Bevel gear numerical calculation method, system and device and readable storage medium

Abstract

The invention discloses a bevel gear numerical calculation method, system and device and a readable storage medium. The bevel gear numerical calculation method comprises the steps that gear parameter information is acquired; constructing a finite element model according to the gear parameter information, and calculating an overall stiffness matrix of the finite element model; according to the gear parameter information, a loading contact analysis method is adopted to calculate meshing force of meshing nodes at different rotating angles; applying a fixed displacement boundary condition to the gear inner gear ring of the finite element model to simulate the static state of the gear inner gear ring; mapping the meshing force of the meshing nodes at different corners to the tooth surface of the finite element model to obtain a tooth surface meshing force result so as to realize distribution of the meshing force on the tooth surface; a gear deformation result is calculated according to the overall stiffness matrix and the tooth surface meshing force result; and calculating tooth surface contact stress and tooth root bending stress based on a gear deformation result. According to the bevel gear numerical calculation method provided by the embodiment of the invention, the tooth surface contact stress and the tooth root bending stress can be efficiently and accurately calculated.

Description

Technical Field

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

[0002] At present, there is no standard mathematical representation of bevel gear tooth profiles. Therefore, accurate tooth surface design requires a combination of theory and actual manufacturing processes. Bevel gear numerical values ​​include tooth surface contact stress and tooth root bending stress. By analyzing tooth surface contact stress and tooth root bending stress, the strength of bevel gears can be checked and fatigue life can be predicted. In the prior art, the finite element method is generally used to calculate tooth surface contact stress and tooth root bending stress, but the finite element method is cumbersome to model and has low calculation efficiency. Summary of the invention

[0003] The present invention aims to solve at least one of the technical problems existing in the prior art. To this end, 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 bevel gear design parameters to meet the requirements of strength verification and fatigue life.

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

[0005] According to a bevel gear numerical calculation method according to a first aspect of the present invention, the method comprises: Get gear parameter information; Constructing a finite element model according to the gear parameter information, and calculating an overall stiffness matrix of the finite element model; According to the gear parameter information, a loading contact analysis method is used to calculate the meshing force of meshing nodes at different rotation angles; Applying a fixed displacement boundary condition to the gear ring of the finite element model to simulate a stationary state of the gear ring; Mapping the meshing force of the meshing nodes at different rotation angles to the tooth surface of the finite element model to obtain the meshing force result of the tooth surface to achieve 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; The tooth surface contact stress and tooth root bending stress are calculated based on the gear deformation result.

[0006] The bevel gear numerical calculation method according to the embodiment of the present invention has at least the following beneficial effects: First, a finite element model is constructed and the overall stiffness matrix of the finite element model is calculated. Then, the meshing force of the meshing nodes at different rotation angles is calculated by using the loading contact analysis method. Then, a fixed displacement boundary condition is applied to the inner gear ring of the gear of the finite element model to simulate the static state of the inner gear ring of the gear. Then, the meshing force of the meshing nodes at different rotation angles is mapped to the tooth surface of the finite element model as a force boundary condition to obtain the tooth surface meshing force result to achieve 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 the tooth surface contact stress and tooth root bending stress are finally calculated. The numerical calculation method of bevel gears in 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 tooth root bending stress.

[0007] According to some embodiments of the present invention, the gear deformation result is calculated based on the overall stiffness matrix and the tooth surface meshing force result, and is implemented by the following constraint formula: F； in, K represents the global stiffness matrix, represents the gear deformation result, F Represents the tooth surface meshing force result.

[0008] According to some embodiments of the present invention, mapping 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 results to achieve the distribution of the meshing force on the tooth surface includes: Obtaining all node numbers on the tooth surface of the finite element model; Determining the correspondence between each of the node numbers and each of the meshing nodes; According to the corresponding relationship, the meshing force of each meshing node at different rotation angles is 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.

[0009] According to some embodiments of the present invention, the step of calculating the gear deformation result according to the overall stiffness matrix and the tooth surface meshing force result includes: Decomposing the overall stiffness matrix using the Cholesky decomposition method to obtain a decomposition result; The gear deformation result is calculated based on the decomposition result and the tooth surface meshing force result.

[0010] According to some embodiments of the present invention, the meshing force of each meshing node is obtained by the following steps: According to the gear parameter information, the contact deformation result is calculated by using the influence coefficient method; The meshing force of each meshing node is determined according to the contact deformation result.

