor (the fatigue notch factor at the bottom of the bolt of the ordinary threaded connection) is defined as:

[0094]

[0095] In the formula, K f is the fatigue notch coefficient at the bottom of the bolt teeth of the common threaded connection, S e is the fatigue strength of the smooth specimen (smooth specimen), S N is the fatigue strength of the notched specimen.

[0096] Specifically, the fatigue notch factor K f Calculated by any of the following formulas ① to ④:

[0097] ① The fatigue notch coefficient K at the bottom of the common threaded connection bolt obtained by the Peterson method f The calculation formula is as follows:

[0098]

[0099] In the formula, K f is the fatigue notch coefficient at the bottom of the bolt of the common threaded connection, q is the sensitivity coefficient, 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).

[0100] Among them, the Peterson parameter of the bolts made of tempered steel is 0.0635mm, and the Peterson parameter of the bolts made of normalized steel is 0.254mm.

[0101] For medium and high strength steel (limit stress u>560MPa (megapascals) for bolts, the approximate calculation formula for α is as follows:

[0102]

[0103] Where α is the Peterson parameter, σ b For tensile strength.

[0104] ② The fatigue notch coefficient K at the bottom of the bolt of the common threaded connection obtained by the Neuber method f The calculation formula is as follows:

[0105]

[0106] In the formula, K f is the fatigue notch coefficient at the bottom of the bolt teeth of the common threaded connection pair; 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.

[0107] ③ The fatigue notch coefficient K at the bottom of the common threaded connection bolt obtained by the Siebel-Stieler method f The calculation formula is as follows:

[0108]

[0109] In the formula, K f K is the fatigue notch factor at the bottom of the bolt teeth of the common threaded connection. t is the stress concentration factor; S q is a material constant, a function of the yield limit, defined as S q =f(σ s ), σ s is the yield limit; χ is the relative stress gradient.

[0110] ④ The fatigue notch coefficient K at the bottom of the bolt of the common threaded connection obtained by Zhao Shaobian method f The calculation formula is as follows:

[0111]

[0112] In the formula, K f K is the fatigue notch factor at the bottom of the bolt teeth of the common threaded connection. 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.

[0113] For example: when the steel is in the hot-rolled state and has not been heat treated, A is taken as 0.336 and b is taken as 0.345.

[0114] The raw materials used for high-strength bolts are generally taken as 0.290 for A and 0.152 for b after quenching and tempering heat treatment; if they are normalized heat treated, A is taken as 0.423 and b is taken as 0.279.

[0115] In step (7), the random load processing method includes a cycle counting method and a power spectrum method.

[0116] Preferably, the random load processing method uses the rain flow counting method in the cycle counting method, which can be easily implemented through a computer program when the amount of random load data is large.

[0117] In step (7), the steps of obtaining the local stress-strain response at the bottom of the common thread by combining the cyclic stress-strain curve and the hysteresis loop curve with the modified Neuber method are as follows:

[0118] Step I: Given the nominal stress S1 or nominal strain e1, obtain the corresponding e1 or S1 from the cyclic stress-strain curve.

[0119] Specifically, the modified Neuber curve and the cyclic stress-strain curve (σ a -ε a Curve), the following relationship is used to obtain the nonlinear equation system:

[0120]

[0121] Solve the nonlinear equations to obtain the local gap σ1 and ε1.

[0122] e1 or S1 can also be obtained from the cyclic stress-strain curve.

[0123] Step II: After the load is reversed, if ΔS or Δe is known, the corresponding Δe or ΔS can be obtained from the hysteresis loop curve.

[0124] Specifically, the nonlinear equations are obtained by combining the modified Neuber curve and the hysteresis loop curve (Δσ-Δε curve) using the following relationship:

[0125]

[0126] Solve the nonlinear equations to obtain the local Δσ and Δε of the notch.

[0127] Step III: After the subsequent load reversal, the local response of the notch corresponding to the i-th data point in the load spectrum is σ i and ε i , the local response of the notch corresponding to the i+1th data point in the load spectrum is σi+1 and ε i+1 , the nonlinear equations are obtained by combining the following relations:

[0128]

[0129] Solve the nonlinear equations to obtain the notch local response σ corresponding to the i+1th data point in the load spectrum i+1 and ε i+1 .

