A coupled dynamic modeling method for gearboxes excited by internal multi-source faults

Abstract

The present invention discloses a method for modeling the coupled dynamics of a gearbox excited by multiple internal fault sources, comprising the following steps: S1: Calculation of the time-varying stiffness, damping, and dynamic friction of the gear meshing: Based on the gear morphology and local spalling fault parameters, the functional relationship between the gear meshing stiffness and the driving wheel rotation angle is calculated; in combination with the theory of hybrid elastohydrodynamic lubrication, the dynamic friction and meshing damping of the current gear meshing pair are calculated at each moment by inputting dynamic gear meshing force, surface roughness, and entrainment speed parameters; S2: Calculation of the inner and outer ring forces of each bearing in the gearbox; S3: Constructing and solving the complete equations of the entire gearbox dynamics model. The present invention can accurately obtain the vibration response of the gearbox under the influence of multiple factors such as meshing force, meshing friction, dynamic forces acting on the inner and outer rings of the bearings, elastohydrodynamic lubrication, and fault excitation.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical equipment health status assessment and fault diagnosis, and in particular to a gearbox coupling dynamics modeling method stimulated by internal multi-source faults. Background Art

[0002] Transmission gearboxes are key components in mechanical systems, and their condition directly impacts their operational state. A gearbox failure can result in significant economic losses and even casualties. Signal processing methods, such as mechanical fault feature extraction, are effective approaches for gearbox fault diagnosis. However, these methods often require prior knowledge of fault characteristics as a theoretical foundation. Experimental verification is one of the primary methods for acquiring prior knowledge of fault characteristics, but specific experimental verification for gearboxes often faces significant challenges, such as high cost, unclear fault parameters, and significant system interference. Therefore, dynamic modeling, which generates simulated signals for fault mechanism analysis, is crucial. Gearboxes are characterized by complex internal stress conditions and diverse failure modes. Traditional gearbox dynamic models often simplify other components, such as bearings, to investigate the fault characteristics of a single component. While such models offer some value for fault mechanism research, they fail to accurately reflect the actual behavior of the entire gearbox and the coupling between its components, leaving significant room for improvement. Summary of the Invention

[0003] The object of the present invention is to provide a gearbox coupled dynamics modeling method excited by internal multi-source faults to solve the problems in the prior art.

[0004] To achieve the above object, the present invention provides the following technical solution: a gearbox coupled dynamics modeling method stimulated by internal multi-source faults, comprising the following steps:

[0005] S1: Calculation of time-varying gear mesh stiffness, damping, and dynamic friction: Based on the gear morphology and local spalling fault parameters, the gear mesh stiffness is calculated as a function of the driving wheel rotation angle. Combined with the hybrid elastohydrodynamic lubrication theory, the dynamic friction and mesh damping of the current gear mesh pair are calculated at each moment by inputting dynamic gear mesh force, surface roughness, and entrainment velocity parameters.

[0006] S2: Calculate the forces acting on the inner and outer rings of each bearing in the gearbox: Input the current relative displacement of the inner and outer rings. The normal deformation and tangential velocity of all contact pairs in the bearing can be calculated using the quasi-static relationship between the orbital and rotational motions of the rolling elements. Based on the bearing structural and surface parameters, combined with hybrid elastohydrodynamic lubrication theory and Hertzian contact theory, the damping-considered normal force acting on each rolling element in the bearing can be calculated. These normal forces are combined to obtain the dynamic forces acting on the inner and outer rings of the bearing.

[0007] S3: Construct and solve the complete equations for the entire gearbox dynamics model: Based on the previous steps, introduce the gear meshing transmission error, drive motor, brake, and gearbox housing; establish a complete set of gearbox dynamic differential equations using Newton's second law; use numerical solution methods to solve the differential equations and obtain the dynamic response of the system;

[0008] S4: Analysis of fault characteristics of simulation signals: The most research-significant housing acceleration is selected from the numerical dynamic solution of the gearbox system as the gearbox vibration simulation signal. The simulation signal is analyzed through basic methods such as time domain analysis, power spectrum and envelope spectrum analysis to reveal the vibration behavior of the gearbox under coupled fault conditions.

[0009] Preferably, the specific steps of S1 include:

[0010] S11: Introducing local faults in gears by changing geometric parameters. The present invention introduces local faults in gears in the form of surface spalling; the surface spalling morphology is described as an ellipse with a certain depth h s , width w max With length l max ; This surface peeling will affect the effective contact length L when the gears are meshing s and cross-section properties when calculating stiffness;

[0011]

[0012]

[0013] where x s_center Indicates the center coordinate position of the peeling ellipse, x s_start Indicates the starting coordinate position of the peeling ellipse, x s_end Indicates the end coordinate position of the peeling ellipse; θ s Indicates the inclination angle of the spalling ellipse; this part of the value affected by the fault will affect the calculation of the meshing stiffness, and through the meshing stiffness, affect the entire dynamic system, achieving the purpose of introducing gear faults;

[0014] S12: Calculate the time-varying stiffness of meshing gears. Consider the gear teeth as cantilever beams with variable cross-sections and derive the Hertzian contact stiffness k of a particular gear tooth using the energy method. h , bending stiffness k b , shear stiffness k s , axial compressive stiffness k a and the angular foundation stiffness k f ; The comprehensive series stiffness of the two gear teeth in meshing state is obtained:

[0015]

[0016] Since more than one pair of gear teeth are in contact during the gear meshing process, there are cases where two pairs of gear teeth are in contact at the same time. It is necessary to connect the series stiffness of the two pairs of gear teeth in parallel, and finally obtain the meshing stiffness function with respect to the driving gear rotation angle:

[0017]

[0018] S13: Calculate the elastohydrodynamic lubrication damping and friction coefficient of the gear meshing; first, calculate the current lubricating oil film thickness h of the meshing pair based on the lubrication conditions and physical parameters. c :

[0019]

[0020] Among them, K Hc is the surface micro-peak morphology parameter, set to 1; W is the dimensionless load parameter; U is the dimensionless velocity parameter; G is the dimensionless material parameter; R is the equivalent contact curvature radius; is the dimensionless surface roughness, V is the dimensionless hardness parameter;

