A Numerical Calculation Method, System, Device and Readable Storage Medium for Bevel Gears

Abstract

The present invention discloses a bevel gear numerical calculation method, system, device and readable storage medium. The bevel gear numerical calculation method includes: obtaining gear parameter information; constructing a finite element model according to the gear parameter information and calculating the overall stiffness matrix of the finite element model; calculating the meshing force of the meshing nodes at different rotation angles by using the loaded contact analysis method according to the gear parameter information; applying fixed displacement boundary conditions to the internal gear ring of the gear in the finite element model to simulate the stationary state of the internal gear ring of the gear; mapping the meshing force of the meshing nodes at different rotation angles to the tooth surface of the finite element model to obtain the tooth surface meshing force result, so as to realize the distribution of the meshing force on the tooth surface; calculating the gear deformation result according to the overall stiffness matrix and the tooth surface meshing force result; and calculating the tooth surface contact stress and the tooth root bending stress based on the gear deformation result. The bevel gear numerical calculation method of the embodiment of the present invention can calculate the tooth surface contact stress and the tooth root bending stress efficiently and accurately.

Description

Technical Field

[0001] The present invention relates to the technical field of gears, and more particularly to a bevel gear numerical calculation method, system, device and readable storage medium. Background Art

[0002] Currently, there is no standard mathematical representation of the tooth profile of bevel gears. Therefore, precise tooth surface design requires a combination of theory and actual manufacturing processes. The numerical values of bevel gears include tooth surface contact stress and tooth root bending stress. By analyzing the tooth surface contact stress and tooth root bending stress, the strength check and fatigue life prediction of bevel gears can be carried out. In the prior art, the finite element method is generally used to calculate the tooth surface contact stress and tooth root bending stress. However, the modeling using the finite element method is cumbersome and the calculation efficiency is low. Summary of the Invention

[0003] The present invention aims to at least solve one of the technical problems existing in the prior art. For this reason, the present invention proposes a bevel gear numerical calculation method, which can efficiently and accurately calculate the tooth surface contact stress and tooth root bending stress, and quickly optimize the design parameters of bevel gears to meet the requirements of strength check and fatigue life.

[0004] The present invention also provides a bevel gear numerical calculation system, as well as a control device and a computer-readable storage medium for executing the above bevel gear numerical calculation method.

[0005] According to the bevel gear numerical calculation method of the first aspect embodiment of the present invention, the method includes:

[0006] Obtain gear parameter information;

[0007] Construct a finite element model according to the gear parameter information, and calculate the overall stiffness matrix of the finite element model;

[0008] According to the gear parameter information, use the loaded contact analysis method to calculate the meshing force of the meshing nodes at different rotation angles;

[0009] Apply a fixed displacement boundary condition to the inner gear ring of the finite element model to simulate the stationary state of the inner gear ring of the gear;

[0010] Map the meshing forces of the meshing nodes at different rotation angles to the tooth surface of the finite element model to obtain the tooth surface meshing force result, so as to realize the distribution of the meshing force on the tooth surface;

[0011] Calculate the gear deformation result according to the overall stiffness matrix and the tooth surface meshing force result;

[0012] Calculate the tooth surface contact stress and tooth root bending stress based on the gear deformation result.

[0013] The bevel gear numerical calculation method according to the embodiments of the present invention has at least the following beneficial effects:

[0014] First, a finite element model is constructed and the overall stiffness matrix of the finite element model is calculated. Then, the loading contact analysis method is used to calculate the meshing forces of the meshing nodes at different rotation angles. Next, fixed displacement boundary conditions are applied to the inner gear ring of the finite element model to simulate the stationary state of the inner gear ring of the gear. After that, the meshing forces of the meshing nodes at different rotation angles are mapped to the tooth surface of the finite element model as force boundary conditions to obtain the tooth surface meshing force result, so as to realize the distribution of the meshing force on the tooth surface. Finally, the gear deformation result is solved according to the overall stiffness matrix and the tooth surface meshing force result, and finally the tooth surface contact stress and the tooth root bending stress are calculated. The bevel gear numerical calculation method according to the embodiments of the present invention combines the advantages of the loading contact analysis method and the finite element analysis method, first quickly calculates the meshing forces of the meshing nodes at different rotation angles, and then maps the meshing forces to the finite element model, which can improve the calculation efficiency of the tooth surface contact stress and the tooth root bending stress.

[0015] According to some embodiments of the present invention, the gear deformation result calculated according to the overall stiffness matrix and the tooth surface meshing force result is realized through the following constraint formula:

[0016] F；

[0017] Where, K represents the overall stiffness matrix, represents the gear deformation result, F represents the tooth surface meshing force result.

[0018] According to some embodiments of the present invention, the meshing forces of the meshing nodes at different rotation angles are mapped to the tooth surface of the finite element model to obtain the tooth surface meshing force result, so as to realize the distribution of the meshing force on the tooth surface, including:

[0019] Obtain all the node numbers on the tooth surface of the finite element model;

[0020] Determine the correspondence between each of the node numbers and each of the meshing nodes;

[0021] According to the correspondence, map the meshing forces of each of the meshing nodes at different rotation angles to the tooth surface of the finite element model to obtain the tooth surface meshing force result, so as to realize the distribution of the meshing force on the tooth surface.

