A linear machining path smoothing method and system

Abstract

The present invention discloses a linear machining path fairing method and system. The method includes: S1. According to the linear machining path, using the line segment length constraint and the maximum approximation error constraint, constructing an auxiliary point set; S2. Based on the auxiliary point set, determining the specific positions of the start and end control points of the bi - quadratic B - spline curve of the approximation straight line segment that meets the error requirements through the convex hull property of the quadratic B - spline curve; S3. Based on the specific positions and under the constraint that the curvature values of adjacent spline curves are equal at the connection points, calculating a number of internal control points; S4. Obtaining the target quadratic B - spline curve according to the control points; S5. Using the target quadratic B - spline curve to fair the linear machining path. The present invention meets the accuracy requirements when fairing the path and achieves G<supgt;2< / supgt> continuity at the shape value points, can effectively improve the kinematic performance of the numerical control machine tool when machining the inflection points of the discrete path at high speed, is suitable for machine tool machining, has good real - time performance, and can effectively improve the machining efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of computer-aided manufacturing and numerical control machining, and particularly relates to a linear machining path smoothing method and system. Background Art

[0002] At present, for complex workpieces, the machining paths described by continuous tiny line segments generated by CAD / CAM software often have the characteristics of large data volume and frequent changes in machining directions, resulting in defects such as low machining speed and insufficient surface finish of the machined surface. Summary of the Invention

[0003] The purpose of the present invention is to overcome the defects of the prior art. The present invention provides a linear machining path smoothing method and system. The present invention uses a smooth curve to replace the original continuous tiny line segments to achieve the purpose of trajectory smoothing, which is of great significance for reducing the fluctuation of the feed rate, improving the surface quality of parts, and improving the machining efficiency.

[0004] To achieve the expected effect, the present invention adopts the following technical solutions:

[0005] The present invention discloses a linear machining path smoothing method, including:

[0006] S1. According to the linear machining path, using the line segment length constraint and the maximum approximation error constraint, construct an auxiliary point set;

[0007] S2. Based on the auxiliary point set, determine the specific positions of the start and end control points of the biquadratic B-spline curve that approximates the straight line segment meeting the error requirements through the convex hull property of the quadratic B-spline curve;

[0008] S3. Based on the specific positions and the constraint that the curvature values of adjacent spline curves are equal at the connection points, calculate a number of internal control points;

[0009] S4. Obtain the target quadratic B-spline curve according to the control points;

[0010] S5. Use the target quadratic B-spline curve to smooth the linear machining path.

[0011] Further, the S1 specifically includes:

[0012] Mark a number of type value points on the linear machining path and form a type value point set;

[0013] Connect adjacent two type value points in the type value point set to form a type value point line segment, calculate the length of the type value point line segment and form a type value point line segment length set;

[0014] Set the maximum approximation error of the fitting curve according to the linear machining path;

[0015] Construct auxiliary points for each value point in the value point set and form an auxiliary point set, and the auxiliary point set is respectively constrained by the value point line segment length set and the maximum approximation error of the fitting curve.

[0016] Further, the construction of auxiliary points for each value point in the value point set and the formation of an auxiliary point set specifically include:

[0017] Let the value point set be Q i , i = 0, 1, … n, let the auxiliary point set be P i , i = 0, 1, 2…, 2n + 1, n is a positive integer greater than or equal to 2, point P 2i , Q i , P 2i+1 The three points are on the same straight line, and this straight line is parallel to the straight line where the value point line segment Q i-1 Q i+1 is located.

[0018] Further, the fact that the auxiliary point set is respectively constrained by the value point line segment length set and the maximum approximation error of the fitting curve specifically includes:

[0019] The line segment length between two adjacent auxiliary points P 2i and P 2i+1 in the auxiliary point set is constrained by the value point line segment length set, and the distance from the auxiliary point P 2i to the value point line segment Q i-1 Q i does not exceed the maximum approximation error of the fitting curve, and the distance from the auxiliary point P 2i+1 to the value point line segment Q i Q i+1 does not exceed the maximum approximation error of the fitting curve.