[0011] According to some embodiments of the present invention, the contact deformation result includes an initial contact deformation relationship, a total elastic deformation relationship of the gear pair, and a torque balance relationship, and determining the meshing force of each meshing node according to the contact deformation result includes: The meshing force of each meshing node is determined according to the initial contact deformation relationship, the total elastic deformation relationship of the gear pair and the torque balance relationship.

[0012] According to some embodiments of the present invention, the global stiffness matrix is ​​obtained by the following steps: Calculating multiple unit stiffness matrices of the finite element model according to the gear parameter information; The individual unit stiffness matrices are superimposed and assembled into the overall stiffness matrix.

[0013] According to a bevel gear numerical calculation system of a second aspect of the present invention, the system comprises: A gear parameter information acquisition module is used to acquire gear parameter information; A finite element model building module, used to build a finite element model according to the gear parameter information and calculate the overall stiffness matrix of the finite element model; A meshing force calculation module, used to calculate the meshing force of meshing nodes at different rotation angles using a loading contact analysis method according to the gear parameter information; A fixed displacement boundary condition applying module, used for applying a fixed displacement boundary condition to the gear inner ring of the finite element model to simulate the stationary state of the gear inner ring; A meshing force mapping module is used to map the meshing force of the meshing nodes at different rotation angles onto the tooth surface of the finite element model to obtain the meshing force result of the tooth surface, so as to realize the distribution of the meshing force on the tooth surface; A gear deformation result calculation module, used for calculating the gear deformation result according to the overall stiffness matrix and the tooth surface meshing force result; 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.

[0014] The bevel gear numerical calculation system according to the embodiment of the present invention has at least the following beneficial effects: First, a finite element model is constructed and the overall stiffness matrix of the finite element model is calculated. Then, the meshing force of the meshing nodes at different rotation angles is calculated by using the loading contact analysis method. Then, a fixed displacement boundary condition is applied to the inner gear ring of the gear of the finite element model to simulate the static state of the inner gear ring of the gear. Then, the meshing force of the meshing nodes at different rotation angles is mapped to the tooth surface of the finite element model as a force boundary condition to obtain the tooth surface meshing force result to achieve 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 the tooth surface contact stress and tooth root bending stress are finally calculated. The bevel gear numerical calculation system 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 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 tooth root bending stress.

[0015] According to the third aspect of the present invention, the control device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the bevel gear numerical calculation method as described in the first aspect of the present invention when executing the computer program. Since the control device adopts all the technical solutions of the bevel gear numerical calculation method of the above embodiment, it has at least all the beneficial effects brought by the technical solutions of the above embodiment.

[0016] According to the computer-readable storage medium of the fourth aspect embodiment of the present invention, computer-executable instructions are stored, and the computer-executable instructions are used to execute the bevel gear numerical calculation method as described in the first aspect embodiment. Since the computer-readable storage medium adopts all the technical solutions of the bevel gear numerical calculation method of the above embodiment, it at least has all the beneficial effects brought by the technical solutions of the above embodiment.

[0017] Other features and advantages of the present invention will be set forth in the description which follows, and in part will be apparent from the description, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which: Figure 1 is a flow chart of a bevel gear numerical calculation method according to an embodiment of the present invention; Figure 2 is a schematic diagram of an initial contact state of contact deformation of a spiral bevel gear according to an embodiment of the present invention; Figure 3 is a schematic diagram of a loaded contact state of a spiral bevel gear contact deformation according to an embodiment of the present invention; Figure 4is a discrete schematic diagram of contact areas according to an embodiment of the present invention; Figure 5 This is a force analysis diagram of a spiral bevel gear according to an embodiment of the present invention; Figure 6 is a schematic diagram of a hexahedral 8-node unit according to an embodiment of the present invention; Figure 7 is a schematic diagram of applying a fixed displacement boundary condition according to an embodiment of the present invention; Figure 8 is a schematic diagram of the application of meshing force according to an embodiment of the present invention; Fig. 9 is a contact force cloud diagram at the maximum Mises stress moment of 500 Nm obtained by a bevel gear numerical calculation method according to an embodiment of the present invention; Fig.10 is a Mises cloud diagram of a gear cross section at the moment of maximum Mises stress under 500 Nm obtained by a numerical calculation method for bevel gears according to an embodiment of the present invention; Fig.11 This is a comparison diagram of the maximum Mises of different grid layers of the driving wheel at 500 Nm obtained by the numerical calculation method of bevel gears in one embodiment of the present invention; Fig.12 This is a comparison diagram of the maximum Mises under different analysis steps of the driving wheel at 500 Nm obtained by the numerical calculation method of bevel gears in one embodiment of the present invention; Fig.13 This is a cloud diagram of the tooth root bending stress of the driving wheel at 500 Nm obtained by the bevel gear numerical calculation method according to one embodiment of the present invention; Fig.14 It is a bending stress cloud diagram of the tooth root of the driving wheel under 500Nm obtained by the finite element method in the prior art; Fig.15 It is a comparison diagram of tooth root bending stress under different torques obtained by a bevel gear numerical calculation method according to an embodiment of the present invention and a finite element method in the prior art. DETAILED DESCRIPTION

