CN114818181A - Tooth profile based straight toothed spur gear finite element mesh automatic generation method and computer equipment - Google Patents
Tooth profile based straight toothed spur gear finite element mesh automatic generation method and computer equipment Download PDFInfo
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Abstract
A method for automatically generating a finite element mesh of a straight toothed spur gear based on a tooth profile and computer equipment belong to the technical field of gear simulation and solve the problems of low mesh node precision and low working efficiency of a mesh obtained by the existing method. The method comprises the following steps: establishing a rectangular coordinate system; acquiring a tooth profile line of a half gear tooth; establishing a half gear tooth frame according to the gear profile, the gear inner circle radius and the gear tooth boundary line; dividing the half cog frame into an upper region, a middle region and a lower region; respectively carrying out meshing on the upper area, the middle area and the lower area to obtain all nodes of a half gear tooth section; acquiring all nodes of a single gear tooth according to all nodes of the half gear tooth section; acquiring all nodes of the whole gear according to all nodes of the single gear tooth; and compiling a connection relation to obtain a gear grid model. The method is suitable for automatic generation of the finite element mesh model of the straight spur gear.
Description
Technical Field
The application relates to the technical field of gear simulation, in particular to a tooth profile-based method for automatically generating a finite element mesh of a straight spur gear and computer equipment.
Background
Spur gear transmission is an important mechanical transmission form, and is widely applied to power transmission of vehicles such as automobiles and rail vehicles, mechanical equipment for production and life, and the like. During rotation of the gears, loads are transferred between the gears. When the rotating speed is high and the load is high, marks can be left on the gear, and even the gear is worn and even broken. In order to reduce the damage phenomena of the gears as much as possible, simulation analysis needs to be carried out on the gears, and meshing of the gears is an essential step.
In the prior art, in gear finite element analysis: on one hand, gear meshing requires that a gear three-dimensional geometric model is established first, then the three-dimensional model is led into finite element analysis software, parameters such as the shape and the size of the model are utilized, then a series of mesh parameters are set to generate mesh nodes, and the gear mesh model can be obtained through a complex process. On the other hand: the grid node obtained by the existing cylindrical gear grid division node selection method is low in precision, points need to be taken again at a specific position for division, and workload of grid processing at the later stage is increased. When finite element stress analysis is carried out, the grid quality after structure dispersion directly influences the solving time and the correctness of the solving result. When the grid is sparse or the degree of grid irregularity is large, the accuracy of the solution result is greatly reduced; when the grids are dense, the number of the grids is huge, so that the solving time is greatly increased.
Disclosure of Invention
The invention aims to solve the problems of low mesh node precision and low working efficiency of a mesh obtained by the existing method, and provides a tooth profile-based method for automatically generating a finite element mesh of a straight spur gear and computer equipment.
The invention is realized by the following technical scheme, and on one hand, the invention provides a tooth profile-based method for automatically generating a finite element mesh of a straight spur gear, which comprises the following steps:
step 3, establishing a half gear tooth frame according to the gear contour line, the gear inner circle radius and the gear tooth boundary line;
and 8, compiling connection relations of all nodes of the whole gear to obtain a gear grid model.
Further, the step 4 specifically includes:
step 4.1, acquiring the difference between the vertical coordinates of the starting point and the end point;
step 4.2, setting a preset proportion, and determining a difference value of the vertical coordinate of the boundary line and the vertical coordinate of the terminal point according to the difference of the vertical coordinates and a multiplier of the preset proportion;
4.3, acquiring the boundary line of the half gear tooth frame in the upper and lower directions of the end point according to the difference value between the vertical coordinate of the boundary line and the vertical coordinate of the end point;
and 4.4, dividing the half gear tooth frame into an upper area, a middle area and a lower area according to the boundary line.
Further, the step 5 specifically includes:
step 5.1, setting an upper longitudinal number parameter and an upper transverse number parameter for the upper region, and carrying out grid division on the upper region according to the upper longitudinal number parameter and the upper transverse number parameter to obtain all nodes of the upper region, wherein all nodes of the upper region comprise nodes on a boundary line between the upper region and the middle region;
step 5.2, setting a middle longitudinal number of parts parameter for the middle region, and performing grid division on the middle region according to the middle longitudinal number of parts parameter, the upper transverse number of parts parameter and nodes on a boundary line between the upper region and the middle region by using a quadratic Bezier curve to obtain all nodes of the middle region, wherein all the nodes of the middle region comprise nodes on the boundary line between the middle region and the lower region;
step 5.3, setting a lower longitudinal number of copies parameter for the lower region, and performing grid division on the lower region according to the lower longitudinal number of copies parameter and nodes on a boundary line between the middle region and the lower region to obtain all nodes of the lower region;
and 5.4, acquiring all nodes of the section of half gear tooth according to the upper region node, the middle region node and the lower region node.
Further, the step 5.1 specifically includes:
step 5.1.1, uniformly taking points of a line segment of the upper region on a y axis according to the upper longitudinal part number parameters to obtain a plurality of first upper longitudinal points, and carrying out interpolation point taking on a tooth profile line of the upper region according to the first upper longitudinal points to obtain a plurality of second upper longitudinal points, wherein the longitudinal coordinates of the first upper longitudinal points are equal to the longitudinal coordinates of the second upper longitudinal points in a one-to-one correspondence manner;
step 5.1.2, according to the upper transverse number parameter, equally dividing a first upper longitudinal point and a second upper longitudinal point which are correspondingly equal in vertical coordinate to obtain an upper region transverse node, wherein the upper region transverse node comprises a node on a boundary line between an upper region and a middle region;
and 5.1.3, acquiring all nodes of the upper area according to the first upper longitudinal point, the second upper longitudinal point and the upper area transverse node.
Further, the step 5.2 specifically includes:
step 5.2.1, dividing line segments of the middle area on a y axis according to the middle longitudinal number parameter to obtain a plurality of first middle longitudinal points, and setting the first middle longitudinal points as starting points of a Bezier curve;
step 5.2.2, dividing the tooth profile line of the middle area according to the middle longitudinal part number parameters to obtain a plurality of second middle longitudinal points, and setting the second middle longitudinal points as the end points of the Bezier curve;
step 5.2.3, the first middle longitudinal point and the second middle longitudinal point are in one-to-one correspondence according to a longitudinal sequence, and the normals of the line segments where the corresponding first middle longitudinal point and the second middle longitudinal point are located are intersected to obtain a normal intersection point of the longitudinal points;
step 5.2.4, acquiring a quadratic Bezier curve according to the first middle longitudinal point, the second middle longitudinal point and the normal intersection point of the longitudinal points, wherein the method specifically comprises the following steps:
x＝(1-t) 2 x 0 +2t(1-t)x 1 +t 2 x 2 ,t∈[0,1]
y＝(1-t) 2 y 0 +2t(1-t)y 1 +t 2 y 2 ,t∈[0,1]
wherein (x) 0 ,y 0 ) (x) is the first mid-section longitudinal point coordinate 2 ,y 2 ) Is the second mid longitudinal point, (x) 1 ,y 1 ) Is the intersection point of the normal lines of the longitudinal points;
step 5.2.5, setting a preset increment value, determining a plurality of t values according to the preset increment value, selecting a plurality of points on the secondary Bezier curve according to the plurality of t values, and accumulating the intervals of the plurality of points on the selected secondary Bezier curve to obtain the length of the secondary Bezier curve;
step 5.2.6, dividing the secondary Bezier curve according to the upper transverse number parameter and the length of the secondary Bezier curve to obtain an internal node of the middle area;
dividing the boundary of the middle region without taking points according to nodes on the boundary line between the upper region and the middle region to obtain the nodes on the boundary of the middle region without taking points, wherein the nodes on the boundary of the middle region without taking points comprise the nodes on the boundary line between the middle region and the lower region;
and 5.2.7, acquiring all nodes of the middle area according to the first middle longitudinal point, the second middle longitudinal point, the internal nodes of the middle area and the nodes of the boundary of the middle area where the points are not taken.
