A method for generating a non-interference area in the grinding and polishing process of an integral bladed disk

Abstract

The present invention belongs to the technical field related to machining, and discloses a method for generating a non-interference region in the grinding and polishing of an integral bladed disk. The method includes: extracting features of the area to be machined on the integral bladed disk to construct the NUBRS surface of the area to be machined, and establishing a tool model; generating the machining path of the tool, and obtaining the tool point information corresponding to the machining path in combination with the tool geometric parameters in the tool model; obtaining the boundary information of the NUBRS surface; obtaining the tool axis direction according to the tool point information, and establishing a non-linear equation for the critical tangency between the tool axis direction and the surface to obtain the critical normal vector at the critical point of the tool axis on the boundary; performing a first-order Taylor expansion on the NUBRS surface, and searching for points on the NUBRS surface one by one with special boundary points as the initial points to obtain all the searched points on the NUBRS surface; sorting and intersecting the searched points to obtain a closed non-interference region. This method can quickly construct a non-interference region, effectively avoiding interference and collision during the machining process.

Description

Technical Field

[0001] The present invention belongs to the technical field related to mechanical machining manufacturing, and more specifically, relates to a method for generating an interference-free region in the grinding and polishing process of an integral bladed disk. Background Art

[0002] Complex curved surfaces are widely used in many fields such as aerospace, automotive, and defense equipment, such as aero-engine impellers, large ship propellers, etc., and it is necessary to remove surface materials to improve their quality. The surface quality and profile accuracy of an integral bladed disk have a great impact on the aerodynamic performance and service performance of an aero-engine, and polishing is the key technology to ensure the final surface quality and profile accuracy of the integral bladed disk.

[0003] However, parts such as bladed disks have complex structures, and there are characteristics such as sharp curvature changes in local curved surfaces. When using a robot for machining, while the flexibility of curved surface machining increases, due to space limitations, the complexity of interference problems also increases.

[0004] Currently, there are generally two methods for generating a collision-free tool direction. One is to generate the tool direction according to a certain strategy and then perform interference detection and adjustment, and the other is to directly construct an interference-free region to generate a collision-free tool direction. Compared with the first method, constructing an interference-free region can avoid interference collisions in subsequent tool axis direction planning. The first method of generating first and then adjusting will take a large amount of computing time, and the discrete accuracy and computing time will restrict each other. While directly constructing an interference-free region will greatly shorten the computing time and improve the computing efficiency. However, the existing interference-free paths have problems such as large computational amount, long interference detection time, and high algorithm time complexity. Summary of the Invention

[0005] Aiming at the above defects or improvement requirements of the prior art, the present invention provides a method for generating an interference-free region in the grinding and polishing process of an integral bladed disk. This method quickly constructs an interference-free region, effectively avoids interference collisions during the machining process, and also provides an effective guarantee for subsequent path planning.

[0006] To achieve the above-mentioned purpose, according to one aspect of the present invention, a method for generating an interference-free area for grinding and polishing of an integral blade disk is provided, the method comprising: S1: extracting features of the area to be processed of the integral blade disk to construct a NUBRS surface of the area to be processed, and establishing a tool model; S2: generating a processing path of the tool, and obtaining tool position point information corresponding to the processing path in combination with the tool geometric parameters in the tool model; S3: obtaining boundary information of the NUBRS surface; S4: obtaining the tool axis direction according to the tool position point information, establishing a nonlinear equation of the critical tangency between the tool axis direction and the surface to obtain the critical normal vector of the tool axis at the critical point on the boundary; S5: performing a first-order Taylor expansion on the NUBRS surface, searching the points on the NUBRS surface one by one with a special point on the boundary as the initial point, and obtaining all search points on the NUBRS surface, wherein the special point on the boundary is a point where the critical normal vector coincides with the surface normal vector at the boundary; S6: arranging and intersecting the search points in a directed order to obtain a closed interference-free area.

