Gear crack rigidity calculation and system vibration coupling solving method considering slice coupling

Abstract

The invention provides a gear crack rigidity calculation and system vibration coupling solution method considering slice coupling, which comprises the following steps of: calculating bending rigidity, shearing rigidity and axial compression rigidity of slice gear teeth by adopting a slicing method based on gear tooth number, modulus and gear pair dynamic meshing force to obtain gear tooth rigidity of the slice gear teeth; according to whether the gear has cracks or not, slice coupling rigidities in the healthy state and the crack state of the gear are calculated in combination with the gear tooth rigidities of slice gear teeth; calculating the crack-containing gear time-varying meshing stiffness of a single gear pair by combining the contact stiffness and the matrix stiffness of the gear; based on the outer diameter, the inner diameter and the number of rolling bodies of the ball bearing, the bearing supporting force is calculated by combining the dynamic load borne by the bearing; and according to the time-varying meshing stiffness of the crack-containing gear of the single gear pair and the bearing supporting force, a gear-bearing-coupling system kinetic equation is constructed, and the vibration response of the gear-bearing-coupling system is solved. The method can provide reference for early fault diagnosis of the wind turbine generator gearbox.

Description

Technical Field

[0001] The invention relates to the technical field of wind turbine gearboxes, and in particular to a method for solving gear crack stiffness calculation and system vibration coupling considering slice coupling. Background Art

[0002] Gears are the core components for transmitting force and motion in wind turbine gearboxes. Their mechanical properties and dynamic characteristics directly affect the service performance of wind turbines.

[0003] Gear cracks are an important mode of gear failure, especially in wind turbine gearboxes. Under the action of time-varying wind speed, gears are very likely to crack, causing gear breakage, and then causing the entire wind turbine to shut down. In the prior art, the research directions of gear cracks include: using the three-dimensional boundary element method to explore the influence of the initial crack angle on the crack propagation path, comprehensively considering the lateral and axial stiffness of the gear matrix, and analyzing the dynamic changes of the gear meshing stiffness when the crack propagates along the tooth top and the end face.

[0004] However, the above technical solution cannot reflect the impact of gear cracks on system vibration, and the solution accuracy is insufficient when solving the change of time-varying meshing stiffness of gears under crack state, which will affect the accuracy of early fault detection results of gearboxes. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention proposes a method for solving the coupling between the slice-coupled gear crack stiffness calculation and the system vibration, so as to solve the technical problems in the prior art that the influence of the gear crack on the system vibration is not considered and the solution accuracy is insufficient when solving the change of the time-varying meshing stiffness of the gear under the crack state.

[0006] The technical solution adopted by the present invention is as follows:

[0007] In a first aspect, a method for calculating gear crack stiffness and coupling with system vibration considering slice coupling is provided, comprising the following steps:

[0008] Based on the number of teeth, module and dynamic meshing force of the gear pair, the slicing method is used to calculate the bending stiffness, shear stiffness and axial compression stiffness of the sliced ​​gear teeth to obtain the tooth stiffness of the sliced ​​gear teeth; according to whether there is a crack in the gear, the slicing coupling stiffness of the gear in the healthy state and the cracked state is calculated respectively in combination with the tooth stiffness of the sliced ​​gear teeth; according to the slicing coupling stiffness of the gear in the healthy state and the cracked state, combined with the contact stiffness and matrix stiffness of the gear, the time-varying meshing stiffness of the cracked gear of a single gear pair is calculated; based on the outer diameter, inner diameter and number of rolling elements of the ball bearing, combined with the dynamic load on the bearing, the bearing support force is calculated; according to the time-varying meshing stiffness of the cracked gear of a single gear pair and the bearing support force, the gear-bearing-coupling system dynamics equation is constructed, and the vibration response of the gear-bearing coupling system is solved.

[0009] Furthermore, based on the number of teeth, module and dynamic meshing force of the gear pair, the slicing method is used to calculate the bending stiffness, shear stiffness and axial compression stiffness of the sliced ​​gear teeth, and the tooth stiffness of the sliced ​​gear teeth is obtained, including:

[0010] The meshing angle of the driving wheel, the meshing angle of the driven wheel, the actual meshing angle and the contact line component are calculated according to the number of teeth, the module and the dynamic meshing force of the gear pair; the gear is sliced, and the bending stiffness, shear stiffness and axial compression stiffness of the sliced ​​wheel teeth are calculated according to the ratio of the meshing angle of the driving wheel, the meshing angle of the driven wheel and the actual meshing angle and the contact line component to the number of gear slices; the stiffness of the sliced ​​wheel teeth is calculated according to the bending stiffness, shear stiffness and axial compression stiffness of the sliced ​​wheel teeth.

