Weld vibration fatigue life assessment method based on simplified modal structure stress method

Abstract

The present application relates to the technical field of weld vibration fatigue life evaluation, and particularly relates to a weld vibration fatigue life evaluation method based on a simplified modal structure stress method. Specifically as follows: a simplified finite element model of a welded structure not containing weld details is established, and the structural modal of the simplified finite element model is calculated; the modal coordinate time history is obtained according to the structural modal, and the modal structural stress at the weld toe is calculated through linear difference; the modal coordinate time history and the modal structural stress at the weld toe are superimposed to obtain the structural stress time history at the weld toe; the structural stress change range and the cycle number are obtained through rain flow counting statistics according to the structural stress time history at the weld toe; the equivalent structural stress is calculated; and the damage and fatigue evaluation results of the weld are obtained by using the main S-N curve method. The modal structural stress at the weld toe is calculated through linear difference, the work load of establishing the finite element model can be greatly simplified without establishing the weld details, the modeling complexity is reduced, and the modeling efficiency is improved.

Description

Technical Field

[0001] This invention relates to the field of weld vibration fatigue life assessment technology, and in particular to a weld vibration fatigue life assessment method based on the simplified modal structural stress method. Background Technology

[0002] To achieve rapid vibration fatigue assessment of welded structures under complex load conditions, the application of the master SN curve method necessitates the establishment of finite element models containing weld details. For example, patent CN104200122B discloses a method for predicting the random vibration fatigue life of complex welded structures. Since rail vehicle structures are generally large, and the mesh size is typically large to reduce computational load during structural analysis model creation, if the structural stress method is used to assess weld life, the finite element model needs to be modified to include local weld detail models, resulting in a very tedious model modification workload. A search revealed patent CN116796590A, which discloses a dynamic structural stress calculation method for the fatigue life of welded structures. While it establishes finite element models of key components in the initial stage, subsequent calculations require the creation of refined local modules, which also involves a significant amount of refinement work. Therefore, there is an urgent need to provide a weld fatigue assessment method that reduces the workload of finite element modeling to address these technical problems. Summary of the Invention

[0003] The purpose of this invention is to provide a method for assessing the vibration fatigue life of welds based on the simplified modal structural stress method, thereby solving the above-mentioned technical problems.

[0004] To achieve the above objectives, this invention provides a method for assessing the vibration fatigue life of welds based on the simplified modal stress method, the specific steps of which are as follows:

[0005] Step S1: Establish a simplified finite element model of the welded structure that does not include weld details, and calculate the structural modes of the simplified finite element model;

[0006] Step S2: Obtain the modal coordinate time history based on the structural modes, and calculate the modal structural stress at the weld toe using linear interpolation;

[0007] Step S3: Superimpose the modal coordinate time history and the modal structural stress at the weld toe to obtain the structural stress time history at the weld toe;

[0008] Step S4: Based on the rainflow count statistics of the structural stress time history at the weld toe, obtain the range of structural stress variation and the number of cycles;

[0009] Step S5: Calculate the equivalent structural stress;

[0010] Step S6: Use the main SN curve method to calculate the damage and fatigue assessment results of the weld.

[0011] Preferably, in step S1, the simplified structural dynamics equations of the finite element model are as follows:

[0012]

[0013] Where [M], [C], and [K] are the mass matrix, damping matrix, and stiffness matrix, respectively, and {u(t)} and {f(t)} are the displacement vector and load vector, respectively; and These are the acceleration vector and the velocity vector, respectively, where t is the time point;

[0014] The modal order of the structure is determined based on the frequency range of the external load, and the normalized modal matrix of the mass matrix is ​​[Φ]. n×m , [Φ] n×m =[φ1 … φ i … φ m ], φ i Let be an n-dimensional modal shape vector, i∈[1,m], where n is the number of degrees of freedom of the simplified finite element model and m is the modal order.

[0015] Preferably, in step S2, the modal coordinate time history is obtained based on the structural modes as follows:

[0016] Step S21a: Convert the structural dynamics equations into modal coordinate form. The conversion formula is as follows:

[0017]

[0018] Where {ξ(t)} is the modal coordinate time history variable, and These are the first and second derivatives of {ξ(t)}, respectively;

[0019] Step S22a: Solve the above equation using Newmark's successive integration method or Duhamel integration. The result is the modal coordinates ξ. j (t)(j=1,2,…R), ξ j (t) represents the modal coordinates at time t under the j-th modal order, and R represents the total number of modal orders selected.