[0007] Preferably, step S5 also includes judging the search point. If the dot product of the unit vector in the tool axis direction and the unit normal vector at the search point is less than or equal to a preset value, the next search point is performed. If the dot product of the unit vector in the tool axis direction and the unit normal vector at the search point is greater than a preset value, the search step size is adjusted until the dot product of the unit vector in the tool axis direction and the unit normal vector at the search point is less than or equal to the preset value.

[0008] Preferably, the dot product D of the unit vector in the tool axis direction and the unit normal vector at the search point is i (u, v) is: D i (u, v) = τ i (u, v)·n i (u, v), where τ i (u, v) is the unit vector of the tool axis direction, n i (u, v) is the unit normal vector at the search point, the objective function is min|D(u, v)|, and the constraints are u min 、u max 、v min 、v max are the limit values in the u and v directions.

[0009] Preferably, if the dot product of the unit vector in the tool axis direction and the unit normal vector at the search point is greater than a preset value, a variable scale search is performed in a local range, and the variable scale matrix B is corrected according to the correction formula of the BFGS method. k Correct the step size α k Adaptive adjustment is performed until a critical point is found where the dot product of the unit vector in the tool axis direction and the unit normal vector at the search point is less than or equal to a preset value, and the local search is terminated.

[0010] Preferably, in step S2, the machining path of the tool is obtained by the equal chord height method or the equal arc length method.

[0011] Preferably, the NUBRS surface S(u, v) in step S1 is:

[0012]

[0013] where u and v are two mutually perpendicular vectors in the tangent plane of the area to be machined, m is the maximum subscript of the non-rational B-spline control points in the v direction, n is the maximum subscript of the non-rational B-spline control points in the u direction, {N i，p (u)} is the non-rational B-spline basis function defined on the knot vector u, {N j，q (v)} is the non-rational B-spline basis function defined on the knot vector v, i = 0, 1, …, n, j = 0, 1, …, m, p is the degree of the non-rational B-spline in the u direction, q is the degree of the non-rational B-spline in the v direction, {ω i，j} is the weight factor, and {P i，j} is the control grid in both the u and v directions.

[0014] Preferably, in step S2, the cutter location point information corresponding to the machining path is obtained by offsetting the cutter axis radius along the unit normal vector of the cutter contact point, and the cutter location point information where CL = [x, y, z, i, j, k], x, y, z are the coordinates of the cutter location point in the workpiece coordinate system; i, j, k are the unit normal vectors of the cutter contact point, that is, the direction vectors of the cutter axis.

[0015] Preferably, the non-linear equation in step S4 is:

[0016] A sinβ + B cosβ + C = 0

[0017] where A, B, C are constants, β is the angle between two vectors of n C and n u , where n C is the critical vector, n u is the tangent vector in the u direction, T is the transformation matrix between the workpiece coordinate system and the local coordinate system of the cutter location point, T = [n, n u , n × n u , and n is the surface normal vector.

[0018] Preferably, in step S5, the points on the NUBRS surface are searched one by one with equal step lengths.

[0019] Generally speaking, compared with the prior art through the above technical solution conceived by the present invention, a method for generating a non-interference area in the grinding and polishing process of an integral blisk provided by the present invention has the following beneficial effects:

[0020] 1. Based on the differential characteristics of the blade surface, this application constructs a non-linear equation of the tool axis and the surface boundary, and uses the boundary critical point as the initial value to search for points in the surface one by one. By sorting and intersecting the searched critical points, a non-interference area for machining is constructed. This method can quickly construct a non-interference area, effectively avoiding interference collisions during the machining process, and providing an effective guarantee for subsequent path planning.

[0021] 2. Using the boundary critical point as the initial value, search for points on the surface, and use the variable scale method to search for critical points for points that do not meet the preset conditions. Since the variable scale method has low requirements for the initial point, searching for surface critical points from any starting point on the boundary will not be affected. Among them, the variable scale matrix B k is not easily transformed into a singular matrix, the search process is stable, and it also has the advantage of the fast convergence speed of the Newton method, solving the problem of large computational amount of the Newton method.

