CN115203898A - A coupled dynamics modeling method for gearboxes excited by internal multi-source faults - Google Patents

Abstract

The invention discloses a coupling dynamics modeling method of a gearbox excited by an internal multi-source fault, comprising the following steps: S1: Calculation of variable stiffness, damping and dynamic friction force during gear meshing: according to gear topography and local spalling faults parameters, the function relationship between the gear mesh stiffness and the driving wheel rotation angle is calculated; combined with the hybrid elastohydrodynamic lubrication theory, the dynamic gear meshing force, surface roughness, and entrainment speed parameters are input at each moment to calculate the current gear meshing pair. Friction and mesh damping; S2: Calculate the inner and outer ring forces of each bearing in the gearbox; S3: Build and solve the complete equation 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 force of the inner and outer rings of the bearing, elastohydrodynamic lubrication, fault excitation and the like.

Description

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

technical field

The invention relates to the technical field of health state assessment and fault diagnosis of mechanical equipment, in particular to a coupling dynamics modeling method of a gearbox excited by an internal multi-source fault.

Background technique

The transmission gearbox is one of the key components of the mechanical system, and its state directly affects the operating state of the mechanical system. Once the gearbox fails, it is likely to bring huge economic losses and even lead to casualties. Signal processing methods such as mechanical fault feature extraction are effective ways of gearbox fault diagnosis, and these fault diagnosis methods often require prior knowledge of fault features as a theoretical basis. Experimental verification is one of the main methods to obtain prior knowledge of fault characteristics. However, the experimental verification of specific gearboxes often faces insurmountable problems such as high cost, unclear fault parameters, and large system interference. Therefore, simulation signals are obtained through dynamic modeling. It is a very important method to analyze the failure mechanism. The internal force of the gearbox is relatively complex, and the failure mode is changeable. The traditional dynamic model of the gearbox often studies the failure characteristics of one of the components by simplifying other components (such as bearings). This model has a certain reference for the study of the failure mechanism, but it cannot accurately reflect the actual behavior of the entire gearbox and the coupling between the components, and there is a large room for improvement.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a coupled dynamics modeling method of a gearbox excited by internal multi-source faults, so as to solve the problems in the prior art.

In order to achieve the above object, the present invention provides the following technical solution: a method for modeling the coupling dynamics of a gearbox excited by an internal multi-source fault, comprising the following steps:

S1: Calculation of time-varying stiffness, damping and dynamic friction force of gear meshing: According to the gear topography and local spalling failure parameters, the function relationship between gear meshing stiffness and driving wheel rotation angle is calculated; The parameters of gear meshing force, surface roughness and entrainment speed are calculated at each moment to obtain the dynamic friction force and meshing damping of the current gear meshing pair;

S2: Calculate the force on the inner and outer rings of each bearing in the gearbox: input the relative displacement of the inner and outer rings at the current moment, and obtain the normal deformation and tangential velocity of all contact pairs in the bearing through the quasi-static relationship between the revolution and rotation of the rolling elements; According to the bearing structural parameters and surface parameters, combined with the mixed elastohydrodynamic lubrication theory and the Hertzian contact theory, the normal force of each rolling element in the bearing considering the damping can be calculated; these normal forces can be synthesized to obtain the dynamic inner and outer rings of the bearing force;

S3: Construct the complete equation of the entire gearbox dynamics model and solve it: On the basis of the previous steps, introduce the gear meshing transmission error, drive motor, brake and gearbox housing; establish a complete gearbox dynamics differential through Newton's second law Equation system; use numerical solution method to solve the differential equation system to obtain the dynamic response of the system;

S4: Analysis of simulation signal failure characteristics: Select the most significant casing acceleration from the dynamic numerical solution of the gearbox system as the gearbox vibration simulation signal, and analyze the simulation through basic means such as time domain analysis, power spectrum and envelope spectrum analysis. The signals are analyzed to reveal the vibration behavior of the gearbox under coupled fault conditions.

Preferably, the specific steps of the S1 include:

S11: Introduce local faults of gears through changes in geometric parameters. The present invention introduces 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 , a width w _max and a length l _max ; such surface spalling will affect the effective contact when the gear meshes Section properties when calculating length L _s and stiffness;

Where x _{s_center} represents the center coordinate position of the spalling ellipse, x _{s_start} represents the starting coordinate position of the spalling ellipse, x _{s_end} represents the end coordinate position of the spalling ellipse; θ _s represents the inclination angle of the spalling ellipse; the value affected by the fault will affect Calculation of meshing stiffness, and through meshing stiffness, affects the entire dynamic system to achieve the purpose of introducing gear faults;

S12: Calculate the time-varying stiffness of meshing gears. Considering the gear teeth as a cantilever beam with variable section, the Hertzian contact stiffness k _h , bending stiffness k _b , shear stiffness k _s , axial compressive stiffness _ka and angular foundation stiffness k of a gear tooth are derived by energy method _f ; Obtain the comprehensive series stiffness of the two gear teeth in the meshing state:

Since there are more than one pair of gear teeth in contact during the gear meshing process, and there are two pairs of gear teeth 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 of the driving wheel angle:

S13: Calculate the elastohydrodynamic lubrication damping and friction coefficient of the gear meshing; first, according to the lubrication conditions and physical parameters, calculate the current lubricating oil film thickness h _c of the meshing pair:

