A method of arranging optical fiber sensors for monitoring crack propagation in high speed running gears

Abstract

The application provides a kind of optical fiber sensor arrangement method for monitoring crack propagation of high-speed running gear, comprising: S1, establishing a finite element model of gear without crack, obtaining stress distribution under crack-free state, determining the maximum bending stress region, and extracting the stress component of each node and calculating the principal stress vector direction;S2, according to the stress distribution and the principal stress vector direction, the comprehensive stress peak value is determined as the initial position of crack, and the angle of initial crack is determined according to the principal stress vector direction;S3, insert initial crack at the initial position and angle of crack, carry out dynamic simulation by using extended finite element method, simulate the propagation behavior of initial crack under cyclic loading, and obtain the predicted crack propagation path;S4, the principal stress vector direction of the optical fiber sensor axis and each corresponding point on the crack propagation path is overlapped and aligned, and the optical fiber sensor is laid along the crack propagation path by using the arc topology mode based on high-speed centrifugal force compensation.

Description

Technical Field

[0001] This invention relates to the field of aero-engine testing and fault diagnosis technology, specifically to a method for arranging fiber optic sensors to monitor the propagation of cracks in high-speed gears. Background Technology

[0002] The gear transmission system of an aero-engine is a core component for power transmission and energy conversion in aircraft, and its operating condition directly affects the reliability and safety of the aircraft. Compared with conventional industrial gears, aero-engine gears typically operate under extreme conditions, such as high speed, high load, and drastic temperature changes. Under such harsh conditions, fatigue crack initiation and propagation are among the main modes leading to their eventual failure. Therefore, early detection and warning of gear structural cracks are crucial for avoiding catastrophic accidents and extending the lifespan of critical components. Currently, existing technologies in gear condition monitoring have many limitations in terms of sensor placement. Existing methods rely heavily on engineering experience and qualitative analysis to determine sensor installation locations. Moreover, the traditional sensor placement is not strongly correlated with crack damage mechanisms, failing to form a closed-loop design process from damage mechanism analysis to detection point optimization. Thus, the core problem of existing technologies is the disconnect between sensor placement strategies and the physical process of gear damage evolution under actual working loads, lacking accurate data support. Summary of the Invention

[0003] In view of this, the present invention provides a method for arranging fiber optic sensors to monitor the propagation of cracks in high-speed gears, so as to improve the timeliness and accuracy of monitoring.

[0004] This invention provides the following technical solution: a method for arranging fiber optic sensors to monitor the propagation of cracks in high-speed gears, comprising:

[0005] S1. Establish a crack-free finite element model of the gear, apply the rotational speed and torque load corresponding to the gear's operating conditions to perform transient dynamic simulation, obtain the stress distribution under crack-free conditions, determine the region of maximum bending stress, and use the stress tensor eigenvector decomposition method to extract the stress components of each node and calculate the direction of the principal stress vector. S2. Based on the stress distribution and the direction of the principal stress vector, the peak value of the combined stress is determined as the initial position of the crack, and the angle of the initial crack is determined based on the direction of the principal stress vector. S3. Insert an initial crack at the initial position of the crack and at the angle, and use the extended finite element method to perform dynamic simulation to simulate the propagation behavior of the initial crack under cyclic loading and obtain the predicted crack propagation path. S4. Align the axial direction of the fiber optic sensor with the principal stress vector direction of each corresponding point on the crack propagation path, and deploy the fiber optic sensor along the crack propagation path using an arc topology method based on high-speed centrifugal force compensation.

[0006] Compared with existing technologies, the beneficial effects achieved by at least one of the above-mentioned technical solutions adopted in this invention include: enabling the sensor to act directly on the critical path of crack evolution, allowing the detection system to provide early warning of crack initiation and to track the propagation process of macroscopic cracks in real time. Furthermore, the use of a high-speed centrifugal force-compensated arc topology optimization layout process provides a theoretical basis for the bonding of high-speed rotating gear sensors. Attached Figure Description

[0007] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0008] Figure 1 This is a flowchart of the fiber optic sensor distribution method based on the simulation of crack propagation in high-speed aerospace gears according to the present invention. Figure 2 This is a flowchart of the gear dynamics meshing simulation of the present invention; Figure 3 This is a schematic diagram illustrating the principle of fatigue fracture analysis for this invention. Detailed Implementation

[0009] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0010] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0011] like Figures 1 to 3 As shown, the present invention aims to establish an efficient and high-precision integrated simulation process that can accurately simulate the entire process of tooth root crack initiation and propagation under complex working conditions, reveal its inherent laws, and provide theoretical basis and data support for condition detection, life prediction and condition-based maintenance of aero-engine gears.

