Gear fatigue crack propagation life calculation method and system under random dynamic load are considered

Abstract

The application provides a gear fatigue crack propagation life calculation method and system considering random dynamic load, and the method is as follows: a local plane coordinate system is established at a crack tip, and a crack propagation equation is constructed; time-varying mesh stiffness containing a tooth root crack feature is calculated; a vibration differential equation of a gear mesh pair is constructed and solved, and dynamic meshing forces of the gear pair under different crack states are obtained; the dynamic meshing forces of the gear pair under different crack states are processed, and a load spectrum is prepared, and variable amplitude load data with multi-periodicity are obtained; the variable amplitude load data are taken as boundary conditions, crack propagation is simulated, gear fatigue crack propagation data are read from a finite element data file; stress intensity factors are calculated based on the gear fatigue crack propagation data; and fatigue crack propagation life is estimated based on the Paris formula and the stress intensity factors. The method can improve the reliability and fatigue crack propagation life of the gear, improve the safety of equipment, and reduce maintenance costs.

Description

Technical Field

[0001] This invention relates to the field of fatigue testing of mechanical devices, and specifically to a method and system for calculating the fatigue crack propagation life of gears under random dynamic loads. Background Technology

[0002] Gear drives, characterized by high transmission efficiency, compact structure, reliable operation, long service life, and stable transmission ratio, are widely used in mechanical transmission fields. Generally speaking, gear drive failures primarily involve tooth failure, which manifests in various forms. Among all tooth failure modes, fatigue tooth breakage accounts for the largest proportion, followed by surface contact fatigue; therefore, fatigue failure is one of the most prevalent forms of gear failure. To improve gear reliability and service life, it is necessary to study simulation methods for gear fatigue life and tooth root cracks. Influenced by random factors such as environment and materials, the initiation and propagation process of fatigue cracks exhibits multi-stage and uncertain characteristics. Furthermore, the fault excitation generated by fatigue cracks directly affects the amplitude of alternating loads borne by the teeth, thus affecting the crack propagation speed. Conventional gear fatigue crack models based on static analysis generally assume a fixed initiation and propagation path for cracks under constant cyclic loads. However, since gears in actual operation are subjected to random alternating loads, it is impossible to accurately simulate the crack propagation characteristics and fatigue life of gears. Summary of the Invention

[0003] In order to overcome the defects existing in the prior art, the purpose of this invention is to provide a method and system for calculating the fatigue crack propagation life of gears under random dynamic loads.

[0004] To achieve the above-mentioned objectives of this invention, this invention provides a method for calculating the fatigue crack propagation life of gears under random dynamic loads, comprising the following steps:

[0005] Determine the structural and material parameters of the gear meshing pair;

[0006] Establish a local planar coordinate system at the crack tip and construct the crack propagation equation;

[0007] Calculate the time-varying meshing stiffness k containing tooth root crack characteristics. m ;

[0008] Based on the time-varying meshing stiffness k m The vibration differential equation of the gear meshing pair is constructed based on the lumped parameter model.

[0009] Solve the vibration differential equation of the gear meshing pair to obtain the dynamic meshing force of the meshing pair under different crack states;

[0010] The dynamic meshing force of the gear pair under different crack states is processed and compiled into a load spectrum to obtain variable amplitude load data with multiple periods.

[0011] Based on the extended finite element theory, variable amplitude load data is used as boundary conditions to simulate the crack propagation equation and read gear fatigue crack propagation data from the finite element data file.

[0012] Stress intensity factor K was calculated based on gear fatigue crack propagation data. Ⅰ ;

[0013] The fatigue crack propagation life N is predicted based on the Paris formula and stress intensity factor.

[0014] The preferred scheme for calculating the fatigue crack propagation life of gears under random dynamic loads is as follows: The crack propagation equation is... In the formula, a is the crack length; a0 is the initial crack length; n is the number of crack propagation substeps; a n θ represents the crack propagation step size. n The angle at which the crack propagates.

