CN112052552B - Identification method of gear local fault equivalent excitation force - Google Patents
Identification method of gear local fault equivalent excitation force Download PDFInfo
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Abstract
The invention discloses a method for identifying a local fault equivalent excitation force of a gear, which comprises the following steps: establishing a transmission dynamic model of a normal gear and a fault gear; constructing a gear fault equivalent excitation dynamic model, and constructing a dynamic load identification control model according to the model; constructing a sparse convolution convex optimization model based on the L1 norm; measuring input and output corner signals of the normal gear and the fault gear to respectively obtain dynamic transmission errors of normal gear transmission and fault gear transmission, and calculating residual transmission errors of the fault gear relative to the normal gear; and solving the sparse convolution convex optimization model based on the L1 norm, identifying the equivalent excitation force of the gear fault, and comparing the identified equivalent excitation force of the gear fault with the real equivalent excitation force generated by the gear fault to realize the quantitative diagnosis of the gear fault. The method indirectly measures the equivalent exciting force of the gear fault, accurately identifies the equivalent exciting force of the gear fault, and has the advantages of simple operation and high calculation precision.
Description
Technical Field
The disclosure belongs to the field of mechanical system state monitoring, and particularly relates to a method for identifying local fault equivalent excitation force of a gear.
Background
The vibrations of the gear system include endogenous excitations from the meshing process of the gear pairs such as time-varying stiffness, transmission errors, meshing impacts. The local fault of the gear affects the vibration of a gear transmission system by changing the endogenous excitation of a gear pair, and the existing fault diagnosis method is mainly based on the fault feature extraction of a vibration signal and is difficult to qualitatively judge the severity of the fault. Because the gear fault mainly acts on the internal source excitation of the gear pair, if the change of the internal source excitation force of the gear pair caused by the fault can be accurately identified, the severity of the fault can be accurately judged.
For a long time, research in the field of gear dynamics focuses on solving and analyzing a dynamic response positive problem, and although many current researches establish calculation models of gear pair endogenous excitation such as stiffness excitation and error excitation, the models do not research the endogenous excitation identification, which is the root cause of vibration generation, from the point of anti-problem. From a mathematical point of view, local failures such as pitting, spalling and cracking due to gear failure can all be equivalent to internal dynamic loads. However, the endogenous excitation load in the drive train is difficult to measure directly with force sensors. The dynamic load is indirectly measured by using a gear shaft corner signal which is convenient to measure through the reverse inversion idea, and the measurement is called load identification. Based on the idea of load identification, the sparsity of equivalent excitation caused by the local gear type fault in the time domain is utilized to construct a deconvolution model based on an L1 norm, the equivalent excitation force caused by the local gear type fault is identified through the residual transmission error of the gear convenient to measure, and the gear fault is represented in the gear transmission dynamic model through the form of the equivalent excitation force, so that the severity of the fault can be judged, and the quantitative diagnosis of the fault is realized.
Disclosure of Invention
Aiming at the defects in the prior art, the purpose of the present disclosure is to provide a method for identifying the equivalent excitation force of the local fault of the gear, which adopts a sparse dynamic load identification method to identify the equivalent excitation force of the local fault of the gear, so as to realize the quantitative diagnosis of the local fault of the gear.
In order to achieve the above object, the present disclosure provides the following technical solutions:
a method for identifying local fault equivalent excitation force of a gear comprises the following steps:
s100: establishing a normal gear transmission dynamic model and a fault gear transmission dynamic model based on gear dynamic transmission errors;
s200: constructing a gear fault equivalent excitation dynamic model based on the residual transmission error of the fault gear relative to the normal gear according to the normal gear transmission dynamic model and the fault gear transmission dynamic model, and constructing a dynamic load identification control model according to the gear fault equivalent excitation dynamic model;
s300: discretizing the dynamic load identification control model to obtain a discretized dynamic load identification control model, and establishing a sparse convolution convex optimization model based on an L1 norm based on the discretized dynamic load identification control model;
s400: measuring input and output corner signals of the normal gear and the fault gear to respectively obtain a dynamic transmission error of normal gear transmission and a dynamic transmission error of fault gear transmission, and calculating a difference value between the dynamic transmission error of fault gear transmission and the dynamic transmission error of normal gear transmission to obtain a residual transmission error of the fault gear relative to the normal gear;
s500: and solving the sparse convolution convex optimization model based on the L1 norm according to the residual transfer error of the fault gear relative to the normal gear, identifying the gear fault equivalent excitation force, and establishing an excitation force error minimization function by comparing the identified gear fault equivalent excitation force with the real equivalent excitation force generated by the gear fault to realize the quantitative diagnosis of the gear fault.