[0012] To address the shortcomings of existing technologies, this invention proposes a method for arranging fiber optic sensors for monitoring high-speed gears in aero-engines based on finite element analysis of gear crack propagation, comprising: S1. Crack-free multi-coupled gear dynamics simulation and stress vector field extraction: A finite element model of a high-speed, crack-free aero-engine gear is established to determine its basic parameters. Transient dynamics simulation is performed by applying rotational speed and torque loads corresponding to the aero-engine gear's operating conditions to obtain a high-precision dynamic cloud map of the gear's meshing under crack-free conditions. The maximum bending stress point and region under high-speed rotating load are accurately determined. Furthermore, the stress components at each node are extracted using the stress tensor eigenvector decomposition method. And calculate the direction of the principal stress vector. The location and direction of the initial pre-fabricated crack are determined based on its stress distribution data and the direction of the principal stress vector.

[0013] S2. Analyze the stress distribution cloud map obtained from the dynamic simulation and select the initial crack location in the stress concentration area. Based on the stress cloud map analysis, obtain the stress distribution near the weight reduction hole in the gear web and at the gear root. Calculate the direction of the principal stress vector using the stress tensor eigenvector decomposition method. Determine the initial crack location at the peak of the combined stress, and determine the angle of the initial crack based on the direction of the principal stress vector.

[0014] S3. Insert an initial crack at the determined initial crack position and angle, and perform dynamic simulation again using fracture mechanics criteria to simulate the crack propagation behavior under cyclic loading, obtaining one or more predicted crack propagation paths. Furthermore, calculate the stress intensity factor at the crack tip in different directions in real time, and based on the fracture criteria, simulate the crack propagation path. This path is the crack propagation path. .

[0015] S4. Fiber optic sensor vector alignment and "arc topology" optimization layout based on high-speed centrifugal force compensation, aligning the fiber optic sensor axis with the first principal stress vector direction at corresponding points on path L. Alignment is achieved through overlapping. A pre-defined micro-arc bonding process is used between fixed points on the gear surface, utilizing the tension component of the optical fiber itself to compensate for the centrifugal force generated by high-speed rotation. This achieves the purpose of inspecting high-speed aerospace gears.

[0016] The stress tensor eigenvector decomposition method in step S1 is as follows. The plane stress tensor at a point on the gear surface is S: Let... , eigenvalue equation det(S- =0, thus obtaining the principal stresses. Corresponding principal stress direction angle Shear stress:

[0017] Thus, the formula for the direction of the stress vector is derived:

[0018] in Principal stress direction angle, Represents the normal stress in the x and y directions. This represents plane shear stress. During deployment, ensure the fiber optic sensor axis is aligned with the coordinate system of that point. With consistent orientation, the physical fields that enable strain capture are matched.

[0019] In step S2, dynamic simulation is performed by applying the speed and torque loads corresponding to the aero-engine operating conditions to obtain a high-precision, crack-free meshing simulation dynamic cloud map of the gears. This accurately determines the maximum bending stress point and region under high-speed rotating loads, and the location of the pre-existing initial crack is determined based on the stress distribution data. The multi-degree-of-freedom dynamic equations for transient dynamic finite element analysis are as follows:

[0020] Where M is the mass matrix, C is the damping matrix, and K(t) is the time-varying stiffness matrix. For node acceleration, { Let {x} be the velocity and {X} be the displacement. F(t) is the column vector of the external load.

