阅读说明：本技术 一种薄壁球壳类微小构件全表面均布微坑结构加工轨迹的规划方法及装置 (Planning method and device for machining track of all-surface uniformly-distributed micro-pit structure of thin-wall spherical shell type micro component ) 是由 陈明君 郭锐阳 于天宇 童嘉跞 周星颖 王广洲 李国� 于 2021-09-10 设计创作，主要内容包括：一种薄壁球壳类微小构件全表面均布微坑结构加工轨迹的规划方法及装置,涉及加工轨迹规划技术领域,用以解决现有的加工轨迹规划方法不能实现球壳类微小构件的加工点均匀分布的问题。本发明的技术要点包括：首先基于斐波那契原理,对薄壁球壳类微小构件全表面微坑结构进行初步均分,相对于经纬网格加权划分误差减小40％,点集分布均匀性得到提高；进一步提出球面点集均布迭代算法,对基于斐波那契原理生成的分布相对均匀点集进一步均匀优化,坑点间距误差大幅度下降,达到实际加工微小构件的误差要求,进一步提高了薄壁球壳类微小构件表面微坑结构分布的均匀性。本发明可应用于各种不同尺寸球体表面均布点集的实际路径规划中。(A planning method and a device for a machining track of a structure with uniformly distributed micro pits on the whole surface of a thin-wall spherical shell type micro component relate to the technical field of machining track planning and are used for solving the problem that the machining points of the spherical shell type micro component cannot be uniformly distributed by the existing machining track planning method. The technical points of the invention comprise: firstly, based on the Fibonacci principle, the whole-surface pit structure of the thin-wall spherical shell type micro component is preliminarily uniformly divided, the weighted dividing error is reduced by 40% relative to a longitude and latitude grid, and the distribution uniformity of a point set is improved; and further providing a spherical surface point set uniform distribution iterative algorithm, further uniformly optimizing a relatively uniform distribution point set generated based on the Fibonacci principle, greatly reducing the pitch error of pits, meeting the error requirement of actually processing the small component, and further improving the uniformity of the distribution of the micro-pit structure on the surface of the thin-wall spherical shell type small component. The method can be applied to the actual path planning of the point sets uniformly distributed on the surfaces of the spheres with different sizes.)

1. A planning method for processing tracks of uniformly distributed micro-pit structures on the surface of a thin-wall spherical shell type micro component is characterized by comprising the following steps:

firstly, preliminarily generating a micro-pit structure point set which is distributed relatively uniformly on the whole surface of a thin-wall spherical shell type micro component based on a Fibonacci principle;

step two, optimizing the distribution uniformity of the point sets of the micro-pit structure by utilizing a spherical point set uniform distribution iterative algorithm to generate micro-pit structure uniform distribution point sets;

step three, selecting processing initial points in a micro-pit structure uniform distribution point set, and generating a processing track of the micro-pit structure uniformly distributed on the surface of the thin-wall spherical shell type micro component based on the shortest processing path principle; all points on the processing track are distributed points with uniformly distributed points in a micro-pit structure.

2. The planning method for the machining tracks of the uniformly distributed micro-pit structures on the surface of the thin-wall spherical shell type micro component as claimed in claim 1 is characterized in that the specific steps of the first step comprise:

establishing an X axis and a Y axis which are perpendicular to each other in a spherical surface equatorial plane by taking the spherical center of the thin-wall spherical shell type micro component as a coordinate origin to form an X-Y plane, determining a Z axis by a right-hand rule, and establishing a workpiece coordinate system; wherein, the X-Y plane is vertical to the moving direction of the milling cutter;

dividing the spherical surface of the thin-wall spherical shell type micro component into N layers with the same thickness based on the Fibonacci principle, wherein N represents the total number of distribution points in the micro-pit structure point set; the latitude spans of all layers in the N layers are different, the latitude spans of the south and north poles are maximum, one point is taken at the middle point of each layer thickness, and the Z-axis coordinate of the distribution point in the micro-pit structure point set is obtained:

z_n＝R*[(2n-1)/N-1]

wherein n represents a coordinate point serial number; r represents the sphere radius of the thin-wall spherical shell type micro component;

dividing the coordinates of an X axis and a Y axis according to the longitude in an arithmetic progression distribution manner, ensuring that the X axis and the Y axis are distributed relatively uniformly, and obtaining the coordinates of the X axis and the Y axis of the distributed points in the micro-pit structure point set:

wherein the content of the first and second substances,

3. the planning method for the machining tracks of the uniformly distributed micro-pit structures on the surface of the thin-wall spherical shell type micro component as claimed in claim 2 is characterized in that the specific steps of the second step comprise:

step two, calculating the acting force between any two distribution points in the micro-pit structure point setThe force is proportional to the square of the distance between the two points;

step two, acting forceResolved into radial forces passing through the centre of the sphereAnd a tangential force perpendicular to the direction connecting the center of the sphere and the distribution pointCalculating and obtaining radial force of all distribution points in the micro-pit structure point set according to the following formulaModulo T of the vector sum of₁All distribution points tangential forceModulo T of the vector sum of₂：

Step two and step three, in the tangential forceUnder the action of the micro-pit structure point, continuously updating the coordinates of the distributed points in the micro-pit structure point set according to the following formula:

wherein G represents the influence factor of the tangential force on the speed;andrespectively representing the coordinates of the distribution points before and after updating;andrespectively representing the speed of the distribution point before moving and the speed of the distribution point after moving;

step two, the step two to the step two are executed in an iterative cycle mode until the distribution points in the micro-pit structure point set do not move any more, and the coordinates of all the distribution points in the micro-pit structure uniform distribution point set are obtained; wherein, the judgment condition that the distribution points in the micro-pit structure point set do not move is the radial force of all the distribution pointsModulo T of the vector sum of₁And all distribution point tangential forcesModulo T of the vector sum of₂Down to a minimum value and no longer changing.

