Gear tooth breakage failure diagnosis method and related device under friction dynamics coupling condition

Abstract

The application discloses a gear tooth fracture failure diagnosis method and related device under a friction dynamics coupling condition, relates to the technical field of gear tooth fracture failure diagnosis, and comprises the following steps: solving a dynamics model in a gear transmission process under the friction dynamics coupling condition, obtaining a rotation angle of a driving gear and a rotation angle of a driven gear, further calculating a gear tooth root bending stress and a gear bending fatigue safety factor, when it is determined that there is a tooth fracture risk based on the gear bending fatigue safety factor, decomposing vibration signals in the driving gear and the driven gear transmission process by using an ICEEMDAN algorithm, further determining a support vector, calculating a distance between the support vector and a ball center of a benchmark hypersphere constructed by using an SVDD algorithm, and based on the distance, calculating a gear health degree to complete gear tooth fracture failure diagnosis. The application can improve the calculation accuracy of the gear tooth root bending stress and the diagnosis accuracy of the gear tooth fracture failure diagnosis.

Description

Technical Field

[0001] This application relates to the field of gear tooth breakage failure diagnosis technology, and in particular to a method and related device for diagnosing gear tooth breakage failure under tribodynamic coupling conditions. Background Technology

[0002] After gear installation, during the transmission process between the driving and driven gears, the tooth root may experience excessive bending stress, leading to tooth breakage. This tooth root bending stress is a key factor affecting gear performance and reliability. As gear technology continues to advance towards high-speed, heavy-load applications, tooth breakage is becoming increasingly prominent. Currently, most research on gear tooth breakage neglects the influence of the frictional dynamics coupling effect of the gear system, resulting in insufficient accuracy in calculating the bending stress at the gear tooth root. Furthermore, gear tooth breakage failure diagnosis faces challenges such as modal aliasing and high-frequency characteristic loss, limiting signal adaptability and making it difficult to reflect the actual health state of the gear, thus leading to insufficient diagnostic accuracy in gear tooth breakage failure diagnosis. Summary of the Invention

[0003] The purpose of this application is to provide a method and related device for diagnosing gear tooth breakage failure under tribodynamic coupling conditions, which can improve the calculation accuracy of gear tooth root bending stress and the diagnostic accuracy of gear tooth breakage failure.

[0004] To achieve the above objectives, this application provides the following solution:

[0005] Firstly, this application provides a method for diagnosing gear tooth breakage failure under tribodynamic coupling conditions, the method comprising:

[0006] The dynamic model of gear transmission under frictional dynamic coupling is solved to obtain the rotation angle of the driving gear and the rotation angle of the driven gear. Based on the rotation angle of the driving gear and the rotation angle of the driven gear, the bending stress at the root of the gear tooth is calculated.

[0007] Based on the bending stress at the gear tooth root, the gear bending fatigue safety factor is calculated. Based on the gear bending fatigue safety factor, it is determined whether there is a risk of tooth breakage during the transmission process of the driving gear and the driven gear. If there is a risk of tooth breakage, the vibration signal during the transmission process of the driving gear and the driven gear is obtained.

[0008] The vibration signal is decomposed using the ICEEMDAN algorithm to obtain multiple intrinsic mode function components, and one intrinsic mode function component is selected from all the intrinsic mode function components as a support vector.

[0009] The distance between the support vector and the center of the reference hypersphere is calculated. If the distance is less than or equal to the radius of the reference hypersphere, the driving gear and driven gear do not have a broken tooth failure fault. If the distance is greater than the radius of the reference hypersphere, the driving gear and driven gear have a broken tooth failure fault. Based on the distance, the gear health is calculated to complete the gear broken tooth failure diagnosis. The reference hypersphere is constructed using the SVDD algorithm based on the sample support vector of the normal sample vibration signal.

[0010] Secondly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor executes the computer program to implement the above-described method for diagnosing gear tooth breakage failure under tribodynamic coupling conditions.

[0011] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method for diagnosing gear tooth breakage under tribodynamic coupling conditions.

[0012] Fourthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method for diagnosing gear tooth breakage under tribodynamic coupling conditions.

[0013] According to the specific embodiments provided in this application, this application has the following technical effects:

[0014] This application provides a method and related apparatus for diagnosing gear tooth breakage failure under tribodynamic coupling conditions. The method solves the dynamic model of the gear transmission process under tribodynamic coupling conditions to obtain the rotation angles of the driving gear and the driven gear. Based on these rotation angles, the bending stress at the gear tooth root is calculated. This method considers the influence of tribodynamic coupling in the calculation of the gear tooth root bending stress, improving the calculation accuracy. Based on the gear tooth root bending stress, a gear bending fatigue safety factor is calculated. Based on this safety factor, the method determines whether there is a risk of tooth breakage during the transmission process of the driving and driven gears. If a risk of tooth breakage exists, vibration signals during the transmission process of the driving and driven gears are acquired, and the ICEEMDAN algorithm is used to decompose the vibration signals. Multiple intrinsic mode function (IMF) components are obtained, and one IMF component is selected as a support vector. The distance between the support vector and the center of a reference hypersphere constructed using the SVDD algorithm is calculated. If the distance is less than or equal to the radius of the reference hypersphere, the driving and driven gears do not have tooth breakage failure. If the distance is greater than the radius of the reference hypersphere, the driving and driven gears have tooth breakage failure. Based on the distance, the gear health is calculated, thus completing the gear tooth breakage failure diagnosis. By using the ICEEMDAN algorithm to decompose the vibration signal and select the support vector, modal aliasing and high-frequency feature loss can be reduced. Furthermore, by combining this with the reference hypersphere constructed using the SVDD algorithm to complete the gear tooth breakage failure diagnosis, the actual health status of the gear can be accurately reflected, improving the diagnostic accuracy of gear tooth breakage failure. This application can improve the calculation accuracy of gear tooth root bending stress and the diagnostic accuracy of gear tooth breakage failure. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This diagram illustrates the application environment of a gear tooth breakage failure diagnosis method under tribodynamic coupling conditions, as provided in Embodiment 1 of this application.

[0017] Figure 2 This is a flowchart illustrating a method for diagnosing gear tooth breakage under tribodynamic coupling conditions, as provided in Embodiment 1 of this application.

[0018] Figure 3 This is a schematic diagram for calculating the bending stress at the root of a gear as provided in Embodiment 1 of this application.

[0019] Figure 4 This is a schematic diagram of the development angle during gear transmission provided in Embodiment 1 of this application.

[0020] Figure 5 This is a schematic diagram comparing the decomposition results of the EMD (Empirical Mode Decomposition) algorithm and the ICEEMDAN (Intrinsic Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) algorithm provided in Embodiment 1 of this application; wherein, Figure 5 In the diagram, (a) represents the decomposition result of the EMD algorithm. Figure 5 (b) in the figure represents the decomposition result of the ICEEMDAN algorithm.

[0021] Figure 6 This is a schematic diagram of the optimal decision boundary circle for the SVDD (Support Vector Data Description) algorithm in two-dimensional space provided in Embodiment 1 of this application.

[0022] Figure 7 The waterfall diagram of the test bench provided in Embodiment 1 of this application under no-load conditions.

[0023] Figure 8 A waterfall diagram of the test bench provided in Embodiment 1 of this application under load conditions.

