A method for reducing the number of gear finite element meshes through spatial transition

Abstract

The existing gear structured meshing methods usually perform 2D mesh transition on the end face, and the ability to reduce the number of meshes is limited. In order to ensure the accuracy of finite element simulation while reducing the calculation time, the present invention discloses a meshing method that reduces the number of gear finite element meshes through spatial transition, and cuts out the geometric model of a single tooth according to the periodic symmetry characteristics of the gear. The geometric model of the single tooth is further divided into 5 component areas, namely the carburizing area, the tooth core area, the tooth root fillet area, the tooth root area, and the solid area. Then, the cut 5 component areas are respectively subjected to surface cutting and meshing, wherein the carburizing area and the solid area realize the end face mesh transition, the tooth core area, the tooth root fillet area and the tooth root area realize the axial mesh transition, and the spatial transition of the mesh is realized through two 2D mesh transitions on the end face and the axial face. The meshes of the 5 divided component areas can successfully realize the common node operation, which solves the problem of common nodes in mesh space transition very well.

Description

Technical Field

[0001] The invention relates to the technical field of finite element simulation mesh division, and in particular to a division method for reducing the number of gear finite element meshes through space transition. Background Art

[0002] Gear transmission is the most widely used transmission method in various modern mechanical equipment. Gear transmission is accurate, efficient, compact, reliable and has a long service life. During gear transmission, there are pitting wear on the tooth surface and fatigue fracture on the tooth root. In the field of heavy machinery such as shield machines, this form of gear failure has a more obvious impact on the life of the entire heavy machinery. Therefore, a more accurate analysis of the stress distribution and crack propagation mechanism of gear meshing transmission is required. Traditional theoretical calculations cannot meet existing needs, and there is a high cost problem through experiments. With the improvement of computer computing performance, the use of finite element numerical simulation to calculate the stress distribution of gear meshing transmission and analyze the crack propagation mechanism has become a better choice.

[0003] The carburized layer of the gear is the key position of the gear meshing transmission. The maximum equivalent stress occurs inside the gear carburized layer, and the maximum contact pressure position of the gear meshing occurs on the surface of the gear carburized layer. The initiation and expansion of the tooth root crack also first appear in the tooth root carburized layer. Therefore, in the finite element simulation, the gear carburized layer requires a sufficiently high mesh density and number to capture the deformation and stress changes occurring in the carburized layer.

[0004] In finite element simulation, the total number of grids affects the finite element simulation calculation time, while the number of grids at key positions affects the calculation accuracy. It is very necessary to ensure the simulation accuracy while reducing the calculation time. For the finite element structured grid division method of gears, the existing technical solutions mainly use end face 2D grid transition, that is, divide the 2D grid on the gear end face, encrypt the gear tooth part, then perform grid transition on the wheel rim, and finally stretch it into a 3D grid. This method of only performing 2D grid transition on the gear end face to control the number of grids has limited ability to reduce the overall number of gear grids. In addition, there is no common node problem when using 2D grid transition and stretching on the end face to generate a 3D grid, and there is a common node problem when using grid space transition to reduce the number of grids. How to cut and divide the grid to achieve common nodes is a difficult problem that needs to be solved. Summary of the invention

[0005] In view of the shortcomings of the prior art, the purpose of the present invention is to provide a structured meshing method that achieves spatial transition through two mesh transitions on the end face and the axial face to reduce the number of gear finite element meshes, and successfully solves the problem of common nodes in mesh space transition.

[0006] The technical solution of the present invention:

[0007] A method for reducing the number of gear finite element meshes by spatial transition comprises the following steps:

[0008] Step 1: According to the periodic symmetry characteristics of the gear, the gear geometric model is cut for the first time in the 3D modeling software to cut out the geometric model of a single tooth.

[0009] Step 2: Perform a second body cutting on the geometric model of the single tooth to cut out five component areas, namely, the carburized area, the tooth core area, the tooth root fillet area, the tooth root area and the solid area.

[0010] Step 3: Perform a third surface cutting on the five component areas, including end surface cutting on the carburized area and the solid area, and axial surface cutting on the tooth core area, the tooth root fillet area and the tooth root area.

[0011] Step 4: Mesh the five cut component areas separately, wherein 2D meshing is performed on the end faces of the carburized area and the solid area, and then the 2D mesh is dragged along the axial direction of the gear to generate a 3D mesh, so as to achieve end face mesh transition and reduce the number of meshes. 2D meshing is performed on the axial faces of the tooth core area, the tooth root fillet area and the tooth root area, and then a 3D mesh is generated by sweeping along the four edge lines formed by the four faces intersecting with the faces of their respective 2D meshes, so as to achieve axial mesh transition and reduce the number of meshes.

