CN114818181B - Method and equipment for automatically generating finite element grid based on tooth profile straight-tooth cylindrical gear - Google Patents
Method and equipment for automatically generating finite element grid based on tooth profile straight-tooth cylindrical gear Download PDFInfo
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Abstract
A method and computer equipment for automatically generating a straight-tooth cylindrical gear finite element grid based on a tooth profile belong to the technical field of gear simulation, and solve the problems of low grid node precision and low working efficiency obtained by the existing method. The method comprises the following steps: establishing a rectangular coordinate system; acquiring a tooth profile of half gear teeth; establishing a half gear tooth frame according to the tooth profile, the radius of the inner circle of the gear and the gear tooth boundary line; dividing the half gear tooth frame into an upper region, a middle region and a lower region; respectively carrying out grid division on the upper region, the middle region and the lower region 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 writing a connection relation to obtain a gear grid model. The method is suitable for automatically generating the finite element mesh model of the spur gear.
Description
Technical Field
The application relates to the technical field of gear simulation, in particular to an automatic generation method of a straight-tooth cylindrical gear finite element grid based on a tooth profile and computer equipment.
Background
The spur gear transmission is used as an important mechanical transmission form and is widely applied to power transmission of transportation tools such as automobiles, rail vehicles and the like, production and living mechanical equipment and the like. During rotation of the gears, load is transferred between the gears. When the rotation speed is high and the load is high, marks can be left on the gears, and even the gears are worn or even broken. In order to minimize the damage of the gears, simulation analysis is needed for the gears, and gear meshing is an essential step.
In the prior art, in gear finite element analysis: on the one hand, gear mesh division needs to establish a gear three-dimensional geometric model, then the three-dimensional model is imported into finite element analysis software, mesh nodes are generated by utilizing parameters such as the shape, the size and the like of the model and setting a series of mesh parameters, and the gear mesh model can be obtained through a complex flow. On the other hand: the mesh node precision obtained by the existing cylindrical gear mesh dividing node selection method is low, and the mesh nodes are required to be re-sampled at specific positions for dividing, so that the workload of later mesh processing 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 grids are sparse or the degree of grid irregularity is large, the accuracy of the solving result is greatly reduced; when the grids are dense, the huge number of grids greatly increases the solving time.
Disclosure of Invention
The invention aims to solve the problems of low grid node precision and low working efficiency obtained by the existing method, and provides a straight-tooth cylindrical gear finite element grid automatic generation method based on a tooth profile and computer equipment.
The invention is realized by the following technical scheme, and in one aspect, the invention provides a method for automatically generating a straight-tooth cylindrical gear finite element grid based on a tooth profile, which comprises the following steps:
step 1, establishing a rectangular coordinate system by taking a symmetry axis of a gear tooth section in a straight-tooth cylindrical gear as a y axis and taking a straight line passing through the center of the gear and perpendicular to the y axis as an x axis;
step 2, acquiring a tooth profile of half gear teeth under the rectangular coordinate system, wherein the tooth profile takes a tooth profile intersection point with a top circle as a starting point and takes a tooth root tooth profile point as an ending 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 the gear tooth and the gear body;
Step 5, respectively carrying out grid division on the upper region, the middle region and the lower region to obtain all nodes of a half gear tooth section;
step 6, according to all nodes of the half gear tooth section, all nodes of a single gear tooth section are obtained, and according to all nodes of the single gear tooth section, all nodes of a single gear tooth are obtained;
step 7, obtaining the number of gear teeth, and obtaining all nodes of the whole gear according to all nodes of the single gear tooth;
and 8, writing connection relations for all nodes of the whole gear to obtain a gear grid model.
Further, the step 4 specifically includes:
step 4.1, obtaining the difference between the ordinate of the starting point and the ordinate of the end point;
step 4.2, setting a preset proportion, and determining a difference value between the ordinate of the boundary line and the ordinate of the end point according to the difference between the ordinate and the multiplier of the preset proportion;
step 4.3, acquiring boundary lines of the half gear tooth frames at the upper and lower positions of the end point according to the difference value between the ordinate of the boundary lines and the ordinate 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 of copies parameter and an upper transverse number of copies parameter for the upper region, and carrying out grid division on the upper region according to the upper longitudinal number of copies parameter and the upper transverse number of copies 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 copies parameter aiming at the middle area, and carrying out grid division on the middle area by utilizing a quadratic Bezier curve according to the middle longitudinal number of copies parameter, the upper transverse number of copies parameter and nodes on a boundary line between the upper area and the middle area to obtain all nodes of the middle area, wherein all nodes of the middle area comprise nodes on the boundary line between the middle area and the lower area;
step 5.3, setting a lower longitudinal number of copies parameter for the lower region, and carrying out 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 a half gear tooth section 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 line segments of the upper region on the y axis according to the upper longitudinal number parameters, obtaining a plurality of first upper longitudinal points, carrying out interpolation point taking on the tooth profile of the upper region according to the first upper longitudinal points, and obtaining a plurality of second upper longitudinal points, wherein the ordinate of the first upper longitudinal points is equal to the ordinate of the second upper longitudinal points in a one-to-one correspondence manner;
step 5.1.2, equally dividing a first upper longitudinal point and a second upper longitudinal point which are equal in ordinate correspondence according to the upper transverse number of copies parameter 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 region according to the first upper longitudinal point, the second upper longitudinal point and the upper region transverse node.
Further, the step 5.2 specifically includes:
Step 5.2.1, dividing line segments of the middle region on a y axis according to the middle longitudinal number parameters to obtain a plurality of first middle longitudinal points, and setting the first middle longitudinal points as starting points of Bezier curves;
step 5.2.2, dividing the tooth profile of the middle area according to the middle longitudinal part 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, carrying out one-to-one correspondence on the first middle longitudinal point and the second middle longitudinal point according to a longitudinal sequence, intersecting the normals of line segments where the corresponding first middle longitudinal point and the corresponding second middle longitudinal point are positioned, and obtaining a normal intersection point of the longitudinal points;
and 5.2.4, obtaining a secondary 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 secondary Bezier curve is specifically as follows:
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 ) For the first mid-longitudinal point coordinate, (x 2 ,y 2 ) For 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 of parts parameter and the length of the secondary Bezier curve to obtain an internal node of the middle area;
dividing the boundary of the middle area, which is not at the point, according to the nodes on the boundary line between the upper area and the middle area, and obtaining the nodes of the boundary of the middle area, which is not at the point, wherein the nodes of the boundary of the middle area, which is not at the point, comprise the nodes on the boundary line between the middle area and the lower area;
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 non-taking point of the middle area.
Further, the step 5.3 specifically includes:
step 5.3.1, respectively setting two endpoints of a line segment of the lower region on the y axis as a start point and an end point of the Bezier curve from bottom to top, and acquiring a control point of the Bezier curve according to the two endpoints and the lower longitudinal number of copies 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 Lower ver is the lower longitudinal number of copies parameter for the distance between the two endpoints;
step 5.3.2, obtaining 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, taking points of line segments of the lower region on the y axis to obtain a plurality of first lower longitudinal points;
step 5.3.4, taking points of gear tooth boundary lines of the lower region according to the nodes of the line segments of the lower region on the y axis, and obtaining a plurality of second lower longitudinal points, wherein the ordinate of the first lower longitudinal points is equal to the ordinate of the second lower longitudinal points in a one-to-one correspondence manner;
determining a lower transverse score parameter according to nodes on a boundary line between the middle region and the lower region;
dividing equally between a first lower longitudinal point and a second lower longitudinal point which are corresponding and equal in ordinate according to the lower transverse number of parts parameter, and acquiring a lower region transverse node;
and acquiring all nodes of the lower region according to the first lower longitudinal point, the second lower longitudinal point and the lower region transverse node.
Further, the step 6 specifically includes:
Step 6.1, obtaining all nodes of a single gear tooth section according to all nodes of the half gear tooth section by utilizing a symmetrical relation;
step 6.2, removing nodes on one side of the single gear tooth section, and obtaining all nodes of the single gear tooth section of the de-repetition point;
and 6.3, stretching all nodes of the section of the single gear tooth of the de-repetition point according to the thickness parameter of the gear and the number of parts of the gear in the thickness direction, and obtaining all nodes of the single gear tooth.
Further, the step 7 specifically includes:
step 7.1, obtaining coordinates of a tooth profile point, wherein the coordinates of the tooth profile point are (x, y) as follows:
tanθ＝x/y
θ is the radian occupied by half gear teeth on the whole gear;
step 7.2, according to the radian occupied by the half gear tooth on the whole gear, obtaining the radian occupied by one gear tooth on the whole gear, namely alpha=2θ;
step 7.3, changing alpha into an angle system, wherein beta=2θ×180/pi, and beta is a rotation angle;
step 7.4, according to the rotation angle, the number n of teeth on the gear is obtained;
and 7.5, rotating all nodes of the single gear teeth around the circle center axis of the gear according to the rotation angle and the number of teeth on the gear until n gear teeth are obtained, and further obtaining all nodes of the whole gear.
Further, the step 8 specifically includes:
step 8.1, respectively writing connection relations for nodes of single gear teeth in all nodes of the whole gear to obtain an initial gear;
and 8.2, respectively writing connection relations for points on two sides of each gap in the initial gear to obtain a gear grid model.
In another aspect, the invention provides a computer device comprising a memory and a processor, the memory having stored therein a computer program which when executed by the processor performs the steps of a spur gear finite element mesh automatic generation method based on a tooth profile as described above.
The invention has the beneficial effects that:
therefore, the node selection algorithm of the invention performs grid division in regions according to the structural characteristics of the gears. The accuracy of the solving result needs to be improved in some areas because of the larger load applied to the areas, and the grid arrangement of the part is dense; otherwise, the shape is regular, the grid density is normally selected at the position without special requirement in stress analysis, and the engineering requirement is met.
According to the stress characteristics of the cylindrical gear, the invention selects the automatic generation method of the cylindrical spur gear grid suitable for the stress simulation analysis of the cylindrical gear. In the prior art, the gear mesh division needs to establish a gear three-dimensional geometric model, then the three-dimensional model is imported into finite element analysis software, the shape, the size and other parameters of the model are utilized, a series of mesh parameters are set to generate mesh nodes, and the gear mesh model can be obtained through a complex flow. Finally, the gear grid model can be directly generated, and a complex flow is avoided. Firstly, the gear grid 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, proper nodes can be quickly acquired, and the grid generation efficiency is improved;
And secondly, the point-taking algorithm in the application, such as linear interpolation, bezier curve, stretching and rotation, has low calculation complexity, and can select the nodes meeting the precision so as to realize the requirements on the grid quality and the grid generation speed.
The method is suitable for automatically generating the finite element mesh model of the spur gear.
Drawings
In order to more clearly illustrate the technical solution of the present application, the drawings that are needed in the embodiments will be briefly described below, and it will be obvious to those skilled in the art that other drawings can be obtained from these drawings without inventive effort.
FIG. 1 is a graph of tooth profile data (a is a graph of tooth profile, b is a graph of points selected on the tooth profile) according to the present application;
FIG. 2 is a schematic view of a gear tooth segment area according to the present application;
FIG. 3 is a schematic view of the upper region longitudinal division of the present application;
FIG. 4 is a schematic diagram of the overall node distribution of the upper region of the present application;
FIG. 5 is a schematic diagram of nodes in a middle area according to the present application (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 overall node distribution in the middle area of the present application;
FIG. 7 is a schematic view of node selection at the lower region boundary according to the present invention;
FIG. 8 is a schematic diagram of the overall node distribution of the lower region of the present invention;
FIG. 9 is a schematic view of the overall node distribution of a half gear tooth cross-section of the present invention;
FIG. 10 is a schematic representation of the overall node distribution of a single tooth cross-section of the present invention;
FIG. 11 is a graph of the effect of a gear tooth cross-section grid of the present invention;
FIG. 12 is a schematic view of a right side node of a gear section of the present invention;
FIG. 13 is a schematic view of a left side node of a gear section of the present invention;
FIG. 14 is a cross-sectional view of a gear tooth according to the present invention;
FIG. 15 is a full node stretch schematic of a single tooth cross-section of the present invention;
FIG. 16 is a schematic view of the arc occupied by half of the teeth of the present invention on the entire gear;
FIG. 17 is a schematic diagram of the overall node distribution of the entire gear of the present invention;
FIG. 18 is a schematic diagram of the invention for writing a connection relationship for a single gear tooth (the left and right diagrams are distributed in different angles);
FIG. 19 is a diagram of hexahedral connections in the written connections of the present invention;
FIG. 20 is a schematic view of an initial gear of the present invention;
FIG. 21 is an enlarged schematic view of an initial gear of the present invention;
FIG. 22 is a schematic view of a gear mesh model at different angles according to the present invention;
FIG. 23 is a flow chart of a method according to an embodiment of the invention.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary and intended to illustrate the present invention and should not be construed as limiting the invention.
In a first embodiment, a method for automatically generating a finite element mesh of a spur gear based on a tooth profile, the method includes:
step 1, establishing a rectangular coordinate system by taking a symmetry axis of a gear tooth section in a straight-tooth cylindrical gear as a y axis and taking a straight line passing through the center of the gear and perpendicular to the y axis as an x axis;
step 2, acquiring a tooth profile of half gear teeth under the rectangular coordinate system, wherein the tooth profile takes a tooth profile intersection point with a top circle as a starting point and takes a tooth root tooth profile point as an ending 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 the gear tooth and the gear body;
Step 5, respectively carrying out grid division on the upper region, the middle region and the lower region to obtain all nodes of a half gear tooth section;
step 6, according to all nodes of the half gear tooth section, all nodes of a single gear tooth section are obtained, and according to all nodes of the single gear tooth section, all nodes of a single gear tooth are obtained;
step 7, obtaining the number of gear teeth, and obtaining all nodes of the whole gear according to all nodes of the single gear tooth;
and 8, writing connection relations for all nodes of the whole gear to obtain a gear grid model.
The gear tooth boundary line refers to a line at the interface between the gear tooth and the gear tooth.
The method is based on known tooth profile data, mesh nodes are selected only by a mesh dividing method without gear parameters, and gear mesh precision is greatly improved. Although the contour lines used in this patent are also calculated from the gear basic parameters, the gear basic parameters are not used for the selection of the nodes. In the process of object-oriented programming, the embodiment does not need to use the basic parameters of the gears, and avoids complex data analysis in the aspect of selecting the segmentation boundary points.
The method of the embodiment is mainly based on the data of the tooth profile, and then an operator inputs relevant parameters such as grid density and the like to realize point picking and connection, and finally a vtk file which can be used for visualizing the gear grid model is generated.
The embodiment can realize the establishment of the gear mesh model through object-oriented programming in a program.
In a second embodiment, the method for automatically generating a finite element mesh of a spur gear based on a tooth profile according to the first embodiment is further defined, and in this embodiment, the step 4 is further defined, and specifically includes:
step 4.1, obtaining the difference between the ordinate of the starting point and the ordinate of the end point;
step 4.2, setting a preset proportion, and determining a difference value between the ordinate of the boundary line and the ordinate of the end point according to the difference between the ordinate and the multiplier of the preset proportion;
step 4.3, acquiring boundary lines of the half gear tooth frames at the upper and lower positions of the end point according to the difference value between the ordinate of the boundary lines and the ordinate 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 area is the tooth root, and this area has certain requirements on node accuracy, so when dividing the boundary line, considering the coordinate of the lowest point of the tooth slot, that is, the tooth root profile point, as the selection basis of the boundary line, the partition is performed, so that the node selection process is more reasonable and clear.
In a third embodiment, the method for automatically generating a finite element mesh of a spur gear based on a tooth profile according to the first embodiment is further defined, and in this embodiment, the step 5 is further defined, and specifically includes:
step 5.1, setting an upper longitudinal number of copies parameter and an upper transverse number of copies parameter for the upper region, and carrying out grid division on the upper region according to the upper longitudinal number of copies parameter and the upper transverse number of copies 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 copies parameter aiming at the middle area, and carrying out grid division on the middle area by utilizing a quadratic Bezier curve according to the middle longitudinal number of copies parameter, the upper transverse number of copies parameter and nodes on a boundary line between the upper area and the middle area to obtain all nodes of the middle area, wherein all nodes of the middle area comprise nodes on the boundary line between the middle area and the lower area, and do not comprise nodes on the boundary line between the upper area and the middle area;
And 5.3, setting a lower longitudinal number of copies parameter for the lower region, and carrying out 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, wherein the nodes do not comprise the nodes on the boundary line between the middle region and the lower region.
And 5.4, acquiring all nodes of a half gear tooth section according to the upper region node, the middle region node and the lower region node.
In this embodiment, a gear includes teeth and a gear body, where the gear body refers to the whole of the gear except for the 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 tooth and the gear body. Therefore, the division into three areas is most appropriate, and must not be less than three areas, and it is unnecessary to divide more areas, and dividing more areas only increases the workload, and does not further improve the grid accuracy.
In the embodiment, the upper area and the lower area have low requirements on the grid size and the node precision, and the nodes at the two positions are selected simply. The middle area is the tooth root, and the area has certain requirements on node precision. The partition is used for taking the points, so that the node selection process is more reasonable and clearer, and the grid precision is improved.
In a fourth embodiment, the present embodiment is further defined by the method for automatically generating a finite element mesh of a spur gear based on a tooth profile according to the first embodiment, where step 5.1 is further defined, and specifically includes:
step 5.1.1, uniformly taking points of line segments of the upper region on the y axis according to the upper longitudinal number parameters, obtaining a plurality of first upper longitudinal points, carrying out interpolation point taking on the tooth profile of the upper region according to the first upper longitudinal points, and obtaining a plurality of second upper longitudinal points, wherein the ordinate of the first upper longitudinal points is equal to the ordinate of the second upper longitudinal points in a one-to-one correspondence manner;
step 5.1.2, equally dividing a first upper longitudinal point and a second upper longitudinal point which are equal in ordinate correspondence according to the upper transverse number of copies parameter 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 region according to the first upper longitudinal point, the second upper longitudinal point and the upper region transverse node.
In this embodiment, for the characteristics of the upper area, such as the grid size and the node precision requirement are not high, the linear interpolation method is adopted to perform grid division on the upper area, so that the requirement of grid precision can be met, the complexity of data analysis can be reduced, and the efficiency of grid division is further improved.
In a fifth embodiment, the method for automatically generating a finite element mesh of a spur gear based on a tooth profile according to the first embodiment is further defined, and in this embodiment, the step 5.2 is further defined, and specifically includes:
step 5.2.1, dividing line segments of the middle region on a y axis according to the middle longitudinal number parameters to obtain a plurality of first middle longitudinal points, and setting the first middle longitudinal points as starting points of Bezier curves;
step 5.2.2, dividing the tooth profile of the middle area according to the middle longitudinal part 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, carrying out one-to-one correspondence on the first middle longitudinal point and the second middle longitudinal point according to a longitudinal sequence, intersecting the normals of line segments where the corresponding first middle longitudinal point and the corresponding second middle longitudinal point are positioned, and obtaining a normal intersection point of the longitudinal points;
And 5.2.4, obtaining a secondary 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 secondary Bezier curve is specifically as follows:
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 ) For the first mid-longitudinal point coordinate, (x 2 ,y 2 ) For 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 of parts parameter and the length of the secondary Bezier curve to obtain an internal node of the middle area;
dividing the boundary of the middle area, which is not at the point, according to the nodes on the boundary line between the upper area and the middle area, and obtaining the nodes of the boundary of the middle area, which is not at the point, wherein the nodes of the boundary of the middle area, which is not at the point, comprise the nodes on the boundary line between the middle area and the lower area;
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 non-taking point of the middle area.
In the present embodiment, it is possible to apply
Setting a preset value to be 0.005;
starting at t=0, incrementing 0.005 each time, until t=1, yields a point on the quadratic bessel curve.
Each time t increases from 0 to 0.005 to 1, a bezier curve modeled by 201 points is obtained. the smaller the value of t increment, the more points are obtained, and the more accurate the simulated Bezier curve. t may 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 this embodiment, t=0.005 can completely satisfy the requirement for the accuracy of the simulated bezier curve.
In this embodiment, by using the quadratic bezier curve, points satisfying the grid accuracy requirement can be selected in the middle region.
In a sixth embodiment, the present embodiment is further defined by the method for automatically generating a finite element mesh of a spur gear based on a tooth profile according to the first embodiment, where step 5.3 is further defined, and specifically includes:
Step 5.3.1, respectively setting two endpoints of a line segment of the lower region on the y axis as a start point and an end point of the Bezier curve from bottom to top, and acquiring a control point of the Bezier curve according to the two endpoints and the lower longitudinal number of copies 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 Lower ver is the lower longitudinal number of copies parameter for the distance between the two endpoints;
step 5.3.2, obtaining 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, taking points of line segments of the lower region on the y axis to obtain a plurality of first lower longitudinal points;
step 5.3.4, taking points of gear tooth boundary lines of the lower region according to the nodes of the line segments of the lower region on the y axis, and obtaining a plurality of second lower longitudinal points, wherein the ordinate of the first lower longitudinal points is equal to the ordinate of the second lower longitudinal points in a one-to-one correspondence manner;
determining a lower transverse score parameter according to nodes on a boundary line between the middle region and the lower region;
dividing equally between a first lower longitudinal point and a second lower longitudinal point which are corresponding and equal in ordinate according to the lower transverse number of parts parameter, and acquiring a lower region transverse node;
And acquiring all nodes of the lower region according to the first lower longitudinal point, the second lower longitudinal point and the lower region transverse node.
In this embodiment, the application of the quadratic bezier curve is different from the application in the middle region, where appropriate control points are selected so that the lower region is divided longitudinally unevenly. Therefore, grids near the tooth root can be made smaller, and the accuracy of simulation results is ensured.
It should be noted that the bezier curve equation may be selected three times, four times and many times, but the calculation is complicated and the difference from the result of the second time is not great.
In a seventh embodiment, the method for automatically generating a finite element mesh of a spur gear based on a tooth profile according to the first embodiment is further defined, and in this embodiment, the step 6 is further defined, and specifically includes:
step 6.1, obtaining all nodes of a single gear tooth section according to all nodes of the half gear tooth section by utilizing a symmetrical relation;
step 6.2, removing nodes on one side of the single gear tooth section, and obtaining all nodes of the single gear tooth section of the de-repetition point;
and 6.3, stretching all nodes of the section of the single gear tooth of the de-repetition point according to the thickness parameter of the gear and the number of parts of the gear in the thickness direction, and obtaining all nodes of the single gear tooth.
In this embodiment, the point on the whole cross section of the single gear tooth obtained in step 6.1 must have a point overlap during the post-rotation, such as the right boundary of the first gear tooth and the left boundary of the second gear tooth overlap, which is not allowed during the meshing process, so that the point removing operation is indispensable.
It should be noted that the point removing operation may remove the node on the left side or the node on the right side of the section of the single gear tooth, so as to remove the coincident point.
In the stretching in the step 6.3, three-dimensional data of the gear teeth can be obtained according to the data of the gear tooth plane, specifically:
acquiring thickness parameters of the gear and the parts of the gear divided in the thickness direction;
the coordinates of each point on the section of the whole gear are kept unchanged, 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 in the thickness direction, so that the stretching is realized.
In an eighth embodiment, the present embodiment further defines 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 7 is further defined, and specifically includes:
Step 7.1, obtaining coordinates of a tooth profile point, wherein the coordinates of the tooth profile point are (x, y) as follows:
tanθ＝x/y
θ is the radian occupied by half gear teeth on the whole gear;
step 7.2, according to the radian occupied by the half gear tooth on the whole gear, obtaining the radian occupied by one gear tooth on the whole gear, namely alpha=2θ;
step 7.3, changing alpha into an angle system, wherein beta=2θ×180/pi, and beta is a rotation angle;
step 7.4, according to the rotation angle, the number n of teeth on the gear is obtained;
and 7.5, rotating all nodes of the single gear teeth around the circle center axis of the gear according to the rotation angle and the number of teeth on the gear until n gear teeth are obtained, and further obtaining all nodes of the whole gear.
In the embodiment, the angle at which each gear tooth should rotate and the number of teeth of the gear are calculated by using the end point coordinates of the tooth profile, so that the accuracy of grid division is improved, and the number of parameters in the grid generation process can be reduced.
In a ninth embodiment, the method for automatically generating a finite element mesh of a spur gear based on a tooth profile according to the first embodiment is further defined, and in this embodiment, the step 8 is further defined, and specifically includes:
Step 8.1, respectively writing connection relations for nodes of single gear teeth in all nodes of the whole gear to obtain an initial gear;
and 8.2, respectively writing connection relations for points on two sides of each gap in the initial gear to obtain a gear grid model.
In this embodiment, the connection relationship of each individual gear tooth is realized first, and then the connection relationship of the gear tooth and the gap between the gear teeth is realized.
In a tenth embodiment, the present embodiment is a specific example of an automatic generation method of a finite element mesh of a spur gear based on a tooth profile, as shown in fig. 23, specifically:
as shown in fig. 1, the data source needed for this embodiment is based on the coordinate data of the point (marked point in fig. 1 b) on one tooth profile (bold line in fig. 1 a) on one tooth side.
Step one: with points on half cross-section of the tooth
1) Firstly, a rectangular coordinate system is established by taking a symmetry axis of a gear tooth section as a y axis and taking a straight line which passes the center of a gear and is perpendicular to the y axis as an x axis, and coordinate data related to the embodiment are all in the coordinate system.
2) The coordinate data of points on the tooth profile are read, a point class is created in the program, and the data is stored in the form of points in the container v 1. The data used in this example is for a set of discrete points on the tooth profile, not the tooth profile. As shown in fig. 1a, the thickened line is a tooth profile, one tooth profile is obtained by taking the intersection point of the tooth profile and the addendum circle as a starting point and the lowest point of the tooth slot as an end point. The principle of selecting points between a starting point and an end point is as follows: more than 10 points, the dispersion is not needed. As in fig. 1b, the same abscissa 0.3-0.5 pitch is taken for selection.
3) As shown in fig. 2, let h and calculate, the calculation method is: from top to bottom, the ordinate of the start point on the tooth profile minus the ordinate of the end point on the tooth profile, in fig. 1b the gear center coordinates are (0, 0), the tooth profile start point coordinates are (5, 75.6375), the end point coordinates are (10, 63.1375), and h=12.5 is calculated. Taking the straight line of the end point longitudinal coordinate on the tooth profile as a symmetry axis, taking a boundary line at the upper and lower 0.2h respectively, and boundary 1 (the ordinate is 63.1375+0.2x12.5= 65.6375) and boundary 2 (the ordinate is 63.1375-0.2x12.5= 60.6375).
The tooth root part is subjected to a large load during the rotation and engagement of gears, and is easy to break. In order to separate the root portion to be grid-encrypted into a single region, the present embodiment selects two boundary lines, the upper and lower 0.2h on the ordinate of the tooth profile. 0.2h is just one suitable parameter, not fixed: when the parameter is too small, a part of tooth root part is not divided into a middle area, and the grid precision requirement cannot be met; when the number of the grids is too large, the grids are divided with high precision in some non-tooth root parts which do not need the grid to be divided with high precision, so that the number of the grids is increased, and the solving time is increased.
The radius of the inner circle of the gear is set again, and as an input parameter, a parameter 40 (other parameters meeting the grid precision can be input in the program) is selected in this example, and the boundary 3 at the lowest end of the gear tooth is determined (the radius of the inner circle 40 is used as the ordinate of the boundary 3). The 3 broken lines in the figure divide the half gear tooth section into an upper region, a middle region and a lower region, and the following points are respectively adopted in the three regions. The upper region is defined by the tooth top line, a tooth profile, boundary 1 and a section of the tooth cross-section symmetry line (y-axis) in a clockwise direction. The middle area is defined by boundary 1, another tooth profile line, a section of gear tooth boundary line (the gear tooth boundary line refers to the line at the gear tooth and gear tooth boundary), boundary 2 and a section of gear tooth section symmetry line (y axis) in a clockwise direction. The lower region is defined by boundary 2, a segment of the gear tooth boundary line, boundary 3, and a segment of the gear tooth cross-sectional symmetry line (y-axis) in a clockwise direction.
4) In the upper area, an upper area longitudinal number of copies parameter UpperVer is set as an input parameter, and in this embodiment, 4 is selected (other parameters satisfying the grid accuracy may be input in the program). As shown in fig. 3, the interpolation is performed by dividing the points (circular points) into 4 parts in the longitudinal direction, equally dividing the points (triangular points) on the y-axis line segment, and interpolating the points (triangular points) on the tooth profile, wherein the interpolation aims to realize that the triangular points and the circular points are in one-to-one correspondence, and the ordinate is equal. An upper region transverse number of copies parameter w is set as an input parameter, in this example option 6 (other suitable parameters may be entered in the program). And equally dividing the circular points on the y axis and the triangular points on the tooth profile according to the parameter w.
To this end, the upper region and the point on boundary 1 are all extracted. Including all points inside the upper region, all points on the region boundary (also including points on boundary 1). The resulting distribution of points is shown in fig. 4.
5) In the middle area, a middle area longitudinal number of copies parameter MiddleVer is set as an input parameter, and 8 is selected in this example (other parameters meeting grid accuracy can be input in the program). As shown in the left side of fig. 5, according to the pitch of the points on the boundary 1, a line segment with the same pitch length as the points on the boundary 1 is cut out at any one end of the small section diagonal of the gear tooth boundary line in the middle area, after the line segment is cut out, the next section is cut out until a small section remains on the small section diagonal of the gear tooth boundary line, and the small section is insufficient to cut out the line segment with the same pitch length as the points on the boundary 1. And (4) recording the number of the lower sections as n2, dividing the small oblique line section equally according to the number of the sections, and extracting square points. Let n1=w—n2 (the number of segments on boundary 1 is equal to the number of segments on boundary 2 plus the number of segments on the gear tooth interface), n1 is the number of segments divided on boundary 2, and a square point on boundary 2 is extracted. The parameters n1=3 and n2=3 calculated in the present patent data example. As shown in fig. 5a, the points (circles) are equally divided on the y-axis line segment, and the points (triangles) are interpolated on the tooth profile, all divided into 8 parts. Unlike the upper region taking points on the tooth profile, this time it is not necessary to satisfy the same correspondence with the ordinate of the points on the y-axis, but it is necessary to satisfy the tooth profile that can divide this part equally in length, taking points of a triangle. The corresponding relation of boundary points in the middle area is as follows: the circular points (excluding the points at the two ends) on the boundary 1 are in one-to-one correspondence with the square points (excluding the points at the two ends) on the boundary 2 and the gear tooth boundary line, and the circular points (including the points at the two ends) on the y-axis of the middle area are in one-to-one correspondence with the triangular points (including the points at the two ends) on the gear profile curve of the middle area. At this point the points of the middle region boundary are all extracted.
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 on the y-axis, the coordinate of which is (x 0 ,y 0 ) Denoted as P 0 Is the starting point of the bezier curve. Selecting and P 0 Corresponding triangle points, coordinates are (x 2 ,y 2 ) Denoted as P 2 Is the end point of the Bezier curve. Respectively do P 0 、P 2 The intersection point coordinates (x) can be calculated from the normal line of the line segment (thin broken line in the figure) 1 ,y 1 ) 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, t=0 starts, each time increment is 0.005, until t=1, x and y are circularly obtained, 201 points are obtained, the points simulate a Bezier curve, the pitches of the points are accumulated, and the Bezier curve P can be obtained 0 P 2 The bezier curve is equally divided into w=6 parts according to the length, and the sampling points on the bezier curve are shown in fig. 5 b.
The points on the middle region and the boundary 2 are all extracted up to this point, including all points inside the middle region, and some points on the region boundary, where some points refer to all points on the region boundary, excluding the point on the boundary 1, and two points of intersection of the boundary 1 with the y-axis and the tooth profile curve are included in the removed points, because these points are already included in the upper region. The resulting distribution of points is shown in fig. 6.
6) In the lower area, a lower area longitudinal number of copies parameter LowerVer is set as an input parameter, and in this example, 5 is selected (other parameters meeting the grid accuracy may be input in the program). As shown in fig. 7, the y-axis line segment utilizes a quadratic bezier curve to realize unevenly distributed point taking (circular point), so that a part of the grid near the tooth root is smaller, 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 boundary 2 is endpoint P 2 Control point selection P 0 Above, distance P 0 Distance is L P0 P2 * The position of (lower Ver-1)/lower Ver is designated as P 1 Indicated by the cross. L (L) P0 P2 Is point P 1 To P 2 I.e. the distance from boundary 2 to boundary 3. The 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 oblique straight line of the gear tooth boundary line, the triangular points are in one-to-one correspondence with the circular points, the vertical coordinates are the same, the square points transversely divide the boundary 2 into 3 parts according to n1=3 in the previous step, and the points inside the lower area are adopted.
To this end, the lower region and the points on the boundary 3 are all extracted. Including all points within the lower region and some points on the region boundary, where some points refer to all points on the region boundary excluding points on boundary 2, and including the two intersections of boundary 2 with the y-axis and gear tooth boundary since these points are already included in the middle region. A distribution diagram of points is obtained as shown in fig. 8.
7) The points on the half cross section of the gear teeth have been fully extracted as shown in fig. 9.
Step two:
with the symmetrical relationship, points across the entire cross section of the gear tooth are extracted, and points on the y-axis cannot be repeatedly extracted, the distribution diagram is shown in fig. 10.
In this way, the connection relationship can be written according to the nodes in fig. 10, and the tooth cross-section grid effect diagram shown in fig. 11 can be obtained.
Step three:
to ensure that there are no duplicate points between the teeth, the points on the right or left boundary of the gear cross-section need to be removed, as exemplified by the right flank boundary line, i.e., the points marked in fig. 12. The point of the left flank boundary line, i.e. the point marked in fig. 13, will be the point shared between the two gear teeth. Thus, the gear tooth cross-sectional effect diagram shown in FIG. 14 is obtained by removing the midpoint of FIG. 12.
Step four:
according to the actual engineering requirement, setting a thickness parameter t of the gear and the parts m, t and m of the gear divided in the thickness direction as input parameters, and selecting t=30 and m=6 in the example (other parameters meeting the grid precision can be input in the program). In the program, the x and y coordinates of each point on the section are ensured to be unchanged, the z coordinate in the thickness direction of the gear is introduced, and the coordinate value of each point in the z direction is changed according to t and m to realize stretching, as shown in fig. 15.
Step five: determining angle and number of teeth of rotation
In order to achieve a rotation operation, the angle of rotation should first be determined. In the initial data of the present embodiment, the number of teeth is not included, so that the angle by which the teeth rotate around the center axis cannot be calculated from the number of teeth. In this embodiment, the arc taken by a tooth on the entire gear is determined from the abscissa of the last point of the tooth profile (root coordinates (10, 63.1375)). The specific process is as follows:
let the coordinates at the root of the tooth be (x, y) as follows:
tanθ＝x/y
as shown in fig. 16, θ is the arc that half a tooth occupies over the entire gear.
Let α be the arc that one tooth occupies on the whole gear, then there is α=2θ.
When α is changed to the angle system, β=2θ×180/pi.
Therefore, one gear tooth rotates by beta degrees, and the next gear can be obtained.
Let n be the number of teeth on the gear, then n=360°/β. Because of the existence of calculation errors, n may not be an integer, and it is necessary to round up or down, and take the nearest integer to obtain the final number of teeth n, where n is an integer. In this embodiment, n=20 can be calculated from the tooth profile data (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 points on the input tooth profile).
Step six:
the point (fig. 15) obtained in the fourth step is rotated around the gear round spindle by using the rotation angle β obtained in the fifth step. In step five, the number n of teeth of the gear is determined, and the tooth is taken as an initial tooth, and after rotating around the gear round shaft by beta degrees, a second tooth is obtained. The second tooth continues to rotate beta degrees about the center axis, and the third tooth … is obtained and repeated until n teeth are obtained, all of which are shown to the point on the entire gear, as shown in fig. 17.
Step seven: writing a connection relation:
first, the connection relation is written for each of the points of each gear tooth on the whole gear generated in the step six, and 8 points are connected to form a hexahedron. In this embodiment, the file type of the final output object is vtk, which can be checked by using ParaView. According to the file type of vtk, the file header is set, and the numbers of every 8 adjacent points form a group of data, and the data are written into the vtk file to be connected into a small hexahedron. The eight points are in different layers, four points in each layer, together forming a hexahedron. Finally, a three-dimensional shape of one gear tooth is obtained, as shown in fig. 18 (a diagram showing effects at two angles).
Here, 1) the order of points is represented in numbered form, and as shown in fig. 19, the first hexahedron is taken as an example. We need to know the number of points of each layer of section as a, then from front to back, the first layer is from point 0 to point (a-1), and the second layer is from point a to point (2 a-1). And then knowing the transverse parts b of the tooth top part, the arrangement sequence of the first hexahedral point numbers can be accurately described.
2) The first hexahedral sequential dot sequence number refers to:
80bb+11ab+ab+1+a1+a
wherein the first digit "8" means that there are 8 vertices per hexahedral cell. The latter 8 data are numbers to be pointed, and are shown as points 0 # b # b+1 # 1 # a # b+a # b+1+a # 1+a # a ("-" indicates a connection), and are hexahedrons with connection completed, as shown in fig. 19.
According to this rule, points on the whole 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 point-removing operation in step three. ( And (3) injection: FIG. 20 already contains the connection between all nodes and the inside of each tooth, but does not contain the connection between teeth )
This step writes the connection between the points on both sides of each slot so that a complete gear is formed as shown in fig. 22 (different angles).
Step nine:
and outputting the vtk file according to the vtk file format. The vtk file may be viewed with ParaView.
In this embodiment, the number of teeth is calculated in the fifth step. The data source of this embodiment has no number of teeth, but the number of teeth determines the number of rotations during the rotation operation. The number of teeth can be calculated using the coordinate data of the last point on the tooth profile and the rounding function to provide the number of rotations. (the basic parameter of the gear is calculated from the data of the points on the tooth profile, and the inverse operation is performed.)
In this embodiment, in steps seven and eight, the connection relation is written for each individual tooth, and then the tooth is connected to the gap between the teeth. And step seven, writing each gear tooth in an independent connection relationship, so that a plurality of gear teeth in fig. 18 form a gear with a gap in fig. 20, and then performing step eight operation, and connecting points on two sides of the gear gap, namely 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 the overall operation sequence in this embodiment is: and (3) stretching the section point obtained in the step (III) in the step (IV), then obtaining the rotation angle and the number of teeth, and then rotating. This method can be exchanged for: the rotation angle and the number of teeth are firstly 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 (8)
1. An automatic generation method of a straight-tooth cylindrical gear finite element grid based on a tooth profile is characterized by comprising the following steps:
step 1, establishing a rectangular coordinate system by taking a symmetry axis of a gear tooth section in a straight-tooth cylindrical gear as a y axis and taking a straight line passing through the center of the gear and perpendicular to the y axis as an x axis;
step 2, acquiring a tooth profile of half gear teeth under the rectangular coordinate system, wherein the tooth profile takes a tooth profile intersection point with a top circle as a starting point and takes a tooth root tooth profile point as an ending 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 the gear tooth and the gear body; the method specifically comprises the following steps:
step 4.1, obtaining the difference between the ordinate of the starting point and the ordinate of the end point;
step 4.2, setting a preset proportion, and determining a difference value between the ordinate of the boundary line and the ordinate of the end point according to the difference between the ordinate and the multiplier of the preset proportion;
step 4.3, acquiring boundary lines of the half gear tooth frames at the upper and lower positions of the end point according to the difference value between the ordinate of the boundary lines and the ordinate of the end point;
Step 4.4, dividing the half gear tooth frame into an upper area, a middle area and a lower area according to the boundary line;
step 5, respectively carrying out grid division on the upper region, the middle region and the lower region to obtain all nodes of a half gear tooth section; the method specifically comprises the following steps:
step 5.1, setting an upper longitudinal number of copies parameter and an upper transverse number of copies parameter for the upper region, and carrying out grid division on the upper region according to the upper longitudinal number of copies parameter and the upper transverse number of copies 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 copies parameter aiming at the middle area, and carrying out grid division on the middle area by utilizing a quadratic Bezier curve according to the middle longitudinal number of copies parameter, the upper transverse number of copies parameter and nodes on a boundary line between the upper area and the middle area to obtain all nodes of the middle area, wherein all nodes of the middle area comprise nodes on the boundary line between the middle area and the lower area, and do not comprise nodes on the boundary line between the upper area and the middle area;
Step 5.3, setting a lower longitudinal number of copies parameter for the lower region, and carrying out 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, wherein the nodes do not comprise the nodes on the boundary line between the middle region and the lower region;
step 5.4, acquiring all nodes of a half gear tooth section according to the upper region node, the middle region node and the lower region node;
step 6, according to all nodes of the half gear tooth section, all nodes of a single gear tooth section are obtained, and according to all nodes of the single gear tooth section, all nodes of a single gear tooth are obtained;
step 7, obtaining the number of gear teeth, and obtaining all nodes of the whole gear according to all nodes of the single gear tooth;
and 8, writing connection relations for all nodes of the whole gear to obtain a gear grid model.
2. The method for automatically generating the straight-tooth cylindrical gear finite element mesh based on the tooth profile according to claim 1, wherein the step 5.1 specifically comprises the following steps:
step 5.1.1, uniformly taking points of line segments of the upper region on the y axis according to the upper longitudinal number parameters, obtaining a plurality of first upper longitudinal points, carrying out interpolation point taking on the tooth profile of the upper region according to the first upper longitudinal points, and obtaining a plurality of second upper longitudinal points, wherein the ordinate of the first upper longitudinal points is equal to the ordinate of the second upper longitudinal points in a one-to-one correspondence manner;
Step 5.1.2, equally dividing a first upper longitudinal point and a second upper longitudinal point which are equal in ordinate correspondence according to the upper transverse number of copies parameter 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 region according to the first upper longitudinal point, the second upper longitudinal point and the upper region transverse node.
3. The method for automatically generating the straight-tooth cylindrical gear finite element mesh based on the tooth profile according to claim 1, wherein the step 5.2 specifically comprises the following steps:
step 5.2.1, dividing line segments of the middle region on a y axis according to the middle longitudinal number parameters to obtain a plurality of first middle longitudinal points, and setting the first middle longitudinal points as starting points of Bezier curves;
step 5.2.2, dividing the tooth profile of the middle area according to the middle longitudinal part 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, carrying out one-to-one correspondence on the first middle longitudinal point and the second middle longitudinal point according to a longitudinal sequence, intersecting the normals of line segments where the corresponding first middle longitudinal point and the corresponding second middle longitudinal point are positioned, and obtaining a normal intersection point of the longitudinal points;
And 5.2.4, obtaining a secondary 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 secondary Bezier curve is specifically as follows:
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 ) For the first mid-longitudinal point coordinate, (x 2 ,y 2 ) For 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 of parts parameter and the length of the secondary Bezier curve to obtain an internal node of the middle area;
dividing the boundary of the middle area, which is not at the point, according to the nodes on the boundary line between the upper area and the middle area, and obtaining the nodes of the boundary of the middle area, which is not at the point, wherein the nodes of the boundary of the middle area, which is not at the point, comprise the nodes on the boundary line between the middle area and the lower area;
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 non-taking point of the middle area.
4. The method for automatically generating the straight-tooth cylindrical gear finite element mesh based on the tooth profile according to claim 1, wherein the step 5.3 specifically comprises the following steps:
step 5.3.1, respectively setting two endpoints of a line segment of the lower region on the y axis as a start point and an end point of the Bezier curve from bottom to top, and acquiring a control point of the Bezier curve according to the two endpoints and the lower longitudinal number of copies 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 Lower ver is the lower longitudinal number of copies parameter for the distance between the two endpoints;
step 5.3.2, obtaining 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, taking points of line segments of the lower region on the y axis to obtain a plurality of first lower longitudinal points;
step 5.3.4, taking points of gear tooth boundary lines of the lower region according to the nodes of the line segments of the lower region on the y axis, and obtaining a plurality of second lower longitudinal points, wherein the ordinate of the first lower longitudinal points is equal to the ordinate of the second lower longitudinal points in a one-to-one correspondence manner;
Determining a lower transverse copy parameter according to nodes on a boundary line between the middle area and the lower area;
dividing equally between a first lower longitudinal point and a second lower longitudinal point which are corresponding and equal in ordinate according to the lower transverse number of parts parameter, and acquiring a lower region transverse node;
and acquiring all nodes of the lower region according to the first lower longitudinal point, the second lower longitudinal point and the lower region transverse node.
5. The method for automatically generating the straight-tooth cylindrical gear finite element mesh based on the tooth profile according to claim 1, wherein the step 6 specifically comprises:
step 6.1, obtaining all nodes of a single gear tooth section according to all nodes of the half gear tooth section by utilizing a symmetrical relation;
step 6.2, removing nodes on one side of the single gear tooth section, and obtaining all nodes of the single gear tooth section of the de-repetition point;
and 6.3, stretching all nodes of the section of the single gear tooth of the de-repetition point according to the thickness parameter of the gear and the number of parts of the gear in the thickness direction, and obtaining all nodes of the single gear tooth.
6. The method for automatically generating the straight-tooth cylindrical gear finite element mesh based on the tooth profile according to claim 1, wherein the step 7 specifically comprises the following steps:
Step 7.1, obtaining coordinates of a tooth profile point, wherein the coordinates of the tooth profile point are (x, y) as follows:
tanθ＝x/y
θ is the radian occupied by half gear teeth on the whole gear;
step 7.2, according to the radian occupied by the half gear tooth on the whole gear, obtaining the radian occupied by one gear tooth on the whole gear, namely alpha=2θ;
step 7.3, changing alpha into an angle system, wherein beta=2θ×180/pi, and beta is a rotation angle;
step 7.4, according to the rotation angle, the number n of teeth on the gear is obtained;
and 7.5, rotating all nodes of the single gear teeth around the circle center axis of the gear according to the rotation angle and the number of teeth on the gear until n gear teeth are obtained, and further obtaining all nodes of the whole gear.
7. The method for automatically generating the straight-tooth cylindrical gear finite element mesh based on the tooth profile according to claim 1, wherein the step 8 specifically comprises the following steps:
step 8.1, respectively writing connection relations for nodes of single gear teeth in all nodes of the whole gear to obtain an initial gear;
and 8.2, respectively writing connection relations for points on two sides of each gap in the initial gear to obtain a gear grid model.
8. A computer device comprising a memory and a processor, the memory having stored therein a computer program, characterized in that the processor, when running the computer program stored in the memory, performs the steps of the method of any one of claims 1 to 7.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210421255.XA CN114818181B (en) | 2022-04-21 | 2022-04-21 | Method and equipment for automatically generating finite element grid based on tooth profile straight-tooth cylindrical gear |
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