[0011] Furthermore, the slice coupling stiffness of the gear under healthy condition is calculated according to the following formula:

[0012]

[0013] In the above formula, C c represents the slice coupling factor, k t(n-1) represents the gear tooth stiffness of the (n-1)th slice, k t(n) represents the gear tooth stiffness of the nth slice, M represents the module, and Δl represents the ratio of the tooth width to the number of gear tooth slices.

[0014] Furthermore, when there is a crack in the gear, the following formula is used to calculate the crack bending stiffness k of the slicer gear tooth: bc and the crack shear stiffness k sc :

[0015]

[0016] In the above formula, represents the meshing angle variable, is the driving wheel meshing angle, is the meshing angle of the driven gear, is the actual meshing angle of the driving wheel; is the actual meshing angle of the driven wheel, Δy is the ratio of the contact line component to the number of gear slices, E is the elastic modulus, q(y) is the ordinate of the crack end point, R b is the base circle radius, and v is the Poisson's ratio.

[0017] Furthermore, the slice coupling stiffness under the gear crack state is calculated according to the following formula:

[0018]

[0019] k bc is the crack bending stiffness, k sc is the crack shear stiffness, k ax is the axial compressive stiffness.

[0020] Furthermore, the time-varying mesh stiffness k(t) of the cracked gear of a single gear pair is calculated as follows:

[0021]

[0022] In the above formula, k h is the Hertzian contact stiffness; k bc1 is the bending stiffness of the active wheel slicing gear teeth, k bc2 k is the crack bending stiffness of the driven wheel slicing tooth; sc1 is the shear stiffness of the active wheel slicing gear teeth, k sc2 k is the shear stiffness of the driven wheel slicing teeth; ax1 is the axial compression stiffness of the driving wheel, k ax2 is the axial compression stiffness of the driven wheel, k f1 is the base stiffness of the driving wheel, k f2 is the base stiffness of the driven wheel; k tc represents the slice coupling stiffness under the gear crack state, k c represents the slice coupling stiffness of the gear in a healthy state, a 1 ,a 2 is the driving wheel slice coupling stiffness determination coefficient, a 3 ,a 4 is the determination coefficient of the driven wheel slice coupling stiffness.

[0023] Furthermore, the bearing support force includes axial force and radial force, which are calculated using the following formula:

[0024]

[0025] In the above formula, F ca Indicates the axial force between the inner and outer ring raceways of the bearing, F cr Indicates the radial force between the inner and outer ring raceways of the bearing, Kc It represents the comprehensive contact stiffness between the ball raceways, σ represents the contact deformation, λ represents the bearing coefficient, and for ball bearings, λ is taken as 1.5. It represents the contact angle of the bearing after loading, and H(σ) is the judgment coefficient of the Heaviside function.

[0026] Furthermore, the dynamic equation of the gear-bearing-coupling system is as follows:

[0027]

[0028] In the above formula, m a Indicates quality, represents acceleration, k a represents stiffness, x a represents displacement, c a represents damping, Indicates speed, F a Indicates the stress condition.

[0029] Furthermore, the Runge-Kutta method is used to solve the vibration response of the gear-bearing coupling system, and the stiffness, damping, vibration displacement, vibration velocity, vibration acceleration of the gear and bearing components and the dynamic meshing force of the gear are obtained.

[0030] In a second aspect, a computer program product is provided, comprising a computer program / instruction, which, when executed by a processor, implements the steps of the method for solving the gear crack stiffness calculation and system vibration coupling considering the slice coupling described in the first aspect.

[0031] It can be seen from the above technical solution that the beneficial technical effects of the present invention are as follows:

[0032] When establishing the gear-bearing-coupling system dynamics equation, the slice coupling effect of the cracked gear along the tooth width direction was considered, and the slice coupling stiffness of the cracked gear in the tooth width direction was introduced to construct the system dynamics equation. The constructed system dynamics equation also comprehensively considers time-varying factors such as the dynamic meshing force of the gear pair and the dynamic support force of the rolling bearing, which can more accurately analyze the influence of the tooth root crack on the time-varying meshing stiffness of the gear and the vibration characteristics of the system; the solved dynamic meshing force of the gear and the vibration displacement of the bearing can provide an important reference for the early fault diagnosis of the wind turbine gearbox. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for the specific embodiments or the prior art description. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn according to the actual scale.