[0012] Step 5: For the 3D mesh formed by the mesh division of the five component areas, set the tolerance, perform the common node operation, and perform the free edge check to determine whether all meshes have achieved common nodes. If there is no common node position, increase the tolerance for the mesh in this area and perform the common node operation again. Repeat the above process until all meshes have achieved common nodes.

[0013] Step 6: Based on the periodic symmetry characteristics of the gear, copy and rotate the mesh of a single tooth to form a complete gear mesh, and perform common node operations.

[0014] Furthermore, the second body cutting of the geometric model of a single tooth in step 2 specifically includes the following steps:

[0015] Step 2.1: Using 3D modeling software, on the 2D sketch of the end face of a single tooth, entity references are made to all edge lines on the end face of the single tooth, and according to the actual carburizing depth of the gear, the involute tooth profile, the root fillet and the root are equidistantly copied, and the lines before and after the equidistant are extended and connected to form two elongated carburizing zone surfaces on the end face of the gear;

[0016] Step 2.2: On the end face 2D sketch of the single tooth, connect the two end points between the tooth profile and the tooth root fillet after equal spacing to form a tooth core area surface that is approximately an isosceles trapezoid;

[0017] Step 2.3: On the end face 2D sketch of a single tooth, the bottom edge of the tooth core area surface of the approximate isosceles trapezoid is equally divided into four parts, and an auxiliary line is made along the radius direction of the gear at the intersection of the tooth root fillet and the tooth root after equal spacing on one side of the tooth root of the single tooth, and one quarter of the length of the bottom edge of the tooth core area surface of the approximate isosceles trapezoid is intercepted on the auxiliary line and the line segment of the tooth root fillet on the other side along the radius direction, and connected with the four equal points of the tooth core area surface of the approximate isosceles trapezoid to form two tooth root fillet area surfaces;

[0018] Step 2.4: On the end face 2D sketch of the single tooth, a vertical line is drawn from the lower end point of the root fillet area surface on the root side of the single tooth to the root direction to form a root area surface; through steps 2.1-2.4, a total of 7 closed geometric surfaces are divided, namely, 2 carburized area surfaces, 1 tooth core area surface, 2 root fillet area surfaces, 1 root area surface, and 1 solid area surface;

[0019] Step 2.5: Select the remaining five surfaces except the two carburizing zone surfaces, perform stretching and cutting, and the cutting length is the gear tooth width to form a carburizing zone geometry;

[0020] Step 2.6: Select the remaining 6 faces except the one tooth core area face, perform stretching and cutting, and the cutting length is the gear tooth width to form the tooth core area geometry;

[0021] Step 2.7: Select the remaining five faces except the two tooth root fillet area faces, perform stretching and cutting, and the cutting length is the gear tooth width to form the tooth root fillet area geometry;

[0022] Step 2.8: Select the remaining 6 surfaces except the one tooth root area surface, perform stretching and cutting, and the cutting length is the gear tooth width to form the tooth root area geometry;

[0023] Step 2.9: Select the remaining 6 faces except the 1 solid area face, perform stretching and cutting, and the cutting length is the gear tooth width to form a solid area geometry;

[0024] Step 2.10: Combine the five combined areas formed in steps 2.5 to 2.9 to restore the geometric model of a single tooth.

[0025] Furthermore, in step 3, the three-time face cutting of the five component regions is performed, which specifically comprises the following steps:

[0026] Step 3.1: Determine the specific parameters of the mesh to be divided. The parameters include the following five aspects: the number of involute meshes of the carburizing zone tooth profile 3N1, the number of fillet meshes of the carburizing zone tooth root 3N2, the number of tooth root meshes of the carburizing zone 3N3, the number of axial meshes of the carburizing zone 3N4, and the number of meshes that need to be encrypted in the carburizing zone perpendicular to the carburizing direction N5. N1-N5 are any positive integers;

[0027] Step 3.2: In the finite element meshing software, the end face of the carburized zone is cut. First, the end face of the carburized zone is divided into the carburized surface of the tooth profile, the carburized surface of the tooth root fillet, and the carburized surface of the tooth root. Then, the carburized surface is evenly divided into the surface carburized surface and the inner carburized surface. The inner carburized surface of the tooth profile, the inner carburized surface of the tooth root fillet, and the inner carburized surface of the tooth root are divided into N1, N2, and N3 small planes respectively. A small plane is separately divided from the nearest end point of the tooth profile surface carburized surface close to the tooth top circle;