是无量纲表面粗糙度，V是无量纲硬度参数；Among them, K _Hc is the surface micro-peak topography parameter, which is 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 radius of curvature;

is the dimensionless surface roughness, V is the dimensionless hardness parameter;

According to the oil film thickness, lubricant viscosity and contact area, the contact damping c _film of the gear contact pair can be calculated approximately:

According to the friction theory under the condition of mixed elastohydrodynamic lubrication in gear meshing, the dynamic friction coefficient can be calculated by the following formula:

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 contact pairs, respectively; S is the root-mean-square surface roughness; P _h is the Hertzian contact pressure, and b ₁ to b ₉ are constant value 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 in the gear meshing process, it is necessary to calculate the friction force on each pair of meshing gear teeth separately and then synthesize it; first, calculate the load on each pair of teeth according to the load distribution coefficient S _ri :

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

The subscript p means acting on the driving wheel, and the subscript g means acting on the driven wheel;

In general, step 1 provides the calculation method of the force generated by the gear meshing part. This part of the calculation fully describes the dynamic behavior of the gear meshing and constitutes the part of the gear meshing in the overall model.

Preferably, 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 of the bearing in series, which is equivalent to a spring damping system; therefore, it is necessary to first obtain the stiffness and damping under each contact pair; The Hertzian contact stiffness can be obtained from the formula:

where E _b , ν _b and Σρ are Young's modulus, Poisson's ratio and the sum of the raceway curvature, respectively; δ ^* dimensionless deformation coefficient; zone is generated, and the lubrication damping in the inlet zone can be calculated by the following formula:

where η ₀ is the lubricating viscosity; R _x is the effective curvature of the entrainment direction; a is the length of the major semi-axis of the contact ellipse; the point contact lubricating oil film thickness h _c can be calculated from 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 contact pair of the bearing raceway is not completely elastically lubricated, considering the influence of the surface condition on the thickness of the oil film, the correction coefficient is introduced in the calculation of the film thickness as follows:

Among them, C and r are fixed value coefficients with values of 0.87 and 1.5 respectively; h _cT is the corrected film thickness;

After obtaining the stiffness and damping of each contact pair, the equivalent series stiffness damping of the rolling elements 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 ; natural frequency of free vibration of ω contact pair;

S22: Calculate the contact force of the inner and outer rings of the bearing according to the contact geometry and local faults; use the displacement excitation of the half-sine profile to describe the local faults in the bearing raceway. The displacement excitation equation is as follows:

是第j个滚动体相对于故障位置的角度，可由下式计算：where R _r is the rolling element radius; L _defect is the local fault length; φ _l is the angle range corresponding to the fault length;

is the angle of the jth rolling element relative to the fault position, which can be calculated by the following formula:

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:

Among them, λ(δ) is the control function. When δ is a positive value, the output of this function is 1. In other cases, the output is 0, which ensures that the 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 represents the inner ring rotation angle, which is obtained from the bearing geometry; δ ^j represents the jth The deformation of each rolling element position can be calculated by the following formula:

In this formula, c ₀ represents the radial clearance.

Preferably, the S3 specifically includes:

A complete dynamic model of the gearbox is established; since the industrial gearbox contains 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, due to the The shaft length is relatively short, so the bending of the shaft and the rocking motion of the shaft are not considered; each shaft has two degrees of freedom of movement in the X and Y directions and rotational degrees of freedom; the gearbox housing is fixed to all bearing outer rings , there are translation degrees of freedom in two directions; the inner ring of the bearing is fixedly connected with 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; so far, the gearbox can be constructed For a nine-degree-of-freedom dynamic model, the system equations are as follows:

是电机的转速。F_pg是动态啮合力，可由下式计算得到：where θ _L , θ _p and θ _g are the dynamic rotation angles of the load, the driving wheel and the driven wheel, respectively; m _p , m _g and m _f represent the masses of the driving wheel, the driven wheel and the gearbox casing in turn; _IL , I _p and I _g represents the moment of inertia of the load, the driving wheel and the driven wheel in turn; T _Load is the torque applied to the load,

is the speed of the motor. F _pg is the dynamic meshing force, which can be calculated from the following equation:

where k _m and _cm 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;

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.

Preferably, the S3 specifically includes:

Analysis of the fault characteristics of the simulated signal; according to the numerical results obtained by the differential equation, the vibration response of the gearbox system in a period of time can be obtained; through the time domain analysis of the response, the change characteristics of the physical variables in the gearbox during the whole process can be known; at the same time The characteristics of the gearbox vibration in the time domain under the failure mode can be analyzed and obtained; the Fourier transform is used to convert the acceleration signal in the time domain into a signal in the frequency domain, and the power spectrum of the simulated signal can be obtained. Through the power spectrum, the gearbox in different modes can be obtained. The frequency domain response of different fault modes is analyzed; the characteristics of different fault modes on the power spectrum are summarized by analyzing the reflection of different failure modes in the frequency domain response of the gearbox; the envelope of the original simulation signal is obtained by Hilbert transform, and then the envelope The envelope spectrum of the simulated signal can be obtained by Fourier transform; the characteristic frequency components of the gearbox vibration can be obtained more clearly through the envelope spectrum, and the frequency characteristics of the envelope spectrum of different failure modes can be defined.

A computer device includes a memory, a processor, and a computer program stored on the memory and executable on the processor, the processor implementing the steps of any one of the methods when the processor executes the program.

