Optimization method for five-axis machining linear track

Abstract

The invention discloses a five-axis linear track global geometric fairing method based on double-B-spline weaving. Control points of double B splines are sequentially assigned to weave a cutter center point and a rotating shaft spline curve under the constraint of contour errors, so that the global fairing of a five-axis linear track is realized; the two spline curve tracks establish a relation through a normalized arc length ratio (ALP), and the smoothness of tool motion is ensured on the premise of considering the original tool posture. According to the method, the calculation process is simple and efficient, iterative optimization is not needed, and the requirement of an industrial scene for real-time performance can be met.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of numerical control machining, in particular to a method for optimizing linear trajectory of five-axis machining. BACKGROUND

[0002] In five-axis NC machining trajectory optimization, as a typical smoothing method, global smoothing can significantly improve the geometric continuity of the trajectory (such as from G0 to G2 continuity) by reconstructing discrete small line segment trajectories into continuous spline curves (such as B-spline or NURBS), thereby improving the quality of the machined surface and the motion smoothness.

[0003] The existing global smoothing method generally determines the spline curve through fitting, but the strategy of global fitting needs to balance the fitting accuracy and curve smoothing through multiple rounds of iterative optimization. Especially when dealing with high-density data points or complex trajectories, frequent adjustment of constraint conditions and control error will greatly increase the computational load, making it difficult to meet the efficiency requirements in the five-axis machining scene with high real-time requirements.

[0004] Another key challenge of global smoothing method in five-axis trajectory optimization is to construct the parameterization synchronization relationship of tool center displacement spline and tool axis direction vector spline synchronously. The essence is to ensure the motion smoothness of the tool center point trajectory and the tool axis vector trajectory while strictly meeting the geometric contour error constraint. SUMMARY

[0005] Based on the problems existing in the above global smoothing method, the present application provides a five-axis linear trajectory global geometric smoothing method based on double B-spline weaving. By assigning the control points of double B-spline to weave tool center point and rotation axis spline curve under the contour error constraint, the global smoothing of five-axis linear trajectory is realized; the two spline curve trajectories are related through normalized arc length proportion (ALP), which ensures the smoothness of tool motion under the consideration of original tool posture. The calculation process of this method is simple and efficient, and does not need iterative optimization, which can meet the real-time requirements of industrial scenes.

[0006] The present application is realized by the following technical scheme: a five-axis linear trajectory global geometric smoothing method based on double B-spline weaving, comprising the following steps: S1, obtaining the position vector of the tool center point of the five-axis machining tool from the G code file and the tool direction vector .

[0007] S2, if the number of five-axis linear trajectories obtained in S1 meets the requirements of the preset value, then enter S3, otherwise, return to S1.

[0008] S3, convert a series of tool direction vectors to rotation axis angle coordinates using the following formula.

[0009] S4, a series of tool center point position vectors Global fairing of B-spline curve is performed.

[0010] S5, a series of rotation axis position vectors Global fairing of B-spline curve is performed.

[0011] S6, for two spline curve trajectories, a relationship is established by arc length ratio.

[0012] S3 further comprises: The tool direction vector is expressed as For an AC-axis cradle five-axis machine tool, the tool direction vector can be converted into the coordinates of the rotation axis AC of the five-axis machine tool through the kinematics relationship of the five-axis machine tool, and the expression is as follows: Step 4 further comprises: A k-order uniform B-spline can be defined as: Wherein is the number of control points ; is a series of k-order B-spline basis functions, which can be defined as: Wherein is the node vector of the uniform B-spline, which can be expressed as .

[0013] For a cubic uniform B-spline ( ), the node vector can be written as , and the parameter of which ranges from .

[0014] Considering the local modification characteristics of the B-spline, the curve segment of the cubic uniform B-spline in the interval is determined by only four control points: , , and . The calculation of the curve segment is further expressed as: The present application takes the continuous four points as the fairing unit , and the middle line segment in the fairing unit is the target line segment to be faired. Among them, the first and third B-spline segments and Respectively smoothing Half of the corner on both sides; second B-spline segment For replacement Middle part.

[0015] The number of B-spline segments inserted in each unit (3 to 1 segments) depends on The length of the inner to be smoothed It should be noted that adjacent units share 3 common G01 points, for example, the last three points 、 、 And In unit The first three points 、 And Coincide with the first three points in unit Therefore, the smoothing of the entire trajectory can be achieved by sequentially smoothing the line segments In each unit, and supplementing the smoothing of the first and last linear path segments. The invention refers to this process of replacing line segments with B-spline segments in sequence and finally forming a whole uniform B-spline as weaving of spline curve.