[0034] Figure 1 A schematic flow chart of a method for solving the coupling of gear crack stiffness calculation and system vibration considering the slice coupling in an embodiment of the present invention;

[0035] Figure 2 This is a schematic diagram of the parallel-stage transmission principle of a wind turbine gearbox according to an embodiment of the present invention;

[0036] Figure 3 This is a schematic diagram of a helical gear slice model of a wind turbine gearbox according to an embodiment of the present invention;

[0037] Figure 4 A schematic diagram of a rolling bearing according to an embodiment of the present invention;

[0038] Figure 5 A schematic diagram of the gear-tooth slicing coupling effect according to an embodiment of the present invention;

[0039] Figure 6 is a comparison diagram of the time-varying meshing stiffness of the gear pair according to the embodiment of the present invention;

[0040] Figure 7 This is a diagram showing the effect of cracks on the vibration displacement of the driving wheel in an embodiment of the present invention;

[0041] Figure 8 This is a diagram showing the effect of cracks on the vibration displacement of the bearing 1 according to an embodiment of the present invention. DETAILED DESCRIPTION

[0042] The following embodiments of the technical solution of the present invention are described in detail in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and are therefore only used as examples, and cannot be used to limit the protection scope of the present invention.

[0043] It should be noted that, unless otherwise specified, the technical terms or scientific terms used in this application should have the common meanings understood by those skilled in the art to which the present invention belongs.

[0044] Example

[0045] Starting from the failure mechanism of the fault, this application explores the influence between gear cracks and the time-varying meshing stiffness of the gear and the system vibration, and provides a method for solving the coupling of gear crack stiffness calculation and system vibration considering the slice coupling, including the following steps:

[0046] Step S1, based on the number of teeth, module and dynamic meshing force of the gear pair, the bending stiffness, shear stiffness and axial compression stiffness of the sliced ​​gear teeth are calculated by using the slice method to obtain the gear tooth stiffness of the sliced ​​gear teeth;

[0047] Step S1 includes the following sub-steps:

[0048] Step S11, calculating the driving wheel meshing angle, the driven wheel meshing angle, the actual meshing angle and the contact line component according to the number of teeth, the module and the dynamic meshing force of the gear pair.

[0049] Specifically, the initial value of the dynamic meshing force of the gear pair is selected as the gear load, and then the driving wheel meshing angle, the driven wheel meshing angle, the actual meshing angle and the contact line component are calculated according to the number of teeth and module of the gear. The calculation method of this step is not limited, and any achievable method in the prior art can be selected for implementation.

[0050] Step S12: Slice the gear and calculate the bending stiffness, shear stiffness, and axial compression stiffness of the sliced ​​gear teeth according to the meshing angle of the driving gear, the meshing angle of the driven gear, the actual meshing angle, and the ratio of the contact line component to the number of gear slices.

[0051] In a specific embodiment, Figure 2 This is a schematic diagram of the parallel-stage transmission principle of a wind turbine gearbox. Figure 3 is a schematic diagram of the helical gear slice model. Figure 3 The bending stiffness k of the sliced ​​gear teeth shown in the figure is solved by the slice method bx , shear stiffness k sx , axial compression stiffness k ax , calculated according to the following formula (1):

[0052]

[0053] In the above formula, It represents the meshing angle variable, which refers to the angle between the meshing force and the perpendicular line of the gear centerline; is the driving wheel meshing angle, is the meshing angle of the driven gear, is the actual meshing angle of the driving wheel; is the actual meshing angle of the driven gear, Δy is the ratio of the contact line component to the number of gear slices, E is the elastic modulus, and v is the Poisson's ratio.

[0054] Step S13, calculating the slicing wheel tooth stiffness according to the bending stiffness, shear stiffness, and axial compression stiffness of the slicing wheel teeth

[0055] The slicing wheel tooth stiffness k is calculated according to the following formula (2): tx :

[0056]

[0057] The k calculated in the above formula (2) is tx , is the slicing wheel tooth stiffness in a healthy state.

