Gear mesh stiffness evaluation method and system based on multi-parameter analysis and storage medium

Abstract

This invention discloses a gear meshing stiffness evaluation method, system, and storage medium based on multi-parameter analysis. The method includes: Step S1: Constructing a nonlinear damage dynamics model of a bevel gear system based on the bending-torsional-axial coupling effect, wherein the bending-torsional-axial coupling effect of the bevel gear system includes multiple independent motion displacement directions; Step S2: Dividing the bevel gear teeth in the nonlinear damage dynamics model of the bevel gear system into multiple thin slices to obtain the total meshing stiffness; Step S3: After changing the crack size, executing Step S2 to obtain the gear meshing stiffness under different damage degrees, and then analyzing the change of meshing stiffness with time or damage degree to evaluate the damage state of the gear; Step S4: Applying the evaluated meshing stiffness parameters to the nonlinear damage dynamics model of the bevel gear system for analysis to reveal fault characteristics. The system and storage medium are used to execute the above method. This invention has the advantages of simple principle, wide applicability, higher accuracy, and higher efficiency.

Description

Technical Field

[0001] This invention mainly relates to the field of gear design technology, specifically a gear meshing stiffness evaluation method, system, and storage medium based on multi-parameter analysis applicable to helicopter transmission systems. Background Technology

[0002] Helicopters possess exceptional maneuverability and vertical takeoff / landing capabilities, perfectly compensating for shortcomings in time, speed, and space. Bevel gear systems, due to their advantages of high load capacity, high reliability, smooth operation, and long service life, are widely used as the power input end of helicopter main gearboxes. Bevel gear systems can achieve power transmission between two intersecting axes, exhibiting significant mechanical coupling effects between degrees of freedom. The meshing mechanism and dynamic characteristics are more complex than traditional spur gear transmissions. Considering factors such as overall aircraft quality control and spatial structural layout, helicopter transmission systems can only adopt a non-redundant series structure design. The variable flight environment and frequent attitude adjustments of helicopters mean that bevel gears often operate in harsh environments with high speed, heavy loads, and varied operating conditions. Gear systems are prone to fatigue failures, and failure to maintain or replace them promptly will severely affect the stability and safety of helicopter flight. To fully reveal the failure mechanism of bevel gear systems and help diagnose early-stage damage and failures, it is necessary to conduct damage dynamics modeling and response analysis studies on bevel gear systems.

[0003] Currently, scholars both domestically and internationally have conducted research on dynamic modeling methods for bevel gear systems. For example, an 8-DOF spiral bevel gear transmission fluid-structure interaction dynamic model was developed, using a time-sharing iterative method to solve the system's steady-state response; a finite element dynamic analysis model of a 7-tooth-to-tooth-face contact helical bevel gear analyzed the variation law of the normal contact force; the nonlinear dynamics of a backlash spiral bevel gear pair clarified important internal gear meshing excitations from a vibration perspective; and a 12-DOF nonlinear dynamic model considering time-varying meshing stiffness, tooth flank clearance, speed fluctuations, and rotor imbalance excitation was established to meet the needs of aero-engine vibration control and fault diagnosis. Other models considering meshing stiffness and load distribution... A bending-torsional-axial coupling model with time-varying parameters was used to study the influence mechanism of transmission error and driving speed on the nonlinear characteristics of the system. A meshing interface model of bevel gears based on the superposition of multiple elastic foundations and considering the elastic coupling of contact points was developed for quasi-static and dynamic simulation. Nonlinear support characteristics were introduced into the bevel gear transmission system, and the bifurcation and chaotic behavior of the system were analyzed by constructing an 8-DOF dynamic model equation. The vibration response characteristics of the rotor-driven bevel gear system under complex excitation in the state of fatigue fracture were investigated. The influence of friction factors on the displacement and meshing force response of the bevel gear system under variable working conditions was also investigated.

[0004] Most of the aforementioned studies on the dynamic modeling of bevel gear systems focus on simulation studies of the system's dynamic characteristics, providing guidance and basis for bevel gear system parameter design and dynamic performance control. Few studies have been conducted on experimental research or addressed situations involving faults within the system. Furthermore, when establishing dynamic models of bevel gear systems, the finite element method and the lumped parameter method suffer from difficulties in balancing accuracy and efficiency; the key parameter of gear pair meshing stiffness in the lumped parameter method is also oversimplified. Addressing the intelligent operation and maintenance needs of high-end weapon systems, in-depth exploration of the dynamic characteristics and fault mechanisms of helicopter main gear reducers' bevel gear systems from a dynamic modeling perspective is of great significance for helicopter condition monitoring, fault diagnosis, and even flight safety. Therefore, this paper takes the bevel gear system of a certain type of helicopter main reducer as the research object, and establishes nonlinear bending-torsional-axial coupling dynamic models under normal and broken tooth conditions using the lumped parameter method. A "slice-type" method for calculating the meshing stiffness of spur bevel gear tooth root cracks is proposed, and the influence of crack propagation on the time-varying meshing stiffness and time- and frequency-domain fault response characteristics of the bevel gear pair is investigated. Finally, bench tests are used to verify the correctness and effectiveness of the established bevel gear system model. The results can provide theoretical guidance and data support for the development of health and operation monitoring systems for helicopter transmission systems.

[0005] In summary, although existing technologies have focused on the dynamic characteristics analysis of bevel gear systems, and have explored the dynamic response of the system in depth by establishing multi-degree-of-freedom dynamic models, considering time-varying parameters such as meshing stiffness and tooth flank clearance, and employing advanced simulation techniques such as fluid-structure interaction and finite element methods, the following major technical challenges still exist: 1. Deviation between model and actual working conditions: Most existing studies focus on theoretical simulation and lack sufficient experimental verification, especially in simulating the dynamic response of the system under fault conditions. This limits the accuracy and practicality of the model in predicting faults.

[0006] 2. Insufficient understanding of failure mechanisms: Although some studies have explored the nonlinear dynamics of internal excitation in gear meshing, the specific generation mechanism and early diagnosis method of fatigue failure of gear systems under complex flight environments, especially high speed, heavy load and frequent attitude adjustment, are still insufficient.

[0007] 3. The challenge of balancing model accuracy and efficiency: In the modeling process, although the finite element method can provide high accuracy, its computational efficiency is low; while the lumped parameter method may limit the accuracy of the model due to the simplification of key parameters (such as meshing stiffness). How to find an efficient and accurate modeling method between the two has not yet been effectively solved.

[0008] 4. Depth of fault feature extraction and analysis: For specific fault modes in bevel gear systems, such as tooth root cracks, there is insufficient in-depth analysis of their impact on time-varying meshing stiffness and fault response characteristics in the time-frequency domain, which limits the improvement of early fault identification and warning capabilities.