[0019] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0020] In the description of the present invention, if there is a description of first, second, etc., it is only for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0021] In the description of the present invention, it should be understood that descriptions involving orientation, such as orientation or positional relationship indicated as up, down, etc., are based on the orientation or positional relationship shown in the drawings, and are 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 therefore should not be understood as a limitation on the present invention.

[0022] In the description of the present invention, it should be noted that, unless otherwise clearly defined, terms such as setting, installing, connecting, etc. should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meanings of the above terms in the present invention in combination with the specific content of the technical solution.

[0023] At present, there is no standard mathematical representation of the tooth profile of bevel gears. Therefore, accurate tooth surface design requires a combination of theory and actual manufacturing process. Bevel gear numerical values ​​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 performed. In the prior art, the finite element method is generally used to calculate the tooth surface contact stress and tooth root bending stress, but the contact analysis of the finite element method is a strong 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 computational cost. In contact analysis, searching for nodes and units that may be in contact is a time-consuming process, especially in large-scale models, where the number of nodes and units is huge, and contact search will significantly increase the calculation time. Contact problems require special contact algorithms to deal with, such as penalty function method, Lagrange multiplier method, etc. These algorithms usually require additional computing resources and gradually approach the actual contact state, which increases the calculation time.

[0024] Based on this, an embodiment of the present invention provides 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 bevel gear design parameters to meet the requirements of strength verification and fatigue life.

[0025] The following will be combined Figures 1 to 15 A clear and complete description is given of the numerical calculation method for bevel gears according to an embodiment of the present invention. Obviously, the embodiment described below is only a part of the embodiments of the present invention, but not all of the embodiments.

[0026] A bevel gear numerical calculation method according to a first aspect of the present invention includes: Get gear parameter information; Construct a finite element model based on gear parameter information and calculate the overall stiffness matrix of the finite element model; According to the gear parameter information, the meshing force of the meshing nodes at different rotation angles is calculated by using the loading contact analysis method; Apply fixed displacement boundary conditions to the gear ring of the finite element model to simulate the stationary state of the gear ring; The meshing force of the meshing nodes at different rotation angles is mapped to the tooth surface of the finite element model to obtain the meshing force results of the tooth surface, so as to realize the distribution of the meshing force on the tooth surface; The gear deformation results are calculated based on the overall stiffness matrix and the tooth surface meshing force results; The tooth surface contact stress and tooth root bending stress are calculated based on the gear deformation results.

[0027] It is understandable that the loading contact analysis method is mainly used to perform basic tooth surface performance analysis on bevel gears. It can quickly obtain contact marks, load transmission errors, calculate the meshing force of meshing nodes at different rotation angles, etc. It has high calculation efficiency, but because it does not consider the real three-dimensional model, it cannot accurately calculate the tooth surface contact stress and tooth root bending stress. The meshing force can be quickly obtained by the loading contact analysis method, and the meshing force can be mapped to the finite element model to quickly and accurately calculate the tooth surface contact stress and tooth root bending stress, combining the advantages of both.

[0028] The gear parameter information is shown in Table 1: Table 1

[0029] like Figure 2 and Figure 3 As shown, Figure 2 is a schematic diagram of an initial contact state of a spiral bevel gear contact deformation according to an embodiment of the present invention, Figure 3 Schematic diagram of the loaded contact state of the contact deformation of the spiral bevel gear according to an embodiment of the present invention. and Represent the tooth surfaces of the driving wheel and the driven wheel respectively. In the process of elastic deformation, and Along the meshing force direction, and The displacement of the two tooth surfaces is close to each other. According to the geometric relationship, the total deformation of the two tooth surfaces is: Formula (1) in, is the total deformation, for Displacement along the meshing force direction for Displacement along the direction of meshing force.

