CN112363455A

CN112363455A - Tool path determination method and system based on dynamics constraint

Info

Publication number: CN112363455A
Application number: CN202011200917.8A
Authority: CN
Inventors: 袁春明; 马鸿宇; 高小山; 张立先
Original assignee: Academy of Mathematics and Systems Science of CAS
Current assignee: Academy of Mathematics and Systems Science of CAS
Priority date: 2020-11-02
Filing date: 2020-11-02
Publication date: 2021-02-12
Anticipated expiration: 2040-11-02
Also published as: CN112363455B

Abstract

The invention relates to a tool path determining method and system based on dynamic constraint. The method comprises the steps of obtaining a triangular mesh curved surface with a boundary; extracting the boundary according to the triangular mesh curved surface with the boundary; based on residual height constraint, offsetting each point on the currently offset boundary according to the feeding direction, and determining a contour offset curve of the currently offset boundary; eliminating self-crossed profile curves in the profile bias curves based on residual height constraint; repeating the processing until all the boundary offsets in the triangular mesh curved surface with the boundary are finished; determining a Fermat spiral line in each sub-area of the triangular mesh curved surface with the boundary based on the dynamic constraint according to each contour bias curve; determining communicated Fermat helices by adopting a spiral-contourr tree according to the Fermat helices in all the sub-regions; and determining a tool path according to the communicated Fermat spiral. The invention considers the dynamic constraint when generating the path, thereby effectively improving the feeding rate during processing.

Description

Tool path determination method and system based on dynamics constraint

Technical Field

The invention relates to the field of tool path determination, in particular to a tool path determination method and system based on dynamics constraint.

Background

The high-precision numerical control machining technology occupies a larger and larger proportion in the manufacturing of complex workpieces. The main flow of numerical control machining includes Computer Aided Design (CAD), Computer Aided Manufacturing (CAM), post-processing, and machining. With the rapid development of numerical control machine tools, people put higher demands on the precision and efficiency of the CAM in practical numerical control machining. Tool path planning plays a very important role in the CAM because the tool must follow the path of the planned tool location. Therefore, the quality of the tool location locus determines the machining precision and the machining efficiency to a certain extent.

Studies on tool path planning can be broadly divided into two categories: parametric form based studies and topological form based studies. The traditional path planning method based on the parameter form mainly comprises an isoparametric method, an isoplanar method and an isoparametric height method. The traditional path planning method based on the topological form is mainly divided into a direction parallel trajectory planning method, a spiral trajectory planning method and a space filling curve planning method.

The isoparametric method is mainly applied to the parametric curved surface S (u, v). And when the path is planned, keeping any one of the u and v parameters unchanged, and mapping the isoparametric line on the parameter plane to the parameter curved surface in Euclidean space to further generate the tool path. However, this method may cause the local area processing tracks to be too dense, the residual height distribution to be uneven, and the surface processing quality and the overall processing efficiency to be affected. The iso-planar method uses the intersection of a cluster of parallel planes (drive surfaces) and a curved surface to be machined to create a tool path. The key to this type of process is how to select the drive faces. Quinsit et al select the drive face by maximizing the material removal rate. Hu et al construct a scalar field based on residual height constraints and dynamic constraints, and then use the scalar field to select the optimal drive surface. The path generated by the iso-planar method hardly satisfies the residual height constraint because the processing line pitch thereof is kept constant and the curved surface to be processed is complicated. And the equal residual height method is that after the cutter position point Pi, j on the ith path is given, the cutter position point Pi +1, j corresponding to the next path is calculated in the direction vertical to the current feeding direction by using the preset maximum residual height. For the equal residual height method, the selection of the initial path is very important. The good initial path can effectively improve the processing efficiency. Giri et al gives a way to choose the initial path by analyzing the curvature of the surface. Chiou et al first propose a potential field method using the principle of energy field, and then select an initial path according to the maximum material removal rate. Lee et al calculate the machining bandwidth by effectively cutting the ellipse, and then generate the constant residual height tool machining path. Min et al propose a new equal residual height method based on the similarity of adjacent paths, and have very high computational efficiency.