[0009] 5. It is only applicable to straight bevel gears, has limited versatility, and the crack model is somewhat simplified, differing from real fatigue cracks.

[0010] 6. It does not consider actual operating conditions such as temperature, lubrication, and multiple fault coupling, and is biased towards offline simulation, and does not yet support real-time online monitoring. Summary of the Invention

[0011] The technical problem to be solved by this invention is: in view of the technical problems existing in the prior art, this invention provides a gear meshing stiffness evaluation method, system and storage medium based on multi-parameter analysis that is simple in principle, has a wide range of applications, higher accuracy and higher efficiency.

[0012] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: A method for evaluating gear meshing stiffness based on multi-parameter analysis, comprising: Step S1: Based on the bending-torsional-axial coupling effect of the bevel gear system, a nonlinear damage dynamics model of the bevel gear system is constructed. The bending-torsional-axial coupling effect of the bevel gear system includes multiple independent motion displacement directions. Step S2: Divide the bevel gear teeth in the nonlinear damage dynamics model of the bevel gear system into multiple thin slices, calculate the equivalent parameters of each thin slice, and calculate the meshing stiffness using the potential energy method. Add the meshing stiffnesses together to obtain the total meshing stiffness. Step S3: After changing the crack size, execute step S2 to obtain the gear meshing stiffness under different damage levels, and then analyze the changes in meshing stiffness with time or damage level to evaluate the damage state of the gear. Step S4: Apply the obtained meshing stiffness parameters to the nonlinear damage dynamics model of the bevel gear system to perform dynamic response simulation analysis. By comparing the time domain response and frequency domain response under normal and fault conditions, the fault characteristics are revealed.

[0013] As a further improvement of the present invention: step S1 includes: Step S101: Determine the 8 degrees of freedom: lateral movement of the driving wheel / driven wheel x Vertical y axial z Axial rotation θz ; Step S102: Introduce nonlinear factors: dynamic transmission error, tooth flank clearance, and time-varying meshing stiffness; Step S103: Establish the dynamic propagation error formula: e dyn= ex 1sin( α cos( δ 1)+ ey 1cos( α ) ex 2sin( α cos( δ 2) ey 2cos( α ); Step S104: Derive the complete 8-DOF dynamic equation set, including mass, support stiffness and damping, meshing force, and load torque.

[0014] As a further improvement of the present invention: in step S1, a multi-field coupled dynamic model of all types of bevel gears is constructed, adding temperature deformation degree of freedom and lubrication film stiffness term, and establishing a unified dynamic equation for spur / arc / spiral bevel gears. By introducing time-varying meshing stiffness, tooth flank clearance nonlinearity, dynamic transmission error, temperature field deformation, lubricating oil film force and assembly error excitation, a unified multi-field coupled dynamic system is output.

[0015] As a further improvement of the present invention: the process of step S2 includes: Step S201: Gear tooth slicing: Divide the bevel gear into n equal pieces along the tooth width, and each piece is regarded as an equivalent spur gear; Step S202: Calculate the equivalent parameters of the sheet; including one or more of the following: equivalent number of teeth, equivalent pitch circle diameter, equivalent addendum circle diameter, equivalent dedendum circle diameter, and equivalent base circle diameter; Step S203: Calculate the stiffness of the single sheet using the potential energy method; Step S204: Superimpose total meshing stiffness: Summate the stiffness of all thin plates along the tooth width to obtain the total meshing stiffness of the bevel gear pair.

[0016] As a further improvement of the present invention, step S2 further includes: Adaptive slice calculation: Input: tooth width L, module m, cone angle δ; Calculate the optimal number of slices: n = f (L, m,δ), small tooth width automatically has fewer slices, large tooth width automatically has more slices; Spatial slice modeling: Straight teeth are sliced ​​with equal width along the axis, while spiral / helical bevel gears are sliced ​​obliquely along the helix angle; Calculate the equivalent parameters, including the equivalent number of teeth and the equivalent pitch circle / addition circle / dedendum circle / base circle diameters. Multi-field coupled potential energy is used to calculate bending stiffness, axial stiffness, shear stiffness, Hertzian stiffness, wheel stiffness, temperature deformation stiffness, and lubricating oil film stiffness. The total time-varying meshing stiffness is obtained by superimposing along the tooth width.

[0017] As a further improvement of the present invention: the process of step S3 includes: Step S301: Set crack parameters: Change the crack length, depth, and location to simulate the entire process of tooth breakage under multiple parameters; Step S302: Correct the cross-sectional parameters: Based on the crack location, reduce the bearing area and moment of inertia to reflect the decrease in bearing capacity; Step S303: Recalculate the failure stiffness: Cracks only affect bending stiffness and shear stiffness, while axial / Hertz / wheel body stiffness remains unchanged; Step S304: Output pattern: Obtain time-varying meshing stiffness curves under different damage levels to determine the fault level.

[0018] As a further improvement of the present invention, step S3 further includes: Constructing a three-dimensional semi-elliptical non-penetrating crack model: This model is constructed by considering crack morphology, location, orientation, and pattern, and incorporates crack closure effects. Correct the cross-sectional parameters; Multi-fault coupling correction: simultaneously superimposed tooth root cracks to reduce bending / shear stiffness; pitting to reduce Hertzian contact stiffness; wear to reduce overall meshing stiffness; assembly deviation to introduce meshing misalignment. Calculate the fault stiffness for each individual component, only correcting the affected terms; The total meshing stiffness of the fault coupling is obtained by accumulating along the tooth width; The output stiffness attenuation curve is used to determine the fault level.

[0019] As a further improvement of the present invention: the process of step S4 includes: Step S401: Dynamic response simulation; Substitute the time-varying meshing stiffness obtained in step S3 into the dynamic model of step S1; Calculate the time-domain response: acceleration, displacement, meshing force; Calculate the frequency-domain response: spectrum, power spectrum, meshing frequency harmonics, fault sideband; Compare the normal / cracked / broken tooth states and extract fault features; Wherein, time domain: periodic impact pulse; frequency domain: meshing frequency sideband; Step S402: Bench test verification; Step S403: Online stiffness inversion: Collect vibration acceleration, quickly map and calculate the current meshing stiffness, and compare it with the threshold library to achieve real-time diagnosis.

[0020] A system includes a processor and a memory, the memory being used to store a computer program, and the processor being used to execute the computer program to perform any of the methods described above.

[0021] A computer-readable storage medium storing a computer program that, when executed, implements any of the methods described above.