Preferably, the normal gear drive dynamics model is represented as:
the faulty gear drive dynamics model is represented as:
and is
Wherein, X DTE 、
Respectively representing the dynamic transmission errors of a normal gear transmission and a fault gear transmission,
respectively representing the speeds of the normal gear transmission and the fault gear transmission dynamic transmission errors,
acceleration, I, representing the dynamic transmission error of a normal gear transmission and a faulty gear transmission, respectively 1 、I 2 Representing the moment of inertia, R, of the driving and driven wheels, respectively 1 、R 2 Representing the base radius of the driving wheel and the driven wheel, M representing the equivalent mass of the gear, T 1 、T 2 Respectively representing the input torque of a driving wheel and the output torque of a driven wheel, F representing the equivalent load of the input torque of the driving wheel and the output torque of the driven wheel, c representing the gear mesh damping, k (t) representing the time-varying mesh stiffness of a normal gear, k f Representing a fault-induced change in the time-varying mesh stiffness of the gear, k 0 Representing the average gear mesh stiffness, e (t),
Respectively, the displacement and speed of the gear static transmission error, b the backlash, f (X) DTE )、
Representing the backlash piecewise function for a normal gear drive and a faulty gear drive, respectively.
Preferably, the gear fault equivalent excitation dynamic model is expressed as:
wherein, X RTE 、
Respectively, the displacement, the speed and the acceleration of the residual transmission error of the fault gear relative to the normal gear, wherein deltaF (beta, t) represents the equivalent exciting force of the gear fault, beta represents the severity of the gear fault, and t represents the time.
Preferably, the dynamic load identification control model is represented as:
and is
Wherein y (t) represents the residual transfer error X RTE H (t) represents the unit impulse response function of the gear fault equivalent excitation dynamic model, k 0 Representing the average meshing stiffness of the gear, m representing the equivalent mass of the gear, omega n Indicating the natural frequency of the system without damping,
representing the relative damping coefficient of the system, ω d Indicating the system has a damping natural frequency, t represents time, tau represents an integral variable, f (t) represents a gearThe fault equivalent excitation force Δ F (β, t).
Preferably, the discrete dynamic load identification control model is represented as:
y＝Hf
the sparse deconvolution convex optimization model based on the L1 norm is expressed as:
the lowest objective function:
wherein | · | purple sweet 2 L2 norm representing vector, | | · | | non-calculation 1 And the L1 norm of the vector is represented, H represents a transfer function matrix obtained through dispersion, f represents a gear fault equivalent excitation force vector to be identified, y represents a residual transfer error vector, and lambda represents a regularization parameter.
Preferably, the dynamic transmission error of the normal gear transmission is expressed as:
X DTE ＝R 1 θ 1 -R 2 θ 2
the dynamic transmission error of the faulty gear transmission is expressed as:
the residual transmission error of the failed gear relative to the normal gear is represented as:
wherein, theta 1 、θ 2 Indicating input and output rotation angle signals, theta, of the normal gear shaft 1f 、θ 2f Indicating the input and output rotational angle signals of the failed gear shaft.