[0021] Analyzing the stress distribution cloud map obtained from dynamic simulation, the initial crack location is selected in the stress concentration area. Particular attention is needed for aerospace gears, in addition to the tooth root region which is generally prone to crack initiation. Based on the stress cloud map data, a detailed analysis of the stress distribution near the weight-reduction holes in the web of lightweight aerospace gears is conducted. The direction of the principal stress vector is calculated using the stress tensor eigenvector decomposition method. The peak value of the combined stress is determined as the initial crack location, and the angle of the initial crack is determined based on the direction of the principal stress vector.

[0022] An initial crack is inserted at the determined initial crack location and angle. A dynamic simulation is then performed again using fracture mechanics criteria to simulate the crack propagation behavior under cyclic loading, obtaining one or more predicted crack propagation paths. Furthermore, the stress intensity factor at the crack tip in different directions is calculated in real time, and the crack propagation path Ln is simulated based on the fracture criteria.

[0023] Based on fiber optic sensor vector alignment and optimized layout using "arc topology" compensation based on high-speed centrifugal force, the axial direction of the fiber optic sensor is aligned with the principal stress vector directions at corresponding points along the crack propagation path Ln. Alignment is performed to achieve the purpose of inspecting high-speed gears in aero engines.

[0024] Step S1 includes: S1.1: The parameters of the crack-free gear model include the number of teeth of the driving and driven gears, module, tooth width, pitch circle, addendum circle, dedendum circle, pressure angle, addendum coefficient, and clearance coefficient.

[0025] The aforementioned dynamic simulation includes: S1.2: In the finite element analysis software, the gear dynamics analysis model is meshed using tetrahedral elements. The mesh is then refined for the tooth contact area to improve calculation accuracy.

[0026] S1.3: Set simulation conditions for the finite element model, use the generalized Lagrange method for solution, and set the interface treatment to adjust the contact to adaptively capture the meshing contact. Set the boundary conditions to apply a rotation angle of 0 to 200° to the pinion (driving gear) and a torque of 1000 N·m to the driven gear. The calculation time is 0.01 s.

[0027] S1.4: The stress components of each node also need to be extracted using the stress tensor eigenvector decomposition method. And calculate the direction of the principal stress vector. The location and direction of the initial pre-fabricated crack are determined based on its stress distribution data and the direction of the principal stress vector.

[0028] The initial crack initiation location was determined by performing transient dynamic finite element analysis on the gear pair to obtain the equivalent stress distribution cloud map within typical working load cycles. The stress peak points in key areas such as the tooth root transition curve and the weight reduction holes in the aerospace gear were precisely identified; these locations were established as the potential initial crack locations for gear damage. In other words, the location of the pre-existing crack was determined. The formula for solving the principal stress of the damage criterion adapted to the finite element analysis is as follows:

[0029] In the formula The normal stress in the x-direction, The normal stress is in the y-direction. This is the shear stress.

[0030] Step 3 includes: The finite element method is used, and the simulation conditions include setting the initial crack parameters, including the initial crack location, the initial crack length L, and the initial crack direction α.

[0031] The material and contact properties under high-speed operating conditions are set, and the high-speed aero-engine rotational speed is applied at the reference point of the driving gear; the drag torque corresponding to the high-speed operation is applied at the reference point of the driven gear.

[0032] The crack propagation angle θn is calculated based on the maximum tangential stress fracture criterion, and the crack propagation process is visualized using the Fracture module. The crack propagation path is also obtained. The formula for the crack propagation angle (existing formula) is as follows: ) in It is the crack propagation angle. These correspond to the stress intensity factors for the opening and sliding types, respectively.

[0033] Based on the fiber optic sensor placement according to the crack propagation path, during the analysis, the stress intensity factor at the crack tip is calculated in real time using the Extended Finite Element Method (XFEM) technique. Furthermore, the crack morphology and propagation path are dynamically updated according to the fatigue crack propagation law. The crack propagation amount calculated in a single simulation step using Paris is the core step size basis for path iteration and is directly used for dynamically updating the crack length in XFEM. The core formula of Paris is:

[0034] Single-step extended step size:

[0035] C represents the fatigue parameter of the gear material, and m represents the fatigue coefficient of the gear material. N corresponds to the number of meshing cycles in a single step. Stress intensity factor amplitude at step k. It is the crack propagation step size at step k.