In the direction parallel trajectory planning method, all paths are parallel to a preset straight line. All the tracks are connected end to form a zigzag track. This method is widely used for rough machining because of its simplicity. The spiral trajectory planning method is based on the curved surface boundary contour construction, and each path is an offset curve of a curved surface boundary. The path generated by the method has better continuity, does not need to frequently lift, cut and transfer, and is widely applied to cavity processing. However, for the space filling curve planning method, although the generated path has good continuity, the path is not commonly used because the calculation is complicated and the feeding direction changes frequently.

With the rapid development of CAD/CAM technology in recent years, triangular mesh models are widely applied in the fields of discrete geometric modeling, CNC (computerized numerical control) machining programming, graphics, images and the like. Due to its simple and mature characteristics, the triangular mesh model has become a common free curved surface representation form in computer graphics and numerical control processing. Therefore, the tool path planning research aiming at the triangular mesh model has important practical significance.

However, existing parametric form-based methods cannot be directly applied to triangular mesh models. On the triangular mesh model, there are several different tool path planning methods. Lee uses the profile offset curve under residual height constraint to generate a spiral curve tool path. Zhu et al generated a spiral tool path through a pre-set guideline and presented a method of finding a bias curve based on residual height error. Sun et al focus on numerical control machining of non-zero deficiency triangular mesh curved surfaces and propose a smooth tool path generation method for five-axis machining. However, these methods may result in the generated path not satisfying the residual height constraint when the self-crossing is eliminated.

However, the conventional topological-based method usually generates a tool path only on a simple single-valued curved surface. Therefore, an algorithm for generating a tool path on a free-form surface represented by a triangular mesh model is of interest.

Aiming at a two-dimensional plane and a three-dimensional space grid, Zhao et al realize a new tool path generation method on a triangular grid model: connected Fermat Spirals (CFS). The method uses a thermal approach to generate a shape-aware scalar field, and then concatenates these contours into a CFS. This type of tool path has several advantages: the whole cutter path only comprises a terminal point and a starting point, so that frequent cutter lifting and cutting-in are not needed; the whole curved surface to be processed can be completely covered by the CFS; the start and end points of a single fermat spiral can be chosen arbitrarily on the boundary, thus favouring the continuity of the path. However, Zhao et al primarily considers the generation of tool path trajectories from a geometric perspective, rather than numerical control machining. After the tool path is optimized, the tool path generated by Zhao et al has too many inflection points, and the dynamics constraint is not considered when the Fermat spiral is generated, so that the feeding rate in processing is reduced.

Disclosure of Invention

The invention aims to provide a tool path determining method and system based on dynamic constraint, which take the dynamic constraint into consideration when generating a path, thereby effectively improving the feeding rate during processing.

In order to achieve the purpose, the invention provides the following scheme:

a tool path determination method based on dynamic constraints comprises the following steps:

acquiring a triangular mesh curved surface with a boundary;

extracting the boundary of the triangular mesh curved surface with the boundary; each of said boundaries is represented by a sequence of points;

based on residual height constraint, offsetting each point on the currently offset boundary according to the feeding direction, and determining a contour offset curve of the currently offset boundary;

eliminating self-crossed profile curves in the profile bias curves based on residual height constraint; replacing the currently biased boundary with a next biased boundary, returning to the residual height constraint, biasing each point on the currently biased boundary according to the feeding direction, and determining a contour bias curve of the currently biased boundary until all the boundary biases in the triangular mesh curved surface with the boundary are finished;

determining a Fermat spiral in each sub-region of the triangular mesh curve with the boundary based on the dynamic constraint according to each contour bias curve;

determining communicated Fermat spiral lines by adopting a spiral-contourr tree according to Fermat spiral lines in all sub-areas; the spiral-contour tree is used for representing the adjacency relation of the Fermat spiral among each sub-area;

and determining a cutter path according to the communicated Fermat spiral.

Optionally, the determining, based on the residual height constraint, a contour bias curve of the currently biased boundary by biasing each point on the currently biased boundary according to the feeding direction further includes:

and calculating the path interval and the path interval direction according to the residual height constraint.

