Local smoothing and parameter synchronization method for five-axis linear path based on spiral curve

Abstract

The application relates to the technical field of five-axis technology of numerical control machine tools, and discloses a five-axis linear path local smoothing and parameter synchronization method based on a spiral curve, wherein the transition length of a tool tip transition curve is determined according to a tool tip point approximation error and a segment length constraint condition; the transition length of a tool shaft transition curve is determined according to a tool shaft point approximation error and the segment length constraint condition; the actual trajectory displacement of the tool tip is taken as a shared parameter to realize parameter synchronization between the actual trajectory of the tool tip and the actual trajectory of the tool shaft; the control vertex distribution of the internal displacement B-spline in the adjacent three segments is optimized through a least square method, and only the control vertex distribution of the internal displacement B-spline in the first segment is reserved to obtain the optimal control vertex distribution of the internal displacement B-spline; the application can realize analytical calculation of the arc length of the smoothing curve, and the calculation efficiency is relatively high.

Description

Technical Field

[0001] This invention relates to the field of five-axis CNC machine tool technology, specifically to a method for local smoothing and parameter synchronization of a five-axis linear path based on a helical curve. Background Technology

[0002] In CNC machining, toolpaths generated by Computer-Aided Manufacturing (CAM) software typically consist of numerous discrete straight line segments, often exhibiting tangential discontinuities at their geometric junctions. Directly following the original path can lead to sudden speed changes and acceleration exceeding limits at corners, resulting in motion shocks and mechanical vibrations. To ensure machining smoothness, traditional control methods often require deceleration or even stopping at each transition point, significantly reducing overall machining efficiency. Therefore, local smoothing of toolpaths composed of continuous small line segments is a crucial approach to achieving high-speed, high-precision machining. Through trajectory smoothing and motion constraint optimization, corner pauses and speed fluctuations can be effectively eliminated, increasing feed rates while maintaining contour accuracy and surface quality. This has significant theoretical and engineering value for improving machining performance, accuracy, and surface finish.

[0003] Existing technology 1 (Wan M, Qin XB, Xiao QB, et al. Asymmetrical pythagorean-hodograph (PH) spline-based C3 continuous corner smoothing algorithm for five-axis tool paths with short segments[J]. Journal of Manufacturing Processes, 2021, 64: 1387-1411.) discloses a corner smoothing algorithm for five-axis machine tool paths based on PH spline curves. It constructs an asymmetric PH spline curve with high-order continuity and introduces adjustable variables by adding two additional control points. This allows for independent adjustment of the control points at both ends of the spline, making the spline asymmetric about the angle bisector. This allows for direct connection without linear segment transitions, while simultaneously ensuring synchronization between the tool tip and the tool posture. However, solving for PH spline curves is computationally complex, significantly increasing the computational load and making it difficult to meet real-time requirements.

[0004] Prior art 2 (Xiao QB, Wan M, Liu Y, Qin XB, Zhang W H. 2020. Spacecorner smoothing of CNC machine tools through developing 3D general clothoid[J]. Robotics and Computer Integrated Manufacturing, 64: 101949.) discloses a three-axis path smoothing method based on Clothoid curves, applicable to all types of commands G01, G02, and G03. This curve has the advantage of being able to analytically and accurately calculate approximate error, curvature, and arc length.

[0005] The core feature of the aforementioned existing technology lies in the fact that by employing different types of smoothing curves to smooth the tool path, a smooth trajectory with specific continuity is ultimately generated, and effective control of approximation errors is achieved. However, in the field of five-axis CNC machining, the technical solutions for achieving tool path smoothing using Clothoid curves are still relatively limited, and there is room for improvement in its parameter synchronization strategy, failing to fully leverage the inherent advantages of this curve in curvature, approximation error, and arc length analytical calculation. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method for local smoothing and parameter synchronization of a five-axis linear path based on a helical curve. By adjusting the tool tip position and tool axis position on the machine tool, smoothing of the five-axis tool linear path is achieved.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: A method for local smoothing and parameter synchronization of a five-axis linear path based on a helical curve includes: A spiral curve is inserted within the tool tip corner formed by two adjacent linear tool tip paths as a tool tip transition curve; a spiral curve is also inserted within the tool axis corner formed by two adjacent linear tool axis paths as a tool axis transition curve; the machine tool simultaneously controls the tool tip position and the tool axis position to achieve path smoothing. Based on the approximate error of the tool tip and the segment length constraint, determine the transition length of the tool tip transition curve; Based on the approximate error of the cutter axis point and the segment length constraint, determine the transition length of the cutter axis transition curve; The transition curve and a partial linear path are each treated as a segment, and the actual trajectory is formed alternately. The actual trajectory displacement of the tool tip is used as a shared parameter to achieve parameter synchronization between the actual trajectory of the tool tip and the actual trajectory of the tool axis: the displacement of the actual trajectory of the tool tip within the segment is used as a shared parameter, and the displacement of the actual trajectory of the tool axis within the current segment is uniformly expressed through the displacement B-spline. The control vertex distribution of the displacement B-spline within three adjacent segments is optimized using the least squares method, and only the control vertex distribution of the displacement B-spline within the first segment is retained, in order to obtain the optimal control vertex distribution of the displacement B-spline within the segment.

[0008] In one embodiment, the spiral curve is a Clothoid curve, with a pair of symmetrical Clothoid curves inserted as tool tip transition curves within the tool tip corner formed by two adjacent tool tip linear paths; and a pair of symmetrical Clothoid curves inserted as tool axis transition curves within the tool axis corner formed by two adjacent tool axis linear paths.

[0009] In one embodiment, determining the transition length of the tool tip transition curve based on the tool tip approximation error and segment length constraint specifically includes: ; in, The transition length of the tool tip transition curve at the i-th tool tip corner; and To form the linear paths of two adjacent tool tips at the i-th tool tip corner, Let i be the i-th blade tip point; This indicates calculating the path length. This indicates that for the i-th blade tip corner, given an approximate error... The transition length of the tool tip transition curve is obtained below; Represents the coefficient.

[0010] In one embodiment, for the i-th blade tip corner, given an approximation error... The transition length of the tool tip transition curve obtained below The expression is: ; Indicates the transition curve of the blade tip at Displacement components in orthogonal directions, Indicates the transition curve of the blade tip in Displacement components in the direction, The tangential direction at the midpoint of the tool tip transition curve and the linear path of the tool tip The included angle.

[0011] In one embodiment, determining the transition length of the tool axis transition curve based on the approximate error of the tool axis point and the segment length constraint specifically includes: ; in, The transition length of the tool axis transition curve at the i-th tool axis corner; and To form the linear paths of two adjacent tool axes at the i-th tool axis corner, This is the i-th tool axis point; This indicates calculating the path length. This indicates that for the i-th tool axis corner, given an approximate error... The transition length of the cutter shaft transition curve obtained below; Represents the coefficient.

[0012] In one embodiment, when i = 1, , When i=n, , When i = 2, 3, ..., n-1, , where n is the total number of tool tip corners or tool shaft corners.

[0013] In one embodiment, for the i-th tool axis corner, given an approximation error... The transition length of the cutter shaft transition curve obtained below The expression is: ; Indicates the tool axis transition curve at Displacement components in the direction; Indicates the tool axis transition curve at Displacement components in orthogonal directions; The tangential direction at the midpoint of the tool axis transition curve is linearly related to the tool axis. The included angle.

[0014] In one embodiment, the transition curve and the partial linear path are each treated as a segment, alternately forming the actual trajectory; the actual trajectory displacement of the tool tip is used as a shared parameter to achieve parameter synchronization between the actual trajectory of the tool tip and the actual trajectory of the tool axis: using the displacement of the actual trajectory of the tool tip within the segment as a shared parameter, the displacement of the actual trajectory of the tool axis within the current segment is uniformly expressed through a displacement B-spline, specifically including: The actual trajectory displacement of the cutter axis within the current segment is represented using a 5th order displacement B-spline: the node vector is designed as follows. Control vertex is to The actual displacement of the cutter axis trajectory within the current segment. Represented as: ; The total displacement of the actual trajectory of the tool tip within the current segment: ; ; Let be the arc length of the transition curve at the i-th corner of the actual trajectory of the blade tip. These are the characteristic parameters of the blade tip transition curve. ; The tangential direction at the midpoint of the tool tip transition curve and the linear path of the tool tip The included angle; Indicates the transition curve of the blade tip in Displacement components in the direction; Indicates the transition curve of the blade tip in The displacement components in the orthogonal direction; j represents the index of the control vertex, and P represents the degree of the displacement B-spline; Let u be the displacement B-spline basis function; u is the actual trajectory displacement parameter of the tool tip within the current segment. The first, second, and third derivatives of the displacement B-spline within adjacent segments are equal at the junction.

[0015] In one embodiment, the first, second, and third derivatives of the displacement B-spline within each segment at the junction point are: when hour: ; ; ; when hour: ; ; ; By setting the second and third derivatives at the junction points to zero, the relationship between the control vertices of the displacement B-spline is obtained: ; ; ; in, This represents the arc length of the transition curve at the i-th corner of the actual trajectory of the tool axis. ; These are the characteristic parameters of the tool axis transition curve. ; The tangential direction at the midpoint of the tool axis transition curve is linearly related to the tool axis. The included angle; Indicates the tool axis transition curve at Displacement components in the direction; Indicates the tool axis transition curve at Displacement components in orthogonal directions; It is an operation to calculate the distance between the control vertices of the displacement B-spline. and To form the linear paths of two adjacent tool axes at the i-th tool axis corner, is the transition length of the tool axis smooth curve at the i-th tool axis corner.

[0016] In one embodiment, the step of optimizing the control vertex distribution of the displacement B-spline within three adjacent segments using the least squares method, and retaining only the control vertex distribution of the displacement B-spline within the first segment, to obtain the optimal control vertex distribution of the displacement B-spline within the segment, specifically includes: The relative tangential velocity between the actual trajectory of the tool tip and the actual trajectory of the tool axis for: ; The relative tangential acceleration between the actual trajectory of the tool tip and the actual trajectory of the tool axis for: ; in, This represents the actual tangential velocity of the blade tip trajectory; This represents the tangential acceleration along the actual trajectory of the blade tip. Relative tangential acceleration Further expressed as: ; in, , They represent about The first and second derivatives; Sampling is performed within three adjacent segments of the actual tool axis trajectory. N sampling points are selected, and an objective function is established based on minimizing the relative tangential acceleration between each sampling point and the actual tool tip trajectory. The least squares method is used for constraint. ; in, It is a constant matrix. This represents the actual displacement parameter of the tool tip corresponding to the i-th sampling point. , , Let represent the first and second derivatives of the basis functions of the displacement B-spline curve within each segment, respectively. The control vertices of the displacement B-spline curve within each segment are represented. The control vertices of each segmented displacement B-spline are determined analytically, and parameter synchronization between the actual tool tip trajectory and the actual tool axis trajectory is achieved by sharing the actual tool tip trajectory displacement parameters.

[0017] Compared with the prior art, the beneficial technical effects of the present invention are: First, this invention utilizes Clothoid curve analysis to achieve approximate error constraints on the actual tool tip trajectory and the actual tool axis trajectory, and can also perform analytical calculations of the arc length of the smooth curve, resulting in high computational efficiency. Second, by sharing the displacement parameters of the actual tool tip trajectory, parameter synchronization is achieved while ensuring high-order continuity between the actual tool tip trajectory and the actual tool axis trajectory, avoiding abrupt changes in tool axis velocity and acceleration in five-axis machining, and enabling the tool axis direction to continuously change with the tool tip position. Finally, the least squares method is used to optimize the derivative value of the displacement B-spline at the connection point, thereby obtaining the optimal distribution of control vertices for the displacement B-spline. This is of great significance in improving machining efficiency and ensuring machining accuracy. Attached Figure Description

[0018] Figure 1 This is a flowchart of the method in an embodiment of the present invention.

[0019] Figure 2 This is a schematic diagram of the actual trajectory of the blade tip obtained by smoothing the linear path of the blade tip using a Clothoid curve in an embodiment of the present invention.

[0020] Figure 3 This is a schematic diagram of the actual trajectory of the tool axis obtained by smoothing the linear path of the tool axis using the Clothoid curve in an embodiment of the present invention.

[0021] Figure 4 This is a schematic diagram of the segmentation strategy of "transition curve-linear path-transition curve" in an embodiment of the present invention.

[0022] Figure 5 This is a schematic diagram of the actual trajectory displacement B-spline of the tool axis in an embodiment of the present invention.

[0023] Figure 6 This is a comparison chart of accelerations obtained using the method of this invention and the unsynchronized method. Detailed Implementation

[0024] A preferred embodiment of the present invention will now be described in detail with reference to the accompanying drawings.

[0025] like Figure 1 As shown, this invention discloses a method for local smoothing and parameter synchronization of a five-axis linear path based on a spiral curve, comprising the following steps: S1: Determine the transition length of the tool tip transition curve based on the approximate error of the tool tip and the segment length constraint; S2: Determine the transition length of the tool axis transition curve based on the approximate error of the tool axis point and the segment length constraint; S3: The actual trajectory displacement of the tool tip is used as a shared parameter to achieve parameter synchronization between the actual trajectory of the tool tip and the actual trajectory of the tool axis. The segmentation strategy of "transition curve-linear path-transition curve" is adopted. The displacement of the actual trajectory of the tool tip in the current segment is used as a shared parameter. The displacement of the actual trajectory of the tool axis in the current segment is uniformly expressed by the displacement B spline. S4: Optimize the control vertex distribution of the displacement B-spline within three adjacent segments using the least squares method, and retain only the control vertex distribution of the displacement B-spline within the first segment to obtain the optimal control vertex distribution of the displacement B-spline within the segment.

[0026] In one embodiment, step S1, determining the transition length of the tool tip transition curve based on the tool tip approximation error and segment length constraint, specifically includes: like Figure 2 As shown, a pair of symmetrical Clothoid curves are inserted within the corner formed by the linear path of the cutting edge to create the cutting edge transition curve. Considering the approximation error and segment length constraints, the transition length of the tool tip transition curve is: ; in, Let be the transition length of the tool tip transition curve at the i-th tool tip corner. and To form the linear paths of two adjacent tool tips at the i-th tool tip corner, , Indicates segment length constraints; This indicates calculating the path length. This indicates that for the i-th corner, given an approximation error... The transition length of the smooth curve obtained below; when i = 1, , When i=n, , When i = 2, 3, ..., n-1, n represents the total number of knife-edge corners.

[0027] The expression is: .

[0028] After determining the smooth transition length, the characteristic parameters of the tool tip transition curve are... It can be represented as: ; in, The tangential direction at the midpoint of the tool tip transition curve and the linear path of the tool tip The included angle; Indicates the transition curve of the blade tip in Displacement components in the direction; Indicates the transition curve of the blade tip in Displacement components in orthogonal directions; ; , This represents the integral variable.

[0029] In one embodiment, step S2, determining the transition length of the tool axis transition curve based on the approximate error of the tool axis point and the segment length constraint, specifically includes: like Figure 3 As shown, in a linear path formed by two adjacent tool axes and A pair of symmetrical Clothoid curves are inserted within the corner of the cutter axis to form the cutter axis transition curve. Transition length of the cutter shaft transition curve considering approximation error and segment length constraints. for:

[0030] in, and These are the two adjacent linear paths of the cutter axis that form the i-th cutter axis corner; This indicates calculating the path length. This represents the i-th tool axis corner of the actual tool axis trajectory within a given approximation error. The transition length of the cutter shaft transition curve obtained below; when i=1, , When i=n, , When i = 2, 3, ..., n-1, n represents the total number of corners along the linear path of the knife tip.

[0031] The expression is: .

[0032] After determining the transition length of the tool axis transition curve, the characteristic parameters of the tool axis transition curve are... It can be represented as ; in, The tangential direction at the midpoint of the tool axis transition curve is linearly related to the tool axis. The included angle; Indicates the tool axis transition curve at Displacement components in the direction; Indicates the tool axis transition curve at Displacement components in orthogonal directions; ; .

[0033] In one embodiment, step S3, which uses the actual trajectory displacement of the tool tip as a shared parameter to achieve parameter synchronization between the actual trajectory of the tool tip and the actual trajectory of the tool axis, specifically includes: The actual trajectory of the blade tip in this invention, also known as the smooth curve of the blade tip, is composed of a portion of the linear path of the blade tip. Knife tip transition curve Partial linear path of the blade tip composition.

[0034] The actual trajectory of the tool axis in this invention, also known as the tool axis smooth curve, is composed of a portion of the tool axis linear path. Tool shaft transition curve Partial tool axis linear path composition.

[0035] like Figure 4 As shown, a segmentation strategy of "transition curve-linear path-transition curve" is adopted. The displacement of the actual tool tip trajectory within the current segment is used as a shared parameter. The displacement of the actual tool axis trajectory within the current segment is uniformly expressed through displacement B-splines, specifically including: like Figure 5 As shown, a segmented strategy of "transition curve-straight line-transition curve" is adopted. The actual trajectory displacement of the tool axis within the current segment is represented by a 5th-order B-spline, and the node vector is designed as follows: Control vertex is Therefore, the displacement of the actual tool axis trajectory within the current segment... It can be represented as: ; in, This represents the actual trajectory displacement of the tool axis within the current segment, where j represents the control vertex. The serial number; is the basis function of the displacement B-spline; P represents the degree of the displacement B-spline; u is the actual trajectory displacement parameter of the tool tip within the current segment.

[0036] The total displacement of the actual tool tip trajectory within the current segment: ; ; Let be the arc length of the transition curve at the i-th corner of the actual trajectory of the blade tip.

[0037] To ensure high-order continuity of the actual tool axis trajectory after smoothing, the displacement B-splines within adjacent segments must be high-order continuous at the junction points. This means the first, second, and third derivatives of adjacent displacement B-splines at the junction points must be equal. The first, second, and third derivatives of the displacement B-splines within each segment at the endpoints are: when hour: ; ; .

[0038] when hour: ; ; .

[0039] To simplify the calculation, the second and third derivatives at the connection points are set to 0, thus revealing the relationship between the control vertices of the displacement B-spline: ; ; ; in, This involves finding the distance between the control vertices of the displacement B-spline.

[0040] This represents the arc length of the transition curve at the i-th corner of the actual tool axis trajectory. .

[0041] In one embodiment, step S4, which optimizes the control vertex distribution of the displacement B-splines within three adjacent segments using the least squares method and retains only the control vertex distribution of the displacement B-splines within the first segment to obtain the optimal control vertex distribution of the displacement B-splines within the segment, specifically includes: To achieve the best synchronization effect, this invention uses the least squares method to obtain the control vertex distribution of the displacement B-spline within the segment.

[0042] The relative tangential velocity between the actual trajectory of the tool tip and the actual trajectory of the tool axis It can be represented as: ; Then relative tangential acceleration It can be represented as: ; in, This represents the actual tangential velocity of the blade tip trajectory; This represents the tangential acceleration of the actual trajectory of the blade tip.

[0043] The relative tangential acceleration between the actual trajectory of the tool tip and the actual trajectory of the tool axis This can be further expressed as: ; in, , These represent the actual trajectory displacement of the tool axis. The first and second derivatives of the actual trajectory displacement parameter u of the tool tip.

[0044] This invention employs the least squares method to optimize the control vertex distribution of the displacement B-spline within three adjacent segments, while retaining only the control vertex distribution of the displacement B-spline within the first segment, thereby obtaining the optimal control vertex distribution of the displacement B-spline within each segment. First, N sampling points are selected within three adjacent segments of the actual tool axis trajectory. An objective function is established based on minimizing the relative tangential acceleration between each sampling point and the actual tool tip trajectory, and the least squares method is used for constraint.

[0045] ; in, It is a constant matrix. This represents the actual displacement parameter of the tool tip trajectory corresponding to the i-th sampling point. , , Let represent the first and second derivatives of the basis functions of the displacement B-spline curve within each segment, respectively. This represents the control vertex of the displacement B-spline curve within each segment.

[0046] By analytically determining the control vertices of the displacement B-spline for each segment, parameter synchronization between the actual tool tip trajectory and the actual tool axis trajectory is achieved by sharing the actual tool tip trajectory displacement parameters. Within each segment, one actual tool tip trajectory displacement corresponds to one actual tool axis trajectory displacement; therefore, both the actual tool tip trajectory and the actual tool axis trajectory can be expressed using the same parameters, ultimately achieving synchronization between them.

[0047] like Figure 6 As shown, the solid line represents the tool axis acceleration curve when smoothing is performed using the method of this invention, and the dashed line represents the tool axis acceleration curve when smoothing is performed using the unsynchronized method. The two figures pointed to by the arrows are enlarged partial views. Compared with the traditional solution, this invention eliminates the frequent start-stop of the machine tool caused by the discontinuity of the linear path during five-axis machining by smoothing the linear path segment, thus achieving a significant improvement in machining motion efficiency. At the same time, the proposed parameter synchronization mechanism effectively avoids the acceleration step of the tool axis motion, ensuring the stability of the high-speed machining process.

[0048] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0049] It should be understood that although the steps in the flowcharts of the accompanying drawings are shown sequentially as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some of the steps in the flowcharts of the accompanying drawings may include multiple steps or stages, which are not necessarily completed at the same time, but may be executed at different times, and the execution order of these steps or stages is not necessarily sequential, but may be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0050] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0051] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention, and no reference numerals in the claims should be construed as limiting the scope of the claims.

[0052] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for local smoothing and parameter synchronization of a five-axis linear path based on a spiral curve, characterized in that, include: A spiral curve is inserted within the tool tip corner formed by two adjacent linear tool tip paths as a tool tip transition curve; a spiral curve is also inserted within the tool axis corner formed by two adjacent linear tool axis paths as a tool axis transition curve; the machine tool simultaneously controls the tool tip position and the tool axis position to achieve path smoothing. Based on the approximate error of the tool tip and the segment length constraint, determine the transition length of the tool tip transition curve; Based on the approximate error of the cutter axis point and the segment length constraint, determine the transition length of the cutter axis transition curve; The transition curve and a partial linear path are each treated as a segment, alternately forming the actual trajectory. The actual tool tip trajectory displacement is used as a shared parameter to achieve parameter synchronization between the actual tool tip trajectory and the actual tool axis trajectory. Using the displacement of the actual tool tip trajectory within a segment as the shared parameter, the displacement of the actual tool axis trajectory within the current segment is uniformly expressed using a displacement B-spline. Specifically, this includes representing the corresponding actual tool axis trajectory displacement within the current segment using a 5th-order displacement B-spline. The node vector design is as follows: Control vertex is to The actual displacement of the cutter axis trajectory within the current segment. Represented as: ; The total displacement of the actual trajectory of the tool tip within the current segment: ; ; Let be the arc length of the transition curve at the i-th corner of the actual trajectory of the blade tip. These are the characteristic parameters of the blade tip transition curve. ; The tangential direction at the midpoint of the tool tip transition curve and the linear path of the tool tip The included angle; Indicates the transition curve of the blade tip in Displacement components in the direction; Indicates the transition curve of the blade tip in The displacement components in the orthogonal direction; j represents the index of the control vertex, and P represents the degree of the displacement B-spline; Let be the displacement B-spline basis function; u is the actual trajectory displacement parameter of the tool tip within the current segment; the first, second, and third derivatives of the displacement B-splines within adjacent segments are equal at the junction points; and To form the linear paths of two adjacent tool tips at the i-th tool tip corner, Let i be the i-th blade tip point; This indicates calculating the path length. The transition length of the tool tip transition curve at the i-th tool tip corner; The control vertex distribution of the displacement B-spline within three adjacent segments is optimized using the least squares method, and only the control vertex distribution of the displacement B-spline within the first segment is retained, in order to obtain the optimal control vertex distribution of the displacement B-spline within the segment.

2. The method for local smoothing and parameter synchronization of a five-axis linear path based on a spiral curve according to claim 1, characterized in that, The spiral curve adopts a Clothoid curve. A pair of symmetrical Clothoid curves are inserted as tool tip transition curves within the tool tip corner formed by two adjacent linear paths of the tool tip; a pair of symmetrical Clothoid curves are inserted as tool axis transition curves within the tool axis corner formed by two adjacent linear paths of the tool axis.

3. The method for local smoothing and parameter synchronization of a five-axis linear path based on a spiral curve according to claim 1, characterized in that, The determination of the transition length of the tool tip transition curve based on the approximate error of the tool tip point and the segment length constraint specifically includes: ； in, This indicates that for the i-th blade tip corner, given an approximate error... The transition length of the tool tip transition curve is obtained below; Represents the coefficient.

4. The method for local smoothing and parameter synchronization of a five-axis linear path based on a spiral curve according to claim 3, characterized in that, For the i-th blade tip corner, given an approximation error The transition length of the tool tip transition curve obtained below The expression is: ； Indicates the transition curve of the blade tip in Displacement components in orthogonal directions, Indicates the transition curve of the blade tip in Displacement components in the direction, The tangential direction at the midpoint of the tool tip transition curve and the linear path of the tool tip The included angle.

5. The method for local smoothing and parameter synchronization of a five-axis linear path based on a spiral curve according to claim 1, characterized in that, The determination of the transition length of the tool axis transition curve based on the approximate error of the tool axis point and the segment length constraint specifically includes: ； in, The transition length of the tool axis transition curve at the i-th tool axis corner; and To form the linear paths of two adjacent tool axes at the i-th tool axis corner, This is the i-th tool axis point; This indicates calculating the path length. This indicates that for the i-th tool axis corner, given an approximate error... The transition length of the cutter shaft transition curve obtained below; Represents the coefficient.

6. A method for local smoothing and parameter synchronization of a five-axis linear path based on a spiral curve, as described in claim 3 or 5, characterized in that, When i = 1, , When i=n, , When i = 2, 3, ..., n-1, , where n is the total number of tool tip corners or tool shaft corners.

7. The method for local smoothing and parameter synchronization of a five-axis linear path based on a spiral curve according to claim 5, characterized in that, For the i-th tool axis corner under a given approximation error The transition length of the cutter shaft transition curve obtained below The expression is: ； Indicates the tool axis transition curve at Displacement components in the direction; Indicates the tool axis transition curve at Displacement components in orthogonal directions; The tangential direction at the midpoint of the tool axis transition curve is linearly related to the tool axis. The included angle.

8. The method for local smoothing and parameter synchronization of a five-axis linear path based on a spiral curve according to claim 1, characterized in that, The first, second, and third derivatives of the displacement B-spline within each segment at the junction point are: when hour: ； ； ； when hour: ； ； ； By setting the second and third derivatives at the junction points to zero, the relationship between the control vertices of the displacement B-spline is obtained: ； ； ； in, This represents the arc length of the transition curve at the i-th corner of the actual trajectory of the tool axis. ; These are the characteristic parameters of the tool axis transition curve. ; The tangential direction at the midpoint of the tool axis transition curve is linearly related to the tool axis. The included angle; Indicates the tool axis transition curve at Displacement components in the direction; Indicates the tool axis transition curve at Displacement components in orthogonal directions; It is an operation to calculate the distance between the control vertices of the displacement B-spline. and To form the linear paths of two adjacent tool axes at the i-th tool axis corner, is the transition length of the tool axis smooth curve at the i-th tool axis corner.

9. A method for local smoothing and parameter synchronization of a five-axis linear path based on a spiral curve according to claim 8, characterized in that, The process of optimizing the control vertex distribution of displacement B-splines within three adjacent segments using the least squares method, and retaining only the control vertex distribution of the displacement B-splines within the first segment, to obtain the optimal control vertex distribution of displacement B-splines within the segments, specifically includes: The relative tangential velocity between the actual trajectory of the tool tip and the actual trajectory of the tool axis for: ； The relative tangential acceleration between the actual trajectory of the tool tip and the actual trajectory of the tool axis for: ； in, This represents the actual tangential velocity of the blade tip trajectory; This represents the tangential acceleration of the actual trajectory of the blade tip. Relative tangential acceleration Further expressed as: ； in, , They represent about The first and second derivatives; Sampling is performed within three adjacent segments of the actual tool axis trajectory. N sampling points are selected, and an objective function is established based on minimizing the relative tangential acceleration between each sampling point and the actual tool tip trajectory. The least squares method is used for constraint. ； in, It is a constant matrix. This represents the actual displacement parameter of the tool tip trajectory corresponding to the i-th sampling point. , , Let represent the first and second derivatives of the basis functions of the displacement B-spline curve within each segment, respectively. The control vertices of the displacement B-spline curve within each segment are represented. The control vertices of each segmented displacement B-spline are determined by analysis, and parameter synchronization between the actual tool tip trajectory and the actual tool axis trajectory is achieved by sharing the actual tool tip trajectory displacement parameters.

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