[0024] Figure 9 This is a schematic diagram comparing the time-domain data of gears in broken-tooth meshing and normal meshing, provided in Embodiment 1 of this application; wherein, Figure 9 (a) in the figure compares the data from the broken tooth meshing test with the data from the normal meshing test. Figure 9 (b) in the figure compares the broken tooth meshing test data with the broken tooth meshing simulation data.

[0025] Figure 10 This is a schematic diagram comparing the frequency domain data of gears in broken-tooth meshing and normal meshing, provided in Embodiment 1 of this application; wherein, Figure 10 (a) in the figure compares the data from the broken tooth meshing test with the data from the normal meshing test. Figure 10 (b) in the figure compares the broken tooth meshing test data with the broken tooth meshing simulation data.

[0026] Figure 11 This is a schematic diagram of the distance calculation results provided in Embodiment 1 of this application.

[0027] Figure 12This is a schematic diagram of the gear health calculation results provided in Embodiment 1 of this application.

[0028] Figure 13 This is a schematic diagram of the structure of a computer device provided in Embodiment 2 of this application. Detailed Implementation

[0029] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0030] Example 1

[0031] The gear tooth breakage failure diagnosis method under tribodynamic coupling conditions provided in this application embodiment can be applied to, for example... Figure 1 The application environment shown is as follows. The terminal communicates with the server via a network. The data storage system stores the data the server needs to process. The data storage system can be set up independently, integrated into the server, or placed in the cloud or on another server. The terminal can send diagnostic requests to the server. Upon receiving the request, the server solves the dynamic model of the gear transmission process under frictional dynamic coupling conditions to obtain the rotation angles of the driving gear and the driven gear. Based on these rotation angles, it calculates the gear tooth root bending stress. Based on this stress, it calculates the gear bending fatigue safety factor and determines whether there is a risk of tooth breakage during the transmission process of the driving and driven gears. If a risk of tooth breakage exists... The process involves acquiring vibration signals during the transmission of the driving and driven gears. The ICEEMDAN algorithm is used to decompose these signals, yielding multiple intrinsic mode function (IMF) components. One IMF component is selected as a support vector. The distance between the support vector and the center of a reference hypersphere is calculated. If the distance is less than or equal to the radius of the reference hypersphere, the driving and driven gears do not exhibit tooth breakage failure. If the distance is greater than the radius of the reference hypersphere, tooth breakage failure is present in both gears. Based on this distance, the gear health is calculated, completing the tooth breakage failure diagnosis. The server can then feed back the diagnostic results (existence of tooth breakage failure and gear health) to the terminal.

[0032] Furthermore, in some embodiments, the gear tooth breakage failure diagnosis method under tribodynamic coupling conditions can also be implemented by a server or a terminal independently. For example, the terminal can directly process the diagnosis request to be processed, or the server can obtain the diagnosis request to be processed from the data storage system and process it.

[0033] The terminals can be, but are not limited to, various desktop computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can include smart speakers, smart TVs, smart air conditioners, and smart in-vehicle devices, while portable wearable devices can include smartwatches, smart bracelets, and head-mounted devices. Servers can be implemented using independent servers, server clusters composed of multiple servers, or cloud servers.

[0034] In one exemplary embodiment, such as Figure 2 As shown, a method for diagnosing gear tooth breakage failure under tribodynamic coupling conditions is provided. This method is executed by a computer device, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is applied to... Figure 1 The following steps are used as an example of a server in the example.

[0035] Step S1: Solve the dynamic model of the gear transmission process under the condition of frictional dynamic coupling to obtain the rotation angle of the driving gear and the rotation angle of the driven gear. Based on the rotation angle of the driving gear and the rotation angle of the driven gear, calculate the bending stress at the root of the gear teeth.

[0036] Step S2: Based on the bending stress at the gear tooth root, calculate the gear bending fatigue safety factor, and based on the gear bending fatigue safety factor, determine whether there is a risk of tooth breakage during the transmission process of the driving gear and the driven gear. If there is a risk of tooth breakage, obtain the vibration signal during the transmission process of the driving gear and the driven gear.

[0037] Step S3: The vibration signal is decomposed using the ICEEMDAN algorithm to obtain multiple intrinsic mode function components, and one intrinsic mode function component is selected from all the intrinsic mode function components as a support vector.

[0038] Step S4: Calculate the distance between the support vector and the center of the reference hypersphere. If the distance is less than or equal to the radius of the reference hypersphere, the driving gear and driven gear do not have a broken tooth failure fault. If the distance is greater than the radius of the reference hypersphere, the driving gear and driven gear have a broken tooth failure fault. Based on the distance, calculate the gear health degree to complete the gear broken tooth failure diagnosis. The reference hypersphere is constructed using the SVDD algorithm based on the sample support vector of the normal sample vibration signal.

[0039] By implementing steps S1 to S4 above, this embodiment can consider the influence of frictional dynamics coupling in the calculation of gear tooth root bending stress, thereby improving the calculation accuracy of gear tooth root bending stress. When the risk of tooth breakage is determined based on a more accurate gear tooth root bending stress, the vibration signal is decomposed using the ICEEMDAN algorithm, and support vectors are selected. This reduces modal aliasing and high-frequency feature loss. Furthermore, the distance between the support vectors and the center of the reference hypersphere constructed using the SVDD algorithm is calculated, and the gear health is obtained based on the distance. This completes the diagnosis of gear tooth breakage failure, accurately reflects the actual health status of the gear, and improves the diagnostic accuracy of gear tooth breakage failure.

[0040] To accurately characterize the reliability performance of gears in equipment, in-depth research on gear tooth root bending stress under frictional dynamic coupling conditions is of great significance, thereby correcting the gear tooth breakage failure diagnosis process. Therefore, this embodiment will focus on gears, proposing a transient calculation method for gear tooth root bending stress that incorporates the dynamic meshing force of fluctuating velocity and fluctuating load, conducting gear tooth breakage failure mechanism analysis under frictional dynamic coupling conditions, extracting features for gear tooth breakage failure diagnosis, and performing gear tooth breakage failure diagnosis and health assessment. The following further describes the gear tooth breakage failure diagnosis method under frictional dynamic coupling conditions used in this embodiment, including the following steps.

[0041] (I) Calculation of Bending Stress at Gear Tooth Root

[0042] The traditional method for calculating gear tooth root bending stress can be described as follows: Under static torque load conditions, the 30° tangent method is used for analysis. The plane precisely tangent to the tooth root fillet is selected as the critical analysis section, also known as the dangerous section. On this dangerous section, based on the maximum stress value on the tension side, corresponding coefficients obtained from a table are further introduced for correction, and the gear tooth root bending stress is calculated.

[0043]

[0044] Where, σ FMe For the bending stress at the root of the gear tooth; F t Y represents the maximum stress value on the tension side of the critical section.ε Y is the overlap coefficient; S Y is the stress correction factor; F B0 is the tooth form factor; B0 is the gear tooth width; m is the gear module; K A K is the load utilization factor. γ K is the load sharing factor; V K is the dynamic load factor; Fβ K is the tooth load distribution factor; Fα This is the inter-tooth load distribution coefficient.

