Method for creating machining trajectory of complex curved surface based on streamline field driving

Abstract

The application is a kind of complex curved surface machining track creation method based on streamline field driving, first, the control point and node vector of complex curved surface are obtained, and the parameterized complex curved surface is constructed by using NURBS curved surface equation;The optimal tool path direction of each parameter point on the complex curved surface along the u and v directions is calculated, and the discrete direction field is constructed;Then, the optimal tool path direction of the parameter point along the u and v directions is regarded as the velocity direction in the incompressible plane flow field, and the stream function is inversely calculated according to the plane streamline property;Finally, the streamlines are constructed according to the stream function, and each streamline type tool contact point track is generated according to the streamlines;The final tool contact point track is generated according to all the streamline type tool contact point tracks, the geometric relationship between the tool contact point and the tool position point is considered, the tool position point coordinates are obtained according to the tool contact point coordinates, and the machining track is obtained. The method considers the influence of different curvatures on the machining bandwidth, accurately calculates the track, deletes the path that may collide with the edge of the curved surface and the invalid path, and effectively reduces the path length.

Description

Technical Field

[0001] This invention belongs to the field of freeform surface machining path planning technology, specifically relating to a method for creating complex surface machining trajectories based on streamline field-driven processes. Background Technology

[0002] With the increasingly widespread application of complex curved surfaces in industrial fields, CNC machining technology for complex curved surfaces has received more and more attention. Current five-axis machining toolpath planning methods often only focus on the geometric level, lacking a comprehensive consideration of geometric and physical information during CNC machining, such as material removal rate, the degree of deviation of tool path from the optimal tool path, etc., making it difficult to meet the five-axis machining trajectory planning requirements of parts with complex curved surfaces such as impellers and blades that aim for high efficiency, high geometric accuracy, and high service performance.

[0003] Combining streamlined fields with the machining of complex curved surfaces allows for the planning of machining paths that balance efficiency and aerodynamic characteristics, resulting in smooth trajectories without self-intersections, thus better reflecting actual machining problems. However, current technologies for streamlined field modeling still have limitations in adaptability to the machining of complex curved surfaces, especially the control equations for complex toolpath directions. These equations typically use streamlines directly as trajectory lines, leading to poor matching with the optimal toolpath direction and insufficient consideration of geometric information such as surface curvature. Therefore, local fine-tuning and refinement of the control equations can result in significant fitting deviations. In terms of streamline trajectory design, existing streamline trajectory layout strategies still primarily employ residual height limits. However, due to the unique properties of streamlines, the next streamline trajectory obtained solely based on the minimum row spacing offset of the current streamline trajectory may exceed residual requirements. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the technical problem this invention aims to solve is to provide a method for creating complex surface machining trajectories based on streamline field driving.

[0005] The present invention solves the aforementioned technical problem by adopting the following technical solution:

[0006] A method for creating machining trajectories for complex curved surfaces based on streamline field driving, characterized by the following steps:

[0007] Step 1: Obtain the control points and node vectors of the complex surface, and construct a parameterized complex surface using the NURBS surface equation based on the control points and node vectors;

[0008] Step 2: Calculate the optimal tool path along the u and v directions at each parameter point on the complex surface;

[0009] Step 3: Treat the optimal cutting direction along the u and v directions at the parameter point as the velocity direction in the incompressible planar flow field, and inversely calculate the stream function based on the properties of the planar streamlines;

[0010] Step 4: Generate the trajectory of each streamlined tool contact point;

[0011] 4.1) Construct streamlines based on the stream function, using the intersection of a streamline and the boundary of the parameter domain as the initial seed point, and then... Establish a differential equation, where The differential equations are solved using the fourth-order Runge-Kutta method to trace the streamline path passing through the initial seed point; the streamline path passing through the initial seed point is then mapped in reverse onto the machining surface to obtain the initial streamlined tool contact trajectory.

