A method and system for automatically building a finite element model for bevel gear tooth surface contact analysis

Abstract

The present invention belongs to the technical field of gear simulation, and discloses a method and system for automatically building a finite element model for contact analysis of bevel gear tooth surfaces. The method obtains the surface points and end face boundary points of a single bevel gear tooth by calculating the design parameters of the bevel gear, and further calculates each point on the bevel gear mesh control line segment, and then obtains all mesh points by extended interpolation, thereby generating a complete finite element mesh model of a single bevel gear tooth. The method provided by the present invention realizes the automatic generation of a bevel gear finite element model based on design parameters, avoids the cumbersome manual operation of the existing method, and has the advantage of high efficiency.

Description

Technical Field

[0001] The invention belongs to the technical field of gear simulation, and in particular relates to an automatic modeling method and system for a finite element model for contact analysis of bevel gear tooth surfaces. Background Art

[0002] Spiral bevel gears are widely used in the automotive, aviation, machine tool and other industries, and various industries are paying more and more attention to the performance of spiral bevel gears. With the development of computer technology, the convenience and economy of using CAD and CAE to predict the performance of spiral bevel gears have become increasingly prominent. In engineering practice, finite element software is also needed to perform loading contact analysis on bevel gears to simulate the actual gear meshing process, analyze the contact marks and stress results of the gears, and perform optimization iterations and strength verification in the design stage. However, the mesh modeling quality of the tooth surface is very important and has a significant impact on the results. However, tetrahedral meshing cannot be used for bevel gear contact analysis. High-quality hexahedral meshes must be used for contact analysis. High-quality hexahedral mesh modeling is very cumbersome. Based on the mesh construction of the three-dimensional model, it is necessary to perform surface fitting and construct tooth grooves in the three-dimensional software based on the discrete points on the tooth surface, and then cut the tooth blank model to generate a three-dimensional solid model. Finally, it is necessary to cut the single tooth. The single tooth model is imported into the commercial meshing software for meshing to obtain the mesh model of the single tooth.

[0003] It can be seen that the traditional hexahedral mesh modeling of bevel gears requires designers to have rich software operation experience, and the operation steps are cumbersome and take a long time to process. Summary of the invention

[0004] The technical problem to be solved by the present invention is that the traditional hexahedral mesh modeling steps of bevel gears are cumbersome, time-consuming and labor-intensive. In order to overcome the shortcomings and defects mentioned in the above background technology, a method and system for automatically modeling a finite element model for contact analysis of bevel gear tooth surfaces is provided.

[0005] In order to solve the above technical problems, the technical solution proposed by the present invention is:

[0006] In a first aspect, the present application provides a method for automatically building a finite element model for bevel gear tooth surface contact analysis, comprising:

[0007] S1: Get the tooth surface node of the bevel gear;

[0008] S2: Calculate the boundary nodes of the bevel gear end face;

[0009] S3: Get the internal skeleton nodes of the bevel gear;

[0010] S4: combining the tooth surface nodes, the boundary nodes and the internal skeleton nodes, and performing interpolation processing on the combined nodes to obtain all mesh nodes of the bevel gear;

[0011] S5: constructing a finite element model of the bevel gear based on all mesh nodes of the bevel gear according to a unit combination method.

[0012] In a second aspect, the present application provides a system for constructing a finite element model for bevel gear tooth surface contact analysis, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method described in the first aspect when executing the computer program.

[0013] Compared with the prior art, the present invention has the following beneficial effects:

[0014] The present invention obtains the surface points and end face boundary points of a single bevel gear tooth by calculating the design parameters of the bevel gear, and further calculates the points on the bevel gear mesh control line segment, and then obtains all mesh points by extended interpolation, thereby generating a complete bevel gear single tooth finite element mesh model. The method provided by the present invention realizes the automatic generation of a bevel gear finite element model based on the design parameters, avoids the cumbersome manual operation of the existing method, and has the advantage of high efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0016] Figure 1 It is the traditional modeling steps of bevel gear finite element mesh model;

[0017] Figure 2 This is a flow chart of automatic modeling of a finite element model for bevel gear tooth surface contact analysis according to a preferred embodiment of the present application;