Further, the step 5.3 specifically includes:
step 5.3.1, setting two endpoints of a line segment of the lower region on the y axis as a starting point and an end point of the bezier curve from bottom to top respectively, and acquiring a control point of the bezier curve according to the two endpoints and the lower longitudinal number of parts parameter, wherein the distance between the control point and the lower endpoint of the line segment of the lower region on the y axis is as follows:
L P0 P2 *(LowerVer-1)/LowerVer
wherein L is P0 P2 The distance between the two end points is defined as LowerVer as the lower longitudinal part parameter;
step 5.3.2, acquiring a Bezier curve according to the two end points and the control point of the Bezier curve;
step 5.3.3, according to the Bezier curve, point taking is carried out on the line segment of the lower area on the y axis, and a plurality of first lower longitudinal points are obtained;
step 5.3.4, point taking is carried out on the gear tooth boundary line of the lower area according to the node of the line segment of the lower area on the y axis, and a plurality of second lower longitudinal points are obtained, wherein the longitudinal coordinates of the first lower longitudinal points are equal to the longitudinal coordinates of the second lower longitudinal points in a one-to-one correspondence manner;
determining a lower transverse score parameter according to a node on a boundary line between the middle region and the lower region;
according to the lower transverse number of parts parameter, equally dividing the first lower longitudinal point and the second lower longitudinal point which are correspondingly equal in ordinate, and obtaining a lower region transverse node;
and acquiring all nodes of the lower area according to the first lower longitudinal point, the second lower longitudinal point and the transverse nodes of the lower area.
Further, the step 6 specifically includes:
step 6.1, acquiring all nodes of the section of a single gear tooth according to all nodes of the section of the half gear tooth by using the symmetrical relation;
6.2, removing nodes on one side of the section of the single gear tooth, and obtaining all nodes of the section of the single gear tooth with the repetition points removed;
and 6.3, stretching all nodes of the section of the single gear tooth with the repetition points removed according to the thickness parameter of the gear and the number of parts of the gear divided in the thickness direction, and obtaining all nodes of the single gear tooth.
Further, the step 7 specifically includes:
step 7.1, obtaining the coordinates of the tooth-root tooth profile point, and setting the coordinates of the tooth-root tooth profile point as (x, y), wherein the formula is as follows:
tanθ＝x/y
theta is the radian occupied by half gear teeth on the whole gear;
step 7.2, acquiring the radian of one gear tooth on the whole gear according to the radian of the half gear tooth on the whole gear, namely alpha is 2 theta;
step 7.3, converting the alpha into an angle system, wherein beta is 2 theta 180/pi, and beta is a rotation angle;
7.4, acquiring the number n of teeth on the gear according to the rotation angle;
and 7.5, rotating all the nodes of the single gear tooth around a gear circular mandrel according to the rotating angle and the number of the teeth on the gear until n gear teeth are obtained, and further obtaining all the nodes of the whole gear.
Further, the step 8 specifically includes:
8.1, respectively compiling connection relations of nodes of a single gear tooth in all nodes of the whole gear to obtain an initial gear;
and 8.2, respectively compiling connection relations of points on two sides of each gap in the initial gear to obtain a gear mesh model.
In another aspect, the present invention provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and the processor executes the steps of the method for automatically generating a finite element mesh of a spur gear based on a tooth profile as described above when executing the computer program stored in the memory.
The invention has the beneficial effects that:
therefore, the node selection algorithm in the invention divides the zones into grids according to the structural characteristics of the gears. Because the load borne by some regions is large, the accuracy of a solution result needs to be improved, and the grid arrangement of the part is dense; on the contrary, the grid density is normally selected to meet the engineering requirements if some parts have regular shapes and have no special requirements in stress analysis.
According to the stress characteristics of the cylindrical gear, the invention selects an automatic generation method of the grid of the cylindrical spur gear, which is suitable for the stress simulation analysis of the cylindrical gear. In the prior art, gear meshing needs to establish a gear three-dimensional geometric model firstly, then the three-dimensional model is led into finite element analysis software, parameters such as the shape and the size of the model are utilized, then a series of mesh parameters are set to generate mesh nodes, and the gear mesh model can be obtained through a complex process. Finally, the gear mesh model can be directly generated, and a complex flow is omitted. Firstly, the gear mesh model is directly generated according to the contour line data, so that the process of establishing the gear model and the complex process of analyzing the gear data are avoided, a proper node can be quickly acquired, and the mesh generation efficiency is improved;
secondly, the point-taking algorithm in the invention, such as linear interpolation, Bezier curve, stretching and rotation, has low calculation complexity, and can select nodes meeting the precision so as to realize the requirements on the grid quality and the grid generation speed.
The method is suitable for automatic generation of the finite element mesh model of the straight spur gear.