[0022] According to some embodiments of the present invention, the calculation of the gear deformation result according to the overall stiffness matrix and the tooth surface meshing force result includes:

[0023] Decompose the overall stiffness matrix using the Cholesky decomposition method to obtain the decomposition result;

[0024] Calculate the gear deformation result based on the decomposition result and the tooth surface contact force result.

[0025] According to some embodiments of the present invention, the contact forces at each meshing node are obtained through the following steps:

[0026] Calculate the contact deformation result using the influence coefficient method based on the gear parameter information;

[0027] Determine the contact forces at each meshing node based on the contact deformation result.

[0028] According to some embodiments of the present invention, the contact deformation result includes the initial contact deformation relationship, the combined elastic deformation relationship of the gear pair, and the torque balance relationship. Determining the contact forces at each meshing node based on the contact deformation result includes:

[0029] Determine the contact forces at each meshing node based on the initial contact deformation relationship, the combined elastic deformation relationship of the gear pair, and the torque balance relationship.

[0030] According to some embodiments of the present invention, the overall stiffness matrix is obtained through the following steps:

[0031] Calculate multiple element stiffness matrices of the finite element model based on the gear parameter information;

[0032] Superimpose each of the element stiffness matrices and assemble them into the overall stiffness matrix.

[0033] According to the bevel gear numerical calculation system of the second aspect embodiments of the present invention, the system includes:

[0034] A gear parameter information acquisition module for acquiring gear parameter information;

[0035] A finite element model construction module for constructing a finite element model based on the gear parameter information and calculating the overall stiffness matrix of the finite element model;

[0036] A contact force calculation module for calculating the contact forces at meshing nodes at different rotation angles using the loaded contact analysis method based on the gear parameter information;

[0037] A fixed displacement boundary condition application module for applying a fixed displacement boundary condition to the inner gear ring of the finite element model to simulate the stationary state of the inner gear ring of the gear;

[0038] A meshing force mapping module, configured to map the meshing forces of meshing nodes at different rotation angles to the tooth surfaces of the finite element model, so as to obtain the tooth surface meshing force results, thereby realizing the distribution of the meshing forces on the tooth surfaces;

[0039] A gear deformation result calculation module, configured to calculate the gear deformation results according to the overall stiffness matrix and the tooth surface meshing force results;

[0040] A stress calculation module, configured to calculate the tooth surface contact stress and the tooth root bending stress based on the gear deformation results.

[0041] The bevel gear numerical calculation system according to an embodiment of the present invention has at least the following beneficial effects:

[0042] First, a finite element model is constructed and the overall stiffness matrix of the finite element model is calculated. Then, the loading contact analysis method is used to calculate the meshing forces of meshing nodes at different rotation angles. Next, a fixed displacement boundary condition is applied to the inner gear ring of the gear in the finite element model to simulate the stationary state of the inner gear ring of the gear. After that, the meshing forces of meshing nodes at different rotation angles are mapped to the tooth surfaces of the finite element model as force boundary conditions to obtain the tooth surface meshing force results, thereby realizing the distribution of the meshing forces on the tooth surfaces. Finally, the gear deformation results are solved according to the overall stiffness matrix and the tooth surface meshing force results, and finally the tooth surface contact stress and the tooth root bending stress are calculated. The bevel gear numerical calculation system according to the embodiment of the present invention combines the advantages of the loading contact analysis method and the finite element analysis method, first quickly calculates the meshing forces of meshing nodes at different rotation angles, and then maps the meshing forces to the finite element model, which can improve the calculation efficiency of the tooth surface contact stress and the tooth root bending stress.

[0043] The control device according to the third aspect embodiment of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the bevel gear numerical calculation method as described in the first aspect embodiment above. Since the control device adopts all the technical solutions of the bevel gear numerical calculation method in the above embodiment, it has at least all the beneficial effects brought by the technical solutions of the above embodiment.

[0044] The computer-readable storage medium according to the fourth aspect embodiment of the present invention stores computer-executable instructions, and the computer-executable instructions are used to execute the bevel gear numerical calculation method as described in the first aspect embodiment above. Since the computer-readable storage medium adopts all the technical solutions of the bevel gear numerical calculation method in the above embodiment, it has at least all the beneficial effects brought by the technical solutions of the above embodiment.

[0045] Other features and advantages of the present invention will be described in the following specification, and some of them will become obvious from the specification or be understood by implementing the present invention. Brief Description of the Drawings

[0046] The above and / or additional aspects and advantages of the present invention will become apparent and be readily understood from the following description of embodiments in conjunction with the accompanying drawings, where:

[0047] Figure 1 is a flowchart of a bevel gear numerical calculation method according to an embodiment of the present invention;

[0048] Figure 2 is a schematic diagram of the initial contact state of the spiral bevel gear contact deformation according to an embodiment of the present invention;

[0049] Figure 3 is a schematic diagram of the loaded contact state of the spiral bevel gear contact deformation according to an embodiment of the present invention;

[0050] Figure 4 is a schematic diagram of the discretization of the contact area according to an embodiment of the present invention;

[0051] Figure 5 is a force analysis diagram of the spiral bevel gear according to an embodiment of the present invention;

[0052] Figure 6 is a schematic diagram of a hexahedron 8-node element according to an embodiment of the present invention;

[0053] Figure 7 is a schematic diagram of the application of the fixed displacement boundary condition according to an embodiment of the present invention;