[0028] Step 3.3: Perform surface cutting on the axial surface of the tooth core area, divide the upper and lower short sides formed by the intersection of the axial surface and the two end surfaces of the gear into four equal parts, and connect the upper and lower dividing points close to the left and right edge lines to form two small surfaces and one large surface, and divide the two small surfaces into N4 smaller planes;

[0029] Step 3.4: Perform surface cutting on the axial surface of the tooth root fillet area, and divide the entire plane into N4 small planes along the axial direction;

[0030] Step 3.5: Perform surface cutting on the axial surface of the tooth root area, and divide the entire plane into N4 small planes along the axial direction;

[0031] Step 3.6: Perform surface cutting on the end face of the solid area. First, cut out a surface that is approximately trapezoidal. Then, draw a perpendicular line along the radial direction through one end point of the approximately trapezoid to cut out an elongated quadrilateral surface.

[0032] Furthermore, in step 4, the five divided component areas are respectively gridded, which specifically includes the following steps:

[0033] Step 4.1: Mesh the carburizing zone. On the end face of the carburizing zone, firstly, perform 2D meshing on the surface carburizing layer. Set the number of involute meshes of the carburizing zone tooth profile to 3N1, the number of fillet meshes of the carburizing zone tooth root to 3N2, the number of meshes of the carburizing zone tooth root to 3N3, the number of meshes that need to be encrypted in the carburizing zone surface carburizing layer perpendicular to the carburizing direction to N5, and force the use of quadrilaterals for surface meshing. Then, perform 2D meshing on the inner carburizing layer. Set the number of meshes for each small plane of the inner carburizing layer to 1, with a total of N1+N2+N3 small planes. Force the use of quadrilaterals for surface meshing. After the 2D meshing is completed, drag the 2D mesh along the axial direction. The number of mesh dragging is 3N4 layers, and the dragging length is the tooth width length. Complete the 3D meshing.

[0034] Step 4.2: Mesh the tooth core area. On the axial surface of the tooth core area, first perform 2D meshing. The number of meshes for the two outermost long sides is 3N4, the number of meshes for the two inner long sides is N4, and the number of meshes for the two upper and lower short sides formed by the intersection of the axial surface where the 2D mesh is located and the two end surfaces of the gear is 4. Quadrilaterals are forced to be used for surface meshing. After the 2D meshing is completed, N1 layers of meshes are swept along the four edges formed by the four surfaces intersecting with the surface where the 2D mesh is located to complete the 3D meshing;

[0035] Step 4.3: Mesh the root fillet area. On the axial surface of the root fillet area, first perform 2D meshing. The number of meshes on the long side close to the root fillet is 3N4, and the number of meshes on the other long side opposite to it is N4. The number of meshes on the upper and lower short sides formed by the intersection of the axial surface where the 2D mesh is located and the two end surfaces of the gear is 1. Quadrilaterals are forced to be used for surface meshing. After the 2D meshing is completed, N2 layers of meshes are swept along the four edges formed by the four surfaces intersecting with the surface where the 2D mesh is located to complete the 3D meshing.

[0036] Step 4.4: Mesh the tooth root area. On the axial surface of the tooth root area, first perform 2D meshing. The number of long side meshes close to the carburized layer of the tooth root is 3N4, and the number of other long side meshes opposite to it is N4. The number of upper and lower short side meshes formed by the intersection of the axial surface where the 2D mesh is located and the two end surfaces of the gear is 1. Quadrilaterals are forced to be used for surface meshing. After the 2D meshing is completed, the 4 edges formed by the 4 surfaces intersecting with the surface where the 2D mesh is located are swept by N3 layers of meshes to complete the 3D meshing.

[0037] Step 4.5: Mesh the solid area. First, perform 2D meshing on the end face of the solid area. The number of upper bottom meshes of the approximate trapezoid in the solid area is 2, the number of lower bottom meshes is 4, and the number of oblique edge meshes is N2. The number of left and right sides of the quadrilateral directly below the approximate trapezoid in the solid area is 5, and the number of short side meshes of the slender quadrilateral is N3. Quadrilaterals are forced to be used for surface meshing. After the 2D meshing is completed, the 2D mesh is dragged axially. The number of mesh dragging is N4 layers, and the dragging length is the tooth width length to complete the 3D meshing.