A computer-readable storage medium having a computer program stored thereon, the program implementing the steps of any one of the methods when executed by a processor.

A processor for running a program, wherein the program executes any one of the methods when the program is running.

Compared with the prior art, the beneficial effects of the present invention are:

1. The invention firstly establishes a gearbox dynamics model that fully considers gear meshing, bearing action, and gearbox housing; there is an accurate mathematical description for local bearing failures, gear meshing geometric features, and gear local failures in the gearbox, which can be accurately obtained. The vibration response of the gearbox under the influence of multiple factors such as meshing force, meshing friction, dynamic force of the inner and outer rings of the bearing, elastohydrodynamic lubrication, and fault excitation;

2. Compared with the traditional dynamic model modeling method, the 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 The analysis method can obtain the frequency domain characteristics of the vibration of the gearbox casing under the internal multi-source excitation; compared with the traditional model, the method provided by the present invention can provide a lateral comparison method for the responses of bearings, gears and other positions under the excitation of defects , to provide a more profound mechanism analysis for gearbox fault diagnosis.

Description of drawings

The accompanying drawings are used to provide a further understanding of the present invention, and constitute a part of the specification, and are used to explain the present invention together with the embodiments of the present invention, and do not constitute a limitation to the present invention. In the attached image:

Fig. 1 is the internal part of the gearbox dynamics model of the present invention;

Fig. 2 is the external part of the gearbox dynamics model of the present invention;

Fig. 3 is the flow chart of the gearbox dynamics modeling method of the internal multi-source coupling fault excitation of the present invention;

Fig. 4 is the vibration response of the gearbox casing under the partial failure of the driven wheel and the failure of the bearing outer ring according to the present invention;

Fig. 5 is the vibration response of the gearbox casing under the partial failure of the driven wheel and the failure of the bearing inner ring according to the present invention;

Fig. 6 is the experimental verification of the fault of the inner ring of the high-speed shaft bearing of the present invention and the fault of the driven wheel;

Fig. 7 is the experimental verification of the fault of the outer ring of the high-speed shaft bearing of the present invention and the fault of the driven wheel;

Fig. 8 is the gear parameter table of the present invention;

Fig. 9 is the bearing parameter table of the present invention;

Fig. 10 is the gear box structure parameter table of the present invention;

FIG. 11 is a vibration characteristic frequency table of the gearbox dynamics model of the present invention.

Detailed ways

In order to make the purposes, 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 with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments These are some embodiments of the present invention, but not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention. Thus, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but is merely representative of selected embodiments of the invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

Referring to FIGS. 1-11 , in an embodiment of the present invention, a method for modeling coupled dynamics of a gearbox excited by an internal multi-source fault includes the following steps:

S1: Calculation of time-varying stiffness, damping and dynamic friction force of gear meshing: According to the gear topography and local spalling failure parameters, the function relationship between gear meshing stiffness and driving wheel rotation angle is calculated; The parameters of gear meshing force, surface roughness and entrainment speed are calculated at each moment to obtain the dynamic friction force and meshing damping of the current gear meshing pair;

S2: Calculate the force on the inner and outer rings of each bearing in the gearbox: input the relative displacement of the inner and outer rings at the current moment, and obtain the normal deformation and tangential velocity of all contact pairs in the bearing through the quasi-static relationship between the revolution and rotation of the rolling elements; According to the bearing structural parameters and surface parameters, combined with the mixed elastohydrodynamic lubrication theory and the Hertzian contact theory, the normal force of each rolling element in the bearing considering the damping can be calculated; these normal forces can be synthesized to obtain the dynamic inner and outer rings of the bearing force;

S3: Construct the complete equation of the entire gearbox dynamics model and solve it: On the basis of the previous steps, introduce the gear meshing transmission error, drive motor, brake and gearbox housing; establish a complete gearbox dynamics differential through Newton's second law Equation system; use numerical solution method to solve the differential equation system to obtain the dynamic response of the system;

S4: Analysis of simulation signal failure characteristics: Select the most significant casing acceleration from the dynamic numerical solution of the gearbox system as the gearbox vibration simulation signal, and analyze the simulation through basic means such as time domain analysis, power spectrum and envelope spectrum analysis. The signals are analyzed to reveal the vibration behavior of the gearbox under coupled fault conditions.

Preferably, the specific steps of the S1 include:

S11: Introduce local faults of gears through changes in geometric parameters. The present invention introduces 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 , a width w _max and a length l _max ; such surface spalling will affect the effective contact when the gear meshes Section properties when calculating length L _s and stiffness;

Where x _{s_center} represents the center coordinate position of the spalling ellipse, x _{s_start} represents the starting coordinate position of the spalling ellipse, x _{s_end} represents the end coordinate position of the spalling ellipse; θ _s represents the inclination angle of the spalling ellipse; the value affected by the fault will affect Calculation of meshing stiffness, and through meshing stiffness, affects the entire dynamic system to achieve the purpose of introducing gear faults;

S12: Calculate the time-varying stiffness of meshing gears. Considering the gear teeth as a cantilever beam with variable section, the Hertzian contact stiffness k _h , bending stiffness k _b , shear stiffness k _s , axial compressive stiffness _ka and angular foundation stiffness k of a gear tooth are derived by energy method _f ; Obtain the comprehensive series stiffness of the two gear teeth in the meshing state:

Since there are more than one pair of gear teeth in contact during the gear meshing process, and there are two pairs of gear teeth 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 of the driving wheel angle:

S13: Calculate the elastohydrodynamic lubrication damping and friction coefficient of the gear meshing; first, according to the lubrication conditions and physical parameters, calculate the current lubricating oil film thickness h _c of the meshing pair:

是无量纲表面粗糙度，V是无量纲硬度参数；Among them, K _Hc is the surface micro-peak topography parameter, which is 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 radius of curvature;

is the dimensionless surface roughness, V is the dimensionless hardness parameter;

According to the oil film thickness, lubricant viscosity and contact area, the contact damping c _film of the gear contact pair can be calculated approximately:

According to the friction theory under the condition of mixed elastohydrodynamic lubrication in gear meshing, the dynamic friction coefficient can be calculated by the following formula:

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 contact pairs, respectively; S is the root-mean-square surface roughness; P _h is the Hertzian contact pressure, and b ₁ to b ₉ are constant value 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 in the gear meshing process, it is necessary to calculate the friction force on each pair of meshing gear teeth separately and then synthesize it; first, calculate the load on each pair of teeth according to the load distribution coefficient S _ri :

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

The subscript p means acting on the driving wheel, and the subscript g means acting on the driven wheel.

In general, S1 provides the calculation method of the force 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.

Preferably, 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 of the bearing in series, which is equivalent to a spring damping system; therefore, it is necessary to first obtain the stiffness and damping under each contact pair; The Hertzian contact stiffness can be obtained from the formula:

where E _b , ν _b and Σρ are Young's modulus, Poisson's ratio and the sum of the raceway curvature, respectively; δ ^* dimensionless deformation coefficient; zone is generated, and the lubrication damping in the inlet zone can be calculated by the following formula:

where η ₀ is the lubricating viscosity; R _x is the effective curvature of the entrainment direction; a is the length of the major semi-axis of the contact ellipse; the point contact lubricating oil film thickness h _c can be calculated from 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 contact pair of the bearing raceway is not completely elastically lubricated, considering the influence of the surface condition on the thickness of the oil film, the correction coefficient is introduced in the calculation of the film thickness as follows:

Among them, C and r are fixed value coefficients with values of 0.87 and 1.5 respectively; h _cT is the corrected film thickness;

After obtaining the stiffness and damping of each contact pair, the equivalent series stiffness damping of the rolling elements 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 ; natural frequency of free vibration of ω contact pair;

S22: Calculate the contact force of the inner and outer rings of the bearing according to the contact geometry and local faults; use the displacement excitation of the half-sine profile to describe the local faults in the bearing raceway. The displacement excitation equation is as follows:

是第j个滚动体相对于故障位置的角度，可由下式计算：where R _r is the rolling element radius; L _defect is the local fault length; φ _l is the angle range corresponding to the fault length;

is the angle of the jth rolling element relative to the fault position, which can be calculated by the following formula:

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:

Among them, λ(δ) is the control function. When δ is a positive value, the output of this function is 1. In other cases, the output is 0, which ensures that the 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 represents the inner ring rotation angle, which is obtained from the bearing geometry; δ ^j represents the jth The deformation of each rolling element position can be calculated by the following formula:

In this formula, c ₀ represents the radial clearance.

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, which can accurately describe the dynamic action of the bearing in the gearbox system.

Preferably, the S3 specifically includes:

A complete dynamic model of the gearbox is established; since the industrial gearbox contains 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, due to the The shaft length is relatively short, so the bending of the shaft and the rocking motion of the shaft are not considered; each shaft has two degrees of freedom of movement in the X and Y directions and rotational degrees of freedom; the gearbox housing is fixed to all bearing outer rings , there are translation degrees of freedom in two directions; the inner ring of the bearing is fixedly connected with 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; so far, the gearbox can be constructed For a nine-degree-of-freedom dynamic model, the system equations are as follows:

是电机的转速。F_pg是动态啮合力，可由下式计算得到：where θ _L , θ _p and θ _g are the dynamic rotation angles of the load, the driving wheel and the driven wheel, respectively; m _p , m _g and m _f represent the masses of the driving wheel, the driven wheel and the gearbox casing in turn; _IL , I _p and I _g represents the moment of inertia of the load, the driving wheel and the driven wheel in turn; T _Load is the torque applied to the load,

is the speed of the motor. F _pg is the dynamic meshing force, which can be calculated from the following equation:

where k _m and _cm 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 flank spalling, respectively.

The present invention uses the Runge-Kutta algorithm to solve the dynamic differential equation system, the time step is set to 10μs, and the initial value of the equation is set as follows: x _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 rotational speed is set to 1000RPM, and the load torque is set to 16Nm.

Preferably, the S3 specifically includes:

Analysis of the fault characteristics of the simulated signal; according to the numerical results obtained by the differential equation, the vibration response of the gearbox system in a period of time can be obtained; through the time domain analysis of the response, the change characteristics of the physical variables in the gearbox during the whole process can be known; at the same time The characteristics of the gearbox vibration in the time domain under the failure mode can be analyzed and obtained; the Fourier transform is used to convert the acceleration signal in the time domain into a signal in the frequency domain, and the power spectrum of the simulated signal can be obtained. Through the power spectrum, the gearbox in different modes can be obtained. The frequency domain response of different fault modes is analyzed; the characteristics of different fault modes on the power spectrum are summarized by analyzing the reflection of different failure modes in the frequency domain response of the gearbox; the envelope of the original simulation signal is obtained by Hilbert transform, and then the envelope The envelope spectrum of the simulated signal can be obtained by Fourier transform; the characteristic frequency components of the gearbox vibration can be obtained more clearly through the envelope spectrum, and the frequency characteristics of the envelope spectrum of different failure modes can be defined.