[0036] By determining the direction through the expansion angle and the distance through the expansion step size, the coordinates of the crack tip are iteratively updated step by step, and the complete crack path formula is finally generated as follows:

[0037]

[0038] in These are the coordinates of the crack tip at step k. Then it is the new coordinate of the (k+1)th step.

[0039] According to the first path L1, the fiber optic sensor is radially arranged across the root region of 2 to 3 teeth along the gear surface directly below the tooth root transition curve. According to the second path L2, the fiber optic sensor can be arranged starting from the tooth root and extending towards the gear center or adjacent lightweight hole, continuing to the circumference of the lightweight hole. It then extends from the intermediate shaft. Alternatively, a fiber optic grating can be pre-installed along the principal stress vector direction at a distance of 0.5-1 cm from the crack tip to facilitate real-time monitoring of crack propagation. Based on the simulated crack propagation path Ln (such as the first path L1 or the second path L2), when arranging the fiber optic sensor, it is necessary to ensure that the axis of the fiber optic sensor coincides with and is aligned with the principal stress vector direction at corresponding points on the crack propagation path Ln. This vector alignment maximizes the gain of the strain signal captured by the fiber optic grating and effectively filters out irrelevant shear interference, improving monitoring accuracy. The fiber optic grating spacing no longer uses the traditional equal spacing method but adopts an optimized layout based on high-speed centrifugal force compensation using an "arc topology". The target grating spacing is determined by a combination of geometric curvature constraints and dynamic compensation. To prevent the optical fiber from detaching or breaking due to centrifugal force during high-speed rotation, a compensating arc coefficient is introduced during deployment. This design ensures that even at high speeds of tens of thousands of revolutions per minute, centrifugal force will not cause the optical fiber to peel off; instead, it will cause the micro-arc-shaped units to adhere more tightly to the adhesive layer due to the influence of the tension component.

[0040] Specifically, the radian topology approach based on high-speed centrifugal force compensation includes: A curvature adaptive algorithm is used to determine the target spacing of fiber Bragg gratings based on the geometric curvature constraints and dynamic compensation of the crack propagation path. ;in, For the target grating spacing, Based on the maximum spacing, the local curvature of the k(s) path, Centrifugal acceleration, denoted as the centrifugal acceleration threshold, A as the geometric correction coefficient, and B as the kinetic stability coefficient.

[0041] The preset compensation radian uses the compensation radian coefficient. To confirm: ; ； ; ; Where m is the fatigue coefficient of the gear material. To compensate for the radian coefficient, This refers to the density of the optical fiber material itself. Here, r represents the gear's operating angular velocity, and r is the distance from the gear's center to the placement position. The straight-line distance between adjacent fixed points. q represents the pretension for fiber optic installation, h represents the arc height, and S represents the arc length of the parabola.

[0042] The following is a detailed description of a specific embodiment: S1 establishes a gear dynamics analysis model, where the gear parameters are as follows: Table 1 Geometric Parameters of Spur Gears

[0043] S2 uses tetrahedral elements to mesh the gear dynamics analysis model in the finite element analysis software. Mapped meshing is employed, and mesh refinement is applied to the tooth contact area to improve computational accuracy.

[0044] S3 sets simulation conditions for the finite element model and verifies the effectiveness of the simulation conditions, including: 3.1 The generalized Lagrange method is used for solving the problem, and the interface processing is set to adjust the contact in order to adaptively capture the meshing contact.

[0045] 3.2 The boundary conditions are set as follows: a rotation angle of 0 to 200° is applied to the pinion (driving gear), a torque of 1000 N·m is applied to the driven gear, and the calculation time is 0.01 s.

[0046] 3.3 The effectiveness of the simulation conditions was verified through stress solution analysis. When the simulation conditions were valid, a finite element model with the simulation conditions set was output. When the simulation conditions were invalid, the simulation conditions were reset. The simulation conditions included the applied load and the set boundary conditions. The contact between the meshing surfaces of the two gears was set as frictional contact with a friction coefficient of 0.1 and a normal stiffness factor of 1. The minimum mesh size was 0.1 mm, the mesh number was 187,000 elements, and the average mass was 0.9488. The maximum stress on the tooth surface of the meshing gears was in the range of 350~450 MPa, with the maximum stress at the root of the gear without cracks reaching 426.9 MPa.