[0021] The contact damping c of the gear contact pair can be approximately calculated based on the oil film thickness, lubricant viscosity and contact area. film :

[0022]

[0023] According to the friction theory under mixed elastohydrodynamic lubrication conditions in gear meshing, the dynamic friction coefficient can be calculated as follows:

[0024]

[0025] The intermediate parameters can be obtained by the following formula:

[0026]

[0027] where u pi and u gi are the surface speeds of the driving wheel and the driven wheel in each pair of gear contacts; S is the root mean square surface roughness; P h is the Hertzian contact pressure, b1 to b9 are constant coefficients:

[0028] b 1-9 =-8.92,1.03,1.04,-0.35,2.81,-0.10,0.75,-0.39,0.62

[0029] Since there may be two pairs of teeth meshing during the gear meshing process, it is necessary to calculate the friction force on each pair of meshing teeth and then synthesize it; first, according to the load distribution coefficient S ri Calculate the load on each pair of teeth:

[0030]

[0031] Then the calculation formula of friction force and friction torque can be obtained:

[0032]

[0033] The subscript p indicates the action on the driving wheel, and the subscript g indicates the action on the driven wheel;

[0034] In general, step 1 provides a calculation method for the forces generated by the gear meshing part. This part of the calculation fully describes the dynamic behavior of the gear meshing and constitutes the gear meshing part of the overall model.

[0035] Preferably, the specific steps of S2 include:

[0036] S21: Calculate the equivalent stiffness and damping of the bearing rolling elements. Connect the inner and outer contact pairs of each rolling element in series, which is equivalent to a spring-damper system. Therefore, it is necessary to first calculate the stiffness and damping of each contact pair. The Hertzian contact stiffness of the bearing can be obtained by the formula:

[0037]

[0038] Among them E b , ν b and Σρ are Young's modulus, Poisson's ratio and raceway curvature, respectively; δ * Dimensionless deformation coefficient; According to relevant research on elastohydrodynamic lubrication, the elastohydrodynamic lubrication damping of the rolling element is generated by the inlet area of the lubricating oil film. The lubrication damping of the inlet area can be calculated by the following formula:

[0039]

[0040] Where η0 is the lubricating viscosity; R x is the effective curvature in the entrainment direction; a is the length of the major semi-axis of the contact ellipse; the thickness of the lubricating oil film at the point contact h c It can be calculated by the following formula:

[0041] h c =2.69U 0.67 G 0.53 Q -0.067 (1-0.61e -0.73κ )R x (13)

[0042] Since the bearing raceway contact pair is not completely elastically lubricated, considering the influence of surface conditions on the oil film thickness, a correction factor is introduced in the film thickness calculation as follows:

[0043]

[0044] Where C and r are constant coefficients with values of 0.87 and 1.5 respectively; h cT That is the corrected film thickness;

[0045] After obtaining the stiffness and damping of each contact pair, the equivalent series stiffness and damping of the rolling element can be obtained by the complex stiffness series formula:

[0046]

[0047] in

[0048]

[0049] Where linear stiffness k 1,2 =k b δ 0.5 , linear damping c=c e ;ω is the natural frequency of free vibration of contact pair;

[0050] S22: Calculate the contact forces between the inner and outer rings of the bearing based on the contact geometry and local faults. Use a displacement excitation with a half-sinusoidal profile to describe the local fault in the bearing raceway. The displacement excitation equation is as follows:

[0051]

[0052] where R r is the rolling element radius; L defect is the local fault length; φ l is the angular range corresponding to the fault length; is the angle of the jth rolling element relative to the fault position and can be calculated as follows:

[0053]

[0054] where φ d is the starting position angle of the fault; the force between the inner and outer rings of the bearing can be calculated by the following formula:

[0055]

[0056] Where λ(δ) is the control function. When δ is positive, the output of this function is 1, and in other cases the output is 0, ensuring that contact force is generated only when the inner and outer rings are in contact. The rolling element position angle ψ j =2π(j-1) / N b +ψ c ; and ψ c =0.5(1-D / D m )θ i , where θ i Indicates the inner ring angle, which is obtained from the geometric relationship of the bearing; δj The deformation of the j-th rolling element position can be calculated by the following formula:

[0057]

[0058] In this formula, c0 represents radial clearance.

[0059] Preferably, the S3 specifically includes:

[0060] Establish a complete gearbox dynamic model; since industrial gearboxes contain deep groove ball bearings and spur gears, the vibration of the gearbox is mainly caused by radial excitation; therefore, all axial degrees of freedom of the gearbox are ignored. Since the shaft length of the gearbox is relatively short, the bending and swinging motion of the shaft are not considered; each shaft has two degrees of freedom of movement in the X and Y directions and a degree of freedom of rotation; the gearbox housing is fixed to the outer rings of all bearings and has two directions of translational freedom; the inner ring of the bearing is fixed to the shaft and rotates with the shaft; the gearbox contains a total of four bearings, two on the driving shaft and two on the driven shaft; the gearbox can now be constructed as a nine-degree-of-freedom dynamic model, and the system equation is as follows:

[0061]

[0062] where θ L ,θ p and θ g are the dynamic rotation angles of the load, driving wheel and driven wheel respectively; m p 、m g and m f In turn, I represents the mass of the driving wheel, driven wheel, and gearbox housing; L , I p and I g T represents the moment of inertia of the load, driving wheel and driven wheel respectively; Load is the torque applied to the load, is the motor speed. pg is the dynamic meshing force, which can be calculated as follows:

[0063]

[0064] where k m and c m are the time-varying mesh stiffness and damping calculated in S1; ζ and ξ are the geometric deviation and gear transmission error caused by tooth surface spalling, respectively;

[0065] In general, step 2 gives the force between the inner and outer rings of the bearing; this force fully reflects the dynamic characteristics of the bearing and can accurately describe the dynamic action of the bearing in the gearbox system.