After numerical solution and analysis, the coupled vibration response of the bearing outer ring fault and the gear driven wheel fault is shown in Figure 4. The bearing faults include two cases, namely high-speed shaft bearing faults and low-speed shaft bearing faults. Each fault condition is analyzed by three means: 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 shocks on the gearbox casing. The fault condition inside the gearbox can be judged by the shock in the time domain signal, but the specific fault mode cannot be known only from the time domain. The main frequency components in the power spectrum are the meshing frequency and its harmonic frequency, of which the maximum frequency is 4gmf, which is caused by the modulation of the natural frequency of the gearbox casing, and the natural frequency is determined by the gearbox parameters. The fault of the outer ring of the bearing arouses obvious sidebands separated by the characteristic frequency of the outer ring in the power spectrum. The high-speed shaft and low-speed shaft bearings have different sideband intervals due to different rotational speeds. These sidebands are mainly distributed around 4gmf, which indicates that the bearing characteristic frequency, like the meshing frequency, is modulated by the amplitude of the natural frequency of the gearbox housing. Similarly, the sidebands separated by the rotational speed of the driven wheel caused by the fault of the driven wheel have the same distribution characteristics in the power spectrum, indicating that these frequencies are also modulated by the natural frequency. Since the sidebands caused by gear faults are densely spaced and have low amplitudes, and have the same distribution as the bearing fault sidebands, they are easily covered by the bearing sidebands and are not easy to find. These easily covered frequency bands are marked with red dashed lines in the figure. In the envelope spectrum, the eigenfrequencies appear mainly in the form of fundamental and lower harmonics. At this time, the characteristic frequency of the outer ring of the bearing exceeds the meshing frequency 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 region of the envelope spectrum due to its low frequency and small amplitude, and is marked by a red dotted line. The characteristic frequencies of bearing faults and gear faults in the envelope spectrum and power spectrum are superimposed, and no obvious mutual modulation is found.

The situation of bearing inner ring failure and driven wheel failure is shown in Figure 5. Consistent with the fault of the outer ring, the fault of the inner ring is also considered from the two situations of the high-speed shaft bearing and the low-speed shaft bearing. Under the inner ring fault, the fault position rotates with the inner ring, and the force at the fault position will fluctuate 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 shock caused by the gear failure is the same as that of the outer ring. The frequency domain responses for inner ring fault and driven wheel fault are also shown in Figure 5. The sidebands caused by the gear fault are marked with red dashed lines, and these sidebands are the same as in the case of the bearing outer ring fault, indicating that the mode of the bearing fault does not affect the frequency domain response of the gear fault to the vibration of the gearbox housing. The eigenfrequencies caused by the faults of the inner ring of the shaft are more complicated. In addition to the sidebands spaced by the eigenfrequencies of the inner ring, the eigenfrequencies in the power spectrum and the envelope spectrum are also modulated by the rotational frequency of the bearing. 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 this invention. Consistent with the fault of the outer ring, the characteristic frequency of the fault of the inner ring of the bearing is also not modulated with the characteristic frequency of the gear fault, and they are superimposed on each other.

To further verify the correctness of the invention, a single-stage spur gear transmission gearbox is used to drive it through an AC motor. The load is applied by a magnetic powder brake mounted at the end of the output shaft. The vibration signal is acquired by sensors mounted on the gearbox casing. The partial failure of the gear is set on the driven wheel, and the partial fault of the bearing is set in the high-speed shaft bearing. In order to eliminate the noise interference of the experimental signals, the experimental signals were all denoised. The frequency band of [9216Hz, 10240Hz] is selected to filter the simulated and experimental signals. Figure 6 shows the comparison of experimental and simulation results for inner ring bearing failure and driven wheel failure. Figure 7 shows the comparison between the experimental and simulation results under the outer ring bearing fault and the driven wheel fault. The green point in the figure identifies the gear fault characteristic frequency, that is, the rotational frequency of the driven wheel, and the red point marks the bearing fault characteristic frequency and meshing frequency. It can be seen from the experimental comparison diagram that although there are some errors in the frequency amplitude, the frequency characteristics are basically the same, which shows that the experiment can prove the industrial gearbox dynamics modeling method provided by the invention for the internal multi-source coupling fault excitation. accuracy.

In order to solve the problem that the traditional dynamic model is incomplete and cannot provide a theoretical basis for the vibration of the gearbox subject to the internal multi-source fault mechanism, the present invention starts from the traditional gear meshing model, and fully considers the dynamic force of the bearing, the casing of the gearbox, the elasto-hydrodynamic force In terms of lubrication and local fault description, a new dynamic modeling method for industrial gearboxes excited by internal multi-source coupled faults is constructed. And based on the dynamic model, the vibration response of the gearbox casing under the internal multi-source coupling fault mechanism is studied. Using the classical Fourier transform and envelope spectrum analysis methods, the vibration characteristics of the gearbox under different failure modes are analyzed, and the superposition mechanism of the partial faults of bearings and gears on the gearbox casing is revealed, which is used for signal processing such as fault feature extraction. The method provides a theoretical basis. 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 dynamics modeling method of the internal multi-source coupling fault excitation of the invention has certain validity .