[0038] Beneficial effects of the present invention:

[0039] 1. The present invention provides a method for reducing the number of finite element meshes of gears through spatial transition. On the premise of ensuring the number of meshes at key positions of the carburized layer, the end face mesh transition is achieved through the carburized layer, and the axial mesh transition is achieved at the tooth core and tooth root close to the carburized layer. The spatial transition of the mesh is achieved through two mesh transitions. This method is more effective in reducing the number of meshes than the traditional method of performing mesh transition on the end face. Therefore, the present invention can more effectively reduce the time required for simulation calculation while ensuring the accuracy of finite element simulation.

[0040] 2. Through the grid division method provided by the present invention, a single tooth is divided into 5 combination areas, and specific grid division methods are adopted for the 5 combination areas respectively. Then, the 5 component area grids are combined into an overall grid through common nodes. On the premise of achieving grid space transition, the problem of common node difficulty in gear structured grid space transition is successfully solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a schematic diagram of performing the first body cutting to obtain a single tooth according to the periodic symmetry characteristics of the gear according to a specific embodiment of the present invention;

[0042] Figure 2 is a schematic diagram of a second body cutting process of a single tooth according to a specific embodiment of the present invention;

[0043] Figure 3 is a schematic diagram of the relative positions of five component areas after a single tooth is cut according to a specific embodiment of the present invention;

[0044] Figures 4a to 4e Schematic diagrams of the third surface cutting process of the carburized zone, the tooth core zone, the tooth root fillet zone, the tooth root zone and the solid zone in the five component zones involved in a specific embodiment of the present invention;

[0045] Figure 5a to Figure 5e They are schematic diagrams of a method for meshing the carburized zone, the tooth core zone, the tooth root fillet zone, the tooth root zone and the solid zone in the five combined zones involved in a specific embodiment of the present invention;

[0046] Figure 6a is a schematic diagram of a grid of a single tooth of an internal gear involved in a specific embodiment of the present invention;

[0047] Figure 6b is a schematic diagram of a grid of a single tooth of a pinion gear involved in a specific embodiment of the present invention;

[0048] Figure 7 It is a schematic diagram of the free edge inspection result after the five component area grids have common nodes according to a specific embodiment of the present invention;

[0049] Figure 8It is a schematic diagram of obtaining a complete gear mesh by replicating the rotation of a single tooth according to a specific embodiment of the present invention. DETAILED DESCRIPTION

[0050] The following is a further description of a structured meshing method for reducing the number of gear finite element meshes through spatial transition according to the present invention in conjunction with an embodiment.

[0051] In this embodiment, the pinion has 16 teeth, the internal gear has 198 teeth, the module is 25 mm, the displacement coefficient is 0.5, the tooth width is 290 mm, the carburizing layer depth of the pinion is 2 mm, and the carburizing layer depth of the internal gear is 3 mm. The operation methods of the pinion and the internal gear are exactly the same. The following mainly describes the internal gear in detail, and the steps are as follows:

[0052] Step 1: Figure 1 As shown, according to the periodic symmetry characteristics of the gear, the internal gear geometric model is cut for the first time through 3D modeling software such as SOLIDWORKS, and the geometric models of individual teeth of the internal gear are cut out based on the minimum symmetry period;

[0053] Step 2: If Figure 2 As shown, the second body cutting is performed on the geometric model of a single tooth of the internal gear, which specifically includes the following steps:

[0054] Step 2.1: On the 2D sketch of the end face of a single tooth of the internal gear, make entity references to all the edges on the end face of the single tooth, and according to the actual carburizing depth of the internal gear of 3mm, copy the involute tooth profile, root fillet and root equidistant by 3mm, extend and connect the lines before and after the equidistant, and form two slender carburizing zone surfaces and one closed geometric surface to be divided on the gear end face;

[0055] Step 2.2: On the 2D sketch of the end face of a single tooth of the internal gear, connect the two end points between the equidistant rear tooth profile and the tooth root fillet to form a tooth core area surface that is approximately an isosceles trapezoid;

[0056] Step 2.3: On the 2D sketch of the end face of a single tooth of the internal gear, divide the bottom edge of the tooth core area surface that is approximately an isosceles trapezoid into four equal parts, and draw an auxiliary line along the radius direction of the gear at the intersection of the equidistant root fillet and the tooth root on one side of the single tooth. Cut a quarter of the length of the bottom edge of the tooth core area surface that is approximately an isosceles trapezoid on the auxiliary line and the line segment along the radius direction of the root fillet on the other side, and connect it with the four equal points of the bottom edge of the tooth core area surface that is approximately an isosceles trapezoid to form two root fillet area surfaces;