Preferably, solving the sparse solution convolution convex optimization model based on the L1 norm comprises the following steps:
s501: converting the sparse deconvolution optimization model into a quadratic convex optimization problem containing equality constraints, and expressing the quadratic convex optimization problem as follows:
minimizing the objective function:
the constraint function is: subject to | f i |≤u i ，i＝1，...，n
Wherein, except for the optimization variable f = (f) 1 ，…，f n )∈R n In addition, a new variable u = (u) is introduced 1 ，…，u n )∈R n As barrier constraints, R represents the real number domain, n represents the number of variables, and the above logarithmic barrier function is defined as:
wherein f is i Representing the ith element in the fault equivalent excitation force vector; u. u i Representing the ith element in the obstacle constraint vector;
s502: the problem of finding the central path associated with minimizing the objective function is:
minimization function:
wherein, t b E (0, ∞) is barrier parameter;
s503: setting the search direction [ Delta f ] of the center route T ，Δu T ] T And updating the current solution:
f new ＝f old +sΔf
u new ＝u old +sΔu
wherein s represents the iteration step of the interior point method, f old 、u old Representing the value before iteration, f new 、u new Representing the iterated values, and representing the search directions of f and u by delta f and delta u;
s504: constructing a dual gap objective function
And Lagrange dual function G (v):
the maximization function:
the constraint function is: subject to (H) T v) i ≤λ
Wherein the dual feasible variable v =2 (Hf-y), v T 、H T Respectively representing transpositions of v and H, wherein i represents the ith variable;
s505: the ratio of the dual gap objective function and the dual function is taken as an iteration termination criterion:
wherein the tolerance epsilon represents the acceptable error magnitude;
if the value f after iteration new If the above formula iteration termination criterion is met, terminating the iteration process to obtain a sparse deconvolution solution f; otherwise, the iterative process returns to step S501 to continue the iterative computation until the above expression is satisfied.
Preferably, the excitation force error minimization function is expressed as:
minimization function:
compared with the prior art, the beneficial effect that this disclosure brought does: compared with the traditional method for extracting fault characteristics in vibration signals to diagnose gear faults, which can only realize qualitative diagnosis, the method can realize quantitative diagnosis of the gear faults by identifying the equivalent exciting force caused by local faults of the gear and comparing the identified equivalent exciting force of the gear faults with the real equivalent exciting force generated by the gear faults.
Drawings
FIG. 1 is a flow chart of a method for identifying a local fault equivalent excitation force of a gear according to an embodiment of the present disclosure;
FIG. 2 is a simulated schematic view of a spur gear crack fault according to another embodiment of the present disclosure;
FIG. 3 is a schematic diagram of a parallel axis gear dynamics model provided by another embodiment of the present disclosure;
FIG. 4 is a time varying mesh stiffness of a crack failure gear provided by another embodiment of the present disclosure;
5 (a) -5 (c) are dynamic transfer errors and residual transfer errors (no noise addition) for normal and crack failure gears provided by another embodiment of the present disclosure, where 5 (a) is the normal gear dynamic transfer error, 5 (b) is the failed gear dynamic transfer error, and 5 (c) is the residual transfer error;
6 (a) -6 (c) are dynamic transfer errors and residual transfer errors (with noise added) for normal and crack failure gears provided by another embodiment of the present disclosure, where 6 (a) is normal gear dynamic transfer error, 6 (b) is failed gear dynamic transfer error, and 6 (c) is residual transfer error;
fig. 7 (a) and 7 (b) are identification results (no noise added in transmission error) of equivalent excitation force caused by gear crack failure provided by another embodiment of the present disclosure, where 7 (a) is the failed equivalent excitation force and 7 (b) is an enlarged view of the equivalent excitation force;
fig. 8 (a) and 8 (b) are identification results (with noise added in transmission error) of equivalent excitation force caused by gear crack failure provided by another embodiment of the present disclosure, where 8 (a) is the failed equivalent excitation force and 8 (b) is an enlarged view of the equivalent excitation force.
