CN110516388B - Harmonic mapping-based curved surface discrete point cloud model circular cutter path generation method - Google Patents

Harmonic mapping-based curved surface discrete point cloud model circular cutter path generation method Download PDF

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CN110516388B
CN110516388B CN201910819441.7A CN201910819441A CN110516388B CN 110516388 B CN110516388 B CN 110516388B CN 201910819441 A CN201910819441 A CN 201910819441A CN 110516388 B CN110516388 B CN 110516388B
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马建伟
姜文文
贾振元
王健
贺广智
王福吉
刘巍
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Dalian University of Technology
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Abstract

The invention discloses a harmonic mapping-based curved surface discrete point cloud model circular cutter path generation method, belongs to the technical field of free-form surface part precision machining, and relates to a harmonic mapping-based curved surface discrete point cloud model circular cutter path generation method. The method adopts a parameterized indirect subdivision method combined with a Delaunay algorithm to perform triangular mesh subdivision on a spatial discrete point cloud model. Based on a harmonic mapping method, the three-dimensional space grid is flattened to a two-dimensional plane by taking the minimum energy deformation as a constraint, and simultaneously, the deformation generated by each triangular patch in the harmonic mapping process is measured by adopting a mapping stretch coefficient. And generating an annular tool path on the two-dimensional plane obtained by conversion by calculating the vector and curvature of the triangular grid method and the feed step length and the line spacing. And finally, inversely mapping the tool path back to the three-dimensional space to generate a processing track. The method generates the circular cutter path of the curved surface discrete point cloud model by a harmonic mapping method, improves the processing quality and the processing efficiency, and is suitable for the precision processing of free-form surface parts.

Description

Harmonic mapping-based curved surface discrete point cloud model circular cutter path generation method
Technical Field
The invention belongs to the technical field of precision machining of free-form surface parts, and relates to a curved surface discrete point cloud model circular cutter path generation method based on harmonic mapping.
Background
With the rapid development of digital measurement technology, reverse engineering has been widely applied to numerical control machining of free-form surfaces. However, since the free-form surface type workpiece cannot be expressed by a specific parameter equation, generally has complex geometric characteristics, and cannot directly generate a tool path by a traditional numerical control modeling method, the realization of high-precision and high-efficiency tool path planning based on the discrete point cloud of the free-form surface is still a hotspot studied in computer aided manufacturing. The research on tool path planning of the free-form surface discrete point cloud mainly focuses on three aspects: firstly, a point cloud model is properly processed to directly generate a tool track, but the related geometric calculation is extremely complex; secondly, planning a tool path based on a reconstructed surface, wherein a point cloud is required to be subjected to a series of processing such as feature extraction, region blocking, surface fitting and cutting in the process of point cloud reconstruction of the surface, and a certain error exists between the reconstructed surface and the original point cloud; and thirdly, converting the point cloud model into a triangular mesh curved surface, and planning a tool path in a two-dimensional parameter domain through dimension reduction processing. Therefore, a method for generating a curved surface discrete point cloud model circular cutting tool path based on harmonic mapping is researched, stretching deformation generated in the harmonic mapping process is considered, a high-precision machining tool path is generated by free-form surface discrete point cloud data, and the precision machining of free-form surface workpieces is realized.
Von willebrand et al patent 'mesh free-form surface annular cutter path planning method based on improved Butterfly subdivision', patent publication No. CN 105739432B. According to the method, a circular cutting machining model of a triangular mesh free-form surface is constructed, a model boundary is used as an initial tool path and is biased inwards to form a spiral tool path, and the method still needs to perform intersection calculation on a biased space tool path. Technical literature "Iso-parametric tool-path planning for point clouds", zuo Qiang et al, Computer-aid Design, 2013, 45 (11): 1459-1468 which employs a conformal mapping based mesh parameterization method, however, the tool path generated by this method has conformal distortion.
Disclosure of Invention
Aiming at the defects of the prior art, the invention discloses a curved surface discrete point cloud model circular cutter path generation method based on harmonic mapping. The method comprises the steps of firstly, carrying out triangular mesh subdivision on a space point cloud model by adopting a parameterized indirect subdivision method and combining a Delaunay algorithm, and reducing the dimension of a processing curved surface to a two-dimensional plane by a harmonic mapping method to realize the mapping of boundary vertexes and internal vertexes of a space mesh and a parameter domain mesh. And then planning a processing track in the parameter domain, and finally inversely mapping the processing track to a three-dimensional space to generate a numerical control processing tool path of the free-form surface. The dimension reduction processing method avoids complex intersection calculation in a three-dimensional space, greatly improves the calculation efficiency, introduces the mapping stretch coefficient analysis and deformation in mapping, reduces distortion in the mesh parameterization process, realizes high-precision tool path planning of a free-form surface, and improves the processing quality and the processing efficiency.