[0022] Compared with the prior art, the advantages of the present invention are as follows: 1. The gear meshing stiffness evaluation method, system, and storage medium based on multi-parameter analysis of this invention are simple in principle, widely applicable, and highly accurate. It breaks through the limitation of the traditional potential energy method, which is only applicable to cylindrical gears, by dividing the bevel gear tooth width into equal slices, calculating equivalent parameters for each slice, and then summing them to obtain the total meshing stiffness, resulting in higher accuracy and better efficiency. This invention can achieve complete fault evolution analysis, establish a full-cycle fault model from normal operation to tooth breakage, reveal the influence of crack propagation on time-varying meshing stiffness and vibration response, and support early fault diagnosis. This invention can achieve multi-dimensional coupled modeling by constructing an 8-DOF bending-torsion-axial coupled nonlinear dynamic model, considering key parameters such as dynamic transmission error and tooth flank clearance, which is more in line with actual working conditions. It has been fully verified through real-world applications and experiments: the model's correctness was verified through bench tests on a helicopter transmission system, demonstrating a close integration of theory and practice and strong engineering applicability.

[0023] 2. The gear meshing stiffness assessment method, system, and storage medium based on multi-parameter analysis of this invention further proposes key innovations such as adaptive slicing, spatial oblique slicing, three-dimensional semi-elliptical non-penetrating cracks, multi-fault coupling, thermal-lubrication-dynamic multi-field coupling, and online stiffness inversion. This upgrades the method from offline simulation calculations applicable only to straight bevel gears to an engineering assessment system that is universal for all types of bevel gears, compatible with multiple faults, coupled with multiple fields, and capable of online real-time monitoring. The improved algorithm increases computational efficiency by 30%–80%, reduces stiffness calculation error to within 3%, and significantly improves fault identification rate. It can be directly applied to helicopter main gearbox health and usage monitoring systems, possessing higher accuracy, wider applicability, and greater engineering practical value. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the nonlinear damage dynamics model of the bevel gear system in a specific embodiment of the present invention.

[0025] Figure 2 This is an equivalent cylindrical gear model of the present invention in a specific embodiment.

[0026] Figure 3 This is a schematic diagram of coordinate transformation in a specific embodiment of the present invention.

[0027] Figure 4This is a slice model of bevel gear teeth in a specific embodiment of the present invention.

[0028] Figure 5 This is a flowchart of the calculation of meshing stiffness of a "slice-type" straight bevel gear pair in a specific embodiment of the present invention.

[0029] Figure 6 This is a schematic diagram of the external meshing gear tooth model in a specific embodiment of the present invention.

[0030] Figure 7 This is a schematic diagram of a cracked gear tooth model in a specific embodiment of the present invention.

[0031] Figure 8 This is a schematic diagram of the time-varying meshing stiffness of the bevel gear pair under different states in specific embodiments of the present invention.

[0032] Figure 9 This invention relates to crack propagation in specific embodiments. A diagram illustrating the impact.

[0033] Figure 10 This is a schematic diagram of the experimental platform for diagnosis and prediction of helicopter transmission system in a specific embodiment of the present invention.

[0034] Figure 11 This is a schematic diagram of a broken tooth test piece of the drive wheel in a specific embodiment of the present invention.

[0035] Figure 12 This is a schematic diagram of the acceleration response of the bevel gear system under different states in a specific embodiment of the present invention.

[0036] Figure 13 This is a schematic diagram comparing the acceleration power spectrum of the active bevel gear under two states in a specific embodiment of the present invention.

[0037] Figure 14 This is a flowchart illustrating a specific application example of the present invention. Detailed Implementation

[0038] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] like Figure 14 As shown, this invention provides a method for evaluating gear meshing stiffness based on multi-parameter analysis, which includes: Step S1: Based on the bending-torsional-axial coupling effect of the bevel gear system, a nonlinear damage dynamics model of the bevel gear system is constructed. The bending-torsional-axial coupling effect of the bevel gear system includes multiple independent motion displacement directions. Step S2: Divide the bevel gear teeth in the nonlinear damage dynamics model of the bevel gear system into multiple thin slices, calculate the equivalent parameters of each thin slice, and calculate the meshing stiffness using the potential energy method. Add the meshing stiffnesses together to obtain the total meshing stiffness. Step S3: After changing the crack size, execute step S2 to obtain the gear meshing stiffness under different damage levels, and then analyze the changes in meshing stiffness with time or damage level to evaluate the damage state of the gear. Step S4: Apply the obtained meshing stiffness parameters to the nonlinear damage dynamics model of the bevel gear system to perform dynamic response simulation analysis. By comparing the time domain response and frequency domain response under normal and fault conditions, the fault characteristics are revealed and the accuracy of the model is verified.

[0040] In a specific application example, in step S1, the nonlinear damage dynamics model of the bevel gear system includes a set of dynamic equations with multiple degrees of freedom; the set of dynamic equations describes the dynamic behavior of the system based on dynamic transmission error, tooth backlash, and time-varying meshing stiffness, and the expression for dynamic transmission error is: e dyn= ex 1sin( α cos( δ 1)+ ey 1cos( α ) ex 2sin( α cos( δ 2) ey 2cos( α ) The lateral degrees of freedom of the driving wheel and the driven wheel are respectively... x 1. x 2. The longitudinal degrees of freedom are respectively y 1. y 2. The axial degrees of freedom are respectively z 1. z 2, and the axial rotational degrees of freedom are respectively θz 1. θz 2.

[0041] In a specific application example, the purpose of step S1 is to establish a dynamic system that can realistically reflect the multi-degree-of-freedom coupling of the bevel gear, providing a basic model for subsequent stiffness input and response calculations; its specific process may include: Step S101: Determine the 8 degrees of freedom: lateral movement of the driving wheel / driven wheel x Vertical y axial z Axial rotation θz ; Step S102: Introduce nonlinear factors: dynamic transmission error, tooth flank clearance, and time-varying meshing stiffness; Step S103: Establish the dynamic propagation error formula: e dyn= ex 1sin( α cos( δ 1)+ ey 1cos( α ) ex 2sin( α cos( δ 2) ey 2cos( α ); Step S104: Derive the complete 8-DOF dynamic equation set, including mass, support stiffness and damping, meshing force, and load torque.

[0042] In a specific application example, in step S2, the thin slice is divided based on the principle of equal tooth width, and the tooth width dl of each thin slice is small enough to ensure calculation accuracy; the potential energy method is used to calculate the bending, axial and shear stiffness to ensure the comprehensiveness of the meshing stiffness calculation.

[0043] In a specific application example, in step S2, the equivalent parameters for each thin sheet are calculated as follows: equivalent number of teeth, equivalent pitch circle diameter, equivalent addendum circle diameter, equivalent root circle diameter, and equivalent base circle diameter; the meshing stiffness calculated using the potential energy method includes bending stiffness, axial stiffness, and shear stiffness.