[0030] Figure 2 and Figure 3 middle and Tooth surface and The initial interval between the two corresponding points on h , and They are and Elastic deformation under load. Therefore, the coordination relationship of tooth surface contact deformation can be expressed as: Formula (2) in, is the contact area of ​​the tooth surface.

[0031] In some embodiments of the present invention, the meshing force of each meshing node is obtained by the following steps: According to the gear parameter information, the contact deformation results are calculated using the influence coefficient method; The meshing force of each meshing node is determined based on the contact deformation results.

[0032] It is understandable that the traditional model often uses the Hertz contact theory to calculate the contact deformation, which is mainly based on the curvature radius at the initial meshing point of the two surfaces. The Hertz contact theory cannot achieve effective prediction of the edge contact position, and it is also unable to perform preliminary calculations 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 the spiral bevel gear, which can achieve effective prediction of the edge contact position, and can also perform preliminary calculations of the contact pressure and contact stress corresponding to the edge contact, thereby calculating a more accurate meshing force of each meshing node.

[0033] The present invention uses the influence coefficient method to calculate the contact deformation of spiral bevel gears. In order to solve the elastic contact problem, the initial estimated contact area must be larger than the actual contact area. Therefore, the entire projection of the driving wheel on the tangent plane is set as the initial contact area. O Create a Cartesian coordinate system for the origin, such as Figure 4 As shown. z The 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 as M N A uniformly distributed rectangular grid of points along x Axis and y The grid spacing of the axes is 2 a and 2 b . Each node position can be used ( i , j ) indicates that i and j are the row and column numbers of the nodes respectively. and Discretize. , ) is the node ( i , j ) coordinates. i , j The initial distance between the two surfaces at ) is recorded as .

[0034] When the driving wheel and the driven wheel are in contact, normal contact pressure is generated on the tooth surfaces and each tooth surface is deformed inward. u ( x , y ) indicates that the two tooth surfaces are at point ( x , y ). Contact pressure distribution p ( x , y ) and surface deformation distribution u ( x , y ) can be expressed as: Formula (3) in, is the initial contact area, K ( x , y ) is the influence coefficient, which represents the surface deformation distribution when the unit normal concentrated force acts on the origin. It can be obtained from formula (4): Formula (4) in, and are the Poisson's ratios of the driving wheel and the driven wheel, and are the Young's modulus of the driving wheel and the driven wheel respectively. The initial contact area is discretized into rectangular grid points, so formula (3) can be re-expressed as: Formula (5) in, I represents the set of all nodes in the initial contact area, I= {( i , j ):1 , 1 }, and Indicates that the node ( k , l ) as the center of the cell.

[0035] The influence coefficient can be expressed as: Formula (6) According to formula (2) and formula (5), the coordination relationship of the tooth surface contact deformation of the gear pair (that is, the initial contact deformation relationship in the embodiment of the present invention) can be expressed as: Formula (7) in, and It is calculated using a preset iterative algorithm. is the normal meshing force when single tooth is meshing, All the A collection of nodes.

[0036] In some embodiments of the present invention, the contact deformation result includes an initial contact deformation relationship, a total elastic deformation relationship of the gear pair, and a torque balance relationship. The meshing force of each meshing node is determined according to the contact deformation result, including: The meshing force of each meshing node is determined according to the initial contact deformation relationship, the total elastic deformation relationship of the gear pair and the torque balance relationship.

[0037] The force analysis of spiral bevel gears is as follows: Figure 5 As shown. The normal meshing force when single teeth are meshing can be obtained by the following formula: Formula (8) in, T is the load torque, and are the unit normal vectors of the meshing point exist x Axis and y The component in the axial direction, For the meshing point z The moment arm in the axial direction.

[0038] Under the relationship of total elastic deformation of gear pair, the total elastic deformation of gear pair corresponding to single tooth meshing is It can be expressed as the lateral gear tooth deformation of the driving wheel , Axial gear tooth deformation of driving wheel , Transverse gear tooth deformation of driven wheel , Axial gear tooth deformation of the driven wheel And the maximum contact deformation of the tooth surface The sum is: Formula (9) From formula (9), it can be seen that the deformation coordination relationship of a single-tooth meshing gear pair is mainly a function of the meshing force. When the spiral bevel gear is meshing with multiple teeth, the load distribution between multiple teeth will be involved. Therefore, when multiple teeth are meshing, the deformation coordination relationship of the spiral bevel gear must not only satisfy the formula and, but also the torque balance relationship, that is: Formula (10) in, n is the number of gear teeth involved in meshing, For tooth pair j The meshing force For tooth pair j of z The moment arm in the axial direction, and Gear pairs j Unit normal vector at the meshing point exist x Axis and y Component in the direction of the axis.

