A high-precision global fitting method and device based on dominant points

Abstract

The application discloses a high-precision global fitting method and device based on dominant points, relates to the technical field of computer numerical control machining, and specifically comprises the following implementation steps: firstly, taking the cubic polynomial fitting error as the core basis, dominant points in a tool tip point set are adaptively screened; secondly, according to a point error constraint condition, part of the tool tip points are supplemented as new dominant points through an iterative mode, and then an initial B-spline curve is generated; finally, based on a chord error constraint criterion, part of the midpoints of straight line segments are iteratively supplemented as dominant points, and finally, a target B-spline curve is constructed. The global fitting method effectively optimizes the continuity of the path and the degree of restoration of geometric characteristics under the premise of strictly guaranteeing machining precision, provides a high-quality data basis and technical support for subsequent feed speed planning, and is favorable for improving the overall machining efficiency.

Description

Technical Field

[0001] This invention relates to the field of computer numerical control machining technology, and in particular to a high-precision global fitting method and apparatus based on advantage points. Background Technology

[0002] In the field of modern computer numerical control (CNC) machining, toolpaths composed of numerous tiny straight line segments are widely used. However, such paths only maintain C-axis stability at the junctions of adjacent line segments. 0 Continuous acceleration and deceleration cause abrupt changes in the tool feed direction. To ensure machining accuracy and equipment safety, the CNC system must decelerate or even pause at each corner. The resulting frequent acceleration and deceleration significantly reduces machining efficiency and can easily induce machine tool vibration, affecting the surface quality of the workpiece.

[0003] To improve path smoothness, existing technical solutions mainly fall into two categories: local corner transition and global trajectory fitting. The local corner transition method achieves smoothness by inserting local smoothing curves at sharp corners of the path. While this method can control local transition errors analytically, in micro-segment machining scenarios, the large number of corners leads to a dramatic increase in CNC code size, and it only improves continuity in local areas, offering limited optimization for the curvature smoothness of the entire path.

[0004] Global fitting methods fit the original path to the whole using a high-order continuous parametric curve (such as a B-spline curve), which can fundamentally improve the smoothness of the trajectory and effectively compress the amount of data. However, this method still faces core challenges when facing high-precision machining requirements: First, to ensure the approximation accuracy of the fitted curve to the original tool position (i.e., point error), dense control points are often required, which contradicts the initial intention of reducing the amount of data; second, control point error alone is not enough to strictly guarantee machining accuracy, the maximum deviation between the fitted curve and the original micro-straight line segment (i.e., chord error) is also a key indicator, and existing methods generally lack a coordinated and efficient control mechanism for point error and chord error. This contradiction makes it difficult for existing global fitting methods to achieve the optimal balance between path smoothness, data simplicity, and machining accuracy. Summary of the Invention

[0005] The purpose of this invention is to provide a high-precision global fitting method and apparatus based on advantage points in order to solve the above-mentioned problems.

[0006] The present invention achieves the above objectives through the following technical solutions:

[0007] A high-precision global fitting method based on advantage points includes the following steps:

[0008] Step 1: Based on the cubic polynomial fitting error, adaptively select advantageous points from the set of knife tip points of the original micro-straight line segment path;

[0009] Step 2: Based on the point error constraint, iteratively add some tool tip points to the set of advantageous points, and generate node vectors and initial B-spline curves based on the updated set of advantageous points;

[0010] Step 3: Based on the chord error constraint, iteratively add the midpoints of some straight line segments to the set of dominant points, and update the node vector based on the updated set of dominant points to obtain the final B-spline curve, so as to complete the global fitting of the original micro-straight line segment path.

[0011] Preferably, step one specifically includes:

[0012] Set of knife tip points Perform arc length parameterization for each tool tip point. Assign parameter value ;

[0013] With the parameter value Based on this, the difference in the index of adjacent dominant points is adjusted. And calculate the cubic polynomial fitting error within the corresponding parameter interval. If the fitting error is less than a given threshold... If the difference in the indices of adjacent dominant points is increased, then the difference in the indices of adjacent dominant points is decreased; otherwise, the difference in the indices of adjacent dominant points is decreased, thereby dynamically determining the set of dominant point indices. and a collection of advantages .

[0014] Preferably, step two, "iteratively supplementing some tool tip points according to point error constraints," includes:

[0015] Calculate each tool tip point To the initial B-spline curve Upper projection point distance ;

[0016] If distance exists Greater than the point error threshold The tip of the blade is then selected from the error (i.e., The largest blade tip point is added to the set of advantageous points. :

[0017] Regenerate the node vectors and calculate the new initial B-spline curve based on the least squares method;

[0018] Repeat this process until the point errors of all tool tip points satisfy the point error constraints. There is a slight difference between point error and chord error. For tool tip points, the projection distance from the point to the curve is the point error. In the estimation of chord error, the projection distance from some points to the curve or line is also involved. The projection distance at this time is a component of the chord error, but it is not the point error in the fitting process.

