CN102778859B - Numerical control machining cutter path generation method based on double helix space filling curves - Google Patents

Abstract

The invention discloses a method for generating a CNC machining tool trajectory based on a double-helix space-filling curve, which includes: step 1, determining the order of the filling curve according to the residual height and the shape of the curved surface, and generating a double-helix that meets the required order on a two-dimensional plane. Spiral filling curve; step 2, improve the corner part of the tool path to optimize the tool path; step 3, map the two-dimensional filling curve to the space surface according to the mapping principle to obtain the tool path in NC machining that meets the requirements. The present invention improves the primitive on the basis of the original space-filling curve, so that the length of the entire tool track is shortened, and the direction changes in the entire tool track are less; The track is smooth, which avoids the frequent start and stop of the speed and the frequent change of the feed direction during the machining process due to the 90-degree right-angle connection, and reduces the impact on the machine tool, the tool and the machined surface, thereby improving the quality of the machined surface.

Description

A method for generating tool paths in NC machining based on double-helix space-filling curves

technical field

The invention relates to a tool trajectory planning method in the technical field of machine tools, in particular to a method for generating a numerically controlled tool trajectory based on a double helix space filling curve. the

Background technique

Freeform surfaces are widely used in product design, and tool path generation is the most important content in NC machining of freeform surface parts. The quality of the tool path directly affects its machining accuracy and machining efficiency. At present, the traditional methods of tool trajectory generation methods include equal residual height method, parameter line method, etc. The commonly used methods are curvature matching method and equal gradient method. At the same time. To this end, we propose a new tool path generation method, that is, a double helix filling curve, and at the same time fillet the corners, which can effectively meet the requirements of reducing impact load and improving processing efficiency. the

After searching the literature of the prior art, it was found that "Recent development in CNC machining of freeform surfaces: a state-of-the-art review" (published "Computer-Aided Design" 2010.42, p641-654) published by Ali Lasemi et al. The current tool path planning method is summarized, and the development process of the method and its advantages and disadvantages are described through an overview, but the tool path planning method is not deeply studied. In the search, it was also found that "Algorithm and Improvement of Hilbert Filling Curve for Tool Path Generation" published by Li Dexin et al. (Publication "China Mechanical Engineering" 2011.11.22 (22), p2739-2743), described in detail the Hilbert curve Generating principle, and put forward the way of chamfering to replace the original right-angle transition to generate machining tool path. Thereby reducing the impact of too frequent steering in the tool path on the machine tool, tool and workpiece. Moreover, the Hilbert filling curve generated by it changes many directions, and only this idea is proposed, but the size of the arc is not studied in detail. the

Contents of the invention

The present invention aims at the above-mentioned deficiencies existing in the prior art, provides a kind of numerical control machining tool track generation method based on the double-helix space-filling curve, improves the primitive of the original Hilbert curve, proposes the double-helix filling curve, and By using arcs to smooth the transition at the corners, the impact on the machine tool at the corners can be reduced, the life of the tool can be effectively improved, and higher processing efficiency and surface quality can be obtained. the

The present invention is achieved through the following technical solutions. the

A NC machining tool trajectory generation method based on a double-helix space-filling curve, comprising the following steps:

Step 1, determine the order of the filling curve according to the residual height and surface shape, and generate a double helix filling curve that meets the required order on the two-dimensional plane;

Step 2, improve the corner part of the tool path to optimize the tool path;

Step 3, according to the mapping principle, the two-dimensional filling curve is mapped to the space surface to obtain the tool trajectory in NC machining that meets the requirements. the

The double helix filling curve adopts a matrix generation method, comprising the following steps:

The first step is to get primitives first;

The second step is to subdivide each small square into four different small squares, and connect the primitives of each area according to the generation rules;

In the third step, repeat the second step and subdivide continuously to obtain double helix filling curves of different orders. the

The generation rule is: F _K+1 represents the filling curve of the current order K+1 order, F _K represents the filling curve of the previous order K order, and the cube formed by F _K is subdivided into four equal-sized small Cube, when K is an odd number, reduce F _K and place it in the small cube in the lower left corner, the filling curve in the small cube in the upper right corner is obtained by rotating it clockwise by 90°, and the filling curves in the remaining two small cubes It is obtained symmetrically from top to bottom; when K is an even number, reduce F _K and place it in the small cube in the upper left corner, the filling curve in the small cube in the upper right corner is consistent with it, and the filling curve in the small cube in the lower left corner is Rotate it clockwise by 90°, and the filling curve in the small cube in the lower right corner is obtained by rotating it counterclockwise by 90°. After obtaining the filling curves in the four small cubes, use a straight line to connect each small cube horizontally or vertically. Filling the curve can get the filling curve of F _K+1 .