[0054] Figure 8 is a schematic diagram of the application of the meshing force according to an embodiment of the present invention;

[0055] Figure 9 is a contact force nephogram at the moment of the maximum Mises stress under 500 Nm obtained by the bevel gear numerical calculation method according to an embodiment of the present invention;

[0056] Figure 10 is a Mises nephogram of the gear section at the moment of the maximum Mises stress under 500 Nm obtained by the bevel gear numerical calculation method according to an embodiment of the present invention;

[0057] Figure 11 is a comparison diagram of the maximum Mises of different mesh layers of the driving wheel under 500 Nm obtained by the bevel gear numerical calculation method according to an embodiment of the present invention;

[0058] Figure 12 is a comparison diagram of the maximum Mises at different analysis steps of the driving wheel under 500 Nm obtained by the bevel gear numerical calculation method according to an embodiment of the present invention;

[0059] Figure 13It is the tooth root bending stress nephogram of the driving gear under 500 Nm obtained by the bevel gear numerical calculation method of an embodiment of the present invention;

[0060] Figure 14 It is the tooth root bending stress nephogram of the driving gear under 500 Nm obtained by the finite element method in the prior art;

[0061] Figure 15 It is the comparison chart of the tooth root bending stress under different torques obtained by the bevel gear numerical calculation method of an embodiment of the present invention and the finite element method in the prior art. Detailed implementation manners

[0062] The embodiments of the present invention will be described in detail below. The examples of the embodiments are shown in the drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the drawings are exemplary and are only used to explain the present invention and should not be construed as a limitation of the present invention.

[0063] In the description of the present invention, if the first, second, etc. are described only for the purpose of distinguishing technical features, it cannot be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features or implicitly indicating the sequence of the indicated technical features.

[0064] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by terms such as up, down, etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus cannot be understood as a limitation of the present invention.

[0065] In the description of the present invention, it should be noted that unless otherwise clearly defined, terms such as setting, installation, connection, etc. should be understood in a broad sense, and those skilled in the art can reasonably determine the specific meanings of the above terms in the present invention in combination with the specific content of the technical solution.

[0066] At present, there is no standard mathematical representation of the tooth profile of bevel gears. Therefore, precise tooth surface design requires a combination of theory and actual manufacturing processes. The numerical values of bevel gears include tooth surface contact stress and tooth root bending stress. By analyzing the tooth surface contact stress and tooth root bending stress, the strength check and fatigue life prediction of bevel gears can be carried out. In the prior art, the finite element method is generally used to calculate the tooth surface contact stress and tooth root bending stress. However, the contact analysis of the finite element method is a strongly nonlinear problem, and this nonlinearity mainly comes from the change of the contact relationship. Nonlinear problems usually require iterative solutions, and each iteration will increase the calculation cost. In contact analysis, searching for nodes and elements that may come into contact is a time-consuming process. Especially in large-scale models, the number of nodes and elements is huge, and contact search will significantly increase the calculation time. Contact problems require special contact algorithms to handle, such as the penalty function method, the Lagrange multiplier method, etc. These algorithms usually require additional computing resources and need to gradually approach the actual contact state, increasing the calculation time.

[0067] Based on this, the embodiments of the present invention provide a bevel gear numerical calculation method, system, device and readable storage medium, which can efficiently and accurately calculate the tooth surface contact stress and tooth root bending stress, and quickly optimize the design parameters of bevel gears to meet the requirements of strength check and fatigue life.

[0068] The following will be combined with Figures 1 to 15 to clearly and completely describe the bevel gear numerical calculation method of the embodiments of the present invention. Obviously, the following described embodiments are part of the embodiments of the present invention, not all embodiments.

[0069] The bevel gear numerical calculation method according to the first aspect embodiment of the present invention includes:

[0070] Obtain gear parameter information;

[0071] Construct a finite element model according to the gear parameter information, and calculate the overall stiffness matrix of the finite element model;

[0072] According to the gear parameter information, use the loaded contact analysis method to calculate the meshing force of the meshing nodes at different rotation angles;

[0073] Apply fixed displacement boundary conditions to the inner tooth ring of the gear in the finite element model to simulate the static state of the inner tooth ring of the gear;

[0074] Map the meshing forces of the meshing nodes at different rotation angles to the tooth surface of the finite element model to obtain the tooth surface meshing force result, so as to realize the distribution of the meshing force on the tooth surface;

[0075] Calculate the gear deformation result according to the overall stiffness matrix and the tooth surface meshing force result;

[0076] The tooth surface contact stress and the tooth root bending stress are calculated based on the gear deformation results.

[0077] It can be understood that the loaded contact analysis method mainly conducts basic tooth surface performance analysis on bevel gears, can quickly obtain contact imprints, loaded transmission errors, calculate the meshing forces at the meshing nodes at different rotation angles, etc., and has high calculation efficiency. However, because the real three-dimensional model is not considered, the tooth surface contact stress and the tooth root bending stress cannot be accurately calculated. By quickly obtaining the meshing force through the loaded contact analysis method and mapping the meshing force to the finite element model, the tooth surface contact stress and the tooth root bending stress can be calculated quickly and accurately, combining the advantages of both.

