CN115098988B - Spiral bevel gear endogenous excitation identification method based on transmission error - Google Patents
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Abstract
The invention discloses a transmission error-based spiral bevel gear endogenous excitation identification method, which comprises the steps of constructing an 8-degree-of-freedom gear transmission system dynamics model based on spiral bevel gear dynamic transmission error; constructing an endogenous excitation identification control model according to the spiral bevel gear transmission dynamics model, and constructing a sparse deconvolution model based on an L1 norm according to the endogenous excitation identification control model; acquiring dynamic transmission errors of gear transmission by acquiring input and output rotation angle signals of the gear transmission; and solving the sparse deconvolution model based on the L1 norm according to the dynamic transmission error of the gear transmission to obtain the endogenous excitation force of the spiral bevel gear to be identified, so as to realize the identification of the endogenous excitation force of the gear. The internal excitation force of the gear is calculated by measuring the dynamic transmission error of the spiral bevel gear, the method has the advantages of simplicity in operation and high calculation accuracy, and the indirect measurement of the internal excitation force of the spiral bevel gear is realized.
Description
Technical Field
The invention belongs to the technical field of vibration and noise of mechanical systems, and particularly relates to a spiral bevel gear endogenous excitation identification method based on transmission errors.
Background
The spiral bevel gear has the advantages of stable transmission and the like, and has more application in the military industry and civil use. In the military aspect, the spiral bevel gear is widely applied to tail reducers in helicopters, tank armored vehicles and other equipment; civil applications are also widespread in the transmission systems of heavy, high-load construction machines. Endogenous excitation of the spiral bevel gear is caused by factors such as change of gear meshing tooth pairs, gear tooth loading deformation, gear manufacturing errors and the like. It includes stiffness excitation, error excitation, engagement shock excitation, etc. Due to these internal excitations, the bevel gear drive system may generate vibrations and noise. Due to the limitation of technical conditions, endogenous excitation of gears cannot be directly measured.
The above information disclosed in the background section is only for enhancement of understanding of the background of the invention and therefore may contain information that does not form the prior art that is already known to a person of ordinary skill in the art.
Disclosure of Invention
The invention aims to provide a transmission error-based spiral bevel gear endogenous excitation identification method, which is used for identifying the endogenous excitation force of a spiral bevel gear which cannot be directly measured, exciting load cannot be directly measured through a force sensor, the endogenous excitation force of the spiral bevel gear is indirectly measured through a reverse inversion thought by utilizing a gear shaft corner signal which is convenient to measure, an L1 norm-based deconvolution model is constructed by utilizing the sparsity of the gear endogenous excitation on a frequency domain, and the gear endogenous excitation force is identified through the dynamic transmission error of the gear which is convenient to measure, so that accurate vibration source identification is realized.
In order to achieve the above object, the present invention provides the following technical solutions:
the invention discloses a transmission error-based spiral bevel gear endogenous excitation identification method, which comprises the following steps:
step S100: constructing an 8-degree-of-freedom gear transmission dynamics model based on dynamic transmission errors of the bevel gear pair with arc teeth, wherein the gear transmission dynamics model is expressed as follows:
wherein m 1、m2 represents the mass of the driving wheel and the driven wheel, I 1、I2 represents the rotational inertia of the driving wheel and the driven wheel around the respective axes, T in、Tout represents the input and load moment, the direction of the input moment T in is the same as that of theta 1, the direction of the load moment T out is opposite to that of theta 2, theta 1、θ2 is respectively input the corner signals of the gear shaft gear and the output shaft gear, r m1、rm2 represents the base circle radius of the driving wheel and the driven wheel, x 1、y1、z1 is the displacement of the driving wheel in the x, y and z directions of the established coordinate system, x 2、y2、z2 is the displacement of the driven wheel in the x, y and z directions of the established coordinate system, F x1、Fy1、Fz1 is the component of the meshing force of the driving wheel in the x, y and z directions, and F x2、Fy2、Fz2 is the component of the meshing force of the driven wheel in the x, y and z directions;
Step S200: constructing an endogenous excitation control model according to the gear transmission dynamics model, and establishing a sparse deconvolution model based on an L1 norm according to the endogenous excitation recognition control model;
step S300: acquiring input and output corner signals of gear transmission to obtain dynamic transmission errors of the gear transmission;
Step S400: and solving the L1 norm-based sparse deconvolution model according to the dynamic transmission error to obtain the endogenous excitation force of the spiral bevel gear to be identified.
