CN102637216A - Method for generating numerical-control side milling machining tool path for complicated curved surfaces - Google Patents

Abstract

The invention discloses a tool path generation method for five-axis numerical control side milling of complex composite curved surfaces. In this method, the cross-section line is obtained by intersecting the cross-section plane and the combined surface, and the cross-section line is discretized into points according to a certain precision rule, and then the discrete points on each cross-section plane are fitted by B-spline curve interpolation. Lines are fitted to B-spline surfaces. Calculate the error between the fitted surface and the original combined surface. If the accuracy is not met, return to the curve discretization step, and perform discretization with higher accuracy, fit the curve, and fit the surface until the error of the fitted surface meets the accuracy requirements. Finally The tool path generation algorithm is beneficial to the combination of the overall control of the tool shaft swing angle and the local fine-tuning, and the fitted surface is used as the driving surface to calculate the machining tool path. The method has high efficiency and high precision, and solves the problem of tool path generation in side milling of combined curved surfaces. The tool shaft swings smoothly and evenly, and the processing quality is high.

Description

A tool path generation method for NC side milling of complex composite surfaces

technical field

The invention relates to a tool track generation method for five-axis numerically controlled side milling of complex combined curved surfaces, and belongs to the technical field of CAD (Computer Aided Design)/CAPP (Computer Aided Process Planning)/CAM (Computer Aided Machining). the

Background technique

With the development of CAD/CAM technology and the requirements of product performance, the geometric design of products is becoming more and more complex, and the requirements for manufacturing technology are also getting higher and higher. Composite surfaces refer to surfaces composed of multiple surfaces with common boundaries. More generally, surfaces can overlap, overlap or even have cracks. Composite curved surfaces are very common in aircraft structural parts, mainly due to the following reasons: (1) Due to the needs of part design, the digital model surface of parts is often composed of multiple irregular curved surfaces; (2) The curved surface has been cut several times , splicing and other processing, and finally become a combined surface; (3) due to the imperfect surface modeling function of the CAD system or when the product digital model is converted between different CAD/CAM systems, fragments, cracks and laps will appear between the surface pieces And so on. Due to the needs of product quality and appearance, it is often required to process the combined curved surface at one time to minimize the tool track contact marks on the surface and the boundary of the curved surface. The composite surface in aircraft structural parts mainly exists in the contour, which usually requires five-axis side milling to complete. Five-axis side milling methods generally include single-point offset method, double-point offset method and multi-point offset method. The above various five-axis side milling cutter path generation algorithms can achieve ideal results in the side milling of a single curved surface, which can already meet the general processing needs. However, for the common combination surface processing in the actual production process, it is necessary to artificially process the combination surface in advance. At present, the processing methods of composite surfaces usually adopt projection method, section plane method and surface triangle discretization method. However, the above methods are all proposed for the end milling of combined curved surfaces. There is little research on the processing of combined curved surfaces encountered in five-axis side milling, and there is no published method yet. the

Contents of the invention

The object of the present invention is to provide a complex curved surface side milling processing method that ensures fitting accuracy, improves processing efficiency, and automates work. the

A tool path generation method for CNC side milling machining of complex composite surfaces, comprising the following steps:

Step 1. Preprocessing the data: including the selection of composite surfaces, the selection of guide lines, the reading in of the distance between section planes, and the reading in of precision parameters; the selected composite surfaces are a group that conforms to a certain processing technology and can be processed as a whole surface; the selected guide line is a curve that runs through a certain parameter direction of the combined surface and is basically consistent with the direction of the surface;

Step 2. Generate a section plane equidistantly along the guide line, so that the normal direction of the section plane is consistent with the current tangential direction of the guide line: the rule for generating a section plane is to first generate equidistant points along the guide line, and obtain the current point The tangent direction of the guide line at the position, and then take this point as the center point, and use the corresponding tangent direction as the normal direction to generate a plane, thus obtaining a set of section planes along the tangent direction of the guide line;

