Free-form surface envelope processing track planning method and system based on any curve section tool

Abstract

The invention relates to the technical field of ultra-precision machining, and discloses a free-form surface envelope machining track planning method and system based on an arbitrary curve section tool, and the method comprises the following steps: 1, judging the concavity and convexity of discrete points of a tool section curve, retaining convex envelope points, and rejecting concave envelope points; obtaining a set of all convex envelope points of the tool section curve, and defining the set as a tool section curve full convex envelope contour matrix; 2, calculating a convex envelope interpolation contour of the new tool section curve, and calculating the new tool section curve according to the convex envelope interpolation contour of the new tool section curve; and step 3, according to the new tool section curve in the step 2, obtaining a tool curved surface point cloud, and planning a free-form surface workpiece envelope processing track based on the tool curved surface point cloud.

Description

Technical Field

[0001] The present invention relates to the technical field of ultra-precision machining, and in particular to a method and system for planning a machining trajectory of a free-form surface envelope based on an arbitrary curve section tool. Background Art

[0002] A free-form surface is a surface with complex shape and high flexibility in three-dimensional space. It has wide and important applications in many fields such as industrial design, automobile manufacturing, aerospace, optics, and medical care. The diversity and complexity of free-form surfaces bring new challenges to the manufacturing process.

[0003] The main processing technologies for free-form surfaces include turning, milling and grinding. The corresponding processing tools are turning tools, ball-end milling cutters and ball-end or ring-end grinding wheels. The processing trajectory planning methods are divided into single-point processing and envelope processing. Single-point processing requires relative swinging motion between the tool and the workpiece, so it has high requirements on the motion axis and rigidity of the machine tool. The envelope processing process only requires relative translational motion between the tool and the workpiece, and does not require the machine tool to have a swing axis, so it is more widely used. However, envelope processing generally regards the tool cross-sectional curve as an ideal arc. During the processing, the contact point between the tool cross-sectional arc and the workpiece surface changes continuously, and the error between the tool cross-sectional curve and the ideal arc will be reflected on the free-form surface.

[0004] Therefore, in the actual enveloping processing (turning, milling or grinding) process, the cross-section of the tool (turning tool, ball-end milling cutter, ball-end or ring-end grinding wheel) used can be regarded as an arbitrary curve. The monotonicity and concavity of the arbitrary curve of the tool cross-section change many times, and only the convex envelope points of the curve can effectively contact the workpiece to participate in the processing and material removal. The processing trajectory needs to ensure that the convex envelope points of the tool cross-section curve are tangent to the workpiece surface to eliminate the processing errors caused by the arbitrary curve cross-section shape of the tool. Therefore, there is an urgent need for a free-form envelope processing trajectory planning method for tools with arbitrary curve cross-sections, which can extract the effective contact processing points on the tool cross-section curve, and keep the tool cross-section curve tangent to the workpiece during the processing process, so as to eliminate the processing errors caused by the arbitrary curve cross-section shape of the tool. Summary of the invention

[0005] In order to solve the technical problems existing in the prior art, the present invention discloses a free-form surface enveloping machining trajectory planning method based on an arbitrary curve section tool.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A free-form surface enveloping machining trajectory planning method based on an arbitrary curve section tool comprises the following steps:

[0008] Step 1: determine the convexity of the discrete points of the tool cross-section curve, retain the convex envelope points, discard the concave envelope points, and obtain the set of all convex envelope points of the tool cross-section curve, which is defined as the full convex envelope contour matrix of the tool cross-section curve;

[0009] Step 2: calculating a new convex envelope interpolation profile of the tool cross-section curve, and obtaining a new tool cross-section curve according to the convex envelope interpolation profile of the new tool cross-section curve;

[0010] Step 3 obtains a tool surface point cloud according to the new tool cross-section curve obtained in step 2, and plans the envelope machining trajectory of the free-form surface workpiece based on the tool surface point cloud.

[0011] As a further technical solution, in step 1, the method for determining the concavity and convexity of the discrete points of the tool cross-sectional curve is as follows: Assume that the discrete points of the tool cross-sectional curve (x i ,y i ), where any point has a vector with two adjacent points vector The angle between them is φ, and the cross product of the two vectors is When i ,y i ) is a convex envelope point; otherwise, the point is determined to be a concave envelope point.