[0020] Further, two adjacent auxiliary points in the auxiliary point set satisfy the following expression:

[0021]

[0022] where, l i,1 is the distance from the auxiliary point P 2i to the value point Q i , l i,2 is the distance from the auxiliary point P 2i+1 to the value point Q i , l i is the length of the line segment Q i Q i+1 , ε is the maximum approximation error of the fitting curve, e i is the vector Q i-1 Q i+1The unit vector, α i,1 is the unit vector e i and the vector Q i-1 Q i The included angle of, α i,2 is the unit vector e i and the vector Q i Q i+1 The included angle of.

[0023] Furthermore, the quadratic B-spline curve C i-1 Q i approximating the value point segment Q 2i-1 (u) and C 2i (u) satisfy the following expressions:

[0024]

[0025] wherein, N k,2 , k = 0, 1, 2, 3 are the quadratic B-spline basis functions determined by the knot vector u; Q 2i-1,k is the control point of the curve C 2i-1 (u); Q 2i,k is the control point of the curve C 2i (u); the control point Q 2i-1,0 coincides with the value point Q i-1 , the control point Q 2i,3 coincides with the value point Q i ; the control points Q 2i-1,3 and Q 2i,0 both coincide with the midpoint of the auxiliary point segment P 2i-1 P 2i , the control points Q 2i-1,1 and Q 2i-1,2 are respectively located on the line segments Q i-1 P 2i-1 and P 2i-1 P 2i and are equidistant from the auxiliary point P 2i-1 ; the control points Q 2i,1 and Q 2i,2 are respectively located on the line segments P 2i-1 P 2i and P 2i Q i and are equidistant from the auxiliary point P 2i .

[0026] Furthermore, the S3 specifically includes: based on the specific position, calculating the internal control points under the constraint that the curvature values are equal at the connection points through the four parameters of two adjacent quadratic B-spline curves C i (u) and C i+1 (u).

[0027] Further, the first parameter λ i,1 is the ratio of the distance from the control point Q i,1 to the auxiliary point P i to the length l i,0 of the line segment Q i P i,1 ; the second parameter λ i,2 is the ratio of the distance from the control point Q i,2 to the auxiliary point P i to the length l i,3 of the line segment Q i P i,2 ; since the distances from the control points Q i,1 and Q i,2 to the auxiliary point P i are equal, the following is satisfied

[0028] Further, the third parameter λ i+1,1 satisfies the following expression:

[0029]

[0030] wherein, b i+1 = l i,2 (1 - λ i,2 ) 2 sinθ i+1 , a i+1 = l i+1,1 λ i,2 sinθ i , θ i is the included angle between the vector P i-1 P i and the vector P i P i+1 .

[0031] The present invention also discloses a linear machining path fairing system, including:

[0032] An acquisition module, configured to acquire a linear machining path;

[0033] A fairing module, configured to fair the linear machining path according to the method described in any one of the above.

[0034] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention provides a linear machining path fairing method and system. The present invention approximates each straight line segment of the discrete machining path with a biquadratic B-spline curve. Under the constraints of the approximation error and the line segment length, a curve passing through the type value points and reaching G 2A continuous fairing path solves problems such as easy fluctuation of the feed rate and poor machining quality in the conventional discrete machining path. Compared with the prior art, this method meets the accuracy requirements when fairing the path and reaches G at the interpolation points. 2 Continuous, which can effectively improve the kinematic performance of the numerical control machine tool when machining the inflection points of the discrete path at high speed, is suitable for machine tool machining, has good real-time performance, and can effectively improve the machining efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0036] Figure 1 FIG. is a fairing schematic diagram of a continuous two-line segment machining path provided by an embodiment of the present invention.

[0037] Figure 2 FIG. is a fairing schematic diagram of a separate two-line segment machining path provided by an embodiment of the present invention.

[0038] Figure 3 FIG. is another fairing schematic diagram of a linear machining path provided by an embodiment of the present invention.