Step 3, using the edge quartering method to approach the edge of the composite surface, supplementing the section plane; the edge quartering method is: 1) intersecting the section plane obtained in the above step 2 and the composite surface to obtain a series of section lines respectively, and The first sectional plane that intersects with the composite surface is called the effective sectional plane S ₁ ; 2) the sectional plane in front of the effective sectional plane S ₁ is called S ₀ ; 3) it is generated equidistantly between S ₀ and S ₁ 3 sectional planes S _a , S _b , S _c ; 4) Intersect the sectional planes S _a , S _b , S _c with the combined surface in turn, and take the obtained first effective sectional plane as the first one of the combined surface Section plane, use the obtained first section line as the first section line of the combined surface; 5) do the same for the end of the section plane family;

Step 4. For the group of section lines obtained in step 3, it needs to be discretized into data points, and the distance between the discrete points is determined by the equichord height error and the maximum discrete step length; through the discretization of the section lines, in each A set of points is obtained on the section plane, and the set of points is sorted to obtain a set of ordered point columns, and these discrete data points are fitted to a continuous B-spline curve by using the B-spline curve interpolation method;

Step 5, sorting and hierarchically processing the B-spline curves in step 4. The layering method is to calculate the distance between the first end point of the current section line and the first end point of the next section line, and the distance between the end point of the previous section line and the end point of the next section line, if any of the two distances If the set threshold is exceeded, the current section line will be used as the last section line of the first surface patch, and the next section line will be used as the first section line of the next surface patch;

Step 6. After obtaining the section lines of all sections, the masking method can be used to generate the B-spline surface. The masking method has the following requirements for the control curves: (1) the order of each control curve should be uniform; (2) all All section lines are required to have the same domain of definition; (3) All section lines have a unified node vector; (4) The end points of all section lines and segment points should be relatively close to the distribution along the arc length of the curve;

Step 7. Calculate the fitting error. If the error exceeds the allowable maximum error, return to step 4 to generate discrete points with higher precision, and re-fit the curve and surface until the error is less than the allowable error;

Step 8, using the fitted complete curve and surface as the driving surface to calculate the CNC machining tool path. the

The machining tool path generation of the present invention is based on the combination of the overall fan-shaped swing of the tool shaft and the local interference-removing fine-tuning. The initial direction vector of the tool axis is extracted from the left and right boundaries of the surface, and the angle between the direction vector is equally divided according to the number of tool positions, so that the tool axis swings at an equal angle along each tool position. At each tool position point, calculate the shortest distance between the tool axis and the leading line at the top of the surface. If the shortest distance is less than the tool radius, it means that overcutting occurs. Otherwise, undercutting occurs. Afterwards, the minimum distance point is offset along the normal direction of the surface by a tool radius distance, and the final tool axis vector is obtained by connecting the tool position point and the offset point. the

The method of the present invention can effectively solve the problem of tool trajectory generation in five-axis side milling of combined curved surfaces, and the beneficial effects obtained are as follows:

(1) Since the edge quartering method is used to approach the edge of the combined surface, the edge misalignment caused by the section plane method is partially offset, and the remaining misalignment can be eliminated by making an appropriate offset when generating the tool path;

(2) Due to the use of the discrete method combining the preset step size and the error of the equichord height, the balance between accuracy and data volume is effectively controlled, and discrete points are generated according to the preset step size where the curvature of the curve is small. Larger places adaptively encrypt discrete points to ensure fitting accuracy;

(3) Due to the layered fitting method, the fitting problem of the combined surfaces with irregular contours is effectively solved. Since the combined surface is divided into polygonal regular surfaces and the tool paths are generated separately, the situation of generating empty tool paths is avoided, and the processing efficiency is improved;

(4) It has the function of error judgment and automatic precision improvement, so it can ensure that the error between the fitted surface and the original combined surface is within the allowable range, and ensure that the generated tool path can meet the precision requirements. the

(5) The knife path generated by the tool path generation algorithm based on the overall fan-shaped swing of the tool shaft and local fine-tuning is uniform and stable, with small machining interference and high processing quality. the

Description of drawings

Fig. 1 is a flow chart of the present invention's five-axis side milling numerical control machining method for complex composite curved surfaces. the

Figure 2 is a schematic diagram of the generation of guide lines and section planes, in which L represents the guide line and S represents the section plane. the

Figure 3 is a schematic diagram of the edge quartering method. In the figure, S ₀ , S ₁ , and S ₂ are the 0, 1, and 2nd section planes, and S _a , S _b , and S _c are generated at equal distances between S ₀ and S ₁ section plane.