[0066] Preferably, the S3 specifically includes:

[0067] Analysis of fault characteristics of simulation signals; Based on the numerical results obtained from the differential equations, the vibration response of the gearbox system over a period of time can be obtained; Through the time domain analysis of the response, the changing characteristics of the physical variables in the gearbox during the entire process can be known; At the same time, the characteristics of the gearbox vibration in the time domain under different fault modes can be analyzed; Use Fourier transform to convert the time domain acceleration signal into a frequency domain signal to obtain the power spectrum of the simulation signal, and the frequency domain response of the gearbox under different modes can be obtained through the power spectrum; Analyze the manifestation of different fault modes in the frequency domain response of the gearbox, and summarize the characteristics of different fault modes on the power spectrum; Obtain the envelope of the original simulation signal through Hilbert transform, and then perform Fourier transform on the envelope to obtain the envelope spectrum of the simulation signal; The characteristic frequency components of the gearbox vibration can be obtained more clearly through the envelope spectrum, and the envelope spectrum frequency characteristics of different fault modes can be clarified.

[0068] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the steps of any one of the methods are implemented when the processor executes the program.

[0069] A computer-readable storage medium stores a computer program, which implements the steps of any one of the methods when executed by a processor.

[0070] A processor is used to run a program, wherein the program executes any one of the methods when running.

[0071] Compared with the prior art, the present invention has the following beneficial effects:

[0072] 1. This invention first establishes a gearbox dynamics model that fully considers gear meshing, bearing action, and the gearbox housing. It provides an accurate mathematical description of local bearing faults, gear meshing geometry, and local gear faults within the gearbox. It can accurately determine the vibration response of the gearbox under the influence of multiple factors, including meshing force, meshing friction, dynamic forces acting on the inner and outer rings of the bearings, elastohydrodynamic lubrication, and fault excitation.

[0073] 2. Compared with the traditional dynamic modeling method, this invention fully considers the mathematical description method of local faults of bearings and gears; by analyzing the vibration of the gearbox under different local fault modes, combined with the traditional Fourier transform and envelope spectrum analysis methods, the frequency domain characteristics of the gearbox housing vibration under internal multi-source excitation can be obtained; compared with the traditional model, the method provided by the present invention can provide a lateral comparison method for the responses under excitation of defects in different positions of bearings, gears, etc., providing a more profound mechanism analysis for gearbox fault diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0075] Figure 1 It is the internal part of the gearbox dynamic model of the present invention;

[0076] Figure 2 is the external part of the gearbox dynamic model of the present invention;

[0077] Figure 3 This is a flow chart of the gearbox dynamics modeling method for internal multi-source coupled fault excitation of the present invention;

[0078] Figure 4 The vibration response of the gearbox housing under the condition of a local fault of the driven wheel and a fault of the bearing outer ring of the present invention;

[0079] Figure 5 This is the vibration response of the gearbox housing under the condition of a local fault of the driven wheel and a fault of the inner ring of the bearing;

[0080] Figure 6 This is an experimental verification of the high-speed shaft bearing inner ring fault and the driven wheel fault of the present invention;

[0081] Figure 7 This is an experimental verification of the high-speed shaft bearing outer ring fault and the driven wheel fault of the present invention;

[0082] Figure 8 is the gear parameter table of the present invention;

[0083] Figure 9 This is a bearing parameter table of the present invention;

[0084] Figure 10 This is a table of gearbox structural parameters of the present invention;

[0085] Figure 11 This is the vibration characteristic frequency table of the gearbox dynamics model of the present invention. DETAILED DESCRIPTION

[0086] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the invention for which protection is sought, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0087] See also Figure 1-11 In an embodiment of the present invention, a method for modeling gearbox coupling dynamics under internal multi-source fault excitation includes the following steps:

[0088] S1: Calculation of time-varying gear mesh stiffness, damping, and dynamic friction: Based on the gear morphology and local spalling fault parameters, the gear mesh stiffness is calculated as a function of the driving wheel rotation angle. Combined with the hybrid elastohydrodynamic lubrication theory, the dynamic friction and mesh damping of the current gear mesh pair are calculated at each moment by inputting dynamic gear mesh force, surface roughness, and entrainment velocity parameters.

[0089] S2: Calculate the forces acting on the inner and outer rings of each bearing in the gearbox: Input the current relative displacement of the inner and outer rings. The normal deformation and tangential velocity of all contact pairs in the bearing can be calculated using the quasi-static relationship between the orbital and rotational motions of the rolling elements. Based on the bearing structural and surface parameters, combined with hybrid elastohydrodynamic lubrication theory and Hertzian contact theory, the damping-considered normal force acting on each rolling element in the bearing can be calculated. These normal forces are combined to obtain the dynamic forces acting on the inner and outer rings of the bearing.

[0090] S3: Construct and solve the complete equations for the entire gearbox dynamics model: Based on the previous steps, introduce the gear meshing transmission error, drive motor, brake, and gearbox housing; establish a complete set of gearbox dynamic differential equations using Newton's second law; use numerical solution methods to solve the differential equations and obtain the dynamic response of the system;

[0091] S4: Analysis of fault characteristics of simulation signals: The most research-significant housing acceleration is selected from the numerical dynamic solution of the gearbox system as the gearbox vibration simulation signal. The simulation signal is analyzed through basic methods such as time domain analysis, power spectrum and envelope spectrum analysis to reveal the vibration behavior of the gearbox under coupled fault conditions.

[0092] Preferably, the specific steps of S1 include:

[0093] S11: Introducing local faults in gears by changing geometric parameters. The present invention introduces local faults in gears in the form of surface spalling; the surface spalling morphology is described as an ellipse with a certain depth h s , width w max With length l max ; This surface peeling will affect the effective contact length L when the gears are meshing s and cross-section properties when calculating stiffness;

[0094]

[0095]

[0096] where x s_center Indicates the center coordinate position of the peeling ellipse, x s_start Indicates the starting coordinate position of the peeling ellipse, x s_end Indicates the end coordinate position of the peeling ellipse; θ s Indicates the inclination angle of the spalling ellipse; this part of the value affected by the fault will affect the calculation of the meshing stiffness, and through the meshing stiffness, affect the entire dynamic system, achieving the purpose of introducing gear faults;

[0097] S12: Calculate the time-varying stiffness of meshing gears. Consider the gear teeth as cantilever beams with variable cross-sections and derive the Hertzian contact stiffness k of a particular gear tooth using the energy method. h , bending stiffness k b , shear stiffness k s , axial compressive stiffness k a and the angular foundation stiffness k f ; The comprehensive series stiffness of the two gear teeth in meshing state is obtained:

[0098]

[0099] Since more than one pair of gear teeth are in contact during the gear meshing process, there are cases where two pairs of gear teeth are in contact at the same time. It is necessary to connect the series stiffness of the two pairs of gear teeth in parallel, and finally obtain the meshing stiffness function with respect to the driving gear rotation angle:

[0100]

[0101] S13: Calculate the elastohydrodynamic lubrication damping and friction coefficient of the gear meshing; first, calculate the current lubricating oil film thickness h of the meshing pair based on the lubrication conditions and physical parameters. c :

[0102]

[0103] Among them, K Hcis the surface micro-peak morphology parameter, set to 1; W is the dimensionless load parameter; U is the dimensionless velocity parameter; G is the dimensionless material parameter; R is the equivalent contact curvature radius; is the dimensionless surface roughness, V is the dimensionless hardness parameter;

[0104] The contact damping c of the gear contact pair can be approximately calculated based on the oil film thickness, lubricant viscosity and contact area. film :

[0105]

[0106] According to the friction theory under mixed elastohydrodynamic lubrication conditions in gear meshing, the dynamic friction coefficient can be calculated as follows:

[0107]

[0108] The intermediate parameters can be obtained by the following formula:

[0109]

[0110] where u pi and u gi are the surface speeds of the driving wheel and the driven wheel in each pair of gear contacts; S is the root mean square surface roughness; P h is the Hertzian contact pressure, b1 to b9 are constant coefficients:

[0111] b 1-9 =-8.92,1.03,1.04,-0.35,2.81,-0.10,0.75,-0.39,0.62

[0112] Since there may be two pairs of teeth meshing during the gear meshing process, it is necessary to calculate the friction force on each pair of meshing teeth and then synthesize it; first, according to the load distribution coefficient S ri Calculate the load on each pair of teeth:

[0113]

[0114] Then the calculation formula of friction force and friction torque can be obtained:

[0115]

[0116] The subscript p indicates the action on the driving wheel, and the subscript g indicates the action on the driven wheel.

[0117] In general, S1 provides a method for calculating the forces generated by the gear meshing part. This part of the calculation fully describes the dynamic behavior of the gear meshing and constitutes the gear meshing part of the overall model.

[0118] Preferably, the specific steps of S2 include:

[0119] S21: Calculate the equivalent stiffness and damping of the bearing rolling elements. Connect the inner and outer contact pairs of each rolling element in series, which is equivalent to a spring-damper system. Therefore, it is necessary to first calculate the stiffness and damping of each contact pair. The Hertzian contact stiffness of the bearing can be obtained by the formula:

[0120]

[0121] Among them E b , ν b and Σρ are Young's modulus, Poisson's ratio and raceway curvature, respectively; δ * Dimensionless deformation coefficient; According to relevant research on elastohydrodynamic lubrication, the elastohydrodynamic lubrication damping of the rolling element is generated by the inlet area of the lubricating oil film. The lubrication damping of the inlet area can be calculated by the following formula:

[0122]

[0123] Where η0 is the lubricating viscosity; R x is the effective curvature in the entrainment direction; a is the length of the major semi-axis of the contact ellipse; the thickness of the lubricating oil film at the point contact h c It can be calculated by the following formula:

[0124] h c =2.69U 0.67 G 0.53 Q -0.067 (1-0.61e -0.73κ )R x (13)

[0125] Since the bearing raceway contact pair is not completely elastically lubricated, considering the influence of surface conditions on the oil film thickness, a correction factor is introduced in the film thickness calculation as follows:

[0126]

[0127] Where C and r are constant coefficients with values of 0.87 and 1.5 respectively; h cT That is the corrected film thickness;

[0128] After obtaining the stiffness and damping of each contact pair, the equivalent series stiffness and damping of the rolling element can be obtained by the complex stiffness series formula:

[0129]

[0130] in

[0131]

[0132] Where linear stiffness k 1,2 =kb δ 0.5 , linear damping c=c e ;ω is the natural frequency of free vibration of contact pair;

[0133] S22: Calculate the contact forces between the inner and outer rings of the bearing based on the contact geometry and local faults. Use a displacement excitation with a half-sinusoidal profile to describe the local fault in the bearing raceway. The displacement excitation equation is as follows:

[0134]

[0135] where R r is the rolling element radius; L defect is the local fault length; φ l is the angular range corresponding to the fault length; is the angle of the jth rolling element relative to the fault position and can be calculated as follows:

[0136]

[0137] where φ d is the starting position angle of the fault; the force between the inner and outer rings of the bearing can be calculated by the following formula:

[0138]

[0139] Where λ(δ) is the control function. When δ is positive, the output of this function is 1, and in other cases the output is 0, ensuring that contact force is generated only when the inner and outer rings are in contact. The rolling element position angle ψ j =2π(j-1) / N b +ψ c ; and ψ c =0.5(1-D / D m )θ i , where θ i Indicates the inner ring angle, which is obtained from the geometric relationship of the bearing; δ j The deformation of the j-th rolling element position can be calculated by the following formula:

[0140]

[0141] In this formula, c0 represents radial clearance.

[0142] In general, S2 gives the force between the inner and outer rings of the bearing. This force fully reflects the dynamic characteristics of the bearing and can accurately describe the dynamic action of the bearing in the gearbox system.

[0143] Preferably, the S3 specifically includes:

[0144] Establish a complete gearbox dynamic model; since industrial gearboxes contain deep groove ball bearings and spur gears, the vibration of the gearbox is mainly caused by radial excitation; therefore, all axial degrees of freedom of the gearbox are ignored. Since the shaft length of the gearbox is relatively short, the bending and swinging motion of the shaft are not considered; each shaft has two degrees of freedom of movement in the X and Y directions and a degree of freedom of rotation; the gearbox housing is fixed to the outer rings of all bearings and has two directions of translational freedom; the inner ring of the bearing is fixed to the shaft and rotates with the shaft; the gearbox contains a total of four bearings, two on the driving shaft and two on the driven shaft; the gearbox can now be constructed as a nine-degree-of-freedom dynamic model, and the system equation is as follows:

[0145]

[0146] where θ L ,θ p and θ g are the dynamic rotation angles of the load, driving wheel and driven wheel respectively; m p 、m g and m f In turn, I represents the mass of the driving wheel, driven wheel, and gearbox housing; L , I p and I g T represents the moment of inertia of the load, driving wheel and driven wheel respectively; Load is the torque applied to the load, is the motor speed. pg is the dynamic meshing force, which can be calculated as follows:

[0147]

[0148] where k m and c m are the time-varying mesh stiffness and damping calculated in S1; ζ and ξ are the geometric deviation and gear transmission error caused by tooth surface spalling, respectively.