[0045] However, in the complex dynamic process of gear transmission, key factors such as time-varying meshing stiffness and transmission error jointly affect the load distribution on the tooth profile. Even under the condition that the external load remains constant, the load on the tooth profile will still change significantly over time due to these factors. Simultaneously, with the continuous change of the meshing point, the bending moment arm from the meshing point to the critical section also exhibits dynamic changes, further increasing the complexity of stress analysis. Traditional methods for calculating gear tooth root bending stress, while using dynamic load coefficients and tooth form coefficients for correction, can approximate the change in gear tooth root bending stress to some extent. However, this traditional method ignores the dynamic change characteristics of stress during meshing, and therefore cannot accurately reflect the true change history of gear tooth root bending stress during meshing. Furthermore, correcting the influence of load distribution on gear tooth root bending stress using inter-tooth load distribution coefficients may also reduce the calculation accuracy of gear tooth root bending stress by simplifying the actual meshing process. To more accurately capture the dynamic change characteristics of gear tooth root bending stress during transmission, the following method is proposed: Figure 3 This illustrates an improved method for vibration response wave load under tribodynamic coupling conditions. Figure 3 In the middle, a Fen Let be the pressure angle, e be the point of contact with the force, and b be the point of contact with the force. Fm Let K be the bending lever arm, and s be the critical point. Fn b is the tooth thickness, h is the gear width. Fe For the bending lever arm, with b Fm The method is similar, but from a different perspective, namely the bending lever arm. This method abandons the simplified treatment of approximately constant loads in traditional methods and simulates the dynamic effects in the gear transmission process more realistically. Specifically, it establishes a dynamic model of the gear transmission process under the condition of frictional dynamic coupling, solves the dynamic model to obtain the rotation angle of the driving gear and the rotation angle of the driven gear, and calculates the dynamic transmission error, dynamic meshing force, dynamic circumferential force and gear tooth root bending stress in sequence based on the rotation angle of the driving gear and the rotation angle of the driven gear.

[0046] The dynamic model is as follows:

[0047]

[0048]

[0049] Where m1 is the mass of the driving gear; The x-direction translational acceleration of the driving gear; x is the stiffness coefficient of the driving gear in the x direction; x1 is the translational displacement of the driving gear in the x direction. is the damping coefficient in the x-direction of the driving gear; λ is the translational velocity of the driving gear in the x-direction. f f is the coefficient of frictional direction; 1i Let m1 be the first frictional force of the i-th gear; m2 is the mass of the driven gear. Let x be the translational acceleration of the driven gear in the x-direction; x is the stiffness coefficient of the driven gear in the x-direction; x2 is the translational displacement of the driven gear in the x-direction. The damping coefficient in the x-direction of the driven gear; f is the translational velocity of the driven gear in the x-direction. 2i The second frictional force of the i-th gear; The translational acceleration in the y-direction of the driving gear; y is the stiffness coefficient in the y direction of the driving gear; y1 is the translational displacement in the y direction of the driving gear. y is the damping coefficient of the driving gear; k is the translational velocity in the y-direction of the driving gear. t R is the gear stiffness coefficient. b1 R is the base circle radius of the driving gear; θ1 is the rotation angle of the driving gear; b2 θ2 is the base circle radius of the driven gear; θ2 is the rotation angle of the driven gear; y2 is the translational displacement of the driven gear in the y direction; c t This refers to the gear damping coefficient; The rotational angular velocity of the driving gear; The angular velocity of the driven gear; Let be the translational velocity in the y-direction of the driven gear; Let y be the translational acceleration of the driven gear. y is the stiffness coefficient of the driven gear in the y direction; Iy is the damping coefficient of the driven gear in the y direction; I1 is the moment of inertia of the driving gear. k is the rotational angular acceleration of the driving gear. p θ is the torsional stiffness coefficient of the external shaft system of the driving gear. m c is the rotation angle of the motor; p The torsional damping coefficient of the external shaft system of the driving gear; H is the angular velocity of the motor. 1i Ii is the first frictional force arm of the i-th gear; I2 is the moment of inertia of the driven gear; k is the rotational angular acceleration of the driven gear. g θ is the torsional stiffness coefficient of the external shaft system of the driven gear. b c is the rotation angle of the load; g The torsional damping coefficient for the connection of the external shaft system of the driven gear; H is the rotational angular velocity of the load; 2i I is the second frictional force arm of the i-th gear; m The moment of inertia of the motor shaft system; M1 is the angular acceleration of the motor; M2 is the torque applied by the motor; I b The moment of inertia of the load shaft system; M1 is the rotational angular acceleration of the load; M2 is the torque applied by the load; H 11 (t) represents the first frictional force arm of the driving gear at time t; α A The development angle at point A during gear transmission is the initial engagement point; mod() represents the remainder operation; f m Z represents the frictional force of the fluid oil film; Z represents the number of teeth; α represents the frictional force of the fluid oil film D H is the development angle at point D during gear transmission, where point D is the transition point from double-tooth meshing to single-tooth meshing; 12 (t) represents the first frictional force arm of the driven gear at time t; α B H is the development angle at point B during gear transmission, where point B is the transition point from single-tooth meshing to double-tooth meshing; 21 (t) represents the second frictional force arm of the driving gear at time t; β2 is the actual meshing angle; H 22 (t) represents the second frictional force arm of the driven gear at time t.

[0050] In gear transmission, the motor drives the driving gear, the driving gear drives the driven gear, and the driven gear drives the load.

[0051] like Figure 4 As shown, Figure 4 In the middle, O p Let P, A, B, C, D, and E represent the different positions from engagement to disengagement. P is the engagement reference point, A is the engagement start point (i.e., engagement point), B is the transition point from single-tooth meshing to double-tooth meshing, C is the node, D is the transition point from double-tooth meshing to single-tooth meshing, and E is the engagement end point (i.e., disengagement point). Single-tooth meshing means that at any given time, only one pair of teeth is engaged, transmitting power and motion. Double-tooth meshing means that at any given time, two pairs of teeth are engaged simultaneously, jointly transmitting power and motion. ALet α be the development angle of point A. B Let α be the development angle of point B. C Let α be the development angle of point C. D Let α be the development angle of point D. E Let β2 be the development angle at point E, and R be the actual engagement angle. b Let be the base circle radius of the gear. The formula for calculating the friction direction coefficient is:

[0052]

[0053] Where sign() is the sign function; α C -α A The α value represents the development angle from the meshing initiation point to the node; that is, the direction coefficient changes from positive to negative after the meshing point passes the node. `mod()` performs the remainder operation. D -α A This represents the unfolding angle corresponding to a single pitch.

[0054] Both the first and second friction forces are equal, and equal to the total friction force during the transmission process of the driving and driven gears. The specific method for calculating the total friction force includes:

[0055] (1) Using pressure as input, the fluid shear stress is calculated using the Bair-Winer viscoelastic non-Newtonian fluid model. Based on the fluid shear stress, the fluid oil film friction force is calculated.

[0056] The formula for calculating fluid shear stress is:

[0057]

[0058] in, is the first derivative of γ, where γ is the shear strain; For τ m The first derivative, τ m For fluid shear stress; G ∞ τ is the ultimate shear modulus of the fluid. L η is the ultimate shear stress of the fluid; η is the kinematic viscosity of the lubricating oil.

[0059] Fluid limiting shear modulus G ∞ and fluid ultimate shear stress τ L Both are rheological property parameters, and both are affected by pressure p and temperature T. The calculation formula is:

[0060]

[0061] τ L =0.25G ∞ ;

[0062] Where p is pressure and T is temperature.