The technical scheme adopted by the invention is a curved surface discrete point cloud model circular cutting tool path generation method based on harmonic mapping, and the method is characterized in that firstly, a parameterized indirect dissection method is adopted to combine with a Delaunay algorithm to carry out triangular mesh dissection on a space point cloud model, and the topological relation of the triangular mesh is reconstructed; adopting a harmonic mapping parameterization method to perform dimensionality reduction processing on the three-dimensional grid, and introducing a mapping stretch coefficient to analyze mapping deformation; calculating normal vectors and curvatures of any point in the grid unit in the parameter domain, calculating a feed step length and a line spacing, and generating a tool path in the parameter domain; finally, inversely mapping the tool path in the parameter domain back to the three-dimensional space to generate a processing tool path; the method comprises the following specific steps:
step 1, free-form surface discrete point cloud model triangular mesh subdivision
Performing triangulation on the space point cloud model by adopting a parameterized indirect subdivision method and a Delaunay algorithm; the process is as follows: firstly, parameterizing a three-dimensional space point cloud into a two-dimensional plane domain, and performing Delaunay triangulation with boundary constraint on the parameterized point cloud; then, constructing a topological connection relation among parameterized point sets in a plane domain, and carrying out boundary extraction and sequencing processing on the topological connection relation; finally, mapping the plane triangular mesh back to the three-dimensional space according to the topological relation, thereby obtaining a triangular mesh generation result of the three-dimensional space point cloud;
the process relates to the construction of topological relation among parameterized point clouds and a point cloud boundary extraction and ordering algorithm:
1) parameterized point cloud topological relation construction
Firstly, preliminarily establishing a triangular topological relation of a triangular mesh model, sequentially reading mesh vertex index numbers based on the preliminarily established triangular topological relation, and storing the mesh vertex index numbers in a new mesh vertex array; then, searching all triangular grid units containing the vertex by using the preliminarily established topological relation, and sequentially finding and storing the triangular grid units in a grid index number array corresponding to the vertex; because the vertex storage is random, the appearance sequence is random in the process of searching the triangular mesh unit containing the vertex; carrying out right-hand rule processing on the newly established topological relation between the vertex and the neighborhood triangle number to enable the vertex neighborhood triangle number to be arranged in a counterclockwise way;
2) point cloud boundary extraction and sorting algorithm
In the circular cutting process, a longest boundary is usually selected as an initial tool path, and then a final processing track is generated in an iteration mode, so that the boundary extraction needs to be carried out on a curved surface discrete point cloud model; for the triangular mesh model of the parametric point cloud in the plane domain, if a certain edge only belongs to one triangular plate, the edge is called as a boundary edge; if a certain edge belongs to two triangular plates, the edge is called an inner edge; a closed space polygon formed by connecting boundary edges end to end is called a boundary; finding out all boundary edges in the triangular mesh model according to the definition of the boundary edges; in the algorithm implementation, as the initially obtained edge set is unordered, the edge set needs to be ordered and organized to form an end-to-end complete boundary; the process is as follows:
firstly, initializing a parameterized triangular mesh model boundary set array { edges }, and setting used attributes as false; then, traversing the edge set of the triangular mesh, wherein the TRICount is the quantity attribute of the triangle where the edge is located, and finding an arbitrary edge with a TRICount attribute value of 1, namely an arbitrary boundary edge; two end points of the edge are respectively used as a previous point and a current point of the polygon boundary, a subsequent point is searched through the current point, and the cycle process is as follows:
firstly, traversing all adjacent triangles of a current point, and finding an edge meeting the following conditions:
satisfying the condition of 1 in the adjacent triangle; the used attribute value is false; the edge formed by the previous point and the current point has only 1 intersection point;
setting one end of the edge which is not coincident with the current point as a subsequent point, resetting the previous point and the current point, enabling the previous point to the current point and the current point to the subsequent point, and setting the used attribute of the edge as true. If closed, the step III is carried out, otherwise, the step I is carried out;
saving and outputting the boundary set of the tracking result, and ending the process;
step 2, reducing the dimension of the spatial triangular mesh based on harmonic mapping
The key of the harmonic mapping method is to find an energy equation called an objective function, give the boundary condition of the objective function, and then solve the extreme value of the objective function to obtain a parameterization. The process is as follows: finding the boundary point of a given model to be processed, and mapping the boundary point to a predetermined boundary of a planar domain according to a certain rule; for non-boundary points, in order to ensure that the deformation energy generated after model mapping is minimum, the elastic potential energy of the mapped grid needs to be ensured to be minimum, so that the mapping problem is converted into the problem of solving the energy minimum. The process involves spatial triangular mesh model boundary vertex mapping and interior vertex mapping.
1) Boundary vertex mapping
Let the triangular mesh TM of the space curved surface have k boundary vertices, BV ═ v i1,2,3, k), each vertex being ordered in its adjacency. Defining by way of example to a planar unit circle field parameter
V＝{v1,v2,...,vmIs the set of all vertices, m is the number of all vertices, T ═ T1,t2,...,tnThe triangle is a set of all triangles, and n is the number of all triangles; let TM (T, V) map to plane PlOne circular domain of (x-x)0)2+(y-y0)2+(z-z0)2On 1, determining the corresponding position of the boundary point of the mesh curved surface on the plane circular domain by adopting an accumulative chord length method, and enabling the ith side boundary edge L of the ViTwo vertexes of viAnd vi+1Then, in the mapped triangle vertex set V, its corresponding two vertices
Figure BDA0002187121500000051
Central angle formed by the central point o of the plane circle
Figure BDA0002187121500000052
It should satisfy:
Figure BDA0002187121500000053
wherein, | LiL represents the edge LiLength of (d).
2) Internal vertex mapping
Let the mapping relation be xi, xi (v)i)＝(xi,yi,zi)TWhere ξ (v)i) (i ═ 1,2, 3.. times, k) is the result of mapping the boundary vertices to the planar circular domain, and the curved surface mesh harmonically maps the elastic potential energy E (ξ) as:
Figure BDA0002187121500000054
in the formula, Ki,jIs a vertex vi、vjFormed edge Li,jThe elastic coefficient of (a). Let limit Li,jIs 2 triangles
Figure BDA0002187121500000055
And
Figure BDA0002187121500000056
and if the two are shared, then:
Figure BDA0002187121500000057
in the formula (I), the compound is shown in the specification,
Figure BDA0002187121500000058
is triangular
Figure BDA0002187121500000059
Area of (L)i,jRepresenting a vertex vi、vjThe side formed by the method is analogized.