Optionally, the determining, based on the residual height constraint, a contour bias curve of the currently biased boundary by biasing each point on the currently biased boundary according to the feeding direction specifically includes:

acquiring the position and the feeding direction of the ith point on the current offset boundary;

determining a defined plane according to the position of the ith point and the feeding direction; the definition plane is intersected with the triangular mesh curved surface with the boundary;

determining a bias point corresponding to the ith point according to a line segment of the defined plane, which is intersected with the triangular mesh curved surface with the boundary, and the path interval direction corresponding to the ith point;

and determining a profile offset curve of the currently offset boundary according to all offset points of the currently offset boundary.

Optionally, the determining, by each of the profile bias curves, a fermat spiral in each sub-region of the triangular mesh surface with the boundary based on the dynamic constraint specifically includes:

acquiring a point with the maximum curvature on the contour offset curve;

and taking the point with the maximum curvature as a transfer point, increasing the angle corresponding to the point with the maximum curvature based on the dynamic constraint, and determining the Fermat spiral line in each sub-area of the triangular mesh surface with the boundary.

Optionally, the determining, according to the fermat spirals in all the sub-regions, a connected fermat spiral by using a spiral-contour tree further includes:

and smoothing the communicated Fermat spiral line by adopting a high-speed piecewise interpolation algorithm.

A tool path determination system based on kinematic constraints, comprising:

the triangular mesh curved surface acquisition module with the boundary is used for acquiring a triangular mesh curved surface with the boundary;

the boundary extraction module is used for extracting the boundary of the triangular mesh curved surface with the boundary; each of said boundaries is represented by a sequence of points;

the contour bias curve determining module is used for biasing each point on the currently biased boundary according to the feeding direction based on residual height constraint and determining a contour bias curve of the currently biased boundary;

the contour bias curve optimization module is used for eliminating self-crossed contour curves in the contour bias curves based on residual height constraint; replacing the currently biased boundary with a next biased boundary, returning to the residual height constraint, biasing each point on the currently biased boundary according to the feeding direction, and determining a contour bias curve of the currently biased boundary until all the boundaries in the triangular mesh curved surface with the boundary are biased;

the Fermat spiral determining module is used for determining the Fermat spiral in each sub-area of the triangular mesh curved surface with the boundary based on the dynamic constraint according to each contour bias curve;

the connected Fermat spiral determining module is used for determining the connected Fermat spiral by adopting a spiral-contourr tree according to the Fermat spirals in all the sub-areas; the spiral-contour tree is used for representing the adjacency relation of the Fermat spiral among each sub-area;

and the cutter path determining module is used for determining a cutter path according to the communicated Fermat spiral.

Optionally, the method further includes:

and the path interval and path interval direction determining module is used for calculating the path interval and the path interval direction according to the residual height constraint.

Optionally, the contour bias curve determining module specifically includes:

an ith point position and feed direction acquiring unit for acquiring a position and feed direction of an ith point on the currently biased boundary;

a defined plane determining unit for determining a defined plane according to the position of the ith point and the feeding direction; the definition plane is intersected with the triangular mesh curved surface with the boundary;

a bias point determining unit corresponding to the ith point, configured to determine a bias point corresponding to the ith point according to a line segment where the defined plane intersects the triangular mesh curved surface with the boundary and a path interval direction corresponding to the ith point;

and the contour bias curve determining unit is used for determining the contour bias curve of the currently biased boundary according to all the bias points of the currently biased boundary.

Optionally, the fermat spiral determining module specifically includes:

a point with the maximum curvature and a point with the minimum curvature acquiring unit, which are used for acquiring the point with the maximum curvature on the contour bias curve;

and the Fermat spiral determining unit is used for taking the point with the maximum curvature as a transfer point, increasing the corresponding angle with the maximum curvature based on the dynamic constraint and determining the Fermat spiral in each sub-area of the triangular mesh curve with the boundary.

