[go: up one dir, main page]

CN114239420B - Root crack detection method based on data twin driving - Google Patents

Root crack detection method based on data twin driving Download PDF

Info

Publication number
CN114239420B
CN114239420B CN202111610112.5A CN202111610112A CN114239420B CN 114239420 B CN114239420 B CN 114239420B CN 202111610112 A CN202111610112 A CN 202111610112A CN 114239420 B CN114239420 B CN 114239420B
Authority
CN
China
Prior art keywords
stiffness
gear
meshing
model
root
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202111610112.5A
Other languages
Chinese (zh)
Other versions
CN114239420A (en
Inventor
徐凤宝
刘贵杰
王泓晖
陈帅
谢迎春
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Ocean University of China
Original Assignee
Ocean University of China
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Ocean University of China filed Critical Ocean University of China
Priority to CN202111610112.5A priority Critical patent/CN114239420B/en
Publication of CN114239420A publication Critical patent/CN114239420A/en
Application granted granted Critical
Publication of CN114239420B publication Critical patent/CN114239420B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Geometry (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • General Engineering & Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Artificial Intelligence (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)

Abstract

The invention relates to the field of gear fault detection, in particular to a tooth root crack detection method based on data twin driving. The method comprises the following steps: s1, establishing a meshing stiffness numerical calculation model; s2, establishing a meshing stiffness physical entity model; s3, correcting the gear engagement numerical calculation model obtained in the step S1 by using the gear engagement physical entity model obtained in the step S2, and obtaining an engagement stiffness data twin model; s4, constructing a sample space of gear crack damage through the meshing stiffness digital twin model, constructing the sample space for machine learning to perform model training, and realizing prediction of gear crack damage. The method ensures the accuracy of fault detection and simultaneously avoids the situation of fault misjudgment caused by noise of the vibration signal.