[0149] The present invention uses the Runge-Kutta algorithm to solve the dynamic differential equations, the time step is set to 10 μs, and the initial value of the equation is set as follows: p =-3.5×10 -6 m,y p =-8.4×10 -6 m,x g =3.5×10 -6 m and y g =8.4×10 -6 m; the speed is set to 1000RPM, and the load torque is set to 16Nm.

[0150] Preferably, the S3 specifically includes:

[0151] Analysis of fault characteristics of simulation signals; Based on the numerical results obtained from the differential equations, the vibration response of the gearbox system over a period of time can be obtained; Through the time domain analysis of the response, the changing characteristics of the physical variables in the gearbox during the entire process can be known; At the same time, the characteristics of the gearbox vibration in the time domain under different fault modes can be analyzed; Use Fourier transform to convert the time domain acceleration signal into a frequency domain signal to obtain the power spectrum of the simulation signal, and the frequency domain response of the gearbox under different modes can be obtained through the power spectrum; Analyze the manifestation of different fault modes in the frequency domain response of the gearbox, and summarize the characteristics of different fault modes on the power spectrum; Obtain the envelope of the original simulation signal through Hilbert transform, and then perform Fourier transform on the envelope to obtain the envelope spectrum of the simulation signal; The characteristic frequency components of the gearbox vibration can be obtained more clearly through the envelope spectrum, and the envelope spectrum frequency characteristics of different fault modes can be clarified.

[0152] After numerical solution and analysis, the coupled vibration response of the bearing outer ring fault and the gear driven wheel fault is as follows Figure 4 As shown in the figure, bearing failures include two types: high-speed shaft bearing failure and low-speed shaft bearing failure. Each fault scenario is analyzed using time domain signals, power spectrum, and envelope spectrum. The time domain signals show that bearing outer race failure and driven pulley failure produce significant impact on the gearbox housing. The impact in the time domain signals can be used to identify internal gearbox faults, but the specific fault mode cannot be determined from the time domain alone. The dominant frequency components in the power spectrum are the meshing frequency and its harmonics, with the largest frequency being 4GMF. This is caused by modulation of the gearbox housing's natural frequency, which is determined by the gearbox parameters. Bearing outer race failures produce distinct sidebands in the power spectrum, spaced apart by the outer race's characteristic frequency. Due to the different speeds of the high-speed and low-speed shaft bearings, the spacing between these sidebands also varies. These sidebands are primarily distributed near 4GMF, indicating that the bearing characteristic frequency, like the meshing frequency, is amplitude-modulated by the gearbox housing's natural frequency. Similarly, the sidebands caused by the driven gear fault, spaced at intervals of the driven gear speed, exhibit the same distribution characteristics in the power spectrum, indicating that these frequencies are also modulated by the natural frequency. Because the sidebands caused by the gear fault are closely spaced, have lower amplitudes, and share the same distribution as the sidebands caused by the bearing fault, they are easily obscured by the bearing sidebands, making them difficult to detect. These easily obscured bands are indicated by red dashed lines in the figure. In the envelope spectrum, the characteristic frequencies primarily appear as the fundamental frequency and low-order harmonics. The characteristic frequency of the bearing outer race now exceeds the meshing frequency to become the dominant frequency component, but the meshing frequency is still visible in the envelope spectrum. The rotational frequency component caused by the gear fault, due to its lower frequency and smaller amplitude, is primarily concentrated in the low-frequency region of the envelope spectrum and is indicated by the red dashed line. The characteristic frequencies of the bearing and gear faults appear superimposed in the envelope and power spectra, with no apparent mutual modulation observed.

[0153] See the following for bearing inner ring failure and driven wheel failure: Figure 5 . Similar to the outer ring fault, the inner ring fault is also considered from the perspective of high-speed shaft bearings and low-speed shaft bearings. In the case of inner ring fault, the fault position rotates with the inner ring, and the force at the fault position fluctuates between the maximum value and zero, so the bearing time domain impact will be smaller than that of the outer ring, but the impact caused by the bearing fault can still be found. The impact caused by the gear fault is the same as that of the outer ring. The frequency domain response of the inner ring fault and the driven wheel fault is also shown in Figure 5 In the figure, the sidebands caused by the gear fault are marked with red dotted lines. These sidebands are the same as those in the case of the bearing outer ring fault, which shows that the bearing fault pattern will not affect the frequency domain response of the gear fault to the gearbox housing vibration. The characteristic frequencies caused by the shaft inner ring fault are more complex. In addition to the sidebands separated by the inner ring characteristic frequency, the characteristic frequencies in the power spectrum and envelope spectrum are also modulated by the bearing rotation frequency. This is consistent with the conclusions obtained from the dynamic model of a single bearing, which also proves the correctness of the model established by this invention. Consistent with the outer ring fault, the characteristic frequency of the bearing inner ring fault is also not modulated with the characteristic frequency of the gear fault, and they are superimposed on each other.

[0154] To further verify the correctness of this invention, a single-stage spur gear transmission gearbox driven by an AC motor was used. The load was applied via a magnetic powder brake mounted at the end of the output shaft. Vibration signals were acquired via a sensor mounted on the gearbox housing. A localized gear fault was set on the driven wheel, and a localized bearing fault was set in the high-speed shaft bearing. To eliminate noise interference in the experimental signals, the experimental signals were denoised. A frequency band of [9216 Hz, 10240 Hz] was selected for filtering the simulated and experimental signals. Figure 6 The comparison between experimental and simulation results of inner ring bearing fault and driven pulley fault is shown. Figure 7 The experimental and simulation results for both outer ring bearing and driven gear faults are compared. The green dots in the figure indicate the characteristic frequency of the gear fault, i.e., the driven gear rotational frequency, while the red dots indicate the characteristic frequency of the bearing fault and the meshing frequency. The experimental comparison shows that, despite some errors in the frequency amplitudes, the frequency characteristics are generally consistent, demonstrating the accuracy of the proposed method for industrial gearbox dynamic modeling with internal multi-source coupled fault excitation.

