CN-122020859-A - Parameterized swept curved surface design method

CN122020859ACN 122020859 ACN122020859 ACN 122020859ACN-122020859-A

Abstract

The invention provides a parameterized swept curved surface design method, and relates to the field of aircraft design. The method comprises the steps of processing two-dimensional graphs by adopting a discrete sampling method with order preservation and feature preservation, enabling a sampling sequence to have consistent point order index rules and adjacency relations while preserving geometric details, constructing a measurement substrate by utilizing coordinate sequences of a reference graph and an interpolation center under a normalized coordinate system, completing parameterization of other graphs to form an analysis frame with consistent meaning, realizing graph shape change by coordinate transformation based on the frame, guaranteeing smooth deformation among complex graphs by taking an S-shaped curve with acceleration of 0 at two ends as a control rule, describing shape change, size change and sweep path design by using a parameterization curve or a discrete point list, and realizing parameterization generation of a sweep curved surface by combining parameter coordinates of each section graph and assembly strategies of different sections. The method can flexibly adapt to different types of sweeping requirements.

Inventors

SU LIHANG
MA DONGLI
ZHANG LIANG
Guo Duyu
Cui Mutian

Assignees

北京航空航天大学

Dates

Publication Date: 20260512
Application Date: 20260211

Claims (10)

1. The parameterized swept surface design method is characterized by comprising a two-dimensional graph parameterization module and a swept surface generation module, wherein the two-dimensional graph parameterization module is used for completing parameterization of all two-dimensional cross-section graphs and obtaining parameter coordinates corresponding to target graphs, and the parameter coordinates are subjected to transformation design and assembly operation through the swept surface generation module to generate a swept surface; The X axis points to the sweep advancing direction, the Z axis points to the right above the sweep curved surface, the Y axis is obtained by the XZ axis through a right hand rule, the discrete operation of all the two-dimensional graphs is carried out in the YZ plane, the normalization operation is carried out under a normalization coordinate system, and the specified xi is consistent with the Y axis direction, and the eta is consistent with the Z axis direction.
2. The parameterized swept surface design method according to claim 1, wherein the two-dimensional image parameterization module establishes a unified measurement reference for an input reference graph under a normalized coordinate system, solves parameter coordinates of a target graph under the measurement reference by adopting a least square method, and specifically performs the following steps: S1A, inputting parameters comprising a reference graph and a target graph needing to be parameterized and comprising normalized size and interpolation center arrangement, wherein the reference graph selects a section of the beginning end or the tail end of a sweep graph; S2A, describing a reference graph and a target graph as a sampling point sequence with the same index rule, wherein the sampling process comprises preprocessing, defining a first sampling point and a rotating reference axis, defining a sampling direction, and prescribing sampling point numbers and sampling modes; S3A, constructing a measurement substrate by using the normalized reference graph coordinate sequence and the interpolation center coordinate sequence; S4A, converting a parameterized task of the target graph into a solution of a parameter coordinate problem under a measurement substrate by a sampling least square method; and S5A, outputting the least square solving result in the S4A as the parameter coordinates of the target graph, and completing the parameterization of the target graph.
3. The parameterized swept surface design method according to claim 2, wherein the swept surface generation module takes the parameter coordinates of the target graph as input, performs the transformation operation of the cross-section graph through shape change design and size change design, and completes the final generation of the swept surface by combining different assembly strategies and anchor point selection after completing the design of the swept path, and specifically performs the following steps: S1B, inputting the parameter coordinate seat sweep curved surface generating module of the target graph obtained in the S5A, and carrying out shape change design between any two graphs; S2B, designing a sweep path and size change, and performing geometric scaling or scaling along a single direction by taking a graph centroid as a base point to finish graph size change; The method comprises the steps of S3B, assembling strategies including tangential alignment assembling and fixed direction assembling, wherein anchor points are selected to be assembled by taking the centroid of a graph as an anchor point or by taking a certain uniform number point as an anchor point; And S4B, outputting all the transformed graph families and the sweep paths, and completing the generation of the sweep curved surface by using a multi-section curved surface command in three-dimensional modeling software.
4. The parameterized swept surface design method of claim 2, wherein in S2A, the reference pattern and the target pattern each perform discrete sampling of order-preserving feature in CAD software, and the total number of sampling points is M; S2A, constructing an infinite straight line which passes through the centroid and is aligned with the Z axis by taking the centroid as a pole for a closed graph, wherein a point with the minimum Z coordinate is designated as a first sampling point in the intersection point of the infinite straight line and the closed curve; For an open curve, selecting an endpoint with the largest Y coordinate as a first sampling point, and if two sampling points with the same Y coordinate exist, selecting an endpoint with the largest Z coordinate as the first sampling point, and defining a ray along the-Z direction from the first sampling point as a rotation reference axis; uniformly sampling the graph according to the anticlockwise direction, and increasing the number of sampling points according to the sampling direction; The sampling mode in S2A specifically comprises the steps of uniformly sampling the graph with equal arc length, executing additional sampling on the C 0 continuous characteristic positions which need to be reserved, setting the total sampling point number as M, and outputting a discretized coordinate sequence when the sampling point sequence needs to meet the requirement of the sampling point number.
5. The parameterized swept surface design method according to claim 2, wherein in S3A, the measurement substrate is constructed by using a normalized reference graph coordinate sequence and an interpolation center coordinate sequence, the normalized size is marked as L N , the normalized coordinate domain is a square area with a center at an origin and a size of L N ×L N , interpolation centers are orthogonally and uniformly arranged along the direction of ζ and eta in the normalized domain, the normalized coordinate sequence of the interpolation centers is formed according to the sequence from bottom to top, and the total number of the interpolation centers is the product of the number of nodes in the direction of ζ and eta; The measurement substrate is generated by adopting a thin plate spline radial basis function and an affine operator respectively: , ; ; Wherein the method comprises the steps of Representing the normalized sequence of reference pattern sample points, Representing the normalized interpolation center sequence, wherein N represents the number of interpolation centers, phi is a nonlinear measurement matrix generated by a thin plate spline radial basis function, and P is a linear measurement matrix generated by an affine operator; The normalization operation of the reference graph comprises the steps of calculating a centroid by using a sampling point sequence, scaling the reference graph to be within an envelope with the size of 0.97L N ×0.97L N in an equal ratio mode by taking the centroid as a base point, and carrying out integral translation on the sampling point sequence after scaling so that the centroid coincides with an origin point to obtain a normalized reference graph coordinate sequence.
6. The method of claim 5, wherein in S4A, the sampling sequence of the target graph is denoted as q= The parameterization task of the target graph is converted into solving a parameter coordinate problem under the measurement substrate, wherein, Q is approximately equal to phi lambda+PC, and lambda and C are parameter coordinates corresponding to the two measurement substrates respectively, and the parameter coordinate problem under the measurement substrate is expressed as the following least square form: ; ; Wherein, P c is a matrix generated by the normalized interpolation center sequence through an affine operator, P c T Λ=0 is an orthogonal constraint for ensuring uniqueness of the least square problem solution, and the maximum error and the root mean square error are calculated point by point after geometric reconstruction, and the error calculation definition formula is as follows: ; ; ; In e i Representing the sequence of coordinates of the original graphic, Representing the coordinate sequence of the geometrically reconstructed graph.
7. The method for designing a parameterized swept surface according to claim 6, wherein S5A outputs a least squares solution result (Λ, C) as a parameter coordinate of the target graph Q, and the parameterization of the target graph is completed, and the geometric reconstruction of the graph is completed by directly bringing the parameter coordinate into q=ΦΛ+pc.
8. The method for designing a parametric sweep surface according to claim 3, wherein the shape change between any two patterns is performed in S1B by: ; ; ; Wherein P 6 (t) is a function for controlling the deformation speed of the graph, t is a transition parameter for describing the deformation evolution process, (Λ 0, C 0 ) and (Λ 1, C 1 ) represent parameter coordinates of the original graph and the graph after the change, F is a shape adjustment factor, the deformation speed is controlled by adjusting the value of F, and P 6 (t) is a gentle S-shaped curve with two ends and two second derivatives of 0 when F epsilon < -10,10 >.
9. The parameterized swept surface design method of claim 8, wherein the swept paths in the three-dimensional space in S2B are respectively projected to XY and XZ planes and converted into two-dimensional swept paths, which are generated by parameterized CAD curves, analytical curves, or linear stitching; The design of the dimensional change specifically comprises the steps of adopting the scaling of the geometric scale taking the centroid of the target graph as a base point or scaling along a single direction to complete the dimensional change of the graph, controlling the rule of the dimensional change along the way by E s (t), selecting P 6 (t) or other continuous parameterization functions by E s (t), and defining a dimensionless scaling factor s (t) as follows: ; Where s (t) represents a dimensionless scaling factor relative to the starting cross-sectional dimension, s 0 =1,s 1 represents a terminal cross-sectional scaling factor, and the forms of s (t) and s 1 are determined by the selected dimension control index, and when the closed-figure area is taken as a control target, the forms of s (t) and s 1 are as follows: , ; Wherein a 0 and a 1 represent the areas of the start section pattern and the end section pattern, respectively; In the case of the open curve length as the control target, the forms of s (t) and s 1 are as follows: , ; Wherein L 0 and L 1 respectively represent the length of the initial section pattern and the final section pattern, and are the lengths of the curves along a certain direction or the total arc length thereof, and after the form of s (t) is determined, t is mapped to the arc length direction of the sweep path or the X direction thereof, the size change operation along the path section pattern is completed as follows: ; wherein Q (t) and Respectively representing the original graphic family coordinate sequence and the coordinate sequences of the graphic families before and after the size conversion, The centroid coordinates representing the graphic family are obtained by decomposing s (t) into component forms in two directions and converting the two directions, respectively, in the case of dimensional change along the Y or Z direction.
10. The parameterized swept surface design method of claim 9, wherein in the tangential alignment assembly in S3B, the normal vector of each section is kept consistent with the tangential direction of the swept path at the position; After the sweep path is determined, the tangential directions of the two-dimensional paths at the positions of the cross sections are calculated, the attitude angles of the two directions required to be applied in the tangential alignment assembly mode are determined, corresponding rotation operation is completed on the cross sections, the sweep path generated by the parameterized CAD curve is densely sampled, the attitude angles of the two directions are calculated in a differential mode, and the sweep path defined by the analysis method is directly calculated by the first derivative of the positions of the cross sections.

Description

Parameterized swept curved surface design method Technical Field The invention relates to the field of aircrafts, in particular to a parameterized swept curved surface design method. Background Swept curved surfaces are common geometries in aeronautical engineering, generally consisting of several sections that vary continuously along a swept reference line. When the parametric generation is carried out on the swept curved surface, the parametric description of each section graph is needed to be respectively realized, graph transformation and sweep assembly are completed on the basis, and the transformation process is described by using a parametric method, so that the parametric definition and design of the swept curved surface are realized. The existing two-dimensional graph parameterization method is characterized in that deformation disturbance defined by an analytic basis function is applied by taking a reference shape as a center, or a plurality of analytic function families are directly used for fitting a contour, a graph with higher geometric complexity cannot be described, the existing geometric deformation is mainly driven by a control point, the geometric failure problems such as selfing and the like are easily caused under the condition of large geometric deformation, the existing swept curved surface design method lacks uniform parameterization description and control methods for the on-way change of a section graph, the covered sample space is smaller, and the parameterization design of the swept curved surface is limited. Therefore, it is desirable to provide a parametric swept surface design method to solve the above-mentioned problems. Disclosure of Invention The invention aims to provide a parameterized swept surface design method, which is characterized in that a two-dimensional graph is processed through discrete sampling with order preservation and feature preservation, a sampling sequence is enabled to preserve geometric details and have consistent point order indexes and adjacency relations, a measurement substrate is constructed under a normalized coordinate system to complete graph parameterization, a unified analysis frame is formed, an S-shaped curve with acceleration of two ends of 0 is used as a control rule based on the frame, complex graph gentle deformation is realized through coordinate transformation, and parameterization generation of a swept surface is realized by combining the shape, the size and a swept path described by a parameterization curve or a discrete point list and matching a section assembly strategy. The method improves standardization of graphic processing and smoothness of deformation, and provides an efficient parameterization scheme for generating the swept curved surface. In order to achieve the above purpose, the invention provides a parameterized swept surface design method, which comprises a two-dimensional graph parameterization module and a swept surface generation module, wherein the two-dimensional graph parameterization module is used for parameterizing all two-dimensional cross-section graphs and obtaining parameter coordinates corresponding to target graphs, and the parameter coordinates are subjected to transformation design and assembly operation by the swept surface generation module to generate a swept surface; The X axis points to the sweep advancing direction, the Z axis points to the right above the sweep curved surface, the Y axis is obtained by the XZ axis through a right hand rule, the discrete operation of all the two-dimensional graphs is carried out in the YZ plane, the normalization operation is carried out under a normalization coordinate system, and the specified xi is consistent with the Y axis direction, and the eta is consistent with the Z axis direction. Preferably, the two-dimensional image parameterization module establishes a unified measurement reference for an input reference graph under a normalized coordinate system, solves parameter coordinates of a target graph under the measurement reference by adopting a least square method, and specifically executes the following steps: S1A, inputting parameters comprising a reference graph and a target graph needing to be parameterized and comprising normalized size and interpolation center arrangement, wherein the reference graph selects a section of the beginning end or the tail end of a sweep graph; S2A, describing a reference graph and a target graph as a sampling point sequence with the same index rule, wherein the sampling process comprises preprocessing, defining a first sampling point and a rotating reference axis, defining a sampling direction, and prescribing sampling point numbers and sampling modes; S3A, constructing a measurement substrate by using the normalized reference graph coordinate sequence and the interpolation center coordinate sequence; S4A, converting a parameterized task of the target graph into a solution of a parameter coordinate problem under a measu