In the transmission error-based spiral bevel gear endogenous excitation identification method, in step S200, the endogenous excitation control model is expressed as:
In the method, in the process of the invention, Representing the equivalent mass of the gear,/>Representing equivalent excitation,/>C=cos beta m cosαn,βm is the pitch angle of the middle point of the tooth width, alpha n is the pressure angle, and theta 1、θ2 is the rotation angle signal input and output by the gears respectively, X DTE and/orRespectively, dynamic transmission errors and second derivatives thereof, wherein I 1、I2 respectively represents rotational inertia of a driving wheel and a driven wheel, r m1、rm2 respectively represents base circle radiuses of the driving wheel and the driven wheel, T in、Tout respectively represents input torque of the driving wheel and output torque of the driven wheel, c m represents gear meshing damping, k m represents time-varying meshing stiffness of the gear, X n represents relative displacement of meshing tooth surfaces of bevel gear transmission along a normal direction of meshing points, and b represents tooth side gaps.
In the spiral bevel gear endogenous excitation identification method based on the transmission error, in step S200, a sparse deconvolution model based on an L1 norm is expressed as follows:
Wherein, |·| 1 denotes an L1 norm of the vector, D denotes a discrete fourier cosine transform matrix, F D＝DfD denotes an endogenous excitation vector of the spiral bevel gear to be identified, X DTE denotes a dynamic transfer error, F D denotes an endogenous excitation vector of the spiral bevel gear after discrete fourier cosine transform, λ denotes a regularization parameter, h is a sampling interval, M denotes an equivalent mass,
In the spiral bevel gear endogenous excitation identification method based on the transmission error, in step 300, the transmission error of the spiral bevel gear is expressed as:
XDTE＝rm1θ1-rm2θ2。
In the transmission error-based spiral bevel gear endogenous excitation identification method, in step S400, an L1 norm-based sparse deconvolution model of the endogenous excitation is solved by using an ISTA algorithm, wherein the solution process is as follows:
s401: the minimization objective function is:
Wherein, |·| 1 denotes an L1 norm of the vector, D denotes a discrete fourier cosine transform matrix, F D＝DfD denotes an endogenous excitation vector of the spiral bevel gear to be identified, X DTE denotes a dynamic transfer error, F D denotes an endogenous excitation vector of the spiral bevel gear after discrete fourier cosine transform, λ denotes a regularization parameter, h is a sampling interval, M denotes an equivalent mass,
Order theX=f D, the minimization objective function is expressed as:
S402: the minimization objective function is in the form of f (x) +g (x), G (x) =λ| i x i 1, the minimized objective function is converted into the following form by the ISTA algorithm:
s403: minimizing in objective functions g (x) =λ| i x i 1, iterative write-in of each step
Where τ α(x)i＝(|xi|-α)+sign(xi), is a soft threshold operating function,
S404: taking the difference between two adjacent iteration values as an iteration termination criterion:
ε≤xk-xk-1，
Where the tolerance epsilon represents the acceptable error magnitude,
If the value x k after iteration meets the iteration termination criterion, terminating the iteration process to obtain a sparse deconvolution solution F D =dx; otherwise, the iterative process returns to step S401 to continue the iterative computation until the iteration termination criterion is satisfied.
In the technical scheme, the spiral bevel gear endogenous excitation identification method based on the transmission error has the following beneficial effects: the method calculates the endogenous excitation force of the spiral bevel gear by measuring the dynamic transmission error of the gear, is simple to operate, and has high identified endogenous excitation precision. The internal excitation force of the gear is calculated by measuring the dynamic transmission error of the spiral bevel gear, the method has the advantages of simplicity in operation and high calculation accuracy, and the indirect measurement of the internal excitation force of the spiral bevel gear is realized. The dynamic endogenous excitation force of the spiral bevel gear can be accurately calculated, and the method has significance for fault diagnosis of the gear pair and research on the internal mechanism of vibration of the gear pair.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments described in the present application, and other drawings may be obtained according to these drawings for a person having ordinary skill in the art.