[0015] The preferred scheme for calculating the fatigue crack propagation life of gears under random dynamic loads includes the following steps for calculating the meshing stiffness of a single tooth and a single pair of gears:

[0016] The time-varying meshing stiffness k m This includes the meshing stiffness of the single-tooth region and the meshing stiffness of the double-tooth region;

[0017] The calculation steps are as follows:

[0018] Calculate the Hertzian contact stiffness during gear meshing: Where E and v are Young's modulus and Poisson's ratio of the tooth material, and W is the tooth width;

[0019] Calculate the base stiffness of the gear: in, Refers to L * M * ,P * and Q * In the formula, α m The pressure angle; u f S is the distance from the meshing point to the tooth root fillet. f L*, M*, P*, and Q* represent the arc distance between the gear teeth and the gear base; X represents the arc distance between the gear teeth and the gear base. i * The approximate coefficients of the polynomial referred to; h fi θ is the ratio of the root circle radius to the hub radius; f Angle A is the angle between the tooth root and the center axis of the tooth. i B iC i D i and E i The coefficients are constants.

[0020] A stress model of the gear tooth with initial cracks is constructed. Integrating along the tooth height, the bending stiffness and shear stiffness of the gear tooth are calculated piecewise. Specifically, the bending stiffness, shear stiffness, and axial compressive stiffness during gear meshing are as follows: Where x is the coordinate along the tooth height; d is the distance from the meshing point to the tip of the tooth root crack; h is the distance from the meshing point of the gear pair to the center line of the tooth; and G is the shear modulus.

[0021] hy is the distance from the crack initiation point to the center line of the tooth; hc is the distance from the crack end point to the center line of the tooth; de is the distance from the crack initiation point to the meshing point; dt is the distance from the crack end point to the tooth root fillet; Hx is the radius of inertia.

[0022] Meshing stiffness in the single-tooth zone:

[0023] Meshing stiffness in the double-tooth region:

[0024]

[0025] In the formula, g represents the driven gear; p represents the driving gear; and i represents the single and double tooth meshing area.

[0026] The preferred scheme for calculating the fatigue crack propagation life of gears under random dynamic loads is as follows: The vibration differential equation of the gear meshing pair is expressed as:

[0027] in,

[0028] In the formula, M is the mass matrix; m p m is the mass of the driving wheel. g J is the mass of the driven wheel; p J is the moment of inertia of the driving wheel; g The moment of inertia of the driving wheel; and They represent x respectively i y i and θ i The acceleration vector; when i = 1, x i Let y be the displacement vector of the driving wheel in the x-direction. i Let θ be the displacement vector of the driving wheel in the y-direction. i For the angular displacement of the driving gear pair: when i = 2, x i The displacement vector of the driven wheel in the x-direction; y iθ is the displacement vector of the driven wheel in the y-direction; i For the angular displacement of the driven gear pair:

[0029] In the formula, They represent x respectively i y i velocity vector; c px c py k represents the support damping of the drive wheel in the x and y directions, respectively. px k py c represents the support stiffness of the drive wheel in the x and y directions, respectively. gx c gy k represents the support damping of the passive wheel in the x and y directions, respectively. gx k gy α represents the support stiffness of the driven wheel in the x and y directions, respectively; Fm represents the dynamic meshing force of the meshing pair; Tp and Tg represent the input torques of the driving wheel and driven wheel, respectively; R1 and R2 represent the base circle radii of the driving wheel and driven wheel, respectively; α p This represents the gear pressure angle.

[0030] The preferred scheme for calculating the fatigue crack propagation life of gears under random dynamic loads is as follows: Solve the vibration differential equation of the gear meshing pair to obtain the dynamic meshing force F under different tooth crack states. m =k m f(δ,b t )+c m f1(δ,b t ), where k m Represents gear meshing stiffness; c m Represents gear meshing damping; f(δ,b) t () represents the time-varying tooth flank nonlinear function:

[0031]

[0032] f1(δ,b t ) is f(δ,b t The derivative of ); δ is the displacement of the gear pair meshing point; b t For time-varying tooth flank backlash, 2b t =2b0+Δb=2b0+2(R1+R2)(inv(α)-inv(α0)), where b0 represents the initial tooth flank clearance; R i The base circle radius of the gear is represented by α; inv(α) represents the involute function, inv(α) = tan(α) - α, where α is a specified angle value.

[0033] The preferred scheme for calculating the fatigue crack propagation life of gears under random dynamic load is as follows: Based on the rainflow counting principle, the dynamic meshing force of the gear pair under different crack states is processed. First, the obtained dynamic meshing force of the gear pair is filtered to remove small values ​​and retain peak and valley values. Then, the data is discretized. Finally, rainflow cycle counting is performed to compile a load spectrum and obtain variable amplitude load data with multi-periodity.