[0018] Figure 3 It is a schematic diagram of key points of the bevel gear end face in a preferred embodiment of the present application;

[0019] Figure 4 Schematic diagram of the full tooth end surface of a bevel gear in a preferred embodiment of the present application;

[0020] Figure 5 This is a schematic diagram of bevel gear end face node generation in a preferred embodiment of the present application;

[0021] Figure 6 It is a schematic diagram of the mesh generation direction of the bevel gear single tooth finite element model in the preferred embodiment of the present application;

[0022] Figure 7It is a schematic diagram of the grid partitioning of the bevel gear finite element model of the preferred embodiment of the present application;

[0023] Figure 8 This is a schematic diagram of the arrangement order of nodes of a three-dimensional hexahedral linear unit in a preferred embodiment of the present application;

[0024] Fig. 9 It is a schematic diagram of the automated modeling steps of the bevel gear finite element mesh model according to the preferred embodiment of the present application;

[0025] Fig.10 is a finite element model of a driven wheel of a preferred embodiment of the present application;

[0026] Fig.11 It is a finite element model of the driving wheel of the preferred embodiment of the present application;

[0027] Fig.12 It is a schematic diagram of the bevel gear contact analysis automated modeling process in the preferred embodiment of the present application;

[0028] Fig.13 It is a schematic diagram of the tooth side points of the bevel gear teeth of the preferred embodiment of the present application;

[0029] Fig.14 It is a schematic diagram of the bevel gear ring point of the preferred embodiment of the present application;

[0030] Fig.15 It is a five-tooth-full-tooth range gear ring finite element model of the preferred embodiment of the present application;

[0031] Fig.16 It is a finite element model of a five-tooth and two-range gear ring on the left and right sides of the preferred embodiment of the present application;

[0032] Fig.17 is a schematic diagram of contact tooth surface points of a preferred embodiment of the present application;

[0033] Fig.18 Schematic diagram of the gear inner ring coupling point of the preferred embodiment of the present application;

[0034] Fig.19 It is a finite element model for contact analysis of the five-tooth and two-range gear rings on the left and right sides of the preferred embodiment of the present application;

[0035] Fig. 20 Schematic diagram of the contact arrangement of the master and slave gears of the preferred embodiment of the present application;

[0036] Fig.21 Schematic diagram of the coupling between the inner rings of the driving and driven gears of the preferred embodiment of the present application;

[0037] Fig. 22 It is a comparison of the bending stress of the tooth roots of various models in the preferred embodiment of the present application;

[0038] Fig.23 It is a comparison of the contact stress of the tooth surfaces of various models of the preferred embodiment of the present application.

[0039] Reference numerals:

[0040] 7-1: tooth width; 7-2, tooth root; 7-3, tooth profile; 7-4, half tooth thickness; 7-5, tooth bottom. DETAILED DESCRIPTION

[0041] In order to facilitate the understanding of the present invention, the present invention will be described more comprehensively and meticulously below in conjunction with the accompanying drawings and preferred embodiments of the present invention, but the protection scope of the present invention is not limited to the following specific embodiments.

[0042] Unless otherwise defined, all professional terms used below have the same meanings as those generally understood by those skilled in the art. The professional terms used herein are only for the purpose of describing specific embodiments and are not intended to limit the scope of protection of the present invention.

[0043] Unless otherwise specified, various raw materials, reagents, instruments and equipment used in the present invention can be purchased from the market or prepared by existing methods.

[0044] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the usual meanings understood by persons with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, words such as "one" or "one" do not indicate quantity restrictions, but indicate the existence of at least one. Words such as "connect" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship also changes accordingly.

[0045] It should be understood that in the prior art, building a three-dimensional model of a bevel gear is relatively cumbersome and requires the use of powerful three-dimensional modeling software. In addition, the steps of dividing the bevel gear into single teeth are relatively complicated because the spiral bevel gear has a helix angle and is not easy to divide. Secondly, meshing is very time-consuming. Generally speaking, pre-processing takes about half of the time of finite element modeling analysis. It is necessary to perform multiple steps such as geometric cleaning of the three-dimensional model, seeding, generating two-dimensional units, and generating three-dimensional units, which is time-consuming.