ξ(vi) (i ═ 1,2, 3.. times, m) is the result of the mapping of all vertices of the triangular mesh of the spatial surface to the planar circular domain, ξ (v) ("v")i) (i ═ 1,2, 3.., m) in plane PlAx + by + cZ + d is 0, and c is not equal to 0, and xi (v)i)＝(xi,yi,zi)T，ξ(vj)＝(xj,yj,zj)TThen there is zi＝-(axi+byi+d)/c，zj＝-(axj+byj+ d)/c, the energy equation (2) is transformed into the following form:
Figure BDA0002187121500000061
namely:
Figure BDA0002187121500000062
in order to minimize the deformation of the topology of the curved surface triangular mesh TM when mapping onto the planar circular domain, the energy equation (5) should be satisfied as follows:
Figure BDA0002187121500000063
wherein k is the number of boundary vertices of the triangular mesh TM of the space curved surface, and m is the number of all vertices;
let N (v)i) Is and vertex viSet of adjacent vertices, and vj∈N(vi). And (3) solving the partial derivative of each internal vertex in the formula (5) to obtain a linear equation system:
Figure BDA0002187121500000064
writing the formula (7) in a matrix form to obtain an equation system with the size of 2(n-k) x 2(n-k) and the coefficient of the linear coefficient matrix A:
AX＝B (8)
wherein:
Figure BDA0002187121500000071
and solving a sparse positive definite linear equation set (9) by using an ultra-relaxation iterative method to obtain corresponding coordinates of the space curved surface triangular mesh internal points mapped to the plane parameter domain.
In the process of blending and mapping parameterization of the triangular mesh of the space curved surface, considerable stretching deformation exists, and the stretching deformation generated by mapping the parameter mesh to the three-dimensional mesh must be considered for accurate track planning on the planar parameter mesh. The mesh surface parameterization has the characteristic of piecewise linearity, namely, the parameterization result xi of the space mesh surface is continuous and linear for each triangular plate, and a unique affine transformation relation exists between each pair of space triangular plates and the triangular plates in the parameter domain, so that the gradient and the mapping tension coefficient in each triangular plate are constant;
tensile measurement L2(T*) Representing the root mean square of stretching deformation in all directions in the triangular plate, estimating a mapping stretching coefficient sigma approximate to isotropy by adopting a stretching metric, and giving three vertexes v of the triangular plate T in a given spacei、vj、vkAnd its corresponding parameter domain triangle T*Three vertices of
Figure BDA0002187121500000072
The gradient within this triangle patch is then:
Figure BDA0002187121500000073
wherein S is parameter domain triangle T*The area of (a).
S＝((u1-u0)(v2-v0)-(u2-u0)(v1-v0))/2 (11)
Jacobian matrix [ xiu,ξv]The maximum and minimum singular values of (a) are respectively:
Figure BDA0002187121500000081
in which the coefficient a1，a2，a3Comprises the following steps:
Figure BDA0002187121500000082
the triangle-mapped stretch coefficient σ can be expressed as:
Figure BDA0002187121500000083
given parameter domain triangular plate T*Inner initial track point e*According to the space triangle T and the parameter domain triangle T*The affine transformation relationship between the points is that the corresponding track point e in T is obtained by using an area coordinate or a quadratic weighting method, at the moment, the track parameter at the point e needs to be calculated and converted into the point e according to a mapping stretching coefficient sigma*Point, and point;
step 3, inverse mapping of harmonic mapping
The inverse mapping of the harmonic mapping realizes the ascending dimension of the tool path, and the tool path for processing the space grid curved surface is generated; let the plane field PlContact point e of Zhongzhi knife*The triangular plate is
Figure BDA0002187121500000084
The triangular plate corresponds to T { v } in the mesh curved surface TMi,vj,vkAnd obtaining a corresponding space knife contact e according to the principle that the topological structure of the grid triangular plate is not changed before and after mapping. Establishing an affine frame, and taking (alpha, beta) as a point e*In an affine coordinate system
Figure BDA0002187121500000085
And (3) calculating the coordinate of e by adopting a quadratic linear weighting method according to the following parameter coordinates:
e＝vi+α(vj-vi)+β(vk-vi) (15)
step 4, free-form surface discrete point cloud model circular cutting tool path planning
1) Normal vector and curvature calculation for triangular meshes
To facilitate subsequent tool path planning, the computational vector and curvature analyze the geometric characteristics of the tool contact points on the spatial triangular grid. Applying least square surface local fitting method to grid unit vertex normal vector and principal curvature k1、k2And a corresponding main direction d1、d2Making an estimate of k1Is the maximum principal curvature, k2Is the minimum principal curvature. And then, calculating the normal curvature of the grid unit vertex along any direction d according to an Euler formula, wherein the calculation expression is as follows:
k(d)＝k1·cos2θ+k2·sin2θ (16)
in the formula, θ represents an arbitrary direction d and a principal direction d1The included angle therebetween.