[0012] 4.2) Construct an initial path spline interpolation curve based on the initial streamlined tool contact trajectory, and calculate the curvature at each path point based on the initial path spline interpolation curve; when the curvature is 0, the machining bandwidth L at the path point is:

[0013]

[0014] When the curvature is positive, the processing bandwidth at the path point is:

[0015]

[0016] When the curvature is negative, the processing bandwidth at the path point is:

[0017]

[0018] In the formula, R is the radius of curvature at the path point, r is the tool radius, and h is the residual height;

[0019] The parameter increments Δu and Δv along the u and v directions at the parameter point are obtained according to equation (10);

[0020]

[0021] In the formula, n is the normal vector at the parameter point;

[0022] 4.3) Add parameter increments Δu and Δv to the u and v directions of the original parameter point respectively to obtain the new parameter point; calculate the stream function values ​​of the original parameter point and the new parameter point according to equation (4), take the new parameter point corresponding to the minimum stream function value difference as the new seed point, repeat steps 4.1) to 4.3) to track all streamlined tool contact trajectories;

[0023] Step 5: Generate the final tool contact trajectory based on all streamlined tool contact trajectory;

[0024] Step 6: Consider the geometric relationship between the tool contact point and the tool position point, obtain the coordinates of each tool position point according to equation (11), and then obtain the machining trajectory;

[0025]

[0026] In the formula, O is the coordinate of the tool position point, P is the coordinate of the tool contact point, x is the unit tangential vector, z is the unit normal vector, d1 is the distance from the tool contact point to the tool axis, d2 is the distance from the tool contact point along the tool axis to the tool tip, λ is the angle between the tool axis and the unit normal vector z, and ω is the angle between the projection line of the tool axis in the tangential plane and the unit tangential vector x.

[0027] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0028] 1. Based on the properties of the planar flow field, the stream function of the tool path vector field is reconstructed using a polynomial based on B-spline basis functions. The conjugate gradient method is used to solve the asymmetric linear equation system about the control coefficient matrix of the stream function. At the same time, the GMRES method is used to refine the iteration during the iteration process to obtain more accurate equation solutions for constructing a better stream function.

[0029] 2. Considering the influence of different curvatures on the machining bandwidth, calculate the appropriate machining bandwidth based on the residual height under different curvatures to accurately calculate the trajectory and improve machining accuracy.

[0030] 3. Based on the collision and redundancy of the toolpath at the edge of the curved surface, paths that may cause collisions and invalid paths are deleted, effectively reducing the path length. At the same time, the conversion from the tool contact point trajectory to the tool position trajectory is realized. The generation and arrangement of streamlined paths are given, and the local tool movement direction and the overall path arrangement are taken into account. Taking into account the surface information, a smooth toolpath with a shorter total length is generated, which is suitable for high-precision and high-efficiency machining. Attached Figure Description

[0031] Figure 1 It is the overall flowchart;

[0032] Figure 2 Here is a schematic diagram of the optimal tool path direction field; where (a) is a schematic diagram of the parameter domain direction and (b) is a schematic diagram of the machining surface direction.

[0033] Figure 3 This is a schematic diagram of the partial derivative vector and normal vector at the parameter point;

[0034] Figure 4 This is the initial streamlined tool contact trajectory diagram;

[0035] Figure 5 It is a diagram of the knife contact point trajectory;

[0036] Figure 6 It is a tool position trajectory diagram. Detailed Implementation

[0037] Specific embodiments are given below with reference to the accompanying drawings. These specific embodiments are only used to describe the technical solution of the present invention in detail, and are not intended to limit the scope of protection of this application.

[0038] This invention provides a method for generating machining trajectories for complex curved surfaces based on streamlined field driving (hereinafter referred to as the method, see below). Figure 1-6 The process includes the following steps:

[0039] Step 1: Obtain the control points and node vectors of the complex surface using software such as Rhino or other methods. Construct a parameterized complex surface based on the control points and node vectors using the NURBS surface equations. When the number of control points in the u and v directions of the complex surface is (m+1) = 50 and (n+1) = 50, and the degree is k = 3 and l = 3, respectively, then the number of nodes in the node vectors along the u and v directions is (r+1) and (s+1), respectively, where r = m + k + 1, s = n + l + 1, and the repetition at both ends of the node vector is (k+1) and (l+1), respectively.