Description

Root crack detection method based on data twin driving
Technical Field
The invention relates to the field of gear fault detection, in particular to a tooth root crack detection method based on data twin driving.
Background
Gear teeth breakage faults of gears are common faults in gearboxes, and seriously affect the safety and stability of the whole mechanical transmission system. In order to prevent the gear from breaking, it is important to diagnose the fatigue crack damage of the gear. Currently, fault diagnosis of gear cracks using vibration signals is the most common method. The method comprises the steps of firstly extracting a vibration signal of a gear transmission system, carrying out Fourier transformation on the vibration signal to obtain a characteristic value result of the signal, and then carrying out classification regression on the characteristic value by using a machine learning method so as to establish a fault diagnosis model. However, the collection of the vibration signals is easy to be interfered by environmental factors, and meanwhile, various faults in the mechanical system can also affect the vibration signals, so that the collected vibration signals contain noise signals, and the condition that misjudgment is easy to occur in the state of the gear system is judged by utilizing the vibration signals.
In addition, for the method of describing the gear state by using the gear engagement state feature quantity, the most commonly used method is a machine learning method, and although the machine learning method is various and has high accuracy, the machine learning needs to rely on a large amount of fault sample space, and the size of the fault sample space restricts the accuracy of the machine learning, but for a gear system in service, how to acquire fault sample data to train a machine learning model is always a difficult problem.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a tooth root crack detection method based on a digital twin technology, which ensures the accuracy of fault detection and simultaneously avoids the situation of fault misjudgment caused by noise of a vibration signal.
The technical scheme of the invention is as follows: a root crack detection method based on data twin driving comprises the following steps:
s1, establishing a meshing stiffness numerical calculation model;
s2, establishing a meshing stiffness physical entity model;
S3, correcting the gear engagement numerical calculation model obtained in the step S1 by using the gear engagement physical entity model obtained in the step S2, and obtaining an engagement stiffness data twin model;
Setting a shear stiffness correction coefficient as t ks, a bending stiffness correction coefficient as t kb, a compression stiffness correction coefficient as t ka, a damaged shear stiffness correction coefficient as t ksc, a damaged bending stiffness correction coefficient as t kbc and a damaged compression stiffness correction coefficient as t kac, and carrying the parameters into the meshing stiffness numerical calculation model obtained in the step S1 to obtain a corrected meshing stiffness vertical calculation model:
the value of k c1 in the formula (16) is solved by the meshing stiffness physical entity model in the formula step S2, the values of k h、kf1 and k f2 are solved by the step S1, and the formula (16) is arranged to obtain the physical entity model:
The formula (17) is arranged into a matrix form:
U1T＝K1 (3)
Wherein: u 1 is a matrix of stiffness coefficients, T is a correction coefficient matrix, T= [ T kbc,tkac,tksc,tkb,tka,tks]T;K1 ] is a target stiffness value, which is a known quantity and can be expressed as
The meshing stiffness values of the plurality of groups of gears are obtained through measurement and calculation of the meshing stiffness physical entity model, in order to calculate the value of the column vector T, U 1 and K 1 can be respectively expanded, the expanded matrixes are U and K, and the expression is as follows:
Then it can be obtained
UT＝K (6)
Solving the values of all variables in the T matrix, and bringing the values of all the variables into the (16), so as to obtain a meshing stiffness digital twin model, wherein the calculation results of the meshing stiffness digital twin model and the meshing stiffness physical entity model on the stiffness are consistent;
S4, constructing a sample space of gear crack damage through the meshing stiffness digital twin model, constructing the sample space for machine learning to perform model training, and realizing prediction of gear crack damage.
In the invention, the establishment process of the meshing stiffness numerical calculation model in the step S1 is as follows:
The energy stored in the gear comprises hertz energy, bending energy, compression energy and shearing energy, the hertz rigidity, the bending rigidity, the compression rigidity and the shearing rigidity correspond to the energy, the series connection of the meshing rigidity is total meshing rigidity, and the energy formulas are as follows:
Wherein: u h is Hertz energy; u b is bending energy; u a is compression energy; u * is shear energy; f is the force at the engagement point; k h is hertz stiffness; k b is bending stiffness; k a is the compressive stiffness; k s is shear stiffness;
the expression of stiffness caused by flexible deformation is:
Wherein: k f is matrix deformation stiffness; e is the elastic modulus; l is the width of the gear; alpha is the pressure angle of the gear; u f denotes the difference in radius of the reference circle and the root circle; s f represents the tooth root circle tooth thickness; the coefficient L *、M*、P*、Q* is a polynomial coefficient whose expression is:
Wherein: x * represents a coefficient L *、M*、P*、Q*;hf＝rf/r, wherein r f is the radius of a root circle, and r is the radius of a gear shaft hole; θ f represents the central angle of the tooth root circle half tooth thickness, and A, B, C, D, E and F are both parameter values;
The expression of hertz stiffness is:
Wherein: v is poisson's ratio;
Regarding the teeth of the gears as cantilever beams, the formulas for bending energy U b, compression energy U a, and shear energy U s are expressed as:
wherein: i x is the cross-sectional area moment of inertia from root two; m is a bending moment; a x is the cross-sectional area, a x＝2hx L; g is the shear modulus; f a is the component force of the meshing force along the horizontal direction; f b is the component force of the meshing force along the vertical line direction; d is the distance from the meshing point to the root; x is the distance from any point of the meshing area to the root circle;
When root cracks are generated, the effective cross-sectional moment of inertia and the cross-sectional area are changed, and the effective cross-sectional moment of inertia I x and the cross-sectional area A x are expressed as follows:
Wherein: h x is the distance from the inner point of the meshing zone to the center line of the gear teeth; h cl is the distance from the meshing point to the tooth centerline, g c is the distance from the meshing point to the root;
the total meshing stiffness of the gear is in a serial connection form of Hertz stiffness, bending stiffness, compression stiffness, shearing stiffness and stiffness caused by matrix deformation, and for a gear pair with only one tooth root crack, the expression of the meshing stiffness is as follows:
wherein: k c1 represents the gear mesh stiffness of a pair of gear pairs containing root cracks;
for a gear pair containing only one root crack, the stiffness of the two pairs of gears is
k＝kc1+k2 (15)
Wherein: k 2 denotes gear mesh stiffness without root cracks;
the numerical calculation model of the meshing stiffness between gears is expressed as:
k＝f(E,L,v,q,β,Rb,α1,α2) (16)
Wherein: q represents a crack length; beta represents a crack angle; r b represents the base circle radius; alpha 1 represents the engagement position pressure angle; alpha 2 represents the central angle subtended by the tooth half-tooth.
In step S2, the process of establishing the meshing stiffness physical entity model is as follows:
The motion state of the master gear and the slave gear is expressed as follows:
Wherein: j l is the total moment of inertia of the low-speed shaft and low-speed gear; j h is the total moment of inertia of the high-speed gear and the high-speed shaft; t r is the system input torque; f g is gear engagement transmission force; t h is the load torque; θ l is the low speed axis phase angle; θ h is the high speed axis phase angle; r l is the base radius of the low-speed gear; r h is the base radius of the high-speed gear;
The mechanical transmission between gears is expressed as a spring damping system, and the gear meshing force F g in the gear meshing process is expressed as:
Wherein: f g represents the meshing force between gears; c m is gear engagement damping; k (t) is gear engagement stiffness; delta is the relative displacement in the engagement direction, and the expression is:
the stiffness expression between gears is obtained according to the above formula:
The step S4 specifically includes the following steps.
S4.1, establishing a sample space: the sample space of the gear crack damage is constructed by a meshing stiffness digital twin model;
s4.2, establishing a machine learning model;
S4.3, predicting crack damage: and (3) solving the gear engagement stiffness by using a formula (15) according to the rotation speed and the torque of an input shaft and the rotation speed and the torque of an output shaft of the physical entity gearbox, and inputting the gear engagement stiffness obtained by solving into a machine learning model, thereby obtaining the state of the current gear tooth root crack.
The beneficial effects of the invention are as follows:
(1) The application takes the meshing stiffness between gears as the characteristic quantity for judging the state of the gears, calculates the meshing stiffness between gears by measuring the rotating speed and the torque of the input shaft and the output shaft of the gears, and compared with a vibration signal, the rotating speed and the torque signal are easier to measure, and meanwhile, the disturbance of the environment can not be received, thus effectively avoiding the misjudgment condition caused by the acquisition of an error signal by a sensor;
(2) According to the application, the meshing stiffness digital twin model is utilized to obtain the fault template of the physical entity, so that a proper sample space is constructed for machine learning to perform model training, thereby ensuring the accuracy of the machine learning model and the accuracy of fault detection.
Drawings
FIG. 1 is a schematic flow chart of the present application;
FIG. 2 is a schematic diagram of internal parameters of a gear;
FIG. 3 is a schematic diagram of a gear pair transfer chain;
FIG. 4 is a schematic view of a gear root crack.
Detailed Description
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings.
In the following description, specific details are set forth in order to provide a thorough understanding of the present invention. The present invention may be embodied in many other forms than those herein described, and those skilled in the art may readily devise numerous other arrangements that do not depart from the spirit of the invention. Therefore, the present invention is not limited by the specific embodiments disclosed below.