Detailed Description
Specific embodiments of the present disclosure will be described in detail below with reference to fig. 1 to 8 (b). While specific embodiments of the disclosure are shown in the drawings, it should be understood that the disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. As one skilled in the art will appreciate, various names may be used to refer to a component. The description and claims do not intend to distinguish between components that differ in noun but not in function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description which follows is a preferred embodiment of the invention, but is made for the purpose of illustrating the general principles of the invention and not for the purpose of limiting the scope of the invention. The scope of the present disclosure is to be determined by the terms of the appended claims.
For the purpose of facilitating an understanding of the embodiments of the present disclosure, the following detailed description is to be construed in conjunction with the accompanying drawings, and the various drawings are not intended to limit the embodiments of the present disclosure.
In one embodiment, as shown in fig. 1, a method for identifying a local failure equivalent excitation force of a gear includes the following steps:
s100: establishing a normal gear transmission dynamic model and a fault gear transmission dynamic model based on gear dynamic transmission errors;
in the step, the gear dynamic transmission error represents the difference between the ideal position and the real position of gear transmission, so that a normal gear transmission dynamic model and a fault gear transmission dynamic model are established by adopting a centralized parameter method, taking fig. 2 as an example, fig. 2 shows spur gear tooth root cracks, and the influence of the tooth root cracks calculated by adopting a potential energy method on the time-varying rigidity of the gear is shown in fig. 4, and the tooth root cracks can cause the obvious reduction of the meshing rigidity of the gear. Gear dynamics model as shown in fig. 3, the influence of the spur Gear tooth root crack shown in fig. 2 on the meshing stiffness can be introduced into the model shown in fig. 3, gear1 and Gear2 respectively represent a driving wheel and a driven wheel, and θ 1 、θ 2 Respectively representing the rotation angles, T, of the driving and driven wheels 1 、T 2 Representing input and output torques, R, respectively 1 、R 2 Respectively representing the base radii of the driving and driven wheels, I 1 、I 2 Respectively representing driving and drivenThe moment of inertia of the wheel, c represents gear mesh damping, k (t) represents gear mesh stiffness, b represents backlash, and the basic parameters of the parallel shaft gear transmission are shown in the table 1 as an example:
TABLE 1 basic parameters of a gear transmission
| Item | Driving wheel | Driven wheel |
| Number of teeth | 55 | 75 |
| Modulus (mm) | 2 | 2 |
| Angle of pressure (°) | 20 | 20 |
| Tooth width (mm) | 20 | 20 |
| Young's modulus (Pa) | 2.07E11 | 2.07E11 |
| Poisson ratio | 0.3 | 0.3 |
| Rotating speed (Hz) | 20 | 14.67 |
| Input/output torque (Nm) | 4.38 | 5.37 |
| Backlash (μm) | 40 | 40 |
| Crack size (mm) | - | 2 (45 degree direction) |
The normal gear drive dynamics model is represented as:
the faulty gear drive dynamics model is represented as:
and is provided with
Wherein, X DTE 、
Respectively representing the dynamic transmission errors of the normal gear transmission and the fault gear transmission,
respectively representing the speed of the dynamic transmission error of the normal gear transmission and the fault gear transmission,
acceleration, I, representing the dynamic transmission error of a normal gear drive and a faulty gear drive, respectively 1 、I 2 Representing the moment of inertia, R, of the driving and driven wheels, respectively 1 、R 2 Representing the base radius of the driving wheel and the driven wheel, M representing the equivalent mass of the gear, T 1 、T 2 Respectively representing driving wheel input torque and driven wheel output torque, F representing equivalent load of driving wheel input torque and driven wheel output torque, c representing gear mesh damping, k (t) representing normal gear time-varying mesh rigidity, k f Representing a fault-induced change in the time-varying mesh stiffness of the gear, k 0 Representing the average gear mesh stiffness, e (t),
Respectively, displacement and speed of gear static transmission error, b represents backlash, and f (X) DTE )、
Representing the backlash piecewise function for a normal gear drive and a faulty gear drive, respectively.
