CN112052552A - Method for identifying local fault equivalent excitation force of gear - Google Patents

Method for identifying local fault equivalent excitation force of gear Download PDF

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CN112052552A
CN112052552A CN202010672208.3A CN202010672208A CN112052552A CN 112052552 A CN112052552 A CN 112052552A CN 202010672208 A CN202010672208 A CN 202010672208A CN 112052552 A CN112052552 A CN 112052552A
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gear
fault
transmission
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CN112052552B (en
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陈雪峰
沈智宪
乔百杰
罗巍
杨志勃
曹宏瑞
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Xian Jiaotong University
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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

Method for identifying local fault equivalent excitation force of gear
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 intrinsic excitation such as rigidity excitation and error excitation, the models do not research the root cause of vibration generation, namely intrinsic excitation identification, from the perspective of an inverse 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, a deconvolution model based on an L1 norm is constructed by utilizing the sparsity of equivalent excitation caused by the local gear type fault in a time domain, 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 expressed in a 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 purpose, 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 residual transmission errors of a fault gear relative to a 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: 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.
Preferably, the normal gear drive dynamics model is represented as:
Figure BDA0002581680430000031
the faulty gear drive dynamics model is represented as:
Figure BDA0002581680430000032
and is
Figure BDA0002581680430000033
Figure BDA0002581680430000034
Figure BDA0002581680430000035
Figure BDA0002581680430000036
Wherein, XDTE、
Figure BDA0002581680430000039
Respectively representing the dynamic transmission errors of the normal gear transmission and the fault gear transmission,
Figure BDA0002581680430000037
respectively representing the speed of the dynamic transmission error of the normal gear transmission and the fault gear transmission,
Figure BDA0002581680430000038
acceleration, I, representing the dynamic transmission error of a normal gear transmission and a faulty gear transmission, respectively1、I2Representing the moment of inertia, R, of the driving and driven wheels, respectively1、R2Representing the base radii of the driving and driven wheels, M representing the gear equivalentMass, T1、T2Respectively 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, kfRepresenting a fault-induced change in the time-varying mesh stiffness of the gear, k0Representing the average meshing stiffness of the gears, e (t),
Figure BDA0002581680430000041
Respectively, displacement and speed of gear static transmission error, b represents backlash, and f (X)DTE)、
Figure BDA0002581680430000042
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:
Figure BDA0002581680430000043
wherein, XRTE、
Figure BDA0002581680430000044
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:
Figure BDA0002581680430000045
and is
Figure BDA0002581680430000046
Figure BDA0002581680430000047
Figure BDA0002581680430000048
Figure BDA0002581680430000049
Wherein y (t) represents the residual transfer error XRTEH (t) a unit impulse response function, k, representing a gear fault equivalent excitation kinetic model0Representing the average meshing stiffness of the gear, m representing the equivalent mass of the gear, omeganIndicating the natural frequency of the system without damping,
Figure BDA0002581680430000051
representing the relative damping coefficient, ω, of the systemdThe damping natural frequency of the system is shown, t represents time, tau represents an integral variable, and F (t) represents the equivalent exciting force delta F (beta, t) of the gear fault.