The root crack detection method based on data twin driving mainly comprises the following steps.
First, establishing a meshing stiffness numerical calculation model. The meshing stiffness numerical calculation model is a model which is established by utilizing the material properties of the gear itself and is used for representing the meshing stiffness of the gear, and the establishment process of the model is as follows.
The meshing stiffness of the gears was calculated using an energy method. Gear teeth of a gear are regarded as cantilever beams with variable cross sections, gear meshing stiffness is defined as the ratio of tooth surface normal force to deformation amount, and meshing stiffness can be regarded as the ratio of normal force acting on the cantilever beams to deformation generated under the acting force when calculated by using an energy method. The energy stored in the gear mainly comprises Hertz energy, bending energy, compression energy and shearing energy, the Hertz rigidity, the bending rigidity, the compression rigidity and the shearing rigidity correspond to the energy, and the series connection of the meshing rigidities is total meshing rigidity. The energy formulas are as follows:
Wherein: u h is Hertz energy; u b is bending energy; u a is compression energy; u * is shear energy; f is the force at the engagement point; k h is hertz stiffness; k b is bending stiffness; k a is the compressive stiffness; k s is the shear stiffness.
Considering that the gear matrix is flexibly deformed, the rigidity caused by the flexible deformation cannot be ignored, and the expression is as follows:
Wherein: k f is matrix deformation stiffness; e is the elastic modulus; l is the width of the gear; alpha is the pressure angle of the gear; u f denotes the difference in radius of the reference circle and the root circle; s f represents the tooth root circle tooth thickness; the coefficient L *、M*、P*、Q* is a polynomial coefficient whose expression is:
wherein X * represents a coefficient L *、M*、P*、Q*;hf＝rf/r, wherein r f is a root circle radius, and r is a gear shaft hole radius; θ f represents the half-tooth thickness central angle of the root circle. In the application, the meanings of r and u f、θf、Sf are shown in fig. 2, and the values of parameters A, B, C, D, E and F in formula (8) are shown in the following table:
According to the hertz theorem, the hertz stiffness is independent of the contact location, and can be expressed as:
Wherein: v is poisson's ratio.
According to the stress characteristics of the gears, the gear teeth of the gears are regarded as cantilever beams, and the formulas of the bending energy U b, the compression energy U a and the shearing energy U s are expressed as follows:
Wherein: i x is the cross-sectional area moment of inertia from root two; m is a bending moment; a x is the cross-sectional area, a x＝2hx L; g is the shear modulus; f a is the component force of the meshing force along the horizontal direction; f b is the component force of the meshing force along the vertical line direction; d is the distance from the meshing point to the root; x is the distance from any point of the meshing zone to the root circle.
When root cracks occur, the effective cross-sectional moment of inertia and cross-sectional area change, as shown in FIG. 3. The effective cross-sectional moment of inertia I x and cross-sectional area a x can be expressed as:
Wherein: h x is the distance from the inner point of the meshing zone to the center line of the gear teeth; h cl is the distance from the meshing point to the tooth centerline and g c is the distance from the meshing point to the root.
Numerical models of shear stiffness, compression stiffness and bending stiffness with root cracks can be obtained immediately by combining the formula (1), the formula (5), the formula (6) and the formula (7). The total meshing stiffness of the gear, namely, the series connection form of the hertz stiffness, the bending stiffness, the compression stiffness, the shearing stiffness and the stiffness caused by matrix deformation, can be expressed as:
wherein: k c1 denotes a pair of gear mesh stiffness containing root cracks in the gear pair. Proper transmission of gears requires that the gear engagement overlap be greater than 1, i.e. that the gear engagement occurs with two pairs of teeth, the two pairs of gears being rigid for a gear pair containing only one root crack
k＝kc1+k2 (30)
Wherein: k 2 denotes the gear mesh stiffness without root cracks.
The numerical calculation model of the engagement stiffness between gears can be expressed as:
k＝f(E,L,v,q,β,Rb,α1,α2) (31)
Wherein: q represents a crack length; beta represents a crack angle; r b represents the base circle radius; alpha 1 represents the engagement position pressure angle; alpha 2 represents the central angle subtended by the tooth half-tooth. A numerical calculation model of the meshing stiffness is thus given, the stiffness of which is only related to the physical parameters of the gear.
And secondly, establishing a meshing stiffness physical entity model. The meshing stiffness physical entity model is a model which is established by utilizing the input output quantity of the gear and is used for representing the meshing stiffness of the gear, and the establishment process of the model is as follows.
According to the stress characteristics of the gears, the motion state of the master gear and the slave gear can be expressed as:
Wherein: j l is the total moment of inertia of the low-speed shaft and low-speed gear; j h is the total moment of inertia of the high-speed gear and the high-speed shaft; t r is the system input torque; f g is gear engagement transmission force; t h is the load torque; θ l is the low speed axis phase angle; θ h is the high speed axis phase angle; r l is the base radius of the low-speed gear; r h is the base radius of the high-speed gear.