Drawings
In order to more clearly explain the technical solution of the present application, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious to those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic view of profile line data of the present invention (a is a schematic view of a profile line, and b is a schematic view of a point on the profile line);
FIG. 2 is a schematic illustration of a gear tooth region of the present invention;
FIG. 3 is a schematic view of the upper region longitudinal division of the present invention;
FIG. 4 is a schematic diagram of the distribution of all nodes in the upper region according to the present invention;
FIG. 5 is a schematic diagram of a node in a middle area according to the present invention (a is a schematic diagram of node distribution on a boundary of the middle area, and b is a schematic diagram of node selection in the middle area);
FIG. 6 is a schematic diagram of the distribution of all nodes in the middle area according to the present invention;
FIG. 7 is a schematic diagram of node selection on the lower zone boundary of the present invention;
FIG. 8 is a schematic view of the distribution of all nodes in the lower region according to the present invention;
FIG. 9 is a schematic view of the overall node distribution of a half tooth section of the present invention;
FIG. 10 is a schematic view of the overall node distribution of a single tooth section of the present invention;
FIG. 11 is a cross-sectional mesh effect of the gear teeth of the present invention;
FIG. 12 is a right nodal view of a gear section of the present invention;
FIG. 13 is a left nodal view of a gear section of the present invention;
FIG. 14 is a cross-sectional effect of the gear tooth of the present invention;
FIG. 15 is a schematic view of an overall node stretch of a single tooth section of the present invention;
FIG. 16 is a schematic view of the arc of one half of a gear tooth of the present invention over the entire gear;
FIG. 17 is a schematic view of the overall node distribution of the entire gear of the present invention;
FIG. 18 is a schematic diagram of a connection relationship written for a single gear tooth according to the present invention (the left and right diagrams are distributed at different angles);
FIG. 19 is a schematic diagram of a hexahedral connection relationship in the compiling connection relationship according to the present invention;
FIG. 20 is a schematic view of the initial gear of the present invention;
FIG. 21 is an enlarged schematic view of the initial gear of the present invention;
FIG. 22 is a schematic view of a gear mesh model of the present invention at various angles;
FIG. 23 is a flowchart illustrating a method according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are exemplary and intended to be illustrative of the present invention and are not to be construed as limiting the present invention.
In one embodiment, a method for automatically generating a finite element mesh of a spur gear based on a tooth profile includes:
step 3, establishing a half gear tooth frame according to the gear profile, the gear inner circle radius and the gear tooth boundary line;
and 8, compiling connection relations of all nodes of the whole gear to obtain a gear grid model.
It should be noted that the gear tooth boundary line refers to a line at the interface between the gear tooth and the gear tooth.
The mesh nodes are selected by only one mesh division method without gear parameters based on known gear profile data, so that the mesh precision of the gear is greatly improved. Although the contour line used in the patent is also calculated from the basic parameters of the gear, the basic parameters of the gear are not used for selecting the node. Therefore, in the object-oriented programming process, the gear basic parameters are not needed, and complex data analysis is avoided in the aspect of selecting the segmentation boundary points.
In the method of the embodiment, the data of the tooth profile is mainly based, and then the operator inputs related parameters such as grid density and the like to realize point acquisition and connection, and finally vtk files which can be used for visualization of the gear grid model are generated.
The embodiment can realize the establishment of the gear mesh model in a program through object-oriented programming.
In a second embodiment, the present embodiment is further limited to the method for automatically generating a finite element mesh of a spur gear based on a tooth profile in the first embodiment, and in the present embodiment, the step 4 is further limited, and specifically includes:
step 4.1, acquiring the difference between the vertical coordinates of the starting point and the end point;
step 4.2, setting a preset proportion, and determining a difference value of the vertical coordinate of the boundary line and the vertical coordinate of the terminal point according to the difference of the vertical coordinates and a multiplier of the preset proportion;
4.3, acquiring the boundary line of the half gear tooth frame in the upper and lower directions of the end point according to the difference value between the vertical coordinate of the boundary line and the vertical coordinate of the end point;
and 4.4, dividing the half gear tooth frame into an upper area, a middle area and a lower area according to the boundary line.
In this embodiment, the middle part region is tooth root department, and this region has certain requirement to the node precision, so when dividing the boundary line, consider to use the lowest point of tooth's socket namely the coordinate of tooth profile point of tooth root as the basis of choosing of boundary line, carry out the subregion, make the node choose the process more rationally clear.
In a third embodiment, the present embodiment is further limited to the method for automatically generating a finite element mesh of a spur gear based on a tooth profile in the first embodiment, and in the present embodiment, the step 5 is further limited, and specifically includes:
step 5.1, setting an upper longitudinal number parameter and an upper transverse number parameter for the upper region, and carrying out grid division on the upper region according to the upper longitudinal number parameter and the upper transverse number parameter to obtain all nodes of the upper region, wherein all nodes of the upper region comprise nodes on a boundary line between the upper region and the middle region;
step 5.2, setting a middle longitudinal number of parts parameter for the middle region, and performing grid division on the middle region according to the middle longitudinal number of parts parameter, the upper transverse number of parts parameter and the nodes on the boundary line between the upper region and the middle region by using a quadratic Bezier curve to obtain all nodes of the middle region, wherein all the nodes of the middle region comprise the nodes on the boundary line between the middle region and the lower region and do not comprise the nodes on the boundary line between the upper region and the middle region;
and 5.3, setting a lower longitudinal number of parts parameter for the lower area, and carrying out grid division on the lower area according to the lower longitudinal number of parts parameter and the nodes on the boundary line between the middle area and the lower area to obtain all the nodes of the lower area, wherein the nodes on the boundary line between the middle area and the lower area are not included.
And 5.4, acquiring all nodes of the section of half gear tooth according to the upper region node, the middle region node and the lower region node.
In this embodiment, one gear includes gear teeth and a gear body, where the gear body refers to the whole gear except the gear teeth. The upper region corresponds to the gear tooth portion, the lower region corresponds to the gear body portion, and the middle region corresponds to the transition region of the gear teeth and gear body. Therefore, the division into three regions is most appropriate, and certainly not less than three regions, and there is no need to divide more regions, which only increases the workload and does not further improve the grid precision.
In the embodiment, the requirements of the upper area and the lower area on the grid size and the node precision are not high, and the nodes at the two positions are simple to select. The middle area is the tooth root, and the area has certain requirements on the node precision. And (4) taking points by partitioning, so that the node selecting process is more reasonable and clear, and the grid precision is improved.
In a fourth embodiment, the present embodiment is further limited to the method for automatically generating a finite element mesh of a spur gear based on a tooth profile in the first embodiment, and in the present embodiment, the step 5.1 is further limited, and specifically includes:
step 5.1.1, uniformly taking points of a line segment of the upper region on a y axis according to the upper longitudinal part number parameters to obtain a plurality of first upper longitudinal points, and carrying out interpolation point taking on a tooth profile line of the upper region according to the first upper longitudinal points to obtain a plurality of second upper longitudinal points, wherein the longitudinal coordinates of the first upper longitudinal points are equal to the longitudinal coordinates of the second upper longitudinal points in a one-to-one correspondence manner;
step 5.1.2, according to the upper transverse number parameter, equally dividing a first upper longitudinal point and a second upper longitudinal point which are correspondingly equal in vertical coordinate to obtain an upper region transverse node, wherein the upper region transverse node comprises a node on a boundary line between an upper region and a middle region;
and 5.1.3, acquiring all nodes of the upper area according to the first upper longitudinal point, the second upper longitudinal point and the upper area transverse node.
In the embodiment, aiming at the characteristics of the upper region, such as low requirements on the mesh size and the node precision, the linear interpolation method is adopted to perform mesh division on the upper region, so that the requirement on the mesh precision can be met, the complexity of data analysis can be reduced, and the mesh division efficiency is further improved.