[0020] Preferably, in step S2, the structural modes of the simplified finite element model are calculated as follows:

[0021] Step S21b: Calculate the nodal forces of the two rows of nodes closest to the weld toe for each modal vector;

[0022] Select the i-th order mode vector φ i The modal node force vector F at the corresponding weld line b1 is calculated based on the modal array vector.ib1 Modal nodal force vector F at the weld wire node at b2 ib2 Among them, the modal node force vector F at the corresponding weld line b1 is ib1 Includes nodal force f ib1 and nodal torque M ib1 Modal nodal force vector F at the weld joint at point b2 ib2 Includes nodal force f ib2 and nodal torque M ib2 ;

[0023]

[0024] in, [B] is the nodal force merging matrix, which merges the nodal forces of adjacent and shared nodes. [B] is the transformation matrix from local to global coordinates. T Let [B] be the transpose of [K]. e [ ] represents the element stiffness matrix in local coordinates. Let be the nodal displacement vector corresponding to the element at the weld toe of the i-th mode;

[0025] First, calculate the modal stresses at weld lines b1 and b2 respectively. The calculation formulas are as follows:

[0026]

[0027] in, and These are the modal structural stresses at weld lines b1 and b2, respectively.

[0028] A matrix used to average the nodal forces onto the weld line;

[0029] Among them, l g Let g be the side length of the g-th unit along the weld line direction, where g∈[1,n];

[0030] This is the superposition matrix of membrane stress and bending stress;

[0031] Where d is the plate thickness of the weld toe, and [T] is the coordinate transformation matrix from the global coordinate system to the local coordinates of the weld line, which is calculated from the node coordinates of the finite element mesh model;

[0032] Step S22b: Calculate the modal structural stress at the weld toe using linear interpolation;

[0033] The formula for calculating the stress interpolation of each modal structure is as follows:

[0034]

[0035] in, Let be the structural stress at the weld toe corresponding to the i-th mode.

[0036] Preferably, in step S3, the linear superposition of interpolated modal structural stresses is used to obtain the stress time history at the weld toe, as expressed below:

[0037]

[0038] Where, σ s (t) represents the structural stress at the weld toe of the welded structure at time t.

[0039] The preferred formula for calculating equivalent structural stress is as follows:

[0040]

[0041] Where, ΔS S For the equivalent structural stress amplitude, I(r) is a dimensionless function of the curvature ratio r, where r = Δσ. b / Δσ s , Δσ b The second term in the modal structural stress at weld wire b1 is Δσ. s The range of structural stress variation is given by k, which is a constant coefficient, k = 3.6.

[0042] Preferably, in step S6, the formula for calculating the vibration fatigue life of the welded structure under time-domain load based on the master SN curve is as follows:

[0043]

[0044] Among them, C d Both h and n are parameters related to the main SN curve. i The number of loops. Let k represent the range of structural stress variation, and k be the number of levels in which the equivalent structural stress variation range is divided.

[0045] Therefore, the present invention adopts the above-mentioned weld vibration fatigue life assessment method based on simplified modal structural stress method, which has the following beneficial effects: Based on the structural stress method, fatigue assessment of welds of all weld joint types can be calculated using a single main SN curve. Modal structural stress at the weld toe is calculated through linear difference. There is no need to establish weld details, which can greatly simplify the workload of finite element model establishment, reduce modeling complexity, and improve modeling efficiency. The modal superposition method is adopted, which can effectively reduce the degree of freedom of dynamic simulation, thereby providing high solution and fatigue assessment efficiency. This method can be applied to fields such as rail vehicles, automobiles, aerospace, marine, and engineering machinery.

[0046] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0047] Figure 1 This is a flowchart of a method for assessing the vibration fatigue life of welds based on the simplified modal structural stress method according to the present invention.

[0048] Figure 2 A schematic diagram of a finite element model with weld details;

[0049] Figure 3 This is a simplified finite element model diagram of the present invention;

[0050] Figure 4 This is a schematic diagram of the interpolation model. Detailed Implementation

[0051] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product is in use. They are used only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," and "connect" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0052] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0053] like Figure 1 As shown, a method for assessing the vibration fatigue life of welds based on the simplified modal structural stress method is described, with the following specific steps:

[0054] Step S1: Establish a simplified finite element model of the welded structure that does not include weld details, such as... Figures 2-3 As shown, the structural modes of the simplified finite element model are calculated.