[0039] The meshing force of each meshing node needs to be obtained by combining formula (7), formula (8), formula (9) and formula (10).

[0040] It should be noted that the specific principle and process of calculating the meshing force of meshing nodes at different rotation angles using the loading contact analysis method are prior arts known to those skilled in the art and will not be further described herein.

[0041] like Figure 6 As shown, Figure 6 Schematic diagram of a hexahedral 8-node unit in one embodiment of the present invention. The finite element model of the embodiment of the present invention is established using hexahedral units. Each node has 3 degrees of freedom. For a node, its shape function is expressed as: Formula (11) in, are the integration point coordinates, The value of is chosen based on the position of each node in the isoparametric coordinate system.

[0042] In some embodiments of the present invention, the global stiffness matrix is ​​obtained by the following steps: Calculate multiple unit stiffness matrices of the finite element model based on gear parameter information; The stiffness matrices of each unit are superimposed and assembled into an overall stiffness matrix.

[0043] The calculation formula of the element stiffness matrix is ​​as follows:

[0044] Formula (12) in, and are the strain matrices in the global coordinate system and the isoparametric coordinate system, respectively. D is the constitutive matrix, , , is the Gaussian weight, is the number of Gaussian points in each direction, here it is 2, J is the Jacobian matrix.

[0045] Since the hexahedral 8-node element is prone to shear self-locking linearity, in order to ensure the accuracy of the calculation, the B-bar method proposed by Hughes is used to process the linear hexahedral element. Decomposition into volume strain components and the deviatoric strain part : Formula (13) The specific values ​​are as follows: Formula (14) in, Formula (15) in, ( i =1, 2, 3) is of The value when it is 1.

[0046] It should be noted that the specific principle and process of superimposing the individual unit stiffness matrices and assembling them into an overall stiffness matrix are prior arts known to those skilled in the art and will not be elaborated herein.

[0047] like Figure 7 As shown, Figure 7 It is a schematic diagram of applying a fixed displacement boundary condition according to an embodiment of the present invention. It can be understood that applying a fixed displacement boundary condition to the gear ring of the finite element model requires applying a fixed displacement boundary condition to each node of the entire gear ring to simulate the static state of the entire gear ring. Figure 7 The triangle of the inner gear ring in the middle gear represents the fixed constraint, and the global stiffness matrix corresponding to the constraint node will be required K Stiffness matrix at diagonal locations Increase Since the node displacement of the constraint is set to 0, the force of the corresponding node does not need to be operated, indicating that the node is fixed.

[0048] It should be noted that the specific principle and process of applying the fixed displacement boundary condition to the gear ring of the finite element model are prior arts known to those skilled in the art and will not be elaborated herein.

[0049] In some embodiments of the present invention, reference Figure 8 , Figure 8The meshing force of the meshing nodes at different rotation angles is mapped to the tooth surface of the finite element model to obtain the meshing force result of the tooth surface to achieve the distribution of the meshing force on the tooth surface, including: Get all node numbers on the tooth surface of the finite element model; Determine the correspondence between each node number and each meshing node; According to the corresponding relationship, the meshing force of each meshing node under different rotation angles is mapped to the tooth surface of the finite element model to obtain the tooth surface meshing force result to realize the distribution of the meshing force on the tooth surface.

[0050] It can be understood that the meshing force components in each direction corresponding to the meshing node can be calculated based on the fixed finite element model node normal vector. Figure 8 As shown, the direction of the arrow indicates the direction in which the meshing force is applied, and the length of the arrow indicates the relative size of each meshing force.

[0051] In some embodiments of the present invention, the gear deformation result is calculated based on the overall stiffness matrix and the tooth surface meshing force result, which is achieved by the following constraint formula: F Formula (16) in, K represents the global stiffness matrix, represents the gear deformation result, F It represents the meshing force result of the tooth surface.