Fifth, the present embodiment is further limited to the method for automatically generating a finite element mesh of a spur gear based on a tooth profile according to the first embodiment, and in the present embodiment, the step 5.2 is further limited, and specifically includes:
step 5.2.1, dividing line segments of the middle area on a y axis according to the middle longitudinal number parameter to obtain a plurality of first middle longitudinal points, and setting the first middle longitudinal points as starting points of a Bezier curve;
step 5.2.2, dividing the tooth profile line of the middle area according to the middle longitudinal part number parameters to obtain a plurality of second middle longitudinal points, and setting the second middle longitudinal points as the end points of the Bezier curve;
step 5.2.3, the first middle longitudinal point and the second middle longitudinal point are in one-to-one correspondence according to a longitudinal sequence, and the normals of the line segments where the corresponding first middle longitudinal point and the second middle longitudinal point are located are intersected to obtain a normal intersection point of the longitudinal points;
step 5.2.4, acquiring a quadratic Bezier curve according to the first middle longitudinal point, the second middle longitudinal point and the normal intersection point of the longitudinal points, wherein the method specifically comprises the following steps:
x＝(1-t) 2 x 0 +2t(1-t)x 1 +t 2 x 2 ,t∈[0,1]
y＝(1-t) 2 y 0 +2t(1-t)y 1 +t 2 y 2 ,t∈[0,1]
wherein (x) 0 ,y 0 ) (x) is the first mid-section longitudinal point coordinate 2 ,y 2 ) Is the second mid longitudinal point, (x) 1 ,y 1 ) Is the intersection point of the normal lines of the longitudinal points;
step 5.2.5, setting a preset increment value, determining a plurality of t values according to the preset increment value, selecting a plurality of points on the secondary Bezier curve according to the plurality of t values, and accumulating the intervals of the plurality of points on the selected secondary Bezier curve to obtain the length of the secondary Bezier curve;
step 5.2.6, dividing the secondary Bezier curve according to the upper transverse number parameter and the length of the secondary Bezier curve to obtain an internal node of the middle area;
dividing the boundary of the middle region without taking points according to nodes on the boundary line between the upper region and the middle region to obtain the nodes on the boundary of the middle region without taking points, wherein the nodes on the boundary of the middle region without taking points comprise the nodes on the boundary line between the middle region and the lower region;
and 5.2.7, acquiring all nodes of the middle area according to the first middle longitudinal point, the second middle longitudinal point, the internal nodes of the middle area and the nodes of the boundary of the middle area where the points are not taken.
In the present embodiment, the present invention may be applied to a liquid crystal display device
Setting the preset value to be 0.005;
starting from t equal to 0, the values are incremented by 0.005 each time until t equal to 1, and the points on the quadratic bezier curve are obtained.
Each increment of t from 0 to 0.005 to 1 results in a bezier curve simulated by 201 points. the smaller the value of t increment, the more points are obtained, and the more accurate the simulated bezier curve is. t can be chosen to be 0.001, so that the simulated bezier curve will be more accurate, but too many points will increase the computation time of the program. In the present embodiment, t is 0.005, and thus can completely satisfy the requirement for the accuracy of the simulated bezier curve.
In this embodiment, by using a quadratic bezier curve, a point meeting the grid accuracy requirement can be selected in the middle region.
Sixth embodiment, the present embodiment is further limited to the method for automatically generating a finite element mesh of a spur gear based on a tooth profile according to the first embodiment, and in the present embodiment, the step 5.3 is further limited, and specifically includes:
step 5.3.1, setting two endpoints of a line segment of the lower region on the y axis as a starting point and an end point of the Bezier curve from bottom to top respectively, and acquiring a control point of the Bezier curve according to the two endpoints and the lower longitudinal number of parts parameter, wherein the distance between the control point and the lower endpoint of the line segment of the lower region on the y axis is as follows:
L P0 P2 *(LowerVer-1)/LowerVer
wherein L is P0 P2 The distance between the two end points is defined as LowerVer as the lower longitudinal part parameter;
step 5.3.2, acquiring a Bezier curve according to the two end points and the control point of the Bezier curve;
step 5.3.3, according to the Bezier curve, point taking is carried out on the line segment of the lower area on the y axis, and a plurality of first lower longitudinal points are obtained;
step 5.3.4, point taking is carried out on the gear tooth boundary line of the lower area according to the node of the line segment of the lower area on the y axis, and a plurality of second lower longitudinal points are obtained, wherein the longitudinal coordinates of the first lower longitudinal points are equal to the longitudinal coordinates of the second lower longitudinal points in a one-to-one correspondence manner;
determining a lower transverse score parameter according to a node on a boundary line between the middle region and the lower region;
according to the lower transverse number of parts parameter, equally dividing the first lower longitudinal point and the second lower longitudinal point which are correspondingly equal in ordinate, and obtaining a lower region transverse node;
and acquiring all nodes of the lower area according to the first lower longitudinal point, the second lower longitudinal point and the transverse nodes of the lower area.
In the embodiment, the application of the quadratic bezier curve is different from the application in the middle area, and an appropriate control point is selected here, so that the longitudinal division of the lower area is not uniform. Therefore, the grid near the tooth root is small, and the accuracy of the simulation result is ensured.
It should be noted that the bezier curve equation can be selected from three times, four times and many times, but the calculation is complicated and the result is not greatly different from the result of the second time.
Seventh, the present embodiment is further limited to the method for automatically generating a finite element mesh of a spur gear based on a tooth profile according to the first embodiment, and in the present embodiment, the step 6 is further limited, and specifically includes:
step 6.1, acquiring all nodes of the section of a single gear tooth according to all nodes of the section of the half gear tooth by using the symmetrical relation;
6.2, removing nodes on one side of the section of the single gear tooth, and obtaining all nodes of the section of the single gear tooth with the repetition points removed;
and 6.3, stretching all nodes of the section of the single gear tooth without the repetition points according to the thickness parameters of the gear and the number of parts of the gear divided in the thickness direction to obtain all nodes of the single gear tooth.
In this embodiment, the points obtained in step 6.1 on the entire cross section of a single gear tooth must coincide with each other during the later rotation, for example, the right boundary of the first gear tooth coincides with the left boundary of the second gear tooth, and this repetition is not allowed in the meshing process, so the operation of removing the points is indispensable.
It should be noted that the operation of removing the coincident point can remove the node on the left side of the section of a single gear tooth, or can remove the node on the right side.
In the step 6.3, the three-dimensional data of the gear teeth can be obtained according to the data of the gear tooth plane, and the method specifically comprises the following steps:
acquiring a thickness parameter of the gear and the number of parts of the gear divided in the thickness direction;
and the coordinate value of each point in the thickness direction is changed according to the thickness parameter of the gear and the number of parts of the gear divided in the thickness direction, so that the stretching is realized.