[0019] Preferably: the blade tip point Projection parameters on the B-spline curve The solution is obtained using Newton's iteration method, and the iterative formula is as follows:

[0020]

[0021] Wherein, the initial value of the iteration Set as the arc length parameter of the tool tip. .

[0022] Preferably, step three, "iteratively supplementing the midpoints of some straight line segments according to the chord error constraint," includes:

[0023] For each line segment Estimate the chord error between it and the initial B-spline curve. ;

[0024] If the chord error Greater than the chord error threshold Then the midpoint of the line segment Add the new tooltip point and advantage point to the corresponding set; update the node vectors and recalculate the B-spline curve;

[0025] Repeat this process until the estimated chord errors for all line segments satisfy the chord error constraints.

[0026] Preferably: the chord error The forecast is achieved by dividing it into two parts:

[0027] Part One For the corresponding chord on the B-spline curve The bow height error is calculated using the curvature circle approximation method:

[0028]

[0029] in, For B-spline curves in parameters The radius of curvature at that point;

[0030] Part Two a straight line segment With string The distance between them, by the tip of the blade and Project it onto the chord and approximate it by taking the maximum projection distance;

[0031] The chord error Forecast is and sum.

[0032] A high-precision global fitting device based on advantage points for micro-straight-line paths includes:

[0033] The advantage point initial selection module is used to adaptively select advantage points from the set of knife tip points of the original micro-straight line path based on the cubic polynomial fitting error.

[0034] The initial fitting module is used to iteratively add some blade tip points to the set of advantageous points according to the point error constraint, and generate node vectors and initial B-spline curves based on the updated set of advantageous points;

[0035] The fine fitting module is used to iteratively add the midpoints of some straight line segments to the set of dominant points according to the chord error constraint, and update the node vector based on the updated set of dominant points to obtain the final B-spline curve.

[0036] A CNC machining equipment includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the method described above.

[0037] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described above.

[0038] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0039] 1. By employing dual iterative constraints of point error and chord error, the overall deviation between the fitted curve and the original path is precisely controlled, fundamentally ensuring processing accuracy. Simultaneously, based on the adaptive selection of advantageous points using cubic polynomial fitting error, the geometric features of the path can be better restored with fewer control points.

[0040] 2. Replacing discrete micro-straight line segments with high-order continuous B-spline curves completely eliminates speed fluctuations and machine tool impacts at corners, laying a solid foundation for implementing high-speed, smooth feed rate planning and effectively improving machining efficiency and surface quality.

[0041] 3. Replacing a massive number of micro-segment instructions with a simple parametric curve significantly reduces the amount of CNC code data and lowers the system's transmission and computational burden. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 This is a schematic diagram of chord error prediction.

[0044] Figure 2 This is a flowchart of a high-precision global fitting method based on advantage points as described in this invention.

[0045] Figure 3 This is a straight line segment path listed in Embodiment 2 of the present invention.

[0046] Figure 4 These are the advantages and initial B-spline curves determined in steps S1 and S2 of Embodiment 2 of the present invention.

[0047] Figure 5 These are the advantages determined in step S3 of Embodiment 2 of the present invention and the final B-spline curve.

[0048] Figure 6 This refers to the point error of the final B-spline curve in Embodiment 2 of the present invention.

[0049] Figure 7 This is the chord error of the final B-spline curve in Embodiment 2 of the present invention. Detailed Implementation

[0050] The present invention will be further described below with reference to the accompanying drawings:

[0051] Example 1

[0052] like Figure 2 As shown, a high-precision global fitting method based on dominant points first selects some of the tool-tip points of the micro-straight line path as dominant points based on the cubic polynomial fitting error. Then, according to the point error constraint, some tool-tip points are gradually added as new dominant points, thereby generating node vectors and initial B-spline curves. Finally, a chord error upper bound prediction method is designed, and based on this, the midpoints of some straight line segments are added as dominant points, thereby updating the node vectors and determining the final B-spline curve.

[0053] The specific steps are as follows:

[0054] Step 1: Adaptively select the dominant point among the blade tip points based on the cubic polynomial fitting error.

[0055] Let the tip of the knife be on the given straight line path. First, the sampling arc length parameterization method assigns parameters to each tool tip point as follows:

[0056]

[0057] in It is the sum of the lengths of all line segments in the toolpath, i.e. To fit the original straight line path using a B-spline curve with fewer control points, some points are selected as dominant points at the tool tip. This invention selects dominant points based on the fitting error of a cubic function, and the specific process is as follows:

[0058] Sub-step 11: Initialize the sequence number Advantage point sequence set Number of advantages Given a lower bound for the difference in the indices of adjacent dominant points. and upper limit Initialize the difference in the indices of adjacent dominant points. .

[0059] Sub-step 12: If Proceed to sub-step 13; otherwise, let and Proceed to sub-step 16.

[0060] Sub-step 13: Use a cubic polynomial function Fitting the set of knife tip points and its corresponding parameter set Calculate the fitting error .like Less than a given threshold Proceed to sub-step 14; otherwise, let Proceed to sub-step 15.

[0061] Sub-step 14: If and ,make If yes, proceed to sub-step 13; otherwise, proceed to sub-step 15.

[0062] Sub-step 15: Identify new advantages, let , , and Proceed to sub-step 12.

[0063] Sub-step 16: Determine the set of advantages ,in .

[0064] Step 2: Iteratively add dominant points based on point error constraints to generate an initial B-spline curve.

[0065] Based on the parameters of the dominant point, the nodes in the initial node vector are generated using the averaging method as follows:

[0066]

[0067] in For the first The parameters for each advantage point are as follows: . The number of advantageous points, specifically Thus, the initial node vector is obtained. Subsequently, the control points of the initial B-spline curve were determined using the least squares method. as follows:

[0068]

[0069] in , , For definition in The B-spline basis functions are then used. Thus, the expression for the initial B-spline curve is obtained. .

[0070] To calculate the point error, the tool tip point needs to be determined. exist Projection point on ,Right now yes upper distance The nearest point. Should satisfy It can be initialized first as Then, Newton's iteration method is used for updating, and the calculation formula is as follows:

[0071]

[0072] This iterative process continues until... Stop when the time comes.

[0073] To effectively constrain point errors, this invention adds advantageous points according to the following process, thereby regenerating an initial B-spline with higher fitting accuracy. Repeating this process several times yields an initial B-spline curve that satisfies the point error constraints. The process for adding advantageous points is as follows:

[0074] Sub-step 21: Calculate the tool tip point exist Projection point on .

[0075] Sub-step 22: For ,calculate and Distance between .like ,in Given an upper limit for error, let Otherwise, let .

[0076] Sub-step 23: If Determine the maximum error ,Will Add to the set of advantages If the condition is met, proceed to sub-step 24; otherwise, proceed to sub-step 25.

[0077] Sub-step 24: Determine if satisfied Serial number To satisfy Serial number Corresponding marker Proceed to sub-step 23.

[0078] Sub-step 25: Based on the new set of advantages Regenerate node vectors And generate the initial B-spline curve. .

[0079] Step 3: Iteratively add dominant points based on the chord error constraint to generate the final B-spline curve.

[0080] Chord error refers to the deviation between a straight line segment and a B-spline curve. To effectively constrain chord error, it is first necessary to make a reasonable estimate of it. For example... Figure 1 As shown, for the straight line segment Corresponding chord error First determine the tip of the blade. and In the initial B-spline curve Projection point on and String error Divided into two parts ,in Represents the initial B-spline curve Upper Wind Bow height error, This represents a line segment. and line segments The distance between them. This invention uses the curvature circle approximation method to predict. The calculation formula is as follows:

[0081]

[0082] in for exist The curvature at a given point is calculated using the following formula:

[0083]

[0084] Point the tip of the knife and Projected onto line segment Above, the projection point is obtained. and as follows:

[0085]

[0086] but It can be approximated as:

[0087]

[0088] Then, check each straight line segment. Corresponding chord error .like , then a new point on the original straight line segment path will be added. Also considered as the blade tip point, the parameter is denoted as Simultaneously, this point is also considered a dominant point, and the node vector is regenerated. The initial B-spline curve is then updated based on the least squares method. The process of chord error estimation, dominant point supplementation, and curve updating is repeated until the estimated chord errors of all line segments meet the chord error constraints, or the preset maximum number of iterations is reached, ultimately obtaining a B-spline curve that meets the accuracy requirements.

[0089] Furthermore, this embodiment also discloses a high-precision global fitting device based on advantage points for micro-straight-line paths, comprising:

[0090] The advantage point initial selection module is used to adaptively select advantage points from the set of knife tip points of the original micro-straight line path based on the cubic polynomial fitting error.

[0091] The initial fitting module is used to iteratively add some blade tip points to the set of advantageous points according to the point error constraint, and generate node vectors and initial B-spline curves based on the updated set of advantageous points;

[0092] The fine fitting module is used to iteratively add the midpoints of some straight line segments to the set of dominant points according to the chord error constraint, and update the node vector based on the updated set of dominant points to obtain the final B-spline curve.

[0093] Furthermore, this embodiment also discloses a CNC machining equipment, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the method described above.

[0094] Furthermore, this embodiment also discloses a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method described above.

[0095] Example 2

[0096] A high-precision global fitting method based on advantage points for micro-straight paths is proposed in this embodiment. The method uses a butterfly-shaped path (e.g., consisting of 1264 knife-edge points and 1263 micro-straight line segments) as an example. Figure 3 Taking the example shown, the implementation process of the present invention will be described in detail. A given point error threshold... =0.02mm, threshold value for cubic polynomial fitting error =0.001mm.

[0097] The specific steps include:

[0098] S1: Adaptively select initial advantage points based on cubic polynomial fitting error.

[0099] First, the original set of knife tip points... Perform arc length parameterization. Calculate the total path length. And accordingly, assign parameter values ​​to each tool tip point according to formula (1). .

[0100] Subsequently, the adaptive advantage selection process is executed:

[0101] Initialization: Set the starting sequence number Advantage point sequence set The initial value of the difference in the index of adjacent dominant points 5. Lower limit upper limit .

[0102] Execute in a loop: for the current sequence number In the interval [ , Within the range, a cubic polynomial function is used to fit the corresponding blade tip point, and the maximum fitting error is calculated.

[0103] If the fitting error is less than =0.001mm, and < And if the end of the path has not been reached, then let = +1, continue trying to expand the fitting interval.

[0104] If the fitting error exceeds the threshold or the interval cannot be expanded further, then the current valid maximum interval endpoint index will be changed. 1. Add to the advantage set A and update = 1. Simultaneously reset .

[0105] Ultimately, 125 initial advantage points were selected from 1264 blade tip points, such as... Figure 4 As shown by the solid black dots in the image.

[0106] S2: Iteratively supplement dominant points based on point error constraints to generate an initial B-spline curve.

[0107] First, based on the 125 dominant points and their parameters obtained in step S1, the initial node vector U is generated using the averaging method (Formula (2)). Then, the initial B-spline curve is calculated using the least squares method (Formula (3)). control points, to obtain as follows Figure 4 The initial fitting result is shown by the blue curve in the middle.

[0108] Next, iterative optimization of the point error constraint is performed:

[0109] s21: For each blade tip point The method of Newton's iteration (formula (4)) is used to calculate its value at 10 ... Projection point on initial parameters The iteration termination condition is .

[0110] s22: Calculate the projected distance of all tool tip points .

[0111] s23: Find the largest error among them .like = 0.02mm, then the corresponding cutting tip point Add to the advantage set

[0112] s24: To avoid numerical instability caused by inserting too many dominant points in local regions, the projection parameters are adjusted. Set the supplementary marker for the blade tip within a certain range to zero.

[0113] s25: Based on the new set of dominant points, regenerate the node vectors and calculate the new B-spline curve.

[0114] s26: Repeat steps s21-s25 until the point error of all tool tip points meets the requirements.

[0115] This embodiment, through this iterative process, has added a total of 27 advantages (such as...). Figure 4 (As shown by the solid red dots in the middle), and an initial B-spline curve that satisfies the point error constraint was obtained.

[0116] S3: Iteratively supplement the dominant points based on the chord error constraint to generate the final B-spline curve.

[0117] Based on the initial B-spline curve satisfying the point error constraint, the chord error between it and the original micro-straight line segment is further controlled.

[0118] For each line segment Estimate its chord error using the following steps. :

[0119] s31: Find the endpoint and exist Projection point on and .

[0120] s32: Calculate the bow height error Take the midpoint of the parameters The radius of curvature at that point is calculated according to formula (6). According to formula (5), calculate the chord of the B-spline curve itself. Bow height error .

[0121] s33: Calculate position deviation According to formula (7), the tip of the knife is... Projected onto line segment Above, the projection point is obtained. and According to formula (8), take and The larger value in is used as .

[0122] s34: Estimated total sine error: = + .

[0123] Check all straight line segments; if the estimated chord error of a certain segment is... Then the midpoint of the line segment As a new blade tip point (its parameters) Add to the advantage set.

[0124] Subsequently, the node vectors are updated, and the control points of the B-spline curve are recalculated using the least squares method to obtain the updated B-spline curve.

[0125] The process of chord error prediction and dominance point addition was repeated. In this embodiment, a total of 19 midpoints were added as dominance points (e.g., Figure 5 (As shown by the solid green dots), the final B-spline curve that satisfies both point error and chord error constraints is obtained, as shown below. Figure 5 As shown by the blue curve.

[0126] To verify the effectiveness of this invention, an error analysis was performed on the final obtained B-spline curve. For example... Figure 6 and Figure 7 As shown, the point errors of all tool tip points and the chord errors of all straight line segments are strictly less than the given threshold. =0.02mm. This indicates that the method described in this invention, while ensuring high precision, successfully fits a path composed of a large number of micro-straight line segments into a smooth, continuous high-order B-spline curve, significantly improving the geometric quality of the trajectory and laying a solid foundation for subsequent high-performance feed rate planning.

[0127] The foregoing has shown and described the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are only illustrative of the principles of the present invention. Various changes and modifications can be made to the present invention without departing from the spirit and scope of the present invention, and all such changes and modifications fall within the scope of the present invention as claimed.

Claims

1. A high-precision global fitting method based on advantage points, characterized in that, Includes the following steps: Step 1: Based on the cubic polynomial fitting error, adaptively select advantageous points from the set of knife tip points of the original micro-straight line segment path; Step 2: Based on the point error constraint, iteratively add some tool tip points to the set of advantageous points, and generate node vectors and initial B-spline curves based on the updated set of advantageous points; Step 3: Based on the chord error constraint, iteratively add the midpoints of some straight line segments to the set of dominant points, and update the node vector based on the updated set of dominant points to obtain the final B-spline curve, so as to complete the global fitting of the original micro-straight line segment path.

2. The high-precision global fitting method based on advantage points according to claim 1, characterized in that: Step one specifically includes: Set of knife tip points Perform arc length parameterization for each tool tip point. Assign parameter value ; With the parameter value Based on this, the difference in the index of adjacent dominant points is adjusted. And calculate the cubic polynomial fitting error within the corresponding parameter interval. If the fitting error is less than a given threshold... If the difference in the indices of adjacent dominant points is increased, then the difference in the indices of adjacent dominant points is decreased; otherwise, the difference in the indices of adjacent dominant points is decreased, thereby dynamically determining the set of dominant point indices. and a collection of advantages .

3. The high-precision global fitting method based on advantage points according to claim 1, characterized in that: Step two, "iteratively supplementing some tool tip points according to the point error constraint," includes: Calculate each tool tip point To the initial B-spline curve Upper projection point distance ; If distance exists Greater than the point error threshold If the blade tip point is the largest error, then the blade tip point with the largest error is selected and added to the set of advantageous points. : Regenerate the node vectors and calculate the new initial B-spline curve based on the least squares method; Repeat this process until the point errors of all tool tip points satisfy the stated point error constraints.

4. The high-precision global fitting method based on advantage points according to claim 3, characterized in that: The tip of the blade Projection parameters of the initial B-spline curve The solution is obtained using Newton's iteration method, and the iterative formula is as follows: Wherein, the initial value of the iteration The parameter value set for this tool tip point .

5. The high-precision global fitting method based on advantage points according to claim 1, characterized in that: Step three, "iteratively supplementing the midpoints of some line segments according to the chord error constraint," includes: For each line segment Estimate the chord error between it and the initial B-spline curve. ; If the chord error Greater than the chord error threshold Then the midpoint of the line segment Add the new tool tip point and dominant point to the existing tool tip point set and dominant point set; update the node vector and recalculate the B-spline curve; Repeat this process until the estimated chord errors for all line segments satisfy the chord error constraints.

6. The high-precision global fitting method based on advantage points according to claim 5, characterized in that: The chord error The forecast is achieved by dividing it into two parts: Part One For the corresponding chord on the B-spline curve The bow height error is calculated using the curvature circle approximation method: in, For B-spline curves in parameters Curvature at that point; Part Two a straight line segment With string The distance between them, by the tip of the blade and Project it onto the chord and approximate it by taking the maximum projection distance; The chord error Forecast is and sum.

7. A high-precision global fitting device based on advantage points, characterized in that, include: The advantage point initial selection module is used to adaptively select advantage points from the set of knife tip points of the original micro-straight line path based on the cubic polynomial fitting error. The initial fitting module is used to iteratively add some blade tip points to the set of advantageous points according to the point error constraint, and generate node vectors and initial B-spline curves based on the updated set of advantageous points; The fine fitting module is used to iteratively add the midpoints of some straight line segments to the set of dominant points according to the chord error constraint, and update the node vector based on the updated set of dominant points to obtain the final B-spline curve.

8. A CNC machining equipment, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 6.

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