FIG. 1 is a flow chart of a method for identifying endogenous excitation force of a gear based on transmission error of a spiral bevel gear, according to an embodiment of the present invention;
FIG. 2 is a kinetic model of a spiral bevel gear provided by an embodiment of the present invention;
FIG. 3 is a graph showing dynamic transmission errors for an arcuate gear bevel gear pair at 2400rpm under 40% load conditions in accordance with another embodiment of the present invention;
Fig. 4 (a) to fig. 4 (b) are time-frequency diagrams of identification results under the conditions of 2400rpm and 40% load of the bevel gear pair with arc teeth according to another embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, based on the embodiments of the invention, which are apparent to those of ordinary skill in the art without inventive faculty, are intended to be within the scope of the invention.
Accordingly, the following detailed description of the embodiments of the invention provided in fig. 1-4 (b) of the drawings is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, based on the embodiments of the invention, which are apparent to those of ordinary skill in the art without inventive faculty, are intended to be within the scope of the invention.
It should be noted that: like reference numerals and letters denote like items in the following figures, and thus once an item is defined in one figure, no further definition or explanation thereof is necessary in the following figures.
In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings are merely for convenience in describing the present invention and simplifying the description, and do not indicate or imply that the apparatus or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present invention.
Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include one or more such feature. In the description of the present invention, the meaning of "a plurality" is two or more, unless explicitly defined otherwise.
In the present invention, unless explicitly specified and limited otherwise, the terms "mounted," "connected," "secured," and the like are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally formed; can be directly connected or indirectly connected through an intermediate medium, and can be communicated with the inside of two elements or the interaction relationship of the two elements. The specific meaning of the above terms in the present invention can be understood by those of ordinary skill in the art according to the specific circumstances.
In the present invention, unless expressly stated or limited otherwise, a first feature "above" or "below" a second feature may include both the first and second features being in direct contact, as well as the first and second features not being in direct contact but being in contact with each other through additional features therebetween. Moreover, a first feature being "above," "over" and "on" a second feature includes the first feature being directly above and obliquely above the second feature, or simply indicating that the first feature is higher in level than the second feature. The first feature being "under", "below" and "beneath" the second feature includes the first feature being directly under and obliquely below the second feature, or simply means that the first feature is less level than the second feature.
In order to make the technical scheme of the present invention better understood by those skilled in the art, the present invention will be further described in detail with reference to the accompanying drawings.
In one embodiment, the spiral bevel gear modeling and endogenous excitation identification method based on the transmission error comprises the following steps:
s100: constructing an 8-degree-of-freedom gear transmission dynamics model based on dynamic transmission errors of the bevel gear pair with the arc teeth; the model considers more comprehensive degrees of freedom and is more accurate compared with the prior art.
S200: constructing an endogenous excitation control model according to the spiral bevel gear transmission dynamics model, and establishing a sparse deconvolution model based on an L1 norm according to the load identification control model;
s300: acquiring dynamic transmission errors of gear transmission by acquiring input and output rotation angle signals of the gear transmission;
S400: and solving the sparse deconvolution model based on the L1 norm according to the dynamic transmission error of the gear transmission to obtain the endogenous excitation force of the spiral bevel gear to be identified.
In one embodiment, in step S100, the kinetic model of the spiral bevel gear transmission is established as follows:
Force analysis of driving wheel
The small gear is set as the driving wheel, and the large gear is set as the driven wheel. The flank midpoint pitch circle is subjected to normal force F n, which we can break down into force along the cone line F 1, force along the circumference F 2, and force along the perpendicular cone line and directed toward the axis F 3. In the established coordinate system, the forces in the directions of the respective coordinate axes are thus resolved into:
Ft＝F2 (3)
Driven wheel force analysis
Similar to the force analysis process of the driving wheel, the index circle at the middle point of the tooth surface of the driven wheel is subjected to normal force F n ', and the normal force F 1', force F 2 'along the circumferential direction and force F 3' along the vertical cone line and pointing to the axis can be decomposed. The driven wheel circumferential force F 2' is the same as the driven wheel circumferential force F 2 in the opposite direction.
Since δ 1+δ2 =90°, therefore
Ft′＝F2′ (6)
Decomposition of displacement freedom degree of main and driven wheels of spiral bevel gear
Fig. 2 shows a model of the established spiral bevel gear transmission dynamics, wherein a three-dimensional coordinate system O-XYZ is established by using two perpendicular and intersecting axes of the gears, each gear has 3 translational degrees of freedom x i,yi,zi and 1 rotational degree of freedom θ i, and i=1, 2 respectively represent a driving wheel and a driven wheel. The gear mesh is then equivalent to spring k m and damping c m, with the tooth surface midpoint pitch circle subjected to normal force F n as the meshing force direction.
Through the decomposition of the displacement freedom degree of the driving wheel, the relative displacement X n of the meshing tooth surfaces of the two bevel gears along the normal direction of the meshing point can be obtained:
Xn＝(x1-x2)a+(y1-y2)b+(z1-z2-rm1θ1+rm2θ2)c+e(t) (7)
Wherein e (t) represents the static transmission error of the bevel gear transmission ,a＝cosδ1cosαn sinβm+sinδ1sinαn, b＝sinδ1cosαn sinβm-cosδ1sinαn,c＝cosβm cosαn.
Assuming the meshing force F n experienced by the drive wheel, the meshing force F n experienced by the drive wheel, taking into account stiffness and damping, can be expressed as:
According to the stress analysis of the driving wheel, the meshing force of the driving wheel is decomposed into the directions of all coordinate axes on a coordinate system O-XYZ:
Fx1＝Fn cosαn sinβm cosδ1+Fn sinαn sinδ1＝aFn (9)
Fy1＝Fn cosαn sinβm sinδ1-Fn sinαn cosδ1＝bFn (10)
Fz1＝Fn cosβm cosαn＝cFn (11)
And the force analysis of the driving wheel is carried out, and the meshing force of the driven wheel is decomposed into the directions of all coordinate axes on a coordinate system O-XYZ:
Fx2＝-Fn cosαn sinβm sinδ2-Fn sinαn cosδ2＝-aFn (12)
Fy2＝-Fn cosαn sinβm cosδ2+Fn sinαn sinδ2＝-bFn (13)
Fz2＝-Fn cosβm cosαn＝-cFn (14)
Establishing a kinetic equation that considers the backlash
In the actual meshing process of the gears, the influence of the tooth side clearance on the dynamic meshing force needs to be considered, and then the meshing force expression suffered by the gear teeth becomes as follows:
Wherein f (X n) is a relative displacement function in the normal direction of the meshing point, and the expression is:
Wherein b is half of the gear normal meshing gap.
The set of kinetic equations is as follows:
Wherein m 1、m2 represents the mass of the driving wheel and the driven wheel, I 1、I2 represents the rotational inertia of the driving wheel and the driven wheel around the respective axes, T in、Tout represents the input and load moment, the direction of the input moment T in is the same as theta 1, and the direction of the load moment T out is opposite to theta 2.
Since the 6 translational degrees of freedom of the arcuate gear bevel gear pair cannot be measured, we constrain the 6 translational degrees of freedom, then equation (33) is:
Wherein:
Fz1＝Fn cosβm cosαn＝cFn,Fz2＝-Fn cosβm cosαn＝-cFn,c＝cosβm cosαn,
In a preferred embodiment of the method, in step S200, the endogenous excitation control model is expressed as:
In the method, in the process of the invention, C=cos β m cosαn,θ1、θ2, I 1、I2 represents rotational inertia of the driving wheel and the driven wheel respectively, r m1、rm2 represents base radius of the driving wheel and the driven wheel, M represents equivalent mass of the gears, T in、Tout represents input torque of the driving wheel and output torque of the driven wheel respectively, c m represents gear engagement damping, k m represents time-varying engagement stiffness of the gears, X n represents relative displacement of engagement tooth surfaces of bevel gear transmission along normal direction of engagement point, and b represents tooth side gap.
In a preferred embodiment of the method, in step S200, a sparse deconvolution model based on the endogenous excitation of the L1 norm may be built as follows:
Wherein, F D＝F-cFn,
Since the endogenous excitation of the gear has sparse characteristics in the frequency domain, the endogenous excitation control equation obtained by dispersing the trapezoidal criterion is converted into the discrete Fourier transform (the endogenous excitation force F D＝DfD) of the endogenous excitation force: D represents a discrete fourier cosine transform matrix. The sparse deconvolution model based on the L1 norm can thus be expressed as:
In the formula, |·| 1 represents the L1 norm of the vector, D represents the discrete Fourier cosine transform matrix, F D＝DfD represents the endogenous excitation vector of the spiral bevel gear to be identified, X DTE represents the dynamic transmission error, F D represents the endogenous excitation vector of the spiral bevel gear after discrete Fourier cosine transform, and lambda represents the regularization parameter.
In a preferred embodiment of the method, in step 300, the spiral bevel gear transmission error is expressed as:
XDTE＝rm1θ1-rm2θ2
in a preferred embodiment of the method, in step S400, the solution process of the sparse deconvolution model based on the L1 norm of the endogenous excitation by using the ISTA algorithm is as follows:
s401: the minimization objective function is:
Order the F D =x, the minimization objective function can be expressed as:
S402: the minimization objective function is in the form of f (x) +g (x), f (x) and g (x) are convex, f (x) is steerable, and g (x) is sufficiently simple. Wherein, G (x) =λ| |x|| 1. The ISTA algorithm is suitable for solving such problems. The minimized objective function can be converted into the following form by the ISTA algorithm:
S403: we can now see that if g (x) is a function of the split, the coordinate reduction is performed for each dimension separately, i.e. the n-dimensional minimum problem is converted into n-dimensional minimum problems. In the minimized objective function g (x) =λ| i x i 1, the problem is solved analytically, and each iteration step can be written as
Where τ α(x)i＝(|xi|-α)+sign(xi) is a soft threshold operating function.
S404: taking the difference between two adjacent iteration values as an iteration termination criterion:
ε≤xk-xk-1
Where the tolerance ε represents the acceptable error size.
If the value x k after iteration meets the iteration termination criterion, terminating the iteration process to obtain a sparse deconvolution solution F D =dx; otherwise, the iterative process returns to step S401 to continue the iterative computation until the above equation is satisfied.
In one embodiment, as shown in fig. 1, a method for identifying endogenous excitation force of spiral bevel gear based on transmission error includes the following steps:
S100: constructing an 8-degree-of-freedom gear transmission dynamics model based on dynamic transmission errors of an arc tooth bevel gear pair, wherein the transmission errors of the gear pair are differences between ideal positions and actual positions of gear transmission;
In this step, a spiral bevel gear is taken as an example, and specific parameters thereof are shown in table 1:
TABLE 1 basic parameters for spiral bevel gear drive
By adopting a centralized parameter method to construct an 8-degree-of-freedom gear transmission dynamics model based on the dynamic transmission error of the spiral bevel gear pair, the model is shown in fig. 2, and the dynamics model of spiral bevel gear transmission is expressed as follows:
Wherein m 1、m2 represents the mass of the driving wheel and the driven wheel, I 1、I2 represents the rotational inertia of the driving wheel and the driven wheel around the respective axes, T in、Tout represents the input and load moment, the direction of the input moment T in is the same as theta 1, and the direction of the load moment T out is opposite to theta 2.
Since the 6 translational degrees of freedom of the bevel gear pair with curved teeth cannot be measured, we restrict the 6 translational degrees of freedom, and the above formula can be expressed as:
Wherein: ,
Fz1＝Fn cosβm cosαn＝cFn,Fz2＝-Fn cosβm cosαn＝-cFn,c＝cosβm cosαn
S200: constructing an endogenous excitation control model according to the spiral bevel gear transmission dynamics model, and establishing a sparse deconvolution model based on an L1 norm according to the load identification control model;
In this step, the constructed endogenous excitation control model is represented as:
In the method, in the process of the invention, c＝cosβm cosαn
In the formula, theta 1、θ2 is a rotation angle signal input and output by a gear respectively, I 1、I2 is rotational inertia of a driving wheel and a driven wheel respectively, r m1、rm2 is base circle radius of the driving wheel and the driven wheel, M is equivalent mass of the gear, T in、Tout is input torque of the driving wheel and output torque of the driven wheel respectively, c m is gear engagement damping, k m is time-varying engagement stiffness of the gear, X n is relative displacement of an engagement tooth surface of bevel gear transmission along the normal direction of an engagement point, and b is tooth side clearance.