[0016] S5 further comprises: Rotary axis trajectory Smooth in the machine coordinate system. The inserted rotary axis B-spline is defined by the following elements: basis function Control points And order Its mathematical expression is as follows: S6 further comprises: The invention proposes a double B-spline synchronous control method based on the arc length ratio relationship, aiming to realize the Continuity between tool motion and tool direction motion, so as to ensure the feed speed planning of each mechanical axis of the machine tool under the jerk constraint condition.

[0017] Suppose Is a set of linear tool center point trajectories Sampled on a fixed step , while the corresponding sampling points on the rotary axis linear trajectory Need to be determined according to the following linear equation: Where And Is a set of corresponding five-axis G01 points . And Are line segments And rotary axis segments on the linear trajectory. The ALP at a point on the linear trajectory can be defined as: where is the subscript of the tool center line segment containing the sampling point . and are the start point and end point of the segment group respectively. Similarly, the ALP at a point on the fairing B-spline can be defined as: where is the arc length of the B-spline from to , and are the start point and end point of the whole B-spline curve.

[0018] The sampling points on the linear tool center point trajectory (with ) and the points on the fairing B-spline are corresponding points with the same ALP value, i.e. . The points on the linear rotation axis trajectory and the B-spline trajectory for the rotation axis fairing also satisfy this correspondence, i.e. . Therefore, the synchronization relationship between the tool center point B-spline and the rotation axis B-spline can be determined by the following steps: S1, sampling the linear tool center point trajectory with a fixed step to obtain ; S2, calculating the corresponding points on the linear rotation axis trajectory by the above formula; S3, calculating the ALP values of and respectively, and taking them as the ALP values of the corresponding points and on the two B-spline curves.

[0019] Since the sampling points on the linear trajectory have a corresponding relationship with , the points on the corresponding B-spline also naturally have a corresponding relationship with . It can be inferred that these paired ALP values can be directly used to establish the discrete synchronization relationship between the tool center point B-spline and the rotation axis B-spline, without the need to accurately locate the point coordinates on the B-spline. The finally obtained discrete synchronization relationship is mapped as: Compared with the prior art, the present invention has the following advantages and beneficial effects: Under the premise of strictly ensuring the accuracy of machining contours and the coordination of tool movement, a non-iterative "double B spline weaving" mechanism based on direct assignment of control points and arc length correlation was used to achieve efficient global smoothing of five-axis linear trajectories, which significantly improved computational efficiency and met the urgent real-time requirements of industrial sites. Attached Figure Description

[0020] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of the global geometric smoothing method for five-axis linear trajectory based on double B-spline weaving of the present invention; Figure 2 This is a schematic diagram illustrating the B-spline smoothing principle of the tool center point trajectory in this invention. Figure 3 This is a schematic diagram illustrating the principle of B-spline smoothing of the rotation axis trajectory in this invention. Figure 4 This is a diagram showing the parameter synchronization relationship between the cutting center point and the smooth trajectory of the rotation axis in this invention; Detailed Implementation

[0021] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings, but the present invention can be implemented in many different ways as defined in the claims.

[0022] Example A global geometric smoothing method for five-axis linear trajectories based on double B-spline weaving, such as Figure 1 As shown, it includes the following steps: Obtain the position vector of the five-axis machining tool center point from the G-code file. and tool direction vector .

[0023] For unit Inner middle segment The smoothing (replacement of B-spline segments) is handled in three ways depending on the segment length.

[0024] Case 1: If line segment The length condition must be met: Where the threshold and The quantitative description will follow later. Three consecutive B-spline segments are required. , and Replacement is required, at which point 6 control points need to be solved. The location.

[0025] like Figure 2 As shown, and That is, unit The first and second line segments are also units. The second and third line segments can be represented as follows: and Corner From unit The final B-spline segment With unit The first B-spline segment Common smoothness. According to the above formula, and intersection It can be calculated using the following formula: If the preset maximum value of the tool center point trajectory smoothing error is ,but and The maximum distance can be defined as: Three control points to be determined , and It can be determined as follows: in , .

[0026] Case 2: If the middle line segment The length is insufficient, but the following conditions are met: Then the second B-spline segment needs to be removed. At this time, unit Will be and The two B-spline segments are smoothed, and their control points are: Five points were determined. The first three of these were control points. , and In the previous unit It was identified in the middle, but due to the processing Time assumption (Right now Since it is a long line segment, control points are required. Make corrections. Finally, control points. , and may be expressed as: wherein and may be modified as: and Case 3: If the middle line segment of a unit is short, satisfying: then the unit will only be smoothed by a B-spline segment determined by four control points . The first two control points and have been determined when the previous unit is processed, and the calculation formulae of the last two control points and are as follows: As shown in Figure 3 , the determination method of the rotation axis B-spline control point is the same as that of the tool tip point B-spline control point in principle, and only needs to convert the G01 point from the coordinate point in the three-dimensional space into the rotation axis angle in the two-dimensional space, that is, it can be done.

[0027] By linearly connecting the discrete synchronization relationship points , the first-order continuous kinematic relationship between the tool center point B-spline and the rotation axis B-spline can be obtained. However, such tool center point motion with only continuity cannot support smooth machine tool motion with bounded jerk. Therefore, the present application introduces a second-order sliding convolution window to improve the continuity of the double B-spline synchronization relationship. In order to realize the overall continuity of the five-axis smoothing trajectory, a second-order convolution window function is used to smooth the linear synchronization relationship, which can be expressed as: In the formula, is a spatial domain variable, represents the length constant of the convolution window.

[0028] As shown in Figure 4 , the function formed by linearly connecting the discrete points is regarded as the initial function to be smoothed, and the second-order window function is applied to the points on the initial function ​convolution operation, the smoothed points may be expressed as: wherein and is a linear function of the line on which the convolution window boundary lies is the subscript of and denotes the domain of the th linear function . By sliding the convolution window from the starting point to the end point , a function with continuity can be generated.

[0029] The present application takes "non-iterative, direct weaving, arc length synchronization" as the core, significantly improves the calculation efficiency of five-axis linear trajectory global smoothing under the premise of ensuring processing precision and motion smoothness, solves the key pain points of poor real-time performance and difficult attitude synchronization of traditional methods, and has significant industrial application value.

[0030] Although the embodiments of the present application have been shown and described, those skilled in the art can understand that various changes, modifications, replacements and variations can be made to these embodiments without departing from the principles and purposes of the present application, and the scope of the present application is defined by the claims and their equivalents.

Claims

1. An optimization scheme for five-axis machining linear trajectories, characterized in that The method comprises the following steps: (1) Obtain the position vector of the tool nose point of the five-axis machining tool from the G code file and the tool direction vector ; (2) If the number of five-axis linear trajectories acquired by S1 meets the requirement of the preset value, S3 is entered, otherwise, S1 is returned; (3) A series of tool direction vectors are converted into the rotary axis angle coordinates by using the following formula: (4) The position vector of the tool center point Global fairing of B-spline curve; (5) the position vector of the rotating shaft global fairing of B-spline curve; (6) For two spline curve trajectories, a relationship is established by using the arc length ratio.

2. According to step (3) of claim 1, characterized in that: (1) The tool direction vector is expressed as For the AC-axis cradle five-axis machine tool, the tool direction vector can be converted into the coordinates of the rotating axis AC through the kinematics of the five-axis machine tool, and the expression is as follows: 。 3. According to step (4) of claim 1, characterized in that: (1) The k-order uniform B-spline can be defined as: ， wherein is a control point of the number; is a series of B-spline basis functions of order B, which can be defined as: ， wherein is a node vector of uniform B-splines, which can be expressed as For cubic uniform B-splines ( ), the node vector can be written as In this case, the parameter ranges from ; (2) Considering the local modification property of B-spline, the cubic uniform B-spline curve segment in the interval is determined by only four control points: , , , and . The calculation of the curve segment is further expressed as: ； (3), the present application will be continuous 4 points As a fairing unit And the intermediate line segment in the fairing unit For the target line segment to be fairing. Wherein the first, third B-spline segment And Respectively fairing Half of the two sides of the corner; the second B-spline segment For replacing The middle part; (4) The number of B-spline segments inserted in each unit (3 to 1 segment) depends on The inner court is smooth The length. Adjacent cells share 3 common G01 points, for example, cell... The last three points , and With unit The first three points , and They overlap. Therefore, by sequentially smoothing the line segments in each unit... By smoothing the linear path segments at the beginning and end, the entire trajectory can be smoothed. This invention refers to the process of sequentially replacing line segments with B-spline segments to ultimately form a uniform B-spline as spline curve weaving.

4. The step (5) according to claim 1, characterized in that: Rotational axis trajectory The fairing is done in the mechanical coordinate system. The inserted rotational axis B-spline is defined by the following elements: basis functions , control points and degree , whose mathematical expression is as follows: 。 5. According to step (6) of claim 1, characterized in that: (1) Defining the sampling points on the linear tool center point trajectory (With ) the corresponding points on the smoothing B-spline are the corresponding points with the same ALP value, i.e. The rotation axis linear trajectory and the points on the B-spline trajectory for the rotation axis smoothing also satisfy this correspondence, i.e. Therefore, the synchronization relationship between the tool center point B-spline and the rotation axis B-spline can be determined by the following steps: S1, with a fixed step size sampling the linear cutter center point trajectory to obtain ; S2, calculating the corresponding point on the linear rotation axis trajectory by the above formula ; S3, respectively calculating the ALP values of the points on the two B-spline curves respectively, and taking them as the corresponding points on the two B-spline curves respectively the ALP values of the points (2) The discrete synchronization relationship is mapped as: 。

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