[0155] To address the incompleteness of traditional dynamic models and their inability to provide a theoretical basis for gearbox vibrations driven by internal multi-source fault mechanisms, this paper, starting from the traditional gear meshing model, fully considers aspects such as bearing dynamic forces, gearbox housing, elastohydrodynamic lubrication, and local fault description, and constructs a new dynamic modeling method for industrial gearboxes driven by internal multi-source coupled faults. Based on this dynamic model, the vibration response of the gearbox housing under internal multi-source coupled fault mechanisms is studied. Using classic Fourier transform and envelope spectrum analysis methods, the gearbox vibration characteristics under different fault modes are analyzed, revealing the mechanism of the superposition of bearing and gear local faults on the gearbox housing, providing a theoretical basis for signal processing methods such as fault feature extraction. Finally, by comparing the experimental signals measured on a gearbox test bench with the simulated signals obtained in this invention, the effectiveness of this method for industrial gearbox dynamic modeling driven by internal multi-source coupled faults is demonstrated.

[0156] The invention is described in detail below in combination with simulation signal analysis and experimental verification.

[0157] The schematic diagram of the gearbox dynamic model is as follows Figure 1 and Figure 2 As shown, the internal and external models affect each other through the bearing force to form a complete gearbox. The gearbox parameters used in this invention are Figure 8-10 As shown:

[0158] The S4 includes:

[0159] Fault feature analysis of simulation signals; Based on the numerical results obtained from the differential equations, the vibration response of the gearbox system over a period of time can be obtained; Through the time domain analysis of the response, the changing characteristics of the physical variables in the gearbox during the entire process can be known; At the same time, the time domain characteristics of the gearbox vibration under different fault modes can be analyzed; The time domain acceleration signal is converted into a frequency domain signal using Fourier transform to obtain the power spectrum of the simulation signal, and the frequency domain response of the gearbox under different modes can be obtained through the power spectrum; The manifestation of different fault modes in the frequency domain response of the gearbox is analyzed, and the characteristics of different fault modes on the power spectrum are summarized; The envelope of the original simulation signal is obtained through Hilbert transform, and then the envelope is Fourier transformed to obtain the envelope spectrum of the simulation signal; The characteristic frequency components of the gearbox vibration can be obtained more clearly through the envelope spectrum, and the envelope spectrum frequency characteristics of different fault modes can be clarified;

[0160] After numerical solution and analysis, the coupled vibration response of the bearing outer ring fault and the gear driven wheel fault is as follows Figure 4As shown in the figure; the bearing failure includes two cases, namely high-speed shaft bearing failure and low-speed shaft bearing failure; each fault case is analyzed using three methods: time domain signal, power spectrum and envelope spectrum; from the time domain signal, it can be seen that the bearing outer ring failure and the driven wheel failure will produce obvious impact on the gearbox housing; the fault condition inside the gearbox can be judged by the impact in the time domain signal, but the specific fault mode cannot be known from the time domain alone; the main frequency components in the power spectrum are the meshing frequency and its harmonics, among which the largest frequency is 4gmf, which is caused by the modulation of the natural frequency of the gearbox housing, and the natural frequency is determined by the gearbox parameters; the bearing outer ring failure excites obvious sidebands with the outer ring characteristic frequency as the interval in the power spectrum, and the high-speed shaft and low-speed shaft bearings have different sideband intervals due to different speeds; these sidebands are mainly distributed near 4gmf, which shows that the bearing characteristic frequency is affected by the gearbox like the meshing frequency. The amplitude modulation of the natural frequency of the wheel box housing; similarly, the sidebands excited by the driven wheel fault, which are spaced at intervals of the driven wheel speed, have the same distribution characteristics in the power spectrum, indicating that these frequencies are also modulated by the natural frequency; since the sidebands excited by the gear fault are closely spaced and have low amplitudes, and have the same distribution as the sidebands of the bearing fault, they are easily covered by the bearing sidebands and difficult to find; these easily covered frequency bands are marked with red dotted lines in the figure; in the envelope spectrum, the characteristic frequencies mainly appear in the form of fundamental frequencies and low-order harmonics; the characteristic frequency of the bearing outer ring exceeds the meshing frequency at this time and becomes the main frequency component, but the meshing frequency is still visible in the envelope spectrum; the rotational frequency component caused by the gear fault is mainly concentrated in the low-frequency area of the envelope spectrum due to its low frequency and small amplitude, and is marked with a red dotted line; the characteristic frequencies of the bearing fault and the gear fault in the envelope spectrum and power spectrum are superimposed, and no obvious mutual modulation phenomenon is found;

[0161] See the following for bearing inner ring failure and driven wheel failure: Figure 5 ; Same as the outer ring fault, the inner ring fault is also considered from the perspective of high-speed shaft bearing and low-speed shaft bearing; In the case of inner ring fault, the fault position rotates with the inner ring, and the force at the fault position fluctuates between the maximum value and zero, so the time domain impact of the bearing will be smaller than that of the outer ring, but the impact caused by the bearing fault can still be found; The impact caused by the gear fault is the same as that of the outer ring; The frequency domain responses of the inner ring fault and the driven wheel fault are also shown in Figure 5The sidebands caused by the gear fault are marked with red dotted lines. These sidebands are the same as those in the case of the bearing outer ring fault, which shows that the bearing fault mode will not affect the frequency domain response of the gear fault to the gearbox housing vibration. The characteristic frequencies caused by the shaft inner ring fault are more complex. In addition to the sidebands separated by the inner ring characteristic frequency, the characteristic frequencies in the power spectrum and envelope spectrum are also modulated by the bearing rotation frequency. This is consistent with the conclusion obtained from the dynamic model of a single bearing, which also proves the correctness of the model established by the invention. Consistent with the outer ring fault, the characteristic frequency of the bearing inner ring fault is also not modulated with the characteristic frequency of the gear fault, and they are superimposed on each other.