[0058] Step S2: Calculate the slice coupling stiffness of the gear in a healthy state and in a cracked state according to whether the gear has cracks and the tooth stiffness of the sliced ​​gear teeth.

[0059] Step S2 includes the following sub-steps:

[0060] Step S21, judging whether there is a crack on the gear, the judging method is not limited and can be implemented in any achievable method in the prior art.

[0061] Step S22: When there is no crack, the slicing coupling stiffness k of the healthy gear is calculated according to the following formula in combination with the gear tooth stiffness of the slicing gear teeth: c :

[0062]

[0063] In the above formula, C c represents the slice coupling factor. When slice coupling is considered, the value is 1. t(n-1) represents the gear tooth stiffness of the (n-1)th slice, k t(n) represents the gear tooth stiffness of the nth slice, and the value is calculated by formula (2); M represents the module, and Δl represents the ratio of the tooth width to the number of gear tooth slices.

[0064] In some embodiments, considering the differences in the loading state of the slicing gear teeth, in order to accurately characterize the slicing coupling stiffness, a numerical method is used to correct the slicing coupling stiffness calculated by equation (3), and the correction process is as follows:

[0065] According to formula (1), the initial value k of the gear tooth slice stiffness in the healthy state is calculated: t(0) ;

[0066] Based on the calculated initial value k of the gear tooth slice stiffness t(0) , and then calculate the initial value of the slice coupling stiffness k according to formula (3): t(0) , and set the initial meshing deformation of the gear to u t0 ;

[0067] According to the static equilibrium equation F = k t u t , solve the load component F of the slicing gear teeth i , and then sum the load components to obtain the dynamic meshing force F of the gear pair mt(i) ;

[0068] Compare the calculated dynamic meshing force F of the gear pair mt(i) The initial value of the dynamic meshing force F of the gear pair input mt(0) , and define ε F is the convergence accuracy of the model ε F =|F mt(i) -F mt(i-1) |(i=1,2,3,…n), when ε F≤1.5, the calculation ends and the slice coupling stiffness is output; when ε F >1.5, based on the static equilibrium equation F=k t u t Calculate u t , and iterative calculations are continuously performed until the convergence accuracy meets the requirements, and the corrected slice coupling stiffness is output.

[0069] Step S23: When there is a crack, the slice coupling stiffness of the gear under the crack state is calculated according to the crack bending stiffness and crack shear stiffness.

[0070] After considering the crack, the bending stiffness and shear stiffness in equation (1) are modified, and the crack bending stiffness k of the slicing wheel tooth is bc and the crack shear stiffness k sc It can be expressed as the following formula:

[0071]

[0072] In the above formula, represents the meshing angle variable, is the driving wheel meshing angle, is the meshing angle of the driven gear, is the actual meshing angle of the driving wheel; is the actual meshing angle of the driven wheel, Δy is the ratio of the contact line component to the number of gear slices, E is the elastic modulus, q(y) is the ordinate of the crack end point, R b is the base circle radius, and v is the Poisson's ratio.

[0073] In some embodiments, the ordinate q(y) of the crack end point will be affected by two parameters, namely the effective cross-sectional area and the moment of inertia. Therefore, before using formula (4) to correct the bending stiffness and shear stiffness, the effective cross-sectional area and the moment of inertia of the gear can be calculated first, and (y) can be obtained based on the effective cross-sectional area and the moment of inertia, and then q(y) can be substituted into formula (4) for correction calculation.

[0074] After considering crack failure, the slice coupling stiffness k of the gear under crack state is tc It can be expressed as:

[0075]

[0076] In the above formula, k bc is the crack bending stiffness, k sc is the crack shear stiffness, k ax is the axial compressive stiffness, obtained in step 1. The axial compressive stiffness is not affected by cracks, so no correction is required.

[0077] For multiple gears in the system, there may be both healthy gears and cracked gears. Therefore, the slice coupling stiffness of the gears in healthy and cracked states needs to be solved in this step for use in subsequent steps.

[0078] S3. Based on the slice coupling stiffness of the gear in the healthy state and the crack state, combined with the contact stiffness and matrix stiffness of the gear, the time-varying meshing stiffness of the cracked gear of a single gear pair is calculated.

[0079] The slice coupling stiffness of the gear in a healthy state and a cracked state is obtained through step S2.