[0022] 3. By constructing a non-linear equation for the critical state of the tool axis direction tangent to the surface, this non-linear equation takes into account the non-uniqueness of the normal vector on the boundary and the matrix transformation under different coordinate systems, so it can accurately and comprehensively calculate the ideal critical vector. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 is a step diagram of the method for generating a non-interference area in the grinding and polishing process of an integral blisk of this application;

[0024] Figure 2 is a schematic diagram of the tangent plane and normal vector of the blade parametric surface of this application;

[0025] Figure 3 is a schematic diagram of the tool structure parameters of this application;

[0026] Figure 4 is a schematic diagram of the critical state of the tool axis and the surface boundary of this application;

[0027] Figure 5 is a schematic diagram of the tool axis and the boundary contact curve of this application;

[0028] Figure 6 is a schematic diagram of the solution process of the boundary critical point of this application;

[0029] Figure 7 is a comparison diagram of the running time of the second Newton-Raphson method, the first Newton-Raphson method, the particle swarm optimization algorithm (PSO), and the first Newton-Raphson of this application;

[0030] Figure 8 It is a comparison chart of the error of the function values of the second Newton-Raphson method, the first Newton-Raphson method, the particle swarm optimization algorithm (PSO), and the first Newton-Raphson method in this application;

[0031] Figure 9 It is a schematic diagram of the critical point search process on the surface in this application;

[0032] Figure 10 It is a schematic diagram of the critical state where the tool axis is tangent to the inspection surface in this application;

[0033] Figure 11 It is a schematic diagram of the local coordinate system of the tool in this application;

[0034] Figure 12A It is a schematic diagram of the spherical coordinate system of the critical tool axis vector in this application;

[0035] Figure 12B It is a schematic diagram of the central plane of the spherical coordinate system of the critical tool axis vector in this application. Detailed implementation manners

[0036] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0037] This application provides a method for generating a non-interference region in the grinding and polishing of an integral blisk. This method is based on the differential characteristics of the surface and aims to efficiently and quickly construct a non-interference region, avoid interference collisions during the machining process, and provide an effective guarantee for subsequent path planning, such as Figure 1 As shown, this method includes the following steps S1 to S6.

[0038] S1: Extract the features of the area to be machined on the integral blisk to construct the NUBRS surface of the area to be machined, and establish a tool model.

[0039] In a specific grinding and polishing scenario, the open integral blisk is ground and polished, and the machining features are extracted. The blade surface of the integral blisk can be defined as a NUBRS surface of degree p in the u direction and degree q in the v direction. The u direction and the v direction are perpendicular to each other, and the plane where they are located is the tangent plane of the blisk surface.

[0040] The NUBRS surface S(u, v) is:

[0041]

[0042] Among them, u and v are two mutually perpendicular vectors in the tangent plane of the area to be processed, m is the maximum subscript of the non-rational B-spline control points in the v direction (the number of control points is m + 1), n is the maximum subscript of the non-rational B-spline control points in the u direction (the number of control points is n + 1), {N i，p (u)} is the non-rational B-spline basis function defined on the knot vector u, {N j，q (v)} is the non-rational B-spline basis function defined on the knot vector v, i = 0, 1,..., n, j = 0, 1,..., m, p is the degree of the non-rational B-spline in the u direction, q is the degree of the non-rational B-spline in the v direction, {ω i，j} is the weight factor, {P i，j} is the control grid in both the u and v directions.

[0043] As Figure 2 shown, the normal vector n(u, v) of this tangent plane is:

[0044] n(u, v) = n u (u, v) × n v (u, v)

[0045] Among them, n u (u, v) and n v (u, v) are the tangent vectors in the u direction and v direction respectively.

[0046] In the grinding and polishing process of this embodiment, a cylindrical grinding head is selected as the grinding and polishing tool. This tool consists of two parts. As Figure 3 shown, the lower half is the grinding and polishing part, which is a cylinder with a radius of r, and the upper part is the tool shank part, which is a cylinder with a radius of r H , where 0 < r < r H , and point O is the tool tip point of the tool.

[0047] The tool model can be constructed based on the geometric parameters of the tool.