[0046] For example, see Figure 1 , based on the mesh construction of the three-dimensional model, it is necessary to construct the mesh at discrete points on the tooth surface ( Figure 1-1 ) is used to fit the surface and construct the tooth groove ( Figure 1-2 ), and then cut the tooth blank model ( Figure 1-3 ), generate a 3D solid model ( Figure 1-4 ), and finally you need to cut the single tooth ( Figure 1-5 ). Import the single tooth model into commercial meshing software for meshing ( Figure 1-6 ), we can get the mesh model of a single tooth ( Figure 1-7 ). In this way, the designer is required to have more software experience and needs to allocate a large amount of time for processing, which is time-consuming and laborious. Based on this, the present application provides a method and system for automatically building a finite element model for contact analysis of bevel gear tooth surfaces.

[0047] See also Figure 2 The present application provides a method for automatically building a finite element model for bevel gear tooth surface contact analysis, comprising:

[0048] S1: Get the tooth surface node of the bevel gear;

[0049] S2: Calculate the boundary nodes of the bevel gear end face;

[0050] S3: Get the internal skeleton nodes of the bevel gear;

[0051] S4: combining the tooth surface nodes, the boundary nodes and the internal skeleton nodes, and performing interpolation processing on the combined nodes to obtain all mesh nodes of the bevel gear;

[0052] S5: constructing a finite element model of the bevel gear based on all mesh nodes of the bevel gear according to a unit combination method.

[0053] The above-mentioned automatic modeling method of the finite element model for bevel gear tooth surface contact analysis obtains the surface points and end surface boundary points of a single bevel gear tooth by calculating the design parameters of the bevel gear, and further calculates the points on the bevel gear mesh control line segment, and then obtains all mesh points by extended interpolation, thereby generating a complete bevel gear single tooth finite element mesh model. The method provided by the present invention realizes the automatic generation of the bevel gear finite element model based on the design parameters, avoids the cumbersome manual operation of the existing method, and has the advantage of high efficiency.

[0054] Below, a complete example is used to explain in detail the steps of the automatic modeling method of the bevel gear tooth surface contact analysis finite element model:

[0055] 1. Tooth surface modeling

[0056] The modeling of the tooth surface of the spiral bevel gear depends on the relative motion model between the tool and the workpiece and the shape equation of the tool. In CNC machining, the adjustment of machining parameters no longer depends on the machine tool structure, so a unified motion model under different machining methods can be obtained; the actual shape of the spiral bevel gear is closely related to the shape of the grinding wheel. The development motion of the linear tool under the unified motion model is used as the basic model for the modeling of the tooth surface of the spiral bevel gear, and the meshing principle is solved to obtain the tooth surface points. In other words, the tooth surface modeling can be achieved by existing methods, which will not be elaborated here.

[0057] 2. Finite element meshing

[0058] The surface points and end face boundary points of the bevel gear are calculated based on the design parameters.

[0059] In one example, the design parameters include but are not limited to the number of teeth, tooth width, helix angle, module, shaft angle, external taper, hand direction, pitch angle, face angle, root angle, addendum height, and root height.

[0060] The key nodes of the bevel gear mesh are as follows: Figure 3 As shown, A, C, E, I and J are the boundary points of a single tooth, D, F and H are the midpoints of CE, EI and AJ respectively, point B is the intersection of the tooth profile and the tooth root, point G is the point between HF, and the above are all positions after two-dimensional projection. In fact, this surface is a conical surface, and the corresponding positional relationship is different from that in two dimensions.

[0061] In this example, the mesh density in the tooth profile direction can be controlled by controlling the number of nodes between AB, the mesh density in the gear thickness direction can be controlled by controlling the number of nodes between AH, the mesh density at the tooth root can be controlled by controlling the number of nodes between BC, and the mesh density of other parts can be set as needed.