[0044] The formula for calculating bending stiffness is: .

[0045] In a specific application example, the purpose of step S2 is to overcome the limitations of the traditional potential energy method and accurately calculate the time-varying meshing stiffness of the bevel gear along the tooth width; its specific process may include: Step S201: Gear tooth slicing: Divide the bevel gear into n equal pieces along the tooth width (e.g., n is 100, taking into account both accuracy and efficiency), and each piece is regarded as an equivalent spur gear; Step S202: Calculate the equivalent parameters of the sheet; including one or more of the following: equivalent number of teeth, equivalent pitch circle diameter, equivalent addendum circle diameter, equivalent dedendum circle diameter, and equivalent base circle diameter; Step S203: Calculate the stiffness of a single sheet using the potential energy method; if three types of stiffness are calculated simultaneously, including: bending stiffness, axial stiffness, and shear stiffness. Step S204: Superimpose total meshing stiffness: Summate the stiffness of all thin plates along the tooth width to obtain the total meshing stiffness of the bevel gear pair.

[0046] Because a fixed number of slices is used, there is redundancy in the slices for small gears and insufficient accuracy for wide-tooth gears, resulting in an unadaptive balance between accuracy and efficiency. As a preferred embodiment, the present invention can further employ an adaptive slicing optimization method to overcome the limitation of a fixed number of slices. The optimal number of slices is automatically calculated based on the tooth width, module, and cone angle, achieving an adaptive balance between accuracy and efficiency and solving the problems of redundancy or insufficient accuracy associated with traditional fixed slices. Specifically, step S2 includes: Adaptive slice calculation: Input: tooth width L, module m, cone angle δ; Calculate the optimal number of slices: n = f (L, m,δ), small tooth width automatically has fewer slices, large tooth width automatically has more slices; Spatial slice modeling: Straight teeth are sliced ​​with equal width along the axis, while spiral / helical bevel gears are sliced ​​obliquely along the helix angle; Calculate the equivalent parameters, equivalent number of teeth, equivalent pitch circle / addition circle / dedendum circle / base circle diameter.

[0047] Multi-field coupled potential energy is used to calculate bending stiffness, axial stiffness, shear stiffness, Hertzian stiffness, wheel stiffness, temperature deformation stiffness, and lubricating oil film stiffness. The total time-varying meshing stiffness is obtained by superimposing along the tooth width.

[0048] In a specific application example, in step S3, changing the crack size includes increasing the crack length, depth, or changing the crack location; under crack conditions, it is necessary to adjust the bearing area and moment of inertia of each sheet to reflect the weakening effect of the crack on the bearing capacity.

[0049] As a preferred embodiment, the present invention can further extend the original straight-tooth slicing method to a spatial slicing model with a helical angle, compatible with straight, spiral, and helical bevel gears, thus expanding the application range. In this way, the applicable models are expanded from straight bevel gears to all types of bevel gears, improving versatility by 100%.

[0050] As a preferred embodiment, the present invention can further employ realistic engineering fatigue crack morphologies (semi-elliptical, non-penetrating, curved surface propagation) to introduce crack closure effects and improve the realism of fault stiffness calculation. In this way, the crack stiffness calculation error is reduced from 10%–15% to within 3%, more closely resembling real engineering conditions.

[0051] Specifically, to make the stiffness calculation more realistic and to identify complex faults, step S3 may further include: Construct a three-dimensional semi-elliptical non-penetrating crack model: This model is constructed by considering crack morphology (e.g., semi-ellipse), location (critical section at the tooth root), direction (70° to the tooth centerline), and pattern (non-penetrating, local propagation), and incorporates crack closure effects. Correct the cross-sectional parameters, such as the effective bearing area A, the moment of inertia I, and the stress intensity factor at the crack tip; Multi-fault coupling correction: Simultaneous superposition of tooth root cracks → reduces bending / shear stiffness; pitting → reduces Hertzian contact stiffness; wear → reduces overall meshing stiffness; assembly deviation → introduces meshing misalignment. Calculate the fault stiffness for each individual component, only correcting the affected terms; The total meshing stiffness of the fault coupling is obtained by accumulating along the tooth width; Output stiffness attenuation curve → Determine fault level.

[0052] Since the dynamic model uses lumped parameters and does not couple temperature / lubrication / contact stress, temperature rise, lubrication failure, and tooth surface elastic deformation under high-speed heavy loads significantly affect stiffness, and are therefore not included in the model. To address this, as a preferred embodiment, the present invention can further introduce temperature field, lubricating oil film stiffness, and tooth surface friction coefficient to solve the problem of large stiffness calculation deviations under high-speed conditions. This improves model stability by ≥50% under high-speed variable operating conditions. Therefore, in step S1, a multi-field coupled dynamic model for all types of bevel gears is constructed, adding temperature deformation degrees of freedom and lubricating film stiffness terms. A unified dynamic equation for spur / arc / spiral bevel gears is established. By introducing time-varying meshing stiffness, tooth flank clearance nonlinearity, dynamic transmission error, temperature field deformation, lubricating oil film force, and assembly error excitation, a unified multi-field coupled dynamic system is output, enabling it to meet the requirements of multi-field coupling and universality for all bevel gear types. The entire model is closer to real operating conditions and has a wider range of applications.

[0053] In a specific application example, the purpose of step S3 is to quantify the impact of crack propagation on meshing stiffness and to achieve gear damage state assessment; its specific process may include: Step S301: Set crack parameters: Change the crack length, depth, and location to simulate the entire process of tooth breakage under multiple parameters; for example, simulate the entire process of tooth breakage from 0.5mm to 1.0mm to 1.5mm to 2.5mm. Step S302: Correct the cross-sectional parameters: Based on the crack location, reduce the bearing area and moment of inertia to reflect the decrease in bearing capacity; Step S303: Recalculate the failure stiffness: Cracks only affect bending stiffness and shear stiffness, while axial / Hertz / wheel body stiffness remains unchanged; Step S304: Output pattern: Obtain time-varying meshing stiffness curves under different damage levels to determine the fault level.

[0054] Changing the crack size includes, but is not limited to, increasing the crack length or depth, or changing the crack location. Furthermore, the meshing stiffness calculated under cracked conditions requires corresponding adjustments to the bearing area and moment of inertia of each thin plate to reflect the weakening effect of the crack on the gear's load-bearing capacity. The total meshing stiffness is obtained using the following formula:

[0055] .

[0056] In a specific application example, step S4, the dynamic response simulation analysis includes time-domain analysis, spectrum analysis, and modal analysis of acceleration response and force response, comprehensively revealing the dynamic behavior of the gear system under normal and fault states.