Calculating the normal vector and the curvature of the knife contact point by adopting a quadratic linear weighting method and by judging the position of the knife contact point in the grid unit and combining the normal vector and the curvature information of the vertex of the grid unit;
v1、v2and v3Three vertexes of the space triangular mesh unit are respectively arranged,
Figure BDA0002187121500000091
the normal vector of any knife contact e in the grid cell is the corresponding unit normal vector
Figure BDA0002187121500000092
Expressed as:
Figure BDA0002187121500000093
wherein (u, v) represents e in an affine coordinate system
Figure BDA0002187121500000094
The parameter coordinates of (a). When e is located on the triangle patch edge, equation (17) degenerates to a linear interpolation equation. Similarly, the normal curvature of the knife contact point positioned in the triangular grid unit along any direction is calculated by the method;
2) calculation of circular cutting tool path parameters
And calculating the tool path parameters, including the calculation of the feed step length and the feed line distance. Planning the feed step length by using a step length screening method; order to
Figure BDA0002187121500000095
The method is characterized in that dense points are formed by discretizing processing cutter contact points through parameters such as B spline curve fitting and the like, and epsilon represents a known approximation error;
given a starting point
Figure BDA0002187121500000096
Then at point
Figure BDA0002187121500000097
Then selecting a point in order
Figure BDA0002187121500000098
Then it is ready to
Figure BDA0002187121500000099
And
Figure BDA00021871215000000910
each point P in betweeni(i＝m1+1,...,m2-1) computing it to line segment
Figure BDA00021871215000000911
The distance of (c):
Figure BDA00021871215000000912
if it is in accordance with di<ε(i＝m1+1,...,m2-1) that is
Figure BDA0002187121500000101
And
Figure BDA0002187121500000102
the approximation error of the curve where the line segment formed by two points approximates is less than a given value, and the curve segment is sequentially picked up
Figure BDA0002187121500000103
The next point of (1), i.e. order m2＝m2+1, repeat the above steps until there is a point P if anyi(i∈m1+1,...,m2-1) to the straight line segment
Figure BDA0002187121500000104
Is in accordance with di>Epsilon. At this time
Figure BDA0002187121500000105
And
Figure BDA0002187121500000106
the line segment formed by the two points is the longest line segment which meets the approaching precision condition. Retention
Figure BDA0002187121500000107
Click on and delete
Figure BDA0002187121500000108
And
Figure BDA0002187121500000109
all points in between. For the whole curve, points must be added
Figure BDA00021871215000001010
As a new starting point and repeat the above steps.
The cutting path CL is calculated by equation (19):
Figure BDA00021871215000001011
in the formula, RtRadius of ball head cutter, h is residual height, RbThe curvature radius is, the positive sign is taken when the model is a convex curved surface, and the negative sign is taken when the model is a concave curved surface.
Introducing mapping stretching coefficient sigma, and calculating the track spacing CL at the knife contact point corresponding to the mapping domain*，
Figure BDA00021871215000001012
3) Generation of circular cutting path in space and parameter domain
The generation method of the circular cutting tool track in the space and parameter domain is explained by combining the calculation method of the circular cutting tool track parameters:
the extracted space triangular mesh model boundary is fitted by adopting a cubic non-uniform B spline, namely:
Figure BDA00021871215000001013
in the formula, DiAs a control point, Ni,3(t) is a cubic B-spline basis function.
And dispersing the boundary curve according to certain precision, mapping the knife contact on the first knife track determined by adopting a step length screening method to the parameter domain according to a harmonic mapping rule, and obtaining the knife contact of the first knife track of the parameter domain. And updating the tool path as the previous tool path.
② calculating the previous tool path n1The line spacing CL of the offset of each knife contact on the space grid curved surface corresponds to the theoretical offset line spacing CL of the knife contacts in the mapping domain*Taking the minimum value of line spacing
Figure BDA0002187121500000111
And normally offsetting the actual line space along the previous tool path in the mapping domain to obtain the current tool path.
And thirdly, inversely mapping the current tool path of the mapping domain to the space grid curved surface based on the harmonic mapping inverse mapping method in the step 3 to obtain the next tool path tool contact of the space grid curved surface. Judgment of
Figure BDA0002187121500000112
If the result is 1, go to (r), and if the result is 0, go to (r).
Fourthly, the iteration of the tool path is finished, and the contact track of the circular cutting processing tool in the space and parameter domain is generated.
The obtained space grid curved surface processing cutter contact cannot be directly used for processing, and the conversion from the processing cutter contact to the processing cutter point and the connection between the track points need to be completed so as to be used for processing. In numerical control machining, a tool nose point is often used as a tool location point, and a conversion relation between a machining tool contact and the machining tool location point is as follows:
Figure BDA0002187121500000113
in the formula, wmIs a group of spatial tool positions emIs a group of contact points of the space knife,
Figure BDA0002187121500000114
is the normal vector of the contact point of the knife,
Figure BDA0002187121500000115
in the direction of the knife axis, RtIs the tool radius.
The method has the advantages that the method aims at solving the problems of complex point cloud tool path planning algorithm and low processing precision in the actual processing process of the free-form surface part, triangular gridding is carried out on the curved surface discrete point cloud model, the complex space tool path planning problem is converted into the two-dimensional plane tool path planning problem through a harmonic mapping method, mapping deformation is reduced as much as possible, and finally the processing tool path of the free-form surface part is generated through inverse mapping of the harmonic mapping, so that the processing quality and the processing efficiency are improved. The dimension reduction processing method avoids complex intersection calculation in a three-dimensional space, greatly improves the calculation efficiency, introduces the mapping stretch coefficient analysis and deformation in mapping, reduces distortion in the mesh parameterization process, realizes high-precision tool path planning of a free-form surface, and improves the processing quality and the processing efficiency.
Drawings
FIG. 1-flowchart of the overall process.