[0080] The time-varying mesh stiffness k(t) of a cracked gear in a single gear pair is calculated as follows:

[0081]

[0082] In the above formula, subscripts 1 and 2 correspond to the driving wheel and the driven wheel respectively;

[0083] k h is the Hertzian contact stiffness; k bc1 is the bending stiffness of the active wheel slicing gear teeth, k bc2 k is the crack bending stiffness of the driven wheel slicing tooth; sc1 is the shear stiffness of the active wheel slicing gear teeth, k sc2 k is the shear stiffness of the driven wheel slicing teeth; ax1 is the axial compression stiffness of the driving wheel, k ax2 is the axial compression stiffness of the driven wheel, k f1 is the base stiffness of the driving wheel, k f2 is the matrix stiffness of the driven wheel;

[0084] k tc represents the slice coupling stiffness under the gear crack state, k c represents the slice coupling stiffness of the gear in a healthy state, a 1 ,a 2 is the determination coefficient of the driving wheel slice coupling stiffness. When a certain slice gear pair of the driving wheel has cracks, a 1 =1, a 2 =0, when a certain gear pair of the driving wheel is in a healthy state, a 1 =0,a 2 =1; a 3 ,a 4 is the determination coefficient of the driven wheel slice coupling stiffness. When a slice gear pair of the driven wheel has a crack, a 3 =1, a 4 =0, when a certain slicing gear pair of the driven wheel is in a healthy state, a 3 =0,a 4=1;

[0085] k h , k b , k s , k a , k f Calculate as follows:

[0086]

[0087] In the above formula, v is Poisson's ratio, E is elastic modulus, B is gear width; x is the distance between the gear and the base circle, h is the gear height, is the driving wheel meshing angle, I x represents the moment of inertia of the gear at a distance x from the base circle; G represents the shear modulus, A x Indicates the cross-sectional area; L * 、M * , P * , Q * , S are the calculation coefficients of gear pair stiffness, and u is the gear depth.

[0088] S4. Based on the outer diameter, inner diameter and number of rolling elements of the ball bearing, combined with the dynamic load on the bearing, calculate the bearing support force, which includes axial force and radial force.

[0089] This step includes the following sub-steps:

[0090] S41, calculating the distance between the centers of curvature of the inner and outer rings of the ball bearing before the ball bearing is loaded based on the outer diameter, inner diameter and number of rolling elements of the ball bearing;

[0091] According to the initial contact angle of the ball, calculate the contact angle of the ball after the bearing is loaded;

[0092] According to the ball contact angle after the bearing is loaded, calculate the distance between the centers of curvature of the inner and outer rings of the bearing after the bearing is loaded;

[0093] The specific calculation formula for this step is as follows:

[0094]

[0095] In the above formula, α b0 Indicates the ball contact angle before the bearing is loaded, α b1 Indicates the ball contact angle after the bearing is loaded, L 0 Indicates the distance between the centers of curvature of the inner and outer rings of the bearing before loading, L 1 represents the distance between the centers of curvature of the inner and outer rings of the bearing after loading, x, y, and z represent the translational vibration displacement vector of the inner ring of the bearing, and r n represents the radius of the inner ring of the bearing, Λ represents the angular deformation of the bearing after being loaded, θ nrepresents the azimuth angle of the ball n; σ represents the contact deformation, and c represents the working clearance of the bearing.

[0096] S42. Use Hertz contact theory to determine the load state of the bearing. Consider the input end bearing as a 3-DOF model, obtain the normal deformation of the bearing, and decompose the normal contact pressure into axial force and radial force.

[0097] The Hertz contact theory is used to determine the load state of the bearing and obtain the normal deformation of the bearing. Specifically, the Heaviside function is introduced to determine the load state of the bearing, and the axial and radial components of the normal contact pressure are:

[0098]

[0099] In the above formula, F ca Indicates the axial force between the inner and outer ring raceways of the bearing, F cr Indicates the radial force between the inner and outer ring raceways of the bearing, K c It represents the comprehensive contact stiffness between the ball raceways, σ represents the contact deformation, λ represents the bearing coefficient, and for ball bearings, λ is taken as 1.5. It represents the contact angle of the bearing after loading, and H(σ) is the judgment coefficient of the Heaviside function.