[0052] In some embodiments of the present invention, the gear deformation result is calculated based on the overall stiffness matrix and the tooth surface meshing force result, including: The overall stiffness matrix is ​​decomposed by using the Cholesky decomposition method to obtain the decomposition result; The gear deformation results are calculated based on the decomposition results and the tooth surface meshing force results.

[0053] The Cholesky decomposition method is used to decompose the overall stiffness matrix, and then the gear deformation result is calculated based on the decomposition result and the tooth surface meshing force result, which will make the calculation speed faster.

[0054] It should be noted that the specific principle and process of the Cholesky decomposition method are prior arts known to those skilled in the art and will not be described in detail here.

[0055] After obtaining the gear deformation results, the tooth surface contact stress and tooth root bending stress can be calculated based on the gear deformation results. After obtaining the gear deformation results, the strain value of the Gauss point is solved, and then the strain value of the Gauss point is interpolated to the unit node to obtain the strain of each unit node. The stress value of each unit node is obtained according to the constitutive relationship formula, and finally the stress value is smoothed: Formula (17) in, For strain, B is the element strain matrix, For displacement.

[0056] Formula (18) in, is the stress value, D is the elastic matrix.

[0057] The von Mises stress and maximum principal stress of the node are used to predict the strength and life of the gear. The calculation formula is as follows: Formula (19) Formula (20) Formula (21) in, for x , y and z Normal stress in the direction, , , for x , y and z Shear stress in the direction. The von Mises stress at any point can be obtained according to formula (19), formula (20) and formula (21). The maximum real root of formula (20) is the maximum principal stress.

[0058] The tooth surface contact stress is obtained by analyzing the von Mises stress, and the tooth root bending stress is obtained by analyzing the maximum principal stress.

[0059] It should be noted that how to calculate the tooth surface contact stress and the tooth root bending stress based on the gear deformation result is an existing technology known to those skilled in the art and will not be elaborated here.

[0060] According to the numerical calculation method of bevel gears of the embodiment of the present invention, a finite element model is first constructed and the overall stiffness matrix of the finite element model is calculated, and then the meshing force of the meshing nodes at different rotation angles is calculated by using the loading contact analysis method, and then the fixed displacement boundary condition is applied to the inner gear ring of the gear of the finite element model to simulate the static state of the inner gear ring of the gear, and then the meshing force of the meshing nodes at different rotation angles is mapped to the tooth surface of the finite element model as the force boundary condition, and the tooth surface meshing force result is obtained to realize the distribution of the meshing force on the tooth surface, and 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 numerical calculation method of bevel gears 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 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.

[0061] like Fig. 9 and Fig.10 As shown, Fig. 9 is a contact force cloud diagram at the maximum Mises stress moment of 500 Nm obtained by a bevel gear numerical calculation method according to an embodiment of the present invention, Fig.10 This is a Mises cloud diagram of the gear cross section at the moment of maximum Mises stress at 500 Nm obtained by the bevel gear numerical calculation method according to an embodiment of the present invention. From the contact force distribution, it can be seen that the current analysis step is a single-tooth contact, so that the Mises stress of the current analysis step is the maximum value of the entire meshing cycle. Fig.10 yes Fig. 9 The Mises cloud of a small piece of gear teeth in the middle frame is Fig. 9 The three-dimensional expression of Fig.10 It can be seen that the Mises stress in the subsurface is the largest, which is also the cause of failures such as spalling.

[0062] The tooth surface contact stress is 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. FIG11 shows a comparison diagram of the maximum Mises of different mesh layers of the driving wheel at 500 Nm obtained by the numerical calculation method of bevel gears according to an embodiment of the present invention. Fig. 9It can be seen that no matter whether the result is obtained by the finite element method or the numerical calculation method of the bevel gear of the embodiment of the present invention, in the process from the surface to the inside, the Mises stress value first decreases and then increases, and continues to decay after reaching the maximum value, which is also in line with the classic Hertz contact conclusion. Since the contact area calculated by the numerical calculation method of the bevel gear 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 of the fifth layer of the finite element model as the driving wheel rotates. It can be seen that within one meshing cycle, the results of the numerical calculation method of the bevel gear of the embodiment of the present invention and the finite element method are very similar, and the maximum Mises error is 1.12%.