The tool trajectory is drawn in one stroke from the beginning to the end, and adopts the primitive in the form of a double helix. The tool trajectory of different orders is generated by transforming the formula, and the corner part of the tool trajectory is treated as an arc, and then the mapping principle is used to achieve Get the tool path on the surface. the

The arc processing is that when the two tool tracks are not on the same straight line, a turning point will be formed, and an arc with a radius of r is used to connect the two tool tracks for smooth processing. According to the residual height h and the tool The effective cutting radius R is used to calculate the line spacing L that meets the requirements of surface machining accuracy, and r is calculated based on L. the

The radius of the transition arc is about r, where the applicable minimum radius formula is: The L is the line spacing of the tool path.

The present invention improves the primitive on the basis of the original space-filling curve, so that the length of the entire tool path is shortened, and there are fewer direction changes in the entire tool path; moreover, arc transition is performed at the corner, so that The whole trajectory is smooth, which avoids the frequent start and stop of the speed and the frequent change of the feed direction during the machining process due to the 90-degree right-angle connection, and reduces the impact on the machine tool, the tool and the machined surface, thereby improving the machined surface. quality. the

The tool path generation methods adopted in the prior art all focus on one aspect of machining efficiency and quality, and the tool paths are connected by multiple line segments. And there are too many corners in some methods, which have caused impacts on machine tools, cutting tools and workpieces. the

Compared with the prior art, the present invention adopts the double helix filling curve, not only shortens the length of the entire tool track, but also reduces the number of turns to about 70% of the previous ones, and the processing quality is better than most methods, especially In areas where the curvature of the surface changes significantly. At the same time, the present invention adopts circular arcs for smooth processing when corners are transitioned, the obtained tool trajectory is continuous, the speed at the corners transitions smoothly and will not drop to zero, and the feed direction will not change abruptly, ensuring the machining The medium feed speed will not start and stop frequently and the feed direction will not change suddenly. At the same time, the transition arc is related to the preset surface accuracy, which can ensure the accuracy of the processed surface and realize the smooth transition of the inflection point in NC machining. the

Description of drawings

Fig. 1 (a) is the basic unit of the double helix filling curve in the present invention, (b) is the generation rule of the filling curve when K is an odd number, (c) is the generation rule of the filling curve when K is an even number;

Fig. 2 is the two-dimensional double helix filling curve optimized in the present invention;

Fig. 3 is the mapping principle of double helix filling curve among the present invention;

Figure 4 shows the tool paths generated by various tool path planning methods;

Among them, (a) is the Hilbert filling curve, (b) is the double helix filling curve, (c) is the improved double helix filling curve;

Fig. 5 is multi-segment tool path of the present invention and transition curve therebetween;

Fig. 6 is a schematic diagram of calculating line spacing in plane processing in the present invention;

Fig. 7 is a schematic diagram of calculating line spacing of concave surface processing in the present invention;

Fig. 8 is a schematic diagram of calculation of line distance in convex surface processing in the present invention. the

Detailed ways

The embodiments of the present invention are described in detail below: the present embodiment is implemented under the premise of the technical solution of the present invention, and detailed implementation and specific operation process are provided, but the protection scope of the present invention is not limited to the following implementation example. the

The present embodiment provides a method for generating a CNC machining tool path based on a double-helix space-filling curve, comprising the following steps:

Step 1, determine the order of the filling curve according to the residual height and surface shape, and generate a double helix filling curve that meets the required order on the two-dimensional plane;

Step 2, improve the corner part of the tool path to optimize the tool path;

Step 3, according to the mapping principle, the two-dimensional filling curve is mapped to the space surface to obtain the tool trajectory in NC machining that meets the requirements. the