[0057] Step 2.4: On the 2D sketch of the end face of a single tooth of the internal gear, draw a vertical line from the lower end point of the root fillet area surface on the root side of the single tooth to the root direction to form the root area surface. Through the above steps, a total of 7 closed geometric surfaces are divided, namely 2 carburized area surfaces, 1 tooth core area surface, 2 root fillet area surfaces, 1 root area surface, and 1 solid area surface;

[0058] Step 2.5: Select the remaining 5 faces except the 2 carburizing zone faces, and perform stretching and cutting. The cutting length is 290mm of the gear tooth width to form the carburizing zone geometry;

[0059] Step 2.6: Select the remaining 6 faces except one tooth core area face, and perform stretching and cutting. The cutting length is 290mm of the gear tooth width to form the tooth core area geometry;

[0060] Step 2.7: Select the remaining 5 faces except the 2 root fillet areas, and perform extrusion cutting. The cutting length is 290mm of the gear tooth width to form the root fillet area geometry;

[0061] Step 2.8: Select the remaining 6 faces except one root area face, and perform extrusion cutting. The cutting length is 290mm of the gear tooth width to form the root area geometry;

[0062] Step 2.9: Select the remaining 6 faces except one solid area face, and perform extrusion cutting. The cutting length is 290mm of the gear tooth width to form a solid area geometry;

[0063] Step 2.10: Figure 3 As shown, the five combined areas formed in steps 2.5 to 2.9 are combined to restore the geometric model of a single tooth.

[0064] Step 3: Perform a third surface cutting on the five component areas, including end surface cutting on the carburized area and the solid area, and axial surface cutting on the tooth core area, the tooth root fillet area, and the tooth root area, specifically including the following steps:

[0065] Step 3.1: Determine the specific parameters of the mesh to be divided. The number of meshes for the involute line of the carburizing zone tooth profile is 57, the number of meshes for the fillet of the carburizing zone tooth root is 12, the number of meshes for the tooth root of the carburizing zone is 6, the number of meshes for the axial direction of the carburizing zone is 21, and the number of meshes that need to be encrypted in the carburizing zone perpendicular to the carburizing direction is 2;

[0066] Step 3.2: If Figure 4aAs shown, in the finite element meshing software HYPERMESH, the end face of the carburized zone is cut by the quickedit function. First, the end face of the carburized zone is divided into the carburized surface of the tooth profile, the carburized surface of the tooth root fillet, and the carburized surface of the tooth root. Then the carburized surface is evenly divided into the surface carburized surface and the inner carburized surface. The thickness of the two is 1.5 mm. The inner carburized surface of the tooth profile, the carburized surface of the tooth root fillet, and the inner carburized surface of the tooth root are divided into 19, 4, and 2 small planes respectively, and a small plane is separately divided from the nearest end point of the tooth profile surface carburized surface close to the tooth top circle;

[0067] Step 3.3: If Figure 4b As shown, the axial surface of the tooth core area is cut by the quickedit function, and the upper and lower short sides formed by the intersection of the axial surface and the two end surfaces of the gear are divided into four equal parts, and the upper and lower dividing points close to the left and right edge lines are connected to form two small surfaces and one large surface, and the two small surfaces are divided into seven smaller planes;

[0068] Step 3.4: If Figure 4c As shown in the figure, the axial surface of the root fillet area is cut by the quickedit function, and the entire plane is divided into 7 small planes along the axial direction;

[0069] Step 3.5: If Figure 4d As shown in the figure, the axial surface of the tooth root area is cut by the quickedit function, and the entire plane is divided into 7 small planes along the axial direction;

[0070] Step 3.6: If Figure 4e As shown in the figure, the end face of the solid area is cut by the quickedit function. First, a trapezoidal surface is cut out, and then a perpendicular line is drawn along the radial direction through one end point of the trapezoid to cut out an elongated quadrilateral surface.

[0071] Step 4: Grid division is performed on the five divided component areas respectively, which specifically includes the following steps:

[0072] Step 4.1: Figure 5a As shown, the carburizing zone is meshed. On the end face of the carburizing zone, the surface carburizing layer is firstly meshed in 2D by the automesh function. The number of meshes of the involute line of the tooth profile in the carburizing zone is set to 57, the number of meshes of the fillet of the tooth root in the carburizing zone is set to 12, the number of meshes of the tooth root in the carburizing zone is set to 6, and the number of meshes that need to be encrypted in the surface carburizing layer in the carburizing zone perpendicular to the carburizing direction is set to 2. The surface meshing is forced to be divided by quadrilaterals. Secondly, the inner carburizing layer is meshed in 2D. The number of meshes for each small plane of the inner carburizing layer is set to 1, a total of 19+4+2 small planes, and the surface meshing is forced to be divided by quadrilaterals. After the 2D meshing is completed, the 2D mesh is dragged along the axial direction by the drag function. The number of mesh dragging is 21 layers, and the dragging length is the tooth width length of 290mm, completing the 3D meshing.