[0063] The bending stress at the tooth root is directly related to the bending fatigue strength of the gear and is the main cause of gear tooth fracture. Unlike contact fatigue, gear bending fatigue failure often initiates at the surface of the tooth root, manifested as cracks at the tooth root, which gradually expand and lead to gear tooth fracture. Fig.13 and Fig.14 The maximum principal stress at the tooth root is shown, which is essential for verifying the bending strength and providing the parameters required to predict bending fatigue. Fig.13 is a cloud diagram of the tooth root bending stress of the driving wheel at 500 Nm obtained by the numerical calculation method of the bevel gear in one embodiment of the present invention, Fig.14 It is a fuzzy diagram of the tooth root bending stress of the driving wheel under 500Nm obtained by the finite element method in the prior art. The difference between the two methods in stress distribution and magnitude is very small. Fig.15 The maximum tooth root bending stress at different rotation angles during the entire meshing cycle is shown. Under loads of 50, 100, 200, 500 and 1000 Nm, the maximum tooth root bending stress trends at different rotation angles by the bevel gear numerical calculation method and the finite element method of the embodiment of the present invention are consistent, with only slight differences in magnitude. See Table 2 for specific errors: Table 2

[0064] in is the maximum error of the maximum tooth root bending stress during the entire meshing cycle, In the whole meshing cycle, the error of the maximum and minimum tooth root bending stresses does not exceed 4%, which shows that the numerical calculation method of the bevel gear in the embodiment of the present invention has a high calculation accuracy.

[0065] The numerical calculation method for bevel gears in the embodiment of the present invention not only ensures accuracy, but also greatly improves its calculation efficiency, as shown in Table 3. Compared with the finite element method, its calculation speed is 66.7 times faster, which greatly improves the efficiency of parameter calculation required for strength verification and fatigue life prediction of bevel gears.

[0066] Table 3 Number of units Calculation time Proposed method 732780 991.5 s Finite element software 732780 17.34 h It should be noted that the bevel gear numerical calculation method of the embodiment of the present invention can be applied to gear transmission systems 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 here.

[0067] 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.

[0068] A gear parameter information acquisition module is used to acquire gear parameter information; A finite element model building module is used to build a finite element model based on gear parameter information and calculate the overall stiffness matrix of the finite element model; The meshing force calculation module is used to calculate the meshing force of meshing nodes at different rotation angles using the loading contact analysis method according to the gear parameter information; A fixed displacement boundary condition application module is used to apply fixed displacement boundary conditions to the gear ring of the finite element model to simulate the stationary state of the gear ring; 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 meshing force results of the tooth surface, so as to realize the distribution of the meshing force on the tooth surface; The gear deformation result calculation module is used to calculate the gear deformation result based on the overall stiffness matrix and the tooth surface meshing force result; The stress calculation module is used to calculate the tooth surface contact stress and tooth root bending stress based on the gear deformation results.

[0069] Since the bevel gear numerical calculation system adopts all the technical solutions of the bevel gear numerical calculation method of the above embodiment, it at least has all the beneficial effects brought by the technical solutions of the above embodiment.

[0070] According to the bevel gear numerical calculation system of the embodiment of the present invention, a finite element model is first constructed and the overall stiffness matrix of the finite element model is calculated, and then the meshing force of the meshing node under different rotation angles is calculated by using the loading contact analysis method, and then the fixed displacement boundary condition is applied to the gear inner ring of the finite element model to simulate the static state of the gear inner ring, and then the meshing force of the meshing node under different rotation angles is mapped to the tooth surface of the finite element model as the force boundary condition, and the tooth surface meshing force result is obtained to realize the distribution of the meshing force on the tooth surface, and 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 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 force of the meshing node under 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.

[0071] In addition, an embodiment of the present invention further provides a control device, which includes: a memory, a processor, and a computer program stored in the memory and executable on the processor. The processor and the memory may be connected via a bus or other means.

[0072] The memory, as a non-transient computer-readable storage medium, can be used to store non-transient software programs and non-transient computer executable programs. In addition, the memory may include a high-speed random access memory, and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some embodiments, the memory may optionally include a memory remotely disposed relative to the processor, and these remote memories may be connected to the processor via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0073] The non-transient software program 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, the bevel gear numerical calculation method of the above embodiment is executed.

[0074] The device embodiments described above are merely illustrative, and the units described as separate components may or may not be physically separated, that is, they may be located in one place or distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0075] In addition, an embodiment of the present invention further provides a computer-readable storage medium, which stores computer-executable instructions, and the computer-executable instructions are executed by a processor or controller, for example, by the above-mentioned processor, so that the above-mentioned processor can execute the bevel gear numerical calculation method in the above-mentioned embodiment.

