CN106952350B - A kind of deformation of free method suitable for class cylindrical three-dimensional curved surface - Google Patents
A kind of deformation of free method suitable for class cylindrical three-dimensional curved surface Download PDFInfo
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Abstract
The invention discloses a kind of three-dimensional free surface deformation methods for similar cylindrical object, for solving the problems, such as that existing curved surface deformation method is weak for cylindrical object deformability, the ability radially and circumferentially deformed for similar cylindrical object is improved.The specific steps are：The first step indicates three-dimension curved surface using discrete point coordinate data under rectangular coordinate system, establishes deformation of free controller chassis around the curved surface and obtains the coordinate of controller chassis；Second step defines cylindrical-coordinate system and the rectangular co-ordinate of curved surface and controller chassis is converted to circular cylindrical coordinate, establishes virtual box under cylindrical-coordinate system；Third step establishes the mathe-matical map relationship based on deformation of free method using controller chassis and virtual box under cylindrical-coordinate system, parameter coordinate required for solution obtains；4th step modifies the coordinate of controller chassis under cylindrical-coordinate system and solution obtains deformed surface points coordinate；The circular cylindrical coordinate of deformed curved surface is converted to rectangular co-ordinate by the 5th step.
Description
Technical field
The present invention relates to airplane design technical field, specially a kind of free form surface suitable for class cylindrical three-dimensional curved surface
Deformation method.
Background technique
In recent years, the Optimization Design for Aerodynamic method based on Fluid Mechanics Computation has become an important research neck
Domain and design tool have obtained the concern of many researchers and project planner, and the big aircraft adhered to for country is sent out
Open up strategic important role.Three-dimension curved surface deformation method (also referred to as parametric method) is as the weight in optimum design method
Module is wanted, effect is to enable a designer to change three-dimension curved surface shape using mathematical variable.Curved surface deformation method is for outer
The modification of shape needs to meet continuity, slickness, meets requirement in the engineerings such as geometrical characteristic, and needed for curved surface deformation method
The number for the design variable wanted has vital influence for the efficiency of optimum design method.Civil aircraft nacelle design flies
The demand of machine Die Design proposes requirement to the deformation method of similar cylindrical surface.
There are some defects when existing some curved surface deformation methods are applied to cylindrical or similar cylindrical object, mainly
Problem is that existing curved surface deformation method has stronger rectangular coordinate system feature, it is difficult to required for obtaining for cylindrical object
Radially and circumferentially deformation, in addition required for design variable number it is more, if by it be applied in Aerodynamic optimization design if can
Greatly increase the demand of calculation amount and time.
Summary of the invention
The purpose of the invention is to overcome existing curved surface deformation method to deform energy for the curved surface of similar cylindrical object
Hypodynamic problem provides one kind with specific aim and efficient design method for the curved design of this type objects.
The technical scheme is that：
A kind of deformation of free method suitable for class cylindrical three-dimensional curved surface, it is characterised in that：Including following
Step：
Step 1：According to design requirement, class cylinder design object is chosen, obtains class cylinder using surface forming tool
The basic shape of design object, and class cylinder design object is indicated using discrete point coordinate data under rectangular coordinate system；
Step 2：Deformation of free controller chassis is established around class cylinder design object, and is obtained under rectangular coordinate system
Controller chassis coordinate；
Step 3：Cylindrical-coordinate system is defined, the rectangular co-ordinate of class cylinder design object and controller chassis is converted into cylinder
Coordinate, and virtual box is established in cylindrical-coordinate system；
Step 4：Under cylindrical-coordinate system, according to controller chassis and virtual box and it is based on deformation of free method, is established
Mathe-matical map relationship
And it solves and obtains parameter coordinate；Wherein X is that class cylinder design object needs the global of any point on deformation surface to sit
Vector is marked, (u, v, w) is parameter coordinate vector corresponding with X, Pi,j,kIt is the world coordinates vector at control point, Bi,p(u),Bj,q
(v),Bk,rIt (w) is successively p, q and r B-spline basic function, W respectivelyi,j,kFor weight factor；
Step 5：Under cylindrical-coordinate system, according to deformation requirements, several control points P is modifiedi,j,kCoordinate, and deforming
The coordinate for modifying virtual box in the process, keeps that the angle coordinate residual quantity of modified frame control point and virtual controlling point is constant, diameter
It is equal to coordinate, axial coordinate is equal；
Step 6：The curved surface circular cylindrical coordinate of deformed class cylinder design object is converted into rectangular co-ordinate, obtains class circle
The deformation result of cylindrical design object.
Beneficial effect
Method of the invention has the advantages that following several respects compared with prior art：
Due to use coordinate transformation method so that the method for the present invention be able to carry out it is good radially and circumferentially deform, from
And less design variable number can be used and reach Amoebida.Virtual box method of the invention can guarantee on the boundary of frame
The single order and second order at place or the derivative continuity of higher order, to solve using common deformation of free method for justifying
Existing continuity problem when cylindrical objects.
Additional aspect and advantage of the invention will be set forth in part in the description, and will partially become from the following description
Obviously, or practice through the invention is recognized.
Detailed description of the invention
Above-mentioned and/or additional aspect of the invention and advantage will become from the description of the embodiment in conjunction with the following figures
Obviously and it is readily appreciated that, wherein：
Fig. 1 is controller chassis arrangement schematic diagram；
Fig. 2 is coordinate conversion schematic diagram；
Fig. 3 is virtual box cross-sectional under rectangular coordinate system；
Fig. 4 is virtual box schematic diagram under cylindrical-coordinate system.
Specific embodiment
The embodiment of the present invention is described below in detail, the embodiment is exemplary, it is intended to it is used to explain the present invention, and
It is not considered as limiting the invention.
As stated in the background art, the purpose of the invention is to overcome existing curved surface deformation method for similar cylinder thing
The problem of the curved surface deformability deficiency of body provides one kind with specific aim and efficient design for the curved design of this type objects
Method, this method be based on deformation of free is theoretical, right angle circular cylindrical coordinate conversion method and virtual box method, specifically include with
Lower step：
Step 1：According to design requirement, class cylinder design object, such as civil aircraft engine cylinder nacelle are chosen
Curved surface or plane nose three-dimension curved surface obtain the basic shape of class cylinder design object using surface forming tool, and straight
The three-dimension curved surface of class cylinder design object is indicated under angular coordinate system using discrete point coordinate data.
Step 2：Three-dimension curved surface around class cylinder design object establishes deformation of free controller chassis, and obtains right angle
Controller chassis coordinate under coordinate system.As shown in Figure 1, design object is cylindrical body, the intersection point (control of solid line, dotted line and line segment
Point) collectively constitute controller chassis.The topological structure of controller chassis is non-parallel hexahedron, in order to for similar cylindrical outer shape, one
A little control points are completely coincident in the axle center of cylinder.
Step 3：Cylindrical-coordinate system is defined, by class cylinder design object three-dimension curved surface (curved surface to be deformed) and controller chassis
Rectangular co-ordinate be converted to circular cylindrical coordinate, and virtual box is established in cylindrical-coordinate system.
Coordinate conversion needs to define rectangular coordinate system oxyz, the rectangular coordinate system o'x'y'z' being connected with curved surface, cylinder and sits
Mark system o θ rh.θ indicates that angle coordinate, r indicate that radial coordinate, h indicate axial coordinate.Fig. 1 show with controller chassis be connected it is straight
The definition mode of angular coordinate system o'x'y'z'.Fig. 2 shows that the mathematics transformational relation of o'x'y'z' and cylindrical-coordinate system, coordinate turn
Two steps can be divided by changing, and the first step is the transformation between oxyz and o'x'y'z', and second step is o'x'y'z' and circular cylindrical coordinate
Transformation between system, the conversion of this two steps coordinate, which carries out linear transformation using matrix, can be completed.After completing coordinate conversion, need
Virtual box is constructed under cylindrical-coordinate system.Fig. 3, Fig. 4 show the definition mode of virtual box method.C, D that Fig. 3 is shown, E, F, G,
H, I, J are the control points manually arranged, and these points (being named as virtual controlling point below) of A, B, L, M are straight with I, J, D, E
Angular coordinate is identical.After rectangular co-ordinate is converted to circular cylindrical coordinate, angle coordinate is assigned to these virtual controlling points of A, B, L, M and is increased
Amount, so that these angle coordinates put mutually are distinguished with I, J, D, E, so that the angle coordinate of these virtual controlling points is located at [0,2 π]
Except.The shadow region that Fig. 4 is shown is that the frame manually arranged is converted to the region for including, two sides adjacent thereto after circular cylindrical coordinate
Transparent frame be called virtual box.There is no limit two in frame of example herein for the quantity of virtual controlling point for virtual box method
Two virtual controlling point A, B and L, M have been respectively adopted in boundary, can be protected according to this arrangement of the theory of deformation of free
Demonstrate,prove second dervative continuity, that is, continual curvature in frame boundary.
Step 4：Under cylindrical-coordinate system, according to controller chassis and virtual box and it is based on deformation of free method, is established
Mathe-matical map relationship
And it solves and obtains parameter coordinate；Wherein X is that class cylinder design object needs the global of any point on deformation surface to sit
It marks vector (being used herein as circular cylindrical coordinate), X length is three if in three dimensions.This table is all used for all the points on surface
Up to formula (being used herein as world coordinates indicates the coordinate in physical space, to mutually distinguish with parameter coordinate), each point will be each
From world coordinates in above-mentioned expression formula, therefore each point has unique parameter coordinate vector (u, v, w) corresponding with X.l
+ 1, m+1 and n+1 is the number of control points along tri- directions i, j and k.Pi,j,kIt is that the world coordinates vector at control point (makes herein
With circular cylindrical coordinate, the coordinate including virtual controlling point), Bi,p(u),Bj,q(v),Bk,rIt (w) is successively p, q and r B-spline respectively
Basic function；Wi,j,kFor weight factor.
The recursive form of B-spline basic function is with Bi,p(u) it is defined as：
Agreement 0/0=0 is needed herein.P indicates the power of B-spline in formula, and u is parameter coordinate, uiFor knot vector, subscript i
For node serial number.In the case of three-dimensional, u, v and w are respectively substituted into respectively.Knot vector needed for formula is according to following public affairs
Formula is established, and three-dimensional situation then establishes three components respectively.
Wherein, p indicates rank (degree), i.e., p+1 times (order), control point sum is l+1, knot vector total length
For l+p+2, example is (u0,u1,u2,...,ul+p+1)。
The method for solving of specific parameter coordinate uses Newton iteration method.
Step 5：Under cylindrical-coordinate system, according to deformation requirements, several control points P is modifiedi,j,kCoordinate, and deforming
The coordinate for modifying virtual box in the process, keeps that the angle coordinate residual quantity of modified frame control point and virtual controlling point is constant, diameter
It is equal to coordinate, axial coordinate is equal；Such as the angle coordinate residual quantity of I and A remains unchanged.θI-θA=θI'-θA', θIAnd θAIt is
Angle coordinate before deformation, θI' and θA' it is deformed angle coordinate.All virtual controlling points are all made of this processing mode.Most
Afterwards, equations are substituted into and obtains deformed surface points circular cylindrical coordinate X'.
Step 6：The curved surface circular cylindrical coordinate X' of deformed class cylinder design object is converted into rectangular co-ordinate, obtains class
The deformation result of cylinder design object.
Although the embodiments of the present invention has been shown and described above, it is to be understood that above-described embodiment is example
Property, it is not considered as limiting the invention, those skilled in the art are not departing from the principle of the present invention and objective
In the case where can make changes, modifications, alterations, and variations to the above described embodiments within the scope of the invention.
Claims (1)
1. a kind of deformation of free method suitable for class cylindrical three-dimensional curved surface, it is characterised in that：Include the following steps：
Step 1：According to design requirement, class cylinder design object is chosen, obtains class cylinder design using surface forming tool
The basic shape of object, and class cylinder design object is indicated using discrete point coordinate data under rectangular coordinate system；
Step 2：Deformation of free controller chassis is established around class cylinder design object, and obtains the control under rectangular coordinate system
Frame coordinate；
Step 3：Cylindrical-coordinate system is defined, the rectangular co-ordinate of class cylinder design object and controller chassis is converted into cylinder and is sat
Mark, and virtual box is established in cylindrical-coordinate system；
The method for establishing virtual box is：
On angle coordinate axis in cylindrical-coordinate system, virtual box is established in controller chassis two sides, and the virtual controlling in virtual box
Point is identical as coordinate of the control point corresponding in controller chassis under rectangular coordinate system, differs 2 π in cylindrical-coordinate system lower angle coordinate；
Step 4：Under cylindrical-coordinate system, according to controller chassis and virtual box and it is based on deformation of free method, establishes mathematics
Mapping relations
And it solves and obtains parameter coordinate；Wherein X be class cylinder design object need the world coordinates of any point on deformation surface to
Amount, (u, v, w) is parameter coordinate vector corresponding with X, Pi,j,kIt is the world coordinates vector at control point, Bi,p(u),Bj,q(v),
Bk,rIt (w) is successively p, q and r B-spline basic function, W respectivelyi,j,kFor weight factor；
Step 5：Under cylindrical-coordinate system, according to deformation requirements, several control points P is modifiedi,j,kCoordinate, and in deformation process
The coordinate of middle modification virtual box, keeps that the angle coordinate residual quantity of modified frame control point and virtual controlling point is constant, radial sits
Mark that equal, axial coordinate is equal；
Step 6：The curved surface circular cylindrical coordinate of deformed class cylinder design object is converted into rectangular co-ordinate, obtains class cylinder
The deformation result of design object.
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| JP2001250128A (en) * | 2000-03-03 | 2001-09-14 | Namco Ltd | Game system and information storage medium |
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| EP1008957A1 (en) * | 1998-06-02 | 2000-06-14 | Sony Corporation | Image processing device and image processing method |
| CN103392180A (en) * | 2011-02-24 | 2013-11-13 | 西门子产品生命周期管理软件公司 | Global deformation for a modeled object |
| CN104050720A (en) * | 2014-06-24 | 2014-09-17 | 中国科学院深圳先进技术研究院 | Point cloud curve plane reconstruction method and system |
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Effective date of registration: 20240302 Address after: 710089 No.12 Fenghuang North Street, Yanliang District, Xi'an City, Shaanxi Province Patentee after: Xi'an Lanhua Aviation Manufacturing Co.,Ltd. Country or region after: China Address before: 710072 No. 127 Youyi West Road, Shaanxi, Xi'an Patentee before: Northwestern Polytechnical University Country or region before: China |