[0063] Fluid oil film friction force f m This can be achieved by adjusting the fluid shear stress τ m The result is obtained by integration within the computational domain, and the formula is as follows:

[0064]

[0065] Where Ω is the computational domain, which is a two-dimensional computational region determined by the user based on experience, x is the x-coordinate of a certain position, and y is the y-coordinate of a certain position.

[0066] (2) Based on the pressure, the dry shear stress is calculated, and based on the dry shear stress, the dry friction force is calculated.

[0067] In the dry contact zone, the friction coefficient is taken as 0.14 based on experience. The dry shear stress is obtained by multiplying it by the corresponding pressure. The calculation formula is as follows:

[0068] τ c =0.14p;

[0069] Where, τ c This is dry shear stress.

[0070] The dry friction force is obtained by integrating the dry shear stress. The calculation formula is as follows:

[0071]

[0072] Among them, f c It is dry friction, which is the friction generated by the contact of micro-protrusions.

[0073] (3) Calculate the sum of fluid oil film friction and dry friction to obtain the total friction force.

[0074] Combining the fluid oil film friction and dry friction, the total friction force f is obtained, and the calculation formula is as follows:

[0075] f = f c +f m ;

[0076] The dynamic relative displacement difference between the driving gear and the driven gear is the dynamic transmission error. The formula for calculating the dynamic transmission error is:

[0077] δ=R b1 θ1-R b2 θ2+y1-y2+e;

[0078] Where δ represents the dynamic transmission error; R b1 R is the base circle radius of the driving gear; θ1 is the rotation angle of the driving gear; b2θ1 is the base circle radius of the driven gear; θ2 is the rotation angle of the driven gear; y1 is the translational displacement of the driving gear in the y direction; y2 is the translational displacement of the driven gear in the y direction; e is the gear manufacturing error, that is, the error in tooth pitch and tooth profile that exists during the gear manufacturing process, and the calculation formula is:

[0079] e(t) = e r sin(2πf mm t+φ);

[0080] Where e(t) is the gear manufacturing error at time t; e r This is a comprehensive error resulting from manufacturing errors such as gear meshing pressure angle error and pitch error; f mm φ is the meshing frequency; φ is the initial phase.

[0081] The formula for calculating the dynamic meshing force (i.e., undulating load) during gear transmission is as follows:

[0082] F dp =k t δ;

[0083] Among them, F dp For dynamic meshing force; k t This is the gear stiffness coefficient.

[0084] The dynamic circumferential force is calculated based on the relationship between dynamic meshing force and dynamic circumferential force. The formula for calculating the dynamic circumferential force is as follows:

[0085] F dp cos(α)=F t K V ;

[0086] Where α is the meshing pressure angle; F t For dynamic circumferential force; K V This is the dynamic load factor.

[0087] By replacing the maximum stress value on the tension side of the critical section in the traditional formula for calculating gear tooth root bending stress with dynamic circumferential force, dynamic load correction is performed based on the frictional dynamic coupling effect. This transforms the dynamic meshing force into a dynamic circumferential force, more realistically simulating the dynamic effects in gear transmission and avoiding the static simplification errors of traditional methods. The formula for calculating gear tooth root bending stress is now:

[0088]

[0089] Where, σ FMe Y represents the bending stress at the root of the gear tooth. ε Y is the overlap coefficient; S Y is the stress correction factor; FB0 is the tooth form factor; B0 is the gear tooth width; m is the gear module; K A K is the load utilization factor. γ K is the load sharing factor; Fβ K is the tooth load distribution factor; Fα This is the inter-tooth load distribution coefficient.

[0090] In this embodiment, the dynamic model of the gear transmission process under the condition of frictional dynamic coupling is solved to obtain the rotation angle of the driving gear and the rotation angle of the driven gear. Based on the rotation angle of the driving gear and the rotation angle of the driven gear, the bending stress at the root of the gear tooth is calculated.

[0091] Specifically, the gear tooth root bending stress is calculated based on the rotation angles of the driving gear and the driven gear. This includes: calculating the dynamic transmission error during the transmission process of the driving gear and the driven gear based on the rotation angles of the driving gear and the driven gear; calculating the dynamic meshing force based on the dynamic transmission error; calculating the dynamic circumferential force based on the dynamic meshing force; and calculating the gear tooth root bending stress based on the dynamic circumferential force.

[0092] (II) Assessment of the risk of tooth breakage

[0093] After calculating the bending stress at the gear tooth root, this embodiment further calculates the gear bending fatigue safety factor. Specifically, it combines the ultimate bending stress and the life factor to calculate the gear bending fatigue safety factor. The formula for calculating the gear bending fatigue safety factor is as follows:

[0094] S s =(σ Flim K FN ) / σ FMe ;

[0095] Among them, S s σ is the safety factor for gear bending fatigue. Flim K represents the ultimate bending stress related to the gear material. FN σ is the lifespan factor, which can be taken as 0.9; FMe This represents the bending stress at the root of the gear teeth.

[0096] This embodiment further assesses the risk of tooth breakage based on the gear bending fatigue safety factor and the preset safety factor. The value of the preset safety factor is shown in Table 1 below.

[0097] Table 1. Values ​​of the preset safety factor

[0098] Usage Requirements Preset safety factor High reliability 2.00 High reliability 1.60 General reliability 1.25 Low reliability 1.00

[0099] In this embodiment, the preset safety factor is defined according to high reliability and relatively high reliability. Specifically, the preset safety factor is set to 1.60. If the gear bending fatigue safety factor is greater than 1.60, it is considered that there is no risk of tooth breakage.

[0100] In this embodiment, the gear bending fatigue safety factor is calculated based on the gear tooth root bending stress. Based on the gear bending fatigue safety factor, it is determined whether there is a risk of tooth breakage during the transmission process of the driving gear and the driven gear. If there is a risk of tooth breakage, the vibration signal during the transmission process of the driving gear and the driven gear is acquired to perform the next step of gear tooth breakage failure diagnosis.

[0101] Specifically, based on the gear bending fatigue safety factor, it is determined whether there is a risk of tooth breakage during the transmission of the driving gear and the driven gear. This includes: if the gear bending fatigue safety factor is greater than the preset safety factor, it is determined that there is no risk of tooth breakage during the transmission of the driving gear and the driven gear; if the gear bending fatigue safety factor is less than or equal to the preset safety factor, it is determined that there is a risk of tooth breakage during the transmission of the driving gear and the driven gear.

[0102] Among them, when acquiring vibration signals, vibration sensors can be used to acquire vibration signals during the transmission process of the driving gear and the driven gear.

[0103] (III) Diagnosis of Gear Tooth Breakage

[0104] (1) Feature extraction

[0105] The EMD algorithm, as an adaptive signal processing method, aims to adaptively decompose a signal into a series of single-component signals with unique frequency components based on its different frequency characteristics. However, the EMD algorithm exhibits certain limitations in application, particularly in the processing of local characteristics, where its robustness needs improvement. Furthermore, imperfect mode aliasing and stopping conditions also limit its effectiveness in complex signal analysis. To address these issues, the ICEEMDAN algorithm is considered. The core idea of ​​ICEEMDAN is to directly calculate the local mean of the original signal and then extract the Intrinsic Mode Function (IMF) component from this local mean. This strategy of obtaining IMF components from the local mean effectively reduces residual noise and the probability of spurious components in the IMF components, thus achieving simplification and purification of the IMF components. Using the ICEEMDAN algorithm, not only can the shortcomings of the EMD algorithm in adaptive mode decomposition be overcome, but background noise interference can also be effectively reduced, providing a clearer and more accurate signal foundation for subsequent analysis.