[0062] It is worth noting that see Figure 4 Unlike spur gears, helical gears, herringbone gears, etc., the end face of a bevel gear is not a plane, but a conical surface. When determining the mesh nodes, the mesh nodes need to fall on the conical surface of the end face.

[0063] For further information, see Figure 5 ,in Figure 5 (a) is the boundary connection diagram of the bevel gear. Figure 5 (b) is the skeleton line segment diagram of the bevel gear. Figure 5 (c) is a schematic diagram of the skeleton line segments of the bevel gear after interpolation processing, where 1 to 6 represent the skeleton line segments of the bevel gear. Figure 5 The boundary points in are known through the bevel gear design parameters. First, determine Figure 3 The position of point G in the figure is determined by the three-dimensional coordinates of the four nodes A, B, H, and F, and the gear rotates around the Z axis. The specific calculation method is as follows:

[0064] Calculate the scaling factor K:

[0065] K = |AB| / (0.8×|HF|)(0.1);

[0066] In the formula, A represents the boundary point of the end face tooth top, B represents the intersection of the end face tooth profile and the tooth root on the same side as A, H represents the midpoint of the end face tooth top, and F represents the midpoint of the end face tooth bottom.

[0067] Calculate the angle θ between the angle points H and F and the X-axis on the XY plane H and θ F :

[0068]

[0069] In the formula, H y Indicates the y coordinate value of point H, H x Indicates the x coordinate value of point H, F y Indicates the y coordinate value of point F, F x Represents the x-coordinate value of point F.

[0070] Then calculate the radius difference ΔR between point H and point F about the origin on the XY plane HF value:

[0071]

[0072] Then calculate the angle θ between point G and the X-axis on the XY plane G :

[0073] θ G =θ H -k(θ H -θ F )(0.4);

[0074]

[0075] In the formula, R G represents the radius of point G on the XY plane about the origin, H z represents the z coordinate value of point H, F z represents the coordinate value of point F, (G x , G y , G z ) represents the three-dimensional coordinates of the target point G.

[0076] In this way, point G is determined on the end face of the cone. In this way, the points on line segments 1, 2, 5, and 6 can be determined in the same way as point G. The points on line segment 1 are determined based on HG, and the proportional factor is determined based on the number of points on the line segment.

[0077] k = i / (L+1)(0.7);

[0078] L is the number of points in the line segment, excluding the endpoints, and i is the i-th point in the line segment. It is worth noting that the scale factor K is used to find point G, and the scale factor k is used to find other points on the line segment.

[0079] For line segments 3 and 4, since the stress generated by contact analysis varies greatly in shallow areas, more mesh layers need to be set on the surface. Therefore, a bias coefficient is added to the points on line segments 3 and 4.

[0080] Assuming that the bias coefficient is M (M>=1), L+1 values ​​are uniformly generated between 1 and M, and their set is S, which satisfies the following calculation formula. It is worth pointing out that the calculation formula is based on line segment 3 as an example, and other line segments are similar.

[0081]

[0082] In the formula, represents the radius of the starting point B on the line segment BG about the origin on the XY plane, (B x , B y , B z ) represents the three-dimensional coordinates of point B, It represents the angle between the starting point B on the line segment BG and the X-axis on the XY plane. Indicates the position of the starting point B on the line segment BG in the Z direction, ΔR BG Represents the radius difference of the line connecting point B and point G about the origin on the XY plane, θ BG It represents the angle difference between the starting point B and the end point G on the line segment BG and the X-axis on the XY plane, Z BG It represents the distance difference between point B and point G in the Z direction. represents the radius of the i-th interpolation point in the BG segment, S i Represents the scale factor of the i-th interpolation point in the BG segment, Represents the angle between the i-th interpolation point in the BG line segment and the X-axis on the XY plane, Respectively represent the X, Y and Z positions of the i-th interpolation point in the BG segment.

[0083] When M is equal to 1, the nodes on the line segment are evenly distributed. If M is not 1, the generated line segment nodes are denser the closer to the surface.