S200: constructing a gear fault equivalent excitation dynamic model based on the residual transmission error of the fault gear relative to the normal gear according to the normal gear transmission dynamic model and the fault gear transmission dynamic model, and constructing a dynamic load identification control model according to the gear fault equivalent excitation dynamic model;
in this step, the gear fault equivalent excitation dynamic model is expressed as:
wherein X RTE 、
Respectively, the displacement, the speed and the acceleration of the residual transmission error of the fault gear relative to the normal gear, wherein deltaF (beta, t) represents the equivalent exciting force of the gear fault, beta represents the severity of the gear fault, and t represents the time.
According to the gear fault equivalent excitation dynamic model, a unit impulse response function is obtained:
and is provided with
Then
The dynamic load identification control model is expressed as:
wherein y (t) represents the residual transfer error X RTE H (t) represents the unit impulse response function of the gear fault equivalent excitation dynamic model, k 0 Representing the average meshing stiffness of the gear, m representing the equivalent mass of the gear, omega n Indicating the natural frequency of the system without damping,
representing the relative damping coefficient, ω, of the system d The system is shown to have a damping natural frequency, t represents time, tau represents an integral variable, and F (t) represents a gear fault equivalent exciting force delta F (beta, t).
S300: dispersing the load identification control model to obtain a dispersed dynamic load identification control model, and establishing a sparse convolution convex optimization model based on an L1 norm based on the dispersed dynamic load identification control model;
in this step, the dynamic load identification control model is discretized by adopting a trapezoidal rule, specifically:
n is the data length of the measured response, and is written in a matrix-vector compact form as follows:
y＝Hf
because the gear local fault equivalent excitation has sparsity in a time domain, a sparse convolution convex optimization model based on an L1 norm is constructed and expressed as follows:
minimizing the objective function:
wherein | · | purple sweet 2 Represents the L2 norm of the vector, | | · | | non-woven phosphor 1 L1 norm of the vector is represented, H represents a transfer function matrix obtained through dispersion, f represents an equivalent excitation force vector of the gear fault to be identified, y represents a residual transfer error vector, and lambda representsA regularization parameter.
S400: measuring input and output corner signals of the normal gear and the fault gear to respectively obtain a dynamic transmission error of normal gear transmission and a dynamic transmission error of fault gear transmission, and calculating a difference value between the dynamic transmission error of fault gear transmission and the dynamic transmission error of normal gear transmission to obtain a residual transmission error of the fault gear relative to the normal gear;
in this step, the dynamic transmission error of the normal gear transmission is expressed as:
X DTE ＝R 1 θ 1 -R 2 θ 2
the dynamic transmission error of the faulty gear transmission is expressed as:
the residual transmission error of the failed gear relative to the normal gear is represented as:
wherein, theta 1 、θ 2 Indicating input and output rotation angle signals of normal gear shaft and theta 1f 、θ 2f Indicating the input and output rotational angle signals of the failed gear shaft.
The obtained dynamic transmission errors of the normal gear transmission and the fault gear transmission are shown in fig. 5 (a) and fig. 5 (b), and the dynamic transmission errors are represented as the characteristic of periodic variation in a time domain diagram; the residual transmission error of the failed gear transmission relative to the normal gear transmission is shown in fig. 5 (c), and the failure can cause the residual transmission error to have an obvious peak value and has a sparse characteristic in a time domain; meanwhile, in order to simulate the noise which may occur in the signal acquisition process, the noise with the signal-to-noise ratio of 19dB is added into the dynamic transmission error of the normal gear transmission and the fault gear transmission. The obtained dynamic transmission errors of the normal gear transmission and the fault gear transmission containing noise are shown in fig. 6 (a) and fig. 6 (b), the residual transmission error of the fault gear transmission relative to the normal gear transmission is shown in fig. 6 (c), and obvious noise components appear in the residual transmission error;
s500: solving the sparse solution convolution convex optimization model based on the L1 norm according to the residual transfer error of the fault gear relative to the normal gear, identifying the gear fault equivalent excitation force, establishing an excitation force error minimization function by comparing the identified gear fault equivalent excitation force with the real equivalent excitation force generated by the gear fault, and realizing the quantitative diagnosis of the gear fault.