[0106] The decomposition process of the ICEEMDAN algorithm is as follows:

[0107] 1) Construct the first group of N signals X1 containing controllable noise. (n) :

[0108] X1 (n) =x I +e1E I1 (ω (n) ), (n=1,2,···,N);

[0109] Among them, X1 (n) x is the nth signal containing controllable noise in group 1; I The original signal is e1; the first desired signal-to-noise ratio is e1; E I1 For the first IMF operator; ω (n) It is the nth Gaussian white noise with zero mean and unit variance.

[0110] 2) Calculate each X1 (n) The difference between the first and second IMFs is used to calculate the average of the first decomposition residuals s. I1 :

[0111] s I1 = <X1 (n) -E I1 (X1 (n) )>;

[0112] Where <·> is the operator for calculating the average of N signals.

[0113] 3) Convert the original signal x I Subtract the residual s from the first decomposition I1 The first IMF component I of the original signal is obtained. I1 :

[0114] I I1 =x I -s I1 ;

[0115] 4) When the number of decompositions k ≥ 2, construct the k-th group of N signals X containing controllable noise. k (n) :

[0116] X k (n) =s Ik-1 +e k E Ik (ω (n) ), (n=1,2,···,N);

[0117] Among them, X k (n) s is the nth signal containing controllable noise in the kth group; Ik-1 e is the residual of the (k-1)th decomposition;k E represents the expected signal-to-noise ratio for the k-th iteration. Ik Let be the operator for the k-th IMF.

[0118] 5) Calculate each X k (n) The difference between the first and second IMFs is used to calculate the average of the residuals from the k-th decomposition, s. Ik :

[0119] s Ik = <X k (n) -E I1 (X k (n) )>;

[0120] 6) Decompose the residual s of the (k-1)th decomposition. Ik-1 Subtract the residual s from the kth decomposition Ik The k-th IMF component I is obtained. Ik :

[0121] I Ik =s Ik-1 -s Ik ;

[0122] 7) Let k = k + 1, return to 4), until the residuals satisfy the Cauchy convergence criterion, that is, the standard deviation σ between two adjacent IMF components (i.e. the IMF component obtained in the current decomposition and the IMF component obtained in the previous decomposition) is less than 0.2, at which point the iteration stops.

[0123] Using the vibration signal as the original signal, multiple intrinsic mode function components can be obtained by decomposing it through the above steps. The ICEEMDAN algorithm can be used instead of the EMD algorithm to suppress mode aliasing and high-frequency feature loss.

[0124] To further investigate the performance of the ICEEMDAN algorithm in overcoming the mode aliasing problem in the EMD algorithm, the same signal was decomposed using both the ICEEMDAN and EMD algorithms, and then compared and analyzed. Figure 5 As shown, Figure 5 (a) shows the decomposition result of the measured rotational speed signal using the EMD algorithm. IMF1 significantly contains multiple components of different frequencies, a phenomenon known as mode aliasing. Furthermore, the eight IMF components (IMF1-IMF8) lack clear frequency characteristics. In contrast, Figure 5(b) shows the decomposition result of the same measured speed signal using the ICEEMDAN algorithm. The measured speed signal was also decomposed into 8 independent IMF components and 1 residual def. In the ICEEMDAN algorithm decomposition result, the mode mixing phenomenon of IMF1-IMF4 is suppressed compared with the EMD algorithm decomposition result. The IMF components as a whole can more clearly reflect the signal components, and the energy distribution is more uniform. Based on the above comparative analysis, it can be seen that the ICEEMDAN algorithm performs well in suppressing the mode mixing problem of the EMD algorithm. Its decomposition result is significantly better than that of the EMD algorithm, providing a higher guarantee for the accuracy of signal processing.

[0125] In summary, compared to the traditional EMD algorithm, the ICEEMDAN algorithm exhibits significant advantages. These advantages are primarily reflected in its stronger robustness to noise interference, effectively improving the accuracy of signal decomposition. Furthermore, the ICEEMDAN algorithm excels in handling the short-term characteristics of data, effectively avoiding over-decomposition and under-decomposition, further enhancing the reliability of the decomposition. In particular, the ICEEMDAN algorithm demonstrates superior performance in the decomposition of nonlinear and non-stationary signals, providing a powerful tool for processing complex signals.

[0126] Kurtosis is a concept designed to quantify the intensity of the impact component in a vibration signal and reveal the relative proportion of the fault impact component in the vibration signal. As a dimensionless parameter, kurtosis describes the peak strength of a waveform. Its value is directly related only to the impact component in the vibration signal and is independent of external factors such as the specific dimensions of the gear, speed variations, and load distribution. The formula for calculating kurtosis is:

[0127]

[0128] Where K is the kurtosis; E(x) I -μ) 4 For the original signal x I The fourth-order mathematical expectation; μ is the mean of the original signal; σ is the standard deviation of the original signal.

[0129] Each IMF component obtained from the ICEEMDAN algorithm is taken as the original signal x. I Substituting these values ​​into the kurtosis calculation formula, we obtain the kurtosis of each IMF component, and select the IMF component with the largest kurtosis as the filtered IMF component.

[0130] In this embodiment, the vibration signal is decomposed using the ICEEMDAN algorithm to obtain multiple intrinsic mode function components, and one intrinsic mode function component is selected from all intrinsic mode function components as a support vector.

[0131] Specifically, selecting one intrinsic mode function component from all intrinsic mode function components as a support vector involves: calculating the kurtosis of each intrinsic mode function component and selecting the intrinsic mode function component corresponding to the maximum kurtosis value as the support vector.

[0132] (2) Health assessment

[0133] The SVDD algorithm, a commonly used method for evaluating gear dynamics performance, is an advanced single-value classification technique. This algorithm possesses significant advantages such as low sample dependence, high computational efficiency, and strong robustness, making it particularly suitable for processing small sample datasets. For gear tooth breakage failure diagnosis, noise reduction and feature parameter extraction are performed on the vibration signals during gear transmission to obtain support vectors. Subsequently, the SVDD algorithm is used to perform a minimum hypersphere description on the sample support vectors. A feature domain, i.e., a reference hypersphere, is constructed using the sample support vectors to characterize the gear's faulty operating state. Finally, gear tooth breakage failure diagnosis is performed using the distance between the support vectors and the center of the reference hypersphere. In this process, the SVDD algorithm not only achieves hypersphere description and outlier detection but also simplifies the solution process by introducing a kernel function to transform the nonlinear problem in low-dimensional space into a linear problem in high-dimensional space.