In the present embodiment, the method of matrix generation double helix filling curve method is adopted, comprising the following steps:

The first step is to get primitives first;

The second step is to subdivide each small square into four different small squares, and connect the primitives of each area according to the generation rules;

In the third step, repeat the second step and subdivide continuously to obtain double helix filling curves of different orders. the

The specific generation rules are as follows: as shown in Figure 1(b) and (c), F _K+1 represents the filling curve of the current order K+1, and F _K represents the filling curve of the previous order _K. The formed cube is subdivided into four small cubes of the same size. When K is an odd number, reduce F _K and place it in the small cube in the lower left corner. The filling curve in the small cube in the upper right corner is to rotate it clockwise by 90 ° obtained, the filling curves in the remaining two small cubes are symmetrical up and down; when K is an even number, reduce F _K and place it in the small cube in the upper left corner, and the filling curve in the small cube in the upper right corner is consistent with it , the fill curve in the small cube in the lower left corner is obtained by rotating it 90° clockwise, and the fill curve in the small cube in the lower right corner is obtained by rotating it counterclockwise by 90°, after obtaining the fill curves in the four small cubes , use a straight line to horizontally or vertically connect the filling curves in each small cube to get the filling curve of F _K+1 .

The specific principle is as follows:

Denote the scanning matrix of the 2 ⁿ -order double helix filling curve as H ₂ ⁿ , and $h_2=\left[\begin{array}{cccc}1& 2& 3& 4\\ 14& 13& 12& 5\\ 15& 10& 11& 6\\ 16& 9& 8& 7\end{array}\right],$ Then the recursive algorithm for constructing the double helix filling curve scanning matrix is as follows:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}& {\mathrm{<span\; class="notranslate">\; 4</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; h</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}\\ <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; 4</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; 4</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}\end{array}\right]\\ \left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; 4</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}\\ {\mathrm{<span\; class="notranslate">\; 4</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; h</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; 4</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}}_{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; )</span>\end{array}\right]\end{array}\right.$

In the formula: E is the identity matrix of the corresponding order; if k is an even number, the above formula is used, and if k is an odd number, the following formula is used. the

The tool path is drawn in one stroke from the beginning to the end, and the primitive in the form of a double helix is used to generate tool paths of different orders through the transformation formula, and the corner part of the tool path is processed by arcs, and then the mapping principle is used to obtain the curved surface The tool path above; the arc processing is that when the two tool paths are not on the same straight line, an inflection point will be formed, and an arc with a radius of r is used to connect the two tool paths for smooth processing. According to the residual height H and the effective cutting radius R of the tool are used to calculate the line spacing L that meets the requirements of surface machining accuracy, and r is calculated according to L; the radius of the transition arc is about r, and the applicable minimum radius formula is: L is the line spacing of the tool path. Specifically, as shown in Figure 5, the two tool trajectories form an inflection point because the two tool trajectories are not on the same straight line. The line spacing between adjacent paths in the figure is L, and if two tool paths are to be connected smoothly, the radius of the transition arc must be given reasonably. According to the line spacing and residual height of the tool track, if the distance D between the two ends of the arc is less than the line spacing L, the transition arc will be skipped directly, which does not play a role in smoothly connecting the tool track; when the radius of the arc is greater than the line spacing, the corresponding Overcutting will occur between adjacent tool paths, so the radius of the arc can be roughly set within this range. As shown in Figure 2, Then the arc radius we can choose is between [0.707L, L].

The line spacing is known according to different curved surfaces, residual heights and effective cutting radius of the tool: as shown in Figure 6, the line spacing of plane processing is: As shown in Figure 7, the line spacing of concave surface processing is: As shown in Figure 8, the line spacing of drawing processing is: Among them, L represents the line spacing between tool paths, R represents the effective cutting radius of the tool, h represents the residual height, and R _n represents the normal radius of curvature along the line distance direction.

The double-helix filling curve is generated on a two-dimensional plane, and the surface of the part to be processed is a complex free-form surface in space. It is necessary to use the mapping principle in Figure 3 to project the generated filling curve onto the surface. Thus, the tool path of the double-helix space-filling curve on the free-form surface is obtained. as shown in picture 2. the

Taking the generation of a specific Bezier freeform surface NC machining tool path as the force, a double helix tool path is generated. This curved surface is like a unimodal surface, which has both a surface with a sharp change in curvature and a top surface with a small curvature change, which can comprehensively judge the quality of CNC machining. Its control fixed-point coordinates are as follows:

Px=[100,140,140,100;180,190,190,180;230,220,230,220;310,270,270,310];

Py=[100,170,220,290;100,170,220,290;100,170,220,290;100,170,220,290];

Pz=[100,150,150,100;180,210,210,180;180,210,210,180;100,150,150,100];

Using MATLAB programming, the obtained Hilbert tool trajectory, double helix filling curve trajectory and improved double helix filling trajectory. Figure 4. the

Curve Type Tool path length (unit length) corner Fillet Hilbert fill curve 1.5905*10 ³ 50 0 double helix filling curve 1.5868*10 ³ 28 0 Improved double helix filling curve 1.1536*10 ³ 0 28

It can be clearly seen in Table 1 that the newly proposed method reduces the variation by about half. Compared with the improved Hilbert curve and double helix filling curve, the impact on the tool during processing is significantly reduced, which is conducive to improving the surface processing quality, and at the same time the length of the tool path is significantly reduced.

Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. the

Claims (5)

1. the method for numerical control (NC) machining tool path generation based on double helix space filling curve, is characterized in that, comprises the following steps:

Step 1, determines the exponent number of space filling curve according to residual height and curve form, generate the double helix space filling curve of the exponent number that meets the requirements on two dimensional surface;

Step 2, improves the corner part of cutter path, optimizes cutter path;

Step 3, thus according to mapping principle, two-dimentional space filling curve is mapped to and on space curved surface, obtains the cutter path in satisfactory digital control processing;

Described cutter path is for being from the beginning to the end unicursal one-tenth, and adopt the primitive of bifilar helix form, by transformation for mula, generate the cutter path of different rank, corner part in cutter path is carried out to circular arc processing, thereby re-use mapping principle, obtain the cutter path on curved surface.

2. the method for numerical control (NC) machining tool path generation based on double helix space filling curve according to claim 1, is characterized in that, described double helix space filling curve adopts matrix generating method, comprises the following steps:

The first step, first obtains primitive;

Second step, is subdivided into four different little squares again by each little square, and according to create-rule, connects the primitive of regional;

The 3rd step, repeats second step and constantly segments, and obtains the double helix space filling curve of different rank.

3. the method for numerical control (NC) machining tool path generation based on double helix space filling curve according to claim 2, is characterized in that, described create-rule is: F _k+1the space filling curve that represents current exponent number K+1 rank, F _kthe space filling curve on single order K rank in expression, by F _kformed square is subdivided into the little square of four equal sizes, when K is odd number, by F _kdwindle in the little square that is placed on the lower left corner, the space filling curve in the little square in the upper right corner is for being turned clockwise 90 ° of gained, and the space filling curve remaining in two little squares is that upper and lower symmetry obtains; When K when even number, by F _kdwindle in the little square that is placed on the upper left corner, space filling curve in the little square in the upper right corner is consistent with it, the lower left corner little square in space filling curve be the 90 ° of gained that turned clockwise, space filling curve in the little square in the lower right corner is for being rotated counterclockwise 90 ° of gained, obtain after four space filling curves in little square, with straight line level or the space filling curve that vertically connects in each little square, can obtain F _k+1space filling curve.

4. the method for numerical control (NC) machining tool path generation based on double helix space filling curve according to claim 1, it is characterized in that, described circular arc is treated to, when two cutter paths are not on same straight line, to form a flex point, with the circular arc that a radius is r, connect two cutter rails it is carried out to round and smooth processing, according to residual height h and the effective radius of clean-up R of cutter, calculate and learn the line-spacing L that meets surface machining accuracy requirement, according to L, calculate and learn r.

5. the method for numerical control (NC) machining tool path generation based on double helix space filling curve according to claim 4, is characterized in that, the radius size of described transition arc is about r, and wherein, applicable least radius formula is: described L is the line-spacing of cutter path.