In an eighth embodiment, the present embodiment is further limited to the method for automatically generating a finite element mesh of a spur gear based on a tooth profile in the first embodiment, and in the present embodiment, the step 7 is further limited, and specifically includes:
step 7.1, obtaining the coordinates of the tooth-root tooth profile point, and setting the coordinates of the tooth-root tooth profile point as (x, y), wherein the formula is as follows:
tanθ＝x/y
theta is the radian occupied by half gear teeth on the whole gear;
step 7.2, acquiring the radian of one gear tooth on the whole gear according to the radian of the half gear tooth on the whole gear, namely alpha is 2 theta;
step 7.3, converting the alpha into an angle system, wherein beta is 2 theta 180/pi, and beta is a rotation angle;
7.4, acquiring the number n of teeth on the gear according to the rotation angle;
and 7.5, rotating all the nodes of the single gear tooth around a gear circular mandrel according to the rotating angle and the number of the teeth on the gear until n gear teeth are obtained, and further obtaining all the nodes of the whole gear.
In the embodiment, the rotation angle of each gear tooth and the number of the gear teeth are calculated by using the tooth profile line end point coordinates, so that the grid division precision is improved, and the use number of parameters in the grid generation process can be reduced.
In a ninth implementation manner, the present implementation manner is to further limit the method for automatically generating a finite element mesh of a spur gear based on a tooth profile in the first implementation manner, and in the present implementation manner, the step 8 is further limited, and specifically includes:
8.1, respectively compiling connection relations of nodes of a single gear tooth in all nodes of the whole gear to obtain an initial gear;
and 8.2, respectively compiling connection relations of points on two sides of each gap in the initial gear to obtain a gear mesh model.
In this embodiment, the connection relationship of each individual gear tooth is first achieved, and then the connection relationship of the gear teeth and the gaps between the gear teeth is achieved.
Tenth embodiment, the present embodiment is a specific example of the method for automatically generating a finite element mesh of a spur gear based on a tooth profile, as shown in fig. 23, specifically, the method includes:
as shown in fig. 1, the data source required by this embodiment is based on the coordinate data of a point (the mark point in fig. 1 b) on one tooth profile line (the bold line on fig. 1 a) on one side of the gear tooth.
The method comprises the following steps: taking points on half cross-section of gear teeth
1) Firstly, a gear tooth section symmetry axis is taken as a y axis, a straight line passing through the center of a circle of the gear and perpendicular to the y axis is taken as an x axis, and a rectangular coordinate system is established.
2) Coordinate data of points on the tooth profile are read, a point class is created in the program, and the data are stored in the form of points in the container v 1. In this embodiment, data from a discrete set of points on the profile line is used, rather than data from the profile line. As shown in fig. 1a, the thickened line is a tooth profile line, and one tooth profile line is obtained by using the intersection point of the tooth profile line and the addendum circle as a starting point and the lowest point of the tooth socket as an end point. Selection principle of points between the starting point and the end point: more than 10 points, not too much dispersion. As shown in FIG. 1b, the same abscissa is taken at a distance of 0.3-0.5.
3) As shown in fig. 2, let h and calculate, the calculation method is: from top to bottom, the ordinate of the starting point on the tooth profile line minus the ordinate of the ending point on the tooth profile line, in fig. 1b, the coordinate of the center of the gear is (0, 0), the coordinate of the starting point of the tooth profile line is (5, 75.6375), the coordinate of the ending point is (10, 63.1375), and h is calculated to be 12.5. Taking a straight line on which the longitudinal coordinate of the terminal point on the tooth profile line is located as a symmetry axis, taking a boundary line at the upper and lower 0.2h respectively, wherein the boundary line is 1 (the ordinate is 63.1375+0.2 × 12.5 ═ 65.6375) and 2 (the ordinate is 63.1375-0.2 × 12.5 ═ 60.6375).
It should be noted here that, during the rotation and engagement of the gear, the tooth root portion is subjected to a large load, and is prone to cracking and other problems. In order to make the tooth root portion to be subjected to grid encryption separately form an area, the embodiment selects two boundary lines of 0.2h above and below the ordinate of the tooth profile line. 0.2h is just one suitable parameter and is not fixed: when the parameter is too small, part of the tooth root part cannot be divided into the middle area, and the grid precision requirement cannot be met; when the size is too large, the non-tooth root parts which do not need to be divided by the grids at high precision are divided at high precision, so that the number of the grids can be increased, and the solving time is increased.
The inner circle radius of the gear is set again to serve as an input parameter, 40 is selected in the example (other parameters meeting the grid precision can be input in the program), and the boundary 3 at the lowest end of the gear tooth is determined (the inner circle radius 40 is used as the vertical coordinate of the boundary 3). The 3 dotted lines in the figure divide the section of half gear tooth into an upper region, a middle region and a lower region, and points are respectively taken in the three regions. The upper region is defined clockwise by a tooth crest straight line, a section of tooth profile line, a boundary 1 and a section of a tooth section symmetry line (y axis). The middle area is formed by a boundary 1, another section of tooth profile line, a section of tooth boundary line (the tooth boundary line refers to the line at the boundary of the tooth and the tooth), a boundary 2 and a section of tooth section symmetry line (y axis) which are enclosed clockwise. The lower region is defined clockwise by boundary 2, a section of gear tooth boundary, boundary 3, and a section of gear tooth section symmetry line (y-axis).
4) In the upper region, an upper region vertical number of copies parameter UpperVer is set as an input parameter, and 4 is selected in this embodiment (other parameters satisfying the grid accuracy may be input in the program). As shown in fig. 3, the number of the points is 4 in the longitudinal direction, points (circular points) are equally divided on the y-axis line segment, interpolation points (triangular points) are interpolated on the tooth profile line, and the interpolation aims are to make the triangular points and the circular points correspond to each other one by one and to make the vertical coordinates equal. An upper region lateral parts parameter w is set as an input parameter, in this example 6 (other suitable parameters may be input in the program). And the round point on the y axis and the triangular point on the tooth profile line are equally divided according to the parameter w.
Up to this point, the upper region and the point on the boundary 1 are all extracted. Including all points inside the upper region, all points on the region boundary (including also points on boundary 1). A distribution of points is obtained as shown in figure 4.
5) In the middle area, a middle area longitudinal number of parts parameter middlewer is set as an input parameter, in this example 8 is selected (other parameters meeting grid precision may also be input in the program). As shown in fig. 5, according to the distance between the points on the boundary 1, at any end of the small segment of the oblique line segment of the gear tooth boundary line in the middle area, a line segment with the same length as the distance between the points on the boundary 1 is cut out, and after the line segment is cut out, the next line segment is cut out until a small segment remains on the small segment of the oblique line segment of the gear tooth boundary line, and the small segment is not enough to cut out the line segment with the same length as the distance between the points on the boundary 1. And (4) recording the number of the segments as n2, bisecting the small oblique line segment according to the segment number, and acquiring square points. Let n1 be w-n2 (the number of segments on boundary 1 equal to the number of segments on boundary 2 plus the number of segments on the gear tooth boundary line), and n1 be the number of segments divided on boundary 2, and the square point on boundary 2 is taken. The parameter n1 and n2 calculated in the present patent data example are 3 and 3, respectively. As shown in fig. 5a, points (circle points) are equally divided on the y-axis line segment, and points (triangle points) are interpolated on the tooth profile line and are equally divided into 8 parts. Different from the point taking of the upper area on the tooth profile line, the point taking does not need to meet the requirement that the point on the y axis corresponds to the same longitudinal coordinate, but the point taking needs to meet the requirement that the part of the tooth profile line can be equally divided according to the length, and a triangular point is taken. The corresponding relation of the boundary points in the middle area is as follows: the circular points (excluding the points at the two ends) on the boundary 1 correspond to the square points (excluding the points at the two ends) on the boundary 2 and the gear tooth boundary line one by one, and the circular points (including the points at the two ends) on the middle area y axis correspond to the triangular points (including the points at the two ends) on the middle area tooth profile curve one by one. The points of the middle zone boundary are now all picked.