Optionally, the method further includes:

and the path smoothing processing module is used for smoothing the communicated Fermat spiral by adopting a high-speed piecewise interpolation algorithm.

According to the specific embodiment provided by the invention, the invention discloses the following technical effects:

the invention provides a tool path determining method and system based on dynamics constraint, which are characterized in that the boundary of a triangular mesh curved surface with a boundary is extracted, each point on the current biased boundary is biased according to the feeding direction based on residual height constraint, the contour bias curve of the current biased boundary is determined, the determination of the contour bias curve of the boundary is repeated, the space filling of the triangular mesh curved surface with the boundary is further realized, the Fermat spiral line in each sub-area of the triangular mesh curved surface with the boundary is determined based on the dynamics constraint according to each contour bias curve, and the connected Fermat spiral line is determined by adopting a spiral-contourr tree according to the Fermat spiral lines in all sub-areas. Namely, a continuous cutter path communicated with the Fermat spiral line is generated, and the dynamic constraint is considered when the path is generated, so that the feeding speed in processing is effectively improved.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without inventive labor.

FIG. 1 is a flow chart of a tool path determination method based on dynamic constraints according to an embodiment of the present invention;

FIG. 2 is a schematic diagram of a boundary of a triangular mesh surface with a boundary and a contour bias curve of the boundary;

FIG. 3 is a schematic diagram of a profile offset curve after elimination of the self-crossed profile curve;

FIG. 4 is a schematic diagram of a Fermat spiral determination process;

FIG. 5 is a schematic view of a connected Fermat spiral;

FIG. 6 is a schematic diagram of a tool path determination system based on dynamic constraints according to the present invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.

Fig. 1 is a flow chart showing a method for determining a tool path based on dynamic constraints, as shown in fig. 1, the method for determining a tool path based on dynamic constraints, provided by the present invention, includes:

s101, acquiring a triangular mesh curved surface with a boundary.

S102, extracting the boundary of the triangular mesh curved surface with the boundary; each of the boundaries is represented by a sequence of points.

S103, based on residual height constraint, offsetting each point on the currently offset boundary according to the feeding direction, and determining a contour offset curve of the currently offset boundary. And the contour bias curve of the boundary of the current bias is an equivalent bias curve with equal residual height.

Before S103, further comprising:

Residual height may occur on the work surface as the tool moves along the tool path trajectory. The distance between the path traces is the knife contact path spacing. The calculation of the path pitch is related to the relief of the surface. A ball nose cutter is used to machine the curved surface. The path pitch depends on the local radius of curvature R of the curved surface, the feed direction, the tool radius R and the height h remaining on the curved surface. The maximum residual height h that is usually constrained is much smaller than the tool radius r, so the calculation of the path pitch can be simplified. Tool path spacing in plane when machining with ball nose tool_fTool path spacing on convex surface l_convexTool path spacing on concave surface l_concaveCan be approximated by the following equation:

where e is the bow error (chord error) for tool path smoothing. To ensure that the path spacing is strictly greater than 0, e should be less than

Thus, the smoothed tool path can strictly satisfy the residual height constraint.

S103 specifically comprises the following steps:

acquiring the position of the ith point on the boundary of the current offset and the feeding direction.

The specific calculation process of the feeding direction of each point is as follows:

suppose there is a point P on the boundary_0，iThe direction of feed at that point

Can be calculated by the following formula:

in the formula, P_0，i-1And P_0，i+1Are respectively of the same type as P_0，iTwo adjacent dots.

Passing through point P_0，iAnd the direction of feed

Determining a definition plane F_0，i：

Define plane F_0，iAnd intersecting with the triangular mesh model to obtain a series of intersection line segments. These line segments can be regarded as points P_0，iCorresponding bias point P_1，iApproximation of geodesic lines therebetween. And the total length of these segments should be equal to the path spacing under the residual height constraint. But there may be two sets of such line segments. The direction of the path interval needs to be calculated

Make the bias point P_1，iIn the correct orientation. Direction of path interval

Can be composed of

And point P_0，iNormal vector of treatment

Is calculated by cross multiplication.