[0039] Figure 4 FIG. is a flowchart of a linear machining path fairing method using a biquadratic B-spline curve approximation provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0041] See Figures 1 to 4 , the present invention discloses a linear machining path fairing method, including:

[0042] S1. According to the linear machining path of the tool, construct an auxiliary point set by using the line segment length constraint and the maximum approximation error constraint;

[0043] In one embodiment, the S1 specifically includes:

[0044] Mark a number of interpolation points on the linear machining path and form an interpolation point set;

[0045] Connect two adjacent value points in the value point set to form a value point line segment, calculate the length of the value point line segment and form a value point line segment length set;

[0046] Set the maximum approximation error of the fitting curve according to the linear machining path;

[0047] Construct auxiliary points for each value point in the value point set to form an auxiliary point set, and the auxiliary point set is respectively constrained by the value point line segment length set and the maximum approximation error of the fitting curve.

[0048] Further, the construction of auxiliary points for each value point in the value point set to form an auxiliary point set specifically includes:

[0049] Let the value point set be Q i , i = 0, 1, …n, let the auxiliary point set be P i , i = 0, 1, 2…, 2n + 1, n is a positive integer greater than or equal to 2, point P 2i , Q i , P 2i+1 The three points are on the same straight line, and this straight line is parallel to the straight line where the value point line segment Q i-1 Q i+1 is located.

[0050] Further, the auxiliary point set being respectively constrained by the value point line segment length set and the maximum approximation error of the fitting curve specifically includes:

[0051] The line segment length between two adjacent auxiliary points P 2i and P 2i+1 in the auxiliary point set is constrained by the value point line segment length set, and the distance from the auxiliary point P 2i to the value point line segment Q i-1 Q i does not exceed the maximum approximation error of the fitting curve, and the distance from the auxiliary point P 2i+1 to the value point line segment Q i Q i+1 does not exceed the maximum approximation error of the fitting curve.

[0052] Further, two adjacent auxiliary points in the auxiliary point set satisfy the following expression:

[0053]

[0054] where, l i,1 is the distance from the auxiliary point P 2i to the value point Q i , l i,2 is the distance from the auxiliary point P 2i+1 to the value point Q iThe distance, l i is the length of line segment Q i Q i+1 ε is the maximum approximation error of the fitting curve, and e i is the vector Q i-1 Q i+1 The unit vector of, α i,1 is the unit vector e i and the vector Q i-1 Q i The included angle of, α i,2 is the unit vector e i and the vector Q i Q i+1 The included angle of.

[0055] P0 coincides with Q0, and P 2n+1 coincides with Q n Construct an auxiliary point P1 such that the line segment P1P2 is parallel to the line segment Q0Q1 and the quadrilateral P0P1P2Q1 is an isosceles trapezoid; construct an auxiliary point P 2n such that the line segment P 2n-1 P 2n is parallel to the line segment Q n-1 Q n and the quadrilateral P 2n+1 P 2n P 2n- 1Q n-1 is an isosceles trapezoid; thus, the auxiliary points P1 and P 2n simultaneously satisfy the line segment length constraint and the maximum approximation error constraint.

[0056] S2. Based on the set of auxiliary points, determine the specific positions of the start and end control points of the bi - quadratic B - spline curve of the approximation line segment that meets the error requirements through the convex hull property of the quadratic B - spline curve;

[0057] Furthermore, the bi - quadratic B - spline curves C i-1 Q i (u) and C 2i-1 (u) that approximate the line segment of the shape value points Q 2i satisfy the following expressions:

[0058]

[0059] In the formula, N k,2 , k = 0, 1, 2, 3 are the quadratic B - spline basis functions determined by the knot vector u (the value range of u is U = [0, 0, 0, 0.5, 1, 1, 1]); Q 2i-1,k is the control point of the curve C 2i-1 (u); Q 2i,k is the control point of the curve C 2i (u); the control point Q 2i-1,0 and the shape value point Qi-1 Coincide, control point Q 2i,3 and the value point Q i coincide; control point Q 2i-1,3 and Q 2i,0 both coincide with the midpoint of the auxiliary point line segment P 2i-1 P 2i The control point Q 2i-1,1 and Q 2i-1,2 are respectively located on the line segment Q i-1 P 2i-1 and P 2i-1 P 2i and are equidistant from the auxiliary point P 2i-1 The control point Q 2i,1 and Q 2i,2 are respectively located on the line segment P 2i-1 P 2i and P 2i Q i and are equidistant from the auxiliary point P 2i The distance is equal.