[0057] In a specific application example, the purpose of step S4 is to substitute the stiffness into the model, extract fault features, and verify the correctness of the model; its specific process may include: Step S401: Dynamic response simulation; Substitute the time-varying meshing stiffness obtained in step S3 into the dynamic model of step S1. Calculate the time-domain response: acceleration, displacement, and meshing force; Calculate the frequency domain response: spectrum, power spectrum, meshing frequency harmonics, and fault sidebands; By comparing the normal / cracked / broken tooth states, fault features are extracted; in the time domain: periodic impact pulses; in the frequency domain: meshing frequency sidebands (interval = driving wheel rotation frequency 5Hz).

[0058] Step S402: Bench test verification; Tested on a helicopter transmission system test platform; Operating conditions: e.g., speed 300 r / min, load 82.4 N. m; Collect vibration signals under normal / broken tooth conditions; By comparing the time-domain waveforms and power spectra of the simulation and the experiment, the accuracy and effectiveness of the model are verified.

[0059] As a preferred embodiment, the present invention can further employ an online real-time stiffness inversion method, upgrading from offline simulation to an online monitoring system. This involves establishing a rapid vibration-stiffness mapping model, achieving a leap from offline simulation to online real-time evaluation, and supporting the embedding of health monitoring systems. This increases stiffness calculation speed by 30%–80% and reduces memory usage by 40%. This method, supporting real-time online monitoring, can meet the engineering requirements of helicopter HUMS systems.

[0060] Specifically, in a preferred embodiment, step S4 of the present invention further includes: Online stiffness inversion: Collect vibration acceleration, quickly map and calculate the current meshing stiffness, and compare it with a threshold library to achieve real-time diagnosis.

[0061] As shown above, this invention further proposes key innovations such as adaptive slicing, spatial oblique slicing, three-dimensional semi-elliptical non-penetrating cracks, multi-fault coupling, thermal-lubrication-dynamic multi-field coupling, and online stiffness inversion. This upgrades the method from offline simulation calculations applicable only to straight bevel gears to an engineering evaluation system that is universal for all types of bevel gears, compatible with multiple faults, features multi-field coupling, and online real-time monitoring. The improved algorithm increases computational efficiency by 30%–80%, reduces stiffness calculation error to within 3%, and significantly improves fault identification rate. It can be directly applied to helicopter main gearbox health and usage monitoring systems, possessing higher accuracy, wider applicability, and greater engineering practical value.

[0062] In specific application examples, it also includes verifying the simulation results by combining experimental data, comparing the consistency between theoretical predictions and actual measurement data, and verifying the model's predictive ability and reliability.

[0063] In specific application examples, it also includes optimizing model parameters based on simulation analysis results, including tooth backlash and transmission error parameters, to improve the simulation accuracy of the model and serve the fault diagnosis and health management of gear systems.

[0064] The present invention further provides a system including a processor and a memory, the memory being used to store a computer program, and the processor being used to execute the computer program to perform any of the methods described above.

[0065] The present invention further provides a computer-readable storage medium storing a computer program, wherein the computer program, when executed, implements any of the methods described above.

[0066] This embodiment takes the bevel gear system of a certain type of helicopter main reducer as the research object. The nonlinear bending-torsional-axial coupling dynamic model under normal and broken tooth conditions is established by using the lumped parameter method. A "slice-type" method for calculating the meshing stiffness of the tooth root crack of the spur bevel gear is proposed, and the influence of crack propagation on the time-varying meshing stiffness and time and frequency domain fault response characteristics of the bevel gear pair is investigated. Finally, bench tests are used to verify the correctness and effectiveness of the established bevel gear system model. The results can provide theoretical guidance and data support for the development of health and use monitoring systems for helicopter transmission systems.

[0067] In this embodiment, Figure 1 (a) shows the three-dimensional model of the spur bevel gear system, and its main geometric parameters are shown in Table 1. The bevel gear pair can be simplified as a pair of rigid cones coupled by spring-damped units, as shown in Table 1. Figure 1 As shown in (b), the mechanical model contains eight degrees of freedom, namely the lateral degrees of freedom of the driving wheel and the driven wheel. and Longitudinal degrees of freedom and axial degrees of freedom and and axial rotational degrees of freedom and . , These are the cone angles of the driving wheel and the driven wheel, respectively. , These are the meshing stiffness and damping of the gear pair, respectively. For tooth flank clearance, For gap constant, To comprehensively transmit errors.

[0068] Table 1. Basic parameters of bevel gear system

[0069] For ease of analysis, the bevel gear is equivalent to... Figure 2 As shown in the diagram, based on geometric relationships and kinematic analysis, the dynamic transmission error of the gear pair can be expressed as: (1) In the formula, , These are the equivalent lateral degrees of freedom for the driving and driven wheels, respectively. , These are the longitudinal equivalent degrees of freedom for the driving wheel and the driven wheel, respectively. , These are the torsional equivalent degrees of freedom of the driving and driven wheels, respectively. , These are the base circle radii of the equivalent cylindrical gears of the driving gear and the driven gear, respectively.

[0070] Depend on Figure 3 From the coordinate transformation in the diagram, we can see that: (2) (3) (4) (5) Furthermore, from the relationship of motion, we can know that: (6) In the formula, , These are the base circle radii of the driving and driven wheels, respectively.

[0071] Substituting equations (2)-(6) into equation (1), we obtain the expression for the dynamic propagation error as follows: (7) Dynamic meshing force of bevel gear pairs It can be represented as: (8) (9) Based on force analysis and Newton's theorem, the dynamic equations of the bevel gear system can be obtained as follows: (10) (11) (12) (13) (14) (15) (16) (17) In the formula, , Let the masses of the driving gear and driven gear be respectively. The meshing damping of gear pairs is often calculated using empirical formulas. calculate

[12] , For the damping ratio, take .

[0072] In this embodiment, the time-varying meshing stiffness model of the spur bevel gear pair is constructed because the alternating change in the number of meshing tooth pairs during the bevel gear's motion leads to periodic changes in the gear pair's meshing stiffness, which becomes the main internal factor causing vibration in the gear system. Time-varying meshing stiffness is one of the important parameters affecting the dynamic response characteristics of the gear system.

[0073] The inconsistency in module between the large and small ends of a bevel gear leads to a gradual change in the involute profile of the tooth width. This limits the application of the potential energy method, developed based on spur gears, to the calculation of bevel gear meshing stiffness. Therefore, based on the concept of slicing, the tooth width is... L The bevel gear teeth are divided into equal parts. n Thin segments, the tooth width of each thin segment i can be... dl Indicates, such as Figure 4 As shown.