[0162] To further verify the correctness of the invention, a gearbox test bench was used for experimental verification. This single-stage spur gear transmission gearbox is driven by an AC motor. The load is applied via a magnetic powder brake installed at the end of the output shaft. The vibration signal is acquired by a sensor installed on the gearbox body. The local gear fault is set on the driven wheel, and the local bearing fault is set in the high-speed shaft bearing. To eliminate noise interference in the experimental signals, the experimental signals are denoised. The frequency band of [9216Hz, 10240Hz] is selected to filter the simulation and experimental signals. Figure 6 The comparison between experimental and simulation results of inner ring bearing fault and driven wheel fault is presented; Figure 7 The figure shows a comparison of experimental and simulation results for outer ring bearing faults and driven gear faults. The green dots in the figure indicate the characteristic frequency of the gear fault, i.e., the driven gear rotation frequency, while the red dots indicate the characteristic frequency of the bearing fault and the meshing frequency. The experimental comparison diagram shows that although there are some errors in the frequency amplitudes, the frequency characteristics are basically consistent, indicating that the experiment can prove the accuracy of the industrial gearbox dynamic modeling method for internal multi-source coupled fault excitation provided by this invention.

[0163] In order to solve the problem that the traditional dynamic model is incomplete and cannot provide a theoretical basis for the gearbox vibration affected by the internal multi-source fault mechanism, the present invention starts from the traditional gear meshing model, fully considers the dynamic force of the bearing, the gearbox housing, elastohydrodynamic lubrication and local fault description, and constructs a new industrial gearbox dynamic modeling method excited by internal multi-source coupling faults; and based on this dynamic model, the vibration response of the gearbox housing under the internal multi-source coupling fault mechanism is studied; the gearbox vibration characteristics under different fault modes are analyzed using the classic Fourier transform and envelope spectrum analysis methods, revealing the superposition mechanism of bearing and gear local faults on the gearbox housing, providing a theoretical basis for signal processing methods such as fault feature extraction; finally, by comparing the experimental signal measured by the gearbox test bench with the simulation signal obtained in the invention, it is proved that the industrial gearbox dynamic modeling method excited by internal multi-source coupling faults of the present invention has certain effectiveness.

[0164] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art will be able to modify the technical solutions described in the aforementioned embodiments or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for modeling coupled dynamics of a gearbox excited by internal multi-source faults, characterized by: The following steps are involved: S1: Calculation of time-varying gear mesh stiffness, damping, and dynamic friction: Based on the gear morphology and local spalling fault parameters, the gear mesh stiffness is calculated as a function of the driving wheel rotation angle. Combined with the hybrid elastohydrodynamic lubrication theory, the dynamic friction and mesh damping of the current gear mesh pair are calculated at each moment by inputting dynamic gear mesh force, surface roughness, and entrainment velocity parameters. S2: Calculate the inner and outer ring forces of each bearing in the gearbox: Input the current relative displacement of the inner and outer rings, and calculate the normal deformation and tangential velocity of all contact pairs in the bearing using the quasi-static relationship between the orbital and rotational motions of the rolling elements. Based on the bearing structural and surface parameters, combined with the hybrid elastohydrodynamic lubrication theory and Hertz contact theory, calculate the damping-considered normal force acting on each rolling element in the bearing. Combine these normal forces to obtain the dynamic inner and outer ring forces of the bearing. S3: Construct and solve the complete equations for the entire gearbox dynamics model: Based on the previous steps, introduce the gear meshing transmission error, drive motor, brake, and gearbox housing; establish a complete set of gearbox dynamic differential equations using Newton's second law; use numerical solution methods to solve the differential equations and obtain the dynamic response of the system; S4: Analysis of fault characteristics of simulation signals: The most research-significant housing acceleration is selected from the numerical dynamic solution of the gearbox system as the gearbox vibration simulation signal. The simulation signal is analyzed through basic methods such as time domain analysis, power spectrum and envelope spectrum analysis to reveal the vibration behavior of the gearbox under coupled fault conditions.

2. The method for modeling gearbox coupling dynamics under internal multi-source fault excitation according to claim 1, characterized in that: The specific steps of S1 include: S11: Introducing local gear faults by changing geometric parameters; introducing local faults in the gear in the form of surface spalling; the surface spalling morphology is described as an ellipse with a certain depth h s , width w max With length l max ; This surface peeling will affect the effective contact length L when the gears are meshing s and cross-section properties when calculating stiffness; where x s_center Indicates the center coordinate position of the peeling ellipse, x s_start Indicates the starting coordinate position of the peeling ellipse, x s_end Indicates the end coordinate position of the peeling ellipse; θ s Indicates the inclination angle of the spalling ellipse; this part of the value affected by the fault will affect the calculation of the meshing stiffness, and through the meshing stiffness, affect the entire dynamic system, achieving the purpose of introducing gear faults; S12: Calculate the time-varying stiffness of meshing gears; consider the gear teeth as cantilever beams with variable cross-sections and derive the Hertzian contact stiffness k of a particular gear tooth using the energy method. h , bending stiffness k b , shear stiffness k s , axial compressive stiffness k a and the angular foundation stiffness k f ; get two The comprehensive series stiffness of the gear teeth in meshing state: Since more than one pair of gear teeth are in contact during the gear meshing process, there are cases where two pairs of gear teeth are in contact at the same time. It is necessary to connect the series stiffness of the two pairs of gear teeth in parallel, and finally obtain the meshing stiffness function with respect to the driving gear rotation angle: S13: Calculate the elastohydrodynamic lubrication damping and friction coefficient of the gear meshing; first, calculate the current lubricating oil film thickness h of the meshing pair based on the lubrication conditions and physical parameters. c : Among them, K Hc is the surface micro-peak morphology parameter, set to 1; W is the dimensionless load parameter; U is the dimensionless velocity parameter; G is the dimensionless material parameter; R is the equivalent contact curvature radius; is the dimensionless surface roughness, V is the dimensionless hardness parameter; The contact damping c of the gear contact pair is approximately calculated based on the oil film thickness, lubricant viscosity and contact area. film : According to the friction theory under the mixed elastohydrodynamic lubrication conditions in gear meshing, the dynamic friction coefficient can be calculated as follows: The intermediate parameters can be obtained by the following formula: where u pi and u gi are the surface speeds of the driving wheel and the driven wheel in each pair of gear contacts; S is the root mean square surface roughness; P h is the Hertzian contact pressure, b1 to b9 are constant coefficients: b 1-9 ＝-8.92,1.03,1.04,-0.35,2.81,-0.10,0.75,-0.39,0.62 Since there may be two pairs of teeth meshing during the gear meshing process, it is necessary to calculate the friction force on each pair of meshing teeth and then synthesize it; first, according to the load distribution coefficient S ri Calculate the load on each pair of teeth: Then the calculation formula of friction force and friction torque can be obtained: The subscript p indicates the action on the driving wheel, and the subscript g indicates the action on the driven wheel.