In another embodiment, the step S500 includes the steps of:
s501: converting the sparse deconvolution optimization model into a quadratic convex optimization problem containing equality constraints, and expressing the quadratic convex optimization problem as follows:
minimizing the objective function:
constraint function: subject to | f i |≤u i ，i＝1，...，n
Wherein, except for the optimization variable f = (f) 1 ，…，f n )∈R n In addition, a new variable u = (u) is introduced 1 ，…，u n )∈R n As barrier constraints, R represents the real number domain, n represents the number of variables, and the above logarithmic barrier function is defined as:
wherein, f i Representing the ith element in the fault equivalent excitation force vector; u. of i Representing the ith element in the obstacle constraint vector;
s502: the central path problem associated with minimizing the objective function is derived:
the minimization function:
wherein, t b E (0, ∞) is barrier parameter;
s503: setting the search direction [ Delta f ] of the center path T ，Δu T ] T And updating the current solution:
f new ＝f old +sΔf
u new ＝u old +sΔu
wherein s represents the iteration step of the interior point method, f old 、u old Representing the value before iteration, f new 、u new Representing the iterated values, and representing the search directions of f and u by delta f and delta u;
s504: constructing a dual gap objective function
And Lagrange dual function G (v):
the maximization function:
constraint function: subject to (H) T v) i ≤λ
Wherein the dual feasible variable v =2 (Hf-y), v T 、H T Respectively representing transpositions of v and H, wherein i represents the ith variable;
s505: taking the ratio of the dual gap objective function and the dual function as an iteration termination criterion:
wherein the tolerance epsilon represents the acceptable error magnitude;
if the value f after iteration new If the above formula iteration termination criterion is met, terminating the iteration process to obtain a sparse deconvolution solution f; otherwise, the iterative process returns to step S501 to continue the iterative computation until the above expression is satisfied.
In another embodiment, in step S500, the excitation force error minimization function is expressed as:
the minimization function:
in this embodiment, since the gear fault is expressed in the gear transmission dynamic model in the form of the equivalent excitation force, quantitative diagnosis of the fault can be achieved by comparing the identified gear fault equivalent excitation force with the real equivalent excitation force generated by the gear fault and by solving the β value in the above minimization function, that is, the severity of the gear fault.
Fig. 7 (a), 7 (b), 8 (a), 8 (b) show the true equivalent excitation force Δ F (β, t) due to a gear failure compared to the identified failure equivalent excitation force F. Fig. 7 (a) and 7 (b) show the residual transfer error signal input as a noise-free signal, and the relative error obtained using the L1-norm sparse deconvolution model is 0.15%, fig. 8 (a) and 8 (b) show the residual transfer error signal input as a noise signal, and the relative error obtained using the L1-norm sparse deconvolution model is 0.38%, as shown in table 2.
TABLE 2 comparison of the recognition results of the equivalent excitation force of gear failure under different noise intensities with the theoretical values
| Signal-to-noise ratio (dB) | Relative error (%) |
| Noiseless | 0.15 |
| 19 | 0.38 |
As can be seen from the table 2, the sparse deconvolution model based on the L1 norm has good anti-noise performance, and can identify the equivalent excitation force caused by the gear fault with high precision and stability.
The gear fault is expressed in a gear transmission dynamic model in an equivalent exciting force mode, and meanwhile, the size of the tooth root crack fault can be verified by comparing the exciting force F caused by the fault and the real exciting force delta F (beta, t) caused by the fault, which are obtained by solving through a sparse dynamic load recognition method. Taking the residual transmission error and the fault excitation force under 19dB noise as an example, since the true excitation force of the gear fault cannot be explicitly represented by β, the relative error of the excitation force error minimization function value at different fault degrees is calculated by an enumeration method, as shown in table 3. When the crack of the tooth root is 2mm, the relative error is minimum, the depth of the crack of the tooth root can be judged to be about 2mm, and the depth is consistent with the real crack depth of the gear, namely 2mm, so that the quantitative diagnosis of the gear fault is realized.