[0134] The core idea of ​​the SVDD algorithm is to treat all data points in the normal state as a set, and to construct a system by optimizing the boundary of this set. Figure 6 The diagram illustrates a reference hypersphere designed to maximize the inclusion of data points in the normal state. Data points in the state to be evaluated that are outside the reference hypersphere are considered abnormal, and the greater the distance of a data point from the reference hypersphere, the greater its deviation from the normal state. Based on this core idea, the SVDD algorithm effectively distinguishes data points, and the corresponding mathematical model is expressed as follows:

[0135] Assume the training dataset is {x} Ii ,i=1,2,···,n},x Ii Let be the support vector of the i-th normal state data point, i.e., the i-th normal sample vibration signal, and n be the total number of sample support vectors. The training dataset can be considered as a whole, encompassing almost all data points under normal conditions, and can be represented as:

[0136] F r (r F ,a F ) = r F 2 ;

[0137] Among them, F r As a reference hypersphere; r F a is the radius;F The center of the ball.

[0138] Based on the core idea of ​​the SVDD algorithm, a minimum reference hypersphere should be sought within the current feature space to ensure that all data points {x} in normal states are within this hypersphere. Ii The numbers i = 1, 2, ..., n all lie within the reference hypersphere.

[0139] ||x Ii -a F || 2 ≤r F 2 ;

[0140] To effectively control model complexity, ensure stronger generalization ability during training, and avoid overfitting, a relaxation factor ξ is introduced into the SVDD algorithm. i , making x Ii To the center of the ball a F The distance should be less than or equal to a value slightly greater than r. F Threshold:

[0141]

[0142] Where F is the reference hypersphere; ξ i C is the i-th relaxation factor; c The penalty parameter controls the radius of the reference hypersphere and ensures the number of data points contained within it.

[0143]

[0144] Therefore, the core of the problem lies in finding the optimal solution to the equation that satisfies specific conditions. To achieve this goal, the Lagrange multiplier method is introduced into the original equation, thereby deriving the corresponding Lagrange equation:

[0145]

[0146] Where L is the Lagrange equation; α I and γ i All are Lagrange factors, all greater than or equal to 0; ξ is the relaxation factor.

[0147] Further research on r F a F ξ i Taking the partial derivative, we get:

[0148]

[0149] Where, α Ii Let be the Lagrange factor corresponding to the i-th term; C is the penalty factor.

[0150] By analyzing the constraint relationships of the quadratic programming problem, we can obtain:

[0151]

[0152] Where, α Ij x is the Lagrange factor corresponding to the j-th term; Ij Let be the data point of the j-th normal state, that is, the sample support vector of the vibration signal of the j-th normal sample.

[0153] The data points in the normal state are defined as support vectors x. Isv That is, setting the data points in the normal state as support vectors, once these support vectors x Isv Once successfully calculated, the position of the center of the reference hypersphere can be accurately determined:

[0154]

[0155] in, Let be the i-th support vector, which is the data point in the i-th normal state.

[0156] By determining the support vectors, the radius of the reference hypersphere can be further calculated to describe and quantify its geometric properties.

[0157]

[0158] Given that collecting data from actual machine tests after gear fracture involves destructive testing, which is complex and costly, this embodiment employs a vibration testing bench for non-destructive fault response analysis during gear tooth fracture failure diagnosis to reduce testing difficulty and cost. This verifies the effectiveness of the broken tooth meshing mechanism and its modeling method. The overall structure of the testing bench is designed to simulate the dynamic behavior of gears under fault conditions and is equipped with a DC motor with a maximum speed of 1800 r / min to simulate the power output of the host machine. The DC motor is connected to the gear system (i.e., gearbox) via a coupling, and the gear system is connected to the load via a coupling. A pair of spur gears is installed in the gear system, and their structural parameters are consistent with those of the gear under study, thereby ensuring a high degree of similarity between the test conditions and actual application scenarios.

[0159] To accurately determine the inherent frequency characteristics of the test bench, this embodiment employs a speed-increasing method. The shaft speed is controlled to increase uniformly from an initial 200 r / min to a target value of 1500 r / min, aiming to simulate the range of speed variations that might be encountered in actual operating conditions. During the test, a magnetoelectric sensor located above the gearbox captures and records the speed signals. These speed signals are analyzed and processed using Fast Fourier Transform (FFT) to obtain a spectral waterfall plot under speed variations. Figure 7 and Figure 8 As shown, waterfall plots of the test bench under both no-load and loaded conditions are displayed. The waterfall plots clearly show that, regardless of whether under no-load or loaded conditions, the first natural frequency of the test bench remains stable around 99.40 Hz. Due to the limitations of the test bench structure and its maximum rotational speed, other natural frequencies were not observed in this test. This result limits the reference range for simulation comparison, focusing primarily on the comparative analysis of the first natural frequency. To verify the accuracy of the experimental results, free vibration analysis was performed on the simulation model of the test bench. The calculation results show that the first natural frequency is 98.78 Hz, with a deviation of only 0.6% compared to the measured value. This indicates that the resonant rotational speed corresponding to the first natural frequency of the test bench is close to 6000 r / min, far exceeding the maximum rotational speed tested. Therefore, in practical applications, there is no need to overly concern oneself with the potential impact of resonance effects.

[0160] This study investigates the changes in the system vibration response of gears under broken tooth failure conditions. The calculations assume the driving gear is normal, while a single tooth of the driven gear fractures completely. The experimental data comparing the instantaneous rotational speeds of the gears in the time domain under normal meshing and broken tooth meshing conditions are as follows: Figure 9 As shown in (a), the comparison results of experimental and simulation data of instantaneous rotational speed in the time domain under broken tooth meshing are as follows: Figure 9 As shown in (b) above, the corresponding frequency domain comparison results are as follows: Figure 10 As shown.

[0161] from Figure 9 and Figure 10 The results clearly show that the vibration response exhibits significant periodicity under broken tooth failure conditions. When encountering broken tooth failure, the captured test signal forms a clear impact signal marker at the fault location. Simulation also reveals a similar periodic vibration impact pattern. Under this fault condition, the overall vibration amplitude increases significantly, especially at the instant the gear meshes into the broken tooth region, where the intensity of the periodic vibration impact increases sharply. Quantitative analysis reveals that the average amplitude of the rotational speed under broken tooth conditions increases by 225% compared to the normal gear condition, and reaches as high as 6.16 times at the impact point. Furthermore, a dense distribution of sidebands appears in the vicinity of the meshing frequency and its harmonics. The vibration impact excitation caused by broken tooth failure leads to a multiple increase in the overall amplitude in the frequency domain compared to the normal gear condition.

[0162] This embodiment can utilize the aforementioned test bench to obtain vibration signals from normal samples in order to construct a reference hypersphere.

[0163] Data point x of the state to be evaluated Iz The distance d between the center of the reference hypersphere and the reference hypersphere can be expressed as:

[0164]

[0165] When using the SVDD algorithm to evaluate gear performance status, the first step is to construct a reference hypersphere using data points from the equipment under normal conditions. If the data point for the state to be evaluated is located within this reference hypersphere, the corresponding state is determined to be normal; conversely, if the data point is located outside the reference hypersphere, the corresponding state is determined to be abnormal. Furthermore, the farther the data point for the state to be evaluated is from the reference hypersphere, the lower the reliability of its status evaluation. Reliability is represented by health status, and the formula mapping distance to gear health status is:

[0166] h = e -(y / y')2 ;

[0167] Where h is the gear health score; the lower the gear health score, the lower the reliability of the gear tooth breakage failure diagnosis; y is the distance; y' is the average distance, which is equal to the average of the distance y and the distance between each sample support vector and the center of the reference hypersphere.