Preferably, the discrete dynamic load identification control model is represented as:
y＝Hf
the sparse solution convolution convex optimization model based on the L1 norm is expressed as:
the lowest objective function:
Figure BDA0002581680430000052
wherein | · | purple sweet2L2 norm representing vector, | · | | | non-volatile memory1The 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:
XDTE＝R1θ1-R2θ2
the dynamic transmission error of the faulty gear transmission is expressed as:
Figure BDA0002581680430000053
the residual transmission error of the failed gear relative to the normal gear is represented as:
Figure BDA0002581680430000054
wherein, theta1、θ2Indicating input and output rotation angle signals, theta, of the normal gear shaft1f、θ2fIndicating 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:
Figure BDA0002581680430000061
constraint function: subject to | fi|≤ui，i＝1，...，n
Wherein, except for the optimization variable f ═ f (f)1，…，fn)∈RnIn addition, a new variable u ═ is introduced (u)1，…，un)∈RnAs barrier constraints, R represents the real number domain, n represents the number of variables, and the above logarithmic barrier function is defined as:
Figure BDA0002581680430000062
wherein f isiRepresenting the ith element in the fault equivalent excitation force vector; u. ofiRepresenting the ith element in the obstacle constraint vector;
s502: the central path problem associated with minimizing the objective function is derived:
minimization function:
Figure BDA0002581680430000063
wherein, tbE (0, ∞) is barrier parameter;
s503: setting the search direction [ Delta f ] of the center routeT，ΔuT]TAnd updating the current solution:
fnew＝fold+sΔf
unew＝uold+sΔu
wherein s represents the iteration step of the interior point method, fold、uoldRepresenting the value before iteration, fnew、unewRepresenting 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
Figure BDA0002581680430000064
And Lagrange dual function g (v):
the maximization function:
Figure BDA0002581680430000065
constraint function: subject to (H)Tv)i≤λ
Wherein, the dual feasible variable v is 2(Hf-y), vT、HTRespectively 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:
Figure BDA0002581680430000071
wherein the tolerance represents an acceptable error magnitude;
if the value f after iterationnewSatisfy the above formula iteration termination criterionThen, terminating the iterative 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:
Figure BDA0002581680430000072
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.
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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 failed gears provided by another embodiment of the present disclosure, wherein 5(a) is normal gear dynamic transfer error, 5(b) is failed gear dynamic transfer error, and 5(c) is 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. This specification and claims do not intend to distinguish between components that differ in name but not 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.
To facilitate an understanding of the embodiments of the present disclosure, the following detailed description is to be considered in conjunction with the accompanying drawings, and the drawings are not to be construed as limiting 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 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;
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 θ1、θ2Respectively representing the rotation angles, T, of the driving and driven wheels1、T2Representing input and output torques, R, respectively1、R2Respectively representing the base radii of the driving and driven wheels, I1、I2The moment of inertia of a driving wheel and a driven wheel is respectively represented, c represents gear meshing damping, k (t) represents gear meshing rigidity, b represents tooth side clearance, and the basic parameters of the parallel shaft gear transmission are shown in a table 1:
TABLE 1 basic parameters of 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:
Figure BDA0002581680430000101
the faulty gear drive dynamics model is represented as:
Figure BDA0002581680430000102
and is
Figure BDA0002581680430000103
Figure BDA0002581680430000111
Figure BDA0002581680430000112
Figure BDA0002581680430000113
Wherein, XDTE、
Figure BDA0002581680430000118
Respectively representing the dynamic transmission errors of the normal gear transmission and the fault gear transmission,
Figure BDA0002581680430000114
respectively representing the speed of the dynamic transmission error of the normal gear transmission and the fault gear transmission,
Figure BDA0002581680430000115
respectively representing normal gear drive and fault gear drive dynamic transmissionAcceleration of error, I1、I2Representing the moment of inertia, R, of the driving and driven wheels, respectively1、R2Representing the base radius of the driving wheel and the driven wheel, M representing the equivalent mass of the gear, T1、T2Respectively 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, kfRepresenting a fault-induced change in the time-varying mesh stiffness of the gear, k0Representing the average meshing stiffness of the gears, e (t),
Figure BDA0002581680430000116
Respectively, displacement and speed of gear static transmission error, b represents backlash, and f (X)DTE)、
Figure BDA0002581680430000117
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 residual transmission errors of a fault gear relative to a 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:
Figure BDA0002581680430000121
wherein, XRTE、
Figure BDA0002581680430000122
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:
Figure BDA0002581680430000123
and is
Figure BDA0002581680430000124
Figure BDA0002581680430000125
Figure BDA0002581680430000126
Then
The dynamic load identification control model is expressed as:
Figure BDA0002581680430000127
wherein y (t) represents the residual transfer error XRTEH (t) a unit impulse response function, k, representing a gear fault equivalent excitation kinetic model0Representing the average meshing stiffness of the gear, m representing the equivalent mass of the gear, omeganIndicating the natural frequency of the system without damping,
Figure BDA0002581680430000128
representing the relative damping coefficient, ω, of the systemdThe damping natural frequency of the system is shown, t represents time, tau represents an integral variable, and F (t) represents the equivalent exciting force delta F (beta, t) of the gear fault.