TABLE 3 comparison of relative errors for the values of the excitation force error minimization functions at different crack depths
| Crack depth beta (mm) | Relative error (%) |
| 1.7 | 0.4170 |
| 1.8 | 0.4160 |
| 1.9 | 0.4155 |
| 2.0 | 0.4154 |
| 2.08 | 0.4156 |
The foregoing describes the general principles of the present application in conjunction with specific embodiments, however, it is noted that the advantages, effects, etc. mentioned in the present application are merely examples and are not limiting, and they should not be considered essential to the various embodiments of the present application. Furthermore, the foregoing disclosure of specific details is for the purpose of illustration and description and is not intended to be limiting, since the foregoing disclosure is not intended to be exhaustive or to limit the disclosure to the precise details disclosed.
The foregoing description has been presented for purposes of illustration and description. Furthermore, the description is not intended to limit embodiments of the application to the form disclosed herein. While a number of example aspects and embodiments have been discussed above, those of skill in the art will recognize certain variations, modifications, alterations, additions and sub-combinations thereof.
Claims (8)
1. A method for identifying a local fault equivalent excitation force of a gear comprises the following steps:
s100: establishing a normal gear transmission dynamic model and a fault gear transmission dynamic model based on gear dynamic transmission errors;
s200: constructing a gear fault equivalent excitation dynamic model based on the residual transmission error of the fault gear relative to the normal gear according to the normal gear transmission dynamic model and the fault gear transmission dynamic model, and constructing a dynamic load identification control model according to the gear fault equivalent excitation dynamic model;
s300: discretizing the dynamic load identification control model to obtain a discretized dynamic load identification control model, and establishing a sparse convolution convex optimization model based on an L1 norm based on the discretized dynamic load identification control model;
s400: measuring input and output corner signals of the normal gear and the fault gear to respectively obtain a dynamic transmission error of normal gear transmission and a dynamic transmission error of fault gear transmission, and calculating a difference value between the dynamic transmission error of fault gear transmission and the dynamic transmission error of normal gear transmission to obtain a residual transmission error of the fault gear relative to the normal gear;
s500: and solving the sparse convolution convex optimization model based on the L1 norm according to the residual transfer error of the fault gear relative to the normal gear, identifying the gear fault equivalent excitation force, and establishing an excitation force error minimization function by comparing the identified gear fault equivalent excitation force with the real equivalent excitation force generated by the gear fault to realize the quantitative diagnosis of the gear fault.
2. The method of claim 1, wherein preferably the normal gear drive dynamics model is represented as:
the faulty gear drive dynamics model is represented as:
and is
Wherein, X DTE 、
Respectively representing the dynamic transmission errors of a normal gear transmission and a fault gear transmission,
respectively representing the speeds of the normal gear transmission and the fault gear transmission dynamic transmission errors,
acceleration, I, representing the dynamic transmission error of a normal gear transmission and a faulty gear transmission, respectively 1 、I 2 Representing the moment of inertia, R, of the driving and driven wheels, respectively 1 、R 2 Representing the base radius of the driving wheel and the driven wheel, M representing the equivalent mass of the gear, T 1 、T 2 Respectively representing the input torque of a driving wheel and the output torque of a driven wheel, F representing the equivalent load of the input torque of the driving wheel and the output torque of the driven wheel, c representing the gear mesh damping, k (t) representing the time-varying mesh stiffness of a normal gear, k f Representing a fault-induced change in the time-varying mesh stiffness of the gear, k 0 Representing the average gear mesh stiffness, e (t),
Respectively, displacement and speed of gear static transmission error, b represents backlash, and f (X) DTE )、
Representing the backlash piecewise function for a normal gear drive and a faulty gear drive, respectively.