By solving forThe sparse deconvolution model of the endogenous excitation based on the L1 norm can be built as follows: /(I)
Wherein, F D＝F-cFn,
Since the endogenous excitation of the gear has sparse characteristics in the frequency domain, the endogenous excitation control equation obtained by dispersing the trapezoidal criterion is converted into the discrete Fourier transform (the endogenous excitation force F D＝DfD) of the endogenous excitation force: D represents a discrete fourier cosine transform matrix. The sparse deconvolution model based on the L1 norm can thus be expressed as:
Wherein, |·| 1 denotes an L1 norm of the vector, D denotes a discrete fourier cosine transform matrix, F D＝DfD denotes an endogenous excitation vector of the spiral bevel gear to be identified, X DTE denotes a dynamic transfer error, F D denotes an endogenous excitation vector of the spiral bevel gear after discrete fourier cosine transform, and λ denotes a regularization parameter.
S300: acquiring dynamic transmission errors of gear transmission by acquiring input and output rotation angle signals of the gear transmission;
In the step, an input rotation angle signal theta 1 and an output rotation angle signal theta 2 of spiral bevel gear transmission are acquired through an angle encoder, and the rotation angle signal is calculated: x DTE＝R1θ1-R2θ2, a dynamic transmission error of the spiral bevel gear can be obtained, such as a transmission error of 2400rpm under 40% load as shown in FIG. 3.
S400: and solving the sparse deconvolution model based on the L1 norm according to the dynamic transmission error of the gear transmission to obtain the endogenous excitation force of the spiral bevel gear to be identified.
In the step, the solution process of the sparse deconvolution model based on the L1 norm of the endogenous excitation by using an ISTA algorithm is as follows, and compared with the prior art solution result such as the original dual interior point method, the ISTA algorithm is more accurate and has higher speed:
s401: the minimization objective function is:
Order the fD＝x。
The minimization of the objective function may be expressed as:
the minimization objective function is in the form of f (x) +g (x), f (x) and g (x) are convex, f (x) is steerable, and g (x) is sufficiently simple. Wherein, G (x) =λ| |x|| 1. The ISTA algorithm is suitable for solving such problems. The original minimization objective function can be converted into the following form through the solving process of the ISTA algorithm:
S402: we can now see that if g (x) is a function of the split, the coordinate reduction is performed for each dimension separately, i.e. the n-dimensional minimum problem is converted into n-dimensional minimum problems. In the minimized objective function g (x) =λ| i x i 1, the problem is solved analytically, and each iteration step can be written as
Where τ α(x)i＝(|xi|-α)+sign(xi) is a soft threshold operating function.
S403: taking the difference between two adjacent iteration values as an iteration termination criterion:
ε≤xk-xk-1
wherein, the tolerance ε represents an acceptable error size;
if the value x k after iteration meets the iteration termination criterion, terminating the iteration process to obtain a sparse deconvolution solution F D =dx; otherwise, the iterative process returns to step S401 to continue the iterative computation until the above equation is satisfied.
FIGS. 4 (a) to 4 (b) are time-frequency diagrams of recognition results of endogenous excitation at 2400rpm under 40% load. Fig. 4 (a) is a time domain diagram, and fig. 4 (b) is a spectrogram diagram. In the figure, fm, fp and fg are respectively the gear pair meshing frequency, the input shaft rotation frequency and the output shaft rotation frequency. From the time domain identification result, the error between the average value of the time domain identification result and the meshing force obtained by directly calculating the output torque under the working condition is respectively as follows: 2.06%. From the frequency domain result, the main spectral lines of the frequency domain identification result under the working condition are the linear combination of the meshing frequency of the gear pair, the rotation frequency of the input shaft, the rotation frequency of the output shaft and the frequency multiplication thereof.
Finally, it should be noted that: the described embodiments are intended to be illustrative of only some, but not all, of the embodiments of the present application and, based on the embodiments herein, all other embodiments that may be made by those skilled in the art without the benefit of the present disclosure are intended to be within the scope of the present application.
While certain exemplary embodiments of the present invention have been described above by way of illustration only, it will be apparent to those of ordinary skill in the art that modifications may be made to the described embodiments in various different ways without departing from the spirit and scope of the invention. Accordingly, the drawings and description are to be regarded as illustrative in nature and not as restrictive of the scope of the invention, which is defined by the appended claims.