[0073] Step 4.2: If Figure 5b As shown, the tooth core area is meshed. On the axial surface of the tooth core area, the automesh function is first used to perform 2D meshing. The number of meshes on the two outermost long sides is 21, the number of meshes on the two inner long sides is 7, and the number of meshes on the upper and lower short sides formed by the intersection of the axial surface where the 2D mesh is located and the two end surfaces of the gear is 4. Quadrilaterals are forced to be used for surface meshing. After the 2D meshing is completed, the solid map function is used to sweep 19 layers of meshes along the four edges formed by the four surfaces intersecting with the surface where the 2D mesh is located to complete the 3D meshing.

[0074] Step 4.3: If Figure 5c As shown, meshing is performed on the tooth root fillet area. On the axial surface of the tooth root fillet, 2D meshing is first performed using the automesh function. The number of meshes on the long side close to the arc is 21, and the number of meshes on the other long side opposite to it is 7. The number of meshes on the upper and lower short sides formed by the intersection of the axial surface where the 2D mesh is located and the two end surfaces of the gear is 1. Quadrilaterals are forced to be used for surface meshing. After the 2D meshing is completed, the solid map function is used to sweep 4 layers of meshes along the 4 edges formed by the 4 surfaces intersecting with the surface where the 2D mesh is located to complete the 3D meshing.

[0075] Step 4.4: If Figure 5d As shown, the tooth root area is meshed. On the axial surface of the tooth root area, the automesh function is used to perform 2D meshing. The number of meshes on the long side close to the carburized layer of the tooth root is 21, and the number of meshes on the other long side opposite to it is 7. The number of meshes on the upper and lower short sides formed by the intersection of the axial surface where the 2D mesh is located and the two end surfaces of the gear is 1. Quadrilaterals are forced to be used for surface meshing. After the 2D meshing is completed, the solid map function is used to sweep two layers of meshes along the four edges formed by the four surfaces intersecting with the surface where the 2D mesh is located to complete the 3D meshing.

[0076] Step 4.5: If Figure 5e As shown, the solid area is meshed. On the end face of the solid area, the automesh function is first used to perform 2D meshing. The number of meshes on the upper bottom of the approximate trapezoid in the solid area is 2, the number of meshes on the lower bottom is 4, and the number of meshes on the oblique side is 4. The number of meshes on the left and right sides of the quadrilateral directly below the approximate trapezoid in the solid area is 5, and the number of meshes on the short side of the slender quadrilateral is 2. The quadrilateral is forced to be used for surface meshing. After the 2D meshing is completed, the 2D mesh is dragged axially by the drag function. The number of mesh dragging is 7 layers, and the dragging length is the tooth width length of 290mm to complete the 3D meshing.

[0077] Step 5: Figure 6aAs shown in the figure, the 3D mesh formed by meshing the five component areas of the internal gear is set with a tolerance of 0.4 mm through the edges function, and a common node operation is performed, and a free edge check is performed, as shown in the figure. Figure 7 As shown in the figure, the free edge check result shows that there are no free edges in the internal space of a single tooth mesh of the internal gear, and all meshes have common nodes, such as Figure 6b As shown, the meshing method for the pinion gear is the same as that for the internal gear;

[0078] Step 6: Figure 8 As shown, according to the periodic symmetry characteristics of the internal gear and the pinion, the mesh of a single tooth is copied and rotated through the rotate function. The rotation angle of the internal gear is 1.818°, and the rotation angle of the pinion is 22.5°. A complete gear mesh is formed, and common node operations and inspections are performed.