[0048]

[0049] S2: Generate the machining path of the tool. Since the tool tip point is obtained by offsetting the tool contact point along the surface normal direction by a tool radius, the tool tip point information corresponding to the machining path can be obtained by combining the tool geometric parameters in the tool model.

[0050] In the secondary development environment based on UG in this embodiment, the equal chord height method is preferably used to generate the path to obtain the tool contact point information, and the tool tip point information corresponding to the machining path is obtained by offsetting along the unit vector of the tool contact point normal direction by the tool axis radius. The tool tip point information Among them, CL = [x, y, z, i, j, k], where x, y, and z are the coordinates of the tool point in the workpiece coordinate system; i, j, and k are the unit normal vectors of the tool contact point, that is, the direction vector of the tool axis. In Figure 4 , the point P CL = [x, y, z].

[0051] S3: Obtain the boundary information of the NUBRS surface.

[0052] Solve the critical points of the surface boundary, and solve the boundaries of the machining surface and the adjacent surface respectively. Specifically, in this embodiment, based on the secondary development environment of UG, relevant functions in UFun are called to extract the boundary information of the blade surface Boundary = [x b , y b , z b , n b , u 1b , v 1b . In the formula, x b , y b , z b are the boundary point coordinates in the workpiece coordinate system, n b is the unit normal vector of this boundary point, u 1b is the unit tangent vector in the u direction of the boundary point, and it is also the first-order partial derivative of the surface function S(u, v) with respect to u at this point; similarly, v 1b is the unit tangent vector in the v direction of the boundary point, and it is also the first-order partial derivative of the surface function S(u, v) with respect to v at this point.

[0053] S4: Obtain the tool axis direction according to the tool point information, and establish a non-linear equation for the critical tangency between the tool axis direction and the surface to obtain the critical normal vector at the critical point of the tool axis on the boundary.

[0054] According to the geometric relationship of the tangency between the tool axis and the surface boundary, it can be obtained that:

[0055] τ(u, v)·n c (u, 0) = 0

[0056] Among them, τ(u, v) is the tool axis direction vector, and n c (u, v) is the critical normal vector at the boundary point.

[0057] The specific tangency situation is as Figure 4 shown. The point P C is the tool contact point on the machining surface, the point P CL is the tool point, and the tool axis attitude will be rotated and adjusted around the point P CL . S C (u, v) is the point on the inspection surface, and the point P is the intersection of the critical normal vector and the tool axis center line. n Mis the unit normal vector at the point S(u, v) on the machined surface, and the unit vector of the cutter axis direction can be obtained.

[0058]

[0059] In the formula, r H is the radius of the tool shank, and n C is the critical normal vector at the blade boundary point.

[0060] (P CL S C + r H ·n C )·n C = P CL S C ·n C + r H

[0061] As Figure 5 shown, for the critical points on the surface, the critical normal vector n C is the normal vector of this point. The cutter axis is tangent to the surface boundary. For the boundary line, any point on it is the tangent point, that is, the critical point. Any vector in the circular cross-section at the critical point is the normal vector. Therefore, the only thing that needs to be determined is the critical normal vector n C . The boundary can be equivalent to a cylindrical pipe with a radius of zero. The critical normal vector n C and the surface normal vector n calculated according to the surface structure are both located on the cylindrical cross-section of this point. At the same time, the tangential vector n u along the v-direction isoparametric line is perpendicular to this conical surface.

[0062] Combined with the general formula of rotational transformation in robotics, the relationship between the rotation of two vectors about an arbitrary axis can be obtained:

[0063]

[0064] In the formula, β is the angle between the two vectors n C and n u . Among them, T is the transformation matrix between the two coordinate systems.