[0060] S3. Based on the specific positions and the constraint that the curvature values of adjacent spline curves are equal at the joint points, a number of internal control points are calculated;

[0061] In one embodiment, the S3 specifically includes: Based on the specific positions, through the four parameters of two adjacent quadratic B-spline curves C i (u) and C i+1 (u), the internal control points are calculated under the constraint that the curvature values are equal at the joint points.

[0062] In another embodiment, the first parameter λ i,1 is the ratio of the distance from the control point Q i,1 to the auxiliary point P i to the length l i,0 of the line segment Q i P i,1 The second parameter λ i,2 is the ratio of the distance from the control point Q i,2 to the auxiliary point P i to the length l i,3 of the line segment Q i P i,2 Since the distances from the control points Q i,1 and Q i,2 to the auxiliary point P i are equal, so it satisfies

[0063] In yet another embodiment, the third parameter λ i+1,1 satisfies the following expression:

[0064]

[0065] In the formula, b i+1 = l i,2 (1 - λ i,2 ) 2 sinθ i+1 , a i+1 = l i+1,1 λ i,2 sinθ i , θ i is the angle between vector P i-1 P i and vector P i P i+1 .

[0066] From a i+1 > 0, b i+1 > 0, it can be known that:

[0067]

[0068] Suppose the curvature of curve C i (u) at the connection point is κ i , then there is:

[0069]

[0070] Let the curvature of curve C i+1 (u) at the connection point be κ i+1 , similarly, it can be obtained that:

[0071]

[0072] Since

[0073]

[0074] Therefore

[0075]

[0076] According to the fact that the distances from the internal control points Q 2i,1 and Q 2i,2 to the auxiliary point P 2i are equal, the fourth parameter λ i+1,2 can be obtained. The fourth parameter λ i+1,2 satisfies the following expression:

[0077]

[0078] To sum up, the double B-spline curve approximating the straight line segment Q i-1 Q i is C 2i-1 (u) and C 2i(u). If the first curve C 2i-1 (u)'s first parameter λ 2i-1,1 is given, then the second parameter λ 2i-1,2 and the two parameters λ 2i of another spline curve C 2i,1 , λ 2i,2 can be calculated, and then all internal control points Q 2i-1,1 , Q 2i-1,2 , Q 2i,1 , Q 2i,2 .

[0079] S4. Obtain the target quadratic B-spline curve according to the control points;

[0080] Specifically, obtain the biquadratic B-spline curve finally used to approximate all the segments of the value points according to the obtained control points. For the i-th line segment Q i-1 Q i , according to the obtained control points Q 2i-1,k and Q 2i,k , k = 0, 1, 2, 3, obtain the curves C 2i-1 (u) and C 2i (u).

[0081] S5. Smooth the linear machining path using the target quadratic B-spline curve.

[0082] The present invention approximates each straight line segment of the discrete linear machining path with a biquadratic B-spline curve. Under the constraints of the maximum approximation error and the segment length, a smooth path passing through the value points and reaching G 2 continuity at the value points is generated, solving problems such as easy fluctuation of the feed rate and poor machining quality in the conventional discrete machining path. Compared with the existing technology based on quadratic B-spline curves, this method meets the accuracy requirements when smoothing the path and reaches G 2 continuity at the value points, can effectively improve the kinematic performance of the numerical control machine tool when machining the inflection points of the discrete path at high speed, is suitable for machine tool machining, has good real-time performance, and can effectively improve the machining efficiency.

[0083] The present invention also discloses a linear machining path smoothing system, including:

[0084] An acquisition module, used to acquire the linear machining path;

[0085] A smoothing module, used to smooth the linear machining path according to any one of the above methods.

[0086] The system embodiments can be correspondingly implemented with the foregoing method embodiments one by one, and will not be elaborated here.

[0087] For complex workpieces, the machining paths described by continuous tiny straight line segments generated by CAD / CAM software often have the characteristics of large data volume and frequent changes in machining directions, resulting in defects such as low machining speed and insufficient surface finish of the machined surface. Therefore, replacing the original continuous tiny straight line segments with smooth curves to achieve the purpose of trajectory smoothing is of great significance for reducing the fluctuation of the feed rate, improving the surface quality of parts, and increasing the machining efficiency. The quadratic B-spline curve has the advantages of simple expression and low computational complexity, meeting the subsequent real-time machining requirements. The trajectory smoothing method based on the quadratic B-spline curve in the present invention can pass through the value points and reach G 2 smoothness.