[0040] Step 2: Construct a discrete direction field, that is, calculate the optimal tool path along the u and v directions at each parameter point on the complex surface;

[0041] Dimensionality reduction mapping is performed on complex surfaces to obtain two-dimensional representations of three-dimensional directions. Discrete direction fields are then constructed. Specifically, using the NURBS surface equations and the definition of derivatives, the partial derivative vectors r along the u and v directions at each parameter point on the complex surface are obtained. u r v With normal vector; here, for ease of calculation, the parameter domain direction is set to (1,0,0), and parameter points are selected from the complex surface by setting the parameter point interval. Here, the parameter point interval is set to 0.02, that is, 51 parameter points are included in both the u and v directions;

[0042] Based on the partial derivative vectors along the u and v directions at the parameter point and the optimal tool path direction, the optimal tool path direction vector f at the parameter point is obtained as follows:

[0043] f = r u du+r v dv(1)

[0044] In the formula, du and dv are the optimal tool paths along the u and v directions at the parameter point, respectively;

[0045] Based on the geometric relationship between the partial derivative vectors along the u and v directions at the parameter points and the optimal tool path vector, we have:

[0046]

[0047]

[0048] In the formula, θ represents the optimal tool path vector and the partial derivative vector r at the parameter point. u The angle between them;

[0049] By combining equations (1) to (3), the optimal tool path (du, dv) along the u and v directions at the parameter point is obtained;

[0050] Step 3: Treat the optimal tool path along the u and v directions at the parameter point as the velocity direction in the incompressible planar flow field, and inversely calculate the stream function based on the properties of the planar streamline to reconstruct the tool path vector field;

[0051] To enhance the overall smoothness of the tool path vector field and improve its flexibility and local control capability, a polynomial based on B-spline basis functions is used to characterize the stream function. The stream function is then expressed as:

[0052] ψ(u,v)=MDN T (4)

[0053]

[0054] In the formula, M is the k-th order B-spline basis function of the node vector along the u direction, and N is the l-th order B-spline basis function of the node vector along the v direction. i,k (u) is the k-th order B-spline basis function value of the i-th control point in the u direction, N j,l (v) is the l-th order B-spline basis function value of the j-th control point in the v direction, and D is the control coefficient matrix of the stream function;

[0055] Based on the optimal tool path direction at the parameter point and the basis functions along the u and v directions of the complex surface, a variable function is constructed such that the tangent direction at a point on the streamline is perpendicular to the gradient direction of the stream function. The optimal tool path directions du and dv along the u and v directions at the parameter point are then obtained as follows:

[0056]

[0057] In the formula, (N') T For N T The derivative of M, M' is the derivative of M;

[0058] Based on equation (6), an asymmetric linear system of equations about the control coefficient matrix of the stream function is established. The conjugate gradient method is used to iteratively solve the asymmetric linear system of equations. At the same time, the GMRES method is used to refine the iteration during the iteration process. The control coefficient matrix D of the stream function is obtained by solving the equation. Substituting the control coefficient matrix D of the stream function into equation (4), the stream function ψ(u,v) is obtained.

[0059] Step 4: Generate the trajectory of each streamlined tool contact point;

[0060] 4.1) Construct contour lines, i.e., streamlines, based on the stream function. Use the intersection point of a streamline with the boundary of the parameter domain as the initial seed point, and then... Establish a differential equation, where The differential equations are solved using the fourth-order Runge-Kutta method to trace the streamline path passing through the initial seed point; the streamline path passing through the initial seed point is then mapped in reverse onto the machining surface to obtain the initial streamlined tool contact trajectory.

[0061] 4.2) Construct an initial path spline interpolation curve based on the initial streamlined tool contact trajectory, and calculate the curvature at each path point based on the initial path spline interpolation curve; calculate the machining bandwidth at the path point based on the curvature. When the curvature is 0, the machining bandwidth L at the path point is:

[0062]

[0063] When the curvature is positive, the processing bandwidth at the path point is:

[0064]

[0065] When the curvature is negative, the processing bandwidth at the path point is:

[0066]

[0067] In the formula, R is the radius of curvature at the path point, r is the tool radius, and h is the residual height. Here, a ball end mill with a radius of 2mm is selected for machining, and the residual height is 0.1mm. To avoid overcutting, the machining bandwidth from the initial path to the second path is specified as the tool radius.

[0068] The parameter increments Δu and Δv along the u and v directions at the parameter point are obtained according to equation (10);

[0069]

[0070] In the formula, n is the normal vector at the parameter point;

[0071] 4.3) Add parameter increments Δu and Δv to the u and v directions of the original parameter points respectively to obtain new parameter points; calculate the stream function values ​​of the original parameter points and the new parameter points according to equation (4), and take the new parameter point corresponding to the minimum stream function value difference as the new seed point. Repeat steps 4.1) to 4.3) to track all streamlined tool contact trajectories; if the parameter point of the last streamlined tool contact trajectory has a value less than 0, delete the corresponding parameter point.

[0072] Step 5: Remove useless parameter points on each streamlined tool contact trajectory, and then backmap each streamlined tool contact trajectory onto the machining surface to obtain the final tool contact trajectory;

[0073] 5.1) Delete the initial streamlined tool contact trajectory, and take the second streamlined tool contact trajectory to the last streamlined tool contact trajectory as the streamlined trajectory;

[0074] 5.2) For each streamlined tool contact trajectory that makes up the streamlined trajectory, find point b on the streamlined tool contact trajectory such that the distance between point b and the endpoint of its neighboring streamlined tool contact trajectory is equal to the machining bandwidth at point b; if the curvature at all path points between point b and the endpoint of the streamlined tool contact trajectory of its neighboring point b is 0, then delete all parameter points between point b and the endpoint of the streamlined tool contact trajectory of its neighboring point b, and then backmap the remaining part of the streamlined tool contact trajectory onto the machining surface to obtain three-dimensional coordinate points, and thus obtain the final tool contact trajectory; if the curvature at at least one path point between point b and the endpoint of the streamlined tool contact trajectory of its neighboring point b is not 0, then backmap the original streamlined tool contact trajectory onto the machining surface to obtain the final tool contact trajectory;

[0075] Step 6: Based on the final tool contact point trajectory, and considering the geometric relationship between the tool contact point and the tool position point, calculate the tool position point trajectory, i.e., the machining trajectory, based on information such as the tool tilt angle and tool diameter;

[0076]

[0077] In the formula, O is the coordinate of the tool position point, P is the coordinate of the tool contact point, x is the unit tangential vector, z is the unit normal vector, d1 is the distance from the tool contact point to the tool axis, d2 is the distance from the tool contact point along the tool axis to the tool tip; λ is the angle between the tool axis and the unit normal vector z, which is set to 30° in this embodiment; ω is the angle between the projection line of the tool axis in the tangential plane and the unit tangential vector x, which is set to 30° in this embodiment.

[0078] Any aspects not covered in this invention are applicable to existing technologies.