Figure 4 is a schematic diagram of the chord height error, in which P _i P _i-1 is the chord on the curvature circle, ρ _i is the curvature radius of the curve at the current point, and δ is the chord height.

Figure 5 is a composite surface of unlayered irregular contours. the

Figure 6 is a composite surface with irregular contours divided into upper and lower complete surfaces; C _k in the figure is the kth section line, and C _k+1 is the k+1th section line.

Fig. 7 is a schematic diagram of the fan-shaped swing method of the cutter axis. In the figure, Axi.0 and Axi.m are the first and last direction vectors of the cutter axis, and Δ _angle is the vector difference between the first and last direction vectors of the cutter axis.

Fig. 8 is a schematic diagram of the fine-tuning method for removing interference of the tool axis. In the figure, Axi.i is the tool axis direction vector of the tool position point P _i obtained by using the fan-shaped discrete method, and Axi.i' is the direction vector translated to the tool position point P _i . Axi.i” is the adjusted final tool axis direction.

Detailed ways

The technical scheme of the present invention is described in detail below in conjunction with accompanying drawing:

Fig. 1 is a flow chart of the five-axis side milling processing method for complex combined curved surfaces of the present invention, as shown in the figure, comprising the following steps:

The first is to select various elements, including combined surfaces and guide lines, and set various parameters, including the distance between section planes, the maximum discrete step size, and the maximum chord height error. As shown in Figure 2, the selected combined surface is a group of surfaces that conform to a certain processing technology and can be processed as a whole; the selected guide line is a curve that runs through a certain parameter direction of the combined surface and is basically consistent with the direction of the surface. The outer contour of the composite surface. The distance between the sectional planes depends on the size of the composite surface, generally 5-20mm. The maximum discrete step depends on the size of the combined surface, generally 5-20mm. The maximum string height error is generally 0.1mm. the

Then generate the sectional plane, the generation rule of the sectional plane is: 1) take data points along the guide line according to the preset sectional plane spacing; 2) obtain the tangential vector of the guide line on each data point in turn; The data point is the center point, and the tangent to the corresponding guide line is the normal vector to create a plane. A set of sectional planes along the tangent direction of the guiding line is thus obtained. the

One problem of using the sectional plane method is that the outline boundary of the combined surface cannot be accurately obtained, so the present invention proposes an edge quartering method to approach the boundary of the combined surface, as shown in FIG. 3 . The rules of the edge quartering method are: 1) intersect the sectional plane with the combined surface to obtain a series of sectional lines, and the first sectional plane that intersects the combined surface is called the effective sectional plane S ₁ ; 2) set S _1. The previous sectional plane is called S ₀ ; 3) Three sectional planes S _a , S _b , S _c are generated equidistantly between S ₀ and S ₁ , and the plane generation rules refer to the previous section; 4) The sectional plane S _a , S _b , S _c are intersected with the combined surface in turn, and the obtained first effective section plane is taken as the first section plane of the combined surface, and the obtained first section line is taken as the first section line of the combined surface Section line; 5) Do the same for the end of the section plane family.

After obtaining a set of section lines, since the section lines in each plane may be multiple curve segments or even discontinuous, it is necessary to first discretize the section lines into data points, and then fit them into a B-spline curve. The spacing between discrete points is determined by the equichord error and the maximum discrete step. As shown in Figure 3, the curvature circle of the curve at the i-th discrete point P _i is used instead of the curve. Since the discrete distance is small, the error caused by such processing can be ignored. According to the simple geometric relationship, the chord height error δ of the parametric curve is shown in formula (1).

