Optimization method of arc-shaped tenon structure based on grid parameterization

Abstract

The present disclosure relates to the field of aviation technology, and particularly relates to a kind of optimization method of arc dovetail structure based on grid parameterization.The optimization method includes: establishing the strength analysis grid model of arc dovetail structure;Create control body associated with the strength analysis grid model, control body can change with the change of the geometric parameter of arc dovetail structure;Grid node coordinates of strength analysis grid model are associated with control body, to enable strength analysis grid model to change with the change of control body;With geometric parameter as design variable, with the maximum stress of arc dovetail structure as optimization goal, combine test design method and proxy model to optimize strength analysis grid model, to make the maximum stress value in arc dovetail structure reduce.The optimization method eliminates the geometric reproduction and grid re-partitioning in traditional optimization method, and the grid quality of new generation of grid parameterization is equivalent to the initial grid quality, not only simplifies the optimization process, but also guarantees the credibility of optimization result.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the field of aviation technology, and particularly relates to an optimization method of an arc-shaped tenon structure based on grid parameterization. BACKGROUND

[0002] The turbine blade of an aero-engine is usually connected with a turbine disc by adopting a fir-tree tenon structure. The traditional fir-tree tenon structure adopts a planar-planar contact form (i.e., the contact surface of the tenon head / tenon groove is planar), which causes the contact edge to be in a high stress gradient state, and is easy to cause crack nucleation and form fretting fatigue failure, thereby seriously affecting the service life of the tenon structure. In view of the shortcomings of the planar-planar contact form of the traditional tenon structure, a new arc-shaped tenon structure adopting a curved surface-curved surface contact form is developed, which reduces the contact stress and stress gradient, and thereby improves the fretting fatigue life. Therefore, it is of great significance to carry out design optimization of the arc-shaped tenon structure for improving the service life of the aero-engine.

[0003] At present, in the optimization design of the arc-shaped tenon structure, the geometric parameters of the arc-shaped tenon structure are usually selected as the design variables, and the maximum stress of the arc-shaped tenon structure is taken as the objective function. The specific steps are as follows: firstly, the geometric parameters of the tenon structure are changed, and the geometric model of the tenon structure is updated based on the CAD software; secondly, the updated geometric model is re-meshed and contact analysis is carried out by using the finite element software; and the above process is iterated based on the optimization algorithm to realize the optimization design of the tenon structure, so that the maximum stress of the arc-shaped tenon structure takes the minimum value.

[0004] The geometric model needs to be updated and the mesh is automatically divided every time, but the contact analysis of the tenon head / tenon groove requires high mesh quality near the contact surface, and the automatically divided mesh often cannot guarantee the mesh accuracy, thereby affecting the reliability of the optimization result. In addition, the arc-shaped tenon structure includes both size variables and shape variables, and the constraint relationship is relatively complex. If the geometric model of the arc-shaped tenon structure is updated every time, not only the optimization process is complex and time-consuming, but also the geometric model is easy to be generated incorrectly when regenerated, thereby affecting the optimization of the arc-shaped tenon structure.

[0005] The above information disclosed in the BACKGROUND section merely to enhance the understanding of the background of the present disclosure, and therefore it can include information known by those of ordinary skill in the art. SUMMARY

[0006] The purpose of the present disclosure is to provide an optimization method of an arc-shaped tenon structure based on grid parameterization, which omits the two steps of geometric regeneration and mesh redivision in the traditional geometric parameterization optimization method, and the mesh quality of the newly generated mesh by grid parameterization is equivalent to the initial mesh quality, which not only simplifies the optimization process, but also guarantees the reliability of the optimization result.

[0007] To achieve the above object, the present disclosure adopts the following technical solutions:

[0008] According to one aspect of the present disclosure, an optimization method for an arc-shaped tenon structure based on mesh parameterization is provided, and the optimization method comprises:

[0009] establishing a strength analysis mesh model of the arc-shaped tenon structure;

[0010] creating a control body associated with the strength analysis mesh model, the control body being capable of changing with changes in geometric parameters of the arc-shaped tenon structure;

[0011] associating mesh node coordinates of the strength analysis mesh model with the control body, so that the strength analysis mesh model can change with changes in the control body;

[0012] taking the geometric parameters as design variables and the maximum stress of the arc-shaped tenon structure as an optimization target, and combining a design of experiments method and a surrogate model to optimize the strength analysis mesh model, so as to reduce the maximum stress value in the arc-shaped tenon structure.

[0013] In an exemplary embodiment of the present disclosure, the arc-shaped tenon structure comprises an arc-shaped tenon head and an arc-shaped tenon groove that cooperate with each other; and the control body associated with the strength analysis mesh model comprises:

[0014] creating a first control body associated with the strength analysis mesh model of the arc-shaped tenon head, control points on the first control body coinciding with a contact boundary at a contact boundary of the strength analysis mesh model of the arc-shaped tenon head;

[0015] creating a second control body associated with the strength analysis mesh model of the arc-shaped tenon groove, control points on the second control body coinciding with a contact boundary at a contact boundary of the strength analysis mesh model of the arc-shaped tenon groove.

[0016] In an exemplary embodiment of the present disclosure, creating the first control body associated with the strength analysis mesh model of the arc-shaped tenon head comprises:

[0017] creating control points on a first profile of the arc-shaped tenon head according to geometric parameters of the arc-shaped tenon head;

[0018] translating the control points on the first profile by a preset distance in a thickness direction of the arc-shaped tenon head to obtain control points on a second profile of the arc-shaped tenon head, the control points on the first profile and the control points on the second profile constituting the first control body.

[0019] In an exemplary embodiment of the present disclosure, the first profile comprises a straight line segment profile and a circular arc segment profile, and creating the control points on the first profile comprises:

[0020] creating control points on the straight line segment profile, the control points on the straight line segment profile including a straight line segment initial end point and a straight line segment terminal end point;

[0021] creating control points on the circular arc segment profile, the control points on the circular arc segment profile including a circular arc segment initial end point, a circular arc segment terminal end point and a circular arc curve equally divided point.

[0022] In an exemplary embodiment of the present disclosure, the coordinates of the circular arc curve equally divided point satisfy a first formula as follows:

[0023]

[0024] wherein, P i the point (i=1, 2, …, n) is the circular arc curve equally divided point, is the horizontal coordinate of the point P i , is the vertical coordinate of the point P i ; O is the center of the circular arc segment profile, x O is the horizontal coordinate of the point O, y O is the vertical coordinate of the point O; R O is the radius of the circular arc segment profile; θ0 is the initial relative angle of the circular arc segment profile; m(θ i , θ0) and n(θ i , θ0) are trigonometric functions with respect to θ i and θ0.

[0025] In an exemplary embodiment of the present disclosure, the circular arc segment profile includes a tooth shoulder circular arc profile and a tooth tip circular arc profile;

[0026] the central angle θ of the tooth shoulder circular arc profile, the horizontal coordinate x O and the vertical coordinate y O of the center O of the tooth shoulder circular arc profile satisfy a second formula as follows:

[0027]

[0028] θ = h1(F1, F2, R, α, β3)

[0029] wherein, F1 is the initial end point of the circular arc segment of the tooth shoulder circular arc profile; F2 is the terminal end point of the circular arc segment of the tooth shoulder circular arc profile; R is the radius of the tooth shoulder circular arc profile; α is the half wedge angle of the arc-shaped tenon structure; β3 is the second tooth pressure angle of the arc-shaped tenon structure;

[0030] the central angle θ of the tooth tip circular arc profile, the horizontal coordinate x O and the vertical coordinate y O of the center O of the tooth tip circular arc profile satisfy a third formula as follows:

[0031]

[0032]

[0033] In the formula, F2 is the first endpoint of the arc segment of the tooth tip arc profile; G2 is the last endpoint of the arc segment of the tooth tip arc profile. Let G2 be the slope of the tangent line. Let F2 be the slope of the tangent line at point F2.

[0034] In one exemplary embodiment of this disclosure, establishing a strength analysis mesh model for the arc-shaped tenon structure includes:

[0035] Establish a three-dimensional model of the arc-shaped tenon structure;

[0036] The three-dimensional model is meshed to obtain the intensity analysis mesh model.

[0037] In one exemplary embodiment of this disclosure, the three-dimensional model has a cross-sectional stretching feature.

[0038] In one exemplary embodiment of this disclosure, the thickness value of the three-dimensional model is T;

[0039] The control point on the first contour is translated by a distance T along the thickness direction of the arc tenon to obtain the control point on the second contour of the arc tenon.

[0040] In one exemplary embodiment of this disclosure, the proxy model is the Kriging proxy model;

[0041] The strength analysis mesh model is optimized by combining experimental design method and surrogate model, including:

[0042] The strength analysis grid model is invoked using the experimental design method to obtain sample point data of the design variables;

[0043] Using the sample point data, the Kriging proxy model is initialized and optimized.

[0044] Set convergence conditions for the accuracy of the Kriging surrogate model and continuously update the Kriging surrogate model until the calculation results converge.

[0045] The present invention discloses an optimization method for arc tenon structures based on mesh parameterization. This optimization method associates the geometric parameters of the arc tenon structure with the control volume, and also associates the mesh node coordinates of the strength analysis mesh model with the control volume. Thus, by changing the geometric parameters of the arc tenon structure, precise control of mesh deformation in the strength analysis mesh model can be achieved.

[0046] In summary, this application replaces the two steps of geometric model regeneration and mesh re-division in existing structural optimization methods with a parametric mesh model. This avoids problems such as interruption and inefficiency caused by errors in the mesh re-division process, and ensures that the quality of the newly generated mesh is comparable to that of the initial mesh, thereby guaranteeing the accuracy of the calculation process. Attached Figure Description

[0047] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0048] Figure 1 This is a flowchart of the optimization method for the arc tenon structure based on mesh parameterization according to the present invention.

[0049] Figure 2 This is a schematic diagram of the arc tenon structure according to the present disclosure.

[0050] Figure 3 This is a schematic diagram of the control points on the tooth shoulder arc contour of the arc tenon according to the present invention.

[0051] Figure 4 This is a schematic diagram of the control points on the arcuate profile of the tooth tip of the arcuate tenon according to the present invention.

[0052] Figure 5 This is a schematic diagram of the control points for the arc-shaped tenon and arc-shaped mortise in the embodiments of this disclosure.

[0053] Figure 6 This is a schematic diagram of the first control body of the arc tenon according to an embodiment of the present disclosure.

[0054] Figure 7 This is a schematic diagram of the control body of the arc tenon structure according to the present disclosure.

[0055] Figure 8 This is a schematic diagram of the control body being divided into l*m*m sub-models according to an embodiment of the present disclosure.

[0056] Figure 9 This is a comparison diagram of the grid structure of the arc tenon before and after the update of the embodiments disclosed herein.

[0057] In the diagram: 1. Arc-shaped tenon structure; 2. Arc-shaped tenon; 3. Arc-shaped mortise. Detailed Implementation

[0058] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are set forth to give a full understanding of embodiments of this disclosure.

[0059] The described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. Numerous specific details are provided in the following description to give a full understanding of embodiments of this disclosure. However, those skilled in the art will recognize that the technical solutions of this disclosure can be practiced without one or more of the specific details described, or other methods, components, materials, etc., can be employed. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring the main technical concept of this disclosure.

[0060] Although relative terms such as "up" and "down" are used in this specification to describe the relative relationship of one component of an icon to another, these terms are used only for convenience, such as the orientation of the examples shown in the accompanying drawings. It will be understood that if the icon's arrangement is flipped so that it is upside down, the component described as "up" will become the component described as "down". Other relative terms such as "high," "low," "top," "bottom," "left," and "right" also have similar meanings.

[0061] When a structure is "on" other structures, it may mean that the structure is integrally formed on the other structure, that the structure is "directly" set on the other structure, or that the structure is "indirectly" set on the other structure through another structure. The terms "a," "one," and "described" are used to indicate the existence of one or more elements / components / etc.; the terms "including" and "having" are used to indicate an open-ended inclusion meaning, and that other elements / components / etc. may exist in addition to the listed elements / components / etc. The terms "first" and "second," etc., are used only as markers and are not a limitation on the number of objects.

[0062] This disclosure provides an optimization method for arc-shaped tenon structures based on mesh parameterization, such as... Figure 1 As shown, the optimization method may include the following steps:

[0063] Step S110: Establish a strength analysis mesh model for the arc-shaped tenon structure;

[0064] Step S120: Create a control volume associated with the strength analysis mesh model. The control volume can change with the change of the geometric parameters of the arc tenon structure.

[0065] Step S130: Associate the grid node coordinates of the strength analysis grid model with the control volume so that the strength analysis grid model can change with the shape of the control volume.

[0066] Step S140: Using geometric parameters as design variables and the maximum stress of the arc tenon structure as the optimization objective, the strength analysis mesh model is optimized by combining experimental design method and surrogate model to reduce the maximum stress value in the arc tenon structure.

[0067] The present invention discloses an optimization method for an arc tenon structure based on mesh parameterization. This optimization method associates the geometric parameters of the arc tenon structure 1 with the coordinates of control points on the control body, and also associates the coordinates of the mesh nodes of the strength analysis mesh model with the control body. Thus, by changing the geometric parameters of the arc tenon structure 1, precise control of mesh deformation in the strength analysis mesh model can be achieved.

[0068] In summary, this application replaces the two steps of geometric model regeneration and mesh re-division in existing structural optimization methods with a parametric mesh model. This avoids problems such as interruption and inefficiency caused by errors in the mesh re-division process, and ensures that the quality of the newly generated mesh is comparable to that of the initial mesh, thereby guaranteeing the accuracy of the calculation process.

[0069] The following describes in detail each step of the optimization method provided in this disclosure with reference to the accompanying drawings:

[0070] In step S110, a strength analysis mesh model of the arc-shaped tenon structure 1 is established. The arc-shaped tenon structure 1 may include mutually cooperating arc-shaped tenons 2 and arc-shaped mortises 3.

[0071] Specifically, step S110 can be divided into the following two steps:

[0072] Step S1101: Establish a three-dimensional model of the arc tenon structure 1 based on the geometric parameters of the arc tenon structure 1.

[0073] It should be noted that, for the sake of simplifying the subsequent calculation process, the arc-shaped tenon structure 1 can have cross-sectional tension characteristics. That is, the three-dimensional model of the arc-shaped tenon structure 1 can be a flat plate model, thereby transforming the three-dimensional strain problem into a plane strain problem. In this case, the thickness T of the flat plate model can be 0.08mm to 0.12mm. Of course, it can also be less than 0.08mm or greater than 0.12mm. No special limitation is made here.

[0074] Step S1102: Mesh the three-dimensional model to obtain the strength analysis mesh model of the arc tenon structure 1.

[0075] It is important to note that mesh generation (the type and number of meshes) directly affects the accuracy and speed of the computation process, including:

[0076] The type of mesh can be a hexahedral mesh or others, and no special limitation is made here. The number of meshes can be set in combination with the dimensional characteristics of the arc tenon structure 1. For example, the mesh can be relatively fine at the contact area between the arc tenon 2 and the arc mortise 3, and relatively sparse in other areas.

[0077] In step S120, a control volume associated with the strength analysis mesh model is created, which can change with the change of the geometric parameters of the arc tenon structure 1.

[0078] Specifically, step S120 may include the following steps:

[0079] Step S1201: Create a first control body associated with the strength analysis mesh model of the arc tenon 2. The control points on the first control body coincide with the contact boundary at the contact boundary of the strength analysis mesh model of the arc tenon 2.

[0080] Step S1202: Create a second control body associated with the strength analysis mesh model of the arc-shaped tenon groove 3. The control points on the second control body coincide with the contact boundary at the contact boundary of the strength analysis mesh model of the arc-shaped tenon groove 3.

[0081] Meanwhile, step S1201 may include the following steps:

[0082] (1) Determine the control points on the first contour of the arc tenon 2 based on the geometric parameters of the arc tenon 2;

[0083] (2) The control points on the first contour are translated by T (thickness of the flat model, 0.08mm to 0.12mm) along the thickness direction of the arc tenon 2 (i.e., the thickness direction of the flat model) to obtain the control points on the second contour of the arc tenon 2. The control points on the first contour and the control points on the second contour form the first control body.

[0084] Next, let's combine... Figures 2 to 6 The process of creating the control body in step S1201 is described in detail:

[0085] It should be clarified that the principle for creating the control points of the curved tenon 2 is: first, use known geometric parameters to directly represent the coordinates of the main control points as much as possible, and then combine the corresponding geometric parameters to calculate the coordinates of the remaining control points.

[0086] For example, such as Figure 2As shown, the main control points of the arc tenon 2 include the tangent points of the arc segment and the straight segment (D, E, F1, F, F2, G1, G, and G2), and the intersection points of the straight segments (A, B, C, and H), where:

[0087] Points A and B are fixed, and their coordinates are known. Therefore, we can use the known geometric parameters ( Figure 2 The coordinates of the remaining main control points are shown in the diagram (already marked). Taking point F as an example, its coordinates can be expressed as:

[0088]

[0089] In the formula, l AB y represents the distance between point A and point B. B This represents the ordinate of point B.

[0090] like Figure 2 As shown, the contact contours of the arc-shaped tenon 2 and the arc-shaped mortise 3 are mainly formed by connecting the tooth shoulder arc contour and the tooth tip arc contour.

[0091] For the tooth shoulder arc profile, such as Figure 3 As shown, the coordinates of the center O and the magnitude of the central angle θ can be determined by F1, F2, R2, α, and β3, as shown in the following formulas:

[0092]

[0093] θ = h1(F1,F2,R2,α,β3)

[0094] In the formula, F1 is the first endpoint of the tooth shoulder arc profile, F2 is the last endpoint of the tooth shoulder arc profile, R2 is the radius of the tooth shoulder arc profile, α is the semi-wedge shape of the arc tenon structure (the angle between straight lines AB and AC), and β3 is the second tooth pressure angle of the arc tenon structure (the angle between the tangent of straight line AC and point F).

[0095] To ensure that the boundary of the first control body of the arc tenon 2 is geometrically consistent with the tooth shoulder arc, the tooth shoulder arc needs to be divided equally according to the size of the central angle, and the dividing point (control point) P on the tooth shoulder arc needs to be determined. i The coordinates of (i = 1, 2, ..., n) are shown below:

[0096]

[0097] in, For P i The x-coordinate of the point For P i The ordinate of point O; point O is the center of the tooth shoulder arc segment profile, x O Let y be the x-coordinate of point O. OR2 is the ordinate of point O; R2 is the radius of the tooth shoulder arc segment profile; θ i θ0 is the central angle corresponding to the evenly divided points on two adjacent shoulder arcs; θ0 is the initial relative angle of the shoulder arc segment profile; m1(θ0) i ,θ0) and n1(θ i ,θ0) are all about θ i The trigonometric functions of θ0.

[0098] For the tooth tip arc profile, such as Figure 4 As shown, the coordinates of the center O and the magnitude of the central angle θ can be determined by F2, G2, R2, and Confirmed, the specific formula is as follows:

[0099]

[0100]

[0101] In the formula, F2 is the first endpoint of the arc segment of the tooth tip arc profile; %2 is the last endpoint of the arc segment of the tooth tip arc profile. Let G2 be the slope of the tangent line. Let F2 be the slope of the tangent line at point F2.

[0102] At this point, the value of R can be obtained based on the coordinates of point O and the magnitude of θ. Therefore, the evenly divided point (control point) P on the tooth tip arc is determined. i The coordinates of (i = 1, 2, ..., n) can be represented as:

[0103]

[0104] in, For P i The x-coordinate of the point For P i The ordinate of the point; point O is the center of the arc segment of the tooth tip profile, x O Let y be the x-coordinate of point O. O θ is the ordinate of point O; R is the radius of the tooth tip arc segment profile; i θ0 is the central angle corresponding to the points where the two adjacent tooth tip arcs are evenly divided; θ0 is the initial relative angle of the tooth tip arc segment profile; m2(θ0) i ,θ0) and n2(θ i, θ0) are all about θ i The trigonometric functions of θ0.

[0105] like Figure 5As shown, the control points on the boundary of the straight line segment are the first and last endpoints of the straight line segment, and all control points are connected in an orderly manner to obtain the first contour of the arc tenon 2 and all its control points. Then, the control points on the first contour are translated by a translation T (thickness of the flat plate model, 0.08mm to 0.12mm) along the thickness direction of the flat plate model to obtain the second contour of the arc tenon 2 and all its control points.

[0106] Thus, the control points on the first contour and the control points on the second contour together form the first control body of the arc tenon 2 (e.g., Figure 6 (As shown). Similarly, the second control body of the arc-shaped tenon 3 can be obtained, which will not be described in detail here. The second control body of the arc-shaped tenon 3 and the first control body of the arc-shaped tenon 2 together constitute the control body of the arc-shaped tenon structure 1 (as shown). Figure 7 (As shown).

[0107] Step S130: Associate the grid node coordinates of the strength analysis grid model with the control volume so that the strength analysis grid model can change with the shape of the control volume.

[0108] like Figure 8 As shown, the control volume can be divided into l*m*m sub-models, where l, m, and n represent the average number of divisions of the control volume along the s, t, and u coordinate axes, respectively. The coordinate vector of node A in the global coordinate system o-xyz can be represented as:

[0109] x=x0+ss+tt+uu

[0110] Where s, t, and u represent local coordinate coefficients and 0 ≤ s, t, u ≤ 1, s, t, and u represent unit vectors along the coordinate axes, and x0 represents the coordinate vector of the local coordinate system in the global coordinate system.

[0111] In the local coordinate system, the coordinates of node A can be expressed as:

[0112]

[0113]

[0114]

[0115] In the global coordinate system, the control point coordinate vector p i,j,k (i∈[0...l],j∈[0...m],k∈[0...n]) can be represented as:

[0116]

[0117] The coordinates of the grid nodes in the control volume can be represented using Bernstein basis functions as follows:

[0118]

[0119] Among them, B il (s), B jm (t), B kn (u) represents the Bernstein basis function, and

[0120]

[0121]

[0122]

[0123] When the control node moves △p i,j,k When the distance is specified, the coordinate displacement vector of the grid node can be expressed as:

[0124]

[0125] After associating control points with geometric design variables, the coordinate values ​​of the control points can be understood as functions of the geometric design variables. When the geometric design variables change, the coordinate values ​​of the control points on the control volume also change accordingly.

[0126] Let the coordinates of an initial control point be (x i 0 ,y i 0 ,z i 0 (i = 1, 2, ..., n), the coordinates at the j-th grid update are (x i j ,y i j ,z i 0 (i = 1, 2, ..., n)(j = 1, 2, ..., n), where n represents the total number of control points and m represents the total number of intensity mesh updates. Therefore, changing the geometric design variables can be expressed as:

[0127]

[0128] Because the stress concentration phenomenon of the arc tenon structure 1 mainly occurs on the contact surface of the arc tenon 2 and the arc tenon groove 3, in the parametric deformation process, only the displacement of the control points on the contact contour of the arc tenon 2 and the arc tenon groove 3 is considered, while the control points on the other boundaries are treated as fixed points. Then, each time the geometric design variables are updated, a new set of (Δx,Δy) values ​​will be obtained on the contact boundary of the arc tenon 2 and the arc tenon groove 3, thereby realizing the update of the strength analysis mesh model.

[0129] likeFigure 9 As shown, the lighter-colored part represents the grid structure of the original curved tenon 2, while the darker-colored part represents the grid structure of the updated curved tenon 2.

[0130] In addition, the changes in the grid structure before and after the update of the curved tenon 3 are similar to those of the curved tenon 2, and will not be described in detail here.

[0131] Step S140: Using geometric parameters as design variables and the maximum stress of the arc tenon structure as the optimization objective, the strength analysis mesh model is optimized by combining experimental design method and surrogate model to obtain the minimum value of the maximum stress.

[0132] First, it is necessary to solve for the maximum stress of the curved tenon structure. Specifically, this can be achieved by following these steps:

[0133] (1) Add the material properties of the strength analysis mesh model to establish the finite element model of the arc tenon structure 1.

[0134] (2) Define the boundary conditions of the finite element model, including applying constraints to the finite element model and defining the loads on the finite element model.

[0135] In detailed analysis, a centrifugal load can be applied to the arc-shaped tenon 2, and a radial displacement constraint can be applied to the lower surface of the arc-shaped tenon 3. Then, symmetrical boundary conditions can be applied to the left side of the finite element model, and periodic boundary conditions can be applied to the right side.

[0136] (3) Calculate based on boundary conditions to obtain the location of the maximum stress on the arc tenon structure 1.

[0137] Secondly, the strength analysis mesh model is optimized by combining experimental design method and surrogate model. The surrogate model can be the Kriging surrogate model, or other surrogate models, without special restrictions.

[0138] Specifically, optimizing the intensity analysis mesh model may include the following steps:

[0139] (1) Use the experimental design method to call the strength analysis grid model to obtain sample point data of the design variables;

[0140] (2) Using the sample point data, initialize the Kriging proxy model and carry out optimization design;

[0141] (3) Set convergence conditions for the accuracy of the Kriging surrogate model and continuously update the Kriging surrogate model until the calculation results converge.

[0142] Therefore, the optimization method for arc tenon structure based on mesh parameterization provided in this disclosure can quickly obtain the geometric parameters and the corresponding maximum stress sample point data of arc tenon structure 1. Then, by using the Kriging myopia model and combining the sample point data, the optimal value of the maximum stress can be solved, which simplifies the solution process in the prior art and improves the efficiency of optimization design.

[0143] It should be understood that this disclosure is not limited to the detailed structure and arrangement of the components presented in this specification. This disclosure can have other embodiments and can be implemented and performed in various ways. The foregoing variations and modifications fall within the scope of this disclosure. It should be understood that this disclosure, as disclosed and defined in this specification, extends to all alternative combinations of two or more individual features mentioned or apparent in the text and / or drawings. All these different combinations constitute multiple alternative aspects of this disclosure. The embodiments described in this specification illustrate the best known mode for implementing this disclosure and will enable those skilled in the art to utilize this disclosure.

Claims

1. An optimization method for arc-shaped tenon structures based on mesh parameterization, characterized in that, The optimization method includes: Establish a strength analysis mesh model for the arc-shaped tenon structure; A control volume is created that is associated with the strength analysis mesh model, and the control volume can change as the geometric parameters of the arc tenon structure change; The grid node coordinates of the intensity analysis grid model are associated with the control volume so that the intensity analysis grid model can change as the control volume changes; Using the geometric parameters as design variables and the maximum stress of the arc-shaped tenon structure as the optimization objective, the strength analysis mesh model is optimized by combining experimental design method and surrogate model, so as to reduce the maximum stress value in the arc-shaped tenon structure; The arc-shaped tenon structure includes mating arc-shaped tenons and arc-shaped grooves; a control volume associated with the strength analysis mesh model is created, including: Create a first control body associated with the strength analysis mesh model of the arc tenon, wherein the control points on the first control body coincide with the contact boundary at the contact boundary of the strength analysis mesh model of the arc tenon; Create a second control body associated with the strength analysis mesh model of the arc-shaped tenon, wherein the control points on the second control body coincide with the contact boundary at the contact boundary of the strength analysis mesh model of the arc-shaped tenon; Creating a first control volume associated with the strength analysis mesh model of the curved tenon, including: Control points on the first contour of the arc tenon are created based on the geometric parameters of the arc tenon; The control points on the first contour are translated a predetermined distance along the thickness direction of the arc tenon to obtain the control points on the second contour of the arc tenon. The control points on the first contour and the control points on the second contour constitute the first control body. The first contour includes a straight line segment contour and a circular arc segment contour. Control points are created on the first contour, including: Create control points on the outline of the line segment, the control points of the line segment outline include the first endpoint and the last endpoint of the line segment; Create control points on the arc segment profile, including the first endpoint of the arc segment, the last endpoint of the arc segment, and the points where the arc curve is evenly divided.

2. The optimization method according to claim 1, characterized in that, The coordinates of the points where the circular arc curve divides equally satisfy the following first formula: In the formula, P i Point is the point where the circular arc curve is evenly divided, where, for The x-coordinate of the point for The ordinate of the point; point O is the center of the arc segment outline. Let O be the x-coordinate of point O. The ordinate of point O; The radius of the arc segment profile; The central angle of the arc segment profile; The central angle is the angle between the two adjacent points where the arc curves are evenly divided. and All are about and Trigonometric functions.

3. The optimization method according to claim 2, characterized in that, The arc segment profile includes a tooth shoulder arc profile and a tooth tip arc profile; The central angle of the tooth shoulder arc profile x-coordinate of the center point O and ordinate The following second formula is satisfied: In the formula, The first endpoint of the arc segment of the tooth shoulder arc profile; The point at the end of the arc segment of the tooth shoulder arc profile; The radius of the tooth shoulder arc profile; The semi-wedge angle of the arc-shaped tenon structure; The pressure angle of the second tooth of the arc-shaped tenon structure; The central angle of the tooth tip arc contour , the abscissa of the center O point and the ordinate satisfy the following third formula: In the formula, The first endpoint of the arc segment of the tooth tip arc profile; This refers to the end point of the arc segment of the tooth tip arc profile; for The slope of the tangent line at the point; for The slope of the tangent line at the point.

4. The optimization method according to claim 1, characterized in that, Establishing a strength analysis mesh model for the arc-shaped tenon structure includes: Establish a three-dimensional model of the arc-shaped tenon structure; The three-dimensional model is meshed to obtain the intensity analysis mesh model.

5. The optimization method according to claim 4, characterized in that, The three-dimensional model has cross-sectional stretching features.

6. The optimization method according to claim 5, characterized in that, The thickness value of the three-dimensional model is T; The control points on the first contour are translated by a distance T along the thickness direction of the arc tenon to obtain the control points on the second contour of the arc tenon.

7. The optimization method according to claim 1, characterized in that, The proxy model is the Kriging proxy model; The strength analysis mesh model is optimized by combining experimental design method and surrogate model, including: The strength analysis grid model is invoked using the experimental design method to obtain sample point data of the design variables; Using the sample point data, the Kriging proxy model is initialized and optimized. Set convergence conditions for the accuracy of the Kriging surrogate model and continuously update the Kriging surrogate model until the calculation results converge.

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