The invention will be described in detail below in combination with simulation signal analysis and experimental verification.

The schematic diagram of the gearbox dynamic model is shown in Figure 1 and Figure 2 below. The internal and external models interact with each other through the bearing force to form a complete gearbox. The parameters of the gearbox used in the present invention are shown in Figures 8-10:

The S4 includes:

Analysis of the fault characteristics of the simulated signal; according to the numerical results obtained by the differential equation, the vibration response of the gearbox system in a period of time can be obtained; through the time domain analysis of the response, the change characteristics of the physical variables in the gearbox during the whole process can be known; at the same time The characteristics of the gearbox vibration in the time domain under the failure mode can be analyzed and obtained; the Fourier transform is used to convert the acceleration signal in the time domain into a signal in the frequency domain, and the power spectrum of the simulated signal can be obtained. Through the power spectrum, the gearbox in different modes can be obtained. The frequency domain response of different fault modes is analyzed; the characteristics of different fault modes on the power spectrum are summarized by analyzing the reflection of different failure modes in the frequency domain response of the gearbox; the envelope of the original simulation signal is obtained by Hilbert transform, and then the envelope The envelope spectrum of the simulated signal can be obtained by Fourier transform; the characteristic frequency components of the gearbox vibration can be obtained more clearly through the envelope spectrum, and the frequency characteristics of the envelope spectrum of different failure modes can be defined;

After numerical solution and analysis, the coupled vibration response of bearing outer ring fault and gear driven wheel fault is shown in Figure 4; the bearing fault includes two cases, namely high-speed shaft bearing fault and low-speed shaft bearing fault; each fault condition They are all analyzed by three means of time domain signal, power spectrum and envelope spectrum; from the time domain signal, it can be seen that the fault of the outer ring of the bearing and the fault of the driven wheel will produce obvious impact on the gearbox casing; the time domain signal can be used for analysis. The impact in the gear box is used to judge the fault situation inside the gearbox, but the specific fault mode cannot be known only from the time domain; the main frequency components in the power spectrum are the meshing frequency and its harmonic frequency, of which the maximum frequency is 4gmf, which is It is caused by the modulation of the natural frequency of the gearbox shell, and the natural frequency is determined by the parameters of the gearbox; the fault of the outer ring of the bearing arouses obvious sidebands separated by the characteristic frequency of the outer ring in the power spectrum. , the sideband intervals are also different; these sidebands are mainly distributed around 4gmf, which indicates that the bearing characteristic frequency, like the meshing frequency, is modulated by the amplitude of the natural frequency of the gearbox casing; similarly, the driven wheel failure is caused by the driven wheel. The sidebands with the interval of rotation speed have the same distribution characteristics in the power spectrum, indicating that these frequencies are also modulated by the natural frequency; the sidebands caused by the gear fault are densely spaced and have lower amplitudes, and they have the same characteristics as the bearing fault sidebands. Therefore, it is easy to be covered by the bearing sidebands and not easy 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 frequency and low-order harmonics; At this time, the characteristic frequency of the outer ring of the bearing exceeds the meshing frequency 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 envelope spectrum due to its low frequency and small amplitude. The low-frequency area is marked by a red dotted line; the characteristic frequencies of bearing faults and gear faults in the envelope spectrum and power spectrum are superimposed, and no obvious mutual modulation phenomenon is found;

The faults of the inner ring of the bearing and the fault of the driven wheel are shown in Figure 5; the same as the fault of the outer ring, the fault of the inner ring is also considered from the two situations of the high-speed shaft bearing and the low-speed shaft bearing; under the fault of the inner ring, the fault position rotates with the inner ring, and the fault occurs. The position force will fluctuate between the maximum value and zero, so the impact of the bearing in the time domain will be smaller than that of the outer ring, but the impact caused by the bearing failure can still be found; the impact caused by the gear failure is the same as that of the outer ring; the inner ring failure The frequency domain response with the driven wheel failure is also shown in Figure 5; the sidebands caused by the gear failure are marked with red dashed lines, and these sidebands are the same as in the case of the bearing outer ring failure, indicating that the mode of the bearing failure does not affect the gears The frequency domain response of the fault to the vibration of the gearbox casing; the eigenfrequencies caused by the fault of the inner ring of the shaft are more complicated. In addition to the sidebands spaced by the eigenfrequencies of the inner ring, the eigenfrequencies in the power spectrum and the envelope spectrum are also affected by the bearing rotation frequency. The modulation phenomenon; 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 There is a modulation phenomenon with the gear fault characteristic frequency, which is superimposed on each other;