[0088] Based on the same inventive concept, the present invention also discloses an electronic device, which may include: a processor, a communication interface, a memory, and a communication bus. Among them, the processor, the communication interface, and the memory complete communication with each other through the communication bus. The processor can call the logical instructions in the memory to execute a linear machining path smoothing method, including:

[0089] S1. According to the linear machining path, construct an auxiliary point set by using the line segment length constraint and the maximum approximation error constraint;

[0090] S2. Based on the auxiliary point set, determine the specific positions of the start and end control points of the biquadratic B-spline curve that approximates the straight line segment and meets the error requirements through the convex hull property of the quadratic B-spline curve;

[0091] S3. Based on the specific positions and the constraint that the curvature values of adjacent spline curves are equal at the connection points, calculate a number of internal control points;

[0092] S4. Obtain the target quadratic B-spline curve according to the control points;

[0093] S5. Smooth the linear machining path by using the target quadratic B-spline curve.

[0094] In addition, when the logical instructions in the above-mentioned memory are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The foregoing storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs that can store program codes.

[0095] On the other hand, an embodiment of the present invention also provides a computer program product. The computer program product includes a computer program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions. When the program instructions are executed by a computer, the computer can execute a linear machining path smoothing method provided by each of the above method embodiments, including:

[0096] S1. According to the linear machining path, using the line segment length constraint and the maximum approximation error constraint, construct an auxiliary point set;

[0097] S2. Based on the auxiliary point set, determine the specific positions of the start and end control points of the biquadratic B-spline curve that approximates the straight line segment meeting the error requirements through the convex hull property of the quadratic B-spline curve;

[0098] S3. Based on the specific positions and the constraint that the curvature values of adjacent spline curves are equal at the connection points, calculate a number of internal control points;

[0099] S4. Obtain the target quadratic B-spline curve according to the control points;

[0100] S5. Use the target quadratic B-spline curve to smooth the linear machining path.

[0101] On another aspect, an embodiment of the present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it is configured to execute a linear machining path smoothing method provided by each of the above embodiments, including:

[0102] S1. According to the linear machining path, using the line segment length constraint and the maximum approximation error constraint, construct an auxiliary point set;

[0103] S2. Based on the auxiliary point set, determine the specific positions of the start and end control points of the bi - quadratic B - spline curve that approximates the straight - line segment and meets the error requirements through the convex - hull property of the quadratic B - spline curve;

[0104] S3. Based on the specific positions and under the constraint that the curvature values of adjacent spline curves are equal at the connection points, calculate a number of internal control points;

[0105] S4. Obtain the target quadratic B - spline curve according to the control points;

[0106] S5. Use the target quadratic B - spline curve to smooth the linear machining path.

[0107] It should be understood that although the steps in the flowchart of the accompanying drawings are shown sequentially according to the arrows, these steps do not necessarily have to be executed in the order indicated by the arrows. Unless otherwise clearly stated in this article, there is no strict order restriction for the execution of these steps, and they can be executed in other orders. Moreover, at least some of the steps in the flowchart of the accompanying drawings may include multiple sub - steps or multiple stages. These sub - steps or stages do not necessarily have to be completed at the same time, but can be executed at different times, and their execution order does not necessarily have to be sequential, but can be executed alternately or in turn with at least a part of other steps or sub - steps or stages of other steps.