3. The method for modeling gearbox coupling dynamics under internal multi-source fault excitation according to claim 2, characterized in that: The specific steps of S2 include: S21: Calculate the equivalent stiffness and damping of the bearing rolling elements. Connect the inner and outer contact pairs of each rolling element in series, which is equivalent to a spring-damper system. Therefore, it is necessary to first calculate the stiffness and damping of each contact pair. The Hertzian contact stiffness of the bearing can be obtained by the formula: Among them E b , ν b and Σρ are Young's modulus, Poisson's ratio and raceway curvature, respectively; δ * Dimensionless deformation coefficient; According to relevant research on elastohydrodynamic lubrication, the elastohydrodynamic lubrication damping of the rolling element is generated by the inlet area of the lubricating oil film. The lubrication damping of the inlet area can be calculated by the following formula: Where η0 is the lubricating viscosity; R x is the effective curvature in the entrainment direction; a is the length of the major semi-axis of the contact ellipse; the thickness of the lubricating oil film at the point contact h c It can be calculated by the following formula: h c =2.69U 0.67 G 0.53 Q -0.067 (1-0.61e -0.73κ )R x (13) Since the bearing raceway contact pair is not completely elastically lubricated, considering the influence of surface conditions on the oil film thickness, a correction factor is introduced in the film thickness calculation as follows: Where C and r are constant coefficients with values of 0.87 and 1.5 respectively; h cT That is the corrected film thickness; After obtaining the stiffness and damping of each contact pair, the equivalent series stiffness and damping of the rolling element can be obtained through the complex stiffness series formula: in Where linear stiffness k 1,2 =k b δ 0.5 , linear damping c=c e ;ω is the natural frequency of free vibration of the contact pair; S22: Calculate the contact forces between the inner and outer rings of the bearing based on the contact geometry and local faults. Use a displacement excitation with a half-sinusoidal profile to describe the local fault in the bearing raceway. The displacement excitation equation is as follows: where R r is the rolling element radius; L defect is the local fault length; φl is the angular range corresponding to the fault length; is the angle of the jth rolling element relative to the fault position and can be calculated as follows: where φ d is the starting position angle of the fault; the force between the inner and outer rings of the bearing can be calculated by the following formula: Where λ(δ) is the control function. When δ is positive, the output of this function is 1, and in other cases the output is 0, ensuring that contact force is generated only when the inner and outer rings are in contact. The rolling element position angle ψ j =2π(j-1) / N b +ψ c ; and ψ c =0.5(1-D / D m )θ i , where θ i Indicates the inner ring angle, which is obtained from the geometric relationship of the bearing; δ j The deformation of the j-th rolling element position can be calculated by the following formula: In this formula, c0 represents radial clearance.

4. The method for modeling gearbox coupling dynamics under internal multi-source fault excitation according to claim 3, characterized in that: The S3 specifically includes: A complete gearbox dynamic model is established. Since industrial gearboxes contain deep groove ball bearings and spur gears, the vibration of the gearbox is mainly caused by radial excitation. Therefore, all axial degrees of freedom of the gearbox are ignored. Since the shaft length of the gearbox is relatively short, the bending and swinging motion of the shaft are not considered. Each shaft has two degrees of freedom of movement in the X and Y directions and a degree of freedom of rotation. The gearbox housing is fixed to the outer rings of all bearings and has two directions of translational freedom. The inner ring of the bearing is fixed to the shaft and rotates with the shaft. The gearbox contains four bearings, two on the driving shaft and two on the driven shaft. The gearbox is thus constructed as a nine-degree-of-freedom dynamic model, and the system equations are as follows: where θ L ,θ p and θ g are the dynamic rotation angles of the load, driving wheel and driven wheel respectively; m p 、m g and m f In turn, I represents the mass of the driving wheel, driven wheel, and gearbox housing; L , I p and I g T represents the moment of inertia of the load, driving wheel and driven wheel respectively; Load is the torque applied to the load, is the motor speed, F pg is the dynamic meshing force, which can be calculated as follows: where k m and c m are the time-varying mesh stiffness and damping calculated in S1; ζ and ξ are the geometric deviation and gear transmission error caused by tooth surface spalling, respectively.

5. The method for modeling gearbox coupling dynamics under internal multi-source fault excitation according to claim 4, characterized in that: The S3 specifically includes: Analysis of fault characteristics of simulation signals; based on the numerical results obtained from the differential equations, the vibration response of the gearbox system over a period of time is obtained; through time domain analysis of the response, the changing characteristics of the physical variables in the gearbox during the entire process are known; at the same time, the characteristics of the gearbox vibration in the time domain under different fault modes are analyzed; the time domain acceleration signal is converted into a frequency domain signal using Fourier transform to obtain the power spectrum of the simulation signal, and the frequency domain response of the gearbox under different modes is obtained through the power spectrum; the manifestation of different fault modes in the frequency domain response of the gearbox is analyzed, and the characteristics of different fault modes on the power spectrum are summarized; the envelope of the original simulation signal is obtained through Hilbert transform, and then the envelope is Fourier transformed to obtain the envelope spectrum of the simulation signal; the characteristic frequency components of the gearbox vibration are more clearly obtained through the envelope spectrum, and the envelope spectrum frequency characteristics of different fault modes are clarified.

6. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the method according to any one of claims 1 to 5 are implemented.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

8. A processor, characterized in that: The processor is configured to run a program, wherein the program executes the method according to any one of claims 1 to 5 when running.

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