Claims

1. A method for reducing the number of gear finite element meshes through spatial transition, characterized in that: The following steps are involved: Step 1: According to the periodic symmetry characteristics of the gear, the gear geometric model is cut for the first time in the 3D modeling software to cut out the geometric model of a single tooth; Step 2: Perform a second body cutting on the geometric model of the single tooth to cut out five component areas, namely, a carburized area, a tooth core area, a tooth root fillet area, a tooth root area and a solid area; Step 3: performing a third surface cutting on the five component areas, including end surface cutting on the carburized area and the solid area, and axial surface cutting on the tooth core area, the tooth root fillet area and the tooth root area; Step 4: Mesh the five cut component areas respectively, wherein 2D meshing is performed on the end faces of the carburized area and the solid area, and then the 2D mesh is dragged along the axial direction of the gear to generate a 3D mesh, so as to achieve end face mesh transition and reduce the number of meshes; 2D meshing is performed on the axial faces of the tooth core area, the tooth root fillet area and the tooth root area, and then a 3D mesh is generated by sweeping along the four edge lines formed by the four faces intersecting with the faces where the respective 2D meshes are located, so as to achieve axial mesh transition and reduce the number of meshes; Step 5: For the 3D mesh formed after the mesh division of the five component areas, set the tolerance, perform the common node operation, and perform the free edge check to determine whether all meshes have achieved common nodes. If there is no common node position, increase the tolerance for the mesh in this area and perform the common node operation again; repeat the operation until all meshes have achieved common nodes; Step 6: Based on the periodic symmetry characteristics of the gear, copy and rotate the mesh of a single tooth to form a complete gear mesh, and perform common node operations.

2. A method for reducing the number of gear finite element meshes by spatial transition according to claim 1, characterized in that: The second body cutting of the geometric model of the single tooth in step 2 specifically includes the following steps: Step 2.1: Using 3D modeling software, on the 2D sketch of the end face of a single tooth, entity references are made to all edge lines on the end face of the single tooth, and according to the actual carburizing depth of the gear, the involute tooth profile, the root fillet and the root are equidistantly copied, and the lines before and after the equidistant are extended and connected to form two elongated carburizing zone surfaces on the end face of the gear; Step 2.2: On the end face 2D sketch of the single tooth, connect the two end points between the tooth profile and the tooth root fillet after equal spacing to form a tooth core area surface that is approximately an isosceles trapezoid; Step 2.3: On the 2D sketch of the end face of the single tooth, the bottom side of the tooth core area of ​​the approximate isosceles trapezoid is divided into four parts, and an auxiliary line is made along the radius direction of the gear at the intersection of the tooth root fillet and the tooth root after equal spacing on one side of the tooth root of the single tooth, and one quarter of the length of the bottom side of the tooth core area of ​​the approximate isosceles trapezoid is intercepted on the auxiliary line and the line segment of the tooth root fillet on the other side along the radius direction, and connected with the equally divided points of the tooth core area of ​​the approximate isosceles trapezoid to form two tooth root fillet area surfaces; Step 2.4: On the end face 2D sketch of the single tooth, a vertical line is drawn from the lower end point of the root fillet area surface on the root side of the single tooth to the root direction to form a root area surface; through the above steps 2.1-2.4, a total of 7 closed geometric surfaces are divided, namely, 2 carburized area surfaces, 1 tooth core area surface, 2 root fillet area surfaces, 1 root area surface, and 1 solid area surface; Step 2.5: Select the remaining five surfaces except the two carburizing zone surfaces, perform stretching and cutting, and the cutting length is the gear tooth width to form a carburizing zone geometry; Step 2.6: Select the remaining 6 faces except the one tooth core area face, perform stretching and cutting, and the cutting length is the gear tooth width to form the tooth core area geometry; Step 2.7: Select the remaining five faces except the two tooth root fillet area faces, perform stretching and cutting, and the cutting length is the gear tooth width to form the tooth root fillet area geometry; Step 2.8: Select the remaining 6 surfaces except the one tooth root area surface, perform stretching and cutting, and the cutting length is the gear tooth width to form the tooth root area geometry; Step 2.9: Select the remaining 6 faces except the 1 solid area face, perform stretching and cutting, and the cutting length is the gear tooth width to form a solid area geometry; Step 2.10: Combine the five combined areas formed in steps 2.5 to 2.9 to restore the geometric model of a single tooth.