[0100] S5. Construct the gear-bearing-coupling system dynamic equation based on the time-varying meshing stiffness of the cracked gear and the bearing support force of a single gear pair

[0101] According to the time-varying meshing stiffness of the cracked gear and the bearing support force of a single gear pair, the dynamic equation of the gear-bearing-coupling system is constructed. Specifically:

[0102] For gears, the dynamic equation is as follows: 1 For example:

[0103]

[0104] In the above formula, m 1 represents the mass of the driving wheel, g represents the acceleration due to gravity,

[0105] It represents the acceleration of the driving wheel in the x, y, and z directions.

[0106] k sx1 , k sy1 , k sz1 represents the shear stiffness of the driving wheel in the x, y, and z directions,

[0107] k sx2 , k sy2 , k sz2represents the shear stiffness of the driven wheel in the x, y, and z directions,

[0108] x 1 ,y 1 、z 1 It represents the displacement of the driving wheel in the x, y, and z directions.

[0109] x b1 ,y b1 、z b1 represents the vibration displacement of bearing 1 in the x, y, and z directions,

[0110] x b2 ,y b2 、z b2 represents the vibration displacement of bearing 2 in the x, y, and z directions,

[0111] c sx1 、c sy1 、c sz1 represents the bending damping of support axis 1 in the x, y, and z directions,

[0112] c sx2 、c sy2 、c sz2 represents the bending damping of the support shaft 2 in the x, y, and z directions,

[0113] Indicates the speed of the driving wheel in the x, y, and z directions,

[0114] represents the vibration speed of bearing 1 in the x, y, and z directions,

[0115] represents the vibration speed of bearing 2 in the x, y, and z directions,

[0116] F x 、F x 、F z They represent the forces on the driving wheel in the x, y, and z directions respectively.

[0117] J g1 represents the moment of inertia of the driving wheel, c t1 represents the torsional damping of the supporting shaft, k t1 represents the torsional stiffness of the supporting shaft;

[0118] represents the rotation acceleration of the driving wheel around the z-axis, represents the rotation speed of the driving wheel around the z-axis, θ 1 It represents the angular displacement of the driving wheel around the z-axis;

[0119] represents the torsional vibration speed of the input shaft, θi represents the angular displacement of the input shaft;

[0120] F m represents the dynamic meshing force of the gear pair, Indicates the base circle radius of the driving wheel.

[0121] For the bearing, its dynamic equation is as follows, taking bearing 1 as an example:

[0122]

[0123] In the above formula, J i Input shaft moment of inertia, k t1 is the torsional stiffness of the supporting shaft, T i is the input torque of the system;

[0124] is the torsional vibration acceleration of the input shaft, is the torsional vibration speed of the input shaft, θ i is the torsional angular displacement of the input shaft, is the rotation speed of the driving wheel around the z axis, θ 1 is the angular displacement of the driving wheel around the z-axis;

[0125] m b1 represents the mass of bearing 1, g represents the acceleration due to gravity,

[0126] represents the vibration acceleration of bearing 1 in the x, y, and z directions,

[0127] represents the vibration speed of bearing 1 in the x, y, and z directions,

[0128] x b1 ,y b1 、z b1 represents the vibration displacement of bearing 1 in the x, y, and z directions,

[0129] k sx1 , k sy1 , k sz1 It represents the shear stiffness of the driving wheel support shaft in the x, y, and z directions,

[0130] c sx1 、c sy1 、c sz1 represents the bending damping of support axis 1 in the x, y, and z directions,

[0131] x 1 ,y 1 、z 1 It represents the displacement of the driving wheel in the x, y, and z directions.

[0132] Indicates the speed of the driving wheel in the x, y, and z directions,

[0133] F bx1 、F by1 、F bz1 Indicates the forces on bearing 1 in the x, y, and z directions;

[0134] In this embodiment, in the gear-bearing system, the gear includes a driving wheel 1 and a driven wheel 2, and also includes bearing 1, bearing 2, bearing 3, bearing 4, support shaft 1 and support shaft 2. The dynamic equation of the driven wheel is similar to formula (10), and the dynamic equation of the bearing is similar to (11), which will not be repeated.

[0135] The dynamic equations of all gears and bearings are coupled together, and the dynamic equations of the gear-bearing-coupling system are established as follows:

[0136]

[0137] In the above formula, m a Indicates quality, represents acceleration, k a represents stiffness, x a represents displacement, c a represents damping, Indicates speed, F a Indicates the stress condition. Those skilled in the art should understand that the stiffness k a Associated with the time-varying mesh stiffness of the cracked gear, the stress condition F a Associated with bearing support force.