[0084] In other words, the set S is actually the coefficient. When there are two points in the line segment, if M is 1, the set S is {1 1 1}, and the two points in the line segment are at 1 / 3 2 / 3 respectively. If M is 3, the set S is {1 2 3}, and the two points in the line segment are at 1 / 63 / 6 respectively. This is to make the node spacing of the surface attachment smaller, and the closer to the middle, the sparser, so that the stress of the surface layer can be calculated better.

[0085] Based on the points that have been generated, it can be expanded to other internal points, and then the remaining points can be interpolated along the tooth width direction based on the tooth surface points to complete the generation of all points.

[0086] Furthermore, the schematic diagram of the gear grid is as follows: Figure 6 As shown in the figure, line segment ① controls the mesh length direction of the upper gear tooth profile, and line segment ② controls the width direction. The tooth root is controlled by line segment ② in length direction, and line segment ③ in width direction. The lower part of the gear has line segment ④ controlling the length direction, and line segment ③ controlling the width direction. In this way, plus the tooth length direction is controlled by line segment ⑤, the complete mesh control is completed. Specifically, in one example, the various parts of the gear are as follows Figure 7 As shown, the gear includes a tooth width 7-1, a tooth root 7-2, a tooth profile 7-3, a half tooth thickness 7-4, and a tooth bottom 7-5.

[0087] It needs to be explained that the order of node composition of the unit is the prerequisite for the correct calculation of stiffness. The hexahedral mesh is divided into six faces, such as Figure 8 As shown, the surfaces are arranged counterclockwise, with surface 1 being the bottom, surface 2 being the top, surface 3 being the left, surface 4 being the front, surface 5 being the right, and surface 6 being the back. The node order of surface 1 is 1, 4, 3, 2. The node order of surface 2 is 5, 6, 7, 8. The node order of surface 3 is 1, 2, 6, 5. The node order of surface 4 is 2, 3, 7, 6. The node order of surface 5 is 3, 4, 8, 7. The node order of surface 6 is 4, 1, 5, 8.

[0088] Finally, if Fig. 9 As shown in the figure, according to the generated mesh nodes, the complete bevel gear finite element single tooth model can be generated in the above order. Figure 9-1 ), boundary nodes( Figure 9-2 ) and internal nodes ( Figure 9-3 ), all points are shown as ( Figure 9-4 ), forming a cross-sectional 2D mesh ( Figure 9-5 ), the corresponding 2D mesh can directly form a 3D mesh, and the model file is written according to the INP file format used in the commercial finite element software ABAQUS, and finally imported into ABAQUS to verify the results ( Figure 9-6 ).

[0089] In an experiment, the efficiency and accuracy of the existing three-dimensional modeling and the single tooth modeling method provided by the present application are compared as shown in Table 1 below:

[0090] Table 1 Comparison of efficiency and accuracy of existing three-dimensional modeling and the method for modeling a single tooth provided by this application

[0091]

[0092] It is worth noting that the finite element model of the bevel gear generated in the above method is a single-tooth finite element model. Figure 12-1 As a further solution, the single-tooth finite element can be arrayed circularly to obtain a multi-tooth finite element model such as Figure 12-2 , optionally, as Figure 10-11 As shown in the figure, the bevel gear finite element model with the corresponding number of teeth can be automatically generated according to the number of teeth required for the bevel gear, and the parameters of its finite element mesh are fully parameterized, and its mesh density and the number of gear teeth required to be generated can be freely set. Figure 12-3 Based on the tooth side nodes, a circular array is performed according to the required range of the gear ring to obtain the nodes of the gear ring, and the finite element model of multiple teeth and gear ring is obtained as follows Figure 12-4 Extract the inner ring nodes of the gear finite element model as follows Figure 12-5 , extract the nodes of each contact tooth surface as Figure 12-6 The extraction of the above two node sets is automatically performed according to the node generation process. The driving wheel is fixed, and the driven wheel rotates around the Y axis and then couples the inner ring nodes of each gear to the coupling node. The inner ring of the driving wheel is coupled to the rp point, and the inner ring of the driven wheel is coupled to the rg point. Figure 12-7 As shown. Perform surface-to-surface contact analysis on each contacting tooth surface to model the contact of the tooth surfaces. The specific method is as follows:

[0093] Among them, the types of bevel gears include driving wheels and driven wheels, and the types of finite element models of bevel gears include multi-tooth belt matrix mesh model, multi-tooth mesh model, and full-tooth mesh model. In other words, the finite element model of the bevel gear finally generated specifically includes the multi-tooth belt matrix mesh model of the driving wheel, the multi-tooth mesh model of the driving wheel, the full-tooth mesh model of the driving wheel, the multi-tooth belt matrix mesh model of the driven wheel, the multi-tooth mesh model of the driven wheel, and the full-tooth mesh model of the driven wheel. Moreover, when performing a specific finite element contact analysis, the types of finite element models of the driving wheel and the driven wheel correspond.

[0094] Specifically, contact analysis of bevel gears using the finite element method requires a ring gear unit to provide the matrix stiffness of the gear. However, if the finite element model is divided into all teeth, the number of grids is too large and the calculation is time-consuming. In order to ensure that the model has matrix stiffness while reducing the number of grids, only the matrix grid model of the gear is generated for the non-meshing teeth, and the grid model of the gear teeth is not generated.

[0095] Obtain the grid points on the left and right sides of the multi-tooth finite element mesh model. Since the gear rotates around the Z axis, after the number of teeth of the generated multi-tooth finite element gear is known, the remaining ungenerated gear ring angles can be calculated using the following formula.

[0096] θ=2π / Z p ×(Z p -N)(1.11);

[0097] Zp is the total number of teeth and N is the number of teeth that have been generated.

[0098] Assuming that L columns of grids need to be generated in the ungenerated gear ring part, the angle occupied by the length range of each column of grids is θ / L.

[0099] Known Fig.13 The nodes on the left and right tooth side surfaces shown in the figure can be obtained by rotating the left node three-dimensional coordinate point set S0 around the Z axis, with each rotation degree, to obtain all the gear ring mesh nodes.

[0100] S L =M×S0(1.12)

[0101] in:

[0102]

[0103] Where M represents the rotation matrix;

[0104] Get the following Fig.14 The three-dimensional coordinate set of the gear ring points is obtained, and then the common nodes of the multi-tooth finite element model and the gear ring finite element are merged, that is, there can only be one node at the same coordinate point.

[0105] The gear unit number generated by the array is the unit number of the first gear tooth plus the total number of nodes of the first gear tooth multiplied by the gear number minus 1. Finally, the same nodes between the gear teeth are merged, and the merged node numbers are adjusted to obtain the final overall unit number to obtain the multi-tooth finite element model.

[0106] According to the generated mesh nodes, a complete bevel gear finite element model (full tooth mesh model) can be generated according to the node composition order of the unit. Fig.15 shown.

[0107] In a possible implementation, if Fig.16 As shown, it is also possible to generate only a finite element model of part of the gear ring (multi-tooth mesh model) to reduce the number of meshes and speed up the calculation efficiency. It is only necessary to rotate the left tooth side nodes of the multi-tooth finite element model counterclockwise and the right tooth side nodes clockwise. The rest of the operations are similar to the full-tooth range gear ring. It is worth noting that the multi-tooth belt matrix mesh model refers to the model of the full-tooth mesh model minus the multi-tooth mesh model.

[0108] In this example, the mesh nodes of the tooth surface and the mesh nodes of the inner ring of the gear are recorded in the modeling stage as follows Figure 17-Figure 18 shown. Fig.17 is a schematic diagram of the contact tooth surface points, Fig.18 This is a schematic diagram of the coupling points of the gear inner ring. For each gear, there is a set of any contact tooth surface node, and a set of the entire inner ring gear.

[0109] The driven wheel rotates counterclockwise around the Y axis. If the axis angle is 90°, the rotation axis of the driven wheel is changed to the X axis, and the driving wheel still rotates around the Z axis.

[0110] like Figure 19-21 As shown, the contact analysis surface is set according to the driving wheel as the master surface, and the meshing surface corresponding to the driven wheel is set as the slave surface. If the number of gear teeth is N, N surface-to-surface contact analysis interaction pairs are set. The points of the inner ring of the master and driven gears are coupled to two different points, and the three-dimensional coordinate positions of the two points are the origins. The driving wheel is coupled to rp, and the driven wheel is coupled to rg. rp and rg are two different points with values ​​of 0 in all directions.