[0130] Step IV: Determine the average stress based on the local stress-strain response. The expression for the average stress (Morrow average stress) is as follows:

[0131] σ m =(σ i +σ i+1 ) / 2

[0132] In the formula, σ m is the mean stress, σ i is the local response of the notch corresponding to the i-th data point in the load spectrum, σ i+1 is the local response of the notch corresponding to the i+1th data point in the load spectrum.

[0133] In step (7), the expression of the cyclic stress-strain curve is as follows:

[0134]

[0135] In the formula, ε a is the strain amplitude, σ a is the stress amplitude, E is the cyclic elastic modulus, K′ is the cyclic strength coefficient, and n′ is the cyclic strain hardening exponent.

[0136] In step (7), the expression of the hysteresis loop curve is as follows:

[0137]

[0138] Where Δε is the local strain range of the notch, Δσ is the local stress range of the notch, E is the cyclic elastic modulus, K′ is the cyclic strength coefficient, and n′ is the cyclic strain hardening exponent.

[0139] In step (8), the fatigue cumulative damage law is based on the modified linear cumulative damage theory, that is, the modified Palmgren-Miner cumulative damage theory, which is expressed by the following formula:

[0140]

[0141] Where n i is the number of actual load cycles, N i ni The failure cycle life under the stress level, a is a constant.

[0142] A large number of studies have shown that under constant amplitude load, a is often taken as 1, and under random load, when a is taken as 0.7, the fatigue life estimation result is safer than Miner's law, and the fatigue life estimation accuracy is generally improved compared with Miner's law.

[0143] The present invention belongs to the field of fatigue life prediction of bolt structures, and provides a fatigue life prediction method for ordinary threaded connection bolts, which can predict the fatigue life of ordinary threaded high-strength bolts of larger specifications used in the wind power field. The method is based on a modified local stress-strain method, and adopts a method combining material testing and structural simulation analysis. Considering the complex situation of the high stress zone at the bottom of the ordinary threaded high-strength bolt, by taking certain correction measures, selecting appropriate damage parameters, only performing a material fatigue performance test on the sample once to obtain the corresponding fatigue parameters, the fatigue life prediction of the bolt with high accuracy is realized, and the prediction method has high prediction accuracy, wide application range, and greatly reduced cost. The parameters in the prediction method have realistic physical meanings, and the prediction results have certain scientificity, accuracy and effectiveness. The present invention only needs to use a small number of samples to perform low-cycle fatigue tests to obtain fatigue parameters. Compared with the existing traditional (classical) bolt life prediction method based on the nominal stress method and requiring a large number of bolt fatigue tests to obtain SN curves, the economic cost and time cost of the test are greatly reduced, the process is easy to implement, the cost is low, and the accuracy of the fatigue life prediction results is also greatly improved, which can effectively solve the problem of inaccurate fatigue life prediction results of bolt components. In practical applications, the fatigue life prediction results of the bolts of ordinary threaded connection pairs are usually taken as the fatigue life prediction results of ordinary threaded connection pairs to achieve the prediction of the fatigue life of ordinary threaded connection pairs.

[0144] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0145] The present invention obtains fatigue parameters through material strain fatigue test, and uses finite element simulation technology to perform systematic simulation analysis on the bolt structure, thereby realizing fatigue life prediction of common threaded connection pair bolts under large-size service conditions.

[0146] The present invention has good prediction accuracy, especially for common threaded connection bolts of 36 mm and above. The prediction accuracy of the fatigue life of the prediction method of the present invention is much better than the prediction accuracy of the fatigue life based on the SN curve.

[0147] The present invention has good universality and is applicable to bolts with other thread forms that have high loads and large local deformations.

[0148] The present invention is based on material strain fatigue test, finite element simulation technology and local stress-strain solution, and can obtain life prediction of large-sized in-service bolts of engineering equipment. The method is simple, accurate and efficient, and can save labor costs, test costs and test time to a great extent.

[0149] The prediction results of the prediction method of the present invention can be used to guide the operation and maintenance monitoring and detection of bolts, improve the bearing capacity and service safety of bolt fasteners, and have important scientific value and engineering significance for optimizing bolt parameters and preventing fatigue fracture.

[0150] To facilitate understanding, here is an example:

[0151] Fatigue life prediction method for common threaded connection bolts, such as Figure 1 As shown, the following steps are included:

[0152] (1) A strain fatigue test (axial constant amplitude low cycle fatigue test of metal materials) is performed on a smooth small specimen by a strain control method to obtain the cycle life (fatigue test life) N corresponding to the strain amplitude at each strain level (strain level). f Valid data points, at the same time, the corresponding total strain amplitude Δε at each strain amplitude level is also obtained t / 2, plastic strain amplitude Δε p / 2, elastic strain amplitude Δε e / 2 and stress amplitude Δσ / 2.