[0138] The Runge-Kutta method is used to solve the vibration response of the gear-bearing coupling system in equation (12), and the stiffness, damping, vibration displacement, vibration velocity, vibration acceleration of the gear and bearing components, as well as the dynamic meshing force of the gear can be obtained. The Runge-Kutta method is a high-precision classic single-step method for solving ordinary differential equations. For example, for the displacement X, the result obtained is as follows:

[0139] X=(X i ,x b1 ,y b1 ,z b1 ,x 1 ,y 1 ,z 1 ,X 1 ,x b2 ,y b2 ,z b2 ,x b3 ,y b3 ,zb3 ,x 2 ,y 2 ,z 2 ,X 2 ,x b4 ,y b4 ,z b4 ,X o ) T (13)

[0140] In the above formula, X i represents the torsional vibration displacement of the input shaft, X o represents the torsional vibration displacement of the output shaft, X 1 , X 2 Both represent the rotation displacement of the gear around the z axis, x i ,y i ,z i (i=1,2) represents the vibration displacement of the gear in the x, y, and z directions, x bi , Indicates the vibration displacement of the bearing in the x, y, and z directions.

[0141] To illustrate again, for the dynamic meshing force of gears, it can be obtained based on the above relationship: dynamic meshing force multiplied by the base circle radius of the gear is equal to torque.

[0142] The solving equations for other indicators such as stiffness and damping can be implemented according to the calculation principles of the prior art and will not be repeated here.

[0143] In some embodiments, in order to obtain a more accurate solution to formula (12), the initial results obtained by solving formula (12), including vibration displacement, vibration velocity, vibration acceleration, etc., can be input into the gear-bearing-coupling system dynamics equation again, and multiple iterative calculations are performed until a preset end time is reached. Specifically, the end time is set according to actual needs.

[0144] The technical solution of this embodiment takes into account the slicing coupling effect of the cracked gear along the tooth width direction when establishing the gear-bearing-coupling system dynamics equation, and introduces the slicing coupling stiffness of the cracked gear in the tooth width direction to construct the system dynamics equation. The constructed system dynamics equation also comprehensively considers time-varying factors such as the dynamic meshing force of the gear pair and the dynamic support force of the rolling bearing, and can more accurately analyze the influence of the tooth root crack on the time-varying meshing stiffness of the gear and the vibration characteristics of the system; the solved dynamic meshing force of the gear and the vibration displacement of the bearing can provide an important reference for the early fault diagnosis of the wind turbine gearbox.

[0145] In some embodiments, a computer program product is also provided, including a computer program / instruction, which, when executed by a processor, implements the steps of the method for solving the gear crack stiffness calculation and system vibration coupling considering the slice coupling as described above.

[0146] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

Claims

1. A method for calculating the crack stiffness of gears with slice coupling and solving the coupling of system vibration, characterized in that: The following steps are involved: Based on the number of teeth, module and dynamic meshing force of gear pair, the bending stiffness, shear stiffness and axial compression stiffness of the sliced ​​gear teeth are calculated by slice method to obtain the gear stiffness of the sliced ​​gear teeth. According to whether there is a crack in the gear, the slice coupling stiffness of the gear in the healthy state and the crack state is calculated respectively in combination with the tooth stiffness of the sliced ​​gear teeth; According to the slice coupling stiffness of the gear in healthy state and crack state, combined with the contact stiffness and matrix stiffness of the gear, the time-varying meshing stiffness of the cracked gear of a single gear pair is calculated; Calculate the bearing support force based on the outer diameter, inner diameter and number of rolling elements of the ball bearing, combined with the dynamic load on the bearing; According to the time-varying meshing stiffness of the cracked gear and the bearing support force of a single gear pair, the dynamic equation of the gear-bearing-coupling system is constructed, and the vibration response of the gear-bearing coupling system is solved.

2. The method for calculating gear crack stiffness and coupling system vibration considering slice coupling according to claim 1 is characterized in that: Based on the number of teeth, module and dynamic meshing force of the gear pair, the slicing method is used to calculate the bending stiffness, shear stiffness and axial compression stiffness of the sliced ​​gear teeth, and the tooth stiffness of the sliced ​​gear teeth is obtained, including: Calculate the driving wheel meshing angle, driven wheel meshing angle, actual meshing angle and contact line component according to the number of teeth, module and dynamic meshing force of the gear pair; The gear is sliced, and the bending stiffness, shear stiffness, and axial compression stiffness of the sliced ​​gear teeth are calculated based on the meshing angle of the driving gear, the meshing angle of the driven gear, the actual meshing angle, and the ratio of the contact line component to the number of gear slices. The slicing wheel tooth stiffness is calculated based on the slicing wheel tooth's bending stiffness, shear stiffness, and axial compression stiffness.