[0055] In step S1, the simplified structural dynamics equations of the finite element model are as follows:

[0056]

[0057] Where [M], [C], and [K] are the mass matrix, damping matrix, and stiffness matrix, respectively, and {u(t)} and {f(t)} are the displacement vector and load vector, respectively; and These are the acceleration vector and the velocity vector, respectively, where t is the time point;

[0058] The modal order of the structure is determined based on the frequency range of the external load, and the normalized modal matrix of the mass matrix is ​​[Φ]. n×m , [Φ] n×m =[φ1 … φ i … φ m ], φ i Let be an n-dimensional modal shape vector, i∈[1,m], where n is the number of degrees of freedom of the simplified finite element model and m is the modal order.

[0059] Step S2: Obtain the modal coordinate time history based on the structural modes, and calculate the modal structural stress at the weld toe using linear interpolation.

[0060] The time history of modal coordinates obtained from the structural modes is as follows:

[0061] Step S21a: Convert the structural dynamics equations into modal coordinate form. The conversion formula is as follows:

[0062]

[0063] Where {ξ(t)} is the modal coordinate time history variable, and These are the first and second derivatives of {ξ(t)}, respectively;

[0064] Step S22a: Solve the above equation using Newmark's successive integration method or Duhamel integration. The result is the modal coordinates ξ. j (t)(j=1,2,…R), ξ j (t) represents the modal coordinates at time t under the j-th modal order, and R represents the total number of modal orders selected.

[0065] The structural modes of the simplified finite element model are calculated as follows:

[0066] Step S21b: Calculate the nodal forces of the two rows of nodes closest to the weld toe for each modal vector;

[0067] Select the i-th order mode vector φ i The modal node force vector F at the corresponding weld line b1 is calculated based on the modal array vector. ib1 Modal nodal force vector F at the weld wire node at b2 ib2 Among them, the modal node force vector F at the corresponding weld line b1 is ib1 Includes nodal force f ib1 and nodal torque M ib1 Modal nodal force vector F at the weld joint at point b2 ib2 Includes nodal force fib2 and nodal torque M ib2 ;

[0068]

[0069] in, [B] is the nodal force merging matrix, which merges the nodal forces of adjacent and shared nodes. [K] is the element local coordinate to global coordinate transformation matrix. e [ ] represents the element stiffness matrix in local coordinates. Let be the nodal displacement vector corresponding to the element at the weld toe in the i-th mode.

[0070] Calculate the modal stresses at weld lines b1 and b2 respectively, using the following formulas:

[0071]

[0072] in, and These are the modal structural stresses at weld lines b1 and b2, respectively.

[0073] A matrix used to average the nodal forces onto the weld line;

[0074] Among them, l g Let g be the side length of the g-th unit along the weld line direction, where g∈[1,n];

[0075] This is the superposition matrix of membrane stress and bending stress;

[0076] Where d is the plate thickness of the weld toe, and [T] is the coordinate transformation matrix from the global coordinate system to the local coordinates of the weld line, which is calculated from the node coordinates of the finite element mesh model.

[0077] Step S22b: Calculate the modal structural stress at the weld toe using linear interpolation, such as... Figure 4 As shown.

[0078] The formula for calculating the stress interpolation of each modal structure is as follows:

[0079]

[0080] in, Let be the structural stress of the i-th modal.

[0081] Step S3: Superimpose the modal coordinate time history and the modal structural stress at the weld toe to obtain the structural stress time history at the weld toe.

[0082] The stress time history at the weld toe is obtained by linear superposition of interpolated modal structural stresses, as expressed below:

[0083]

[0084] Where, σ s (t) represents the structural stress at the weld toe of the welded structure at time t.

[0085] Step S4: Based on the rainflow count statistics of the structural stress time history at the weld toe, obtain the range of structural stress variation and the number of cycles.

[0086] Step S5: Calculate the equivalent structural stress; the formula for calculating the equivalent structural stress is as follows:

[0087]

[0088] Where, ΔS S For the equivalent structural stress amplitude, I(r) is a dimensionless function of the curvature ratio r, where r = Δσ. b / Δσ s , Δσ b The second term in the modal structural stress at weld wire b1 is Δσ. s The range of structural stress variation is given by k, which is a constant coefficient, k = 3.6.

[0089] Step S6: Use the main SN curve method to calculate the damage and fatigue assessment results of the weld.