[0078] The gear parameter information is shown in Table 1:

[0079] Table 1

[0080]

[0081] As Figure 2 and Figure 3 shown, Figure 2 is a schematic diagram of the initial contact state of the spiral bevel gear contact deformation in an embodiment of the present invention, Figure 3 is a schematic diagram of the loaded contact state of the spiral bevel gear contact deformation in an embodiment of the present invention. and respectively represent the tooth surfaces of the driving gear and the driven gear. During the elastic deformation process, and have displacements of and respectively along the meshing force direction to approach each other. According to the geometric relationship, the total deformation amount of the two tooth surfaces is obtained:

[0082] Formula (1)

[0083] wherein, is the total deformation amount, is the displacement amount along the meshing force direction is the displacement amount along the meshing force direction.

[0084] Figure 2 and Figure 3 in and are respectively two corresponding points on the tooth surfaces and The initial interval between the two is h , and are respectively and Elastic deformation under load. Therefore, the tooth surface contact deformation coordination relationship can be expressed as:

[0085] Formula (2)

[0086] Wherein, is the contact area of the tooth surface.

[0087] In some embodiments of the present invention, the meshing forces at each meshing node are obtained through the following steps:

[0088] According to the gear parameter information, the influence coefficient method is used to calculate the contact deformation result;

[0089] Determine the meshing forces at each meshing node according to the contact deformation result.

[0090] It can be understood that the traditional model often uses the Hertz contact theory to calculate the contact deformation, which is mainly calculated based on the curvature radii at the initial meshing points of two surfaces. The Hertz contact theory cannot effectively predict the edge contact position, and at the same time, it cannot perform the preliminary calculation of the contact pressure and contact stress corresponding to the edge contact. Therefore, the present invention uses the influence coefficient method to calculate the contact deformation of spiral bevel gears, which can effectively predict the edge contact position, and at the same time, can perform the preliminary calculation of the contact pressure and contact stress corresponding to the edge contact, so as to calculate the more accurate meshing forces at each meshing node.

[0091] The present invention uses the influence coefficient method to calculate the contact deformation of spiral bevel gears. To solve the elastic contact problem, the initially estimated contact area must be larger than the actual contact area. Therefore, the entire projection of the driving gear on the tangent plane is set as the initial contact area. Taking the initial contact point O as the origin to establish a Cartesian coordinate system, as Figure 4 shown. Wherein z axis is parallel to the normal vector of the initial contact point, and the plane xoy coincides with the tangent plane. The initial contact area is discretized into M N evenly distributed rectangular grid points, where the grid spacings along the x axis and y axis are 2 a and 2 b respectively. The position of each node can be represented by ( i , j ), where i and j are the row number and column number of the node respectively. The tooth surfaces and are discretized in the same way. ( , ) is the node (i , j ), the coordinates. The nodes ( i , j ) The initial distance between the two surfaces is denoted as .

[0092] When the driving wheel and the driven wheel are in contact, a normal contact pressure is generated on the tooth surface and each tooth surface deforms inward. u ( x , y ) represents the deformation amount of the two tooth surfaces at the point ( x , y ). The contact pressure distribution p ( x , y ) and the surface deformation distribution u ( x , y ) The relationship between them can be expressed as:

[0093] Formula (3)

[0094] Among them, is the initial contact area, K ( x , y ) is the influence coefficient, which represents the surface deformation distribution of the unit normal concentrated force acting on the origin. It can be obtained from formula (4):

[0095] Formula (4)

[0096] Among them, and are the Poisson's ratios of the driving wheel and the driven wheel respectively, and are the Young's moduli of the driving wheel and the driven wheel respectively. The initial contact area is discretized into rectangular grid points. Therefore, formula (3) can be rewritten as:

[0097] Formula (5)

[0098] Among them, I represents the set of all nodes in the initial contact area, I= {( i , j ): 1 , 1 }, and represent the surface deformation and pressure distribution of the unit centered on the node ( k , l ).

[0099] The influence coefficient can be expressed as:

[0100] Formula (6)

[0101] According to Formula (2) and Formula (5), the tooth surface contact deformation coordination relationship of the gear pair (i.e., the initial contact deformation relationship in the embodiments of the present invention) can be expressed as:

[0102] Formula (7)

[0103] Wherein, and are calculated by using a preset iterative algorithm. is the normal meshing force when single-tooth meshing, is all the set of nodes in the initial contact area.

[0104] In some embodiments of the present invention, the contact deformation results include the initial contact deformation relationship, the total elastic deformation relationship of the gear pair, and the torque balance relationship. Determining the meshing force of each meshing node according to the contact deformation results includes:

[0105] Determine the meshing force of each meshing node according to the initial contact deformation relationship, the total elastic deformation relationship of the gear pair, and the torque balance relationship.

[0106] The force analysis of the spiral bevel gear is as Figure 5 shown. The normal meshing force when single-tooth meshing can be obtained by the following formula:

[0107] Formula (8)

[0108] Wherein, T is the load torque, and are the unit normal vectors of the meshing point in the x axis and y the components in the direction of the axis, is the moment arm of the meshing point around the z axis.