S300: discretizing the 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;
in this step, the dynamic load identification control model is discretized by adopting a trapezoidal rule, specifically:
Figure BDA0002581680430000131
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 solution convolution convex optimization model based on an L1 norm is constructed and expressed as:
minimizing the objective function:
Figure BDA0002581680430000132
wherein | · | purple sweet2L2 norm representing vector, | · | | | non-volatile memory1The 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.
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:
XDTE＝R1θ1-R2θ2
the dynamic transmission error of the faulty gear transmission is expressed as:
Figure BDA0002581680430000141
the residual transmission error of the failed gear relative to the normal gear is represented as:
Figure BDA0002581680430000142
wherein, theta1、θ2Indicating input and output rotation angle signals of normal gear shaft and theta1f、θ2fIndicating 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 noise which may occur in the signal acquisition process, noise with a signal-to-noise ratio of 19dB is added into dynamic transmission errors of normal gear transmission and 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:
Figure BDA0002581680430000151
constraint function: subject to | fi|≤ui，i＝1，...，n
Wherein, except for the optimization variable f ═ f (f)1，…，fn)∈RnIn addition, a new variable u ═ is introduced (u)1，…，un)∈RnAs barrier constraints, R represents the real number domain, n represents the number of variables, and the above logarithmic barrier function is defined as:
Figure BDA0002581680430000152
wherein f isiRepresenting the ith element in the fault equivalent excitation force vector; u. ofiRepresenting the ith element in the obstacle constraint vector;
s502: the central path problem associated with minimizing the objective function is derived:
minimization function:
Figure BDA0002581680430000153
wherein, tbE (0, ∞) is barrier parameter;
s503: setting the search direction [ Delta f ] of the center routeT，ΔuT]TAnd updating the current solution:
fnew＝fold+sΔf
unew＝uold+sΔu
wherein s represents the iteration step of the interior point method, fold、uoldRepresenting the value before iteration, fnew、unewRepresenting 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
Figure BDA0002581680430000154
And Lagrange dual function g (v):
the maximization function:
Figure BDA0002581680430000155
constraint function: subject to (H)Tv)i≤λ
Wherein, the dual feasible variable v is 2(Hf-y), vT、HTRespectively 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:
Figure BDA0002581680430000161
wherein the tolerance represents an acceptable error magnitude;
if the value f after iterationnewIf 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:
minimization function:
Figure BDA0002581680430000162
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 input as a noise-free residual transfer error signal, and the relative error obtained using the sparse deconvolution model with the L1 norm is 0.15%, fig. 8(a) and 8(b) show the input as a noisy residual transfer error signal, and the relative error obtained using the sparse deconvolution model with the L1 norm 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 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 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 residual transmission errors of a fault gear relative to a 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: 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.
2. The method of claim 1, wherein preferably the normal gear drive dynamics model is represented as:
Figure FDA0002581680420000011
the faulty gear drive dynamics model is represented as:
Figure FDA0002581680420000021
and is
Figure FDA0002581680420000022
Figure FDA0002581680420000023
Figure FDA0002581680420000024
Figure FDA0002581680420000025
Wherein, XDTE、
Figure FDA00025816804200000210
Respectively representing the dynamic transmission errors of the normal gear transmission and the fault gear transmission,
Figure FDA0002581680420000026
respectively representing the speed of the dynamic transmission error of the normal gear transmission and the fault gear transmission,
Figure FDA0002581680420000027
acceleration, I, representing the dynamic transmission error of a normal gear transmission and a faulty gear transmission, respectively1、I2Representing the moment of inertia, R, of the driving and driven wheels, respectively1、R2To representBase circle radius of driving wheel and driven wheel, M represents gear equivalent mass, T1、T2Respectively 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, kfRepresenting a fault-induced change in the time-varying mesh stiffness of the gear, k0Representing the average meshing stiffness of the gears, e (t),
Figure FDA0002581680420000028
Respectively, displacement and speed of gear static transmission error, b represents backlash, and f (X)DTE)、
Figure FDA0002581680420000029
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:
Figure FDA0002581680420000031
wherein, XRTE、
Figure FDA0002581680420000032
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:
Figure FDA0002581680420000033
and is
Figure FDA0002581680420000034
Figure FDA0002581680420000035
Figure FDA0002581680420000036
Figure FDA0002581680420000037
Wherein y (t) represents the residual transfer error XRTEH (t) a unit impulse response function, k, representing a gear fault equivalent excitation kinetic model0Representing the average meshing stiffness of the gear, m representing the equivalent mass of the gear, omeganIndicating the natural frequency of the system without damping,
Figure FDA0002581680420000038
representing the relative damping coefficient, ω, of the systemdThe damping natural frequency of the system is shown, t represents time, tau represents an integral variable, and F (t) represents the equivalent exciting force delta F (beta, t) of the gear fault.
5. The method of claim 1, wherein the discrete dynamic load identification control model is represented as:
y＝Hf
the sparse solution convolution convex optimization model based on the L1 norm is expressed as:
minimizing the objective function:
Figure FDA0002581680420000041
wherein | · | purple sweet2L2 norm representing vector, | · | | | non-volatile memory1The 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 transmission is represented as:
XDTE＝R1θ1-R2θ2
the dynamic transmission error of the faulty gear transmission is expressed as:
Figure FDA0002581680420000043
the residual transmission error of the failed gear relative to the normal gear is represented as:
Figure FDA0002581680420000044
wherein, theta1、θ2Indicating input and output rotation angle signals, theta, of the normal gear shaft1f、θ2fIndicating the input and output rotational angle signals of the failed gear shaft.
7. The method of claim 1, wherein solving the sparse solution convex convolution optimization model based on the L1 norm 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:
Figure FDA0002581680420000042
constraint function: subject to | fi|≤ui，i＝1，...，n
Wherein, except for the optimization variable f ═ f (f)1，…，fn)∈RnIn addition, a new variable u ═ is introduced (u)1，…，un)∈RnAs barrier constraints, R represents the real number domain, n represents the number of variables, and the above logarithmic barrier function is defined as:
Figure FDA0002581680420000051
wherein f isiRepresenting the ith element in the fault equivalent excitation force vector; u. ofiRepresenting the ith element in the obstacle constraint vector;
s502: the central path problem associated with minimizing the objective function is derived:
minimization function:
Figure FDA0002581680420000052
wherein, tbE (0, ∞) is barrier parameter;
s503: setting the search direction [ Delta f ] of the center routeT，ΔuT]TAnd updating the current solution:
fnew＝fo1d+sΔf
unew＝uold+sΔu
wherein s represents the iteration step of the interior point method, fold、uoldRepresenting the value before iteration, fnew、unewRepresenting 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
Figure FDA0002581680420000053
And Lagrange dual function g (v):
the maximization function:
Figure FDA0002581680420000054
constraint function: subject to (H)Tv)i≤λ
Wherein the dual feasible variable v is 2(Hr-y), vT、HTRespectively 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:
Figure FDA0002581680420000061
wherein the tolerance represents an acceptable error magnitude;
if the value f after iterationnewIf 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:
Figure FDA0002581680420000062
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