[0108] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A linear machining path smoothing method, characterized in that Including: S1. Construct an auxiliary point set according to the linear machining path, using the line segment length constraint and the maximum approximation error constraint; the specific steps of S1 include: Mark a number of type value points on the linear machining path to form a type value point set; Connect adjacent two type value points in the type value point set to form a type value point line segment, calculate the length of the type value point line segment and form a type value point line segment length set; Set the maximum approximation error of the fitting curve according to the linear machining path; Construct auxiliary points for each value point in the value point set to form an auxiliary point set, and the auxiliary point set is respectively constrained by the value point line segment length set and the maximum approximation error of the fitting curve; the specific steps of constructing auxiliary points for each value point in the value point set to form an auxiliary point set include: Let the value point set be Q i , i = 0, 1, … n, let the auxiliary point set be P i , i = 0, 1, 2…, 2n + 1, n is a positive integer greater than or equal to 2, points P 2i , Q i , P 2i+1 are on the same straight line, and this straight line is parallel to the straight line where the value point line segment Q i-1 Q i+1 is located; the specific steps of the auxiliary point set being respectively constrained by the value point line segment length set and the maximum approximation error of the fitting curve include: The line segment length between two adjacent auxiliary points P 2i and P 2i+1 in the auxiliary point set is constrained by the value point line segment length set, and the distance from the auxiliary point P 2i to the value point line segment Q i-1 Q i does not exceed the maximum approximation error of the fitting curve, and the distance from the auxiliary point P 2i+1 to the value point line segment Q i Q i+1 does not exceed the maximum approximation error of the fitting curve; The following expression is satisfied for two adjacent auxiliary points in the auxiliary point set: where, l i,1 is the distance from the auxiliary point P 2i to the value point Q i ; l i,2 is the distance from the auxiliary point P 2i+1 to the value point Q i ; l i is the length of the line segment Q i Q i+1 ; ε is the maximum approximation error of the fitting curve, e i is the unit vector of the vector Q i-1 Q i+1 ; α i,1 is the included angle between the unit vector e i and the vector Q i-1 Q i ; α i,2 is the included angle between the unit vector e i and the vector Q i Q i+1 ; S2. Based on the auxiliary point set, determine the specific positions of the start and end control points of the biquadratic B-spline curve of the approximation straight line segment that meets the error requirements through the convex hull property of the quadratic B-spline curve; S3. Based on the specific positions and under the constraint that the curvature values of adjacent spline curves are equal at the connection points, calculate a number of internal control points; S4. Obtain the target quadratic B-spline curve according to the control points; S5. Use the target quadratic B-spline curve to smooth the linear machining path.

2. The linear machining path fairing method according to claim 1, characterized in that The line segment Q approaching the type value point i-1 Q i The biquadratic B-spline curve C 2i-1 C(u) and C 2i (u) satisfy the following expressions: where N k,2 , k = 0, 1, 2, 3 are the quadratic B-spline basis functions determined by the knot vector u; Q 2i-1,k is the control point of curve C 2i-1 (u); Q 2i,k is the control point of curve C 2i (u); The control point Q 2i-1,0 coincides with the hodograph point Q i-1 , and the control point Q 2i,3 coincides with the hodograph point Q i ; The control points Q 2i-1,3 and Q 2i,0 both coincide with the midpoint of the auxiliary point line segment P 2i-1 P 2i , and the control points Q 2i-1,1 and Q 2i-1,2 are respectively located on the line segments Q i-1 P 2i-1 and P 2i-1 P 2i , and are equidistant from the auxiliary point P 2i-1 ; The control points Q 2i,1 and Q 2i,2 are respectively located on the line segments P 2i-1 P 2i and P 2i Q i , and are equidistant from the auxiliary point P 2i .

3. The linear machining path fairing method according to claim 2, wherein, The S3 specifically includes: Based on the specific position, through four parameters of two adjacent quadratic B-spline curves C i (u) and C i+1 (u), the internal control points are calculated under the constraint that the curvature values are equal at the connection points.

4. The linear machining path fairing method according to claim 3, characterized in that The first parameter λ i,1 is the distance from the control point Q i,1 to the auxiliary point P i and the ratio of the length l i,0 of the line segment Q i P i,1 ; the second parameter λ i,2 is the distance from the control point Q i,2 to the auxiliary point P i and the ratio of the length l i,3 of the line segment Q i P i,2 ; since the distances from the control points Q i,1 and Q i,2 to the auxiliary point P i are equal, it satisfies 5. The linear machining path fairing method according to claim 4, wherein The third parameter λ i+1,1 satisfies the following expression: where b i+1 = l i,2 (1 - λ i,2 ) 2 sinθ i+1 , a i+1 = l i+1,1 λ i,2 sinθ i , θ i is the angle between vector P i-1 P i and vector P i P i+1 .

6. A linear machining path smoothing system, characterized in that, Including: A collection module, used to collect the linear machining path; A smoothing module, used to smooth the linear machining path according to the method described in any one of claims 1-5.

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