[0034] The preferred scheme for calculating the fatigue crack propagation life of gears under random dynamic loads is as follows: The expression for gear fatigue crack propagation data is:

[0035]

[0036] In the formula, I represents the total number of grid cells; N i The shape function representing the standard finite element mode; u i H(x) represents the nodal displacements in the standard finite element mode; H(x) represents the displacement jump characteristics on both sides of the crack; a i The extended node degrees of freedom represent the extended functions associated with the jump discontinuous extensions; F(x) represents the tip asymptotic field function; b i The nodal degrees of freedom represent the expansion of the crack tip.

[0037] The preferred scheme for calculating the fatigue crack propagation life of gears under random dynamic loading is as follows: The specific steps for calculating the stress intensity factor based on gear fatigue crack propagation data are as follows:

[0038] An integration region is selected on the fatigue crack surface of the gear, and the energy release rate J at the crack tip is calculated within the integration region.

[0039] Where: Γ represents the integration path; W represents the strain energy density; σ represents the stress vector on the boundary of the integration path; ds represents the displacement on the integration path; x, y represent the local coordinates of the crack; u represents the displacement vector on the integration path;

[0040] Under elastic deformation, stress intensity factor In the formula, E represents the elastic modulus; v represents Poisson's ratio.

[0041] The preferred scheme for calculating the fatigue crack propagation life of gears under random dynamic loading is as follows: The Paris formula for calculating the fatigue crack propagation life is:

[0042] Where C and m are material constants, ΔK represents the range of stress intensity factors, and K is the stress intensity factor K between adjacent crack lengths. Ⅰ The difference between them, where N represents the fatigue crack propagation life.

[0043] This application also proposes a gear fatigue crack propagation life analysis system considering random dynamic loads, including a data acquisition module, a processing module, and a storage module. The data acquisition module and the processing module are communicatively connected. The data acquisition module acquires the structural and material parameters of the gear meshing pair and sends them to the processing module. The processing module is communicatively connected to the storage module. The storage module is used to store at least one executable instruction. The executable instruction causes the processing module to execute the gear fatigue crack propagation life calculation method considering random dynamic loads as described above.

[0044] The beneficial effects of this invention are:

[0045] This invention obtains the dynamic meshing force under different crack lengths by using the vibration differential equation of the gear meshing pair, which includes crack characteristics and time-varying backlash. The dynamic meshing force is processed into a dynamic load spectrum by rainflow counting and used as a load boundary condition. The load spectrum is then substituted into the finite element model to analyze and calculate the fatigue crack propagation life of the gear. The conclusions have the following significance for gear fatigue design.

[0046] (1) Improve the reliability and life of gears: By studying the fatigue crack propagation life of gears, we can find out the causes of gear fatigue failure, thereby optimizing gear design and materials, improving the reliability and life of gears, and reducing the impact of gear failures on equipment operation.

[0047] (2) Improve equipment safety: Gears are important components of many mechanical devices. If fatigue cracks occur in gears during use, it may lead to equipment failure or accidents. By studying the fatigue crack propagation life of gears, equipment safety can be improved and accidents caused by gear failures can be reduced.

[0048] (3) Reduce maintenance costs: Gear failures require repair or replacement, which leads to increased downtime and maintenance costs. By studying the fatigue crack propagation life of gears, the time of gear failure can be predicted, allowing for earlier repairs and reducing downtime and maintenance costs.

[0049] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0050] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0051] Figure 1 It is a six-degree-of-freedom gear dynamics lumped parameter model;

[0052] Figure 2 It is a force model of a gear tooth containing an initial crack;

[0053] Figure 3 This is a flowchart of dynamic load processing;

[0054] Figure 4 This is a schematic diagram of the two-dimensional integral region;

[0055] Figure 5 It is a gear tooth extended finite element model;

[0056] Figure 6 It is the dynamic meshing force of gears during the dynamic crack propagation process;

[0057] Figure 7 It is a rainflow histogram of the dynamic meshing force of gears during crack propagation;

[0058] Figure 8 This is a comparison diagram of fatigue crack paths of gears under dynamic and static loads;

[0059] Figure 9 This is a comparison chart of fatigue crack propagation life of gears under dynamic and static loads. Detailed Implementation

[0060] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0061] In the description of this invention, unless otherwise specified and limited, it should be noted that the terms "installation", "connection" and "linking" should be interpreted broadly. For example, they can refer to mechanical or electrical connections, or internal connections between two components. They can be direct connections or indirect connections through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms according to the specific circumstances.