FIG. 2-harmonic mapping stretch distortion plot; wherein, { o; xyz is a rectangular coordinate system of space, { o; ou, ov } is parameter domain coordinate system, T is space triangular patch, T*The triangular patch of the parameter domain is corresponding to the triangular patch of the space triangular patch after harmonic mapping, and xi is the harmonic mapping relation between the triangular mesh of the space triangular patch and the triangular mesh of the parameter domain.
Fig. 3-surface roughness of parts machined with tool path planned by the method.
Fig. 4-surface of a part machined by the method.
FIG. 5 shows the surface roughness of a part machined by a tool path planning method after point cloud reconstruction.
Fig. 6-part surface processed with point cloud reconstruction method.
Detailed Description
The detailed description of the embodiments of the invention is provided with reference to the accompanying drawings.
Aiming at the problems of complex point cloud tool path planning algorithm and low processing precision in the actual processing process of free-form surface parts, the invention provides a curved surface discrete point cloud model circular cutting tool path generation method based on harmonic mapping, and the whole process is shown in the attached figure 1.
The implementation process of the present invention is described in detail by taking a curved surface discrete point cloud model with a bounding box size of 40 × 40 × 3mm as an example.
Firstly, in step 1, a parameterized indirect subdivision method is adopted to combine with a mature Delaunay algorithm to carry out triangulation on a discrete point cloud model of a space curved surface, and the triangulation comprises 3452 triangular plates and 2093 vertexes. And constructing a topological connection relation among the point sets, expressing by using a point table and a triangle adjacency table to improve the vertex neighborhood triangle information searching capability, and extracting and sequencing the boundary of the triangular mesh.
And 2, mapping the boundary vertex and the internal vertex of the space triangular mesh model based on a harmonic mapping method, introducing a deformation amount generated in a mapping and stretching coefficient analysis mapping process, flattening the three-dimensional space mesh to a two-dimensional plane, and generating a harmonic mapping and stretching deformation diagram as shown in the attached figure 2.
From step 4, estimating the normal vector of the grid cell vertex
Figure BDA0002187121500000131
Principal curvature k1、k2And a corresponding main direction d1、d2And calculating the normal curvature of the grid cell vertex along any direction d according to the Euler formula. And calculating the normal vector and the curvature of the cutter contact point by combining the normal vector and the curvature information of the vertex of the grid unit, and planning the cutter path in the parameter domain by a calculation method of the girdling processing feed step length feed line distance. And 3, mapping the tool path in the parameter domain back to the three-dimensional space based on the inverse mapping method of harmonic mapping in the step 3, completing the conversion from the machining tool contact to the machining tool position point and the connection between the track points, and finally generating the machining path of the three-dimensional space curved surface discrete point cloud model.
The method is used for planning the tool path of the free-form surface discrete point cloud model, compared with the method for planning the tool path after point cloud reconstruction, and the processing time and the surface roughness are used as the judgment standards for the quality of processing. The experimental processing equipment is a Mikron HSM500 high-speed milling center, a ball end milling cutter with phi 4 is selected for processing experiments, the rotating speed of a main shaft is set to be 5000r/min, the feeding speed is 250mm/min, and the size of the residual height is 20 micrometers.
The roughness of the machined surface is measured by utilizing a Talyrnd Hobson roughness profiler, a measuring instrument clamp is fixed in the measuring process, and the roughness of the same position of the machined surface is ensured to be measured by adjusting the position of a probe every time. Each set was measured 3 times and averaged, with one set of measurements shown in figure 3. The surface roughness Ra of the part machined by the tool path planned by the method is 0.9459 mu m, the machining time is 11min42s, and the machining surface is shown in a figure 4; as shown in fig. 5, the surface roughness Ra of the part machined by the method of planning the tool path after point cloud reconstruction is 1.2637 μm, the machining time is 13min54s, and the machined surface is shown in fig. 6. Compared with a point cloud reconstruction method, the tool path processing planned by the method has the advantages that the processing surface roughness is reduced by 25.15%, and the time required by the processing process is shortened by 15.66%. It can be obviously seen that when a complex pattern with variable curvature is processed, the circular cutting processing track planned by the point cloud reconstruction method has a sharp corner, and a high-quality circular cutting processing track with consistent boundary and smooth and continuous track can be generated by using the method, and the processing efficiency is obviously improved.