[0090] The formula for calculating the vibration fatigue life of welded structures under time-domain load based on the master SN curve is as follows:

[0091]

[0092] Among them, C d Both h and n are parameters related to the main SN curve. i The number of loops. Let k represent the range of structural stress variation, and k be the number of levels in which the equivalent structural stress variation range is divided.

[0093] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for assessing the vibration fatigue life of welds based on the simplified modal structural stress method, characterized in that, The specific steps are as follows: Step S1: Establish a simplified finite element model of the welded structure that does not include weld details, and calculate the structural modes of the simplified finite element model. The structural dynamic equations of the simplified finite element model are as follows: in, , , These are the mass matrix, damping matrix, and stiffness matrix, respectively. and These are the displacement vector and the load vector, respectively. and These are the acceleration vector and the velocity vector, respectively. For a specific moment; The modal order of the structure is determined based on the frequency range of the external load. The normalized modal matrix of the mass matrix is: , , Let i be the mode shape vector of the i-th order. , where n is the number of degrees of freedom of the simplified finite element model, and m is the modal order; Step S2: Obtain the modal coordinate time history based on the structural modes, and calculate the modal structural stress at the weld toe using linear interpolation, including: Step S21b: Select the i-th order mode shape vector Based on modal shape vectors Calculate the corresponding solder wire Modal node force vector and solder wire Modal node force vector Among them, the corresponding solder wire Modal node force vector Includes nodal forces and nodal torque ; welding wire Modal node force vector Includes nodal forces and nodal torque ; in, This is a node force merging matrix, which merges the node forces of adjacent and shared nodes. This is the transformation matrix from local coordinates to global coordinates. for The transpose of the matrix, The element stiffness matrix in local coordinates. Let be the nodal displacement vector corresponding to the element at the weld toe of the i-th mode; Calculate the bonding wires separately and solder wire The modal stress is calculated using the following formula: A matrix used to average the nodal forces onto the weld line; in, For the first along the welding line direction The side length of each unit, ; This is the superposition matrix of membrane stress and bending stress; in, The thickness of the plate at the weld toe. This is the coordinate transformation matrix from the global coordinate system to the local coordinates of the weld line; Step S22b: Calculate the modal structural stress at the weld toe using linear interpolation: The formula for calculating the modal structural stress at each weld toe is as follows: in, The modal stress at the i-th weld toe is... and They are respectively welding wires and weld Modal structural stress, For wire bonding Spacing with solder wire b For wire b and wire The spacing; Step S3: Superimpose the modal coordinate time history and the modal structural stress at the weld toe to obtain the structural stress time history at the weld toe; Step S4: Perform rainflow counting statistics based on the stress time history of the structure at the weld toe to obtain the stress variation range and cycle number of the structure; Step S5: Calculate the equivalent structural stress; Step S6: The main SN curve method is used to calculate the weld vibration fatigue life assessment results.

2. The method for assessing the vibration fatigue life of welds based on the simplified modal structural stress method according to claim 1, characterized in that: In step S2, the modal coordinate time history is obtained based on the structural modes as follows: Step S21a: Convert the structural dynamics equations into modal coordinate form. The conversion formula is as follows: in, For modal coordinate time history variables, and They are respectively The first and second derivatives; Step S22a: Solve the above equation using Newmark's successive integration method or Duhamel integration. The result is the modal coordinates. , For the first Under each modal order Modal coordinates at time step.

3. The method for assessing the vibration fatigue life of welds based on the simplified modal structural stress method according to claim 2, characterized in that: In step S3, the expression for the structural stress at the weld toe is as follows: in, for The structural stress at the weld toe of the welded structure is constant.

4. The method for assessing the vibration fatigue life of welds based on the simplified modal structural stress method according to claim 3, characterized in that: The formula for calculating equivalent structural stress is as follows: in, For equivalent structural stress, It is a dimensionless function of the curvature ratio r. , This is the second term in the modal structural stress at weld line b1. The range of structural stress variation, The constant coefficients, .

5. The method for assessing the vibration fatigue life of welds based on the simplified modal structural stress method according to claim 4, characterized in that: In step S6, the formula for calculating the vibration fatigue life of the welded structure under time-domain load based on the master SN curve is as follows: in, and These are all parameters related to the main SN curve. The number of loops. The number of levels used to classify the range of stress variation in the equivalent structure.

Images