[0153] According to the specimen requirements of GB / T 15248-2008 "Method for axial constant amplitude low cycle fatigue test of metallic materials", the specimens with equal cross-section were processed, and the surface roughness of the specimen test section met the requirements of the national standard. The fatigue test was completed on the MTS hydraulic fatigue tester, and the strain levels were 0.4%, 0.5%, 0.55%, 0.7%, 0.8%, 0.9% and 0.12%, respectively. The cycle life N corresponding to the strain amplitude was obtained at each strain level. f The number of valid data points is 2. The test frequencies are 1.25Hz, 1.00Hz, 0.909Hz, 0.714Hz, 0.625Hz, 0.556Hz and 0.417Hz respectively. The test ends when the cyclic stress decreases by 20% to 30%.

[0154] (2) The total strain amplitude Δε t / 2, elastic strain amplitude Δε e / 2, plastic strain amplitude Δε p / 2 respectively corresponds to the cycle life N f The curve is plotted in a double logarithmic coordinate system to obtain the total strain life curve ( Figure 1 (where is the strain-life curve), such as Figure 2 shown.

[0155] Based on the total strain-life curve, the total strain-life equation (the fitting relationship between the total strain amplitude and the fatigue life, namely Figure 1 The Manson-Coffin equation in the paper is used to solve the problem of the total strain amplitude Δε at each strain level. t / 2 and corresponding cycle life N f The power function is fitted in the double logarithmic coordinate system to obtain the following total strain amplitude Δε t / 2 and corresponding cycle life N f The fitting relationship between:

[0156]

[0157] In the formula, Δε t / 2 is the total strain amplitude, σ f ′ is the fitting coefficient (fatigue strength coefficient), E is the cyclic elastic modulus, N f is fatigue life (cycle life), b is fitting index (fatigue strength index), ε f ′ is the fitting coefficient (fatigue ductility coefficient), and c is the fitting index (fatigue ductility index).

[0158] Among them, the fatigue strength coefficient σ f ′=1.33772GPa (gigaPa), fatigue ductility coefficient ε f ′=0.30835, fatigue strength index b=-0.07040, fatigue ductility index c=-0.55703, cyclic elastic modulus E=194530MPa (megapascals).

[0159] (3) The total strain amplitude Δε t / 2 and stress amplitude Δσ / 2 are plotted in a rectangular coordinate system to obtain the fitting relationship between the total strain amplitude and the stress amplitude ( Figure 1 (where ) is the cyclic stress-strain curve, such as Figure 3 shown.

[0160] The least square method is used to calculate the total strain amplitude Δε at each strain level. t / 2 and stress amplitude Δσ / 2 are fitted by power function, and the fitting relationship between the total strain amplitude and stress amplitude is obtained as follows:

[0161]

[0162] In the formula, Δε t / 2 is the total strain amplitude, Δσ / 2 is the stress amplitude, E is the cyclic elastic modulus, K′ is the fitting coefficient (cyclic strength coefficient), and n′ is the fitting exponent (cyclic strain hardening exponent).

[0163] Among them, the fitting coefficient (cyclic strength coefficient) K′=1343.231 MPa, the fitting index (cyclic strain hardening index) n′=0.10235, and the cyclic elastic modulus E=194530 MPa.

[0164] (4) Based on the total strain life equation, the average stress obtained by the local stress-strain response at the tooth bottom is used to correct the total strain life equation, and the average stress-corrected total strain life equation is obtained.

[0165] Among them, the average stress obtained by local stress-strain response is σ m , the expression of mean stress is as follows:

[0166] σ m =(σ max +σ min ) / 2

[0167] In the formula, σ m is the average stress (in MPa), which is half of the sum of the maximum stress and the minimum stress in the stress cycle, σ max is the maximum local stress at the thread notch, σ min is the minimum local stress at the thread notch.

[0168] The calculation formula of the total strain life equation after mean stress correction is as follows:

[0169]

[0170] In the formula, ε a is the strain amplitude, σ m is the average stress, E is the cyclic elastic modulus, N f is the fatigue life (cycle life).