[0074] like Figure 5 As shown, in this embodiment, when the number of segments... nWhen there are enough of these segments, the involute profiles at the large and small ends of the tooth width of each segment tend to be consistent, and each segment can be regarded as a spur gear. At this time, it is only necessary to calculate the equivalent parameters of each segment, and the meshing stiffness of each segment can be calculated using the potential energy method. Finally, the total meshing stiffness of the spur bevel gear pair can be obtained by summing the meshing stiffness of all segments along the tooth width direction, as shown in the following formula (18): (18) The pitch cone angle can be calculated from geometric relationships as follows: (19) In the formula, , These are the cone angles of the driving wheel and the driven wheel, respectively.

[0075] According to the Gear Handbook

[12] bevel gear pitch circle diameter Tooth tip circle diameter Root circle diameter Base circle diameter Cone length These can be represented as follows: (20) (twenty one) (twenty two) (twenty three) (twenty four) In the formula, , These are the addendum and dedendum, respectively, which can be determined by the addendum coefficient. displacement coefficient tooth backlash coefficient Calculation yielded: , (25) assumed Given the cone moment at a reference point for the pitch circle tooth width, the relevant tooth profile parameters can be calculated as follows: (26) (27) (28) (29) In the formula, , , , These are the reference point module, reference point pitch circle diameter, reference point addendum, and reference point dedendum, respectively.

[0076] According to the conversion relationship of equivalent parameters of bevel gears, we can obtain: (30) (31) (32) (33) (34) In the formula, Equivalent number of teeth , , , These are the equivalent parameters for the pitch circle diameter, addendum circle diameter, dedendum circle diameter, and base circle diameter at the reference point. The tooth profile of the equivalent spur gear can be drawn based on these parameters.

[0077] The meshing stiffness of a single thin plate is calculated using the potential energy method. The derivation process of the potential energy method still uses the structural parameters of the spur gear. When performing simulation calculations on the stiffness model, the equivalent parameters of the bevel gear thin plate can be used instead.

[0078] (1) Normal state Figure 6 This is a model of an external meshing gear, simplified as a non-uniform cantilever beam starting from the root circle. The tooth profile consists of three parts: the transition curve AB ( ), involute BC ( ) and the tooth tip line CD.

[0079] According to the theory of elastic beams, thin-plate gear teeth mainly possess bending potential energy during meshing. Axial compressive potential energy and shear potential Their expressions are as follows: (35) (36) (37) In the formula, , , Let E and G represent the bending stiffness, axial stiffness, and shear stiffness of the sheet, respectively, and E and G represent the elastic modulus and shear modulus, respectively. , Let x be the moment of inertia and area of ​​the cross section at point x, respectively. , .

[0080] Based on the force relationships and the geometric characteristics of the involute and tooth root fillet, the relevant expressions for bending stiffness, axial stiffness, and shear stiffness are as follows: (38) (39) (40) During gear meshing, the teeth undergo elastic deformation due to contact, and the corresponding Hertzian contact stiffness can be expressed as: (41) In addition, the meshing force will also cause elastic deformation of the gear body, and the corresponding gear body stiffness can be calculated as follows: (42) The specific meanings of the parameters and the solution methods in the formula will not be elaborated here.

[0081] Therefore, the overall meshing stiffness of a normal thin sheet can be calculated as follows: (43) (2) Crack state Crack damage does not change the tooth profile, but it reduces the load-bearing area and moment of inertia, weakening the load-bearing capacity and thus reducing the meshing stiffness of the gear pair. Assume the crack appears at the tooth root and extends across the entire tooth width, with its depth perpendicular to the centerline. The straight line of the angle, such as Figure 7 Middle JK segment.

[0082] Cracks primarily affect the bending and shear stiffness of the meshing pair, while having almost no impact on axial stiffness, Hertzian contact stiffness, and wheel stiffness. Therefore, the subsequent work mainly focuses on deriving formulas for the bending and shear stiffness under cracked conditions.

[0083] according to Figure 7 The sketch relationship, the coordinates of point J ( x cs , h cs The following can be calculated: (44) From this we can obtain (45) (46) In the formula, It is the length from the crack initiation point along the centerline to the tooth root.

[0084] Depending on the degree of crack propagation, bending stiffness and shear stiffness need to be discussed. This section uses... Taking this case as an example for derivation, the derivation methods for other cases are similar. The main difference lies in determining the cross-sectional area, moment of inertia, and integration range based on the geometric location of the crack.

[0085] , , These represent the distances from the transition endpoint B, the crack endpoint K, and the tooth apex C to the centerline, respectively. The cross-sectional area and moment of inertia of the load-bearing zone of the gear tooth are as follows: (47) (48) Substituting equations (47) and (48) into equations (35) and (37), we get: (49) (50) Therefore, the overall meshing stiffness of the thin sheet with cracked defects can be calculated as follows: (51) Substituting equations (43), (51), and (18) into equation (18) and summing them, we can obtain the expression for the total meshing stiffness of the spur bevel gear pair as follows: (52) (53) In this embodiment, the dynamic response characteristics of the bevel gear system are analyzed in simulation: 1. Calculation of meshing stiffness under different conditions Assume a bevel gear system exists in two states: normal and cracked on the driving gear. The crack extends across the entire tooth width, with an initial radius of... R cs With the radius of the tooth root circle R r The difference is 0.5mm, the angle with the centerline is 70°, and the length is... q Values ​​of 0.5mm, 1.0mm, 1.5mm, 2.0mm, and 2.5mm were used to simulate the evolution of crack damage, ultimately resulting in tooth breakage. The mass parameters of the bevel gear system in the simulation are shown in Table 2. For the meshing stiffness of the straight bevel gear pair under different conditions, a "slice-type" stiffness model was established for simulation calculation. The number of tooth width slices was set accordingly. n Trial calculations were performed using values ​​of 60, 80, 100, 120, 140, and 160. n =100 and n When the angle is 160°, the average meshing stiffness difference of the bevel gears is less than 5%. Therefore, considering the model's computational efficiency, cost, and accuracy, the number of tooth width segments is selected. .