Points inside the region are then extracted using a quadratic bezier curve. The specific operation is as follows:
as shown in fig. 5 b. Selecting a point which is already acquired on the y axis and has the coordinate of (x) 0 ,y 0 ) Is denoted by P 0 And is the starting point of the bezier curve. Selecting and P 0 Corresponding triangular point with coordinates of (x) 2 ,y 2 ) Is denoted by P 2 The end point of the Bezier curve is shown. Make P separately 0 、P 2 The intersection coordinates (x) can be calculated at the normal (thin dashed line in the figure) of the line segment where it is located 1 ,y 1 ) Is marked as a hollow point P 1 。
According to the quadratic Bezier curve equation
x＝(1-t) 2 x 0 +2t(1-t)x 1 +t 2 x 2 ,t∈[0,1]
y＝(1-t) 2 y 0 +2t(1-t)y 1 +t 2 y 2 ,t∈[0,1]
In the program, x and y are cyclically obtained by starting with t equal to 0 and incrementing by 0.005 each time until t equal to 1, 201 points are obtained in total, the points simulate a bezier curve, and the distances between the points are added up to obtain a bezier curve P 0 P 2 The Bezier curve is divided equally into 6 parts according to the length of the curve, and the W is equal to the W in the Bezier curveThe sampling point on the line is shown in fig. 5 b.
To this end, all points on the middle region and the boundary 2 are extracted, including all points inside the middle region, and some points on the boundary of the region, where some points refer to all points on the boundary of the region with the point on the boundary 1 removed, and two intersection points of the boundary 1 with the y-axis and the tooth profile curve are also included in the removed points, because the removed points are already included in the upper region. A distribution of points is obtained as shown in figure 6.
6) In the lower area, one lower area vertical copy number parameter LowerVer is set as an input parameter, and 5 is selected in this example (other parameters satisfying the grid accuracy may be input in the program). As shown in fig. 7, uneven distribution and point taking (circular points) are realized on the y-axis line segment by using a quadratic bezier curve, so that the part of the grid near the tooth root is small, and the accuracy of the simulation result is ensured. The point on the y-axis and on the boundary 3 is the starting point P 0 The point on the y-axis and on the boundary 2 being the end point P 2 Control point selection of P 0 Upper, distance P 0 A distance L P0 P2 (LowerVer-1)/LowerVer, set as P 1 Denoted by crosses. L is a radical of an alcohol P0 P2 Is a point P 1 To P 2 I.e. the distance from boundary 2 to boundary 3. Distribution points on the y axis of the middle area in fig. 7 can be adopted, triangular points are adopted at the same height of the inclined straight line of the gear tooth boundary line, the triangular points correspond to the circular points one by one, the vertical coordinates are the same, the boundary 2 is transversely divided into 3 parts by the square points according to the condition that n1 in the previous step is 3, and points in the lower area are adopted.
Up to this point, the lower region and the point on the boundary 3 are all extracted. Including all points inside the lower region, and some points on the region boundary, where some points refer to all points on the region boundary minus points on boundary 2, and also including the two intersections of boundary 2 with the y-axis and gear tooth boundaries, because these points that are removed are already contained in the middle region. The distribution of points shown in fig. 8 was obtained.
7) The point on half the cross section of the gear tooth has been fully extracted as shown in figure 9.
Step two:
with the symmetrical relationship, points across the entire cross-section of the gear tooth are taken and the points on the y-axis cannot be taken repeatedly, the profile is shown in FIG. 10.
In this way, the connection relationship can be programmed according to the nodes in fig. 10, and then the tooth section mesh effect graph shown in fig. 11 can be obtained.
Step three:
to ensure that there are no repeating points between the teeth, it is necessary to remove points at the right or left boundary of the gear cross-section, for example, to remove the right-hand tooth-plane boundary line, i.e., the points marked in FIG. 12. The point of the left cog face boundary line, i.e. the point marked in fig. 13, will be the point common between the two cogs. Thus, by removing the midpoint in FIG. 12, a cross-sectional view of the gear tooth as shown in FIG. 14 is obtained.
Step four:
according to actual engineering requirements, a thickness parameter t of the gear and the number m of parts of the gear divided in the thickness direction are set as input parameters, wherein t is 30 and m is 6 in the example (other parameters meeting grid precision can be input in a program). And ensuring that the x and y coordinates of each point on the section are kept unchanged in the program, introducing the z coordinate in the thickness direction of the gear, and changing the coordinate value of each point in the z direction according to t and m to realize stretching, as shown in FIG. 15.
Step five: determining angle of rotation and number of teeth
To implement the rotation operation, first the angle of rotation should be determined. In the initial data of this embodiment, the number of teeth is not included, so the angle of rotation of the gear tooth around the circular spindle cannot be calculated according to the number of teeth. In this embodiment, the curvature of a tooth over the entire gear is determined by the abscissa and ordinate of the last point of the tooth profile (coordinate (10, 63.1375) at the root). The specific process is as follows:
let the coordinates at the tooth root be (x, y), there is the following formula:
tanθ＝x/y
as shown in FIG. 16, θ is the arc of half a tooth over the entire gear.
Let α be the arc that a tooth occupies across the gear, then α is 2 θ.
When the angle is changed from alpha, beta is 2 theta 180/pi.
Therefore, one gear tooth rotates by beta degrees to obtain the next gear.
If the number of teeth on the gear is n, n is 360 °/β. Because of the existence of calculation errors, n may not be an integer at this time, and needs to be rounded up or down to get an integer nearest to n, which is an integer, to obtain the final number of teeth n. In the present embodiment, n is 20 (in the program, the number of teeth is not fixed, and the number of teeth can be changed by changing the coordinate data of the point on the input tooth profile) calculated from the tooth profile data.
Step six:
the rotation angle β obtained in step five is used to rotate the point (fig. 15) obtained in step four around the gear circle center axis. In step five, the number n of teeth of the gear is determined, except for the tooth that has already been realized, which is used as the starting tooth and which is rotated by β degrees about the gear circle center axis, to obtain a second tooth. The second gear tooth continues to rotate around the circular mandrel by β degrees, resulting in a third gear tooth … repeating this operation until n gear teeth are obtained, so far the entire point on the gear is shown, as shown in FIG. 17.
Step seven: writing a connection relation:
firstly, respectively compiling a connection relation for each gear tooth point in the points on the whole gear generated in the step six, and connecting 8 points to form a hexahedron. In this embodiment, the final output object has a file type of. vtk, which can be viewed using ParaView. According to the file type of vtk, a header is set, and the numbers of every 8 adjacent dots constitute a set of data, written in the vtk file, connected into a small hexahedron. The eight points are on different layers, and each layer has four points, which together form a hexahedron. The three-dimensional shape of a tooth is obtained as shown in fig. 18 (two-angle illustration).
It should be noted that, the order of the points 1) is presented in the form of numbers, and as shown in fig. 19, the first hexahedron is taken as an example. It is required to know the number of points in the cross section of each layer as a, and from front to back, the points of the first layer are 0 to (a-1), and the points of the second layer are a to (2 a-1). Then knowing the transverse part b of the tooth top part, the arrangement sequence of the first hexahedron point number can be accurately described.
2) The first hexahedron-ordered dot sequence number refers to:
8 0 b b+1 1 a b+a b+1+a 1+a
the first number "8" indicates that each hexahedral element has 8 vertices. The following 8 data are reference numbers, and represent a connection of a hexahedron having a connection completed, as shown in fig. 19, where the number is 0 — > b +1 — > a — > b +1+ a — >1+ a ("-") indicates a connection.
According to this rule, points on the entire gear in fig. 17 are numbered, and the connection relationship is output in the vtk file by a program algorithm. Resulting in a three-dimensional geometry as shown in fig. 20.
Step eight:
fig. 21 is an enlarged view of fig. 20, and it can be seen from fig. 21 that there is a gap between every two teeth. This is due to the operation of the out-pointing in step three. (Note: FIG. 20 already contains all the nodes and connections inside each cog, but not the cogs and the connections between cogs)
This step programs the connection between the points on either side of each slot so that a complete gear is formed, as shown in fig. 22 (different angles).
Step nine:
the vtk file is output in the vtk file format. vtk files may be viewed with ParaView.
In this embodiment, the number of teeth is determined in step five. The data source of this embodiment has no tooth number, but the tooth number determines the rotation number during the rotation operation, and is indispensable. The number of teeth can be calculated by using the coordinate data of the last point on the tooth profile line and the rounding function, so that the number of times of rotation is provided. (corresponding to a basic gear parameter of calculating the number of teeth from data of points on a tooth profile, belonging to an inverse operation.)
In the implementation, in the seventh step and the eighth step, the connection relation of each single gear tooth is compiled, and then the gear teeth and the gaps between the gear teeth are connected. Step seven is to compile each gear tooth in an individual connection relationship, so that a plurality of gear teeth in fig. 18 form a gear with a gap in fig. 20, and then to perform step eight, and to connect points on two sides of the gap of the gear, that is, the left and right boundaries of the gear teeth, so as to obtain the whole gear, as shown in fig. 22.
It should be further noted that, in this embodiment, the overall operation sequence is: and (4) stretching the section points obtained in the third step, then calculating the rotation angle and the number of teeth, and then rotating. This method can be replaced by: firstly, the rotation angle and the number of teeth are calculated, then the point in the third step is rotated to obtain a section of the whole gear, and finally, the stretching is carried out.
Claims (10)
1. A method for automatically generating a finite element mesh of a spur gear based on a tooth profile is characterized by comprising the following steps:
step 1, establishing a rectangular coordinate system by taking a symmetrical axis of a section of one gear tooth in a straight spur gear as a y axis and taking a straight line which passes through the center of the gear and is vertical to the y axis as an x axis;
step 2, acquiring a tooth profile line of a half gear tooth under the rectangular coordinate system, wherein the tooth profile line takes the intersection point of the tooth profile line and an addendum circle as a starting point and takes a tooth root tooth profile point as an end point;
step 3, establishing a half gear tooth frame according to the gear profile, the gear inner circle radius and the gear tooth boundary line;
step 4, dividing the half gear tooth frame into an upper area, a middle area and a lower area, wherein the upper area corresponds to a gear tooth part, the lower area corresponds to a gear body part, and the middle area corresponds to a transition area of a gear tooth and the gear body;
step 5, respectively carrying out grid division on the upper area, the middle area and the lower area to obtain all nodes of a half gear tooth section;
step 6, acquiring all nodes of a single gear tooth section according to all nodes of the half gear tooth section, and acquiring all nodes of a single gear tooth according to all nodes of the single gear tooth section;
step 7, acquiring the number of gear teeth, and acquiring all nodes of the whole gear according to all nodes of the single gear tooth;
and 8, compiling connection relations of all nodes of the whole gear to obtain a gear grid model.
2. The method for automatically generating the finite element mesh of the spur gear based on the tooth profile according to claim 1, wherein the step 4 specifically comprises:
step 4.1, acquiring the difference between the vertical coordinates of the starting point and the end point;
step 4.2, setting a preset proportion, and determining a difference value of the vertical coordinate of the boundary line and the vertical coordinate of the terminal point according to the difference of the vertical coordinates and a multiplier of the preset proportion;
4.3, acquiring the boundary line of the half gear tooth frame in the upper and lower directions of the end point according to the difference value between the vertical coordinate of the boundary line and the vertical coordinate of the end point;
and 4.4, dividing the half gear tooth frame into an upper area, a middle area and a lower area according to the boundary line.
3. The method for automatically generating the finite element mesh of the spur gear based on the tooth profile as claimed in claim 1, wherein the step 5 specifically comprises:
step 5.1, setting an upper longitudinal number parameter and an upper transverse number parameter for the upper region, and carrying out grid division on the upper region according to the upper longitudinal number parameter and the upper transverse number parameter to obtain all nodes of the upper region, wherein all nodes of the upper region comprise nodes on a boundary line between the upper region and the middle region;
step 5.2, setting a middle longitudinal number of parts parameter for the middle region, and performing grid division on the middle region according to the middle longitudinal number of parts parameter, the upper transverse number of parts parameter and nodes on a boundary line between the upper region and the middle region by using a quadratic Bezier curve to obtain all nodes of the middle region, wherein all the nodes of the middle region comprise nodes on the boundary line between the middle region and the lower region;
step 5.3, setting a lower longitudinal number of parts parameter for the lower region, and carrying out grid division on the lower region according to the lower longitudinal number of parts parameter and nodes on a boundary line between the middle region and the lower region to obtain all nodes of the lower region;
and 5.4, acquiring all nodes of the cross section of the half gear tooth according to the nodes of the upper region, the nodes of the middle region and the nodes of the lower region.