3. The method of claim 1, wherein the gear fault equivalent excitation kinetic model is represented as:
wherein X RTE 、
Respectively, the displacement, the speed and the acceleration of the residual transmission error of the fault gear relative to the normal gear, wherein deltaF (beta, t) represents the equivalent exciting force of the gear fault, beta represents the severity of the gear fault, and t represents the time.
4. The method of claim 1, wherein the dynamic load identification control model is represented as:
and is provided with
Wherein y (t) represents the residual transfer error X RTE H (t) represents the unit impulse response function of the gear fault equivalent excitation dynamic model，k 0 Represents the average meshing stiffness of the gear, m represents the equivalent mass of the gear, omega n Indicating that the system has no damping natural frequency,
representing the relative damping coefficient of the system, ω d The system is shown to have a damping natural frequency, t is time, tau is an integral variable, and F (t) is gear fault equivalent exciting force delta F (beta, t).
5. The method of claim 1, wherein the discrete dynamic load identification control model is represented as:
y＝Hf
the sparse deconvolution convex optimization model based on the L1 norm is expressed as follows:
minimizing the objective function:
wherein | · | purple sweet 2 Represents the L2 norm of the vector, | | · | | non-woven phosphor 1 And the L1 norm of the vector is represented, H represents a transfer function matrix obtained through dispersion, f represents a gear fault equivalent excitation force vector to be identified, y represents a residual transfer error vector, and lambda represents a regularization parameter.
6. The method of claim 1, wherein the dynamic transmission error of the normal gear drive is expressed as:
X DTE ＝R 1 θ 1 -R 2 θ 2
the dynamic transmission error of the faulty gear transmission is expressed as:
the residual transmission error of the faulty gear with respect to the normal gear is expressed as:
wherein, theta 1 、θ 2 Indicating input and output rotation angle signals, theta, of the normal gear shaft 1f 、θ 2f Indicating the input and output rotational angle signals of the failed gear shaft.
7. The method of claim 1, wherein solving the L1 norm based sparse deconvolution convex optimization model comprises the steps of:
s501: converting the sparse deconvolution optimization model into a quadratic convex optimization problem containing equality constraints, and expressing the quadratic convex optimization problem as follows:
minimizing the objective function:
the constraint function is: subject to | f i |≤u i ，i＝1，...，n
Wherein, except for the optimization variable f = (f) 1 ，…，f n )∈R n In addition, a new variable u = (u) is introduced 1 ，…，u n )∈R n As barrier constraints, R represents the real number domain, n represents the number of variables, and the above logarithmic barrier function is defined as:
wherein f is i Representing the ith element in the fault equivalent excitation force vector; u. of i Representing the ith element in the obstacle constraint vector;
s502: the central path problem associated with minimizing the objective function is derived:
minimization function:
wherein, t b ∈(0，Infinity) is a barrier parameter;
s503: setting the search direction [ Delta f ] of the center path T ，Δu T ] T And updating the current solution:
f new ＝f o1d +sΔf
u new ＝u old +sΔu
wherein s represents the iteration step of the interior point method, f old 、u old Representing the value before iteration, f new 、u new Representing the iterated values, and representing the search directions of f and u by delta f and delta u;
s504: constructing a dual gap objective function
And Lagrange dual function G (v):
the maximization function:
the constraint function is: subject to (H) T v) i ≤λ
Wherein the dual feasible variable v =2 (Hr-y), v T 、H T Respectively representing transpose of v and H, wherein i represents the ith variable;
s505: the ratio of the dual gap objective function and the dual function is taken as an iteration termination criterion:
wherein the tolerance epsilon represents the acceptable error magnitude;
if the value f after iteration new If the above formula iteration termination criterion is met, terminating the iteration process to obtain a sparse deconvolution solution f; otherwise, the iterative process returns to step S501 to continue the iterative computation until the above expression is satisfied.
8. The method of claim 1, wherein the excitation force error minimization function is expressed as:
minimization function:
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