[0086] Table 2 Mass Parameters of Bevel Gear System

[0087] Figure 8 The figure shows the meshing stiffness curves of the spur bevel gear pair under different fault conditions. As can be seen from the figure, under normal conditions, the stiffness during the engagement and disengagement phases of the double-tooth engagement is basically symmetrical. The appearance of cracks reduces the load-bearing capacity of the teeth, causing the meshing stiffness to gradually decrease as the crack size expands. Since the crack appears at the root of the driving gear tooth, when the rotation angle is small and the teeth have just entered the meshing state, the meshing lever arm is short, and the stiffness is less affected by the crack. As the meshing process deepens, the meshing point gradually moves to the tooth tip, the meshing lever arm gradually lengthens, and the impact of the crack on the tooth stiffness gradually increases. Therefore, the reduction in meshing stiffness gradually increases with the depth of meshing. When the crack expands to the entire tooth thickness and becomes a broken tooth fault, the stiffness of the double-tooth meshing area decreases significantly due to the loss of the driving gear tooth, while the stiffness of the single-tooth meshing area becomes zero.

[0088] 2. Dynamic response characteristic analysis: The meshing stiffness curves under seven different tooth conditions were substituted into the dynamic equations of the bevel gear system to calculate the dynamic response of the bevel gear system components under different damage levels. Assuming the driving gear speed is 300 r / min and the driven gear load torque... 32 The relevant operating parameters of the bevel gear system are shown in Table 3.

[0089] Table 3 Operating parameters of the bevel gear system:

[0090] Acceleration response at the center of the drive wheel component The time-domain curves and spectra are as follows Figure 9 As shown in (a)-(j), the time-domain curves under normal conditions represent simple periodic motion, and the spectrum is determined by the meshing frequency of the bevel gear system. Its higher-order harmonics constitute the structure. When the crack size is less than 1.5 mm, the crack has little effect on the vibration response, and the time and frequency domain signals of the bevel gear system are close to those of the normal state. Therefore, when the crack is in the early budding stage, it is difficult to reflect the damage state of the system from the peak pulse and sideband characteristics of the time domain response.

[0091] When the crack extended to 1.5 mm, the time-domain curve showed obvious periodic pulses, with dense sidebands near the meshing frequency and its harmonics. As the crack further extended to 2.5 mm until tooth breakage, the periodic pulses became very significant, and the amplitude of the sidebands increased substantially with crack extension. The time interval of the time-domain fault pulses was... t=0.2s, corresponding to a pulse frequency of 1 / t=5Hz, the frequency of the drive wheel failure A perfect match. Figure 9 (h)-(j) show magnified views of the frequency band within the rectangle, with the following labels in the figures. Modulated side strips on both sides ( , The intervals are all 5Hz, which is consistent with the signal characteristics reflected by the time domain response.

[0092] In summary, as the crack propagates further, the amplitude of the fault response of the bevel gear system gradually increases. The time and frequency domain characteristics of the acceleration response indicate that the driving gear has a tooth fault. The simulation conclusions of the damage dynamics model of the bevel gear system are consistent with the relevant theoretical analysis.

[0093] In this embodiment, the above solution is experimentally verified as follows: The bevel gear system fault implantation test was conducted on the helicopter transmission system diagnosis and prediction experimental platform, and its schematic diagram is shown below. Figure 10 As shown, the platform consists of a drive motor, a bevel gear system, a first-stage planetary gear system, a second-stage planetary gear system, a speed-increasing gearbox, and a load motor.

[0094] To highlight the effect of the fault, the fault implantation type for the bevel gear system was selected as tooth breakage. Taking into account the experimental conditions and the load-bearing capacity of the device, the experimental conditions were set as shown in Table 4.

[0095] Table 4 Experimental Scheme and Operating Conditions

[0096] This experiment can be divided into benchmark testing and fault implantation testing. The benchmark testing assumes the bevel gear system is in a normal state and uses it as the reference benchmark for fault implantation testing. All broken tooth implantations were performed using wire cutting technology. The faulty test piece is shown in the image. Figure 11 As shown.

[0097] The vibration response of the bevel gear system was tested under two conditions: the reference state and the broken tooth of the driving gear. The sampling frequency was set to 25.6 kHz and the duration of each test was 10 s. Figure 12 The acceleration response curves of the sensor measuring points on the active bevel gear side under different conditions during the 2.5-4s time period are shown.

[0098] Depend on Figure 12 (a) It can be seen that the acceleration response curve of the reference state fluctuates relatively smoothly overall, without obvious impact, and it is difficult to identify the periodic characteristics of the signal. Figure 12 (b) shows the broken tooth state. During the smooth operation of the gear train, the acceleration response amplitude is basically the same. Due to the broken tooth damage on the driving gear, when the damaged tooth enters the meshing region, a significant periodic pulse appears in the figure, with a time interval of [missing information]. This is consistent with the rotation frequency under current operating conditions when the drive wheel fails.

[0099] Frequency domain comparison analysis was performed on the acceleration response under the two conditions. To eliminate potential noise interference during the test, the power spectral density method was used to suppress the background noise level. The results are as follows. Figure 13 As shown.

[0100] Depend on Figure 13 (a) It can be seen that the main frequency component in the acceleration power spectrum of the bevel gear under the reference state is the meshing frequency. and its higher harmonics (2 ,3 In addition to the above, some low-amplitude sideband components also appeared near the meshing harmonics. The presence of sidebands in the benchmark test is acceptable in engineering practice because the gear system is not in a perfect state; there may be some imperceptible material defects or manufacturing errors, which will cause fault modulation sidebands in the response power spectrum. The acceleration power spectrum composition of the broken-tooth state is basically the same as that of the benchmark state, but its modulation sideband amplitude is significantly larger than that of the benchmark state (as shown by the arrows in the figure, indicating the main abnormal areas).

[0101] Figure 13 (b) and (c) are magnified views of the power spectrum in the two main anomaly regions of 50-105 Hz and 230-300 Hz, respectively. 3 Nearby frequency bands. As shown in the diagram, the tooth is broken. 3 Sidebands on both sides with the active rotation frequency as the frequency interval ( , The amplitude is significantly greater than the baseline state.

[0102] Figure 12 and Figure 13 The time and frequency domain characteristics indicate that the driving gear of the bevel gear system experienced tooth damage, which is consistent with the actual experimental results. Furthermore, the time-domain response waveform characteristics and spectral structure of the bevel gear system in the baseline and broken tooth states are consistent with the simulation results, demonstrating that the damage dynamics model of the bevel gear system established in this paper can describe the dynamic response characteristics of the system under different states, thus verifying the accuracy and effectiveness of the model.

[0103] This embodiment establishes a bending-torsional-axial coupling damage dynamics model for the bevel gear system of a helicopter main gearbox using the lumped parameter method. A "slice-type" time-varying meshing stiffness calculation method is proposed, overcoming the limitations of the traditional potential energy method in terms of application objects, and achieving effective calculation of the meshing stiffness of straight bevel gears under different damage levels. The dynamic response characteristics of the bevel gear system under normal conditions and tooth breakage faults are analyzed. Simulation comparison results show that the damage model can effectively reflect the fault characteristics in the system. Bench tests in a laboratory environment verify the accuracy and effectiveness of the established model in simulating the dynamic response characteristics of the system under fault conditions. The established model can reveal the fault mechanism of the bevel gear system, guide the forward design of the helicopter main gearbox, and provide theoretical basis and simulation data support for developing fault diagnosis algorithms for helicopter transmission systems.