[0012] As a further technical solution, the method for determining the set of all convex envelope points of the tool cross-section curve is as follows: After all points are determined in order of concavity and convexity, a new tool cross-section curve discrete point matrix (x' i ,y' i ). i ,y' i ) to find the second-order derivative. If the second-order derivative exists at a point greater than or equal to zero, repeat the matrix (x' i ,y' i ) determines and extracts the convex envelope points until the discrete matrix (x' i ,y' i )The second-order derivative at each point is always less than zero, and the set of all convex envelope points of the tool cross-section curve is obtained.

[0013] As a further technical solution, in step 2, the method for determining the convex envelope interpolation profile of the new tool cross-section curve is as follows:

[0014] Assume that any point (x' i ,y' i ) and the y-axis has an angle θ i ,θ i =arctan(x' i / y' i ) then any point of the fully convex envelope contour can be written as a parametric equation,

[0015]

[0016] Define the parameter variable matrix θ j , the interval is Δθ, for the above parametric equation based on the variable θ j Perform linear interpolation to obtain the new convex envelope interpolation profile of the tool cross-section curve (x j ,y j )

[0017]

[0018] As a further technical solution, in step 2, the method for determining the new tool cross-section curve is as follows:

[0019] Calculation tool cross-section curve convex envelope interpolation profile (x j ,y j ) The slope k of each point j ,

[0020]

[0021] The slope is a step function. Extract the midpoint of each step and set the coordinates of the midpoint to (x' j ,k' j ), based on the parameter variable matrix θ j Realign x' j -k' j Perform linear interpolation to obtain a monotonically increasing slope curve x j -k h In the variable x h Upper slope k h By integrating, we can get the new tool cross-section curve T(x h ,y h )

[0022]

[0023] As a further technical solution, for turning tools, the new tool cross-section curve T(x h ,y h ) is regarded as the front face contour of the turning tool for further free-form surface turning trajectory planning.

[0024] As a further technical solution, for a ball end mill or a grinding wheel, the tool is symmetrical about the tool bar (y h =0 axis) and the new tool section curve T(x h ,y h ) is extended to three-dimensional space; define h = Rotation matrix R(β) about axis 0

[0025]

[0026] The three-dimensional ball end mill or grinding wheel surface point cloud is:

[0027]

[0028] As a further technical solution,

[0029] For the annular grinding wheel, let the origin of the two-dimensional interpolation contour T(0,0) be in the grinding wheel annular coordinate system W(x w ,y w ,z w ) is (0, -r); the grinding wheel rotates around the center axis of the ring (x w =0) rotation, so it is necessary to rotate the two-dimensional interpolation profile T(x h ,y h ) is extended to three-dimensional space. Define w = Rotation matrix R(α) about axis 0

[0030]

[0031] The point cloud of the three-dimensional toroidal grinding wheel surface is:

[0032]

[0033] As a further technical solution, the specific details are as follows:

[0034] Solve the three-dimensional normal vector nor(nx,ny,nz) of the tool surface point cloud; let the workpiece free surface point cloud matrix be F(X,Y,Z), and solve the three-dimensional normal vector NOR(NX,NY,NZ) of the workpiece free surface point cloud; obtain the tool surface point cloud tangent point coordinates L(x l ,y l ,z l ); then the envelope machining trajectory of the free-form surface workpiece is P(X p ,Y p ,Z p )

[0035]

[0036] In a second aspect, the present invention further provides a free-form surface enveloping machining trajectory planning system based on an arbitrary curve section tool, comprising:

[0037] Module 1: is configured to determine the convexity of discrete points of the tool cross-sectional curve, retain the convex envelope points, discard the concave envelope points, and obtain the set of all convex envelope points of the tool cross-sectional curve, which is defined as the full convex envelope contour matrix of the tool cross-sectional curve;

[0038] Module 2: configured to calculate a new tool cross-sectional curve convex envelope interpolation profile, and obtain a new tool cross-sectional curve according to the new tool cross-sectional curve convex envelope interpolation profile;

[0039] Module 3: is configured to obtain a tool surface point cloud according to the new tool cross-section curve in step 2, and plan the envelope machining trajectory of the free-form surface workpiece based on the tool surface point cloud.