[0171] (5) Through finite element simulation technology, an axisymmetric bolt model is used to convert loads through the conversion relationship between distal load and nominal stress. The axial average stress corresponding to the nominal stress at the thread notch is loaded on the end face of the ordinary threaded connection bolt away from the thread engagement part. The finite element mesh size is gradually reduced, and the finite element mesh near the bolt tooth bottom is repeatedly encrypted. For the mesh encryption area of ​​the metric threaded bolt, Figure 4 As shown in the figure, the mesh encryption area of ​​the MJ threaded bolt is as follows Figure 5 As shown in the figure, multiple simulations are performed until the relative error between the two results is less than 0.1%. At this time, the local stress distribution of the metric thread bolt root area converges as shown in the figure. Figure 6 As shown in the figure, the local stress distribution of the MJ thread bolt tooth bottom area converges as shown in the figure. Figure 7 As shown, the stress concentration factor K at the bottom of the bolt teeth of the common threaded connection pair with high accuracy and convergence can be calculated. t .

[0172] The calculation example of ordinary threaded connection bolt pair was performed with an initial finite element mesh size of 0.4 mm, and five encryptions were performed. Each time the finite element mesh size was reduced to 0.5 times the previous finite element mesh size, the mesh size was 0.0125 mm when the result converged.

[0173] Through the analysis of finite element simulation results, when the nominal diameter of the ordinary threaded connection bolt is 36mm, the stress concentration factor K at the bottom of the general purpose metric thread is t =4.69, stress concentration factor K at the bottom of MJ thread for aerospace t =4.30.

[0174] (6) The fatigue notch coefficient K at the bottom of the bolt teeth of a common threaded connection pair is obtained by using the Peterson method based on point stress and sensitivity coefficient, the Neuber method based on average stress, the Siebel-Stieler method based on relative stress gradient, or the Zhao Shaobian method based on relative stress gradient. f .

[0175] Using the Peterson method, when the nominal diameter of the ordinary threaded connection bolt is 36mm, the fatigue notch coefficient K at the bottom of the general purpose metric thread f =4.27, fatigue notch factor K at the bottom of MJ thread for aerospace f =3.98.

[0176] Using the Neuber method, when the nominal diameter of the ordinary threaded connection bolt is 36 mm, the fatigue notch coefficient K at the bottom of the general purpose metric thread is f =3.99, fatigue notch factor K at the bottom of MJ thread for aerospace f =3.72.

[0177] According to Zhao Shaobian's method, when the nominal diameter of the ordinary threaded connection bolt is 36 mm, the fatigue notch coefficient K at the bottom of the general-purpose metric thread is f =3.83, fatigue notch factor K at the bottom of MJ thread for aerospace f =3.53.

[0178] (7) The number of complete cycles and half cycles and the corresponding cyclic response characteristics are obtained through the random load treatment method of the bolt. The local stress-strain response at the root of the bolt teeth of the ordinary threaded connection is obtained by using the load spectrum after random load treatment and the modified Neuber method, combined with the cyclic stress-strain curve and the hysteresis loop curve.

[0179] Taking the fatigue test of metric threaded high-strength bolts for general use with a nominal diameter of 36mm as an example, according to the requirements of GB / T13682-92 "Axial load fatigue test method for threaded fasteners", the lifting method is used to measure the conditional fatigue limit of the bolts. Bolt specimens are randomly selected from products with qualified dimensions and mechanical properties. After cleaning, the mating surfaces are coated with lubricating oil and then installed on a high-frequency fatigue testing machine for fatigue testing. It first undergoes a 1 / 4 cycle and a full cycle, and then the cycle is repeated until the bolt is fatigue fractured. The solution steps are as follows:

[0180] Step I: Given the nominal stress S1=523MPa, calculate the local notch σ1=914.3695MPa and ε1=0.028038.

[0181] Step II: Load reversal, ΔS known 1-2 =146MPa, and the local notch Δσ=623.2970MPa and Δε=0.0032054 are obtained.

[0182] Step III: Calculate the local notch σ2=291.0725 and ε2=0.024833.

[0183] Step IV: Obtain the mean stress σ m =602.7210MPa.

[0184] The above formulas are combined to obtain a nonlinear equation group, and the predicted fatigue life of ordinary threaded connection bolts is obtained by solving them as follows:

[0185] S1=523MPa,ΔS 1-2 = Bolt fatigue life at 146MPa N f is 41.5689×10 4 (The upper and lower limits of its 2-time lifespan band are 83.1378×10 4 and 20.7845×10 4 ), the corresponding bolt fatigue test results are 42.2600×10 4 and 49.3200×10 4 , the results are all located in the 2 times lifetime dispersion band.