Claims

1. A method for creating machining trajectories for complex curved surfaces based on streamlined field driving, characterized in that, The method includes the following steps: Step 1: Obtain the control points and node vectors of the complex surface, and construct a parameterized complex surface using the NURBS surface equation based on the control points and node vectors; Step 2: Calculate the parameters at each point on the complex surface along... u , v The optimal tool path direction; Based on the optimal tool path at the parameter point and along... u , v The partial derivative vector of the direction yields the optimal tool path vector at the parameter point. for: （1） In the formula, , For the parameter point along u , v The partial derivative vector of the direction, For the parameter point along u , v The optimal tool path direction; According to the parameter point along u , v The geometric relationship between the partial derivative vector of the direction and the optimal tool path vector is as follows: （2） （3） In the formula, The optimal tool path vector and its partial derivative vector at the parameter point. The angle between them; By combining equations (1) to (3), we obtain the parameter points along the... u , v The optimal tool path direction; Step 3: Move along the parameter point u , v The optimal cutting direction is considered as the velocity direction in an incompressible planar flow field, and the stream function is obtained by inverse calculation based on the properties of the planar streamlines. The stream function is characterized by a polynomial of B-spline basis functions. for: （4） （5） In the formula, It is along u Direction node vector k B-spline basis functions It is along v Direction node vector l B-spline basis functions yes u Direction first i control points k B-spline basis function values yes v Direction first j control points l B-spline basis function values The control coefficient matrix of the stream function; When the tangent direction at a point on the streamline is perpendicular to the gradient direction of the stream function, the parameter point along... u , v Optimal toolpath , Represented as: （6） In the formula, for The derivative of for The derivative; Based on equation (6), establish a system of nonsymmetric linear equations concerning the control coefficient matrix of the stream function, and solve for the control coefficient matrix of the stream function. This leads to the stream function; Step 4: Generate the trajectory of each streamlined tool contact point; 4.1) Construct streamlines based on the stream function, using the intersection of a streamline and the boundary of the parameter domain as the initial seed point, and then... Establish a differential equation, where The fourth-order Runge-Kutta method is used to solve the differential equations and trace the streamline path that passes through the initial seed point. The streamline path that passes through the initial seed point is then mapped in reverse onto the machining surface to obtain the initial streamlined tool contact trajectory. 4.2) Construct an initial path spline interpolation curve based on the initial streamlined tool contact trajectory, and calculate the curvature at each path point based on the initial path spline interpolation curve; when the curvature is 0, the machining bandwidth at the path point is... L for: （7） When the curvature is positive, the processing bandwidth at the path point is: （8） When the curvature is negative, the processing bandwidth at the path point is: （9） In the formula, R The radius of curvature at the path point. r For the tool radius, h Residual height; The parameter point is obtained according to equation (10) along the... u , v Increment of directional parameters and ; （10） In the formula, n is the normal vector at the parameter point; 4.3) At the original parameter point u , v Add parameter increments in each direction and , to obtain new parameter points; calculate the flow function values ​​of the original parameter points and the new parameter points according to equation (4), take the new parameter point corresponding to the minimum flow function value difference as the new seed point, repeat steps 4.1) to 4.3), and track all streamlined knife contact trajectories; Step 5: Generate the final tool contact trajectory based on all streamlined tool contact trajectory; Step 6: Consider the geometric relationship between the tool contact point and the tool position point, obtain the coordinates of each tool position point according to equation (11), and then obtain the machining trajectory; （11） In the formula, Let x be the coordinates of the tool position point, P be the coordinates of the tool contact point, x be the unit tangential vector, and z be the unit normal vector. d 1 represents the distance from the tool contact point to the tool axis. d 2 represents the distance from the tool contact point along the tool axis to the tool tip. Let z be the angle between the tool axis and the unit normal vector z. The angle between the projection line of the tool axis in the tangential plane and the unit tangential vector x.

2. The method for creating complex surface machining trajectories based on streamlined field driving according to claim 1, characterized in that, In step 5, firstly, the initial streamlined tool contact trajectory is deleted, and the second streamlined tool contact trajectory to the last streamlined tool contact trajectory are taken as streamline trajectories. Then, for each streamlined tool contact trajectory that makes up the streamlined trajectory, find the points on the streamlined tool contact trajectory. , make point The distance between the point and the endpoint of the streamlined tool contact trajectory adjacent to it is equal to the point. Processing bandwidth at the point; if point and neighboring points If the curvature at all path points between the endpoints of the streamlined tool contact trajectory is 0, then the point... and neighboring points All parameter points between the endpoints of the streamlined tool contact trajectory are deleted, and then the remaining part of the streamlined tool contact trajectory is back-mapped onto the machining surface to obtain the final tool contact trajectory; if points and neighboring points If the curvature at at least one path point between the endpoints of the streamlined tool contact trajectory is not zero, then the original streamlined tool contact trajectory is back-mapped onto the machining surface to obtain the final tool contact trajectory.

Images