[0040] The beneficial effects of the present invention are as follows:

[0041] The present invention can extract all convex envelope points of the actual workpiece cross-sectional curve, and solve the fully convex function with the minimum error based on the fully convex envelope contour, and ensure that the slope is monotonically increasing. Based on the newly solved tool cross-sectional curve, it is expanded into a tool three-dimensional space surface point cloud. Based on the tool three-dimensional space surface point cloud, the free-form surface workpiece envelope machining trajectory is planned to minimize the tool curve cross-sectional shape error. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is the tool cross-section curve;

[0043] Figure 2 Schematic diagram of the error between the full convex envelope contour and the interpolated contour of the tool cross-section curve;

[0044] Figure 3 The theoretical residual error calculated by planning the grinding wheel envelope grinding trajectory using the annular grinding wheel as an example; DETAILED DESCRIPTION

[0045] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0046] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless otherwise explicitly stated in the present invention, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "include" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof;

[0047] As introduced in the background technology, the actual tool cross-section curve in the prior art is not an ideal arc but an arbitrary curve, and the monotonicity and convexity of the arbitrary curve change many times. Only the convex envelope points of the curve can effectively contact the workpiece to participate in processing and removing materials, and the tool cross-section curve error will be reflected on the surface of the free-form surface workpiece. In order to solve the above technical problems, the present invention proposes a free-form surface envelope processing trajectory planning method and system based on an arbitrary curve cross-section tool.

[0048] Embodiment 1

[0049] The free-form surface enveloping machining trajectory planning method based on an arbitrary curve section tool proposed in the present invention comprises the following steps:

[0050] Step 1: determine the convexity of the discrete points of the tool cross-section curve, retain the convex envelope points, discard the concave envelope points, and obtain the set of all convex envelope points of the tool cross-section curve, which is defined as the full convex envelope contour matrix of the tool cross-section curve;

[0051] Step 2: calculating a new convex envelope interpolation profile of the tool cross-section curve, and obtaining a new tool cross-section curve according to the convex envelope interpolation profile of the new tool cross-section curve;

[0052] Step 3: According to the new tool cross-section curve in step 2, a tool surface point cloud is obtained, and the envelope machining trajectory of the free-form surface workpiece is planned based on the tool surface point cloud.

[0053] The following is combined with specific Figure 1 , Figure 2 , Figure 3 The free-form surface enveloping machining trajectory planning method based on the arbitrary curve section tool proposed in the present invention is described as follows:

[0054] like Figure 1 As shown, let the tool section curve discrete points (x i ,y i ), where any point has a vector with two adjacent points

[0055]

[0056] vector The angle between them is φ, and the cross product of the two vectors is:

[0057]

[0058] when When i ,y i) is a convex envelope point; otherwise, the point is determined to be a concave envelope point. If the point is determined to be a convex envelope point, it is retained; if the point is determined not to be a concave envelope point, it is discarded. After all points are determined to be concave and convex in order, a new tool cross-section curve discrete point matrix (x' i ,y' i ). i ,y' i ) to find the second-order derivative. If the second-order derivative exists at a point greater than or equal to zero, repeat the matrix (x' i ,y' i ) determines and extracts the convex envelope points until the discrete matrix (x' i ,y' i ) The second-order derivative at each point is always less than zero, then the set of all convex envelope points of the tool cross-section curve is obtained, which is defined as the full convex envelope contour matrix of the tool cross-section curve (x' i ,y' i ).

[0059] Assume that any point (x' i ,y' i ) and the y-axis has an angle θ i ,θ i =arctan(x' i / y' i ) then any point of the fully convex envelope contour can be written as a parametric equation,

[0060]

[0061] Define the parameter variable matrix θ j , the interval is Δθ, for the above parametric equation based on the variable θ j Perform linear interpolation to obtain the new convex envelope interpolation profile of the tool cross-section curve (x j ,y j )

[0062]

[0063] Tool cross section curve convex envelope interpolation profile (x j ,y j ) The slope k of each point j ,

[0064]

[0065] The slope is a step function. Extract the midpoint of each step and set the coordinates of the midpoint to (x' j ,k' j ), based on the parameter variable matrix θ j Realign x' j -k' jPerform linear interpolation to obtain a monotonically increasing slope curve x j -k h In the variable x h Upper slope k h By integrating, we can get the new tool cross-section curve T(x h ,y h )

[0066]

[0067] New tool cross-section curve T(x h ,y h ) is a fully convex function with the smallest error with the fully convex envelope contour of the original tool cross-section curve, and its slope is guaranteed to be monotonically increasing.