[0186] Since there are a lot of fatigue life prediction results, only some of the results are listed here as examples, and the rest of the prediction results are not listed one by one. Figure 8 The fatigue life prediction results and test results of ordinary threaded connection bolts with a nominal diameter of 36 mm are compared in the figure. The fatigue life prediction results are evenly distributed on both sides of the middle line. All fatigue life prediction results are distributed within the 3 times life dispersion zone, among which most of the fatigue life data are distributed within the 2 times life dispersion zone. Figure 8 The triangular thread in the specification is a type of metric thread. M36 refers to a metric threaded connection bolt with a nominal diameter of 36 mm, and MJ36 refers to an MJ threaded connection bolt with a nominal diameter of 36 mm. Figure 8 One of the MJ threaded connection bolts has a corrosion resistant coating of Decker.

[0187] The above examples further prove that the bolt fatigue life prediction method proposed in the present invention has high accuracy, and the results are effective, scientific and reasonable.

[0188] An embodiment of a fatigue life prediction system for common threaded connection bolts:

[0189] A fatigue life prediction system for common threaded connection bolts includes a processor, the processor is used to execute a computer program to implement the steps of a fatigue life prediction method for common threaded connection bolts. The fatigue life prediction method for common threaded connection bolts has been described in detail in an embodiment of a fatigue life prediction method for common threaded connection bolts, and will not be repeated here.

Claims

1. A fatigue life prediction method for common threaded connection bolts, characterized in that: The steps include: The prediction result for predicting the fatigue life of the common threaded connection bolts is obtained by combining the corrected fitting relationship between the total strain amplitude and fatigue life of the common threaded connection bolts based on the Morrow mean stress correction with the fatigue load spectrum and the fatigue cumulative damage law; The modified fitting relationship is obtained by correcting the fitting relationship between the total strain amplitude and fatigue life of the ordinary threaded connection auxiliary bolts by using the Morrow mean stress solved by the local stress-strain response at the root of the ordinary threaded connection auxiliary bolts; The local stress-strain response is obtained by combining the fitting relationship between the total strain amplitude and the stress amplitude, the hysteresis loop curve expression and the modified Neuber hyperbola expression of the common threaded connection bolt, and then combining the fatigue load spectrum and the fatigue notch coefficient at the tooth bottom of the common threaded connection bolt.

2. The fatigue life prediction method for common threaded connection bolts according to claim 1, characterized in that: The fitting relationship between the total strain amplitude and fatigue life of the common threaded connection bolts is obtained by least square method by fitting a power function in a double logarithmic coordinate system using the total strain amplitude and corresponding fatigue life of the common threaded connection bolts at each strain level.

3. The fatigue life prediction method for common threaded connection bolts according to claim 1, characterized in that: The fitting relationship between the total strain amplitude and stress amplitude of the common threaded connection bolt is obtained by least square method by fitting the total strain amplitude and stress amplitude of the common threaded connection bolt at each strain level in a Cartesian rectangular coordinate system through a power function.

4. The fatigue life prediction method for common threaded connection bolts according to claim 1, characterized in that: The fatigue notch coefficient at the tooth bottom of the ordinary threaded connection pair 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 ordinary threaded connection pair bolt, or by using the Neuber method based on average stress for the stress concentration coefficient at the tooth bottom of the ordinary threaded connection pair bolt, or by using the Siebel-Stieler method based on relative stress gradient for the stress concentration coefficient at the tooth bottom of the ordinary threaded connection pair bolt, or by using the Zhao Shaobian method based on relative stress gradient for the stress concentration coefficient at the tooth bottom of the ordinary threaded connection pair bolt.

5. The fatigue life prediction method for common threaded connection bolts according to claim 4, characterized in that: The stress concentration coefficient at the root of the common threaded connection pair bolt is obtained by using finite element simulation technology and an axisymmetric bolt model, loading an axial average stress corresponding to the nominal stress at the thread notch at the end face of the common threaded connection pair bolt away from the thread engagement portion, gradually reducing the size of the finite element grid, and encrypting the finite element grid of the area near the root of the 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 0.1%.

6. The fatigue life prediction method for common threaded connection bolts according to claim 5, 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].

7. A fatigue life prediction system for common threaded connection bolts, comprising a processor, characterized in that: The processor is used to execute a computer program to implement the steps of the fatigue life prediction method for a common threaded connection pair bolt as claimed in any one of claims 1 to 6.

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