4. The method for planning the machining tracks of the uniformly distributed micro-pit structures on the surface of the thin-wall spherical shell type micro-component according to claim 3, wherein in the third step, in the process of generating the machining tracks, a triangulation function Delaunay Tri is adopted to divide a micro-pit structure point set or a micro-pit structure uniformly distributed point set into a spatial tetrahedron, a spatial tetrahedron convex hull is calculated by utilizing a convex hull algorithm, and a polyhedron is drawn to visually observe the distribution condition of the point set.

5. The planning method for the machining tracks of the uniformly distributed micro-pit structures on the surface of the thin-wall spherical shell type micro component as claimed in claim 4, wherein the value range of the total number N of distributed points in the micro-pit structure point set is as follows: n is more than or equal to 50 and less than or equal to 100.

6. The utility model provides a planning device of little component surface equipartition pit structure processing orbit of thin wall spherical shell class which characterized in that includes:

the micro-pit structure generation module is used for preliminarily generating a micro-pit structure point set which is distributed relatively uniformly on the whole surface of the thin-wall spherical shell type micro component based on the Fibonacci principle;

the iteration optimization module is used for optimizing the distribution uniformity of the micro-pit structure point set by utilizing a spherical point set uniform distribution iteration algorithm to generate a micro-pit structure uniform distribution point set;

the trace generation module is used for selecting processing initial points in a centralized manner from the uniformly distributed points of the micro-pit structure and generating processing traces of the uniformly distributed micro-pit structure on the surface of the thin-wall spherical shell type micro-component based on the shortest processing path principle; all points on the processing track are distributed points with uniformly distributed points in a micro-pit structure.

7. The planning device for uniformly distributing machining tracks of the micro-pit structures on the surface of the thin-wall spherical shell type micro-component according to claim 6, wherein the specific step of generating the micro-pit structure point sets with relatively uniform distribution in the micro-pit structure generation module comprises the following steps:

establishing an X axis and a Y axis which are perpendicular to each other in a spherical surface equatorial plane by taking the spherical center of the thin-wall spherical shell type micro component as a coordinate origin to form an X-Y plane, determining a Z axis by a right-hand rule, and establishing a workpiece coordinate system; wherein, the X-Y plane is vertical to the moving direction of the milling cutter;

dividing the spherical surface of the thin-wall spherical shell type micro component into N layers with the same thickness based on the Fibonacci principle, wherein N represents the total number of distribution points in the micro-pit structure point set; the latitude spans of all layers in the N layers are different, the latitude spans of the south and north poles are maximum, one point is taken at the middle point of each layer thickness, and the Z-axis coordinate of the distribution point in the micro-pit structure point set is obtained:

z_n＝R*[(2n-1)/N-1]

wherein n represents a coordinate point serial number; r represents the sphere radius of the thin-wall spherical shell type micro component;

dividing the coordinates of an X axis and a Y axis according to the longitude in an arithmetic progression distribution manner, ensuring that the X axis and the Y axis are distributed relatively uniformly, and obtaining the coordinates of the X axis and the Y axis of the distributed points in the micro-pit structure point set:

wherein the content of the first and second substances,

8. the planning device for the machining track of the uniformly distributed micro-pit structure on the surface of the thin-wall spherical shell type micro component according to claim 7, wherein the iterative optimization module optimizes the micro-pit structure point set to generate the uniformly distributed micro-pit structure point set specifically comprises the following steps:

step two, calculating the acting force between any two distribution points in the micro-pit structure point setThe force is proportional to the square of the distance between the two points;

step two, acting forceResolved into radial forces passing through the centre of the sphereAnd a tangential force perpendicular to the direction connecting the center of the sphere and the distribution pointCalculating and obtaining radial force of all distribution points in the micro-pit structure point set according to the following formulaModulo T of the vector sum of₁All distribution points tangential forceModulo T of the vector sum of₂：

Step two and step three, in the tangential forceUnder the action of the micro-pit structure point, continuously updating the coordinates of the distributed points in the micro-pit structure point set according to the following formula:

wherein G represents the influence factor of the tangential force on the speed;andrespectively representing the coordinates of the distribution points before and after updating;andrespectively representing the speed of the distribution point before moving and the speed of the distribution point after moving;

step two, the step two to the step two are executed in an iterative cycle mode until the distribution points in the micro-pit structure point set do not move any more, and the coordinates of all the distribution points in the micro-pit structure uniform distribution point set are obtained; wherein, the judgment condition that the distribution points in the micro-pit structure point set do not move is the radial force of all the distribution pointsModulo T of the vector sum of₁And all distribution point tangential forcesModulo T of the vector sum of₂Down to a minimum value and no longer changing.

9. The planning device for uniformly distributing machining tracks of the micro-pit structures on the surface of the thin-wall spherical shell type micro-component according to claim 8, wherein in the track generation module, a triangulation function Delaunay Tri is adopted to divide a micro-pit structure point set or a micro-pit structure uniformly distributed point set into a spatial tetrahedron in the process of generating the machining tracks, and the spatial tetrahedron convex hull is calculated by utilizing a convex hull algorithm and a polyhedron is drawn to visually observe the distribution condition of the point set.