[0076] It will be appreciated by those skilled in the art that all or some of the steps and systems in the methods disclosed above may be implemented as software, firmware, hardware, and appropriate combinations thereof. Some or all physical components may 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 may be distributed on a computer-readable medium, which may include a computer storage medium (or non-transitory medium) and a communication medium (or transient medium). As known to those skilled 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 include, but are not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disk (DVD) or other optical disk storage, magnetic cassettes, magnetic tapes, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and can be accessed by a computer. Furthermore, it is well known to those skilled in the art that communication media typically embodies computer readable instructions, data structures, program modules, or other data in a modulated data signal such as a carrier wave or other transport mechanism, and may include any information delivery media.

[0077] The embodiments of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in the relevant technical field without departing from the purpose of the present invention.

Claims

1. A bevel gear numerical calculation method, characterized in that: The method comprises: Get gear parameter information; Constructing a finite element model according to the gear parameter information, and calculating an overall stiffness matrix of the finite element model; According to the gear parameter information, a loading contact analysis method is used to calculate the meshing force of meshing nodes at different rotation angles; Applying a fixed displacement boundary condition to the gear ring of the finite element model to simulate a stationary state of the gear ring; Mapping the meshing force of the meshing nodes at different rotation angles to the tooth surface of the finite element model to obtain the meshing force result of the tooth surface to achieve 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; The tooth surface contact stress and tooth root bending stress are calculated based on the gear deformation result.

2. The bevel gear numerical calculation method according to claim 1, characterized in that: The gear deformation result is calculated based on the overall stiffness matrix and the tooth surface meshing force result, and is achieved through the following constraint formula: F； in, K represents the global stiffness matrix, represents the gear deformation result, F Represents the tooth surface meshing force result.

3. The bevel gear numerical calculation method according to claim 1, characterized in that: The meshing force of the meshing nodes at different rotation angles is mapped to the tooth surface of the finite element model to obtain the tooth surface meshing force result to achieve the distribution of the meshing force on the tooth surface, including: Obtaining all node numbers on the tooth surface of the finite element model; Determining the correspondence between each of the node numbers and each of the meshing nodes; According to the corresponding relationship, the meshing force of each meshing node at different rotation angles is 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.

4. The bevel gear numerical calculation method according to claim 1, characterized in that: The gear deformation result is calculated according to the overall stiffness matrix and the tooth surface meshing force result, including: Decomposing the overall stiffness matrix using the Cholesky decomposition method to obtain a decomposition result; The gear deformation result is calculated based on 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 meshing node is obtained by the following steps: According to the gear parameter information, the contact deformation result is calculated by using the influence coefficient method; The meshing force of each meshing node is determined according to the contact deformation result.

6. The bevel gear numerical calculation method according to claim 5, characterized in that: The contact deformation result includes an initial contact deformation relationship, a total elastic deformation relationship of the gear pair, and a torque balance relationship. The meshing force of each meshing node is determined according to the contact deformation result, including: The meshing force of each meshing node is determined according to the initial contact deformation relationship, the total elastic deformation relationship of the gear pair and the torque balance relationship.

7. The bevel gear numerical calculation method according to claim 1, characterized in that: The overall stiffness matrix is ​​obtained by the following steps: Calculating multiple unit stiffness matrices of the finite element model according to the gear parameter information; The individual unit stiffness matrices are superimposed and assembled into the overall stiffness matrix.

8. A bevel gear numerical calculation system, characterized in that: The system comprises: A gear parameter information acquisition module is used to acquire gear parameter information; A finite element model building module, used to build a finite element model according to the gear parameter information and calculate the overall stiffness matrix of the finite element model; A meshing force calculation module, used to calculate the meshing force of meshing nodes at different rotation angles using a loading contact analysis method according to the gear parameter information; A fixed displacement boundary condition applying module, used for applying a fixed displacement boundary condition to the gear inner ring of the finite element model to simulate the stationary state of the gear inner ring; A meshing force mapping module is used to map the meshing force of the meshing nodes at different rotation angles onto the tooth surface of the finite element model to obtain the meshing force result of the tooth surface, so as to realize the distribution of the meshing force on the tooth surface; A gear deformation result calculation module, used for calculating the gear deformation result according to the overall stiffness matrix and the tooth surface meshing force result; 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.

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

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.

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