In order to further verify the correctness of the invention, a gearbox test bench is used for experimental verification; the single-stage spur gear transmission gearbox is driven by an AC motor; the load is applied by the magnetic powder brake installed at the end of the output shaft; the vibration signal is installed at the end of the output shaft. The sensor on the gearbox box is acquired; the partial fault of the gear is set on the driven wheel, and the partial fault of the bearing is set in the high-speed shaft bearing; in order to eliminate the noise interference of the experimental signal, the experimental signals are all denoised; selected [ The frequency band of 9216Hz, 10240Hz] filters the simulated signal and the experimental signal; Figure 6 shows the comparison between the experimental and simulation results of the inner ring bearing fault and the driven wheel fault; Figure 7 shows the experimental and simulated results under the outer ring bearing fault and the driven wheel fault. Comparison of simulation results; the green point in the figure identifies the gear fault characteristic frequency, that is, the rotational frequency of the driven wheel, and the red point marks the bearing fault characteristic frequency and meshing frequency; it can be seen from the experimental comparison diagram that although there are some errors in the frequency amplitude, But the frequency characteristics are basically the same, which shows that the experiment can prove the accuracy of the industrial gearbox dynamics modeling method provided by the invention for the internal multi-source coupling fault excitation;

In order to solve the problem that the traditional dynamic model is incomplete and cannot provide a theoretical basis for the vibration of the gearbox subject to the internal multi-source fault mechanism, the present invention starts from the traditional gear meshing model, and fully considers the dynamic force of the bearing, the casing of the gearbox, the elasto-hydrodynamic force In terms of lubrication and local fault description, a new dynamic modeling method for industrial gearboxes excited by internal multi-source coupled faults is constructed; and based on the dynamic model, the mechanism of gearbox casing under internal multi-source coupled faults The vibration response of the gearbox was analyzed by using the classical Fourier transform and envelope spectrum analysis methods, and the vibration characteristics of the gearbox under different failure modes were analyzed, and the superposition mechanism of the partial faults of the bearing and gear on the gearbox casing was revealed, which is the fault characteristic. Extraction and other signal processing methods provide a theoretical basis; finally, by comparing the experimental signal measured by the gearbox test bench with the simulated signal obtained in the invention, it is proved that the invention has an industrial gearbox excited by internal multi-source coupling faults The dynamic modeling method has certain validity.

Finally, it should be noted that the above descriptions are only 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 foregoing embodiments, for those skilled in the art, the The technical solutions described in the foregoing embodiments may be modified, or some technical features thereof may be equivalently replaced. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims (8)

1. a gearbox coupling dynamics modeling method excited by internal multi-source faults, is characterized in that: comprise the following steps: S1: Calculation of time-varying stiffness, damping and dynamic friction force of gear meshing: According to the gear topography and local spalling failure parameters, the function relationship between gear meshing stiffness and driving wheel rotation angle is calculated; The parameters of gear meshing force, surface roughness and entrainment speed are calculated at each moment to obtain the dynamic friction force and meshing damping of the current gear meshing pair; S2: Calculate the force on the inner and outer rings of each bearing in the gearbox: input the relative displacement of the inner and outer rings at the current moment, and obtain the normal deformation and tangential velocity of all contact pairs in the bearing through the quasi-static relationship between the revolution and rotation of the rolling elements; According to the bearing structural parameters and surface parameters, combined with the mixed elastohydrodynamic lubrication theory and the Hertzian contact theory, the normal force of each rolling element in the bearing considering the damping can be calculated; these normal forces can be synthesized to obtain the dynamic inner and outer rings of the bearing force; S3: Construct the complete equation of the entire gearbox dynamics model and solve it: On the basis of the previous steps, introduce the gear meshing transmission error, drive motor, brake and gearbox housing; establish a complete gearbox dynamics differential through Newton's second law Equation system; use numerical solution method to solve the differential equation system to obtain the dynamic response of the system; S4: Analysis of simulation signal failure characteristics: Select the most significant casing acceleration from the dynamic numerical solution of the gearbox system as the gearbox vibration simulation signal, and analyze the simulation through basic means such as time domain analysis, power spectrum and envelope spectrum analysis. The signals are analyzed to reveal the vibration behavior of the gearbox under coupled fault conditions. 2. The method for modeling the coupling dynamics of a gearbox excited by an internal multi-source fault according to claim 1, wherein the specific steps of the S1 include: S11: Introduce local faults of gears through changes in geometric parameters. The present invention introduces 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 , a width w _max and a length l _max ; such surface spalling will affect the effective contact when the gear meshes Section properties when calculating length L _s and stiffness;

Where x _{s_center} represents the center coordinate position of the spalling ellipse, x _{s_start} represents the starting coordinate position of the spalling ellipse, x _{s_end} represents the end coordinate position of the spalling ellipse; θ _s represents the inclination angle of the spalling ellipse; the value affected by the fault will affect Calculation of meshing stiffness, and through meshing stiffness, affects the entire dynamic system to achieve the purpose of introducing gear faults; S12: Calculate the time-varying stiffness of meshing gears. Considering the gear teeth as a cantilever beam with variable section, the Hertzian contact stiffness k _h , bending stiffness k _b , shear stiffness k _s , axial compressive stiffness _ka and angular foundation stiffness k of a gear tooth are derived by energy method _f ; Obtain the comprehensive series stiffness of the two gear teeth in the meshing state:

Since there are more than one pair of gear teeth in contact during the gear meshing process, and there are two pairs of gear teeth 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 of the driving wheel angle:

S13: Calculate the elastohydrodynamic lubrication damping and friction coefficient of the gear meshing; first, according to the lubrication conditions and physical parameters, calculate the current lubricating oil film thickness h _c of the meshing pair:

Among them, K _Hc is the surface micro-peak topography parameter, which is 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 radius of curvature;

is the dimensionless surface roughness, V is the dimensionless hardness parameter; According to the oil film thickness, lubricant viscosity and contact area, the contact damping c _film of the gear contact pair can be calculated approximately:

According to the friction theory under the condition of mixed elastohydrodynamic lubrication in gear meshing, the dynamic friction coefficient can be calculated by the following formula:

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 contact pairs, respectively; S is the root-mean-square surface roughness; P _h is the Hertzian contact pressure, and b ₁ to b ₉ are constant value 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 in the gear meshing process, it is necessary to calculate the friction force on each pair of meshing gear teeth separately and then synthesize it; first, calculate the load on each pair of teeth according to the load distribution coefficient S _ri :

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

The subscript p means acting on the driving wheel, and the subscript g means acting on the driven wheel. 3. A gearbox coupling dynamics modeling method excited by internal multi-source faults according to claim 2, wherein 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 of the bearing in series, which is equivalent to a spring damping system; therefore, it is necessary to first obtain the stiffness and damping under each contact pair; The Hertzian contact stiffness can be obtained from the formula:

where E _b , ν _b and Σρ are Young's modulus, Poisson's ratio and the sum of the raceway curvature, respectively; δ ^* dimensionless deformation coefficient; zone is generated, and the lubrication damping in the inlet zone can be calculated by the following formula:

where η ₀ is the lubricating viscosity; R _x is the effective curvature of the entrainment direction; a is the length of the major semi-axis of the contact ellipse; the point contact lubricating oil film thickness h _c can be calculated from 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 contact pair of the bearing raceway is not completely elastically lubricated, considering the influence of the surface condition on the thickness of the oil film, the correction coefficient is introduced in the calculation of the film thickness as follows:

Among them, C and r are fixed value coefficients with values of 0.87 and 1.5 respectively; h _cT is the corrected film thickness; After obtaining the stiffness and damping of each contact pair, the equivalent series stiffness damping of the rolling elements 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 ; natural frequency of free vibration of ω contact pair; S22: Calculate the contact force of the inner and outer rings of the bearing according to the contact geometry and local faults; use the displacement excitation of the half-sine profile to describe the local faults in the bearing raceway. The displacement excitation equation is as follows:

where R _r is the radius of the rolling element; L _defect is the local fault length; φl is the angle range corresponding to the fault length;

is the angle of the jth rolling element relative to the fault position, which can be calculated by the following formula:

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:

Among them, λ(δ) is the control function. When δ is a positive value, the output of this function is 1. In other cases, the output is 0, which ensures that the 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 represents the inner ring rotation angle, which is obtained from the bearing geometry; δ ^j represents the jth The deformation of each rolling element position can be calculated by the following formula:

In this formula, c ₀ represents the radial clearance. 4. The method for modeling the coupling dynamics of a gearbox excited by an internal multi-source fault according to claim 3, wherein the S3 specifically comprises: A complete dynamic model of the gearbox is established; since the industrial gearbox contains 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, due to the The shaft length is relatively short, so the bending of the shaft and the rocking motion of the shaft are not considered; each shaft has two degrees of freedom of movement in the X and Y directions and rotational degrees of freedom; the gearbox housing is fixed to all bearing outer rings , there are translation degrees of freedom in two directions; the inner ring of the bearing is fixedly connected with 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; so far, the gearbox can be constructed For a nine-degree-of-freedom dynamic model, the system equations are as follows:

where θ _L , θ _p and θ _g are the dynamic rotation angles of the load, the driving wheel and the driven wheel, respectively; m _p , m _g and m _f represent the masses of the driving wheel, the driven wheel and the gearbox casing in turn; _IL , I _p and I _g represents the moment of inertia of the load, the driving wheel and the driven wheel in turn; T _Load is the torque applied to the load,

is the speed of the motor. F _pg is the dynamic meshing force, which can be calculated from the following equation:

where k _m and _cm 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 flank spalling, respectively. 5. The method for modeling the coupling dynamics of a gearbox excited by an internal multi-source fault according to claim 4, wherein the S3 specifically comprises: Analysis of the fault characteristics of the simulated signal; according to the numerical results obtained by the differential equation, the vibration response of the gearbox system in a period of time can be obtained; through the time domain analysis of the response, the change characteristics of the physical variables in the gearbox during the whole process can be known; at the same time The characteristics of the gearbox vibration in the time domain under the failure mode can be analyzed and obtained; the Fourier transform is used to convert the acceleration signal in the time domain into a signal in the frequency domain, and the power spectrum of the simulated signal can be obtained. Through the power spectrum, the gearbox in different modes can be obtained. The frequency domain response of different fault modes is analyzed; the characteristics of different fault modes on the power spectrum are summarized by analyzing the reflection of different failure modes in the frequency domain response of the gearbox; the envelope of the original simulation signal is obtained by Hilbert transform, and then the envelope The envelope spectrum of the simulated signal can be obtained by Fourier transform; the characteristic frequency components of the gearbox vibration can be obtained more clearly through the envelope spectrum, and the frequency characteristics of the envelope spectrum of different failure modes can be defined. 6. A computer device comprising a memory, a processor and a computer program stored on the memory and running on the processor, wherein the processor implements any one of claims 1 to 5 when executing the program the steps of the method. 7. A computer-readable storage medium on which a computer program is stored, 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, wherein the processor is used for running a program, wherein the method of any one of claims 1 to 5 is executed when the program is running.

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