10. The planning device for the machining tracks of the uniformly distributed micro-pit structures on the surface of the thin-wall spherical shell type micro component as claimed in claim 9, wherein the value range of the total number N of distributed points in the micro-pit structure point set is as follows: n is more than or equal to 50 and less than or equal to 100.

Technical Field

The invention relates to the technical field of machining track planning, in particular to a method and a device for planning a machining track of a structure in which micro pits are uniformly distributed on the whole surface of a thin-wall spherical shell type micro component.

Background

With the rapid development of science and technology, various thin-wall spherical shell type micro components with high surface quality requirements are widely applied to the fields of national defense and military, aerospace, microelectronics, biomedical treatment and the like. The method is characterized in that tens to hundreds of micro-pit structures with the depth of 0.5-20 mu m and the diameter of 50-200 mu m are processed on the surface of a thin-wall spherical shell with the diameter of 1-5 mm and the shell thickness of 20-120 mu m for energy research, the surface profile error is better than 0.3 mu m, the surface roughness Ra is better than 20nm, pit points are uniformly distributed, and the spacing error reaches the micron order.

Under the constraint of small scale and micro space, due to the existence of a series of problems of cross-scale characteristic structure, fine surface defect, non-uniform material, surface asymmetry, fluid mechanics instability in the processing process and the like, higher urgent needs are provided for the processing technology of the full-spherical uniformly-distributed micro-pit structure of the thin-wall spherical shell type micro component and the planning method of the processing track. In the existing planning method for uniformly distributing machining tracks of micro-pit structures on the whole surface of a thin-wall spherical shell type micro component, for example, longitude and latitude grids are subjected to weighted division, and intersection points of longitude and latitude lines are extracted according to a certain longitude and latitude interval. How to realize the optimal distribution uniformity of the whole-surface micro-pit structure of the thin-wall spherical shell type micro component and the optimal processing track of the cutter, further improve the processing efficiency and reduce the accumulation of errors becomes a hot spot of research of various national researchers and a difficult problem to be solved urgently.

Disclosure of Invention

In view of the above problems, the invention provides a planning method and a device for a machining track of a structure in which micro pits are uniformly distributed on the whole surface of a thin-wall spherical shell type micro component, so as to solve the problem that the machining points of the spherical shell type micro component cannot be uniformly distributed by the existing machining track planning method.

According to one aspect of the invention, the method for planning the processing track of the uniformly distributed micro-pit structure on the surface of the thin-wall spherical shell type micro component comprises the following steps:

firstly, preliminarily generating a micro-pit structure point set which is distributed relatively uniformly on the whole surface of a thin-wall spherical shell type micro component based on a Fibonacci principle;

step two, optimizing the distribution uniformity of the point sets of the micro-pit structure by utilizing a spherical point set uniform distribution iterative algorithm to generate micro-pit structure uniform distribution point sets;

step three, selecting processing initial points in a micro-pit structure uniform distribution point set, and generating a processing track of the micro-pit structure uniformly distributed on the surface of the thin-wall spherical shell type micro component based on the shortest processing path principle; all points on the processing track are distributed points with uniformly distributed points in a micro-pit structure.

Further, the specific steps of the first step include:

establishing an X axis and a Y axis which are perpendicular to each other in a spherical surface equatorial plane by taking the spherical center of the thin-wall spherical shell type micro component as a coordinate origin to form an X-Y plane, determining a Z axis by a right-hand rule, and establishing a workpiece coordinate system; wherein, the X-Y plane is vertical to the moving direction of the milling cutter;

dividing the spherical surface of the thin-wall spherical shell type micro component into N layers with the same thickness based on the Fibonacci principle, wherein N represents the total number of distribution points in the micro-pit structure point set; the latitude spans of all layers in the N layers are different, the latitude spans of the south and north poles are maximum, one point is taken at the middle point of each layer thickness, and the Z-axis coordinate of the distribution point in the micro-pit structure point set is obtained:

z_n＝R*[(2n-1)/N-1]

wherein n represents a coordinate point serial number; r represents the sphere radius of the thin-wall spherical shell type micro component;

dividing the coordinates of an X axis and a Y axis according to the longitude in an arithmetic progression distribution manner, ensuring that the X axis and the Y axis are distributed relatively uniformly, and obtaining the coordinates of the X axis and the Y axis of the distributed points in the micro-pit structure point set:

wherein the content of the first and second substances,

further, the specific steps of the second step include:

step two, calculating the acting force between any two distribution points in the micro-pit structure point setThe force is proportional to the square of the distance between the two points;

step two, acting forceResolved into radial forces passing through the centre of the sphereAnd a tangential force perpendicular to the direction connecting the center of the sphere and the distribution pointCalculating and obtaining radial force of all distribution points in the micro-pit structure point set according to the following formulaModulo T of the vector sum of₁All distribution points tangential forceModulo T of the vector sum of₂：

Step two and step three, in the tangential forceUnder the action of the micro-pit structure point, continuously updating the coordinates of the distributed points in the micro-pit structure point set according to the following formula:

wherein G represents the influence factor of the tangential force on the speed;andrespectively representing the coordinates of the distribution points before and after updating;andrespectively representing the speed of the distribution point before moving and the speed of the distribution point after moving;

step two, the step two to the step two are executed in an iterative cycle mode until the distribution points in the micro-pit structure point set do not move any more, and the coordinates of all the distribution points in the micro-pit structure uniform distribution point set are obtained; wherein, the judgment condition that the distribution points in the micro-pit structure point set do not move is the radial force of all the distribution pointsModulo T of the vector sum of₁And all distribution point tangential forcesModulo T of the vector sum of₂Down to a minimum value and no longer changing.

Further, in the third step, in the process of generating the processing track, a triangulation function Delaunay Tri is adopted to divide the micro-pit structure point set or the micro-pit structure uniform distribution point set into a spatial tetrahedron, a convex hull algorithm is utilized to calculate a convex hull of the spatial tetrahedron, and a polyhedron is drawn to visually observe the distribution condition of the point set.

Further, the value range of the total number N of distributed points in the micro-pit structure point set is as follows: n is more than or equal to 50 and less than or equal to 100.

According to another aspect of the present invention, a planning apparatus for processing tracks of uniformly distributed micro-pit structures on the surface of a thin-walled spherical shell type micro component is provided, the apparatus comprising:

the micro-pit structure generation module is used for preliminarily generating a micro-pit structure point set which is distributed relatively uniformly on the whole surface of the thin-wall spherical shell type micro component based on the Fibonacci principle;

the iteration optimization module is used for optimizing the distribution uniformity of the micro-pit structure point set by utilizing a spherical point set uniform distribution iteration algorithm to generate a micro-pit structure uniform distribution point set;

the trace generation module is used for selecting processing initial points in a centralized manner from the uniformly distributed points of the micro-pit structure and generating processing traces of the uniformly distributed micro-pit structure on the surface of the thin-wall spherical shell type micro-component based on the shortest processing path principle; all points on the processing track are distributed points with uniformly distributed points in a micro-pit structure.

Further, the specific step of generating a relatively uniformly distributed pit structure point set in the pit structure generation module includes:

establishing an X axis and a Y axis which are perpendicular to each other in a spherical surface equatorial plane by taking the spherical center of the thin-wall spherical shell type micro component as a coordinate origin to form an X-Y plane, determining a Z axis by a right-hand rule, and establishing a workpiece coordinate system; wherein, the X-Y plane is vertical to the moving direction of the milling cutter;

dividing the spherical surface of the thin-wall spherical shell type micro component into N layers with the same thickness based on the Fibonacci principle, wherein N represents the total number of distribution points in the micro-pit structure point set; the latitude spans of all layers in the N layers are different, the latitude spans of the south and north poles are maximum, one point is taken at the middle point of each layer thickness, and the Z-axis coordinate of the distribution point in the micro-pit structure point set is obtained:

z_n＝R*[(2n-1)/N-1]

wherein n represents a coordinate point serial number; r represents the sphere radius of the thin-wall spherical shell type micro component;

dividing the coordinates of an X axis and a Y axis according to the longitude in an arithmetic progression distribution manner, ensuring that the X axis and the Y axis are distributed relatively uniformly, and obtaining the coordinates of the X axis and the Y axis of the distributed points in the micro-pit structure point set:

wherein the content of the first and second substances,

further, the iterative optimization module optimizes the micro-pit structure point sets to generate micro-pit structure uniform distribution point sets, and the specific steps of the iterative optimization module comprise:

step two, calculating the acting force between any two distribution points in the micro-pit structure point setThe force is proportional to the square of the distance between the two points;

step two, acting forceResolved into radial forces passing through the centre of the sphereAnd a tangential force perpendicular to the direction connecting the center of the sphere and the distribution pointCalculating and obtaining radial force of all distribution points in the micro-pit structure point set according to the following formulaModulo T of the vector sum of₁All distribution points tangential forceModulo T of the vector sum of₂：

Step two and step three, in the tangential forceUnder the action of the micro-pit structure point, continuously updating the coordinates of the distributed points in the micro-pit structure point set according to the following formula:

wherein G represents the influence factor of the tangential force on the speed;andrespectively representing the coordinates of the distribution points before and after updating;andrespectively representing the speed of the distribution point before moving and the speed of the distribution point after moving;

step two, step four, iteration loop carries out step two one to step two, step three, straightThe distribution points in the micro-pit structure point set do not move any more, and the coordinates of all the distribution points in the micro-pit structure uniform distribution point set are obtained; wherein, the judgment condition that the distribution points in the micro-pit structure point set do not move is the radial force of all the distribution pointsModulo T of the vector sum of₁And all distribution point tangential forcesModulo T of the vector sum of₂Down to a minimum value and no longer changing.

Further, in the trajectory generation module, in the process of generating the processing trajectory, a triangulation function Delaunay Tri is adopted to divide a micro-pit structure point set or a micro-pit structure uniform distribution point set into a spatial tetrahedron, a convex hull algorithm is utilized to calculate a spatial tetrahedron convex hull, and a polyhedron is drawn to visually observe the distribution condition of the point set.

Further, the value range of the total number N of distributed points in the micro-pit structure point set is as follows: n is more than or equal to 50 and less than or equal to 100.