Determining a defined plane according to the position of the ith point and the feeding direction; the definition plane intersects with the triangular mesh surface with the boundary.

And determining a bias point corresponding to the ith point according to a line segment of the defined plane, which is intersected with the triangular mesh curved surface with the boundary, and the path interval direction corresponding to the ith point. The offset distance of the offset points should be equal to the tool path spacing.

A point P on the contour bias curve of the boundary_j，iFrom this point along the path interval direction, the corresponding offset point P is searched forward_j+1，iUp to the fold line P_j，iP_j+1，iIs equal to the tool path spacing based on the residual height constraint.

Moving along the inter-path direction to the farthest point on the existing triangular patch. If the length of the broken line segment P_j，iBeta is greater than path interval l_j，iOffset point P_j+1，iJust above this triangle. If not, the correct triangular patch is selected and the operation is repeated until the appropriate bias point P is found_j+1，i。

As a specific example, a scalar d represents a polyline segment P_j，iThe cumulative length of β, this length is used to fit the geodesic distance. Equation of

Indicating that the point beta should be in the feed direction

On the determined plane. Equation of

Ensuring that the bias is always in the correct direction.

According to the above formula, two problems are considered.

The second problem is how to obtain a triangular patch f satisfying the following condition when the point β reaches the vertex₁： f₁Contains a vertex beta;

dough sheet f₁The included angle between the path and the spacing direction is an acute angle.

For the first problem, β is at the triangular patch f₁So that this problem can be translated to a flat surface. Will be in the direction of feed

Mapping to f₁To use

And (4) showing.

Then go through f₁Each strip is not in the same direction as

A vertical edge. Suppose that edge V is selected₂V₃Any point on the edge can be expressed as: (1-u) V₂+uV₃. The coefficient u may be calculated to determine that the condition β ∈ V is satisfied₂V₃，

Point β of (d). The coefficient u can be calculated by:

if the point β determined by u satisfies the condition: u is 0. ltoreq. u.ltoreq.1 and

that point is the point to be found. If not, the next edge is selected until a suitable point is found.

For the second problem, the goal is to select the correct triangular patch f for the next iteration₁. First find the 1-domain F of the vertex beta₁. Each patch is then considered one by one until the correct triangular patch is found. Under the condition that: f. of₁Including vertices beta and

meaning at patch f₁The upper presence point q satisfies the following system of equations:

wherein

Is a patch f₁The normal vector of (2). By simplifying the above equation, it can be obtained:

if the above-mentioned ratio u/v is a positive number, f is indicated₁The first two conditions are met. It is possible to obtain two patches f satisfying the first two conditions simultaneously₁And f₂. So that the third condition (f) needs to be used₁Acute angle with respect to the direction of separation of the paths) to select the correct plane, which may be expressed as

Wherein

Is the normal vector of the beta point.

After the offset points are obtained according to the feeding direction, the boundary of the curved surface can be offset to obtain a profile offset curve, and the profile offset curve is shown in fig. 2.

S104, eliminating self-bred contour curves in the contour bias curves based on residual height constraint; and replacing the currently biased boundary with a next biased boundary, returning to the residual height constraint, biasing each point on the currently biased boundary according to the feeding direction, and determining the contour bias curve of the currently biased boundary until all the boundary biases in the triangular mesh curved surface with the boundary are finished.

As shown in fig. 3, point P is divided_tTowards P_iPoint stretching allows processing to the entire area. P_tThe distance to the adjacent profile curve is Hausdorf distance, so P needs to be considered_tMaximum distance to the profile curveSatisfies the residual height constraint, i.e. P_tNeeds to be stretched to the point P_MAnd P is_MA distance to B of

Wherein l is P_iThe path spacing at the points based on the residual height constraint.

After that, points B and B are obtained₁And the new path is from point P_MCan be calculated from the following equation:

wherein theta is the angle at which the curve self-crosses,

Is P_iUnit vector of point angular bisector, S₁And S₂Is B₁To the drop foot point corresponding to the original path as shown in fig. 3. Finally, P is added_MAre respectively reacted with S₁And S₂Are connected.