[0111] Specifically, the automatically generated mesh model is already at the exact collision angle, and four analysis steps are set as follows.

[0112] Step 1: Apply a small rotation angle to the driving wheel (small wheel). The purpose is to eliminate the small gap between the contact surfaces caused by errors in geometric modeling and meshing, and rotate 0.0017 radians to make the contact pairs have a small interference.

[0113] Step 2: Keep the driving wheel (small wheel) fixed, release the reference node rotation displacement constraint of the driven wheel (large wheel), and apply an initial torque around its own rotation axis. In order to ensure the convergence of the contact iteration, the torque is 0.1Nm.

[0114] Step 3: Keep the driving wheel (small wheel) fixed and increase the load torque of the driven wheel (large wheel) to the rated value that needs to be set during analysis to complete the application of the load torque.

[0115] Step 4: Keep the boundary conditions of the driven wheel (large wheel) unchanged, release the rotational freedom of the small wheel around its own axis, and let it rotate a certain arc, so as to simulate the actual working condition that the driving wheel (small wheel) drives the driven wheel (large wheel) to operate by offsetting the resistance torque of the driven wheel (large wheel) through the meshing between the contact surfaces. The angle is 2π×(N-1) / Z p radian.

[0116] In one experiment, see Figure 22-23 , Figure 22-23 The figure is a comparison of the maximum stress results of the tooth root bending stress and the tooth surface Mises contact stress of various finite element contact analysis models as the analysis steps increase, where the meshing cycle of one tooth is 30 steps.

[0117] From the results of the tooth root bending stress in one cycle, it can be seen that for the three-tooth model, due to the lack of support of the matrix stiffness, the stress value drops sharply when the left and right gears are meshing, and a complete meshing cycle is not formed. However, whether it is the five-tooth, three-tooth-left and right 2-range gear ring finite element model or the three-tooth-full-range gear ring finite element model, there is a complete meshing cycle, and its stress changes are very similar. The number of units and calculation time of the finite element model of each model are detailed in Table 2.

[0118] Table 2 Experimental parameters

[0119]

[0120] From the results of the Mises stress of the tooth surface within one cycle, it can be seen that for the three-tooth model, due to the lack of support of the matrix stiffness, the stress value does not drop as sharply as the bending stress when the left and right gears are meshing, but it does not form a complete meshing cycle. Regardless of the five-tooth, three-tooth finite element model-two range gear rings on the left and right or the three-tooth finite element model-full range gear ring, there is a complete meshing cycle, and its stress changes are basically the same. The stress value of the three-tooth-left and right finite element model with two tooth range gear rings is basically the same as that of the five-tooth finite element model and the three-tooth-full range gear ring finite element model. However, the calculation time is 65% and 107% less than that of the five-tooth model and the three-tooth-full range gear ring finite element model, respectively, which reduces the calculation time while ensuring accuracy.

[0121] The present application also provides a system for constructing a finite element mesh model of a bevel gear, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program. The system for constructing a finite element mesh model of a bevel gear can implement various embodiments of the above method and achieve the same beneficial effects, which will not be described in detail here.