[0065] T = [n, n u , n × n u

[0066] Therefore, the geometric relationship that the cutter axis direction vector is tangent to the surface boundary can be transformed into a nonlinear equation containing only one unknown β:

[0067] A sinβ + B cosβ + C = 0

[0068] Among them, A, B, and C are constants, and β is the angle between n C and n​u The included angle between two vectors

[0069] Use the Newton - Raphson method to solve the equation:

[0070]

[0071] Find the fixed point β of g(β) M such that g(β M ) = β M For the solution of the root of the equation f(β) = 0, it can be transformed into finding the fixed point of the function g(x). The overall search process is as Figure 6 shown. When searching for the fixed point, it is necessary to first determine whether there is a fixed point, because there may be no case where f(β) = 0. If the judgment of whether there is a fixed point is not made and direct iteration is carried out, it will fall into an infinite loop until the iteration limit is reached. Since f(β) is a periodic continuous function, select [-π, π] as the calculation interval. First, judge the fixed point, solve the extreme points f(β(1)) and f(β(2)) of f(β), and judge whether f(β(1)) and f(β(2)) have different signs. If they have different signs, there must be a fixed point. Perform Newton - Raphson iteration on the boundary points of the existing fixed point to solve the β value, and thus obtain the critical vector n C For the part without a fixed point, spherical quaternion interpolation is used for supplementation.

[0072] In the description of the present invention, the traditional Newton - Raphson method is called the "first - order Newton - Raphson method"; in order to distinguish it from the traditional method, the method of judging whether there is a fixed point and then performing Newton - Raphson iteration is called the "second - order Newton - Raphson method".

[0073] In the present invention, under the same processing environment, the second - order Newton - Raphson method, the first - order Newton - Raphson method, the particle swarm optimization algorithm (PSO), and the combined algorithm of the first - order Newton - Raphson method and the particle swarm optimization algorithm (PSO) proposed by the present invention are respectively used to solve the non - linear equation. The comparison of the running times of the four methods is as Figure 7 shown. The time used by the second - order Newton - Raphson method is 0.0254s, which is 0.15% of the time used by the first - order Newton - Raphson method, 2.54% of the running time of the combined algorithm of the first - order Newton - Raphson method and the particle swarm optimization algorithm (PSO), and 0.34% of the running time of the particle swarm optimization algorithm (PSO), effectively improving the solution speed and also enhancing the solution accuracy.

[0074] It can be seen from Figure 8 that for the solution of the part without fixed points, directly using the Newton-Raphson method once for calculation results in a large deviation from the ideal value; while the Particle Swarm Optimization (PSO) algorithm not only has a large deviation in the solution of the part without fixed points, but also has a deviation in the solution of the fixed point part, with strong uncertainty. Therefore, the quadratic Newton-Raphson method is used for solution, adding a fixed point judgment. For the part without fixed points, spherical quaternion interpolation is used to calculate the tool axis direction of this section, and at the same time, it is judged whether interference and collision occur.

[0075] S5: Perform a first-order Taylor expansion on the NUBRS surface, and search for points on the NUBRS surface one by one with the boundary special points as the initial points to obtain all the search points on the NUBRS surface, where the boundary special points are the points where the critical vector coincides with the surface normal vector at the boundary, and these points are not only the boundary critical points but also the surface critical points.

[0076] Step S5 also includes judging the search points. If the dot product of the unit vector of the tool axis direction and the unit normal vector at the search point is less than or equal to the preset value, then proceed to the next search point. If the dot product of the unit vector of the tool axis direction and the unit normal vector at the search point is greater than the preset value, then adjust the search step length until the dot product of the unit vector of the tool axis direction and the unit normal vector at the search point is less than or equal to the preset value.

[0077] In this application, during the surface search stage, the dot product of the unit vector of the tool axis direction and the unit normal vector at the surface search point is called the critical direction dot product. Therefore, at the tangent point on the surface, the critical direction dot product |D i (u, v)| ≤ ε, where ε is a very small positive value.