[0062] like Figure 1 As shown, this invention provides a method for calculating the fatigue crack propagation life of gears under random dynamic loads, comprising the following steps:

[0063] Determine the structural and material parameters of the gear meshing pair.

[0064] The local planar coordinate system established at the crack tip is a coordinate system with the x-axis as the initial crack propagation direction and the y-axis perpendicular to the initial crack direction. The crack propagation equation is: In the formula, a is the crack length; a0 is the initial crack length; a i θ represents the crack propagation step size; n This represents the angle at which the crack propagates.

[0065] Calculate the time-varying meshing stiffness k containing tooth root crack characteristics. m .

[0066] Specifically, the time-varying meshing stiffness k m This includes the meshing stiffness of the single-tooth region and the meshing stiffness of the double-tooth region;

[0067] In this embodiment, the meshing stiffness of the single-tooth region is:

[0068]

[0069] Meshing stiffness in the double-tooth region:

[0070]

[0071] Where g represents the driven gear, p represents the driving gear; i represents the single / double tooth meshing area, when i is 1 it represents the single tooth area, when i is 2 it represents the double tooth area, k h The Hertzian contact stiffness during gear meshing is calculated using the following formula: E and v are Young's modulus and Poisson's ratio of the tooth material, and W is the tooth width. f The base stiffness of the gear is calculated using the following formula: in,

[0072] Refers to L * M * ,P * and Q * α m The pressure angle; u f S is the distance from the meshing point to the tooth root fillet. f L*, M*, P*, and Q* represent the arc distance between the gear teeth and the gear base; X represents the arc distance between the gear teeth and the gear base. i * The approximate coefficients of the polynomial referred to; h fi θ is the ratio of the root circle radius to the hub radius; f Angle A is the angle between the tooth root and the center axis of the tooth. i B i C i D i and E i is an empirical coefficient, and is a constant.

[0073] k b k represents the bending stiffness during gear meshing. s For shear stiffness, k aFor the axial compressive stiffness, the calculation steps for these three factors are as follows: Construct a force model of the gear tooth with initial cracks, integrate along the tooth height direction, and calculate the bending stiffness and shear stiffness of the gear tooth piecewise. Specifically, the bending stiffness, shear stiffness, and axial compressive stiffness during gear meshing are as follows: Where x is the coordinate along the tooth height, h is the distance from the meshing point of the gear pair to the center line of the tooth, and G is the shear modulus.

[0074] d is the distance from the meshing point to the tip of the tooth root crack; h y h c d e and d t like Figure 2 As shown, hy is the distance from the crack initiation point to the center line of the tooth; hc is the distance from the crack end point to the center line of the tooth; de is the distance from the crack initiation point to the meshing point; dt is the distance from the crack end point to the tooth root fillet; and Hx is the radius of inertia.

[0075] To prevent gear teeth from deforming due to load and heat propagation during meshing, a certain amount of backlash is left during manufacturing. During gear operation, the backlash is a time-varying parameter due to temperature changes, manufacturing errors, and tooth surface wear. This embodiment considers the influence of backlash variation on the dynamic excitation of the gear, calculating the time-varying backlash bt. The expression for the time-varying backlash bt is 2b. t =2b0+Δb=2b0+2(R1+R2)(inv(α)-inv(α0)), where b0 represents the initial tooth flank clearance; R i The base circle radius of the gear is represented by α; inv(α) represents the involute open function, inv(α) = tan(α) - α, where α is a specified angle value, usually taken as 20°.

[0076] Establish such as Figure 1 The six-degree-of-freedom gear dynamics lumped parameter model is shown. Based on this lumped parameter model, the vibration differential equations of the gear meshing pair are constructed. The method for constructing the lumped parameter model is existing technology and will not be elaborated further here.

[0077] The vibration differential equation of the gear meshing pair is expressed as:

[0078] in, M is the mass matrix; m p m is the mass of the driving wheel. g J is the mass of the driven wheel; p J is the moment of inertia of the driving wheel; g The moment of inertia of the driving wheel; and They represent x respectivelyi y i and θ i The acceleration vector, when i = 1, x i Let y be the displacement vector of the driving wheel in the x-direction. i Let θ be the displacement vector of the driving wheel in the y-direction. i For the angular displacement of the driving gear pair: when i = 2, x i Let y be the displacement vector of the driven wheel in the x-direction; i θ is the displacement vector of the driven wheel in the y-direction; i This represents the angular displacement of the driven gear pair.