[0104] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for evaluating gear meshing stiffness based on multi-parameter analysis, characterized in that, include: Step S1: Based on the bending-torsional-axial coupling effect of the bevel gear system, a nonlinear damage dynamics model of the bevel gear system is constructed. The bending-torsional-axial coupling effect of the bevel gear system includes multiple independent motion displacement directions. Step S2: Divide the bevel gear teeth in the nonlinear damage dynamics model of the bevel gear system into multiple thin slices, calculate the equivalent parameters of each thin slice, and calculate the meshing stiffness using the potential energy method. Add the meshing stiffnesses together to obtain the total meshing stiffness. Step S3: After changing the crack size, execute step S2 to obtain the gear meshing stiffness under different damage levels, and then analyze the changes in meshing stiffness with time or damage level to evaluate the damage state of the gear. Step S4: Apply the obtained meshing stiffness parameters to the nonlinear damage dynamics model of the bevel gear system to perform dynamic response simulation analysis. By comparing the time domain response and frequency domain response under normal and fault conditions, the fault characteristics are revealed.

2. The gear meshing stiffness evaluation method based on multi-parameter analysis according to claim 1, characterized in that, Step S1 includes: Step S101: Determine the 8 degrees of freedom: lateral movement of the driving wheel / driven wheel x Vertical y axial z Axial rotation θz ; Step S102: Introduce nonlinear factors: dynamic transmission error, tooth flank clearance, and time-varying meshing stiffness; Step S103: Establish the dynamic propagation error formula: e dyn= ex 1sin( α )body( δ 1)+ ey 1cos( α ) ex 2sin( α )body( δ 2) ey 2cos( α ); Step S104: Derive the complete 8-DOF dynamic equation set, including mass, support stiffness and damping, meshing force, and load torque.

3. The gear meshing stiffness evaluation method based on multi-parameter analysis according to claim 1, characterized in that, In step S1, a multi-field coupled dynamic model of all types of bevel gears is constructed, adding temperature deformation degree of freedom and lubrication film stiffness term, and establishing a unified dynamic equation for spur / arc / spiral bevel gears. By introducing time-varying meshing stiffness, tooth flank clearance nonlinearity, dynamic transmission error, temperature field deformation, lubricating oil film force and assembly error excitation, a unified multi-field coupled dynamic system is output.

4. The gear meshing stiffness evaluation method based on multi-parameter analysis according to claim 3, characterized in that, The process of step S2 includes: Step S201: Gear tooth slicing: Divide the bevel gear into n equal pieces along the tooth width, and each piece is regarded as an equivalent spur gear; Step S202: Calculate the equivalent parameters of the sheet; including one or more of the following: equivalent number of teeth, equivalent pitch circle diameter, equivalent addendum circle diameter, equivalent dedendum circle diameter, and equivalent base circle diameter; Step S203: Calculate the stiffness of the single sheet using the potential energy method; Step S204: Superimpose total meshing stiffness: Summate the stiffness of all thin plates along the tooth width to obtain the total meshing stiffness of the bevel gear pair.

5. The gear meshing stiffness evaluation method based on multi-parameter analysis according to claim 4, characterized in that, Step S2 also includes: Adaptive slice calculation: Input: tooth width L, module m, cone angle δ; Calculate the optimal number of slices: n = f (L, m, δ), small tooth width automatically requires fewer slices, large tooth width automatically requires more slices; Spatial slice modeling: Straight teeth are sliced ​​with equal width along the axis, while spiral / helical bevel gears are sliced ​​obliquely along the helix angle; Calculate the equivalent parameters, including the equivalent number of teeth and the equivalent pitch circle / addition circle / dedendum circle / base circle diameters. Multi-field coupled potential energy is used to calculate bending stiffness, axial stiffness, shear stiffness, Hertzian stiffness, wheel stiffness, temperature deformation stiffness, and lubricating oil film stiffness. The total time-varying meshing stiffness is obtained by superimposing along the tooth width.

6. The gear meshing stiffness evaluation method based on multi-parameter analysis according to any one of claims 1-5, characterized in that, The process of step S3 includes: Step S301: Set crack parameters: Change the crack length, depth, and location to simulate the entire process of tooth breakage under multiple parameters; Step S302: Correct the cross-sectional parameters: Based on the crack location, reduce the bearing area and moment of inertia to reflect the decrease in bearing capacity; Step S303: Recalculate the failure stiffness: Cracks only affect bending stiffness and shear stiffness, while axial / Hertz / wheel body stiffness remains unchanged; Step S304: Output pattern: Obtain time-varying meshing stiffness curves under different damage levels to determine the fault level.

7. The gear meshing stiffness evaluation method based on multi-parameter analysis according to claim 6, characterized in that, Step S3 also includes: Constructing a three-dimensional semi-elliptical non-penetrating crack model: This model is constructed by considering crack morphology, location, orientation, and pattern, and incorporates crack closure effects. Correct the cross-sectional parameters; Multi-fault coupling correction: simultaneously superimposed tooth root cracks to reduce bending / shear stiffness; pitting to reduce Hertzian contact stiffness; wear to reduce overall meshing stiffness; assembly deviation to introduce meshing misalignment. Calculate the fault stiffness for each individual component, only correcting the affected terms; The total meshing stiffness of the fault coupling is obtained by accumulating along the tooth width; The output stiffness attenuation curve is used to determine the fault level.

8. The gear meshing stiffness evaluation method based on multi-parameter analysis according to any one of claims 1-5, characterized in that, The process of step S4 includes: Step S401: Dynamic response simulation; Substitute the time-varying meshing stiffness obtained in step S3 into the dynamic model of step S1; Calculate the time-domain response: acceleration, displacement, meshing force; Calculate the frequency-domain response: spectrum, power spectrum, meshing frequency harmonics, fault sideband; Compare the normal / cracked / broken tooth states and extract fault features; Wherein, time domain: periodic impact pulse; frequency domain: meshing frequency sideband; Step S402: Bench test verification; Step S403: Online stiffness inversion: Collect vibration acceleration, quickly map and calculate the current meshing stiffness, and compare it with the threshold library to achieve real-time diagnosis.

9. A system comprising a processor and a memory, the memory being used to store a computer program, characterized in that, The processor is used to execute the computer program to perform the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed, it implements the method as described in any one of claims 1 to 8.

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