[0047] Using the transient dynamics analysis module, a dynamic simulation of gear meshing is performed on a finite element model with set simulation conditions. This yields a high-precision stress distribution cloud map of the gear under a crack-free state, accurately determining the maximum bending stress point and region under high-speed rotating loads. This location is considered the gear's critical section or subsurface defect. An initial crack will be preset at this point. The multi-degree-of-freedom dynamic equations for transient dynamics finite element analysis are as follows:

[0048] Where [M] is the mass matrix, [C] is the damping matrix, and [K(t)] is the time-varying stiffness matrix. For node acceleration, { Let {x} be the velocity and {X} be the displacement. F(t) is the column vector of the external load.

[0049] The formula for solving the principal stress of the damage criterion adapted to finite element analysis is as follows:

[0050] in It is the crack angle relative to the current direction of the crack. These correspond to the stress intensity factors for the opening and sliding types, respectively.

[0051] The stress tensor eigenvector decomposition method is as follows. Let the plane stress tensor at a point on the gear surface be S: Let... , eigenvalue equation det(S- =0, thus obtaining the principal stresses. Corresponding principal stress direction angle Shear stress:

[0052] Thus, the formula for the direction of the stress vector is derived:

[0053] During deployment, ensure that the fiber optic sensor axis is aligned with the coordinate system of that point. With consistent orientation, the physical fields that enable strain capture are matched.

[0054] A gear crack model with a crack was established. The initial crack parameters were set as follows: the initial crack location was set at the point of maximum stress at the tooth root, the initial crack length was 0.5 mm, and the initial crack direction was 45°. A high-speed aero-engine load was applied. The rotational speed determined by the aero-engine was applied at the reference point of the driving gear: the driving gear speed was 350 r / s = 19000 r / min; a drag torque corresponding to the high-speed operation was applied at the reference point of the driven gear: 1000 N·m.

[0055] The crack propagation of a gear model with cracks was simulated using the finite element method (XFEM) to obtain the crack propagation path at the gear tooth root. The Fracture module was used to demonstrate the crack propagation process.

[0056] During the analysis, the stress intensity factor at the crack tip was calculated in real time using the extended finite element method (XFEM), and the crack morphology and propagation path were dynamically updated according to the fatigue crack propagation law. Paris's law was used as the fatigue crack propagation model, and the ΔK at the crack tip was extracted after each incremental step, and the crack length a was updated accordingly. The formula for the crack propagation angle required to calculate the path is as follows: ) in It is the crack initiation angle in the current direction of the crack. These correspond to the stress intensity factors for the opening and sliding types, respectively.

[0057] The crack propagation amount calculated using Paris in a single simulation step is the core step size criterion for path iteration and is directly used for dynamic crack length updates in XFEM. The core formula of Paris is:

[0058] Single-step extended step size:

[0059] By determining the direction through the expansion angle and the distance through the expansion step size, the coordinates of the crack tip are iteratively updated step by step, and the complete crack path formula is finally generated as follows:

[0060]

[0061] in These are the coordinates of the crack tip at step k. Then it is the new coordinate of the (k+1)th step.

[0062] The fiber optic cable is pasted based on the crack propagation path obtained from simulation analysis to achieve the effect of detecting the life safety of high-speed gears in aero engines.

[0063] According to path L1, the tooth root region of 2 to 3 teeth is traversed radially along the gear surface directly below the tooth root transition curve.

[0064] According to path L2, starting from the tooth root, the path can be laid out towards the gear center or the adjacent lightweight hole, extending to the circumference of the lightweight reduction hole. It then extends out from the intermediate shaft.

[0065] To facilitate real-time extraction of the crack propagation initiation signal, a fiber Bragg grating is placed 0.5-1 cm away from the initial crack tip along the principal stress vector direction, and led out from the central axis. This vector alignment method ensures that the strain signal captured by the fiber Bragg grating is maximized and irrelevant shear interference is effectively filtered out, improving monitoring accuracy.

[0066] The fiber optic cable layout is optimized using an "arc topology" approach based on high-speed centrifugal force compensation. The target grating spacing is determined jointly by geometric curvature constraints and dynamic compensation. To prevent the fiber from detaching or breaking due to centrifugal force during high-speed rotation, a compensating arc coefficient is introduced during the layout process. The micro-arc-shaped unit fits the gear better due to the influence of the tension component.

[0067] The beneficial effects of this invention are as follows: First, a precise model of the crack-free gear was completed using the finite element method (FEM). Meshing, boundary conditions, and stress analysis were performed to determine the maximum stress distribution range of the aero-engine gear. The principal stress vector direction was calculated using the stress tensor eigenvector decomposition method, preparing for the subsequent pre-determining of crack locations and angles. Then, using XFEM crack propagation technology, the gear crack propagation path was simulated, allowing for a better study of the crack propagation law. By directly applying sensors to the critical path of crack evolution, the detection system can provide early warning of crack initiation and track the macroscopic crack propagation process in real time. Furthermore, the "arc topology" optimization layout process with high-speed centrifugal force compensation was employed, providing a theoretical basis for the bonding of sensors to high-speed rotating gears. This invention integrates modern simulation technologies and process design, including dynamics, finite element method, and fracture mechanics. It realistically simulates the strongly coupled physical process of crack propagation altering the system's dynamic characteristics, while the changing dynamic loads react upon crack propagation, providing a certain reference for a deeper understanding of the failure evolution mechanism of high-speed gear systems. This greatly improves the accuracy and timeliness of testing.

[0068] The above description is merely a specific embodiment of the present invention and should not be construed as limiting the scope of the invention. Therefore, substitutions of equivalent components, or equivalent changes and modifications made within the scope of protection of this invention, should still fall within the scope of this invention. Furthermore, the technical features, technical features and technical solutions, and technical solutions in this invention can be freely combined and used.

Claims

1. A method for arranging fiber optic sensors to monitor the propagation of cracks in high-speed gears, characterized in that, include: S1. Establish a crack-free finite element model of the gear, apply the rotational speed and torque load corresponding to the gear's operating conditions to perform transient dynamic simulation, obtain the stress distribution under crack-free conditions, determine the region of maximum bending stress, and use the stress tensor eigenvector decomposition method to extract the stress components of each node and calculate the direction of the principal stress vector. S2. Based on the stress distribution and the direction of the principal stress vector, the peak value of the combined stress is determined as the initial position of the crack, and the angle of the initial crack is determined based on the direction of the principal stress vector. S3. Insert an initial crack at the initial position of the crack and at the angle, and use the extended finite element method to perform dynamic simulation to simulate the propagation behavior of the initial crack under cyclic loading and obtain the predicted crack propagation path. S4. Align the axial direction of the fiber optic sensor with the principal stress vector direction of each corresponding point on the crack propagation path, and deploy the fiber optic sensor along the crack propagation path using an arc topology method based on high-speed centrifugal force compensation. The arc topology method based on high-speed centrifugal force compensation includes: A curvature adaptive algorithm is used to determine the target spacing of fiber Bragg gratings based on the geometric curvature constraints and dynamic compensation of the crack propagation path. ;in, For the target grating spacing, Given the maximum basic spacing, k(s) represents the local curvature of the path. Centrifugal acceleration, Where A is the centrifugal acceleration threshold, B is the geometric correction coefficient, and A is the kinetic stability coefficient. In the arc topology method based on high-speed centrifugal force compensation, the preset compensation arc is achieved using a compensation arc coefficient. To confirm: ； ； ； ； To compensate for the radian coefficient, This refers to the density of the optical fiber material itself. Here, r represents the gear's operating angular velocity, and r is the distance from the gear's center to the placement position. The straight-line distance between adjacent fixed points. q represents the pretension for fiber optic installation, h represents the arc height, and S represents the arc length of the parabola.

2. The fiber optic sensor arrangement method for monitoring crack propagation in high-speed gears according to claim 1, characterized in that, The parameters of the crack-free gear finite element model include: number of teeth of the driving and driven gears, module, tooth width, pitch circle diameter, addendum circle diameter, dedendum circle diameter, pressure angle, addendum coefficient, and clearance coefficient.

3. The fiber optic sensor arrangement method for monitoring crack propagation in high-speed gears according to claim 2, characterized in that, In step S1, the transient dynamic simulation includes: The gear finite element model is meshed with tetrahedral elements, and the mesh of the tooth contact area is refined. The simulation conditions were set, and the generalized Lagrange method was used to solve the problem. The interface processing was set to adjust the contact to adaptively capture the meshing contact. The boundary conditions were set to apply a rotation angle to the driving wheel and a torque to the driven wheel. By performing stress calculation, the stress distribution cloud map under the crack-free state is obtained.

4. The fiber optic sensor arrangement method for monitoring crack propagation in high-speed gears according to claim 3, characterized in that, The stress tensor eigenvector decomposition method includes: The plane stress tensor at a point on the gear surface is expressed as S. The principal stresses are solved using the eigenvalue equations, and the direction angles of the principal stresses are calculated using the formulas. , ; in, The normal stress represents the stress in the x-direction. Represents the normal stress in the y-direction. This represents plane shear stress.

5. The fiber optic sensor arrangement method for monitoring the crack propagation of high-speed gears according to claim 4, characterized in that, In step S2, the initial location of the crack is determined using the multi-degree-of-freedom dynamic equations of transient dynamic finite element analysis: Where [M] is the mass matrix, [C] is the damping matrix, and [K(t)] is the time-varying stiffness matrix. For the nodal acceleration vector, Let {X} be the velocity vector, {X} be the displacement vector, and F(t) be the column vector of the external load. By solving the equation, the equivalent stress distribution cloud map of the gear in a typical working load cycle is obtained, the stress peak point of the tooth root transition curve and the gear weight reduction hole area is accurately located, and the principal stress direction angle is calculated by combining the stress tensor eigenvector decomposition method to determine the initial position and angle of the crack.

6. The fiber optic sensor arrangement method for monitoring the crack propagation of high-speed gears according to claim 5, characterized in that, In step S3, the inserted initial crack is used to create a three-dimensional crack using the extended finite element method, and the parameters are evolved using the maximum principal stress damage criterion, where the principal stress σ is represented as: .

7. The fiber optic sensor arrangement method for monitoring crack propagation in high-speed gears according to claim 6, characterized in that, In step S3, simulating the propagation behavior of the initial crack under cyclic loading includes: Set the initial crack parameters, including the initial crack location, initial crack length L, and initial crack direction α; Apply material and contact properties under high-speed conditions, apply rotational speed at the reference point of the driving gear, and apply resistance torque at the reference point of the driven gear; Calculate the crack propagation angle based on the maximum tangential stress fracture criterion. Where K1 is the opening stress intensity factor and K2 is the sliding stress intensity factor. The crack propagation angle; Calculate the crack propagation step size at step k. Where C is the fatigue parameter of the gear material, and m is the fatigue coefficient of the gear material. N is the number of meshing cycles corresponding to a single step. Let x be the stress intensity factor amplitude at step k. It is the crack propagation step size at step k; The direction is determined by the expansion angle, and the distance is determined by the expansion step size. The coordinates of the crack tip are iteratively updated step by step to generate a complete crack propagation path. ; ;in These are the coordinates of the crack tip at step k. It is the new coordinate of the crack tip at step k+1.

8. The fiber optic sensor arrangement method for monitoring the crack propagation of high-speed gears according to claim 7, characterized in that, Step S4 includes: The fiber optic sensor is regarded as a directional anisotropic sensor, and its axis is completely coincident with the direction of the principal stress vector at each corresponding point on the crack propagation path, so as to ensure that the strain signal captured by the fiber grating has the maximum gain and filters out shear interference. According to the crack propagation path, a first path L1 is arranged radially across the tooth root region of 2 to 3 teeth on the gear surface directly below the tooth root transition curve, and / or a second path L2 is arranged from the tooth root towards the gear center or adjacent lightweight weight reduction hole to the circumference of the weight reduction hole. Fiber gratings are arranged 0.5 cm to 1 cm away from the tip of the initial crack in the direction of the principal stress vector to monitor in real time whether the crack begins to propagate.

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