Claims (1)

1. A curved surface discrete point cloud model circular cutting tool path generation method based on harmonic mapping is characterized in that firstly, a parameterized indirect subdivision method is adopted to combine with a Delaunay algorithm to carry out triangular mesh subdivision on a space point cloud model, and the topological relation of a triangular mesh is reconstructed; adopting a harmonic mapping parameterization method to perform dimensionality reduction processing on the three-dimensional grid, and introducing a mapping stretch coefficient to analyze mapping deformation; calculating normal vectors and curvatures of any point in the grid unit in the parameter domain, calculating a feed step length and a line spacing, and generating a tool path in the parameter domain; finally, inversely mapping the tool path in the parameter domain back to the three-dimensional space to generate a processing tool path; the method comprises the following specific steps:
step 1, free-form surface discrete point cloud model triangular mesh subdivision
Performing triangulation on the space point cloud model by adopting a parameterized indirect subdivision method and a Delaunay algorithm; the process is as follows: firstly, parameterizing a three-dimensional space point cloud into a two-dimensional plane domain, and performing Delaunay triangulation with boundary constraint on the parameterized point cloud; then, constructing a topological connection relation among parameterized point sets in a plane domain, and carrying out boundary extraction and sequencing processing on the topological connection relation; finally, mapping the plane triangular mesh back to the three-dimensional space according to the topological relation so as to obtain a triangular mesh generation result of the three-dimensional space point cloud;
the process relates to the construction of topological relation among parameterized point clouds and a point cloud boundary extraction and ordering algorithm;
1) parameterized point cloud topological relation construction
Firstly, preliminarily establishing a triangular topological relation of a triangular mesh model; based on the preliminarily established triangular topological relation, sequentially reading the grid vertex index numbers, storing the grid vertex index numbers in a new grid vertex array, searching all triangular grid units containing the vertices by using the preliminarily established topological relation, and sequentially finding and storing the triangular grid units in the grid index number array corresponding to the vertices; because the vertex storage is random, the appearance sequence is random in the process of searching the triangular mesh unit containing the vertex; carrying out right-hand rule processing on the newly established topological relation between the vertex and the neighborhood triangle number to enable the vertex neighborhood triangle number to be arranged in a counterclockwise way;
2) point cloud boundary extraction and ordering
In the circular cutting process, a longest boundary is usually selected as an initial tool path and then iteration is carried out to generate a final processing track, so that boundary extraction needs to be carried out on a curved surface discrete point cloud model; for the triangular mesh model of the parametric point cloud in the plane domain, if a certain edge only belongs to one triangular plate, the edge is called as a boundary edge; if a certain edge belongs to two triangular plates, the edge is called an inner edge; a closed space polygon formed by connecting boundary edges end to end is called a boundary; finding out all boundary edges in the triangular mesh model according to the definition of the boundary edges, and in the algorithm implementation, because the initially obtained edge set is disordered, sequencing and organizing are carried out to form a complete boundary which is connected end to end; the process is as follows:
firstly, initializing a parameterized triangular mesh model boundary set array { edges }, and setting used attributes as false;
then, traversing the edge set of the triangular mesh, wherein the TriCount is the quantity attribute of the triangle where the edge is located, finding an arbitrary edge with a TriCount attribute value of 1, namely an arbitrary boundary edge, two end points of the edge are respectively used as a previous point and a current point of a polygon boundary, searching a subsequent point through the current point, and the cycle process is as follows:
firstly, traversing all adjacent triangles of a current point, and finding an edge meeting the following conditions:
satisfying the condition of 1 in the adjacent triangle; the used attribute value is false; the edge formed by the previous point and the current point has only 1 intersection point;
setting one end of the edge which is not overlapped with the current point as a subsequent point, resetting the previous point and the current point, enabling the previous point to the current point and the current point to the subsequent point, and setting the used attribute of the edge as true; if closed, the step III is carried out, otherwise, the step I is carried out;
saving and outputting the boundary set of the tracking result, and ending the process;
step 2, reducing the dimension of the spatial triangular mesh based on harmonic mapping
The key of the harmonic mapping method is to find an energy equation called an objective function, give a boundary condition of the objective function, and then solve an extreme value of the objective function to obtain a parameterization; the process is as follows: finding the boundary point of a given model to be processed, and mapping the boundary point to a predetermined boundary of a planar domain according to a certain rule; for non-boundary points, in order to ensure that the deformation energy generated after model mapping is minimum, the elastic potential energy of the mapped grid is required to be minimum, so that the mapping problem is converted into the problem of solving the energy minimum; the process involves spatial triangular mesh model boundary vertex mapping and interior vertex mapping;
1) boundary vertex mapping
Let the triangular mesh TM of the space curved surface have k boundary vertices, BV ═ vi1,2,3, k, with the vertices in their adjacent relationship; using the parameter to the plane unit circle domain as an example, define V ═ V1,v2,...,vmIs the set of all vertices, m is the number of all vertices, T ═ T1,t2,...,tnThe triangle is a set of all triangles, and n is the number of all triangles; let TM (T, V) map to plane PlOne circular domain of (x-x)0)2+(y-y0)2+(z-z0)2On 1, determining the corresponding position of the boundary point of the mesh curved surface on the plane circular domain by adopting an accumulative chord length method, and enabling the ith side boundary edge L of the ViTwo vertexes of viAnd vi+1Then the set of triangle vertices V after mapping*Wherein its corresponding two vertices
Figure FDA0002769388670000031
Central angle formed by the central point o of the plane circle
Figure FDA0002769388670000032
It should satisfy:
Figure FDA0002769388670000033
wherein, | LiL represents the edge LiLength of (d);
2) internal vertex mapping
Let the mapping relation be xi, xi (v)i)＝(xi,yi,zi)TWhere ξ (v)i) I 1,2, 3.. k, which is the result of mapping the boundary vertex to the plane circle domain, the curved surface mesh is harmonically mapped to the elastic potential energy E (ξ) and is expressed as:
Figure FDA0002769388670000034
in the formula, Ki,jIs a vertex vi、vjFormed edge Li,jThe elastic coefficient of (a); let limit Li,jIs 2 triangles