[0122] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for automatically building a finite element model for bevel gear tooth surface contact analysis, characterized in that: include: S1: Get the tooth surface node of the bevel gear; S2: Calculate the boundary nodes of the bevel gear end face; S3: Get the internal skeleton nodes of the bevel gear; S4: combining the tooth surface nodes, the boundary nodes and the internal skeleton nodes, and performing interpolation processing on the combined nodes to obtain all mesh nodes of the bevel gear; S5: constructing a finite element model of the bevel gear based on all mesh nodes of the bevel gear according to a unit combination method; The S2 includes: Obtain the conical end face of the bevel gear; Determine the boundary nodes of the conical end surface, including points A, C, E, I, J, D, F, H and B, according to the design parameters of the bevel gear and the two-dimensional projection diagram of the conical end surface; Among them, D is the midpoint of CE, F is the midpoint of EI, H is the midpoint of AJ, and B is the intersection of the tooth profile and the tooth root; The S3 includes: Determine a target point G on the end surface of the cone; Determine, according to the target point G, a first line segment, a second line segment, a third line segment, a fourth line segment, a fifth line segment, and a sixth line segment for representing the skeleton of the conical end face; respectively determining nodes on the first line segment, the second line segment, the fifth line segment, and the sixth line segment; Determining nodes on the third line segment and the fourth line segment according to a set bias coefficient; The step of determining the target point G of the cone end surface comprises: Determine the three-dimensional coordinates of A, B, H, and F in the boundary nodes; Calculate the proportional factor K, satisfying the following relationship: K = |AB| / (0.8×|HF|); In the formula, A represents the boundary point of the end face tooth top, B represents the intersection of the end face tooth profile and tooth root on the same side as A, H represents the midpoint of the end face tooth top, and F represents the midpoint of the end face tooth bottom; Calculate the angle θ between the angle points H and F and the X-axis on the XY plane H and θ F ; In the formula, H y Indicates the y coordinate value of point H, H x Indicates the x coordinate value of point H, F y Indicates the y coordinate value of point F, F x Indicates the x coordinate value of point F; Then calculate the radius difference ΔR between point H and point F about the origin on the XY plane HF value: Then calculate the angle θ between point G and the X-axis on the XY plane G : i G =θ H -K(θ H -θ F ); In the formula, R G represents the radius of point G on the XY plane about the origin, H z represents the z coordinate value of point H, F z represents the z coordinate value of point F, (G x , G y , G z ) represents the three-dimensional coordinates of the target point G; Determining nodes on the third line segment and the fourth line segment according to the set bias coefficient includes: Set the bias coefficient to M, M>=1, then generate L+1 values ​​evenly between 1 and M, L is the number of nodes in the line segment, and its set is S, which satisfies the following calculation formula: In the formula, represents the radius of the starting point B on the line segment BG about the origin on the XY plane, (B x , B y , B z ) represents the three-dimensional coordinates of point B, It represents the angle between the starting point B on the line segment BG and the X-axis on the XY plane. Indicates the position of the starting point B on the line segment BG in the Z direction, ΔR BG Represents the radius difference of the line connecting point B and point G about the origin on the XY plane, θ BG It represents the angle difference between the starting point B and the end point G on the line segment BG and the X-axis on the XY plane, Z BG It represents the distance difference between point B and point G in the Z direction. represents the radius of the i-th interpolation point in the BG segment, S i Represents the scale factor of the i-th interpolation point in the BG segment, Represents the angle between the i-th interpolation point in the BG line segment and the X-axis on the XY plane, Respectively represent the position of the i-th interpolation point in the BG line segment in the X, Y and Z directions; When M is equal to 1, the nodes on the line segment are evenly distributed. If M is not 1, the generated line segment nodes are denser the closer to the surface.

2. The automatic modeling method for bevel gear tooth surface contact analysis finite element model according to claim 1 is characterized in that: The S5 includes: Determine the grid surface stereogram of the bevel gear, and determine the surface order of each unit surface in the stereogram counterclockwise; Determining the node order of each node in each unit surface; All mesh nodes of the bevel gear are constructed as a 3D mesh model based on the surface order and the node order.

3. The automatic modeling method for bevel gear tooth surface contact analysis finite element model according to claim 1 is characterized in that: The types of the bevel gear include a driving wheel and a driven wheel, and the types of the finite element model of the bevel gear include a multi-tooth belt matrix grid model, a multi-tooth grid model, and a full-tooth grid model.

4. The automatic modeling method for bevel gear tooth surface contact analysis finite element model according to claim 3 is characterized in that: The method further comprises: S6: Based on the set analysis step, the finite element model of the driving wheel and the finite element model of the driven wheel are controlled to perform actions to perform finite element contact analysis.

5. A system for constructing a finite element model for contact analysis of bevel gear tooth surfaces, 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 steps of the method described in any one of claims 1 to 4 are implemented.

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