The beneficial technical effects of the invention are as follows:

firstly, based on the Fibonacci principle, the full-surface pit structure of the thin-wall spherical shell type micro component is preliminarily uniformly divided, and compared with the weighted division of a longitude and latitude grid, the error is reduced by 40%, and the distribution uniformity of a point set is improved; further providing a spherical point set uniform distribution iterative algorithm, further uniformly optimizing a distributed relatively uniform point set generated based on the Fibonacci principle, wherein the iterative time is only 62 seconds, and the pitch error of pits is reduced from 63 mu m to 36 mu m, so that the error requirement of actual processing superior to 40 mu m is met, and the uniformity of the distribution of the micro-pit structure on the surface of the thin-wall spherical shell type micro component is further improved; based on the shortest principle of a processing path, processing tracks are generated according to the uniformly distributed point sets of the micro-pit structure, the processing efficiency is greatly improved, the requirements of the thin-wall spherical shell type micro-component on the distribution of the surface micro-pit structure, the processing path and the like are met, and the influence of larger errors caused by uneven distribution of the micro-pits on energy research is effectively solved. The invention has certain universality and can be popularized and used in the specific practice of uniformly distributing point sets on the surfaces of spheres with different sizes.

Drawings

The present invention may be better understood by reference to the following description taken in conjunction with the accompanying drawings, which are incorporated in and form a part of this specification, and which are used to further illustrate preferred embodiments of the present invention and to explain the principles and advantages of the present invention.

FIG. 1 is a schematic view of the machining of the surface micro-pit structure of a thin-wall spherical shell type micro-component in the invention;

FIG. 2 is a schematic diagram of a distributed relatively uniform point set generated based on the Fibonacci principle in the present invention;

FIG. 3 is a schematic diagram of a distributed uniform point set optimized by a spherical point set uniform distribution iterative algorithm in the present invention;

FIG. 4 is a schematic diagram of a processing track of a dimple structure on the surface of a thin-walled spherical shell type micro-component in an embodiment of the present invention.

Fig. 5 is a schematic structural diagram of a planning device for processing tracks of uniformly distributed micro-pit structures on the surface of a thin-wall spherical shell type micro component in an embodiment of the present invention.

Detailed Description

In order that those skilled in the art will better understand the disclosure, exemplary embodiments or examples of the disclosure are described below with reference to the accompanying drawings. It is obvious that the described embodiments or examples are only some, but not all embodiments or examples of the invention. All other embodiments or examples obtained by a person of ordinary skill in the art based on the embodiments or examples of the present invention without any creative effort shall fall within the protection scope of the present invention.

Aiming at the technical problems of poor distribution uniformity of the whole-surface micro-pit structure of the thin-wall spherical shell type micro component and optimization of a processing path, the invention provides a planning method for the processing track of the whole-surface uniformly-distributed micro-pit structure of the thin-wall spherical shell type micro component. Firstly, preliminarily generating micro-pit structure coordinates which are distributed relatively uniformly on the whole surface of a thin-wall spherical shell type micro component based on a Fibonacci principle; then, a spherical point set uniform distribution iterative algorithm is provided, and the micro-pit structure coordinates generated based on the Fibonacci principle are further iteratively optimized to generate point set coordinates of the micro-pit structure uniform distribution on the surface of the thin-wall spherical shell type micro component; in order to further improve the processing efficiency and reduce the influence problem caused by error accumulation, UG software secondary development function is utilized to carry out processing sequence planning and generation of processing tracks on the coordinates of the point set of the uniformly distributed micro-pit structure on the whole surface of the thin-wall spherical shell type micro component based on the principle of processing the shortest path of the surface micro-pit structure, and further optimization is carried out to improve the processing efficiency, reduce the accumulated error and realize high-quality processing of the uniformly distributed micro-pit structure on the whole surface of the thin-wall spherical shell type micro component. The planning method of the present invention is described in detail below.

Firstly, preliminarily generating a micro-pit structure point set which is distributed relatively uniformly on the whole surface of a thin-wall spherical shell type micro component based on a Fibonacci principle;

the Fibonacci series has a regular isotropic nature, which is derived from a middle century mathematician, Leonardo Pisano (Leonardo Pisano), the alias Fibonacci (Fibonacci), who found series 0,1,1,2,3,5,8,13,21 … …, where starting with the third number, each number is the sum of the first two numbers. This series was originally discovered when breeding populations of rabbits from different generations were calculated by fibonacci and, upon further investigation, was found to occur in many biological systems such as branching and alignment of plants and tree leaves, petal flowering, hives, etc. When the array tends to infinity, two adjacent numbers F in the array_iAnd F_i+1The ratio between is close to the golden section Φ:

the inverse of the golden section is equal to itself minus 1.

The Fibonacci grid is generated from a helix with uniformly spaced point sets, from 360 DEG phi^-1222.5 or successive points defined by a complementary angle of 360, i.e. 360 (1-phi)^-1)＝360°Φ^-2And 137.5 deg. determines the ordinate. From Gonz a lez (2010), given a natural number N, the N point set coordinates are calculated by the following equation, generating a fibonacci grid:

λ_i＝360°Φ^-1i＝360°×mod(i,Φ)/Φ

i＝-N,-N+1,...,0,N-1,N

the function mod (i, Φ) returns the remainder of i divided by Φ, eliminating unnecessary spiral rotations. From position coordinates λ_i、And 2N +1 grid points at different latitudes are determined, so that the uniform distribution of the point sets is realized.

Therefore, as shown in fig. 1, 4 in the figure represents a thin-wall spherical shell type micro component, a trace of a micro-pit structure machined by a ball-end mill is generated on the surface of the thin-wall spherical shell type micro component, 1 in the figure represents the ball-end mill, 2 represents the generated micro-pit structure, and 3 represents a to-be-machined trace finally generated. Based on the Fibonacci principle, establishing an X axis and a Y axis which are perpendicular to each other in a spherical equatorial plane by taking the spherical center of a thin-wall spherical shell type micro component as a coordinate origin to form an X-Y plane, determining a Z axis by a right-hand rule, and establishing a workpiece coordinate system, wherein the X-Y plane is perpendicular to the moving direction of the milling cutter; based on the Fibonacci principle, the spherical surface is divided into N layers with the same thickness, the latitude spans of all layers are different, the latitude spans of the south and north poles are the largest, and a point is taken at the midpoint of each layer thickness to obtain the Z-axis coordinate of the point:

z_n＝R*[(2n-1)/N-1]

where N denotes the number of each micro pit set, and N is 1,2,3 … N.

The side surfaces of each layer divided from the space can be regarded as a ring surface, and the radius of the ring surface is equal to that of the latitude betaR is multiplied by cos beta, the width of the ring surface is 2R/(N is multiplied by cos beta), thereby obtaining that the area of each ring surface is 4 pi R²and/N, ensuring the uniformity of the lattice distribution on the macro scale.

Further, dividing the X-axis and Y-axis coordinates according to the longitude in an arithmetic progression distribution to ensure that the X/Y-axis distribution is relatively uniform, and obtaining:

thereby obtaining point set coordinates (Xn, Yn, Zn) of N micro-pit structures which are distributed on the whole surface of the thin-wall spherical shell type micro component and are relatively uniform; in the formula, N represents the total number of distributed points in the micro-pit point set and also represents the number of distributed micro-pit structures, and can be 50-100; r represents the sphere radius of the thin-wall spherical shell type micro component, and can be 2, constantAnd further visually displaying the distribution condition of the point set, dividing the point set into space tetrahedrons by adopting a triangulation function Delaunay Tri, calculating the tetrahedral convex hulls by utilizing a convex hull algorithm, and drawing a polyhedron. The N point sets are relatively evenly distributed as shown in fig. 2.

Optimizing the micro-pit structure point set by utilizing a spherical point set uniform distribution iterative algorithm to generate a micro-pit structure uniform distribution point set;

on the basis of the relatively uniform point set coordinates of the whole surface distribution of the thin-wall spherical shell type micro component, based on an ideal condition, when gravity is not considered, and a plurality of point charges with the same charges are distributed on the spherical surface, the point charges are mutually repelled by the same charges so as to uniformly distribute the point charges, a spherical point set uniform distribution iterative algorithm is provided, the point set coordinates of the micro-pit structure generated based on the Fibonacci principle are further iteratively optimized, and the uniformly distributed point sets of the full-surface micro-pit structure of the thin-wall spherical shell type micro component are generated.

In the interaction force physical model between two static point charges in vacuum, a plurality of point charges are distributed on a spherical surface in vacuum, one point charge is taken, and the electric quantity is assumed to be Q₁Position coordinates (x1, y1, z1) taking into account the force exerted on it by the remaining point charge. Consider a charge quantity Q with a peripheral coordinate of (x2, y2, z2)₂The point charges of (a) have an applied force thereon, and the distance R between two point charges is:

calculating formula according to point charge interaction force:

wherein K is an electrostatic constant; it is known that the interaction force between two points of charges is inversely proportional to the square of the distance between them, and the interaction force can be obtained therefrom; similarly, the force of the remaining point charge on the point charge can be found, and then all the forces are combined and then decomposed into radial and tangential.

The invention equates the engineering example of uniformly distributing micro-pit structures on the surface of the thin-wall spherical shell to the physical model of point charge distributed on the spherical surface, equates the outer surface of the thin-wall spherical shell to the spherical surface, equates the micro-pits to the point charge, and then carries out calculation and solving. Solving the acting force based on the point-charge interaction force calculation formula, but simplifying other coefficients in the formula and reducing Q₁、Q₂And K is simplified to 1, and the calculation formula of the acting force at the moment is changed into:

in the formula, the distance R can be calculated according to the specific coordinates of the point set generated by the Fibonacci; the acting force F is obtained by distance calculation, and the point set is different, the distance is different, and the acting force is also different.

Therefore, if N point sets which are relatively uniform are distributed on the whole surface of the thin-wall spherical shell type micro component, the interaction force with the same property exists between any two points, and the force and the distance between the two pointsIs proportional to the square of the point, the interaction force between all points is found. The acting force applied to each point in the point setCan be decomposed into radial force passing through the center of the sphereAnd a tangential force perpendicular to the direction connecting the center of the sphere and the distribution pointBased on radial force of all uniformly distributed pointsModulo T of vector sum₁And tangential force of all uniformly distributed pointsModulo T of vector sum₂The smaller the distribution uniformity of the whole-surface micro pit structure of the thin-wall spherical shell type micro component is, the better the distribution uniformity is, and the specific formula is as follows:

in the above formulaRepresenting the radial component of the force received by the ith point along the thin-wall spherical shell type micro component;representing the component of the force experienced at the ith point along the tangent of a thin-walled spherical shell-like micro-member.

Under the action of tangential force, the spherical point set continuously moves and the moving speed is continuously changed, and a new point set is gradually formed. Comprises the following steps:

wherein the content of the first and second substances,for the speed of all the sets of points in the micro-pit set in the j-1 th iteration,coordinates of all point sets in the micro-pit point set in the j-1 iteration are shown, and G is an influence factor of tangential force on speed and can be self-drawn up according to the iteration condition. The coordinates of the track initial point set are initialized to zero, the initial iteration speed is initialized to 0, and the method comprises the following steps:

continuously carrying out optimization iteration according to the steps until iteration reaches balance, and T is when the iteration reaches balance₁And T₂And when the value is reduced to a smaller value, the uniformity of the distribution of the spherical point set can be realized. The pseudo code of the sphere point set equipartition iterative algorithm is shown below.

And (3) further performing iterative optimization on the point coordinates of the micro-pit structure generated by the Fibonacci principle through the iteration of a spherical point set uniform distribution iterative algorithm to generate a uniform distribution point set of the micro-pit structure on the surface of the thin-wall spherical shell type micro component, wherein the iteration time is only 62 seconds. In order to further visually represent the distribution situation of the point set, the point set is divided into space tetrahedrons by adopting a triangulation function Delaunay Tri, and further, the tetrahedral convex hulls are calculated by utilizing a convex hull algorithm and a polyhedron is drawn. The N uniform spot sets are distributed as shown in fig. 3, where the number N of dimple structures is taken to be 60 and the radius is taken to be 2.

And carrying out error analysis on the generated uniform point set distribution. Tens to hundreds of micro-pit structures are uniformly distributed on the whole surface of the thin-wall spherical shell type micro component, the error of pit point spacing is required to be better than 40 mu m, and the error of the current common longitude and latitude grid weighting distribution method exceeds 0.1mm and cannot meet the processing requirement. In the embodiment of the invention, after the spherical surface N-60 micro pits are divided based on the Fibonacci principle, the pitch error of the pits can be reduced to 63 μm, the error is reduced by 40%, and the uniformity of the spherical point set is improved; further, after optimization by the iterative algorithm of spherical point set uniform distribution, the characterization parameter T of the distribution uniformity of the spherical point set₁And T₂T from uniformly distributed relatively uniform point sets generated based on Fibonacci₁＝4.25N，T₂4.36N to T after optimization of spherical point uniform distribution iterative algorithm₁＝7.66x10^-5N，T₂＝9.16x10^-4N, the pit pitch error sigma is better than 36 μm, the processing requirement of fluid mechanics stability is met, and the distribution uniformity of the spherical point set reaches the optimum.

Step three, selecting processing initial points in a micro-pit structure uniform distribution point set, and generating a processing track of the micro-pit structure uniformly distributed on the surface of the thin-wall spherical shell type micro component based on the shortest processing path principle; wherein, all points on the processing track are distributed points with uniformly distributed points and concentration in a micro-pit structure;

and performing secondary development design on the drilling machining process by utilizing the secondary development function of UG software. UG software has super-strong programming capability, is widely applied to the fields of mechanical parts, mold design and the like, and has the main processing functions of surface milling, cavity milling, drilling and the like. From the CAM module, the drilling function is called out by setting. The method comprises the following specific operations: installing a template _ set folder of a resource folder in a MACH (processing) folder of a directory in UG software, finding a cam _ general.opt file, and calling out a drilling (drill) process; and creating a drilling process of the pit microstructure, and realizing the planning of the micro-pit processing sequence by the 'optimization' function in the hole options specified by the drilling process. Aiming at the processing technological requirements of the global surface micro-pits of the thin-wall spherical shell, a micro-pit point set positioned on the side hemisphere surface of the cutter is selected for path planning. The method comprises the steps of creating a ball end mill with the diameter of 0.1mm, setting a minimum safety distance to prevent the problem of tool collision in the machining process from affecting the surface quality, and selecting the axis direction of the mill to be perpendicular to the surface of the thin-wall spherical shell to ensure that a tool in a track is perpendicular to the surface to be machined.

Taking the example of selecting 17 pit microstructures, namely N is 17 pit microstructures, which are uniformly distributed on a machining side, introducing the coordinates of the pit microstructures into a secondary development program through a 'group' function, finishing the generation of the machining sequence and the machining track of the thin-wall spherical shell type micro-component through a 'shortest tool path' program instruction and 'generating the tool path', and observing the tool path through 'confirming the tool path'. The goto code of the tool path can be led out from the tool path listing, and is converted into a numerical control code executed by a machine tool after post-processing, so that the requirements on the distribution of the micro-pit structure on the surface of the thin-wall spherical shell micro-component, the processing path and the like are well met, the influence caused by fluid mechanics instability and the like in the processing process is effectively avoided, and the finally generated processing track of the micro-pit structure uniformly distributed on the whole surface of the thin-wall spherical shell micro-component is shown in fig. 4.

Based on the Fibonacci principle, the full-surface micro-pit structure of the thin-wall spherical shell type micro component is preliminarily uniformly divided, and compared with the weighted division of a longitude and latitude grid, the error is reduced by 40%, and the distribution uniformity of a point set is improved; providing a spherical point set uniform distribution iterative algorithm, further uniformly optimizing a distributed relatively uniform point set generated based on a Fibonacci principle, wherein the iterative time is only 62 seconds, and the pit pitch error is reduced from 63 mu m to 36 mu m, so that the error requirement of actual processing superior to 40 mu m is met, and the uniformity of the distribution of the micro-pit structure on the surface of the thin-wall spherical shell type micro component is further improved; by carrying out secondary development on commercial software UG and based on the principle of shortest processing path, the generated uniform micro-pit structure point set is subjected to creation of a processing sequence and optimization of the processing path, so that the processing efficiency is greatly improved, the influence problem caused by error accumulation is reduced, and the track scheme is optimal; the generated machining track of the uniformly distributed micro-pit structure well meets the requirements of the thin-wall spherical shell micro-component on the distribution of the surface micro-pit structure, the machining path and the like, and the influence of larger error caused by non-uniform distribution of the micro-pits on energy research is effectively solved. The invention has certain universality and can be popularized and used in the specific practice of uniformly distributing point sets on the surfaces of spheres with different sizes.