[0109] Under the total elastic deformation relationship of the gear pair, the total elastic deformation corresponding to single-tooth meshing can be expressed as the sum of the transverse tooth deformation of the driving wheel, the axial tooth deformation of the driving wheel, the transverse tooth deformation of the driven wheel, the axial tooth deformation of the driven wheel, and the maximum tooth surface contact deformation i.e.:

[0110] Formula (9)

[0111] It can be seen from Equation (9) that the deformation coordination relationship of the single-tooth meshing gear pair is mainly a function of the meshing force. When the spiral bevel gear is in multi-tooth meshing, the load distribution among multiple teeth will be involved. Therefore, when in multi-tooth meshing, in addition to satisfying Equations and, the deformation coordination relationship of the spiral bevel gear must also satisfy the torque balance relationship, that is:

[0112] Equation (10)

[0113] Wherein, n is the number of tooth pairs participating in meshing, is the tooth pair j the meshing force received is the tooth pair j of z the lever arm in the axial direction of the shaft, and are respectively the unit normal vectors at the meshing points of the tooth pair j the components in the directions of the on x axis and y axis.

[0114] The meshing forces at each meshing node need to be obtained by combining Equation (7), Equation (8), Equation (9) and Equation (10).

[0115] It should be noted that the specific principle and process of calculating the meshing force at the meshing node at different rotation angles by using the loaded contact analysis method are the prior art known to those skilled in the art, and will not be further described herein.

[0116] As Figure 6 shown, Figure 6 is a schematic diagram of a hexahedral 8-node element in an embodiment of the present invention. The finite element model of the embodiment of the present invention is established by using hexahedral elements. Each node has 3 degrees of freedom. For the node, its shape function is expressed as:

[0117] Equation (11)

[0118] Wherein, is the integration point coordinate, The value of is selected according to the positions of each node in the isoparametric coordinate system.

[0119] In some embodiments of the present invention, the overall stiffness matrix is obtained through the following steps:

[0120] Calculate multiple element stiffness matrices of the finite element model according to the gear parameter information;

[0121] Superimpose each element stiffness matrix and assemble it into an overall stiffness matrix.

[0122] The calculation formula of the element stiffness matrix is as follows:

[0123]

[0124] Formula (12)

[0125] Wherein, and are the strain matrices in the global coordinate system and the isoparametric coordinate system respectively, D is the constitutive matrix, , , are the Gauss weights, is the number of Gauss points in each direction, which is 2 here, J is the Jacobian matrix.

[0126] Since the 8-node hexahedral element is prone to shear locking, in order to ensure the calculation accuracy, the B-bar method proposed by Hughes is used to process the linear hexahedral element, and the element strain matrix is decomposed into the volumetric strain part and the deviatoric strain part :

[0127] Formula (13)

[0128] The specific values are as follows:

[0129] Formula (14)

[0130] Wherein,

[0131] Formula (15)

[0132] Wherein, ( i = 1, 2, 3) is the value of when takes the value of 1.

[0133] It should be noted that the specific principle and process of superimposing and assembling the element stiffness matrices into the global stiffness matrix are the existing technologies known to those skilled in the art, and will not be elaborated here.

[0134] As Figure 7 shown, Figure 7 is a schematic diagram of applying the fixed displacement boundary condition in an embodiment of the present invention. It can be understood that applying the fixed displacement boundary condition to the inner gear ring of the finite element model means that the fixed displacement boundary condition needs to be applied to each node of the entire inner gear ring to simulate the static state of the entire inner gear ring. Figure 7The triangle of the inner gear ring of the middle gear represents a fixed constraint, and the nodes to be constrained correspond to the global stiffness matrix K The stiffness matrix at the diagonal position Increase times. Since the nodal displacements at this constraint are set to 0, the forces at the corresponding nodes do not need to be operated on, indicating that the nodes are fixed.

[0135] It should be noted that the specific principle and process of applying the fixed displacement boundary condition to the inner gear ring of the gear in the finite element model are the prior art known to those skilled in the art and will not be elaborated here.

[0136] In some embodiments of the present invention, referring to Figure 8 , Figure 8 is a schematic diagram of the application of the meshing force in an embodiment of the present invention. The meshing forces of the meshing nodes at different rotation angles are mapped to the tooth surface of the finite element model to obtain the tooth surface meshing force result, so as to realize the distribution of the meshing force on the tooth surface, including:

[0137] Obtain all the node numbers on the tooth surface of the finite element model;

[0138] Determine the correspondence between each node number and each meshing node;

[0139] According to the correspondence, map the meshing forces of each meshing node at different rotation angles to the tooth surface of the finite element model to obtain the tooth surface meshing force result, so as to realize the distribution of the meshing force on the tooth surface.

[0140] It can be understood that the component forces of the meshing force corresponding to the meshing node in each direction can be calculated according to the normal vector of the finite element model node under fixation. The schematic diagram of the application of the meshing force is as Figure 8 shown, the arrow direction indicates the application direction of the meshing force, and the length of the arrow represents the relative magnitude of each meshing force.

[0141] In some embodiments of the present invention, the gear deformation result is calculated according to the global stiffness matrix and the tooth surface meshing force result, and is realized through the following constraint formula:

[0142] F Formula (16)

[0143] Wherein, K represents the global stiffness matrix, represents the gear deformation result, F represents the tooth surface meshing force result.

[0144] In some embodiments of the present invention, the gear deformation result is calculated according to the global stiffness matrix and the tooth surface meshing force result, including:

[0145] The overall stiffness matrix is decomposed using the Cholesky decomposition method to obtain the decomposition result;

[0146] Based on the decomposition result and the tooth surface contact force result, the gear deformation result is calculated.

[0147] By using the Cholesky decomposition method (Cholesky decomposition) to decompose the overall stiffness matrix, and then calculating the gear deformation result based on the decomposition result and the tooth surface contact force result, the calculation speed will be faster.