[0168] In this embodiment, the distance between the support vector and the center of the reference hypersphere is calculated. If the distance is less than or equal to the radius of the reference hypersphere, the driving gear and the driven gear do not have a broken tooth failure fault. If the distance is greater than the radius of the reference hypersphere, the driving gear and the driven gear have a broken tooth failure fault. Based on the distance, the gear health is calculated to complete the gear broken tooth failure diagnosis. The reference hypersphere is constructed using the SVDD algorithm based on the sample support vector of the normal sample vibration signal.

[0169] Before calculating the distance between the support vector and the center of the reference hypersphere, the gear tooth breakage failure diagnosis method under the tribodynamic coupling condition in this embodiment further includes: constructing a reference hypersphere, specifically including: acquiring normal sample vibration signals, which are vibration signals acquired during the transmission process of the sample driving gear and the sample driven gear when neither of the sample driving gear nor the sample driven gear has broken teeth, and can be acquired through a test bench; for each normal sample vibration signal, the normal sample vibration signal is decomposed using the ICEEMDAN algorithm to obtain multiple sample intrinsic mode function components, and one sample intrinsic mode function component is selected from all sample intrinsic mode function components as the sample support vector; using all sample support vectors as input, the reference hypersphere is constructed using the SVDD algorithm, and the reference hypersphere includes a center and a radius.

[0170] Specifically, selecting one intrinsic mode function component from all sample intrinsic mode function components as the sample support vector involves: calculating the kurtosis of each sample intrinsic mode function component, and selecting the sample intrinsic mode function component corresponding to the maximum kurtosis value as the sample support vector.

[0171] Gear tooth root bending stress is a crucial reference for diagnosing gear tooth breakage failure. Traditional calculations of gear tooth root bending stress are mostly based on static load analysis, while actual gears often operate under dynamic loads. This is especially true for the gear under study, which is subjected to complex internal and external excitations. Based on a frictional dynamics coupled analysis model of the gear transmission system, this study obtains the gear tooth root bending stress under dynamic loads, revealing the tooth breakage failure mechanism under real dynamic loads and providing theoretical guidance for accurate calculation of gear tooth root bending stress and optimization of fault diagnosis performance. First, the bending stress at the gear tooth root of gears with frequent tooth breakage failures under dynamic loads is calculated, using the bending stress safety factor criterion to determine whether it exceeds the allowable bending stress limit of the gear material. Second, based on the ICEEMDAN algorithm, mode aliasing in the signal is suppressed, reducing errors in the fault feature extraction process. Subsequently, based on optimizing the original vibration signal and effectively extracting fault features, the method is combined with the support vector data description method, which has the advantages of handling high-dimensional data, a small amount of abnormal data and nonlinear problems in the data-driven method, to process the degradation trend of gear bending stress performance and map the health status, thereby obtaining the degradation characteristics of gear bending stress mechanical performance and the gear health status.

[0172] This embodiment acquires vibration signals at continuous time points. Each sampling point represents the vibration signal sampled at one time. Based on the analysis of the vibration signals, the distance of the vibration signal at each time point is calculated, and finally, a graph is plotted. Figure 11 The distance curve shown in the image. Figure 11 In the graph, the vertical axis represents the distance calculated by the SVDD algorithm. The magnitude of this distance directly reflects the degree of deviation between the system performance and its normal operating state, i.e., the significance of the degradation. By comparison, it can be observed that the distance curve obtained using the SVDD algorithm shows significant signs of degradation near the 63rd sampling point. To more intuitively analyze the system's degradation state, a health-mapping transformation was performed on the original distance curve, resulting in the following... Figure 12 The health curve shown is as follows: Figure 12 As shown, after the 61st sampling point, the gear quickly enters the failure state. This curve not only meets the basic monotonicity requirement of the life prediction curve, but also effectively preserves the key features of the original degradation curve, providing an important reference for subsequent gear life prediction research.

[0173] This application also provides an application scenario in which the above-described method for diagnosing gear tooth breakage failure under tribodynamic coupling conditions is applied. Specifically, the method for diagnosing gear tooth breakage failure under tribodynamic coupling conditions provided in this embodiment can be applied in gear fault diagnosis scenarios. Gear fault diagnosis scenarios include a diagnosis stage and a display stage. The diagnosis stage is used to complete the diagnosis of gear tooth breakage failure, and the display stage is used to show the user the diagnosis results. The method for diagnosing gear tooth breakage failure under tribodynamic coupling conditions provided in this embodiment belongs to the diagnosis stage.

[0174] Example 2

[0175] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 13 As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operating system and computer programs stored in the non-volatile storage media. The database stores data. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When executed by the processor, the computer program implements a method for diagnosing gear tooth breakage under tribodynamic coupling conditions.

[0176] Those skilled in the art will understand that Figure 13 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0177] In one exemplary embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the gear tooth breakage failure diagnosis method under tribodynamic coupling conditions in Embodiment 1.

[0178] Example 3

[0179] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the gear tooth breakage failure diagnosis method under tribodynamic coupling conditions of Embodiment 1.

[0180] Example 4

[0181] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the gear tooth breakage failure diagnosis method under tribodynamic coupling conditions of Embodiment 1.

[0182] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0183] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0184] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for diagnosing tooth breakage failure of a gear under a frictional dynamics coupling condition, characterized by, The gear tooth fracture failure diagnosis method under the friction dynamics coupling condition comprises the following steps: Solving the dynamics model in the process of gear transmission under the friction dynamics coupling condition to obtain the rotation angle of the driving gear and the rotation angle of the driven gear, and calculating the gear root bending stress based on the rotation angle of the driving gear and the rotation angle of the driven gear; Based on the gear root bending stress, the gear bending fatigue safety factor is calculated, and based on the gear bending fatigue safety factor, it is determined whether there is a risk of tooth fracture in the process of driving the driving gear and the driven gear, if there is a risk of tooth fracture, the vibration signal in the process of driving the driving gear and the driven gear is obtained; The vibration signal is decomposed by using the ICEEMDAN algorithm to obtain a plurality of intrinsic mode function components, and one of the intrinsic mode function components is selected as a support vector from all the intrinsic mode function components. The distance between the support vector and the center of the reference hypersphere is calculated, if the distance is less than or equal to the radius of the reference hypersphere, the driving gear and the driven gear do not have tooth fracture failure, if the distance is greater than the radius of the reference hypersphere, the driving gear and the driven gear have tooth fracture failure, and based on the distance, the gear health degree is calculated to complete the gear tooth fracture failure diagnosis; the reference hypersphere is constructed based on the sample support vector of the normal sample vibration signal by using the SVDD algorithm.