3. The method for calculating gear crack stiffness and coupling system vibration considering slice coupling according to claim 1 is characterized in that: The slice coupling stiffness of the gear under healthy condition is calculated according to the following formula: In the above formula, C c represents the slice coupling factor, k t(n-1) represents the gear tooth stiffness of the (n-1)th slice, k t(n) represents the gear tooth stiffness of the nth slice, M represents the module, and Δl represents the ratio of the tooth width to the number of gear tooth slices.

4. The method for calculating gear crack stiffness and coupling system vibration considering slice coupling according to claim 1 is characterized in that: When there is a crack in the gear, the following formula is used to calculate the crack bending stiffness k of the slicer gear tooth: bc and the crack shear stiffness k sc : In the above formula, represents the meshing angle variable, is the driving wheel meshing angle, is the meshing angle of the driven wheel, ζ1′ is the actual meshing angle of the driving wheel; is the actual meshing angle of the driven wheel, Δy is the ratio of the contact line component to the number of gear slices, E is the elastic modulus, q(y) is the ordinate of the crack end point, R b is the base circle radius, and v is the Poisson's ratio.

5. The method for calculating gear crack stiffness and coupling system vibration considering slice coupling according to claim 4 is characterized in that: The slice coupling stiffness of the gear under crack state is calculated according to the following formula: k bc is the crack bending stiffness, k sc is the crack shear stiffness, k ax is the axial compressive stiffness.

6. The method for calculating gear crack stiffness and coupling system vibration considering slice coupling according to claim 1 is characterized in that: The time-varying mesh stiffness k(t) of a cracked gear in a single gear pair is calculated as follows: The time-varying mesh stiffness k(t) of a cracked gear in a single gear pair is calculated as follows: In the above formula, k h is the Hertzian contact stiffness; k bc1 is the bending stiffness of the active wheel slicing gear teeth, k bc2 k is the crack bending stiffness of the driven wheel slicing tooth; sc1 is the shear stiffness of the active wheel slicing gear teeth, k sc2 k is the shear stiffness of the driven wheel slicing teeth; ax1 is the axial compression stiffness of the driving wheel, k ax2 is the axial compression stiffness of the driven wheel, k f1 is the base stiffness of the driving wheel, k f2 is the base stiffness of the driven wheel; k tc represents the slice coupling stiffness under the gear crack state, k c It represents the slice coupling stiffness of the gear under healthy state, a1 and a2 are the determination coefficients of the slice coupling stiffness of the driving wheel, and a3 and a4 are the determination coefficients of the slice coupling stiffness of the driven wheel.

7. The method for calculating gear crack stiffness and coupling system vibration considering slice coupling according to claim 1 is characterized in that: The bearing support force includes axial force and radial force, which are calculated using the following formula: In the above formula, F ca Indicates the axial force between the inner and outer ring raceways of the bearing, F cr Indicates the radial force between the inner and outer ring raceways of the bearing, K c It represents the comprehensive contact stiffness between the ball raceways, σ represents the contact deformation, λ represents the bearing coefficient, and for ball bearings, λ is taken as 1.

5. It represents the contact angle of the bearing after loading, and H(σ) is the judgment coefficient of the Heaviside function.

8. The method for calculating gear crack stiffness and coupling system vibration considering slice coupling according to claim 1 is characterized in that: The dynamic equation of the gear-bearing-coupling system is as follows: In the above formula, m a Indicates quality, represents acceleration, k a represents stiffness, x a represents displacement, c a represents damping, Indicates speed, F a Indicates the stress condition.

9. The method for calculating gear crack stiffness and coupling system vibration considering slice coupling according to claim 1 is characterized in that: The Runge-Kutta method is used to solve the vibration response of the gear-bearing coupling system, and the stiffness, damping, vibration displacement, vibration velocity, vibration acceleration of the gear and bearing components and the dynamic meshing force of the gear are obtained.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by the processor, the steps of the method for solving the gear crack stiffness calculation and system vibration coupling considering the slice coupling as described in any one of claims 1 to 9 are implemented.

Images