Figure FDA0002769388670000041
And
Figure FDA0002769388670000042
and if the two are shared, then:
Figure FDA0002769388670000043
in the formula (I), the compound is shown in the specification,
Figure FDA0002769388670000044
is triangular
Figure FDA0002769388670000045
Area of (L)i,jRepresenting a vertex vi、vjThe formed edges are analogized in the same way;
ξ(vi) Is the result of mapping all the vertexes of the triangular mesh of the spatial curved surface to the circular domain of the plane, wherein i is 1,2,3i) Are all in the plane PlAx + by + cZ + d is 0, and c is not equal to 0, and xi (v)i)＝(xi,yi,zi)T，ξ(vj)＝(xj,yj,zj)TThen there is zi＝-(axi+byi+d)/c，zj＝-(axj+byj+ d)/c, the energy equation (2) is transformed into the following form:
Figure FDA0002769388670000046
namely:
Figure FDA0002769388670000047
in order to minimize the deformation of the topology of the curved surface triangular mesh TM when mapping onto the planar circular domain, the energy equation (5) should be satisfied as follows:
Figure FDA0002769388670000048
wherein k is the number of boundary vertices of the triangular mesh TM of the space curved surface, and m is the number of all vertices;
let N (v)i) Is and vertex viSet of adjacent vertices, and vj∈N(vi) (ii) a For each inner roof in the formula (5)And (3) point derivation to obtain a linear equation set:
Figure FDA0002769388670000051
writing the formula (7) in a matrix form to obtain an equation system with the size of 2(n-k) x 2(n-k) and the coefficient of the linear coefficient matrix A:
AX＝B (8)
wherein:
Figure FDA0002769388670000052
solving a sparse positive definite linear equation set (9) by using an ultra-relaxation iterative method to obtain corresponding coordinates of the space curved surface triangular mesh internal points mapped to the plane parameter domain;
the method comprises the following steps that a non-negligible stretching deformation exists in the process of harmonizing and mapping parameterization of a spatial curved surface triangular mesh, and the stretching deformation generated by mapping a parameter mesh to a three-dimensional mesh must be considered when accurate track planning is carried out on a plane parameter mesh; the mesh surface parameterization has the characteristic of piecewise linearity, namely, the parameterization result xi of the space mesh surface is continuous and linear for each triangular plate, and a unique affine transformation relation exists between each pair of space triangular plates and the triangular plates in the parameter domain, so that the gradient and the mapping tension coefficient in each triangular plate are constant;
tensile measurement L2(T*) Representing the root mean square of stretching deformation in all directions in the triangular plate, estimating a mapping stretching coefficient sigma approximate to isotropy by adopting a stretching metric, and giving three vertexes v of the triangular plate T in a given spacei、vj、vkAnd its corresponding parameter domain triangle T*Three vertices of
Figure FDA0002769388670000061
The gradient within this triangle patch is then:
Figure FDA0002769388670000062
wherein S is parameter domain triangle T*The area of (d);
S＝((u1-u0)(v2-v0)-(u2-u0)(v1-v0))/2 (11)
jacobian matrix [ xiu,ξv]The maximum and minimum singular values of (a) are respectively:
Figure FDA0002769388670000063
in which the coefficient a1，a2，a3Comprises the following steps:
Figure FDA0002769388670000064
the triangular-patch-mapped stretch coefficient σ is then expressed as:
Figure FDA0002769388670000065
given parameter domain triangular plate T*Inner initial track point e*Can be based on the space triangle T and the parameter domain triangle T*The affine transformation relationship between the points is that the corresponding track point e in T is obtained by using an area coordinate or a quadratic weighting method, the track parameter at the point e needs to be calculated and converted into the point e according to a mapping stretching coefficient sigma*Point, and point;
step 3, inverse mapping of harmonic mapping
The inverse mapping of the harmonic mapping realizes the ascending dimension of the tool path, and the tool path for processing the space grid curved surface is generated; let the plane field PlContact point e of Zhongzhi knife*The triangular plate is
Figure FDA0002769388670000071
The triangular plate corresponds to T { v } in the mesh curved surface TMi,vj,vkObtaining a corresponding space knife contact e according to the principle that the topological structures of the grid triangular plates before and after mapping are not changed; establishing an affine frame, and taking (alpha, beta) as a point e*In an affine coordinate system
Figure FDA0002769388670000072
Calculating the coordinate of e by a quadratic linear weighting method according to the parameter coordinate;
e＝vi+α(vj-vi)+β(vk-vi) (15)
step 4, free-form surface discrete point cloud model circular cutting tool path planning
1) Normal vector and curvature calculation for triangular meshes
In order to facilitate subsequent tool path planning, the geometric characteristics of the tool contact on the space triangular grid are analyzed through the vector and curvature of a calculation method; applying least square surface local fitting method to grid unit vertex normal vector and principal curvature k1、k2And a corresponding main direction d1、d2Making an estimate of k1Is the maximum principal curvature, k2Is the minimum principal curvature; and then, calculating the normal curvature of the grid unit vertex along any direction d' according to an Euler formula, wherein the calculation expression is as follows:
k(d＇)＝k1·cos2θ+k2·sin2θ (16)
in the formula, θ represents an arbitrary direction d' and a main direction d1The included angle therebetween;
calculating the normal vector and the curvature of the knife contact point by adopting a quadratic linear weighting method and by judging the position of the knife contact point in the grid unit and combining the normal vector and the curvature information of the vertex of the grid unit;
v1、v2and v3Three vertexes of the space triangular mesh unit are respectively arranged,
Figure FDA0002769388670000073
is the corresponding unit normal vector, then the gridNormal vector of any knife contact e in unit
Figure FDA0002769388670000074
Expressed as:
Figure FDA0002769388670000075
wherein (u, v) represents e in an affine coordinate system
Figure FDA0002769388670000081
The parameter coordinates of the following; when e is located on the edge of the triangular patch, equation (17) is degenerated into a linear interpolation equation; similarly, the normal curvature of the knife contact point positioned in the triangular grid unit along any direction is calculated by the method;
2) calculation of circular cutting tool path parameters
Calculating the tool path parameters, including the calculation of the feed step length and the feed line distance; planning a feed step length by using a step length screening method; order to
Figure FDA0002769388670000082
The method is characterized in that dense points are formed by discretizing processing cutter contact points through parameters such as B spline curve fitting and the like, and epsilon represents a known approximation error;
given a starting point
Figure FDA0002769388670000083
Then at point
Figure FDA0002769388670000084
Then selecting a point in order
Figure FDA0002769388670000085
Then it is ready to
Figure FDA0002769388670000086
And
Figure FDA0002769388670000087
each point P in betweeniWhere i ═ m1+1,...,m2-1, calculating it to line segment
Figure FDA0002769388670000088
The distance of (c):
Figure FDA0002769388670000089
if it is in accordance with di＜ε,i＝m1+1,...,m21, i.e.
Figure FDA00027693886700000810
And
Figure FDA00027693886700000811
the approximation error of the curve where the line segment formed by two points approximates is less than a given value, and the curve segment is sequentially picked up
Figure FDA00027693886700000812
The next point of (1), i.e. order m2＝m2+1, repeat the above steps until there is a point P if anyiTo the straight line segment
Figure FDA00027693886700000813
Is in accordance with di> epsilon, where i epsilon m1+1,...,m2-1; at this time
Figure FDA00027693886700000814
And
Figure FDA00027693886700000815
the line segment formed by the two points is the longest line segment which accords with the approaching precision condition; retention
Figure FDA00027693886700000816
Point on, andand delete
Figure FDA00027693886700000817
And
Figure FDA00027693886700000818
all points in between; for the whole curve, points must be added
Figure FDA00027693886700000819
As a new starting point and repeating the above steps;
the cutting path CL is calculated by equation (19):
Figure FDA00027693886700000820
in the formula, RtRadius of ball head cutter, h is residual height, RbThe curvature radius is adopted, the positive sign is taken when the model is a convex curved surface, and the negative sign is taken when the model is a concave curved surface;
introducing mapping stretching coefficient sigma, and calculating the track spacing CL at the knife contact point corresponding to the mapping domain*，
Figure FDA0002769388670000091
3) Generation of circular cutting path in space and parameter domain
Explaining a generation method of a circular cutting tool track in a space and parameter domain by combining a calculation method of a circular cutting tool track parameter;
the extracted space triangular mesh model boundary is fitted by adopting a cubic non-uniform B spline, namely:
Figure FDA0002769388670000092
in the formula, DiAs a control point, Ni,3(t) is a cubic B-spline basis function;
discretizing the boundary curve according to certain precision, mapping the knife contact on the first knife track determined by adopting a step length screening method to a parameter domain according to a harmonic mapping rule, and obtaining the knife contact of the first knife track in the parameter domain; updating the tool path to be the previous tool path;
② calculating the previous tool path n1The line spacing CL of the offset of each knife contact on the space grid curved surface corresponds to the theoretical offset line spacing CL of the knife contacts in the mapping domain*Taking the minimum value of line spacing
Figure FDA0002769388670000093
Normally biasing the actual line space along the previous tool path in the mapping domain to obtain the current tool path;
thirdly, based on the harmonic mapping inverse mapping method in the step 3, inversely mapping the current tool path of the mapping domain to the space grid curved surface to obtain the next tool path tool contact of the space grid curved surface; judgment of
Figure FDA0002769388670000094
If the result is 1, switching to the fourth step, and if the result is 0, switching to the second step;
fourthly, the iteration of the tool path is finished, and the contact track of the circular cutting processing tool in the space and parameter domain is generated;
the obtained space grid curved surface processing cutter contact cannot be directly used for processing, the conversion from the processing cutter contact to a processing cutter point needs to be completed, and the connection between the track points can be used for processing; in numerical control machining, a tool nose point is often used as a tool location point, and a conversion relation between a machining tool contact and the machining tool location point is as follows:
Figure FDA0002769388670000095
in the formula, wmIs a group of spatial tool positions emIs a group of contact points of the space knife,
Figure FDA0002769388670000101
is the normal vector of the contact point of the knife,
Figure FDA0002769388670000102
in the direction of the knife axis, RtIs the radius of the ball head cutter.
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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101276484A (en) * 2008-03-31 2008-10-01 浙江大学 Method for generating gridding based on harmonic map
CN105629876A (en) * 2016-02-16 2016-06-01 华侨大学 Multi-cutter optimization combination selection method for triangular grid model numerical control processing

Family Cites Families (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2001076172A (en) * 1999-09-07 2001-03-23 Moriaki Sakakura Method and device for curved-surface generation and storage medium
JP2005228260A (en) * 2004-02-16 2005-08-25 Kitakyushu Foundation For The Advancement Of Industry Science & Technology Distortion distribution calculation method for shaping plate material to objective curved surface
CN103949705B (en) * 2014-05-14 2016-02-17 南京航空航天大学 Cavity feature web cycloidal helical composite milling processing method
CN108682043A (en) * 2018-02-08 2018-10-19 大连理工大学 A kind of complex-curved measure planning method based on parameter mapping
CN109299556B (en) * 2018-10-08 2023-04-07 南京航空航天大学 Annular cutter path generation and optimization method based on image processing
CN109961517B (en) * 2019-03-01 2021-05-07 浙江大学 Triangular mesh reparameterization method for parametric surface fitting

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101276484A (en) * 2008-03-31 2008-10-01 浙江大学 Method for generating gridding based on harmonic map
CN105629876A (en) * 2016-02-16 2016-06-01 华侨大学 Multi-cutter optimization combination selection method for triangular grid model numerical control processing

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