Another embodiment of the present invention provides a planning apparatus for processing tracks of a thin-walled spherical shell type micro component with uniformly distributed micro-pit structures on the surface, as shown in fig. 5, the apparatus includes:

the micro-pit structure generation module 110 is used for preliminarily generating a micro-pit structure point set which is distributed relatively uniformly on the whole surface of the thin-wall spherical shell type micro component based on the Fibonacci principle;

an iterative optimization module 120, configured to optimize distribution uniformity of the micro-pit structure point sets by using a spherical point set uniform distribution iterative algorithm, so as to generate micro-pit structure uniform distribution point sets;

the track generation module 130 is used for selecting a processing initial point in a centralized manner from the uniformly distributed points of the micro-pit structure and generating a processing track of the uniformly distributed micro-pit structure on the surface of the thin-wall spherical shell type micro-component based on the shortest processing path principle; all points on the processing track are distributed points with uniformly distributed points in a micro-pit structure.

The specific steps of generating the relatively uniformly distributed micro-pit structure point set in the micro-pit structure generation module 110 include:

establishing an X axis and a Y axis which are perpendicular to each other in a spherical surface equatorial plane by taking the spherical center of the thin-wall spherical shell type micro component as a coordinate origin to form an X-Y plane, determining a Z axis by a right-hand rule, and establishing a workpiece coordinate system; wherein, the X-Y plane is vertical to the moving direction of the milling cutter;

dividing the spherical surface of the thin-wall spherical shell type micro component into N layers with the same thickness based on the Fibonacci principle, wherein N represents the total number of distribution points in the micro-pit structure point set; the latitude spans of all layers in the N layers are different, the latitude spans of the south and north poles are maximum, one point is taken at the middle point of each layer thickness, and the Z-axis coordinate of the distribution point in the micro-pit structure point set is obtained:

z_n＝R*[(2n-1)/N-1]

wherein n represents a coordinate point serial number; r represents the sphere radius of the thin-wall spherical shell type micro component;

dividing the coordinates of an X axis and a Y axis according to the longitude in an arithmetic progression distribution manner, ensuring that the X axis and the Y axis are distributed relatively uniformly, and obtaining the coordinates of the X axis and the Y axis of the distributed points in the micro-pit structure point set:

wherein the content of the first and second substances,

the specific steps of optimizing the micro-pit structure point set in the iterative optimization module 120 to generate the micro-pit structure uniform distribution point set include:

step two, calculating the acting force between any two distribution points in the micro-pit structure point setThe force is proportional to the square of the distance between the two points;

step two, acting forceResolved into radial forces passing through the centre of the sphereAnd a tangential force perpendicular to the direction connecting the center of the sphere and the distribution pointCalculating and obtaining radial force of all distribution points in the micro-pit structure point set according to the following formulaModulo T of the vector sum of₁All distribution points tangential forceModulo T of the vector sum of₂：

Step two and step three, in the tangential forceUnder the action of the micro-pit structure point, continuously updating the coordinates of the distributed points in the micro-pit structure point set according to the following formula:

wherein G represents the influence factor of the tangential force on the speed;andrespectively representing the coordinates of the distribution points before and after updating;andrespectively representing the speed of the distribution point before moving and the speed of the distribution point after moving;

step two, the step two to the step two are executed in an iterative cycle mode until the distribution points in the micro-pit structure point set do not move any more, and the optimal distribution points are reached, and the coordinates of all the distribution points in the micro-pit structure uniform distribution point set are obtained; wherein, the judgment condition that the distribution points in the micro-pit structure point set do not move is the radial force of all the distribution pointsModulo T of the vector sum of₁And all distribution point tangential forcesModulo T of the vector sum of₂Down to a minimum value and no longer changing.

In the trajectory generation module 130, in the process of generating the processing trajectory, a triangulation function Delaunay Tri is used to divide a micro-pit structure point set or a micro-pit structure uniform distribution point set into a spatial tetrahedron, and a convex hull algorithm is used to calculate a spatial tetrahedron convex hull and draw a polyhedron to visually observe the distribution of the point set.

Further, the value range of the total number N of distributed points in the micro-pit structure point set is as follows: n is more than or equal to 50 and less than or equal to 100.

The function of the planning device for uniformly distributing machining tracks of the micro-pit structures on the surface of the thin-wall spherical shell micro-component in this embodiment can be described by the aforementioned planning method for uniformly distributing machining tracks of the micro-pit structures on the surface of the thin-wall spherical shell micro-component, so that the detailed part in this embodiment can be referred to the above method embodiment, and is not described herein again.

While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this description, will appreciate that other embodiments can be devised which do not depart from the scope of the invention as described herein. The present invention has been disclosed in an illustrative rather than a restrictive sense, and the scope of the present invention is defined by the appended claims.