[0148] It should be noted that the specific principle and process of the Cholesky decomposition method are existing technologies known to those skilled in the art, and will not be elaborated here.

[0149] After obtaining the gear deformation result, the tooth surface contact stress and the tooth root bending stress can be calculated based on the gear deformation result. After obtaining the gear deformation result, the strain value at the Gauss point is solved, and then the strain value at the Gauss point is interpolated to the element nodes to obtain the strain of each element node. According to the constitutive relation formula, the stress value of each element node is obtained, and finally, a smoothing operation is performed on the stress value:

[0150] Formula (17)

[0151] Among them, is the strain, B is the element strain matrix, is the displacement.

[0152] Formula (18)

[0153] Among them, is the stress value, D is the elastic matrix.

[0154] When predicting the strength and life of the gear, the von Mises stress and the maximum principal stress of the node are used. The calculation formulas are as follows:

[0155] Formula (19)

[0156] Formula (20)

[0157] Formula (21)

[0158] Among them, is x , y and z the normal stress in the , , direction, x ,y and z Shear stress in the z direction. According to formulas (19), (20) and (21), the von Mises stress at any point can be obtained, and the largest real root of formula (20) is the maximum principal stress.

[0159] The tooth surface contact stress is analyzed based on the von Mises stress, and the tooth root bending stress is analyzed based on the maximum principal stress.

[0160] It should be noted that how to calculate the tooth surface contact stress and the tooth root bending stress based on the gear deformation results is the prior art known to those skilled in the art, and will not be elaborated here.

[0161] According to the bevel gear numerical calculation method of the embodiment of the present invention, first, a finite element model is constructed and the overall stiffness matrix of the finite element model is calculated. Then, the loading contact analysis method is used to calculate the meshing force of the meshing nodes at different rotation angles. Then, a fixed displacement boundary condition is applied to the inner gear ring of the finite element model to simulate the stationary state of the inner gear ring of the gear. After that, the meshing forces of the meshing nodes at different rotation angles are mapped to the tooth surface of the finite element model as the force boundary condition to obtain the tooth surface meshing force result to realize the distribution of the meshing force on the tooth surface. Finally, the gear deformation result is solved according to the overall stiffness matrix and the tooth surface meshing force result, and finally the tooth surface contact stress and the tooth root bending stress are calculated. The bevel gear numerical calculation method of the embodiment of the present invention combines the advantages of the loading contact analysis method and the finite element analysis method, first quickly calculates the meshing forces of the meshing nodes at different rotation angles, and then maps the meshing forces to the finite element model, which can improve the calculation efficiency of the tooth surface contact stress and the tooth root bending stress.

[0162] Such as Figure 9 and Figure 10 shown, Figure 9 is the contact force nephogram at the moment of the maximum Mises stress under 500 Nm obtained by the bevel gear numerical calculation method of an embodiment of the present invention, Figure 10 is the Mises nephogram of the gear cross-section at the moment of the maximum Mises stress under 500 Nm obtained by the bevel gear numerical calculation method of an embodiment of the present invention. It can be seen from the contact force distribution that the current analysis step is single-tooth contact, making the Mises stress of the current analysis step the maximum value in the entire meshing cycle. Figure 10 is Figure 9 the Mises nephogram of a small piece of tooth profile framed in Figure 9 which is the three-dimensional expression of Figure 10 and it can be seen from

[0163] The tooth surface contact stress is mainly directly related to the contact fatigue strength of the gear and is the main cause of faults such as pitting and wear on the tooth surface. Figure 11 shows the comparison diagram of the maximum Mises of different mesh layers of the driving gear under 500 Nm obtained by the bevel gear numerical calculation method of an embodiment of the present invention. From Figure 9 It can be seen that whether the results obtained by the finite element method or the bevel gear numerical calculation method of the embodiment of the present invention, during the process from the surface layer to the interior, the Mises stress value first decreases and then increases, and continues to decay after reaching the maximum value, which also conforms to the classical Hertz contact conclusion. Since the contact area calculated by the bevel gear numerical calculation method of the embodiment of the present invention is slightly smaller than that of the finite element method, its Mises stress is larger than that of the finite element method. Figure 12 shows the change of the Mises value with the rotation of the driving gear in the fifth layer mesh of the finite element model. It can be seen that within one meshing cycle, the results of the bevel gear numerical calculation method and the finite element method of the embodiment of the present invention are very close, and the maximum Mises error is 1.12%.

[0164] The tooth root bending stress is directly related to the bending fatigue strength of the gear and is the main cause of tooth fracture. Different from contact fatigue, gear bending fatigue failure often starts from the surface of the tooth root, manifested as cracks appearing at the tooth root part, and the cracks gradually expand and lead to tooth fracture. Figure 13 and Figure 14 show the maximum principal stress at the tooth root, which is crucial for verifying the bending strength and providing the parameters required for predicting bending fatigue. Figure 13 is the tooth root bending stress nephogram of the driving gear under 500 Nm obtained by the bevel gear numerical calculation method of an embodiment of the present invention, Figure 14 is the tooth root bending stress nephogram of the driving gear under 500 Nm obtained by the finite element method in the prior art. The differences in stress distribution and magnitude between these two methods are very small. Figure 15 shows the maximum tooth root bending stress at different rotation angles throughout the meshing cycle. Under loads of 50, 100, 200, 500, and 1000 Nm, the trends of the maximum tooth root bending stress of the bevel gear numerical calculation method and the finite element method of the embodiment of the present invention at different rotation angles are the same, and there are only slight differences in magnitude. The specific errors are shown in Table 2:

[0165] Table 2

[0166]

[0167] where is the maximum error of the maximum tooth root bending stress throughout the meshing cycle, is the minimum error. Throughout the meshing cycle, the errors of the maximum and minimum tooth root bending stresses do not exceed 4%, which indicates that the bevel gear numerical calculation method of the embodiment of the present invention has high calculation accuracy.