The mechanical transmission between gears is denoted as a spring damping system, as shown in fig. 4. The meshing force F g during gear meshing can be expressed as:
Wherein: c m is gear engagement damping; k (t) is gear engagement stiffness; delta is the relative displacement in the engagement direction, and the expression is:
the stiffness expression between the gears is obtained according to the above formula:
Equation (15) represents the relationship between the output quantity, i.e., the gear engagement stiffness, and the input quantity, including the rotational speed and the torque.
And thirdly, correcting the gear engagement numerical calculation model obtained in the first step by using the gear engagement physical entity model obtained in the second step, and obtaining an engagement stiffness data twin model.
Since the actual installation error is not considered when the gear engagement numerical calculation model is established, the numerical calculation model has a certain deviation, and therefore the gear engagement numerical calculation model needs to be corrected by using the gear engagement physical entity model. Assuming that the correction coefficient of the shear stiffness is t ks, the correction coefficient of the bending stiffness is t kb, the correction coefficient of the compression stiffness is t ka, the correction coefficient of the damaged shear stiffness is t ksc, the correction coefficient of the damaged bending stiffness is t kbc, and the correction coefficient of the damaged compression stiffness is t kac, the formula (8) becomes:
The value of k c1 in formula (16) can be solved by formula (15), i.e. the value of k c1＝k(t);kh can be solved by formula (4), the values of k f1 and k f2 can be solved by formula (2), and the finishing of formula (16) can be achieved:
further, the formula (17) is arranged into a matrix form:
U1T＝K1 (39)
Wherein: u 1 is a matrix of stiffness coefficients, T is a correction coefficient matrix, T= [ T kbc,tkac,tksc,tkb,tka,tks]T;K1 ] is a target stiffness value, which is a known quantity and can be expressed asA plurality of groups of gear meshing stiffness values can be obtained through measurement and calculation of a physical entity model, U 1 and K 1 can be respectively expanded for obtaining a value of a column vector T, namely numerical meshing stiffness and physical entity model stiffness can be solved through various gear meshing conditions, and finally expanded U 1 and K 1 are obtained. The expanded matrix is U and K, and the expression is:
Then it can be obtained
UT＝K (42)
If the unique solution condition of the non-homogeneous linear equation set is r (U) =r (u|k), the values of the variables in the T matrix can be solved by setting proper matrices U and K, and the values of the variables are brought into formula (16), so as to obtain the meshing stiffness digital twin model. And if the corrected meshing stiffness numerical calculation model has high consistency with the calculation result of the meshing stiffness physical entity model on the stiffness, the establishment of the meshing stiffness digital twin model can be considered to be completed.
And fourthly, constructing a sample space of gear crack damage through the meshing stiffness digital twin model, so as to construct a proper sample space for machine learning to perform model training and realize prediction of the gear crack damage. The method specifically comprises the following steps.
(One) a sample space is established. Because the meshing stiffness digital twin model and the meshing stiffness physical solid model can keep high consistency, a sample space for gear crack damage can be constructed through the meshing stiffness digital twin model, and a large number of sample spaces are obtained through changing parameters such as crack length q, crack angle beta, gear modulus and the like in the formula (10) during construction.
And (II) establishing a machine learning model. For the problem of predicting root crack damage, which belongs to the regression problem in machine learning, a machine learning method commonly used for solving the regression problem comprises the following steps: classification regression trees, support vector machine regression, and gaussian process regression. In order to establish the most suitable crack damage prediction model, the three mechanical learning methods are respectively utilized to establish the model, and the regression effect of the model is compared to select the most suitable model.
And (III) predicting crack damage. After the machine learning model is built, the gear meshing stiffness is solved by utilizing the formula (15) according to the input shaft rotating speed and torque, the output shaft rotating speed and torque of the physical entity gearbox. And then inputting the gear meshing stiffness obtained by solving into a machine learning model, and obtaining the state of the current gear tooth root crack.
The root crack detection method based on the data twin driving provided by the invention is described in detail above. The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to facilitate an understanding of the method of the present invention and its core ideas. It should be noted that it will be apparent to those skilled in the art that various modifications and adaptations of the invention can be made without departing from the principles of the invention and these modifications and adaptations are intended to be within the scope of the invention as defined in the following claims. The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (4)