4. The method for automatically generating the finite element mesh of the spur gear based on the tooth profile as claimed in claim 3, wherein the step 5.1 specifically comprises:
step 5.1.1, uniformly taking points of a line segment of the upper region on a y axis according to the upper longitudinal part number parameters to obtain a plurality of first upper longitudinal points, and carrying out interpolation point taking on a tooth profile line of the upper region according to the first upper longitudinal points to obtain a plurality of second upper longitudinal points, wherein the longitudinal coordinates of the first upper longitudinal points are equal to the longitudinal coordinates of the second upper longitudinal points in a one-to-one correspondence manner;
step 5.1.2, according to the upper transverse number parameter, equally dividing a first upper longitudinal point and a second upper longitudinal point which are correspondingly equal in vertical coordinate to obtain an upper region transverse node, wherein the upper region transverse node comprises a node on a boundary line between an upper region and a middle region;
and 5.1.3, acquiring all nodes of the upper area according to the first upper longitudinal point, the second upper longitudinal point and the upper area transverse node.
5. The method for automatically generating the finite element mesh of the spur gear based on the tooth profile as claimed in claim 3, wherein the step 5.2 specifically comprises:
step 5.2.1, dividing line segments of the middle area on a y axis according to the middle longitudinal number parameter to obtain a plurality of first middle longitudinal points, and setting the first middle longitudinal points as starting points of a Bezier curve;
step 5.2.2, dividing the tooth profile line of the middle area according to the middle longitudinal part number parameters to obtain a plurality of second middle longitudinal points, and setting the second middle longitudinal points as the end points of the Bezier curve;
step 5.2.3, the first middle longitudinal point and the second middle longitudinal point are in one-to-one correspondence according to a longitudinal sequence, and the normals of the line segments where the corresponding first middle longitudinal point and the second middle longitudinal point are located are intersected to obtain a normal intersection point of the longitudinal points;
step 5.2.4, acquiring a quadratic Bezier curve according to the first middle longitudinal point, the second middle longitudinal point and the normal intersection point of the longitudinal points, wherein the method specifically comprises the following steps:
x＝(1-t) 2 x 0 +2t(1-t)x 1 +t 2 x 2 ,t∈[0,1]
y＝(1-t) 2 y 0 +2t(1-t)y 1 +t 2 y 2 ,t∈[0,1]
wherein (x) 0 ,y 0 ) (x) is the first mid-section longitudinal point coordinate 2 ,y 2 ) Is the second mid longitudinal point, (x) 1 ,y 1 ) Is the intersection point of the normal lines of the longitudinal points;
step 5.2.5, setting a preset increment value, determining a plurality of t values according to the preset increment value, selecting a plurality of points on the secondary Bezier curve according to the plurality of t values, and accumulating the intervals of the plurality of points on the selected secondary Bezier curve to obtain the length of the secondary Bezier curve;
step 5.2.6, dividing the secondary Bezier curve according to the upper transverse number parameter and the length of the secondary Bezier curve to obtain an internal node of the middle area;
dividing the boundary of the middle region without taking points according to nodes on the boundary line between the upper region and the middle region to obtain the nodes on the boundary of the middle region without taking points, wherein the nodes on the boundary of the middle region without taking points comprise the nodes on the boundary line between the middle region and the lower region;
and 5.2.7, acquiring all nodes of the middle area according to the first middle longitudinal point, the second middle longitudinal point, the internal nodes of the middle area and the nodes of the boundary of the middle area where the points are not taken.
6. The method for automatically generating the finite element mesh of the spur gear based on the tooth profile as claimed in claim 3, wherein the step 5.3 specifically comprises:
step 5.3.1, setting two endpoints of a line segment of the lower region on the y axis as a starting point and an end point of the Bezier curve from bottom to top respectively, and acquiring a control point of the Bezier curve according to the two endpoints and the lower longitudinal number of parts parameter, wherein the distance between the control point and the lower endpoint of the line segment of the lower region on the y axis is as follows:
L P0P2 *(LowerVer-1)/LowerVer
wherein L is P0P2 The distance between the two end points is defined as LowerVer as the lower longitudinal part parameter;
step 5.3.2, acquiring a Bezier curve according to the two end points and the control point of the Bezier curve;
step 5.3.3, according to the Bezier curve, point taking is carried out on the line segment of the lower area on the y axis, and a plurality of first lower longitudinal points are obtained;
step 5.3.4, point taking is carried out on the gear tooth boundary line of the lower area according to the node of the line segment of the lower area on the y axis, and a plurality of second lower longitudinal points are obtained, wherein the longitudinal coordinates of the first lower longitudinal points are equal to the longitudinal coordinates of the second lower longitudinal points in a one-to-one correspondence manner;
determining a lower transverse score parameter according to a node on a boundary line between the middle region and the lower region;
according to the lower transverse number of parts parameter, equally dividing the first lower longitudinal point and the second lower longitudinal point which are correspondingly equal in ordinate, and obtaining a lower region transverse node;
and acquiring all nodes of the lower area according to the first lower longitudinal point, the second lower longitudinal point and the transverse nodes of the lower area.
7. The method for automatically generating the finite element mesh of the spur gear based on the tooth profile according to claim 1, wherein the step 6 specifically comprises:
step 6.1, acquiring all nodes of the section of a single gear tooth according to all nodes of the section of the half gear tooth by using the symmetrical relation;
6.2, removing nodes on one side of the section of the single gear tooth, and obtaining all nodes of the section of the single gear tooth with the repetition points removed;
and 6.3, stretching all nodes of the section of the single gear tooth with the repetition points removed according to the thickness parameter of the gear and the number of parts of the gear divided in the thickness direction, and obtaining all nodes of the single gear tooth.
8. The method for automatically generating the finite element mesh of the spur gear based on the tooth profile according to claim 1, wherein the step 7 specifically comprises:
step 7.1, obtaining the coordinates of the tooth-root tooth profile point, and setting the coordinates of the tooth-root tooth profile point as (x, y), wherein the formula is as follows:
tanθ＝x/y
theta is the radian occupied by half gear teeth on the whole gear;
step 7.2, acquiring the radian of one gear tooth on the whole gear according to the radian of the half gear tooth on the whole gear, namely alpha is 2 theta;
step 7.3, converting the alpha into an angle system, wherein beta is 2 theta 180/pi, and beta is a rotation angle;
7.4, acquiring the number n of teeth on the gear according to the rotation angle;
and 7.5, rotating all the nodes of the single gear tooth around a gear circular mandrel according to the rotating angle and the number of the teeth on the gear until n gear teeth are obtained, and further obtaining all the nodes of the whole gear.
9. The method for automatically generating the finite element mesh of the spur gear based on the tooth profile according to claim 1, wherein the step 8 specifically comprises:
8.1, respectively compiling connection relations of nodes of a single gear tooth in all nodes of the whole gear to obtain an initial gear;
and 8.2, respectively compiling connection relations of points on two sides of each gap in the initial gear to obtain a gear mesh model.
10. A computer device comprising a memory and a processor, the memory having stored therein a computer program, characterized in that the steps of the method of any of claims 1 to 9 are performed when the processor runs the computer program stored by the memory.
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