3. The method for reducing the number of gear finite element meshes by spatial transition according to claim 1, characterized in that: In step 3, the three-dimensional cutting of the five component regions is performed, which specifically includes the following steps: Step 3.1: Determine the specific parameters of the mesh to be divided. The parameters include the following five aspects: the number of involute meshes of the carburizing zone tooth profile 3N1, the number of fillet meshes of the carburizing zone tooth root 3N2, the number of tooth root meshes of the carburizing zone 3N3, the number of axial meshes of the carburizing zone 3N4, and the number of meshes that need to be encrypted in the carburizing zone perpendicular to the carburizing direction N5. N1-N5 are any positive integers; Step 3.2: In the finite element meshing software, the end face of the carburized zone is cut. First, the end face of the carburized zone is divided into the carburized surface of the tooth profile, the carburized surface of the tooth root fillet, and the carburized surface of the tooth root. Then, the carburized surface is evenly divided into the surface carburized surface and the inner carburized surface. The inner carburized surface of the tooth profile, the inner carburized surface of the tooth root fillet, and the inner carburized surface of the tooth root are divided into N1, N2, and N3 small planes respectively. A small plane is separately divided from the nearest end point of the tooth profile surface carburized surface close to the tooth top circle; Step 3.3: Perform surface cutting on the axial surface of the tooth core area, divide the upper and lower short sides formed by the intersection of the axial surface and the two end surfaces of the gear into four equal parts, and connect the upper and lower dividing points close to the left and right edge lines to form two small surfaces and one large surface, and divide the two small surfaces into N4 smaller planes; Step 3.4: Perform surface cutting on the axial surface of the tooth root fillet area, and divide the entire plane into N4 small planes along the axial direction; Step 3.5: Perform surface cutting on the axial surface of the tooth root area, and divide the entire plane into N4 small planes along the axial direction; Step 3.6: Perform surface cutting on the end face of the solid area. First, cut out a surface that is approximately trapezoidal. Then, draw a perpendicular line along the radial direction through one end point of the approximately trapezoid to cut out an elongated quadrilateral surface.

4. The method for reducing the number of gear finite element meshes by spatial transition according to claim 1, characterized in that: In step 4, the five divided component areas are respectively gridded, which specifically includes the following steps: Step 4.1: Mesh the carburizing zone. On the end face of the carburizing zone, firstly, perform 2D meshing on the surface carburizing layer. Set the number of involute meshes of the carburizing zone tooth profile to 3N1, the number of fillet meshes of the carburizing zone tooth root to 3N2, the number of meshes of the carburizing zone tooth root to 3N3, the number of meshes that need to be encrypted in the carburizing zone surface carburizing layer perpendicular to the carburizing direction to N5, and force the use of quadrilaterals for surface meshing. Then, perform 2D meshing on the inner carburizing layer. Set the number of meshes for each small plane of the inner carburizing layer to 1, with a total of N1+N2+N3 small planes. Force the use of quadrilaterals for surface meshing. After the 2D meshing is completed, drag the 2D mesh along the axial direction. The number of mesh dragging is 3N4 layers, and the dragging length is the tooth width length. Complete the 3D meshing. Step 4.2: Mesh the tooth core area. On the axial surface of the tooth core area, first perform 2D meshing. The number of meshes for the two outermost long sides is 3N4, the number of meshes for the two inner long sides is N4, and the number of meshes for the two upper and lower short sides formed by the intersection of the axial surface where the 2D mesh is located and the two end surfaces of the gear is 4. Quadrilaterals are forced to be used for surface meshing. After the 2D meshing is completed, N1 layers of meshes are swept along the four edges formed by the four surfaces intersecting with the surface where the 2D mesh is located to complete the 3D meshing; Step 4.3: Mesh the root fillet area. On the axial surface of the root fillet area, first perform 2D meshing. The number of meshes on the long side close to the root fillet is 3N4, and the number of meshes on the other long side opposite to it is N4. The number of meshes on the upper and lower short sides formed by the intersection of the axial surface where the 2D mesh is located and the two end surfaces of the gear is 1. Quadrilaterals are forced to be used for surface meshing. After the 2D meshing is completed, N2 layers of meshes are swept along the four edges formed by the four surfaces intersecting with the surface where the 2D mesh is located to complete the 3D meshing. Step 4.4: Mesh the tooth root area. On the axial surface of the tooth root area, first perform 2D meshing. The number of long side meshes close to the carburized layer of the tooth root is 3N4, and the number of other long side meshes opposite to it is N4. The number of upper and lower short side meshes formed by the intersection of the axial surface where the 2D mesh is located and the two end surfaces of the gear is 1. Quadrilaterals are forced to be used for surface meshing. After the 2D meshing is completed, the 4 edges formed by the 4 surfaces intersecting with the surface where the 2D mesh is located are swept by N3 layers of meshes to complete the 3D meshing. Step 4.5: Mesh the solid area. First, perform 2D meshing on the end face of the solid area. The number of upper bottom meshes of the approximate trapezoid in the solid area is 2, the number of lower bottom meshes is 4, and the number of oblique edge meshes is N2. The number of left and right sides of the quadrilateral directly below the approximate trapezoid in the solid area is 5, and the number of short side meshes of the slender quadrilateral is N3. Quadrilaterals are forced to be used for surface meshing. After the 2D meshing is completed, the 2D mesh is dragged axially. The number of mesh dragging is N4 layers, and the dragging length is the tooth width length to complete the 3D meshing.

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