Claims (1)
1. The spiral bevel gear endogenous excitation identification method based on the transmission error is characterized by comprising the following steps of:
Step S100: constructing an 8-degree-of-freedom gear transmission dynamics model based on dynamic transmission errors of the bevel gear pair with arc teeth, wherein the gear transmission dynamics model is expressed as follows:
，
Wherein, 、/>Representing the quality of the driving wheel and the driven wheel,/>、/>Representing the moment of inertia of the driving wheel and the driven wheel about the respective axes,/>、/>Representing input and load moments, input moment/>Direction and/>The same load moment/>Direction and/>In contrast,/>、/>Input the rotation angle signals of the gear shaft gear and the output shaft gear respectively,/>、/>Represents the base circle radius of the driving wheel and the driven wheel,/>The driving wheels are respectively in the established coordinate systemThe displacement in the three directions is used to move the device,Driven wheels in the established coordinate systemDisplacement in three directions,/>The meshing force exerted by the driving wheels is at/>, respectivelyComponents in three directions,/>The meshing force exerted by the driven wheel is respectively equal to/>Components in three directions;
step S200: constructing an endogenous excitation control model according to the gear transmission dynamics model, and establishing a sparse deconvolution model based on an L1 norm according to the endogenous excitation identification control model, wherein the endogenous excitation control model is expressed as:
，
In the method, in the process of the invention, Representing the equivalent mass of the gear,/>Representing equivalent excitation,/>，/>， />Is the pitch angle of the midpoint of the tooth width,/>Is the pressure angle,/>、/>Rotation angle signals input and output by gears respectively,/> 、/>Dynamic transfer errors and their second derivatives, respectively,/>、/>Respectively represent the rotational inertia of the driving wheel and the driven wheel,/>、/>Represents the base circle radius of the driving wheel and the driven wheel,/>、/>Respectively representing the input torque of the driving wheel and the output torque of the driven wheel,/>Representing gear mesh damping,/>Representing the gear time-varying meshing stiffness,/>Representing the relative displacement of the meshing tooth surface of bevel gear transmission along the normal direction of the meshing point,/>Representing the backlash, the sparse deconvolution model based on the L1 norm is expressed as:
，
In the method, in the process of the invention, Representing the L1 norm of the vector,/>Representing a discrete Fourier cosine transform matrix,/>Representing the endogenous excitation vector of the spiral bevel gear to be identified,/>Representing dynamic transfer errors,/>Representing the endogenous excitation vector of the spiral bevel gear after discrete Fourier cosine transformation,/>Representing regularization parameters,/>For sampling interval,/>Representing the equivalent mass of the product,；
Step S300: collecting input and output corner signals of gear transmission to obtain dynamic transmission errors of the gear transmission, wherein the transmission errors of the spiral bevel gears are expressed as follows:
；
Step S400: and solving the L1-norm-based sparse deconvolution model according to the dynamic transmission error to obtain the endogenous excitation force of the spiral bevel gear to be identified, wherein the L1-norm-based sparse deconvolution model of the endogenous excitation is solved by using an ISTA algorithm, and the solving process is as follows:
s401: the minimization objective function is: ，
In the method, in the process of the invention, Representing the L1 norm of the vector,/>Representing a discrete Fourier cosine transform matrix,/>Representing the endogenous excitation vector of the spiral bevel gear to be identified,/>Representing dynamic transfer errors,/>Representing the endogenous excitation vector of the spiral bevel gear after discrete Fourier cosine transformation,/>Representing regularization parameters,/>For sampling interval,/>Representing the equivalent mass of the product,，
Order the、/>The minimization of the objective function is expressed as:
，
S402: minimizing the objective function is Form of/(>)，/>The minimized objective function is converted into the following form by the ISTA algorithm:
，
s403: minimizing in objective functions Iterative write-in of each step
，
Wherein,For a soft threshold operating function,
S404: taking the difference between two adjacent iteration values as an iteration termination criterion:
，
In the formula, tolerance Indicating the magnitude of the error that is acceptable,
If the value after iterationIf the above iteration termination criterion is met, terminating the iteration process to obtain sparse deconvolution/>; Otherwise, the iterative process returns to step S401 to continue the iterative computation until the iteration termination criterion is satisfied.
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