2. The method according to claim 1, wherein, The dynamics model is: wherein m1 is a mass of the driving gear; is a translational acceleration in the x direction of the driving gear; is a stiffness coefficient in the x direction of the driving gear; x1 is a translational displacement in the x direction of the driving gear; is a damping coefficient in the x direction of the driving gear; is a translational velocity in the x direction of the driving gear; λ f is a friction direction coefficient; f 1i is a first friction of the i-th gear; m2 is a mass of the driven gear; is a translational acceleration in the x direction of the driven gear; is a stiffness coefficient in the x direction of the driven gear; x2 is a translational displacement in the x direction of the driven gear; is a damping coefficient in the x direction of the driven gear; is a translational velocity in the x direction of the driven gear; f 2i is a second friction of the i-th gear; is a translational acceleration in the y direction of the driving gear; is a stiffness coefficient in the y direction of the driving gear; y1 is a translational displacement in the y direction of the driving gear; is a damping coefficient in the y direction of the driving gear; is a translational velocity in the y direction of the driving gear; k t is a gear stiffness coefficient; R b1 is a base circle radius of the driving gear; θ1 is a rotational angle of the driving gear; R b2 is a base circle radius of the driven gear; θ2 is a rotational angle of the driven gear; y2 is a translational displacement in the y direction of the driven gear; c t is a gear damping coefficient; is a rotational angular velocity of the driving gear; is a rotational angular velocity of the driven gear; is a translational velocity in the y direction of the driven gear; is a translational acceleration in the y direction of the driven gear; is a stiffness coefficient in the y direction of the driven gear; is a damping coefficient in the y direction of the driven gear; I1 is a rotational inertia of the driving gear; is a rotational angular acceleration of the driving gear; k p is a connecting torsional stiffness coefficient of the driving gear external shaft system; θ m is a rotational angle of the motor; c p is a connecting torsional damping coefficient of the driving gear external shaft system; is a rotational angular velocity of the motor; H 1i is a first friction arm of the i-th gear; I2 is a rotational inertia of the driven gear; ωa(t) is the rotational angular acceleration of the driving gear; k g θ is the connecting torsional stiffness coefficient of the driving gear external shaft system; θ b θ is the rotational angle of the load; c g θ is the connecting torsional damping coefficient of the driving gear external shaft system; H is the rotational angular velocity of the load; H 2i H is the second friction force arm of the ith gear; I m I is the rotational inertia of the motor shaft system; ωm(t) is the rotational angular acceleration of the motor; M1 is the torque applied by the motor; I b I is the rotational inertia of the load shaft system; ωl(t) is the rotational angular acceleration of the load; M2 is the torque applied by the load; H 11 (t) is the first friction force arm of the driving gear at time t; α A α is the development angle of point A in the gear transmission process, and A is the meshing starting point; mod() represents the modulo operation; f m f is the fluid oil film friction force; Z is the number of teeth; α D α is the development angle of point D in the gear transmission process, and D is the transition point from double-tooth meshing to single-tooth meshing; H 12 (t) is the first friction force arm of the driving gear at time t; α B α is the development angle of point B in the gear transmission process, and B is the transition point from single-tooth meshing to double-tooth meshing; H 21 (t) is the second friction force arm of the driving gear at time t; β2 is the actual meshing angle; H 22 (t) is the second friction force arm of the driving gear at time t.

3. The method according to claim 1, wherein, Based on the rotation angle of the driving gear and the rotation angle of the driven gear, the gear root bending stress is calculated, specifically including: Based on the rotation angle of the driving gear and the rotation angle of the driven gear, the dynamic transmission error in the process of driving the driving gear and the driven gear is calculated; Based on the dynamic transmission error, the dynamic meshing force is calculated; Based on the dynamic meshing force, the dynamic circumferential force is calculated; Based on the dynamic circumferential force, the gear root bending stress is calculated; The calculation formula of the dynamic transmission error is: δ = R b1 θ1-R b2 θ2+y1-y2+e; wherein δ is a dynamic transmission error; R b1 R1 is a base circle radius of the driving gear; θ1 is a rotation angle of the driving gear; R b2 R2 is a base circle radius of the driven gear; θ2 is a rotation angle of the driven gear; y1 is a translational displacement in the y direction of the driving gear; y2 is a translational displacement in the y direction of the driven gear; e is a gear manufacturing error; The calculation formula of the dynamic meshing force is: F dp = k t δ; where F dp is the dynamic engagement force; k t is the gear stiffness coefficient; The calculation formula of the dynamic circumferential force is: F dp cos(a) = F t K V ; wherein a is the pressure angle of engagement; F t is the dynamic circumferential force; K V is the dynamic load coefficient; The calculation formula of the gear root bending stress is: wherein σ FMe is the gear root bending stress; Y ε is the degree of coincidence coefficient; Y S is the stress correction coefficient; Y F is the tooth profile coefficient; B0 is the gear tooth width; m is the gear modulus; K A is the load usage coefficient; K γ is the load sharing coefficient; K Fβ is the transverse load distribution coefficient; K Fα is the intertooth load distribution coefficient.

4. The method according to claim 1, wherein, The calculation formula of the gear bending fatigue safety factor is: S s = (σ Flim K FN ) / σ FMe ; wherein S s is the gear bending fatigue safety factor; σ Flim is the ultimate bending stress related to the gear material; K FN is the life factor; σ FMe is the gear root bending stress; Based on the gear bending fatigue safety factor, it is determined whether there is a risk of tooth fracture in the process of driving the driving gear and the driven gear, specifically including: if the gear bending fatigue safety factor is greater than the preset safety factor, it is determined that there is no risk of tooth fracture in the process of driving the driving gear and the driven gear; if the gear bending fatigue safety factor is less than or equal to the preset safety factor, it is determined that there is a risk of tooth fracture in the process of driving the driving gear and the driven gear.

5. The method of tooth breakage failure diagnosis of gears under conditions of frictional kinetics according to claim 1, characterized in that, From all the intrinsic mode function components, one of the intrinsic mode function components is selected as a support vector, specifically including: calculating the kurtosis of each intrinsic mode function component, and selecting the intrinsic mode function component corresponding to the maximum value of the kurtosis as the support vector.

6. The method of tooth breakage failure diagnosis of gears under conditions of frictional kinetics according to claim 1, characterized in that, Before calculating the distance between the support vector and the center of the reference hypersphere, the gear tooth fracture failure diagnosis method under the friction dynamics coupling condition further comprises: constructing a reference hypersphere, specifically including: Obtaining normal sample vibration signals; the normal sample vibration signals are vibration signals obtained in the transmission process of the sample driving gear and the sample driven gear when the sample driving gear and the sample driven gear are both free of broken teeth; For each normal sample vibration signal, the normal sample vibration signal is decomposed by using an ICEEMDAN algorithm to obtain a plurality of sample intrinsic mode function components, and one sample intrinsic mode function component is selected from all the sample intrinsic mode function components as a sample support vector; A reference hypersphere is constructed by using an SVDD algorithm with all the sample support vectors as input; the reference hypersphere includes a sphere center and a radius.

7. The method of diagnosing tooth fracture failure of a gear under conditions of frictional dynamics according to claim 1, characterized in that, The calculation formula of the gear health degree is: h = e -(y / y')2 ; wherein h is the gear health degree, the smaller the gear health degree, the lower the reliability of the gear broken tooth failure diagnosis; y is the distance; y' is the average distance, which is equal to the average value of the distance y and the distance between each sample support vector and the sphere center of the reference hypersphere.

8. A computer device comprising: A memory, a processor and a computer program stored in the memory and capable of running on the processor, characterized in that the processor executes the computer program to implement the gear broken tooth failure diagnosis method under the friction dynamics coupling condition according to any one of claims 1-7.

9. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to implement the gear broken tooth failure diagnosis method under the friction dynamics coupling condition according to any one of claims 1-7.

10. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to implement the gear broken tooth failure diagnosis method under the friction dynamics coupling condition according to any one of claims 1-7. The computer program is executed by the processor to implement the gear broken tooth failure diagnosis method under the friction dynamics coupling condition according to any one of claims 1-7.

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