1. The root crack detection method based on data twin driving is characterized by comprising the following steps of:
s1, establishing a meshing stiffness numerical calculation model;
s2, establishing a meshing stiffness physical entity model;
S3, correcting the gear engagement numerical calculation model obtained in the step S1 by using the gear engagement physical entity model obtained in the step S2, and obtaining an engagement stiffness data twin model;
Setting a shear stiffness correction coefficient as t ks, a bending stiffness correction coefficient as t kb, a compression stiffness correction coefficient as t ka, a damaged shear stiffness correction coefficient as t ksc, a damaged bending stiffness correction coefficient as t kbc and a damaged compression stiffness correction coefficient as t kac, and carrying the obtained meshing stiffness numerical calculation model in the step S1 to obtain a corrected meshing stiffness numerical calculation model:
the value of k c1 in the formula (16) is solved by the meshing stiffness physical entity model in the formula step S2, the values of k h、kf1 and k f2 are solved by the step S1, and the formula (16) is arranged to obtain the physical entity model:
The formula (17) is arranged into a matrix form:
U1T＝K1 (3)
Wherein: u 1 is a matrix of stiffness coefficients, T is a correction coefficient matrix, T= [ T kbc,tkac,tksc,tkb,tka,tks]T;K1 ] is a target stiffness value,
The meshing stiffness values of the plurality of groups of gears are obtained through measurement and calculation of the meshing stiffness physical entity model, U 1 and K 1 are respectively expanded in order to calculate the value of a column vector T, the expanded matrixes are U and K, and the expression is as follows:
And get
UT＝K (6)
Solving the values of all variables in the T matrix, and bringing the values of all the variables into the (16), so as to obtain a meshing stiffness digital twin model, wherein the calculation results of the meshing stiffness digital twin model and the meshing stiffness physical entity model on the stiffness are consistent;
S4, constructing a sample space of gear crack damage through the meshing stiffness digital twin model, constructing the sample space for machine learning to perform model training, and realizing prediction of gear crack damage.
2. The method for detecting the root cracks based on the data twin driving according to claim 1, wherein the process of establishing the meshing stiffness numerical calculation model in the step S1 is as follows:
The energy stored in the gear comprises hertz energy, bending energy, compression energy and shearing energy, the hertz rigidity, the bending rigidity, the compression rigidity and the shearing rigidity correspond to the energy, the series connection of the meshing rigidity is total meshing rigidity, and the energy formulas are as follows:
Wherein: u h is Hertz energy; u b is bending energy; u a is compression energy; u * is shear energy; f is the force at the engagement point; k h is hertz stiffness; k b is bending stiffness; k a is the compressive stiffness; k s is shear stiffness;
the expression of stiffness caused by flexible deformation is:
Wherein: k f is matrix deformation stiffness; e is the elastic modulus; l is the width of the gear; alpha is the pressure angle of the gear; u f denotes the difference in radius of the reference circle and the root circle; s f represents the tooth root circle tooth thickness; the coefficient L *、M*、P*、Q* is a polynomial coefficient whose expression is:
Wherein: x * represents a coefficient L *、M*、P*、Q*;hf＝rf/r, wherein r f is the radius of a root circle, and r is the radius of a gear shaft hole; θ f represents the central angle of the tooth root circle half tooth thickness, and A, B, C, D, E and F are both parameter values;
The expression of hertz stiffness is:
Wherein: v is poisson's ratio;
Regarding the teeth of the gears as cantilever beams, the formulas for bending energy U b, compression energy U a, and shear energy U s are expressed as:
wherein: i x is the cross-sectional area moment of inertia from root two; m is a bending moment; a x is the cross-sectional area, a x＝2hx L; g is the shear modulus; f a is the component force of the meshing force along the horizontal direction; f b is the component force of the meshing force along the vertical line direction; d is the distance from the meshing point to the root; x is the distance from any point of the meshing area to the root circle;
When root cracks are generated, the effective cross-sectional moment of inertia and the cross-sectional area are changed, and the effective cross-sectional moment of inertia I x and the cross-sectional area A x are expressed as follows:
Wherein: h x is the distance from the inner point of the meshing zone to the center line of the gear teeth; h cl is the distance from the meshing point to the tooth centerline, g c is the distance from the meshing point to the root;
the total meshing stiffness of the gear is in a serial connection form of Hertz stiffness, bending stiffness, compression stiffness, shearing stiffness and stiffness caused by matrix deformation, and for a gear pair with only one tooth root crack, the expression of the meshing stiffness is as follows:
wherein: k c1 represents the gear mesh stiffness of a pair of gear pairs containing root cracks;
for a gear pair containing only one root crack, the stiffness of the two pairs of gears is
k＝kc1+k2 (15)
Wherein: k 2 denotes gear mesh stiffness without root cracks;
the numerical calculation model of the meshing stiffness between gears is expressed as:
k＝f(E,L,v,q,β,Rb,α1,α2) (16)
Wherein: q represents a crack length; beta represents a crack angle; r b represents the base circle radius; alpha 1 represents the engagement position pressure angle; alpha 2 represents the central angle subtended by the tooth half-tooth.
3. The method for detecting the root cracks based on the data twin driving according to claim 1, wherein in the step S2, the process of establishing the meshing stiffness physical solid model is as follows:
The motion state of the master gear and the slave gear is expressed as follows:
Wherein: j l is the total moment of inertia of the low-speed shaft and low-speed gear; j h is the total moment of inertia of the high-speed gear and the high-speed shaft; t r is the system input torque; f g is gear engagement transmission force; t h is the load torque; θ l is the low speed axis phase angle; θ h is the high speed axis phase angle; r l is the base radius of the low-speed gear; r h is the base radius of the high-speed gear;
The mechanical transmission between gears is represented as a spring damping system, and the meshing force F g during gear meshing is represented as:
Wherein: c m is gear engagement damping; k (t) is gear engagement stiffness; delta is the relative displacement in the engagement direction, and the expression is:
the stiffness expression between gears is obtained according to the above formula:
4. The method for detecting a root crack based on data twin driving according to claim 1, wherein the step S4 specifically comprises the steps of:
S4.1, establishing a sample space: the sample space of the gear crack damage is constructed by a meshing stiffness digital twin model;
s4.2, establishing a machine learning model;
S4.3, predicting crack damage: and (3) solving the gear engagement stiffness by using a formula (15) according to the rotation speed and the torque of an input shaft and the rotation speed and the torque of an output shaft of the physical entity gearbox, and inputting the gear engagement stiffness obtained by solving into a machine learning model, thereby obtaining the state of the current gear tooth root crack.
CN202111610112.5A 2021-12-27 2021-12-27 Root crack detection method based on data twin driving Active CN114239420B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202111610112.5A CN114239420B (en) 2021-12-27 2021-12-27 Root crack detection method based on data twin driving