[0079] In the formula, They represent x respectively i y i velocity vector; c px c py k represents the support damping of the drive wheel in the x and y directions, respectively. px k py c represents the support stiffness of the drive wheel in the x and y directions, respectively. gx c gy k represents the support damping of the passive wheel in the x and y directions, respectively. gx k gy Tp and Tg represent the support stiffness of the driven wheel in the x and y directions, respectively; Tp and Tg represent the input torques of the driving wheel and driven wheel, respectively; R1 and R2 represent the base circle radii of the driving wheel and driven wheel, respectively; α p The gear pressure angle is represented by these parameters, which are all known. Fm represents the dynamic meshing force of the meshing pair.

[0080] Solving the vibration differential equation of the gear meshing pair, preferably but not limited to using ODE45 in this embodiment, yields the dynamic response of the gear meshing pair and the dynamic meshing force under different tooth crack states. In this embodiment, the dynamic meshing force is F. m =k m f(δ,b t )+c m f1(δ,b t ), where k m Represents gear meshing stiffness; c m The gear meshing damping is represented by the empirical formula f(δ,b). t f1(δ,b) represents the time-varying nonlinear function of tooth flank clearance; t ) is f(δ,b t The derivative of ) Here, δ represents the displacement of the gear pair meshing point; b t This refers to the time-varying tooth flank clearance.

[0081] Based on the rainflow counting principle, the dynamic meshing force of the gear pair under different crack states is processed and compiled into a load spectrum to obtain variable amplitude load data with multiple periods.

[0082] Specifically, in the rainflow counting algorithm, the obtained dynamic meshing force of the gear pair is first filtered to remove small values ​​and retain peak and valley values. Then, the data is discretized, and finally, rainflow cycle counting is performed and corresponding calculations are carried out to compile a load spectrum, thereby obtaining variable amplitude load data with multi-periodity.

[0083] Based on the extended finite element theory, variable amplitude load data is used as boundary conditions to simulate crack propagation, and gear fatigue crack propagation data is read from the finite element data file.

[0084] Specifically, the extended finite element method (EPM) is used to simulate fatigue crack propagation. The EPM is based on the conventional finite element method (FEM) and the unit decomposition method (MDD), retaining the advantages of the traditional FEM. When applying the EPM to analyze fracture problems, the location of the crack surface is not considered initially; the mesh is directly generated on the fatigue crack surface of the gear. The MDD is applied, and additional functions are added to the finite element analysis to increase the degrees of freedom. Element nodes in the crack penetration region are reinforced with a generalized Heaviside function, and element nodes containing the crack tip are reinforced with a crack tip asymptotic displacement field function to reflect the local characteristics of the crack tip region. In this way, the additional functions can indirectly reflect the existence of discontinuities. Therefore, when generating the mesh, the strong discontinuity of the crack is independent of the finite element mesh, thus overcoming the difficulty of high-density mesh generation in high-stress areas and deformation concentration areas such as the crack tip. The gear fatigue crack propagation data is obtained, and its expression is: In the formula, I represents the total number of grid cells; N represents the total number of grid cells. i The shape function representing the standard finite element mode, u i H(x) represents the nodal displacements in the standard finite element model; H(x) represents the displacement jump characteristics on both sides of the crack, which can essentially be considered an extension of the signed distance function. i The extended node degrees of freedom associated with the jump discontinuous extension function are represented by F(x), which represents the tip asymptotic field function. i These represent the nodal degrees of freedom that propagate from the crack tip. These parameters are all known and can be read from the finite metadata file.

[0085] Stress intensity factor calculated based on gear fatigue crack propagation data:

[0086] An integration region is selected on the fatigue crack surface of the gear. In this embodiment, a portion of the aforementioned mesh is selected as the integration region. The energy release rate J at the crack tip is calculated within the integration region, and then the stress intensity factor is indirectly obtained using the corresponding formula. Here, the energy release rate at the crack tip is obtained through interactive integration. Where: Γ represents the integration path; W represents the strain energy density; σ represents the stress vector on the boundary of the integration path, both of which can be obtained by finite element simulation and are known parameters; ds represents the displacement on the integration path; x, y represent the local coordinates of the crack; and u represents the displacement vector on the integration path.