[0078] As Figure 10 shown, the critical direction dot product is:

[0079]

[0080] Therefore, the objective function and constraint conditions can be defined as:

[0081] min|D(u, v)|

[0082]

[0083] The first-order Taylor expansion of the critical direction dot product at the point (u k , v k ) is:

[0084] D(u, v) = D(u k , v k ) + (u - u k )D u′(u k ,v k )+(v - v k )D v ′(u k ,v k ) + o n

[0085] If this point is a critical point, it should satisfy:

[0086] D(u k+1 ,v k+1 ) = D(u k ,v k ) = 0

[0087] Then the relational expressions for the changes in the u - direction and v - direction are as follows:

[0088]

[0089] Check that the first - order Taylor expansion of the surface at the point s(u k ,v k ) is:

[0090] S(u, v) = S(u k ,v k ) + S u ′(u k ,v k )(u - u k ) + S v ′(u k ,v k )(v - v k ) + o n

[0091] Adopt equal - step - size search, and adjacent points satisfy |S(u k+1 ,v k+1 ) - S(u k ,v k )| = l s

[0092] Therefore, determine the search direction according to the relational expressions of Δu and Δv, and perform equal - step - size search with l s as the step size.

[0093] If the dot - product of the unit vector of the cutter - axis direction and the unit normal vector at the search point is greater than the preset value, then perform variable - scale search within a local range. Correct the variable - scale matrix B k according to the correction formula of the BFGS method to adaptively adjust the step size α k , until a critical point that satisfies the dot - product of the unit vector of the cutter - axis direction and the unit normal vector at the search point is less than or equal to the preset value is found, and terminate the local search.

[0094] Perform variable-scale search within a local range. Select any critical point on the blade boundary as the initial point \(x_0 = [u_0, v_0]\) for the search on the surface. Let \(x_0 = x_0+\Delta x_0\), and start the search and judgment for the next point. If \(|D|\leq\varepsilon\), record this point until the entire surface is searched; if not, enter the local search stage.

[0095] In the local search stage, the search direction of the initial point is the same as that of the gradient method, and search is carried out along the direction to find the next point. If the dot product of the directions at this point satisfies \(|D|\leq\varepsilon\), record this point. Except for the search of the initial point, the search for critical points on the surface next will correct the variable-scale matrix \(B\) k according to the BFGS correction formula, so as to adaptively adjust the step size \(\alpha\) k . The BFGS algorithm iteration formula is as follows:

[0096]

[0097] where \(x\) k \(=[u\) k , \(v\) k , and \(\Delta g\) k-1 represents the difference in gradients between two points.

[0098] Combined with the surface characteristics, the gradient formula of \(D(u\) k , \(v\) k ) can be obtained as follows

[0099]

[0100] The variable-scale matrix \(B\) k is corrected by the following formula:

[0101]

[0102] to approximate the gradient to the inverse Hessian matrix to determine the moving direction.

[0103] From the above formulas, the changes \(\Delta u\) and \(\Delta v\) of the surface parameters in the \(u\) - direction and \(v\) - direction can be obtained, and the moving step size is obtained:

[0104]

[0105] Continue the local search until a critical point satisfying \(|D|\leq\varepsilon\) is found, and then terminate the local search. After jumping out of the local search, use this point as the new search starting point for equal-step search. If it is within the surface range and satisfies \(|D|\leq\varepsilon\), save this point and start the search for the next critical point. If \(|D|>\varepsilon\) is encountered, repeat the local search process.

[0106] When the search point is outside the boundary of the inspection surface, substitute the curve parameters of the boundary for the u and v parameter values that exceed the boundary, and continue to search along this boundary line until the entire inspection surface is searched.

[0107] S6: Arrange and intersect the search points in a directed order to obtain a closed interference-free region.

[0108] Establish a local coordinate system at the tool position point, with the tool position point as the origin O of the coordinate system, and the surface normal vector n of this point M as the z m axis, and the direction of the instantaneous movement of the tool as the x m , y m axis. Then, it is obtained by the right-hand rule, as Figure 11 shown.

[0109] As Figure 12A and Figure 12B shown, ρ represents the radial distance from the tool position point in the spherical coordinate system. φ is the angle between the critical tool axis vector τ and the z m axis, and θ is the angle between the projection of the critical tool axis direction τ on the O-x m y m plane and the x axis. In order to avoid local interference, the angle between the critical tool axis direction τ and the surface normal vector n M should not be greater than π / 2. Therefore, the ranges of φ and θ are 0 ≤ φ ≤ π / 2 and 0 ≤ θ < 2π respectively.