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202111610112.5A CN114239420B (en) 2021-12-27 2021-12-27 Root crack detection method based on data twin driving

Publications (2)

Publication Number Publication Date
CN114239420A CN114239420A (en) 2022-03-25
CN114239420B true CN114239420B (en) 2024-09-24

Family

ID=80763235

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202111610112.5A Active CN114239420B (en) 2021-12-27 2021-12-27 Root crack detection method based on data twin driving

Country Status (1)

Country Link
CN (1) CN114239420B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114912256B (en) * 2022-04-22 2024-03-29 西安交通大学 Vibration response analysis method of spiral bevel gear with crack fault

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
AU2020102819A4 (en) * 2020-10-16 2020-12-10 Beihang University Digital-twin-driven method and system for fault diagnosis of subsea production system of offshore oil
CN112836319A (en) * 2021-03-11 2021-05-25 西南交通大学 A Simulation Method Considering Non-Uniformly Distributed Root Cracks

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP3809220B1 (en) * 2019-10-14 2023-01-18 Honda Research Institute Europe GmbH Method and system for semi-supervised deep anomaly detection for large-scale industrial monitoring systems based on time-series data utilizing digital twin simulation data
CN113221271B (en) * 2021-05-08 2022-10-28 西安交通大学 Digital twin-driven quantitative recognition method for cracks of rotating blades of aircraft engine
CN113468809B (en) * 2021-06-30 2022-10-04 重庆大学 Wind power gear box parallel stage tooth root crack mode identification method

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
AU2020102819A4 (en) * 2020-10-16 2020-12-10 Beihang University Digital-twin-driven method and system for fault diagnosis of subsea production system of offshore oil
CN112836319A (en) * 2021-03-11 2021-05-25 西南交通大学 A Simulation Method Considering Non-Uniformly Distributed Root Cracks

Also Published As

Publication number Publication date
CN114239420A (en) 2022-03-25

Similar Documents

Publication Publication Date Title
Doğan et al. Crack detection for spur gears with asymmetric teeth based on the dynamic transmission error
CN112084583B (en) Rotor blade life prediction method and system based on digital twin
CN102542105B (en) Gear load wireless monitoring system and interactive multi-stage gear physical simulation method finished based on same
CN112836319B (en) A Simulation Method Considering Non-Uniformly Distributed Root Cracks
CN114239420B (en) Root crack detection method based on data twin driving
CN114139303A (en) Compilation of bench test load spectrum based on measured S-N curve and actual mining road spectrum
CN111898218A (en) Method for forecasting limit bearing capacity of intermediate shaft of transmission
CN109190227A (en) Based on the complicated tooth base Meshing Stiffness of Spur Gears calculation method of parsing-finite element
CN106441867A (en) Spiral bevel gear tooth root bending stress testing method in consideration with dynamic load based on similarity theory
CN113343383A (en) Dynamic transmission error prediction method for robot joint harmonic reducer
CN113919102B (en) A method and system for analyzing load transfer characteristics of main transmission system of wind turbine generator set
CN117723189B (en) Torque testing system and method
CN115563853A (en) Rolling bearing fault diagnosis method based on digital twinning
CN110044621A (en) The epicyclic gearbox oscillation power of gear distress composes prediction technique
CN108519224A (en) A method to verify the vibration coupling characteristics of two-stage fixed shaft gear transmission system
CN113465915A (en) Gear box gear fault degree determination method based on vibration transmission
CN113733158A (en) Mechanical arm reducer performance testing method and system
CN116992713A (en) Equal-strength optimization method for bevel gear set of differential mechanism of new energy vehicle
CN113468809B (en) Wind power gear box parallel stage tooth root crack mode identification method
CN115326392A (en) Method for predicting fatigue life of PTO assembly of paddy field power machine
CN110046441B (en) Test method for fatigue strength of rotating machinery shafting
CN117077519A (en) Digital twinning-based gearbox fault diagnosis method and diagnosis system thereof
CN105171778A (en) Torsional vibration extraction and analysis method for joint reducer of industrial robot
RU2224232C1 (en) Process of vibration-acoustic diagnostics of transmissions by engagement
CN115452382B (en) Intelligent bearing monitoring method and system based on digital twin model

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant