Method for optimizing machining pose without interference of five-axis CNC lathe

Abstract

The present invention discloses a method for optimizing the non-interference machining pose of a five-axis CNC lathe, including the following steps: Step 1: Obtain the position coordinates of the spiral tool contact points that envelope the workpiece to be machined, and calculate the slopes corresponding to the circumferential cross-section curves at each tool contact point; Step 2: Establish the relationships between the slopes of the cross-section curves corresponding to the tool contact points in five-axis machining and the positive limit swing angle and negative limit swing angle of the tool axis respectively, determine the feasible range a of the positive swing angle of the tool axis and the feasible range b of the negative swing angle of the tool axis, and determine the reachable area c of the tool axis vector without global / local interference; Step 3: Taking the smooth transition of the rotating axis B axis as the optimization goal, smooth the tool axis vector to obtain the optimization sequence of the non-interference machining pose of the five-axis CNC lathe; Step 4: Determine the coordinate origin in the machine tool coordinate system considering the structural characteristics of the tool shank, analyze the position and motion transformation matrix of each axis according to the five-axis linkage process, and post-process the tool contact points and tool axis vectors to obtain the G code that can be recognized by the machine tool.

Description

Technical Field

[0001] The present invention belongs to the technical field of machining, and specifically relates to a method for optimizing the non-interference machining posture of a five-axis CNC lathe. Background Art

[0002] Curved surface parts with complex surface structures are increasingly widely used in fields such as aerospace and medical equipment. To ensure the feasibility and accuracy of complex curved surface machining, machine tools generally require multiple degrees of freedom. Traditional turning machining uses the rotational movement of the workpiece and the linear movement of the turning tool for cutting. Its machining path is generated based on the cross-sectional curve of the revolving surface, and the movement trajectory of the turning tool relative to the workpiece is a helix, that is, at the same cross-sectional position of the workpiece, the position of the turning tool is fixed. For a five-axis lathe, a rotating axis B-axis and a linear axis Y-axis are added on the basis of a traditional lathe. Although the flexibility of the tool axis is increased, the control difficulty of the tool axis vector is also increased, and local / global interference problems are very likely to occur. Therefore, studying the method for optimizing the machining posture of a five-axis lathe is of great significance for realizing the precise and smooth machining of complex curved surface parts and promoting the development of high-end CNC equipment. Summary of the Invention

[0003] In view of this, the purpose of the present invention is to provide a method for optimizing the non-interference machining posture of a five-axis CNC lathe, comprehensively considering the shape of the workpiece to be machined and the machining path trajectory, generating a five-axis turning machining path without global / local interference, and improving the quality of turning machining.

[0004] To achieve the above purpose, the present invention provides the following technical solutions:

[0005] A method for optimizing the non-interference machining posture of a five-axis CNC lathe includes the following steps:

[0006] Step 1: Based on the principle of spiral projection drive, obtain the position coordinates of the spiral tool contact points that envelope the workpiece to be machined, and calculate the slopes of the circumferential cross-sectional curves corresponding to each tool contact point in the path trajectory;

[0007] Step 2: Considering the characteristic that the rotating axis B-axis of the five-axis lathe drives the tool axis to swing: establish the relationships between the slopes of the cross-sectional curves corresponding to the tool contact points in five-axis machining and the positive limit swing angle and negative limit swing angle of the tool axis respectively, and determine the feasible range a of the positive swing angle of the tool axis and the feasible range b of the negative swing angle of the tool axis; combining range a and range b, determine the reachable area c of the tool axis vector without global / local interference;

[0008] Step 3: Taking the smooth transition of the rotating axis B-axis as the optimization goal, perform smoothing processing on the tool axis vector to obtain the optimized sequence of the non-interference machining posture of the five-axis CNC lathe;

[0009] Step 4: Consider the structural characteristics of the tool bar to determine the coordinate origin in the machine tool coordinate system. According to the five-axis linkage process, analyze the position and motion transformation matrix of each axis, and post-process the tool contact point and tool axis vector to obtain the G code that can be recognized by the machine tool.

[0010] Furthermore, in step 1, the method for calculating the slope of the circumferential cross-sectional curve corresponding to each blade contact point in the path trajectory is:

[0011] Based on the spiral projection driving principle, the Archimedean spiral is projected onto the surface of the workpiece to be processed, and the contact position coordinates of the spiral cutter (x f ,y f ,z f ), where f = 0, 1, ..., n, n is the total number of knife contacts in the entire path;

[0012] Build while passing the knife contact (x f ,y f ,z f ) and the plane equation perpendicular to the workpiece axis G(x f ,y f ,z f ), and the plane and the workpiece surface F(x f ,y f ,z f ) to obtain the slope k corresponding to each knife contact point on the circumferential cross-sectional curve. f .

[0013] Furthermore, in step 2, the method for determining the feasible interval a of the tool axis positive swing angle is:

[0014] For tool contact point i, based on the selected tool rake angle γ, local interference judgment is performed on the tool rake face to determine the positive limit swing angle α of the tool axis at tool contact point i in five-axis machining. i :

[0015] α i =γ

[0016] Considering the selected tool shank shape and size D, the tool rake face is globally interfered with, and the cross-sectional curve slope k corresponding to any tool contact point j except tool contact point i in five-axis machining is established. j The positive limit swing angle α with the tool axis j The relationship between:

[0017]

[0018] Among them, L1 is the distance between knife contact i and knife contact j; ε1 is the vector The angle between the tool axis vector at tool contact point i and the tool axis vector; η is the angle between the normal at tool contact point i and the horizontal line; (xi , y i , z i ) are the coordinates of the tool contact point i; (x j , y j , z j ) are the coordinates of the tool contact point j; j ≠ i;

[0019] Obtain the positive limit swing angle α of the tool axis without collision interference j :

[0020]

[0021] Solve the positive limit swing angle of the tool axis for all tool contact points except the tool contact point i, and obtain the feasible interval a of the positive swing angle of the tool axis without local undercut interference and global collision interference at the tool contact point i i :

[0022] a i = (0, α1) ∩ (0, α2) ∩ … ∩ (0, α n )

[0023] Solve the feasible intervals of the positive swing angles of the tool axis for all tool contact points in sequence, and obtain the feasible interval a of the positive swing angle of the tool axis:

[0024] a = [a1, a2…, a n-1 , a n .

[0025] Furthermore, in the second step, the method for determining the feasible interval b of the positive swing angle of the tool axis is as follows:

[0026] For the tool contact point i, based on the selected tool flank angle μ, perform a local interference judgment on the flank face to determine the negative limit swing angle β of the tool axis at the tool contact point i in five-axis machining i :

[0027] β i = μ

[0028] Based on the shape and size D of the selected tool shank, perform a global interference judgment on the flank face, and establish the relationship between the slope k of the cross-sectional curve corresponding to any tool contact point m except the tool contact point i in five-axis machining and the negative limit swing angle β of the tool axis m and the negative limit swing angle β of the tool axis m :

[0029]

[0030] where L2 is the distance between the tool contact point i and the tool contact point m, ε2 is the angle between the vector and the tool axis vector of the tool contact point i, η is the angle between the normal line at the tool contact point i and the horizontal line; (x i , y i , zi ) are the coordinates of the tool contact point i; (x m , y m , z m ) are the coordinates of the tool contact point m; m ≠ i;

[0031] Obtain the positive limit swing angle β of the tool axis without collision interference m :

[0032]

[0033] Find the negative limit swing angle of the tool axis for all tool contact points except the tool contact point i, and obtain the feasible range b of the negative swing angle of the tool axis without local undercut interference and global collision interference at the tool contact point i i :

[0034] b i = (0, β1) ∩ (0, β2) ∩ … ∩ (0, β n )

[0035] Solve the feasible range of the negative swing angle of the tool axis for all tool contact points in sequence, and obtain the feasible range b of the negative swing angle of the tool axis:

[0036] b = [b1, b2…, b n-1 , b n .

[0037] Furthermore, in the second step, by combining the feasible range a of the positive swing angle of the tool axis and the feasible range b of the negative swing angle of the tool axis, obtain the feasible range c of the tool axis:

[0038] c = a ∪ b.

[0039] Furthermore, in the third step, the method for obtaining the optimized sequence of the interference-free machining pose of the five-axis CNC lathe is:

[0040] 31) According to the limit theory, when the distance between two adjacent tool contact points is very short, assume that the feed rate remains constant;

[0041] 32) The equation for solving the smooth swing angle of the tool axis vector without interference for the entire path is:

[0042]

[0043] where Q is the objective function, ω i is the swing angle of the tool axis vector corresponding to the i-th tool contact point, D i is the distance between adjacent tool contact points, f is the feed rate of the five-axis lathe; c represents the feasible range of the tool axis;

[0044] 33) According to the obtained swing angle ω of the tool axis vector i , determine the optimized sequence of the interference-free machining pose of the five-axis CNC lathe:

[0045] U = [ω1, ω2, …, ω n-1 , ω n

[0046] Wherein, U represents the non-interference machining pose optimization sequence of the five-axis CNC lathe.

[0047] Furthermore, in the fourth step, the motion transformation matrix is:

[0048]

[0049] Wherein, F w represents the tool axis vector in the workpiece coordinate system; P w represents the tool point coordinate in the workpiece coordinate system; M RIW represents the coordinate transformation matrix from the C-axis coordinate system to the workpiece coordinate system; M R2R1 represents the coordinate transformation matrix from the B-axis coordinate system to the C-axis coordinate system; M TR2 represents the coordinate transformation matrix from the tool coordinate system to the B-axis coordinate system; R R1 represents the rotation transformation matrix of the C-axis; R R2 represents the rotation transformation matrix of the B-axis; T XYZ represents the translational axis motion transformation matrix; F T represents the initial tool axis vector in the tool coordinate system; P T represents the initial tool point coordinate in the tool coordinate system.

[0050] The beneficial effects of the present invention are as follows:

[0051] The non-interference machining pose optimization method for a five-axis CNC lathe of the present invention proposes a method for determining the attitude of the tool axis vector for global / local non-interference in five-axis turning. Through the post-processing calculation of five-axis turning, an optimized spiral path suitable for a five-axis lathe is obtained, which can achieve precise and smooth machining of complex surface parts, and is of great significance for improving the machining quality of complex surfaces. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to make the objectives, technical solutions, and beneficial effects of the present invention clearer, the present invention provides the following drawings for description:

[0053] Figure 1 is a flowchart of an embodiment of the non-interference machining pose optimization method for a five-axis CNC lathe of the present invention;

[0054] Figure 2 is a schematic diagram for judging local interference of the rake face;

[0055] Figure 3 is a schematic diagram for judging global interference of the rake face;

[0056] ​Figure 4 Schematic diagram of local interference judgment on the flank surface;

[0057] Figure 5 Schematic diagram of global interference judgment of flank face;

[0058] Figure 6 To solve the coordinate system for the post-process;

[0059] Figure 7 It is a five-axis CNC lathe kinematic chain form. DETAILED DESCRIPTION

[0060] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0061] like Figure 1 As shown, the interference-free machining posture optimization method for a five-axis CNC lathe of this embodiment includes the following steps:

[0062] Step 1: Based on the spiral projection drive principle, the position coordinates of the spiral cutter contact points that envelop the workpiece to be processed are obtained, and the slope of the circumferential cross-sectional curve corresponding to each cutter contact point in the path trajectory is calculated.

[0063] Specifically, in this embodiment, the method for calculating the slope of the circumferential cross-sectional curve corresponding to each knife contact point in the path trajectory is:

[0064] Based on the spiral projection driving principle, the Archimedean spiral is projected onto the surface of the workpiece to be processed, and the contact position coordinates of the spiral cutter (x f ,y f ,z f ), where f = 0, 1, ..., n, n is the total number of knife contacts in the entire path;

[0065] Build while passing the knife contact (x f ,y f ,z f ) and the plane equation perpendicular to the workpiece axis G(x f ,y f ,z f ), and the plane and the workpiece surface F(x f ,y f ,z f ) to obtain the slope k corresponding to each knife contact point on the circumferential cross-sectional curve. f .

[0066] Step 2: Consider the characteristic that the rotating axis B of the five-axis lathe drives the tool axis to swing: Establish the relationship between the slope of the cross-sectional curve corresponding to the tool contact point in five-axis machining and the positive limit swing angle and negative limit swing angle of the tool axis respectively, and determine the feasible range a of the positive swing angle of the tool axis and the feasible range b of the negative swing angle of the tool axis; Combine range a and range b to determine the reachable area c of the tool axis vector without global / local interference.

[0067] Specifically, during the five-axis turning process, the tool axis vector changes in real time as the B axis rotates. Due to the complexity of the workpiece to be machined and the complexity of the path trajectory, overcut interference occurs on the front tool face of the tool and collision interference occurs on the tool shank. In this embodiment, the method for determining the feasible range a of the positive swing angle of the tool axis is as follows:

[0068] For the tool contact point i: As Figure 2 shown, based on the selected rake angle γ of the tool, perform a local interference judgment on the front tool face to determine the positive limit swing angle α of the tool axis at the tool contact point i in five-axis machining i :

[0069] α i = γ

[0070] As Figure 3 shown, considering the shape and size D of the selected tool shank, perform a global interference judgment on the front tool face, and establish the relationship between the slope k of the cross-sectional curve corresponding to any tool contact point j other than the tool contact point i in five-axis machining and the positive limit swing angle α of the tool axis j and the positive limit swing angle α of the tool axis j :

[0071]

[0072] where L1 is the distance between the tool contact point i and the tool contact point j; ε1 is the angle between the vector and the tool axis vector at the tool contact point i; η is the angle between the normal line at the tool contact point i and the horizontal line; (x i , y i , z i ) are the coordinates of the tool contact point i; (x j , y j , z j ) are the coordinates of the tool contact point j; j ≠ i;

[0073] Obtain the positive limit swing angle α of the tool axis without collision interference j :

[0074]

[0075] Solve the positive limit swing angle of the tool axis for all other tool contact points except the tool contact point i, and obtain the feasible range a of the positive swing angle of the tool axis without local overcut interference and global collision interference at the tool contact point i i :

[0076] a i =(0, α1) ∩ (0, α2) ∩ … ∩ (0, α n )

[0077] Solve the feasible ranges of the positive spindle angle for all tool contact points in sequence to obtain the feasible range of the positive spindle angle a:

[0078] a = [a1, a2…, a n-1 , a n

[0079] Similarly, the method for determining the feasible range of the positive spindle angle b is as follows:

[0080] For tool contact point i: As Figure 4 shown, based on the selected flank angle μ of the tool, perform a local interference judgment on the flank face to determine the negative limit spindle angle β at tool contact point i in five-axis machining i :

[0081] β i = μ

[0082] As Figure 5 shown, based on the shape and size D of the selected tool shank, perform a global interference judgment on the flank face to establish the relationship between the slope k of the cross-sectional curve corresponding to any tool contact point m other than tool contact point i in five-axis machining and the negative limit spindle angle β m and the negative limit spindle angle β m :

[0083]

[0084] where L2 is the distance between tool contact point i and tool contact point m, ε2 is the angle between the vector and the spindle vector of tool contact point i, η is the angle between the normal at tool contact point i and the horizontal line; (x i , y i , z i ) are the coordinates of tool contact point i; (x m , y m , z m ) are the coordinates of tool contact point m; m ≠ i;

[0085] Obtain the positive limit spindle angle β without collision interference m :

[0086]

[0087] Solve the negative limit spindle angles of all other tool contact points except tool contact point i to obtain the feasible range of the negative spindle angle b without local undercut interference and global collision interference at tool contact point i i : ​

[0088] b i = (0, β1) ∩ (0, β2) ∩ … ∩ (0, β n )

[0089] Solve the feasible range of the negative swing angle of the tool axis for all tool contact points in sequence to obtain the feasible range b of the negative swing angle of the tool axis:

[0090] b = [b1, b2…, b n-1 , b n

[0091] Combine the feasible range a of the positive swing angle of the tool axis and the feasible range b of the negative swing angle of the tool axis to obtain the feasible range c of the tool axis:

[0092] c = a ∪ b

[0093] Step 3: With the smooth transition of the rotating axis B-axis as the optimization goal, perform smoothing processing on the tool axis vector to obtain the optimized sequence of the interference-free machining posture of the five-axis CNC lathe.

[0094] To prevent mutations between adjacent tool axis vectors in the feasible range c in the full path, with the feasible range c of the tool axis as the constraint condition and the smoothing of the tool axis vector as the optimization goal, the Newton descent method is used to determine the optimized sequence U of the interference-free machining posture of the five-axis CNC lathe. Specifically, the method for obtaining the optimized sequence of the interference-free machining posture of the five-axis CNC lathe in this embodiment is as follows:

[0095] 31) According to the limit theory, when the distance between two adjacent tool contact points is very short, assume that the feed rate remains constant;

[0096] 32) The equation for solving the swing angle of the interference-free smooth tool axis vector in the full path is:

[0097]

[0098] where Q is the objective function, ω i is the swing angle of the tool axis vector corresponding to the i-th tool contact point, D i is the distance between adjacent tool contact points, f is the feed rate of the five-axis lathe; c represents the feasible range of the tool axis;

[0099] 33) According to the obtained swing angle ω of the tool axis vector i , determine the optimized sequence of the interference-free machining posture of the five-axis CNC lathe:

[0100] U = [ω1, ω2, …, ω n-1 , ω n

[0101] where U represents the optimized sequence of the interference-free machining posture of the five-axis CNC lathe.

[0102] ​Step 4: Determine the coordinate origin in the machine tool coordinate system considering the tool shank structure characteristics. According to the five-axis linkage process, analyze the positions of each axis and the motion transformation matrix, and post-process the tool contact points and tool axis vectors to obtain G-codes that can be recognized by the machine tool.

[0103] The main work of the post-solving is to convert the tool point coordinates and axis vectors obtained from the pre-processing into the motion amounts of the motion axes that drive the machine tool movement. Taking the obtained coordinate origin as the premise and driving the movement of the CNC machine tool as the ultimate goal, multiple coordinate systems need to be established, and these coordinate systems can form corresponding coordinate systems according to their functional purposes.

[0104] The two rotating axes on the machine tool can be defined as the first rotating axis and the second rotating axis according to their distances from the tool and the workpiece on the motion topological chain: the rotating axis closer to the workpiece on the motion topological chain is the first rotating axis, and the rotating axis closer to the tool is the second rotating axis. Thus, according to the above coordinate system concepts and functional analysis, the post-processing mainly involves 5 coordinate systems: the post-reference coordinate system O0-X0Y0Z0, the tool coordinate system O T -X T Y T Z T 、the first rotating axis coordinate system O R1 -X R1 Y R1 Z R1 、the second rotating axis coordinate system O R2 -X R2 Y R2 Z R2 ,and the workpiece coordinate system O w -X w Y w Z w ,as Figure 6 shown. In this embodiment, the first rotating axis is the C axis, the second rotating axis is the B axis, and there are three translational axes in the middle. The form of the translational chain is as Figure 7 shown. Since the installation order of the translational axes has no influence on the solution results, the positional relationship and installation sequence of the translational axes on both sides of the bed are not considered here.

[0105] The movement process of the tool can be simplified to the position and attitude change process of the tool axis vector and the tool point. Among them, the change of the tip point coordinates reflects the tool position change, and the change of the tool axis vector reflects the tool spatial attitude change. The establishment of the motion equation requires converting the tool point coordinates and tool axis vector in the tool coordinate system to the workpiece coordinate system according to the motion chain sequence.

[0106] The motion transformation matrix includes:

[0107] The rotation transformation matrix of the first axis (C axis):

[0108]

[0109] Rotation transformation matrix of the first axis (B axis):

[0110]

[0111] The motion transformation matrix of the translation axis is independent of the installation order of the translation axis, specifically:

[0112]

[0113] Where, θ R1 represents the angle between the C-axis coordinate system and the workpiece coordinate system; θ R2 represents the angle between the B-axis coordinate system and the workpiece coordinate system; dx, dy, and dz respectively represent the motion speeds of the translation axis.

[0114] By combining the coordinate transformation matrix between coordinate systems, the motion transformation matrix of the motion axis, the initial tool position data, and the tool position data in the workpiece coordinate system, the following motion equation is established in the forward kinematics manner:

[0115]

[0116] Where, F w represents the tool axis vector in the workpiece coordinate system; P w represents the tool point coordinate in the workpiece coordinate system; M RIW represents the coordinate transformation matrix from the C-axis coordinate system to the workpiece coordinate system; M R2R1 represents the coordinate transformation matrix from the B-axis coordinate system to the C-axis coordinate system; M TR2 represents the coordinate transformation matrix from the tool coordinate system to the B-axis coordinate system; R R1 represents the rotation transformation matrix of the C axis; R R2 represents the rotation transformation matrix of the B axis; T XYZ represents the motion transformation matrix of the translation axis; F T represents the initial tool axis vector in the tool coordinate system; P T represents the initial tool point coordinate in the tool coordinate system.

[0117] According to the established equation above and the structural parameters of the five-axis machine tool, the parameters of the X, Y, Z, B, and C axes of the five-axis machine tool can be obtained, and the G code that can be recognized by the machine tool can be obtained.

[0118] The above-described embodiments are merely preferred embodiments given to fully illustrate the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention is subject to the claims.

Claims

1. A method for optimizing the machining pose without interference of a five-axis CNC lathe, characterized in that: It includes the following steps: Step 1: Based on the spiral projection driving principle, obtain the spiral tool contact point position coordinates that envelop the workpiece to be machined, and calculate the slopes corresponding to the circumferential section curves at each tool contact point in the path trajectory; Step 2: Consider the characteristics of the rotation axis B-axis of the five-axis lathe driving the tool axis to swing: establish the relationships between the slopes of the section curves corresponding to the tool contact points in five-axis machining and the positive limit swing angle and negative limit swing angle of the tool axis respectively, and determine the positive tool axis swing angle feasible interval a and the negative tool axis swing angle feasible interval b; combine interval a and interval b to determine the reachable area c of the tool axis vector without global / local interference; Step 3: Take the smooth transition of the rotation axis B-axis as the optimization goal, perform smoothing processing on the tool axis vector, and obtain the interference-free machining pose optimization sequence of the five-axis CNC lathe; Step 4: Determine the coordinate origin in the machine tool coordinate system considering the tool shank structure characteristics, analyze the positions and motion transformation matrices of each axis according to the five-axis linkage process, and perform post-processing on the tool contact points and tool axis vectors to obtain the G code that can be recognized by the machine tool.

2. The method for optimizing the non-interference machining pose of a five-axis CNC lathe according to claim 1, characterized in that: In the above Step 1, the method for calculating the slopes corresponding to the circumferential section curves at each tool contact point in the path trajectory is: Based on the spiral projection driving principle, project the Archimedean spiral onto the surface of the workpiece to be machined, and obtain the spiral tool contact point position coordinates (x f , y f , z f ) that envelope the workpiece to be machined, where f = 0, 1, …, n, and n is the total number of tool contact points in the full path; Construct the plane equation G(x f , y f , z f ) that passes through the tool contact point (x f , y f , z f ) and is perpendicular to the workpiece axis. Obtain the cross-sectional curve formed by the intersection of this plane and the workpiece surface F(x f , y f , z f ). Solve to obtain the slope k f corresponding to each tool contact point on the circumferential cross-sectional curve.

3. The method for optimizing the non-interference machining pose of a five-axis CNC lathe according to claim 1, characterized in that: In the above Step 2, the method for determining the positive tool axis swing angle feasible interval a is: For the tool contact point i, based on the selected rake angle γ of the tool, perform a local interference judgment on the rake face of the tool to determine the positive limit swing angle α of the tool axis at the tool contact point i in five-axis machining i : α i = γ Considering the shape and size D of the selected tool shank, a global interference judgment is made on the rake face of the tool, and the slope k of the cross-sectional curve corresponding to any tool contact point j except the tool contact point i in five-axis machining is established. j and the positive limit swing angle α of the tool axis j The relationship between them is: where, L1 is the distance between tool contact point i and tool contact point j; ε1 is the angle between the vector and the tool axis vector of tool contact point i; η is the angle between the normal line at tool contact point i and the horizontal line; (x i , y i , z i ) are the coordinates of tool contact point i; (x j , y j , z j ) are the coordinates of tool contact point j; j ≠ i; Obtain the positive limit swing angle α of the tool axis without collision interference j :[[]]END]] Solve for the positive limit swing angle of the tool axis for all tool contact points except the tool contact point i, and obtain the feasible range a of the positive swing angle of the tool axis without local undercut interference and global collision interference at the tool contact point i i : a i ＝(0,α1)∩(0,α2)∩…∩(0,α n ) Solve the positive tool axis swing angle feasible intervals of all tool contact points in sequence to obtain the positive tool axis swing angle feasible interval a: a = [a1, a2…, a n-1 , a n .

4. The method for optimizing the non-interference machining pose of a five-axis CNC lathe according to claim 1, characterized in that: In the above Step 2, the method for determining the negative tool axis swing angle feasible interval b is: For the tool contact point i, based on the selected tool clearance angle μ, perform a local interference judgment on the flank face to determine the negative limit swing angle β of the tool axis at the tool contact point i in five-axis machining i : β i = μ Based on the shape and size D of the selected tool shank, a global interference judgment is performed on the flank face, and the slope k of the cross-sectional curve corresponding to any tool contact point m except the tool contact point i in five-axis machining is established m and the negative extreme swing angle β of the tool axis m The relationship between them is: Among them, L2 is the distance between tool contact point i and tool contact point m, and ε2 is the angle between the vector and the tool axis vector of tool contact point i. η is the angle between the normal line at tool contact point i and the horizontal line; (x i , y i , z i ) are the coordinates of tool contact point i; (x m , y m , z m ) are the coordinates of tool contact point m; m ≠ i; Obtain the positive limit swing angle β of the tool axis without collision interference m : Find the negative limit swing angle of the tool axis for all tool contact points except the tool contact point i, and obtain the feasible range b of the negative swing angle of the tool axis without local undercut interference and global collision interference at the tool contact point i i : b i ＝(0,β1)∩(0,β2)∩…∩(0,β n ) Solve the negative tool axis swing angle feasible intervals of all tool contact points in sequence to obtain the negative tool axis swing angle feasible interval b: b = [b1, b2…, b n-1 , b n .

5. The method for optimizing the non-interference machining pose of a five-axis CNC lathe according to claim 1, wherein: In the above Step 2, combine the positive tool axis swing angle feasible interval a and the negative tool axis swing angle feasible interval b to obtain the tool axis feasible region interval c: c = a ∪ b.

6. The optimized machining pose method without interference for a five-axis CNC lathe according to claim 1, characterized in that: In the above Step 3, the method for obtaining the interference-free machining pose optimization sequence of the five-axis CNC lathe is: 31) According to the limit theory, when the distance between two adjacent tool contact points is very short, assume that the feed rate remains constant; 32) The equation for solving the swing angle of the smooth tool axis vector without interference for the entire path is: Among them, Q is the objective function, ω i is the swing angle of the tool axis vector corresponding to the i-th tool contact point, D i is the distance between adjacent tool contact points, f is the feed rate of the five-axis lathe; c represents the tool axis feasible region interval; 33) According to the calculated swing angle ω of the tool axis vector i , determine the optimized posture sequence for interference-free machining of the five-axis CNC lathe: U = [ω1, ω2, …, ω n-1 , ω n ​ where U represents the interference-free machining pose optimization sequence of the five-axis CNC lathe.

7. The method for optimizing the non-interference machining pose of a five-axis CNC lathe according to claim 5, wherein: In the above Step 4, the motion transformation matrix is: Among them, F w represents the tool axis vector in the workpiece coordinate system; P w represents the tool point coordinate in the workpiece coordinate system; M RIW represents the coordinate transformation matrix from the C-axis coordinate system to the workpiece coordinate system; M R2R1 represents the coordinate transformation matrix from the B-axis coordinate system to the C-axis coordinate system; M TR2 represents the coordinate transformation matrix from the tool coordinate system to the B-axis coordinate system; R R1 represents the rotation transformation matrix of the C-axis; R R2 represents the rotation transformation matrix of the B-axis; T XYZ represents the translational axis motion transformation matrix; F T represents the initial tool axis vector in the tool coordinate system; P T represents the initial tool point coordinate in the tool coordinate system.

Images