$\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\sqrt{{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula: P _i P _i+1 is the chord length between the i-th discrete point and the i+1-th discrete point, ρ _i is the curvature radius of the curve at P _i , |P _i P _i+1 | Take a long walk.

Transform the above formula to get formula (2):

$<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

The above formula shows that the distance between the discrete points changes with the change of the radius of curvature and the height of the chord. The maximum allowable error of the chord height is Δ, and the maximum discrete step is iStep. The final discrete step is shown in formula (3):

$<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; iStep</span>}\\ \mathrm{<span\; class="notranslate">\; iStep</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; iStep</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Through the discretization of the section line, a set of points is obtained on each section plane, and this set of points is sorted to obtain a set of ordered point columns, and these discrete data points are fitted into a continuous line by using the B-spline curve interpolation method. The B-spline curve. The B-spline curve can be expressed by equation (4):

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In the formula, p(u) is the B-spline curve, u is the parameter value, n is the serial number of the curve segment, u _i is the node vector, d _i is the i-th control vertex; N _{i, k} (u) is k times B Spline basis functions. It can be seen from the above formula that the B-spline curve can be obtained only by obtaining the control vertices and node vectors. In general engineering applications, the third-order B-spline curve can meet the required smoothness requirements, and the calculation amount of the third-order B-spline curve is relatively small, so the present invention uses the third-order B-spline curve to interpolate the point sequence.

According to the B-spline curve interpolation algorithm, the first and last type value points are respectively used as the first and last points of the spline curve, and the inner type value points are sequentially used as the segmental connection points of the spline curve. At this time, the B-spline curve will be determined by n+1 control vertices d _i (i=0, 1, . . . , n), where n=m+2. The node vector is U=[u ₀ , u ₁ ,..., u _n+4 ], and the first and last segments are respectively 4 heavy nodes, that is, u ₀ =u ₁ =u ₂ =u ₃ =0, u _n+1 ＝u _n+2 ＝u _n+3 ＝u _n+4 ＝1, take normalization definition domain U∈[u ₃ , u _n+1 ]=[0, 1]. For type-valued points p _i (i=0,...,m), the parameterization method of normalized cumulative chord length parameterization is used to obtain the parameter sequence μ _j (j=0,...,m), as shown in formula (5).

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; p</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">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; |</span>}{\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; p</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">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; |</span>}\end{array}\right.<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Assign it to the corresponding node u _i+3 =μ _i (i=0,...,m) in the definition domain, so the node vector is shown in formula (6).

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0,1,2</span>}\\ {\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3,4</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 4</span>}\end{array}\right.$

Substitute the node values in the curve definition domain into the B-spline curve equation in turn, so that the B-spline curve passes through all interpolation points, as shown in the linear equation group (7):

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}}{\overset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3,4</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}\\ {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

表示P₀点处的切矢， 为P_m点处的切矢：  The above equation system contains m+1 equations in total, where m+1 is equal to n-1. In order to find n+1 control vertices, there are still 2 equations missing. The present invention adopts the endpoint tangent vector condition as an additional equation, such as formula (8), wherein

represents the tangent vector at point P ₀ , is the tangent vector at point P _m :

All the control vertices of the B-spline curve can be obtained by combining equations (7) and (8), and then a B-spline curve passing through all the model points can be obtained by fitting. the

After obtaining the section lines of all sections, the B-spline surface can be generated by using the masking method. The masking method has the following requirements for the control curves: (1) the order of each control curve should be uniform; (2) all the section lines are It is required to have the same domain of definition; (3) All section lines have a unified node vector; (4) For the sake of surface smoothness, the endpoints of all section lines and segment points should be distributed relatively close to the arc length of the curve . the

Since the cubic B-spline curve is uniformly used as the control curve interpolation, and the normalized definition domain is adopted, that is, the definition domain of all B-spline curves is [0, 1], so the B-spline curve fitted in the previous section is The first two requirements are met. the

For the 3rd requirement, the present invention adopts average node vector algorithm to determine common node vector, and the rule of this algorithm is to take common node vector as the average value of each section node vector, as shown in formula (9). the

$\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

Where U _j (j=0, 1, ..., s) is the node vector of each section B-spline curve obtained by fitting, s+1 is the number of sections, and U is the desired common node vector. This algorithm can be used to easily obtain the unified node vector, but it may cause no data points in some node intervals, which will cause no constraints on the curve segments in this interval, and abnormal situations will occur, so it is necessary to insert data in this node interval point. The rules for inserting data points are: 1) traverse all the node intervals under the common node vector, and find the node interval with zero data points; 2) take the midpoint of this node interval as the parameter value of the new data point, according to the fitted The obtained B-spline curve equation calculates the coordinates of a new data point, and this data point is added to the initial data point set.

Then, for the common node vectors and data points, the fitting method in the third section is used again to fit a set of cross-sectional B-spline curves with uniform degrees, uniform domains of definition and common node vectors. the

For the 4th requirement, the curved surface with regular rectangular shape naturally meets the requirements. For the irregular curved surface as shown in Fig. 5, the present invention adopts a layered fitting method, and the layered rule is: calculate the current section line and The distance between the first and the end points of the next section line. If there is a sudden change in the distance between the first and the end points (the threshold of the abrupt change is set to 10 times the distance between the section planes according to experience), this section line will be used as the last section line of the current surface patch. The next section line is used as the first section line of the next patch. In this way, the surface slices are layered at the places where the first and last segments change abruptly, as shown in Figure 6, and the combined surface with irregular contours is divided into two complete surfaces, the upper and the lower. As for the more special compound surface with special-shaped contours, it must be fitted after appropriate artificial processing in advance, so it will not be discussed. Finally, a series of B-spline curves with the same degree, domain of definition and node vectors, whose first and last sections are close to each other, is used to obtain a complete and continuous entire surface using the masking method. the

After fitting an overall surface, analyze the error between the original combined surface and the fitted surface. The error analysis function is generally provided by CAD/CAM software and can be used directly. If the maximum error obtained by the analysis exceeds the error requirement, return to the step of discretizing the cross-section line and reduce the discretization interval until a surface that meets the accuracy requirements can be fitted. Finally, this surface can be used as the driving surface to generate the CNC machining tool path. the

The tool path generation algorithm is based on the combination of overall fan-shaped swing of the tool axis and local interference-free fine-tuning. As shown in Figure 7, the initial direction vector of the tool axis is extracted from the left and right boundaries of the curved surface, recorded as Axi.0 and Axi.m, and the difference between Axi.0 and Axi.m is Δ _angle , then Δ _angle = Axi.m- Axi.0, as shown in Figure 8. Divide the included angle of the direction vector equally according to the number of tool points, so that the tool axis swings at an equal angle along each tool point. Suppose there are tool points P _i , i=0, 1..., m, m+1 in total, then the tool The tool axis direction vector corresponding to point P _i should be Axi.i=Axi.0+(i/m)Δ _angle , and this direction vector is translated to P _i point to obtain the initial tool axis direction vector Axi.i'. At the tool position point P _i , calculate the shortest distance between the initial tool axis and the guide line at the top of the surface and get the minimum distance point, which is recorded as Q _i , if the shortest distance is less than the tool radius, it means that gouge interference occurs, otherwise, it means that it occurs undercut. If interference occurs, the minimum distance point Q _i is offset by a distance of one tool radius along the normal direction of the surface, which is recorded as point Q _i ', and the final tool axis can be obtained by connecting the tool position point P _i and the offset point Q _i ' Vector Axi.i". Using the above method to calculate the tool axis vector of each tool position point, the complete machining tool path can be obtained.

The above embodiments are only to illustrate the technical ideas of the present invention, and can not limit the protection scope of the present invention with this. All technical ideas proposed in accordance with the present invention, any changes made on the basis of technical solutions, all fall within the protection scope of the present invention. Inside. the

Claims (5)

1. the NC side milling knife rail generating method of a complex combination curved surface is characterized in that, may further comprise the steps:

Step 1, data are carried out pre-service: comprise choosing of composite surface, the choosing of guide line, the reading in of the reading in of cutting plane spacing, discrete precision; Selected composite surface is a suite face that meets certain processing technology, whole processing; Selected guide line is one to be run through the some parametric directions of composite surface and moves towards the curve of basically identical with curved surface;

Step 2, generate cutting plane equidistantly along guide line; Make the normal direction of cutting plane consistent with the tangential of current guide line: the rule that generates cutting plane is to generate equidistant point along guide line earlier; And try to achieve the tangential direction of guide line on the current point position; Being central point with this point then, is that normal direction generates the plane with the tangential direction of correspondence, obtains one group of cutting plane along the guide line tangential direction thus;

Step 3 utilizes the edge inquartation to approach the composite surface edge, replenishes cutting plane; Said edge inquartation is: 1) cutting plane that obtains in the above-mentioned steps 2 and composite surface are asked friendship, obtain a series of section lines, have the cutting plane of intersection to be called effective cutting plane S first and composite surface ₁2) with effective cutting plane S ₁The cutting plane in front is called S ₀3) at S ₀And S ₁Between 3 cutting plane S of equidistant generation _a, S _b, S _c4) with cutting plane S _a, S _b, S _cAsk friendship with composite surface successively, with first effective cutting plane of trying to achieve first cutting plane, with article one section line of first section line of trying to achieve as composite surface as composite surface; 5) same processing is also done at the end of cutting plane family;

Step 4, to one group of section line that step 3 obtains, need it be separated into data point, the spacing between the discrete point is confirmed by largest chord high level error and maximum discrete steps jointly; Through dispersing of pair cross-section line, on each cutting plane, obtained one group of point, this group point ordering is obtained one group of orderly point range, utilize the B-spline curves interpolation method data point that these are discrete to simulate continuous B-spline curves;

Step 5, to the B-spline curves of step 4 sort, layering handles; The method of layering is the distance of calculating between current section line head-end and next the bar section line head-end; And the distance between starting section line distal point and next the bar section line distal point; If any one in these two distances exceeds preset threshold; Then with the last item section line of current section line, with article one section line of next bar section line as next patch as first patch;

Step 6, after obtaining the section line in all cross sections, just can utilize masked method to generate B-spline surface, masked method has following requirement to the control curve: number of times of (1) every control curve will be unified; (2) all section lines all require to have identical field of definition; (3) all section lines all have unified knot vector; (4) should make the end points of all section lines and waypoint distribute more approaching along curve arc long;

Step 7, calculate error of fitting, allow maximum error, then get back to step 4, generate discrete point, and matched curve curved surface again with higher precision if error surpasses, up to error less than permissible error;

Step 8, the complete curved surface that obtains with match calculate numerical control machining knife rail as driving curved surface.

2. the NC side milling knife rail generating method of complex combination curved surface according to claim 1 is characterized in that the cutting plane spacing is 5-20mm in the above-mentioned steps 1.

3. the NC side milling knife rail generating method of complex combination curved surface according to claim 1 is characterized in that maximum discrete steps is 5-20mm in the above-mentioned steps 1.

4. the NC side milling knife rail generating method of complex combination curved surface according to claim 1 is characterized in that the largest chord high level error is 0.1mm in the above-mentioned steps 1.

5. the NC side milling knife rail generating method of complex combination curved surface according to claim 1; It is characterized in that cutter rail generating algorithm in the above-mentioned steps 8 utilizes the fan-shaped discrete method control of angle cutter shaft pivot angle; Utilize local interference checking fine setting cutter shaft pivot angle; Make the cutter rail cutter shaft swing uniform and stable of generation, machining interference is little.

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