[0110] Those skilled in the art can easily understand that the above are only the preferred embodiments of the present invention and are not used to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for generating a non-interference area in the grinding and polishing process of an integral blisk, characterized in that, The method includes: S1: Extract features from the area to be machined on the integral blisk to construct the NUBRS surface of the area to be machined, and establish a tool model; S2: Generate the machining path of the tool, and obtain the tool position point information corresponding to the machining path in combination with the tool geometric parameters in the tool model; S3: Obtain the boundary information of the NUBRS surface; S4: Obtain the tool axis direction according to the tool position point information, establish a non-linear equation for the critical tangency between the tool axis direction and the surface to obtain the critical normal vector at the critical point of the tool axis on the boundary; S5: Perform a first-order Taylor expansion on the NUBRS surface, and search for points on the NUBRS surface one by one with the special boundary point as the initial point to obtain all the search points on the NUBRS surface, where the special boundary point is the point where the critical normal vector coincides with the surface normal vector at the boundary; S6: Arrange and intersect the search points in a directed order to obtain a closed interference-free area; Step S5 also includes judging the search points. If the dot product of the unit vector of the tool axis direction and the unit normal vector at the search point is less than or equal to the preset value, search for the next search point. If the dot product of the unit vector of the tool axis direction and the unit normal vector at the search point is greater than the preset value, adjust the search step size until the dot product of the unit vector of the tool axis direction and the unit normal vector at the search point is less than or equal to the preset value; If the dot product of the unit vector in the tool axis direction and the unit normal vector at the search point is greater than a preset value, variable scale search is performed within a local range, and the variable scale matrix B is corrected according to the correction formula of the BFGS method k for modification to adaptively adjust the step size α k until a critical point where the dot product of the unit vector in the tool axis direction and the unit normal vector at the search point is less than or equal to the preset value is found, and the local search is terminated.

2. The method according to claim 1, wherein Dot product D of the unit vector in the cutter axis direction and the unit normal vector at the search point i (u, v) is: D i (u, v) = τ i (u, v) · n i (u, v), where τ i (u, v) is the unit vector in the cutter axis direction, n i (u, v) is the unit normal vector at the search point, and the objective function is min|D i (u, v)|, and the constraint conditions are u min 、u max 、v min 、v max are the limit values in the u and v directions.

3. The method according to claim 1, wherein In step S2, the machining path of the tool is obtained by the equal chord height method or the equal arc length method.

4. The method according to claim 1, wherein The NUBRS surface S(u, v) in step S1 is: Among them, u and v are two mutually perpendicular vectors in the cutting plane of the area to be processed, m is the maximum subscript of the non-rational B-spline control points in the v direction, n is the maximum subscript of the non-rational B-spline control points in the u direction, N i,p N(u) is the non-rational B-spline basis function defined on the knot vector u, N j,q N(v) is the non-rational B-spline basis function defined on the knot vector v, i = 0, 1, …, n, j = 0, 1, …, m, p is the degree of the non-rational B-spline in the u direction, q is the degree of the non-rational B-spline in the v direction, w i,j is the weight factor, P i,j is the control grid in both the u and v directions.

5. The method according to claim 1, characterized in that, In step S2, the cutter location point information corresponding to the machining path is obtained by offsetting the cutter axis radius along the normal unit vector of the cutter contact point, and the cutter location point information is where CL = [x, y, z, i, j, k], x, y, and z are the coordinates of the cutter location point in the workpiece coordinate system; i, j, and k are the normal unit vectors of the cutter contact point, that is, the direction vector of the cutter axis.

6. The method according to claim 1, wherein The non-linear equation in step S4 is: Asinβ + Bcosβ + C = 0 where A, B, and C are constants, and β is the angle between two vectors n and n, where n is the critical vector and n is the tangent vector in the u direction. C and n u the angle between two vectors, where n C is the critical vector, n u is the tangent vector in the u direction, T is the transformation matrix between the workpiece coordinate system and the local coordinate system of the tool point, T = [n, n u , n×n u , and n is the surface normal vector.

7. The method according to claim 1, wherein In step S5, the points on the NUBRS surface are searched one by one with an equal step size.

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