And S105, determining the Fermat spiral line in each sub-area of the triangular mesh surface with the boundary based on the dynamic constraint according to each contour bias curve.

S105 specifically comprises the following steps:

and acquiring a point with the maximum curvature on the profile offset curve.

The specific calculation of the normal curvature and the normal vector on the triangular mesh comprises the following steps:

and calculating normal vectors and normal curvatures on the vertexes of the triangular mesh. Vertex V_iNormal vector of (1)

Can be calculated according to the following formula:

in the formula, FⁱIs vertex V_i1-field of; f. of_kIs FⁱMiddle triangular patch, gamma_kIs f_kAt vertex V_iInternal angle of (A)_kIs a triangular patch f_kThe area of (d);

is f_kThe normal vector of (2).

Setting point P on triangular patch f₁By using f₁Calculates the normal and normal curvatures at point P, which can be located precisely by three vertices: p ═ V (1-u-V) V₁+uV₃+vV₂. The coefficients u and v are calculated as follows:

in the formula (I), the compound is shown in the specification,

is a triangular patch f₁The normal vector of (2).

Then, the normal vector of the point P is calculated by the information of the three vertexes and the position of the point P

Sum of normal curvature k_p：

k_p＝(1-u-v)k₁+uk₃+vk₂In the formula, k_iAnd

i is 1, 2, 3 is respectively the vertex V_iAnd i is the normal curvature and normal vector of 1, 2, 3. Up to now, the normal vector and normal curvature of any point on the grid can be calculated.

The switching connection is locally approximate to concentric circular arc connection, so that the number of inflection points in the cutter path is only half, and the path is smoother.

These two curves are projected onto a plane perpendicular to the normal vector of the transfer point and then the intersection of the tangent line with the adjacent profile curve can be tested.

The above steps are used to create a spiral path, which is then connected into a Fermat spiral. As shown in FIG. 4, taking concentric circles as an example, a transfer point P is selected on the second profile curve₂Then the intersection point P is determined by the above steps₁. At P₁The first profile curve is broken at the point and the fiima spiral end point E is formed. Then P is added₁Point and P₂The dots are connected. Then determining the sum of P and P on the fourth contour curve₂Corresponding transfer point P₄And determining the intersection point P₃. Will P₃Is connected to P₄And the above process is repeated until the fermat spiral line is formed.

S106, determining connected Fermat helices by adopting a spiral-contourr tree according to the Fermat helices in all the sub-regions, as shown in FIG. 5; the spiral-contourr tree is used for representing the adjacency relation of the Fermat spiral lines between each sub-area.

After S106, further comprising:

And S107, determining a cutter path according to the communicated Fermat spiral. Two adjacent profile curves may be disconnected and connected to create a continuous path. Repeating this step forms a spiral path. And this spiral path can be converted into a fermat spiral.

Fig. 6 is a schematic structural diagram of a tool path determining system based on dynamic constraints, and as shown in fig. 6, the tool path determining system based on dynamic constraints, provided by the present invention, includes:

a triangular mesh curved surface with boundary obtaining module 601, configured to obtain a triangular mesh curved surface with boundary;

a boundary extraction module 602, configured to extract a boundary of the triangular mesh surface with a boundary; each of the boundaries is represented by a sequence of points.

A contour bias curve determining module 603, configured to bias each point on the currently biased boundary according to the feeding direction based on the residual height constraint, and determine a contour bias curve of the currently biased boundary.

A contour bias curve optimization module 604, configured to eliminate self-intersected contour curves in the contour bias curves based on residual height constraints; and replacing the currently biased boundary with a next biased boundary, returning to the residual height constraint, biasing each point on the currently biased boundary according to the feeding direction, and determining a contour bias curve of the currently biased boundary until all the boundary biases in the triangular mesh curved surface with the boundary are finished.

A fermat spiral determining module 605, configured to determine a fermat spiral in each sub-region of the triangular mesh surface with boundaries based on the dynamic constraints according to each of the contour bias curves.