[0087] Under elastic deformation, the energy release rate J and the stress intensity factor K Ⅰ The following relationship exists In the formula, E represents the elastic modulus; v represents Poisson's ratio.

[0088] Fatigue crack propagation life is predicted based on the Paris formula and stress intensity factor.

[0089] The Paris formula for calculating fatigue crack propagation life is: Here, 'a' represents the crack propagation equation, C and m are material constants, ΔK represents the range of stress intensity factors, and K is the stress intensity factor K between adjacent crack lengths. Ⅰ The difference between the two values, N represents the fatigue crack propagation life. By calculating N, the fatigue crack propagation life of the gear can be obtained.

[0090] This application also proposes a gear fatigue crack propagation life calculation system considering random dynamic loads, which includes a data acquisition module, a processing module, and a storage module. The data acquisition module and the processing module are communicatively connected. The data acquisition module acquires the structural and material parameters of the gear meshing pair and sends them to the processing module. The processing module is communicatively connected to the storage module. The storage module is used to store at least one executable instruction. The executable instruction causes the processing module to perform the gear fatigue crack propagation life calculation method considering random dynamic loads as described above to estimate the gear fatigue crack propagation life.

[0091] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0092] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for calculating the fatigue crack propagation life of gears under random dynamic loads, characterized in that, Includes the following steps: Determine the structural and material parameters of the gear meshing pair; Establish a local planar coordinate system at the crack tip and construct the crack propagation equation; Calculate the time-varying meshing stiffness k containing tooth root crack characteristics. m ; Based on the time-varying meshing stiffness k m The vibration differential equation of the gear meshing pair is constructed based on the lumped parameter model; the vibration differential equation of the gear meshing pair is expressed as: ,in, , , In the formula, M is the mass matrix; m p m is the mass of the driving wheel. g J is the mass of the driven wheel; p J is the moment of inertia of the driving wheel; g The moment of inertia of the driving wheel; , and Represent , and The acceleration vector; when i=1, Let x be the displacement vector of the driving wheel in the x-direction. Let be the displacement vector of the driving wheel in the y-direction. For the angular displacement of the driving gear pair: when i=2, Let x be the displacement vector of the driven wheel in the x-direction; Let be the displacement vector of the passive wheel in the y-direction; For the angular displacement of the driven gear pair: In the formula, , Represent , velocity vector; c px c py k represents the support damping of the drive wheel in the x and y directions, respectively. px k py c represents the support stiffness of the drive wheel in the x and y directions, respectively. gx c gy k represents the support damping of the passive wheel in the x and y directions, respectively. gx k gy R1 and R2 represent the support stiffness of the driven wheel in the x and y directions, respectively; Fm represents the dynamic meshing force of the meshing pair; Tp and Tg represent the input torques of the driving wheel and driven wheel, respectively; R1 and R2 represent the base circle radii of the driving wheel and driven wheel, respectively. Represents the gear pressure angle; Solve the vibration differential equation of the gear meshing pair to obtain the dynamic meshing force of the meshing pair under different crack states; Dynamic meshing force of meshing pairs under different tooth crack states is , where k m Represents gear meshing stiffness; Represents gear meshing damping; Represents the nonlinear function of time-varying tooth flank clearance: ， for The derivative function; b is the displacement of the gear pair meshing point; t For time-varying tooth backlash, Where b0 represents the initial tooth flank clearance; R i The base circle radius of the gear is represented by α; inv(α) represents the involute function, inv(α)=tan(α)−α, where α is a specified angle value; The dynamic meshing force of the gear pair under different crack states is processed and compiled into a load spectrum to obtain variable amplitude load data with multiple periods. Based on the extended finite element theory, variable amplitude load data is used as boundary conditions to simulate the crack propagation equation and read gear fatigue crack propagation data from the finite element data file. Stress intensity factor calculated based on gear fatigue crack propagation data ; The fatigue crack propagation life N is predicted based on the Paris formula and stress intensity factor.

2. The method for calculating the fatigue crack propagation life of gears considering random dynamic loads according to claim 1, characterized in that, The crack propagation equation is: In the formula, a is the crack length; a0 is the initial crack length; n is the number of crack propagation substeps; a n θ represents the crack propagation step size. n The angle at which the crack propagates.

3. The method for calculating the fatigue crack propagation life of gears considering random dynamic loads according to claim 1, characterized in that, The time-varying meshing stiffness k m This includes the meshing stiffness of the single-tooth region and the meshing stiffness of the double-tooth region; The calculation steps are as follows: Calculate the Hertzian contact stiffness during gear meshing: , where E and v are Young's modulus and Poisson's ratio of the tooth material, and W is the tooth width; Calculate the base stiffness of the gear: ,in, , Reference , , and In the formula, α m The pressure angle; u f S is the distance from the meshing point to the tooth root fillet. f L*, M*, P*, and Q* represent the arc distance between the gear teeth and the gear base; X represents the arc distance between the gear teeth and the gear base. i * The approximate coefficients of the polynomial referred to; h fi θ is the ratio of the root circle radius to the hub radius; f Angle A is the angle between the tooth root and the center axis of the gear tooth. i B i C i D i and E i The coefficients are constants. A stress model of the gear tooth with initial cracks is constructed. Integrating along the tooth height, the bending stiffness and shear stiffness of the gear tooth are calculated piecewise. Specifically, the bending stiffness, shear stiffness, and axial compressive stiffness during gear meshing are as follows: Where x is the coordinate in the tooth height direction; d is the distance from the meshing point to the tip of the tooth root crack; h is the distance from the meshing point of the gear pair to the center line of the tooth; and G is the shear modulus. , ;hy is the distance from the crack initiation point to the center line of the tooth; hc is the distance from the crack end point to the center line of the tooth; de is the distance from the crack initiation point to the meshing point; dt is the distance from the crack end point to the tooth root fillet; Hx is the radius of inertia; Meshing stiffness in the single-tooth zone: , Meshing stiffness in the double-tooth region: , In the formula, g represents the driven gear; p represents the driving gear; and i represents the single and double tooth meshing area.

4. The method for calculating the fatigue crack propagation life of gears considering random dynamic loads according to claim 1, characterized in that, Based on the rainflow counting principle, the dynamic meshing force of the gear pair under different crack states is processed. First, the obtained dynamic meshing force of the gear pair is filtered to remove small amplitude values ​​and retain peak and valley values. Then, the data is discretized. Finally, rainflow cycle counting is performed to compile a load spectrum and obtain variable amplitude load data with multi-periodity.

5. The method for calculating the fatigue crack propagation life of gears considering random dynamic loads according to claim 1, characterized in that, The expression for gear fatigue crack propagation data is: ， In the formula, I represents the total number of grid cells; N i The shape function representing the standard finite element mode; u i H(x) represents the nodal displacements in the standard finite element mode; H(x) represents the displacement jump characteristics on both sides of the crack; a i The extended node degrees of freedom represent the extended functions associated with the jump discontinuous extensions; F(x) represents the tip asymptotic field function; b i The nodal degrees of freedom represent the expansion of the crack tip.

6. The method for calculating the fatigue crack propagation life of gears considering random dynamic loads according to claim 1, characterized in that, The specific steps for calculating the stress intensity factor based on gear fatigue crack propagation data are as follows: An integration region is selected on the fatigue crack surface of the gear, and the energy release rate J at the crack tip is calculated within the integration region. ,in: denoted by , W represents the integration path; σ represents the strain energy density; σ represents the stress vector on the boundary of the integration path; ds represents the displacement on the integration path; x, y represent the local coordinates of the crack; u represents the displacement vector on the integration path. Under elastic deformation, stress intensity factor In the formula, E represents the elastic modulus; v represents Poisson's ratio.

7. The method for calculating the fatigue crack propagation life of gears considering random dynamic loads according to claim 1, characterized in that, The Paris formula for calculating fatigue crack propagation life is: Where C and m are material constants, Represents the range of stress intensity factors, which are the stress intensity factors for adjacent crack lengths. The difference between them, where N represents the fatigue crack propagation life.

8. A system for analyzing the fatigue crack propagation life of gears under random dynamic loads, characterized in that, The system includes a data acquisition module, a processing module, and a storage module. The data acquisition module and the processing module are communicatively connected. The data acquisition module acquires the structural and material parameters of the gear meshing pair and sends them to the processing module. The processing module is communicatively connected to the storage module. The storage module is used to store at least one executable instruction. The executable instruction causes the processing module to perform the gear fatigue crack propagation life calculation method considering random dynamic load as described in any one of claims 1 to 7 to estimate the gear fatigue crack propagation life.

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