[0168] While ensuring the accuracy, the calculation efficiency of the bevel gear numerical calculation method according to the embodiments of the present invention has also been greatly improved, as shown in Table 3 specifically. Compared with the finite element method, its calculation speed is 66.7 times faster, greatly improving the calculation efficiency of the parameters required for the strength check and fatigue life prediction of bevel gears.

[0169] Table 3

[0170] Number of units Computation time consumed Proposed method 732780 991.5 s Finite element software 732780 17.34 h

[0171] It should be noted that the bevel gear numerical calculation method according to the embodiments of the present invention can be applied to the gear transmission system in the aviation field, as well as automobiles, ships or other mechanical equipment using gear transmission systems. The specific application scenarios are not specifically limited herein.

[0172] According to the bevel gear numerical calculation system of the second aspect embodiment of the present invention, it includes a gear parameter information acquisition module, a finite element model construction module, a meshing force calculation module, a fixed displacement boundary condition application module, a meshing force mapping module, a gear deformation result calculation module, and a stress calculation module.

[0173] The gear parameter information acquisition module is used to acquire gear parameter information;

[0174] The finite element model construction module is used to construct a finite element model according to the gear parameter information and calculate the overall stiffness matrix of the finite element model;

[0175] The meshing force calculation module is used to calculate the meshing force of the meshing nodes at different rotation angles by using the loaded contact analysis method according to the gear parameter information;

[0176] The fixed displacement boundary condition application module is used to apply fixed displacement boundary conditions to the inner tooth ring of the gear of the finite element model to simulate the stationary state of the inner tooth ring of the gear;

[0177] The meshing force mapping module is used to map the meshing force of the meshing nodes at different rotation angles to the tooth surface of the finite element model to obtain the tooth surface meshing force result, so as to realize the distribution of the meshing force on the tooth surface;

[0178] The gear deformation result calculation module is used to calculate the gear deformation result according to the overall stiffness matrix and the tooth surface meshing force result;

[0179] The stress calculation module is used to calculate the tooth surface contact stress and the tooth root bending stress based on the gear deformation result.

[0180] Since the bevel gear numerical calculation system adopts all the technical solutions of the bevel gear numerical calculation method of the above embodiments, it has at least all the beneficial effects brought by the technical solutions of the above embodiments.

[0181] For the bevel gear numerical calculation system according to an embodiment of the present invention, first, a finite element model is constructed and the overall stiffness matrix of the finite element model is calculated. Then, the loading contact analysis method is used to calculate the meshing force of the meshing nodes at different rotation angles. Next, a fixed displacement boundary condition is applied to the inner gear ring of the finite element model to simulate the stationary state of the inner gear ring of the gear. After that, the meshing forces of the meshing nodes at different rotation angles are mapped to the tooth surface of the finite element model as the force boundary condition to obtain the tooth surface meshing force result, so as to realize the distribution of the meshing force on the tooth surface. Finally, the gear deformation result is solved according to the overall stiffness matrix and the tooth surface meshing force result, and finally the tooth surface contact stress and the tooth root bending stress are calculated. The bevel gear numerical calculation system according to the embodiment of the present invention combines the advantages of the loading contact analysis method and the finite element analysis method, first quickly calculates the meshing force of the meshing nodes at different rotation angles, and then maps the meshing force to the finite element model, which can improve the calculation efficiency of the tooth surface contact stress and the tooth root bending stress.

[0182] In addition, an embodiment of the present invention also provides a control device, which includes: a memory, a processor, and a computer program stored on the memory and executable on the processor. The processor and the memory can be connected through a bus or other means.

[0183] As a non-transitory computer-readable storage medium, the memory can be used to store non-transitory software programs and non-transitory computer-executable programs. In addition, the memory may include a high-speed random access memory, and may also include non-transitory memory, such as at least one magnetic disk storage device, a flash memory device, or other non-transitory solid-state storage devices. In some embodiments, the memory may optionally include a memory remotely disposed relative to the processor, and these remote memories can be connected to the processor through a network. Examples of the above network include but are not limited to the Internet, an enterprise intranet, a local area network, a mobile communication network, and combinations thereof.

[0184] The non-transitory software programs and instructions required to implement the air conditioner control method of the above embodiment are stored in the memory, and when executed by the processor, execute the bevel gear numerical calculation method in the above embodiment.

[0185] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, that is, they may be located in one place, or may be distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0186] In addition, an embodiment of the present invention further provides a computer-readable storage medium storing computer-executable instructions, which are executed by a processor or a controller, for example, executed by the above-mentioned processor, enabling the above-mentioned processor to execute the bevel gear numerical calculation method in the above-mentioned embodiment.

[0187] Those of ordinary skill in the art can understand that all or some of the steps and systems in the methods disclosed above can be implemented as software, firmware, hardware, and their appropriate combinations. Some physical components or all physical components can be implemented as software executed by a processor, such as a central processing unit, a digital signal processor, or a microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include a computer storage medium (or a non-transitory medium) and a communication medium (or a transitory medium). As is well known to those of ordinary skill in the art, the term computer storage medium includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information, such as computer-readable instructions, data structures, program modules, or other data. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory, or other memory technologies, CD-ROM, digital versatile disk (DVD), or other optical disk storage, magnetic cassette, tape, magnetic disk storage, or other magnetic storage devices, or any other medium that can be used to store the desired information and can be accessed by a computer. In addition, as is well known to those of ordinary skill in the art, a communication medium generally includes computer-readable instructions, data structures, program modules, or other data in a modulated data signal, such as a carrier wave or other transmission mechanism, and can include any information delivery medium.

[0188] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments. Various changes can be made without departing from the spirit of the present invention within the scope of knowledge possessed by those of ordinary skill in the art.

Claims

1. A numerical calculation method for bevel gears, characterized in that, The method includes: Obtaining gear parameter information; Constructing a finite element model according to the gear parameter information and calculating the overall stiffness matrix of the finite element model; Calculating the meshing force of the meshing nodes at different rotation angles by using the loaded contact analysis method according to the gear parameter information; Applying fixed displacement boundary conditions to the internal gear ring of the finite element model to simulate the stationary state of the internal gear ring of the gear; Mapping the meshing forces of the meshing nodes at different rotation angles to the tooth surface of the finite element model to obtain the tooth surface meshing force result, so as to realize the distribution of the meshing force on the tooth surface; Calculating the gear deformation result according to the overall stiffness matrix and the tooth surface meshing force result; Calculating the tooth surface contact stress and the tooth root bending stress based on the gear deformation result.

2. The bevel gear numerical calculation method according to claim 1, characterized in that The calculation of the gear deformation result according to the overall stiffness matrix and the tooth surface meshing force result is realized through the following constraint formula: F； Among them, K represents the overall stiffness matrix, represents the gear deformation result, F represents the tooth surface contact force result.

3. The bevel gear numerical calculation method according to claim 1, wherein The mapping of the meshing forces of the meshing nodes at different rotation angles to the tooth surface of the finite element model to obtain the tooth surface meshing force result, so as to realize the distribution of the meshing force on the tooth surface, includes: Obtaining all the node numbers on the tooth surface of the finite element model; Determining the corresponding relationship between each of the node numbers and each of the meshing nodes; Mapping the meshing forces of each of the meshing nodes at different rotation angles to the tooth surface of the finite element model according to the corresponding relationship to obtain the tooth surface meshing force result, so as to realize the distribution of the meshing force on the tooth surface.

4. The bevel gear numerical calculation method according to claim 1, characterized in that The calculation of the gear deformation result according to the overall stiffness matrix and the tooth surface meshing force result includes: Decomposing the overall stiffness matrix by using the Cholesky decomposition method to obtain a decomposition result; Calculating the gear deformation result according to the decomposition result and the tooth surface meshing force result.

5. The bevel gear numerical calculation method according to claim 1, characterized in that The meshing force of each of the meshing nodes is obtained through the following steps: Calculating the contact deformation result by using the influence coefficient method according to the gear parameter information; Determining the meshing force of each of the meshing nodes according to the contact deformation result.

6. The bevel gear numerical calculation method according to claim 5, wherein The contact deformation result includes an initial contact deformation relationship, a gear pair total elastic deformation relationship and a torque balance relationship. The determination of the meshing force of each of the meshing nodes according to the contact deformation result includes: Determining the meshing force of each of the meshing nodes according to the initial contact deformation relationship, the gear pair total elastic deformation relationship and the torque balance relationship.

7. The bevel gear numerical calculation method according to claim 1, wherein The overall stiffness matrix is obtained through the following steps: Calculating a plurality of element stiffness matrices of the finite element model according to the gear parameter information; Superposing each of the element stiffness matrices and assembling them into the overall stiffness matrix.

8. A bevel gear numerical calculation system, characterized in that, The system includes: A gear parameter information acquisition module for acquiring gear parameter information; A finite element model construction module for constructing a finite element model according to the gear parameter information and calculating the overall stiffness matrix of the finite element model; A meshing force calculation module for calculating the meshing force of the meshing nodes at different rotation angles by using the loaded contact analysis method according to the gear parameter information; A fixed displacement boundary condition application module, which is used to apply fixed displacement boundary conditions to the internal gear ring of the finite element model to simulate the static state of the internal gear ring of the gear; A meshing force mapping module, which is used to map the meshing forces of meshing nodes at different rotation angles to the tooth surface of the finite element model to obtain the tooth surface meshing force result, so as to realize the distribution of meshing forces on the tooth surface; A gear deformation result calculation module, which is used to calculate the gear deformation result according to the overall stiffness matrix and the tooth surface meshing force result; A stress calculation module, which is used to calculate the tooth surface contact stress and the tooth root bending stress based on the gear deformation result.

9. A control device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the bevel gear numerical calculation method according to any one of claims 1 to 7.

10. A computer-readable storage medium storing computer-executable instructions, characterized in that, The computer executable instructions are used to execute the bevel gear numerical calculation method according to any one of claims 1 to 7.

Images