A connected fermat spiral determining module 606, configured to determine, according to the fermat spirals in all the sub-regions, connected fermat spirals by using a spiral-contour tree; the spiral-contourr tree is used to represent the adjacency of the fermat spiral between each sub-region.

And a tool path determining module 607 for determining a tool path according to the communicated fermat spiral.

The invention provides a tool path determining system based on dynamic constraint, which further comprises:

The contour bias curve determining module specifically comprises:

and the position and feeding direction acquiring unit is used for acquiring the position and feeding direction of the ith point on the current offset boundary.

A defined plane determining unit for determining a defined plane according to the position of the ith point and the feeding direction; the definition plane intersects with the triangular mesh surface with the boundary.

And the bias point determining unit corresponding to the ith point is used for determining the bias point corresponding to the ith point according to a line segment of the defined plane, which is intersected with the triangular mesh curved surface with the boundary, and the path interval direction corresponding to the ith point.

The Fermat spiral determining module specifically comprises:

and the point acquisition unit is used for acquiring the point with the maximum curvature on the profile offset curve.

The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.

The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims

1. A tool path determination method based on dynamic constraints is characterized by comprising the following steps:

acquiring a triangular mesh curved surface with a boundary;

determining a Fermat spiral line in each sub-region of the triangular mesh curved surface with the boundary based on dynamic constraints according to each contour bias curve;

determining communicated Fermat helices by adopting a spiral-contourr tree according to the Fermat helices in all the sub-regions; the spiral-contour tree is used for representing the adjacency relation of the Fermat spiral among each sub-area;

and determining a cutter path according to the communicated Fermat spiral.

2. The method of claim 1, wherein the determining the contour offset curve of the currently offset boundary by offsetting each point on the currently offset boundary according to the feeding direction based on the residual height constraint further comprises:

3. The method for determining a tool path based on dynamical constraints as claimed in claim 2, wherein the determining a contour bias curve of the currently biased boundary by biasing each point on the currently biased boundary according to the feeding direction based on residual height constraints specifically comprises:

and determining a contour bias curve of the currently biased boundary according to all bias points of the currently biased boundary.

4. The tool path determining method based on dynamic constraints as claimed in claim 1, wherein the determining of the fimbrian spiral in each sub-region of the triangular mesh surface with the boundary based on the dynamic constraints for each contour bias curve specifically comprises:

acquiring a point with the maximum curvature on the contour offset curve;

and taking the point with the maximum curvature as a transfer point, increasing the corresponding angle of the point with the maximum curvature based on the dynamic constraint, and determining the Fermat spiral line in each sub-area of the triangular mesh curved surface with the boundary.

5. The tool path determining method based on dynamic constraints as claimed in claim 1, wherein the determining the connected fermat spiral by using a spiral-contourr tree according to the fermat spirals in all sub-regions further comprises:

6. A tool path determination system based on kinematic constraints, comprising:

the contour bias curve optimization module is used for eliminating self-crossed contour curves in the contour bias curves based on residual height constraint; replacing the currently biased boundary with a next biased boundary, returning to the residual height constraint, biasing each point on the currently biased boundary according to the feeding direction, and determining a contour bias curve of the currently biased boundary until all the boundary biases in the triangular mesh curved surface with the boundary are finished;

7. The tool path determination system based on dynamic constraints as claimed in claim 6, further comprising:

8. The tool path determining system based on dynamic constraints as claimed in claim 7, wherein the profile offset curve determining module specifically comprises:

a bias point determining unit corresponding to the ith point, configured to determine, according to a line segment where the defined plane intersects the triangular mesh curved surface with the boundary and a path interval direction corresponding to the ith point, a bias point corresponding to the ith point;

9. The tool path determining system based on the dynamical constraint of claim 5, wherein the Fermat spiral determining module specifically comprises:

and the Fermat spiral determining unit is used for taking the point with the maximum curvature as a transfer point, increasing the corresponding angle of the point with the maximum curvature based on dynamic constraint and determining the Fermat spiral in each sub-area of the triangular mesh curved surface with the boundary.

10. The tool path determination system based on dynamic constraints as claimed in claim 5, further comprising: