An analysis method for performance degradation of wave foil bearing considering fatigue characteristics of welds

Abstract

This invention provides an analytical method for corrugated foil bearing performance degradation considering weld fatigue characteristics, relating to the fields of mechanical dynamics and rotor system simulation technology. The method comprises three nested iterative calculation layers: in the fluid-structure interaction basic iterative layer, the dynamic air film pressure distribution is solved to obtain the air film thickness and the flat foil deformation at the weld point within the corrugated foil bearing; in the weld point local stiffness self-consistent iterative layer, the actual elastic modulus and estimated local stiffness of the weld material are updated using a continuous damage model, outputting the weld stiffness retention rate and dynamic stiffness damping parameters; in the full life cycle performance evolution iterative layer, the overall dynamic behavior of the system is calculated based on the above parameters, outputting the performance degradation judgment result. This invention can identify the degradation risk of corrugated foil bearings before macroscopic fracture occurs at the weld point and the system exhibits severe vibration.

Description

Technical Field

[0001] This invention relates to the field of mechanical dynamics and rotor system simulation technology, and in particular to an analysis method for the performance degradation of corrugated foil bearings that considers the fatigue characteristics of weld points. Background Technology

[0002] Corrugated bearings are used in many rotating machines due to their advantages of adapting to high-speed operating conditions and high stability.

[0003] like Figure 1 As shown, the basic structure of the corrugated foil bearing mainly consists of flat foil, corrugated foil, and bearing housing. The starting point of the flat foil coincides with the starting point of the corrugated foil, and they are fixedly connected to the inner surface of the bearing housing by welding.

[0004] In terms of performance analysis methods for corrugated foil bearings, conventional methods mostly revolve around fluid-structure interaction calculations. For example, Chinese patent application CN202110986312.4 discloses a method for predicting the load-bearing capacity of a radial corrugated foil hydrodynamic gas bearing. This method solves the Reynolds equation and the structural deformation equation by coupling and iteratively solving them, thereby obtaining the bearing's load-bearing capacity and minimum gas film thickness under different operating conditions.

[0005] In addition, some technical solutions simplify the calculation of the solid domain by treating the wave foil as a spring connection and calculating its stiffness to achieve rapid iterative solution.

[0006] Existing modeling and simulation methods provide important references for understanding the initial operating state of corrugated foil bearings. However, in the actual operation of corrugated foil bearings, the rotor usually operates at high speeds, which means that the weld joints, as stress concentration areas, need to withstand high-frequency cyclic alternating loads. At the same time, the changes in the initial elastic modulus of the material caused by the welding process will become more apparent over the service life.

[0007] Existing modeling schemes often treat the welding points of flat foil and corrugated foil on the bearing housing as ideal fixed constraints, failing to take into account the inherent stress concentration at the weld joints and the degradation characteristics of material properties over the service life. This approach makes it difficult for the analysis model to objectively reflect the dynamic evolution of the local support stiffness of the weld joints under alternating stress. Consequently, discrepancies easily arise between the calculation of dynamic parameters and the assessment of service life of bearings during long-term operation and actual working conditions, making it difficult to accurately track and evaluate the performance degradation trajectory of corrugated foil bearings throughout their entire life cycle. Summary of the Invention

[0008] The purpose of this invention is to provide an analysis method for the performance degradation of corrugated foil bearings that considers the fatigue characteristics of the weld joints, in order to solve the technical problem that existing corrugated foil bearing modeling and analysis does not fully consider the evolution characteristics of local material fatigue damage at the weld joints, which makes it difficult to accurately assess and predict the performance degradation risk of corrugated foil bearings throughout their entire life cycle.

[0009] This invention provides an analysis method for the performance degradation of corrugated foil bearings considering the fatigue characteristics of weld joints. The analysis method includes three iterative calculation layers nested from the inside out, and the specific steps are as follows: In the first fluid-structure interaction basic iterative layer, the dynamic air film pressure distribution is solved to obtain the air film thickness under the coupled state and the first flat foil deformation at the welded joint inside the corrugated foil bearing. In the second layer of self-consistent iteration of local stiffness of weld joint, the deformation of the first flat foil is extracted, and the actual elastic modulus and local stiffness estimate of the weld joint material are updated in combination with the continuous damage model until the local stiffness difference between two adjacent iteration steps meets the preset convergence condition, and the weld joint stiffness retention rate and dynamic stiffness damping parameters with mechanical self-consistency are output. In the third-level full-life-cycle performance evolution iteration layer, the overall dynamic behavior of the system is calculated based on the dynamic stiffness damping parameters and the stiffness retention rate at the weld, so as to output the performance degradation judgment result of the corrugated foil bearing.

[0010] Optionally, in the first fluid-structure interaction basic iterative layer, the dynamic air film pressure distribution is obtained by numerically solving the dimensionless dynamic Reynolds equation; Furthermore, the thickness of the air film is affected by the combined effects of foil deformation, eccentricity, eccentricity angle, and nominal bearing clearance.

[0011] Optionally, in the second layer of self-consistent iteration of local stiffness of the weld joint, the actual elastic modulus of the material at the weld joint is updated in combination with the continuous damage model, including: calculating the continuous damage factor based on the iteration results of the first layer; quantifying the attenuation of material properties due to fatigue based on the difference ratio between the initial elastic modulus and the continuous damage factor, thereby calculating the updated actual elastic modulus.

[0012] Optionally, the continuous damage factor is calculated based on the change in the effective bearing area; The continuous damage factor is equal to the ratio of the effective bearing area of ​​the damaged area considering the first layer of iteration results to the initial effective bearing area of ​​the weld.

[0013] Optionally, the preset convergence condition is: In the second layer of self-consistent iterative layer of local stiffness of weld joints, the difference between the local stiffness of the next iteration step and the local stiffness of the previous iteration step is less than the preset minimum deviation.

[0014] Optionally, in the third layer of full life cycle performance evolution iteration layer, the performance degradation judgment result of the corrugated foil bearing includes a first judgment criterion for the reliability of the weld. The first criterion is to determine whether the stiffness retention rate of the weld is lower than the critical threshold of 70%; if it is lower than the critical threshold, the weld point of the current weld is determined to be unreliable according to the welding dynamics theory.

[0015] Optionally, the performance degradation determination result of the corrugated foil bearing may also include a second determination criterion for the stability of the rotor system; The second criterion includes: substituting the dynamic stiffness and damping parameters obtained through iteration into the rotor dynamics equation to carry out steady-state calculations and obtain the steady-state logarithmic decay rate.

[0016] Optionally, the specific steps for evaluating the bearing condition according to the second determination criterion are as follows: Determine whether the steady-state logarithmic decay rate is less than zero; if the steady-state logarithmic decay rate is less than zero, it proves that the rotor system has become unstable, and thus it is determined that the entire corrugated foil bearing is unreliable.

[0017] Optionally, the basic structure of the corrugated foil bearing consists of a flat foil, a corrugated foil, and a bearing housing; the starting point of the flat foil coincides with the starting point of the corrugated foil, and they are both fixedly connected to the bearing housing through the weld joint.

[0018] Optionally, by applying the first or second judgment criteria to obtain the performance degradation judgment result, the degradation risk of the corrugated bearing can be identified in advance before macroscopic fracture occurs at the weld and the system exhibits severe vibration, so as to avoid secondary damage to the system.

[0019] The present invention has achieved the following beneficial effects: This invention introduces a material fatigue evolution model for the welded area into the traditional fluid-structure interaction (FSI) analysis framework for corrugated foil bearings. By constructing a nested computational layer that includes basic FSI iteration, self-consistent iteration of weld point local stiffness, and performance evolution iteration throughout the entire service life, the continuous damage factor affected by alternating loads is directly applied to the dynamic update process of the estimated local elastic modulus and stiffness at the weld, objectively presenting the variation law of weld point stiffness with the service cycle. Based on the weld stiffness retention rate and dynamic stiffness damping parameters output by the iteration, this invention can identify the support weakening caused by local damage and the steady-state logarithmic decay trend of the rotor system in the evaluation and judgment stage. This provides a quantitative early warning of performance degradation before the bearing experiences solid fracture or the rotor experiences large-scale instability, providing a more objective analytical basis for the life assessment and reliability maintenance of high-speed rotating machinery.

[0020] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description and the accompanying drawings.

[0021] 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

[0022] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is a schematic diagram of the basic structure and welding point location of the corrugated foil bearing in an embodiment of the present invention; Figure 2 This is a flowchart illustrating the nested calculation process of the self-consistent iterative layer for local stiffness of weld points and the basic iterative layer for fluid-structure interaction in an embodiment of the present invention. Figure 3 This is a flowchart illustrating the analysis and judgment of the full life cycle performance degradation of the corrugated foil bearing considering the fatigue characteristics of the solder joints in an embodiment of the present invention. Detailed Implementation

[0023] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0024] This application provides a method for analyzing the performance degradation of corrugated foil bearings considering the fatigue characteristics of weld joints. This method can be executed by a computer device, computing cluster, or embedded computing platform. Specifically, the computer device is equipped with a processor, memory, input / output interfaces, and a communication bus. The memory stores executable algorithm instructions and structured data. The processor reads and runs these instructions to complete the numerical coupling calculation of the hydrodynamics, structural mechanics, and rotor dynamics of the corrugated foil bearing. The core technology of this method lies in constructing three iterative calculation layers nested from the inside out. By passing physical field parameters and structural state variables layer by layer, it achieves numerical and quantitative analysis of the performance degradation trajectory of the corrugated foil bearing during service.

[0025] The basic structure of the corrugated foil bearing consists of a flat foil, a corrugated foil, and a bearing housing. In terms of spatial geometry, the starting points of the flat foil and the corrugated foil coincide, and they are both fixedly connected to the inner surface of the bearing housing via a weld joint. The flat foil is located closer to the rotor, while the corrugated foil is positioned between the flat foil and the bearing housing, providing elastic support. The weld joint is the fundamental connection node that constrains the spatial degrees of freedom of the flat foil and the corrugated foil.

[0026] The analysis method provided in this application embodiment has a first layer as a fluid-structure interaction (FSI) basic iterative layer. In this first FSI basic iterative layer, the computer device mainly performs steady-state and dynamic equilibrium calculations of the fluid and solid domains to obtain the gas film thickness under coupled conditions and the first flat foil deformation at the welded joint inside the corrugated bearing. Further, in this first FSI basic iterative layer, the computer device needs to solve for the dynamic gas film pressure distribution. The dynamic gas film pressure distribution is obtained by numerically solving the dimensionless dynamic Reynolds equation. Specifically, the computer device first constructs a two-dimensional grid discretization space in the circumferential and axial directions of the bearing, sets the number of circumferential nodes and the number of axial nodes, and discretizes the continuous fluid domain. The dimensionless dynamic Reynolds equation is expressed as follows: ; In the dimensionless form of the dynamic Reynolds equations described above This represents dimensionless film pressure. Indicates the dimensionless thickness of the air film. This represents the dimensionless angular coordinates of the circumferential direction of the foil bearing. This represents the dimensionless coordinate of the axial direction of the corrugated foil bearing. This indicates the nominal radius of the inner bore of the corrugated bearing. Indicates the effective axial load-carrying length of the corrugated foil bearing. The dimensionless number representing the corrugated foil bearing. Representing a dimensionless time parameter, this equation forms the basic mathematical model for computer equipment to solve the dynamic pressure distribution in a film fluid domain, used to describe the dynamic pressure effect of compressible fluids under eccentric rotation conditions.

[0027] To perform numerical discretization and solution of the above equations in a computer device, it is necessary to define dimensionless parameters for each term in the equations. The formula for calculating dimensionless pressure is as follows: ; In the above formula for calculating dimensionless pressure, This represents dimensionless film pressure. This represents the actual absolute pressure at any spatial grid node in the film gas flow field. The formula represents the ambient atmospheric pressure of the working environment of the corrugated foil bearing. This formula is used by computer equipment to convert the actual gas film pressure with physical dimensions into a dimensionless parameter to ensure the stability of the matrix condition number in the numerical solution of partial differential equations.

[0028] The formula for calculating the dimensionless gas film thickness is as follows: ; In the above formula for calculating the dimensionless gas film thickness, Indicates the dimensionless thickness of the air film. This represents the actual absolute geometric thickness of the air film at the corresponding spatial grid node. This represents the nominal initial radius clearance of the corrugated foil bearing in a state of no eccentricity and no deformation. This formula is used by computer equipment to normalize the geometric boundaries of the fluid domain.

[0029] The formula for calculating the dimensionless number of a corrugated foil bearing is as follows: ; In the above formula for calculating the dimensionless number of the corrugated foil bearing, This represents the dimensionless number of the corrugated foil bearing. This represents the dynamic viscosity of the lubricating gas in the flow field. Indicates the angular velocity of the rotor. This indicates the nominal radius of the inner bore of the corrugated bearing. Indicates the environmental reference atmospheric pressure. The nominal initial radius clearance is represented by this formula, which integrates fluid properties, rotor kinematic parameters, and bearing geometry, and characterizes the relative strength of the hydrodynamic and compressible effects.

[0030] In the numerical iteration process of calculating the dynamic film pressure distribution, the film thickness at the flow field grid nodes changes in real time with the loading of the structural domain. This film thickness is influenced by the combined effects of foil deformation, rotor eccentricity characteristics (including eccentricity amount and eccentricity angle), and nominal bearing clearance. The computer updates the actual film thickness at each grid node based on the following geometric relationship: ; In the above equation for air film thickness, This represents the actual geometric thickness of the gas film at a specific node in the fluid domain. This indicates the nominal initial radius clearance of the corrugated foil bearing. This indicates the eccentricity of the rotor center. This represents the coordinates of the circumferential angle. Indicates the eccentricity angle of the rotor. This equation represents the combined foil deformation at the structural position corresponding to the node after considering the combined action of the wave foil and the flat foil. This equation establishes an explicit data coupling relationship between the boundary geometry of the fluid domain and the mechanical deformation of the solid domain structure.

[0031] The specific data processing and execution steps of the first layer of fluid-structure interaction basic iterative layer are as follows: The computer device initializes a dimensionless pressure field matrix with all reference pressures and a foil deformation matrix with an initial value of zero in memory. The computer device uses the finite difference method to spatially discretize the dynamic Reynolds equations. Specifically, a second-order central difference scheme is used for the diffusion term on the left side of the equation, and a first-order upwind difference scheme or exponential difference scheme is used for the convection term on the right side of the equation, thereby establishing a system of nonlinear algebraic equations containing the unknowns of each pressure grid node. To solve this system of equations, the computer device transforms it into a linearized form and assembles a global coefficient matrix and a load vector for the right-hand side. The computer device calls the continuous over-relaxation iterative algorithm (SOR) to solve this system of linear equations. During the iteration process, the computer device monitors the residual norm of the pressure matrix in real time. When the residual norm drops below the preset pressure convergence tolerance, the flow field calculation of the current step is stopped, and the updated film pressure distribution matrix is ​​obtained.

[0032] Next, the computer device performs calculations for the solid structural domain. It performs bilinear interpolation on the acquired film pressure distribution matrix, mapping it to the structural mechanics finite element nodes on the flat foil surface, converting the pressure data into nodal load vectors. The computer device loads the finite element models of the flat foil and the corrugated foil. Specifically, the flat foil is discretized using two-dimensional shell elements, and the corrugated foil is discretized using one-dimensional beam elements or equivalent nonlinear spring elements. The computer device assembles the global stiffness matrix of the solid domain in memory. In this step, boundary constraints are applied to the nodes at the weld joints. The computer device solves the solid mechanics equilibrium equations, obtaining the displacement vectors of all structural nodes. The computer device extracts the radially perpendicular normal deformation component from the displacement vectors, generates an updated foil composite deformation distribution matrix, and substitutes it back into the aforementioned film thickness equation to update the geometric boundaries of the fluid domain. The computer device calculates the maximum absolute value of the difference between the deformation matrix before and after the update. If this value is greater than the preset fluid-structure interaction (FSI) convergence tolerance, the computer device recalculates the Reynolds equation coefficients using the updated air film thickness matrix and continues to execute the outer loop. If this value is less than or equal to the preset FSI convergence tolerance, the first FSI basic iteration layer is determined to have converged. After reaching convergence, the computer device extracts the structural node displacement data located at the weld from the structural node displacement vector and outputs it as the first flat foil deformation to the next calculation layer.

[0033] The second layer of the analysis method provided in this application embodiment is a self-consistent iterative layer for the local stiffness of the weld joint. The algorithm logic of this layer is to quantify the fatigue damage evolution of the material based on the stress and deformation state of the current weld joint area, and to correct the local support stiffness of the weld joint in real time. In the second layer of the self-consistent iterative layer for the local stiffness of the weld joint, the computer device extracts the deformation of the first flat foil, and updates the actual elastic modulus and local stiffness estimate of the material at the weld joint in combination with the continuous damage model, continuously feeding back the calculation until the difference in local stiffness between two adjacent iterations meets the preset convergence condition.

[0034] like Figure 2As shown, specifically, the data processing and algorithm execution steps for updating the actual elastic modulus of the weld material using the continuous damage model are as follows: The computer device extracts the deformation of the first flat foil and, combined with the strain-displacement matrix of the elements surrounding the weld node in the finite element model, calculates the micro-strain tensor of the region. Further, using the material's elastic constitutive matrix, the computer device calculates the local stress tensor distribution at the weld and extracts the equivalent Von Mises stress. Due to the high-speed rotation of the bearing rotor, this stress exhibits high-frequency alternating characteristics. The computer device uses the Rainflow Counting Algorithm to extract the stress amplitude and average stress of the stress cycle and uses the Goodman equivalent equation to transform it into a symmetrical cyclic stress amplitude. Based on the set micro-damage evolution rate rule, the computer device calculates the damage increment at a given number of cycles and accumulates them to obtain the total continuous damage factor. The physical basis of the continuous damage factor is the change in the effective bearing area, and its mathematical expression is as follows: ; In the above formula for calculating the continuous damage factor, Indicates the continuous damage factor of the material. This represents the effective load-bearing area cross-sectional parameter of the weld joint in its initial, undamaged state. This formula represents the effective load-bearing area inside the weld joint after considering the first layer of iteration results and experiencing fatigue accumulation. It is the projected area where microcracks and micropores cause the loss of load-bearing capacity. This formula quantifies the degree of geometric decay of the macroscopic mechanical load-bearing effectiveness of the material in the weld joint area due to high-frequency alternating stress.

[0035] Specifically, the damaged effective bearing area Quantitative calculations are performed based on Miner's linear cumulative damage theory. The mathematical derivation is as follows: ; In the formula, Indicates the effective load-bearing area damaged; This represents the effective load-bearing area in the undamaged initial state; Indicates the first Level equivalent symmetrical cyclic stress amplitude The actual number of alternating cycles under the action; Indicates at this stress amplitude The ultimate cycle life at which the material undergoes fatigue failure.

[0036] The specific values ​​were determined using the regression equation based on the known SN curve of the material: ; In the formula, Indicates the first Level equivalent symmetrical cyclic stress amplitude; This represents the fatigue strength index of the material at the weld joint, i.e., the experimental regression constant; This represents the fatigue strength coefficient of the material at the weld joint, i.e., the experimental regression constant. Those skilled in the art can obtain these constants directly from standard material handbooks.

[0037] After obtaining the continuous damage factor, the computer device quantifies the degradation of material properties due to fatigue based on the ratio of the difference between the initial elastic modulus and the continuous damage factor, thereby calculating the updated actual elastic modulus. The calculation formula for this update process is as follows: ; In the updated formula for the actual elastic modulus of the above materials Indicates the first The actual elastic modulus of the weld material after continuous damage reduction in a self-consistent iterative step. This represents the continuous damage factor calculated in the preceding steps. This represents the initial reference elastic modulus of the material at the weld before fatigue damage occurs. This formula establishes a direct linear reduction relationship between the degree of microscopic damage to the macroscopic constitutive parameters of the material.

[0038] After retrieving the updated actual elastic modulus from memory, the computer device executes the local stiffness reconstruction logic. The computer device locates the block matrix corresponding to the weld constraint node in the global stiffness matrix, replaces the original elastic modulus parameters with the currently calculated actual elastic modulus, recalculates the element stiffness matrix integral, and then reassembles it to obtain the local stiffness estimate for the next iteration step (i.e., the updated weld constraint stiffness).

[0039] Subsequently, the computer device executes the core feedback and convergence determination logic of the second layer. The preset convergence condition is: in the second layer of self-consistent iteration of local stiffness of the weld joint, the calculated local stiffness of the next iteration step (let's say it's denoted as...) The local stiffness of the previous iteration (let's say it's the same as the local stiffness of the previous iteration) The absolute value of the difference is less than a preset minimum deviation constant. Specifically, the computer device performs the difference calculation. and compare it with the preset tolerance constant in memory. Perform a floating-point comparison. If the logical comparison result is true (i.e., the convergence condition is met), it indicates that the deformation, stress, and damage at the current weld point are physically consistent with the support stiffness that can be provided, and the second layer of self-consistent iteration ends. If the logical comparison result is false (i.e., the convergence condition is not met), the computer will perform a feedback operation, updating the local stiffness estimate. The process is then passed back to the first-level fluid-structure interaction (FSI) foundational iteration layer. In this first layer, the computer device modifies the boundary constraint parameters of the welded nodes in the solid domain model to reflect this updated local stiffness. The coupled solution loop of the Reynolds equation and the deformation equation is then restarted. Because the stiffness at the weld joint degenerates, the overall deformation pattern of the flat foil under film pressure will change, leading to a redistribution of the film thickness field and pressure field, and ultimately calculating the new first flat foil deformation. This cross-level nested closed loop will continue to execute until the second-level local stiffness difference determination converges.

[0040] Once the second layer of local stiffness self-consistent iteration at the weld joint is determined to be converged, the computer device executes state saving and parameter extraction instructions. The computer device outputs the weld joint stiffness retention rate and dynamic stiffness damping parameters, which possess mechanical self-consistency. The weld joint stiffness retention rate is obtained by the computer device through a division operation, specifically by dividing the local stiffness at convergence by the initial local stiffness before damage. The extraction of the dynamic stiffness damping parameters is achieved through small perturbation theory. Specifically, in the convergent state, the computer device applies minimal horizontal and vertical perturbations to the displacement and velocity distribution at the rotor center in memory, re-solves the dynamic Reynolds equations in partial derivative form, obtains four principal stiffness coefficients, four cross stiffness coefficients, four principal damping coefficients, and four cross damping coefficients, and stores these eight coefficients as the input matrix of the rotor system dynamic model.

[0041] The specific derivation steps for extracting dynamic stiffness and damping parameters based on the small perturbation theory are as follows: Assuming that the rotor experiences a small perturbation at the steady-state equilibrium position, the air film thickness and pressure are expanded into a first-order Taylor series at the equilibrium point: ; ; In the formula, This indicates the transient gas film thickness after being disturbed; This represents the initial gas film thickness at the steady-state equilibrium position; and These represent the minimum disturbance displacements of the rotor center in the horizontal and vertical directions, respectively. Represents the circumferential angular coordinates; This represents the transient film pressure after being disturbed; This represents the initial film pressure at the steady-state equilibrium position; and These represent the minimum disturbance velocities of the rotor center in the horizontal and vertical directions, respectively. and These represent the partial derivatives of the film pressure with respect to the horizontal and vertical displacements, respectively. and These represent the partial derivatives of the film pressure with respect to the horizontal and vertical velocities, respectively.

[0042] Substituting the above expansion into the dimensionless dynamic Reynolds equation, discarding second-order and higher-order small quantities, and separating the variables according to the perturbation variable, we can obtain four variables respectively. , , , The equations are linear partial differential equations in the complex domain with unknowns. After solving for the distribution of the four dynamic pressure derivatives using the finite difference method, the computer equipment performs double numerical integration along the surface of the fluid domain to obtain the four principal and cross stiffness coefficients and the four principal and cross damping coefficients.

[0043] like Figure 3 As shown, the third layer of the analysis method provided in this application embodiment is a full life cycle performance evolution iteration layer. The function of this layer is to simulate the drift trajectory of the overall performance of the corrugated foil bearing as service time or the number of alternating cycles increases. In the third full life cycle performance evolution iteration layer, the computer equipment calculates the overall dynamic behavior of the system as service time or the number of cycles increases based on the dynamic stiffness damping parameters and the stiffness retention rate at the weld, to output the performance degradation judgment result of the corrugated foil bearing.

[0044] In practice, the computer device sets the time step or cycle number step for the lifespan evolution in the main control program. At each macroscopic lifespan node, the computer device calls the first two nested iterative programs to obtain the dynamic stiffness and damping parameters of the current node and the stiffness retention rate matrix data at the weld.

[0045] The performance degradation determination result of the corrugated foil bearing includes a first determination criterion for the reliability of the weld. The instruction steps for the computer device to execute the first determination criterion include: retrieving the weld stiffness retention rate value of the current evolution node from memory, and performing an arithmetic comparison operation with a set 70% critical threshold constant. It is then determined whether the weld stiffness retention rate is lower than the 70% critical threshold. If the arithmetic comparison result is true, i.e., lower than the critical threshold, the computer device sets a set Boolean state flag to failure and directly outputs the determination result based on welding dynamics theory, determining that the weld joint at the current time point is unreliable, i.e., determining connection failure at the microstructural level, and interrupting the cyclic evolution after the current time node.

[0046] The performance degradation determination result of the foil bearing also includes a second determination criterion for the stability of the rotor system. The instruction steps for the computer equipment to execute the second determination criterion include: assembling the eight dynamic stiffness and damping parameters obtained by iterative extraction into the rotor dynamics equation module, performing system-level steady-state calculations, and obtaining the steady-state logarithmic decay rate of each mode.

[0047] The specific algorithm execution process is as follows: The computer equipment first assembles the global mass matrix, global gyro matrix, and global structural stiffness matrix of the rotor system using a finite element beam element model. Then, the dynamic stiffness and damping parameters of the foil bearing are superimposed onto the degree-of-freedom equations corresponding to the support nodes of the rotor system. The computer equipment then transforms this set of second-order ordinary differential dynamic equations into a first-order state matrix using a state-space reduction method.

[0048] The specific matrix construction rule of the state space order reduction method is as follows: introduce a state vector. The transformed first-order state equation is expressed as: ; In the formula, Represents the state vector. This represents the displacement vector of all nodes in the rotor system. Represents the velocity vector of a node; This represents the derivative of the state vector with respect to time. This represents the first-order state matrix of the system.

[0049] State matrix The internal block matrix is ​​specifically constructed as follows: ; In the formula, Represents the system's global quality matrix The inverse matrix; Represents the system's global gyroscope matrix; This represents the overall system stiffness matrix (which is formed by superimposing the rotor structure stiffness matrix with the dynamic stiffness coefficients of the foil bearing extracted in the previous step). This represents the total damping matrix of the system (which is formed by superimposing the rotor structure damping matrix and the dynamic damping coefficient). The identity matrix represents the dimension corresponding to the system's degrees of freedom; This represents the zero matrix of the corresponding dimension.

[0050] The computer device invokes a matrix eigenvalue decomposition algorithm (such as the implicit restart Arnoldi method or the QR algorithm) to solve for all complex eigenvalues ​​of the state matrix. Each complex eigenvalue contains real and imaginary parameters. The computer device then uses these real and imaginary parameters to calculate the steady-state logarithmic decay rate for each positive precession mode, according to a formula.

[0051] The specific logical execution steps for evaluating the bearing status according to the second judgment criterion are as follows: The computer device uses a loop traversal algorithm to check the steady-state logarithmic decay rate array corresponding to the first few key modes one by one. It determines whether there are any elements less than zero in the steady-state logarithmic decay rate array. If the steady-state logarithmic decay rate of any mode is detected to be less than zero (which means that the amplitude of small disturbances in the system will be amplified exponentially over time), the computer device modifies the system status register, proving that the rotor system has become unstable, and thus directly determines that the entire corrugated foil bearing is unreliable at the current evolution node and cannot maintain the normal and stable operation of the mechanical system.

[0052] By applying parallel logical operations of the first and second judgment criteria, if neither triggers an unreliability determination, the computer device records the bearing reliability status of the current node and accumulates the time variable step size, driving the system to enter the calculation of the next life cycle node. This method enables the early identification of the degradation risk of the corrugated foil bearing through the stiffness and damping indices of the theoretical model before macroscopic fracture occurs at the weld and the system exhibits severe vibration instability, thereby avoiding irreversible secondary damage to the system due to sudden support failure during actual operation.

[0053] To further explain in detail the operational logic of the above-mentioned technical solutions in a real complex data processing environment, the following will elaborate on the computation and logical judgment process of the nested iterative architecture in a computer system in conjunction with three specific implementation embodiments.

[0054] The first specific algorithm execution embodiment uses a corrugated foil bearing applied to a certain type of micro gas turbine as the analysis object. The parameter initialization module of the computer equipment receives externally input engineering data: rotor nominal diameter 35 mm, bearing effective length 35 mm, initial radius clearance 30 μm. The thickness of both flat foil and corrugated foil is 0.1 mm, the corrugation pitch is 3.175 mm, and the corrugation height is 0.5 mm. The material is set as Inconel alloy, and its initial elastic modulus, Poisson's ratio, and SN curve regression coefficient are input. The input operating conditions are set as follows: ambient pressure 0.1 MPa, rotor operating speed 100,000 r / min, and static load 30 N. Based on the above parameters, the computer equipment generates a finite element mesh data structure containing 120 × 40 fluid mesh nodes and corresponding nonlinear shell-spring combined elements.

[0055] The computer device initializes its lifecycle counter to 0 hours. Entering the first layer of fluid-structure interaction (FSI) iteration, the computer device executes the discretized Reynolds equation and calls the Gauss-Seidel iterative solver. After multiple FSI loops, the residual pressure distribution in the flow field is below a set threshold, and the program outputs the flat foil deformation in the 0-hour state. Since this is the initial state, the continuous damage factor is zero, the actual elastic modulus at the weld is equal to the initial elastic modulus, and the local stiffness remains consistent. The second layer iteration is directly deemed successful. The computer device extracts the stiffness damping coefficients in the convergent state and stores them in the rotor dynamics module. Solving for the eigenvalues ​​of the state matrix yields a first-order logarithmic decay rate of 0.45. The computer device executes the evaluation logic; the stiffness retention rate is 100% greater than 70%, and 0.45 is greater than zero. The program determines the initial state is reliable.

[0056] Subsequently, the computer equipment accumulates the lifecycle variables for 200 hours. At the 200-hour mark, the computer equipment retrieves the stress amplitude at hour 0 and the high-frequency alternation frequency corresponding to 100,000 r / min, and inputs it into the Miner linear cumulative damage algorithm, calculating that the damage factor increases to 0.05. The computer equipment then inputs the actual elastic modulus update formula, obtaining an updated modulus that is 0.95 times the initial value. The local stiffness matrix is ​​reassembled using this new modulus, resulting in a reduced local stiffness value. The computer equipment judges the rate of change of local stiffness relative to the previous iteration step and finds that it does not meet the tolerance condition. Therefore, the program feeds back the reduced local stiffness to the first layer, modifying the finite element boundary constraint stiffness matrix parameters. This causes a redistribution of the gas film thickness field solution results, generating new pressure peaks and deformations, thereby calculating new local stress and damage increments. The first and second layers nest and transfer data to each other; after three complete inner and outer layer shuttle cycles, the local stiffness update difference falls within the tolerance range. At this point, self-consistent convergence was achieved, and the computer equipment extracted a stiffness retention rate of 94.5% for the 200-hour node. The small perturbation algorithm was then invoked to re-extract the dynamic stiffness and damping. After inputting the rotor dynamics equations, the first-order logarithmic decay rate was calculated to be 0.38. The program determined that the 200-hour node remained reliable.

[0057] The computer equipment continues to automatically cycle through the time evolution. When the lifecycle variable accumulates to the 3800-hour node, after executing the second level of self-consistent convergence, the extracted stiffness retention rate is 76%. The program judges that this value is still greater than 70%. However, when the severely degraded stiffness damping coefficient is passed to the rotor dynamics equation for eigenvalue extraction, the algorithm calculates a sudden change in the logarithmic decay rate of the first-order mode to -0.015. The computer equipment's decision logic detects this negative value and determines that the rotor system has experienced oil film instability or film eddy. The main control program terminates the iteration and outputs the judgment result: at the 3800-hour node, the rotor system is unstable and the bearings are unreliable.

[0058] The second specific algorithm execution embodiment uses a foil bearing applied to a certain type of high-speed centrifugal compressor as the analysis object, focusing on verifying the triggering mechanism of different failure modes. The compressor rotor diameter is increased to 60 mm, and the operating speed is set to 40,000 rpm. Due to the relatively low speed but large aerodynamic force, the static load is set to 150 N. The computer equipment reconfigures the mesh and parameters. During the time-cycle evolution, each lifetime node strictly executes the nested fluid-structure interaction calculation, local stiffness correction calculation, and rotor steady-state characteristic calculation from the inside out. Due to the huge static load, the average local stress converted from the deformation of the first flat foil extracted by the finite element module in the second layer increases significantly. In the rainflow counting algorithm and Goodman equivalent, this leads to a significant increase in the equivalent symmetric stress amplitude, and a larger damage increment per cycle.

[0059] When the time evolution iteration reaches the 1500-hour node, the second-level local stiffness self-consistent iteration converges after 5 nested loops. After convergence, the computer extracts the current continuous damage factor in memory, which increases to 0.32. Substituting it into the actual elastic modulus formula, the modulus decreases to 68% of the initial value. The computing device extracts the stiffness retention rate in the final self-consistent state, and the calculation result is 67.5%. The computer compares 67.5% with the preset threshold of 70%, and determines that the comparison result is valid. At this point, even if the logarithmic decay rate calculated by the computer device calling the rotor module is 0.08 (greater than zero, indicating that the macroscopic dynamics of the system have not yet diverged), the logic branch of the main control program will still be triggered first according to the first judgment criterion. The program directly interrupts subsequent calculations and outputs the log: At the 1500-hour node, the stiffness retention rate is lower than the threshold, and the weld joint unreliably experiences local fracture. This embodiment demonstrates the algorithm's data processing and capture capabilities for pure structural fatigue failure paths.

[0060] The third specific implementation example further explores the influence of thermodynamic parameters on the baseline environment setting and the data robustness of the method. In this example, the object of analysis is a corrugated bearing in an aerospace auxiliary power unit. The baseline pressure of the operating environment dynamically decreases with flight altitude, causing dynamic changes in the parameters of the dimensionless formula. Simultaneously, the operating environment temperature reaches as high as 400 degrees Celsius. During the parameter initialization phase, the computer equipment is configured to call a high-temperature material database, interpolate and reduce the initial baseline elastic modulus of the material based on the temperature characteristic curve, and update the fluid dynamics equation parameters using high-temperature air viscosity.

[0061] In the lifecycle evolution module, in addition to the stress cycle caused by high-frequency rotation speed, the computer equipment also incorporates the low-frequency, high-amplitude stress cycle data generated during start-up and shutdown into the load spectrum array of the damage calculation module. Under low-pressure, low-initial-modulus data settings, the first-layer Reynolds equation solution module and the finite element structural deformation module require more internal loop steps to achieve a residual below the preset tolerance. In the second-layer stiffness self-consistency module, due to the reduced initial modulus base, the same increase in damage factor will lead to a more significant weakening of physical support. The algorithm strictly executes local stiffness judgment logic (absolute difference comparison) at each node; only after self-consistent convergence is feature extraction and lifecycle advancement allowed. This process verifies the data processing completeness of the algorithm structure in this invention. Through rigorous looping of underlying partial differential equations and algebraic equations, the algorithm accurately outputs the bearing's life curve and specific time-domain values ​​of degradation nodes under this extreme condition.

[0062] In the data processing flow described in the above embodiments, a dedicated hardware and software system architecture was constructed to support the physical implementation of the analysis method of this application. A corrugated bearing performance degradation analysis device is instantiated in memory space as multiple specific data processing logic modules. The system is divided into five modules: The first module initializes the mesh data and global matrix, and reads the boundary conditions; the second module performs discrete solutions to the Reynolds equations and calculates nodal displacements of the finite element model under given local stiffness constraints, continuously checks the convergence of the pressure field data through conditional loops, and outputs the displacement array of the flat foil nodes; the third module receives the displacement array, calls the matrix multiplication kernel function to calculate microscopic strain and stress, runs the fatigue cycle counting algorithm, outputs the continuous damage factor, performs scalar operations to update material property parameters, and reconstructs the local constraint stiffness submatrix; this module controls the execution flow between itself and the second module through conditional statements; the fourth module, after the third module confirms convergence, executes the partial differential equations of partial differential perturbation to extract eight dynamic coefficients, performs matrix eigenvalue decomposition to obtain system damping characteristics, and finally compares the extracted parameters with thresholds for judgment; the fifth module acts as a time step controller, updates the outer loop count variable, and triggers log writing operations. This division of logical modules ensures efficient concurrent execution of the entire nested iterative method on the computer processor.

[0063] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for analyzing the performance degradation of corrugated foil bearings considering the fatigue characteristics of weld points, characterized in that, The analysis method includes three iterative computation layers nested from the inside out, with the specific steps as follows: In the first fluid-structure interaction basic iterative layer, the dynamic air film pressure distribution is solved to obtain the air film thickness under the coupled state and the first flat foil deformation at the welded joint inside the corrugated foil bearing. In the second layer of self-consistent iteration of local stiffness of weld joint, the deformation of the first flat foil is extracted, and the actual elastic modulus and local stiffness estimate of the weld joint material are updated in combination with the continuous damage model until the local stiffness difference between two adjacent iteration steps meets the preset convergence condition, and the weld joint stiffness retention rate and dynamic stiffness damping parameters with mechanical self-consistency are output. In the third-level full-life-cycle performance evolution iteration layer, the overall dynamic behavior of the system is calculated based on the dynamic stiffness damping parameters and the stiffness retention rate at the weld, so as to output the performance degradation judgment result of the corrugated foil bearing.

2. The method for analyzing the performance degradation of corrugated foil bearings considering the fatigue characteristics of weld points according to claim 1, characterized in that, In the first fluid-structure interaction basic iterative layer, the dynamic air film pressure distribution is obtained by numerically solving the dimensionless dynamic Reynolds equation; Furthermore, the thickness of the air film is affected by the combined effects of foil deformation, eccentricity, eccentricity angle, and nominal bearing clearance.

3. The method for analyzing the performance degradation of corrugated foil bearings considering the fatigue characteristics of weld points according to claim 1, characterized in that, In the second layer of self-consistent iteration of local stiffness of weld joint, the actual elastic modulus of the weld material is updated in combination with the continuous damage model, including: calculating the continuous damage factor based on the iteration results of the first layer; quantifying the attenuation of material properties due to fatigue based on the difference ratio between the initial elastic modulus and the continuous damage factor, thereby calculating the updated actual elastic modulus.

4. The method for analyzing the performance degradation of corrugated foil bearings considering the fatigue characteristics of weld points according to claim 3, characterized in that, The calculation of the continuous damage factor is based on the change in the effective bearing area; The continuous damage factor is equal to the ratio of the effective bearing area of ​​the damaged area considering the first layer of iteration results to the initial effective bearing area of ​​the weld.

5. The method for analyzing the performance degradation of corrugated foil bearings considering the fatigue characteristics of weld points according to claim 1, characterized in that, The preset convergence condition is: In the second layer of self-consistent iterative layer of local stiffness of weld joints, the difference between the local stiffness of the next iteration step and the local stiffness of the previous iteration step is less than the preset minimum deviation.

6. The method for analyzing the performance degradation of corrugated foil bearings considering the fatigue characteristics of weld points according to claim 1, characterized in that, In the third layer of full life cycle performance evolution iteration layer, the performance degradation judgment result of the corrugated foil bearing includes a first judgment criterion for the reliability of the weld. The first criterion is to determine whether the stiffness retention rate of the weld is lower than the critical threshold of 70%; if it is lower than the critical threshold, the weld point of the current weld is determined to be unreliable according to the welding dynamics theory.

7. The method for analyzing the performance degradation of corrugated foil bearings considering the fatigue characteristics of weld points according to claim 6, characterized in that, The performance degradation determination result of the foil bearing also includes a second determination criterion for the stability of the rotor system. The second criterion includes: substituting the dynamic stiffness and damping parameters obtained through iteration into the rotor dynamics equation to carry out steady-state calculations and obtain the steady-state logarithmic decay rate.

8. The method for analyzing the performance degradation of corrugated foil bearings considering the fatigue characteristics of weld points according to claim 7, characterized in that, The specific steps for assessing the bearing condition according to the second judgment criterion are as follows: Determine whether the steady-state logarithmic decay rate is less than zero; if the steady-state logarithmic decay rate is less than zero, it proves that the rotor system has become unstable, and thus it is determined that the entire corrugated foil bearing is unreliable.

9. The method for analyzing the performance degradation of corrugated foil bearings considering the fatigue characteristics of weld points according to claim 1, characterized in that, The basic structure of the corrugated foil bearing consists of a flat foil, a corrugated foil, and a bearing housing; the starting point of the flat foil coincides with the starting point of the corrugated foil, and they are both fixedly connected to the bearing housing through the weld joint.

10. The method for analyzing the performance degradation of corrugated foil bearings considering the fatigue characteristics of weld points according to claim 7, characterized in that, By applying the first or second judgment criteria to obtain the performance degradation judgment result, the degradation risk of the corrugated foil bearing can be identified in advance before macroscopic fracture occurs at the weld and the system exhibits severe vibration.

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