[0068] Specifically, Figure 2 As shown in the figure, taking the annular grinding wheel as an example, the full convex envelope contour of the tool cross-section curve and the interpolation contour T(x h ,y h ) is as low as ±0.2μm.

[0069] For turning tools, this two-dimensional interpolation profile T(x h ,y h ) is regarded as the front face contour of the turning tool for further free-form surface turning trajectory planning.

[0070] For ball end mills or grinding wheels, the tool is symmetrical about the tool shaft axis (y h =0 axis) rotation, so it is necessary to interpolate this two-dimensional profile T(x h ,y h ) is extended to three-dimensional space. Define h = Rotation matrix R(β) about axis 0

[0071]

[0072] The three-dimensional ball end mill or grinding wheel surface point cloud is:

[0073]

[0074] For the annular grinding wheel, let the origin of the two-dimensional interpolation contour T(0,0) be in the grinding wheel annular coordinate system W(x w ,y w ,z w ) is (0, -r). The grinding wheel revolves around the center axis of the ring (x w =0) rotation, so it is necessary to rotate the two-dimensional interpolation profile T(x h ,y h ) is extended to three-dimensional space. Define w = Rotation matrix R(α) about axis 0

[0075]

[0076] The point cloud of the three-dimensional toroidal grinding wheel surface is:

[0077] W(x w ,y w ,z w )=R(α)·T(x h ,y h -r)

[0078]

[0079] Based on the above tool surface point cloud, plan the free-form surface workpiece envelope machining trajectory. Solve the three-dimensional normal vector nor(nx,ny,nz) of the above tool surface point cloud. Assume that the workpiece free-form surface point cloud matrix is ​​F(X,Y,Z), and solve the three-dimensional normal vector NOR(NX,NY,NZ) of the workpiece free-form surface point cloud. The machining trajectory needs to ensure that the convex envelope point of the tool surface is tangent to the workpiece free-form surface surface, that is, the three-dimensional normal vector of the tool surface point cloud is equal to the three-dimensional normal vector of the workpiece free-form surface point cloud. In this way, the coordinates of the tangent point L(x) of the tool surface point cloud corresponding to the workpiece free-form surface point cloud matrix can be obtained point by point. l ,y l ,z l ). Then the envelope machining trajectory of the free-form surface workpiece is P(X p ,Y p ,Z p )

[0080]

[0081] in, Figure 3 The theoretical residual error calculated by planning the grinding wheel envelope grinding trajectory using the annular grinding wheel is as low as 12nm.

[0082] The present invention can extract all convex envelope points of the actual workpiece cross-sectional curve, and solve the fully convex function with the minimum error based on the fully convex envelope contour, and ensure that the slope is monotonically increasing. Based on the newly solved tool cross-sectional curve, it is expanded into a tool three-dimensional space surface point cloud. Based on the tool three-dimensional space surface point cloud, the free-form surface workpiece envelope machining trajectory is planned to minimize the tool curve cross-sectional shape error.

[0083] Embodiment 2

[0084] This embodiment also provides a free-form surface enveloping machining trajectory planning system based on an arbitrary curve section tool, as follows:

[0085] Module 1: is configured to determine the convexity of discrete points of the tool cross-sectional curve, retain the convex envelope points, discard the concave envelope points, and obtain the set of all convex envelope points of the tool cross-sectional curve, which is defined as the full convex envelope contour matrix of the tool cross-sectional curve;

[0086] Module 2: configured to calculate a new tool cross-sectional curve convex envelope interpolation profile, and obtain a new tool cross-sectional curve according to the new tool cross-sectional curve convex envelope interpolation profile;

[0087] Module 3: is configured to obtain a tool surface point cloud according to the new tool cross-section curve in step 2, and plan the envelope machining trajectory of the free-form surface workpiece based on the tool surface point cloud.

[0088] The specific processing methods corresponding to each module are as follows:

[0089] Furthermore, the module 1 further comprises a first submodule, which is configured to determine the concavity and convexity of the discrete points of the tool cross-sectional curve; assuming that the discrete points (x i ,y i ), where any point has a vector with two adjacent points vector The angle between them is φ, and the cross product of the two vectors is When i ,y i ) is a convex envelope point; otherwise, the point is determined to be a concave envelope point.

[0090] Furthermore, the module 1 also includes a second submodule, and the second submodule is configured to determine the set of all convex envelope points of the tool cross-section curve, and after all points are judged in order of concavity and convexity, a new tool cross-section curve discrete point matrix (x' i ,y' i ). i ,y' i ) to find the second-order derivative. If the second-order derivative exists at a point greater than or equal to zero, repeat the matrix (x' i ,y' i ) determines and extracts the convex envelope points until the discrete matrix (x' i ,y' i )The second-order derivative at each point is always less than zero, and the set of all convex envelope points of the tool cross-section curve is obtained.

[0091] Furthermore, the module 2 also includes a first submodule, and a method for determining the convex envelope interpolation profile of the new tool cross-section curve is as follows:

[0092] Assume that any point (x' i ,y' i ) and the y-axis has an angle θi ,θ i =arctan(x' i / y' i ) then any point of the fully convex envelope contour can be written as a parametric equation,

[0093]

[0094] Define the parameter variable matrix θ j , the interval is Δθ, for the above parametric equation based on the variable θ j Perform linear interpolation to obtain the new convex envelope interpolation profile of the tool cross-section curve (x j ,y j )

[0095]

[0096] Furthermore, the module 2 further includes a second submodule configured to determine a new tool cross-sectional curve; specifically, to calculate a convex envelope interpolation profile (x j ,y j ) The slope k of each point j ,

[0097]

[0098] The slope is a step function. Extract the midpoint of each step and set the coordinates of the midpoint to (x' j ,k' j ), based on the parameter variable matrix θ j Realign x' j -k' j Perform linear interpolation to obtain a monotonically increasing slope curve x j -k h In the variable x h Upper slope k h By integrating, we can get the new tool cross-section curve T(x h ,y h )

[0099]

[0100] The module three also includes a first submodule, a second submodule, and a third submodule arranged in parallel;

[0101] The first submodule is used to generate a free-form surface turning trajectory planning for a turning tool, specifically, the new tool section curve T(x h ,y h ) is regarded as the rake face contour of the turning tool to further plan the free-form surface turning trajectory;

[0102] The second submodule is used to generate a surface point cloud of a ball-end milling cutter or a grinding wheel. Specifically, the tool is symmetrical about the tool bar (y h =0 axis) and the new tool section curve T(x h ,y h ) is extended to three-dimensional space; define h = Rotation matrix R(β) about axis 0

[0103]

[0104] The three-dimensional ball end mill or grinding wheel surface point cloud is:

[0105]

[0106] The third submodule is configured to generate a surface point cloud of an annular grinding wheel; specifically, for an annular grinding wheel, the origin T(0,0) of the two-dimensional interpolation contour is assumed to be in the grinding wheel annular coordinate system W(x w ,y w ,z w ) is (0, -r); the grinding wheel rotates around the center axis of the ring (x w =0) rotation, so it is necessary to rotate the two-dimensional interpolation profile T(x h ,y h ) is extended to three-dimensional space. Define w = Rotation matrix R(α) about axis 0

[0107]

[0108] The point cloud of the three-dimensional toroidal grinding wheel surface is:

[0109]

[0110] The module three also includes a fourth submodule, which is configured to plan the envelope machining trajectory of the free-form surface workpiece based on the surface point cloud generated by the second submodule and the third submodule; specifically as follows:

[0111] Solve the three-dimensional normal vector nor(nx,ny,nz) of the tool surface point cloud above. Assume that the workpiece free surface point cloud matrix is ​​F(X,Y,Z), and solve the three-dimensional normal vector NOR(NX,NY,NZ) of the workpiece free surface point cloud. The machining trajectory needs to ensure that the convex envelope point of the tool surface is tangent to the workpiece free surface surface, that is, the three-dimensional normal vector of the tool surface point cloud is equal to the three-dimensional normal vector of the workpiece free surface point cloud. In this way, the coordinates of the tangent point L(x) of the tool surface point cloud corresponding to the workpiece free surface point cloud matrix can be obtained point by point. l ,y l ,z l ). Then the envelope machining trajectory of the free-form surface workpiece is P(X p ,Y p ,Zp )

[0112]

[0113] Embodiment 3

[0114] This embodiment also provides an electronic device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to complete the steps of the free surface envelope machining trajectory planning method based on an arbitrary curve section tool in the first embodiment.

[0115] Among them, the memory and the processor are connected in a bus manner, and the bus may include any number of interconnected buses and bridges, and the bus connects various circuits of one or more processors and memories together. The bus can also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art, and therefore, this embodiment will not be further described. The bus interface provides an interface between the bus and the transceiver. The transceiver can be one element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices on a transmission medium. The data processed by the processor is transmitted on a wireless medium via an antenna, and further, the antenna also receives data and transmits the data to the processor. The processor is responsible for managing the bus and general processing, and can also provide various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. The memory can be used to store data used by the processor when performing operations.

[0116] For details, please refer to the free-form surface enveloping machining trajectory planning method based on the arbitrary curve section tool provided in the first embodiment, which will not be described in detail here.

[0117] Embodiment 4

[0118] This embodiment also provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps of the free-form surface enveloping machining trajectory planning method based on an arbitrary curve section tool. That is, those skilled in the art can understand that all or part of the steps in the method described in the above-mentioned embodiment can be completed by instructing the relevant hardware through a program, and the program is stored in a storage medium, including a number of instructions for a device (which can be a single-chip microcomputer, chip, etc.) or a processor to execute all or part of the steps of the method described in each embodiment of the present disclosure. The aforementioned storage medium includes: various media that can store program codes, such as a U disk, a mobile hard disk, a read-only memory, a random access memory, a magnetic disk or an optical disk.

[0119] For details, please refer to the free-form surface enveloping machining trajectory planning method based on the arbitrary curve section tool provided in the first embodiment, which will not be described in detail here.

[0120] Embodiment 5

[0121] In a fourth aspect, the present invention further provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of the free surface envelope machining trajectory planning method based on an arbitrary curve section tool in Example 1; no further details are given here.

[0122] Although the above describes the specific implementation methods of the present disclosure in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present disclosure. Technical personnel in the relevant field should understand that on the basis of the technical solution of the present disclosure, various modifications or variations that can be made by those skilled in the art without creative work are still within the scope of protection of the present disclosure.

Claims

1. A free-form surface enveloping machining trajectory planning method based on an arbitrary curve section tool, characterized in that: The following steps are involved: Step 1: determine the convexity of the discrete points of the tool cross-section curve, retain the convex envelope points, discard the concave envelope points, and obtain the set of all convex envelope points of the tool cross-section curve, which is defined as the full convex envelope contour matrix of the tool cross-section curve; Step 2: calculating a new convex envelope interpolation profile of the tool cross-section curve, and obtaining a new tool cross-section curve according to the convex envelope interpolation profile of the new tool cross-section curve; Step 3 obtains a tool surface point cloud according to the new tool cross-section curve obtained in step 2, and plans the envelope machining trajectory of the free-form surface workpiece based on the tool surface point cloud.

2. The free-form surface enveloping machining trajectory planning method based on an arbitrary curve section tool according to claim 1, characterized in that: In the step 1, the method for determining the concavity and convexity of the discrete points of the tool cross-section curve is as follows: Assume that the discrete points (x i ,y i ), where any point has a vector with two adjacent points vector The angle between them is φ, and the cross product of the two vectors is When i ,y i ) is a convex envelope point; otherwise, the point is determined to be a concave envelope point.

3. The free-form surface enveloping machining trajectory planning method based on an arbitrary curve section tool according to claim 1, characterized in that: The method for determining the set of all convex envelope points of the tool cross-section curve is as follows: After all points are judged in order of concavity and convexity, a new discrete point matrix of the tool cross-section curve (x' i ,y' i ); for (x' i ,y' i ) to find the second-order derivative. If the second-order derivative exists at a point greater than or equal to zero, repeat the matrix (x' i ,y' i ) determines and extracts the convex envelope points until the discrete matrix (x' i ,y' i )The second-order derivative at each point is always less than zero, and the set of all convex envelope points of the tool cross-section curve is obtained.

4. The free-form surface enveloping machining trajectory planning method based on an arbitrary curve section tool according to claim 1, characterized in that: The new tool section curve convex envelope interpolation profile is determined as follows: Assume that any point (x' i ,y' i ) and the y-axis has an angle θ i ,θ i =arctan(x' i / y' i ) then the parametric equation of any point of the fully convex envelope is as follows: Define the parameter variable matrix θ j , the interval is Δθ, for the above parametric equation based on the variable θ j Perform linear interpolation to obtain the new convex envelope interpolation profile of the tool cross-section curve (x j ,y j )as follows:

5. The free-form surface enveloping machining trajectory planning method based on an arbitrary curve section tool according to claim 4, characterized in that: The new tool section curve generation method is as follows: Tool cross section curve convex envelope interpolation profile (x j ,y j ) The slope k of each point j , the slope is a step function, extract the midpoint of each step, and set the coordinates of the midpoint to (x' j ,k' j ), based on the parameter variable matrix θ j Realign x' j -k' j Perform linear interpolation to obtain a monotonically increasing slope curve x j -k h ; In variable x h Upper slope k h By integrating, we can get the new tool cross-section curve T(x h ,y h ) 6. The free-form surface enveloping machining trajectory planning method based on an arbitrary curve section tool according to claim 1, characterized in that: In step 3, for the turning tool, the new tool section curve T(x h ,y h ) is regarded as the front face contour of the turning tool for further free-form surface turning trajectory planning.

7. The free-form surface enveloping machining trajectory planning method based on an arbitrary curve section tool according to claim 1, characterized in that: In step 3, for a three-dimensional ball end mill or grinding wheel, the tool is symmetrical about the tool bar (y h =0 axis) and the new tool section curve T(x h ,y h ) is extended to three-dimensional space; define h = The rotation matrix R(β) of the 0 axis is as follows: The three-dimensional ball end mill or grinding wheel surface point cloud is as follows:

8. The free-form surface enveloping machining trajectory planning method based on an arbitrary curve section tool according to claim 1, characterized in that: In step 3, for the annular grinding wheel, the origin of the two-dimensional interpolation contour T(0,0) is set in the grinding wheel annular coordinate system W(x w ,y w ,z w ) is (0, -r); the grinding wheel rotates around the center axis of the ring (x w =0) rotation, so it is necessary to rotate the two-dimensional interpolation profile T(x h ,y h ) is extended to three-dimensional space, and the definition of w = The rotation matrix R(α) of the 0 axis is as follows: The three-dimensional toroidal grinding wheel surface point cloud is as follows:

9. The free-form surface enveloping machining trajectory planning method based on an arbitrary curve section tool according to any one of claims 7 or 8, characterized in that: Based on the surface point cloud, the method of enveloping the machining trajectory of the free-form surface workpiece is as follows: Solve the three-dimensional normal vector nor(nx,ny,nz) of the tool surface point cloud; let the workpiece free surface point cloud matrix be F(X,Y,Z), and solve the three-dimensional normal vector NOR(NX,NY,NZ) of the workpiece free surface point cloud; obtain the tool surface point cloud tangent point coordinates L(x l ,y l ,z l ); then the envelope machining trajectory of the free-form surface workpiece is P(X p ,Y p ,Z p ) 10. A free-form surface enveloping machining trajectory planning system based on an arbitrary curve section tool, characterized in that: include: Module 1: is configured to determine the convexity of discrete points of the tool cross-sectional curve, retain the convex envelope points, discard the concave envelope points, and obtain the set of all convex envelope points of the tool cross-sectional curve, which is defined as the full convex envelope contour matrix of the tool cross-sectional curve; Module 2: configured to calculate a new tool cross-sectional curve convex envelope interpolation profile, and obtain a new tool cross-sectional curve according to the new tool cross-sectional curve convex envelope interpolation profile; Module 3: is configured to obtain a tool surface point cloud according to the new tool cross-section curve in step 2, and plan the envelope machining trajectory of the free-form surface workpiece based on the tool surface point cloud.

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