Freeform surface envelope machining path planning method and system based on arbitrary curve section tool

Abstract

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

Description

Technical Field

[0001] The present invention relates to the field of ultra-precision machining technology, and in particular to a method and system for planning a free-form surface enveloping machining trajectory 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, automotive manufacturing, aerospace, optics, and medicine. 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 used are turning tools, ball-end milling cutters and ball-end or toroidal 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 translation 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. 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 annular 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-sectional shape of the tool. Therefore, there is an urgent need for a free-form surface enveloping processing trajectory planning method for tools with arbitrary curve cross-sections, which can extract the effective contact processing points on the tool cross-sectional curve and keep the tool cross-sectional curve tangent to the workpiece during the processing process, thereby eliminating the processing errors caused by the arbitrary curve cross-sectional 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 in 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: Calculate the convex envelope interpolation profile of the new tool cross-section curve, and obtain the new tool cross-section curve according to the convex envelope interpolation profile of the new tool cross-section curve;

[0010] Step 3: Obtain the tool surface point cloud according to the new tool cross-section curve obtained in step 2, and plan 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-section curve is as follows: Assume that the discrete points of the tool cross-section curve (x i ,y i ), where any point has a vector with two adjacent points vector The angle between them is φ, and the two vectors are cross-producted. When the point (x 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 judged in order of concavity and convexity, a new tool cross-section curve discrete point matrix (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, then 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 ) with the y-axis is θ i ,θ i =arctan(x' i / y' i ) then any point of the fully convex envelope can be written as a parametric equation,

[0015]

[0016] Define the parameter variable matrix θ j , the interval is Δθ, the above parametric equation is 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 as (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 to further plan the free-form surface turning trajectory.

[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 cross-section curve T(x h ,y h ) is extended to three-dimensional space; define around y 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 moves 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 around x w = Rotation matrix R(α) about axis 0

[0030]

[0031] The point cloud of the three-dimensional circular 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), 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 convex envelope points, discard 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 convex envelope interpolation profile of the tool cross-section curve, and obtain a new tool cross-section curve according to the convex envelope interpolation profile of the new tool cross-section curve;

[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] This method extracts all convex envelope points of the actual workpiece cross-sectional curve and, based on the fully convex envelope contour, solves a fully convex function that minimizes the error with it, ensuring a monotonically increasing slope. The newly solved tool cross-sectional curve is then expanded into a three-dimensional point cloud of the tool surface. Based on the three-dimensional point cloud of the tool surface, the envelope machining trajectory of the free-form workpiece is planned, minimizing the error in the tool curve cross-sectional shape. 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 description is illustrative and is 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 meaning as 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 clearly indicated 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 "comprising" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or their combinations;

[0047] As introduced in the background technology, the actual tool cross-sectional 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. The tool cross-sectional 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-sectional tool.

[0048] Example 1

[0049] The present invention proposes a free-form surface enveloping machining trajectory planning method based on an arbitrary curve section tool, comprising 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: Calculate the convex envelope interpolation profile of the new tool cross-section curve, and obtain the 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 cross 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 the point (x 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, the new tool cross-section curve discrete point matrix (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, then 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 ) with the y-axis is θ i ,θ i =arctan(x' i / y' i ) then any point of the fully convex envelope can be written as a parametric equation,

[0060]

[0061] Define the parameter variable matrix θ j , the interval is Δθ, the above parametric equation is 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 as (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 that minimizes the error with the fully convex envelope profile of the original tool cross-section curve and ensures that the slope is monotonically increasing.

[0068] Specifically, such as Figure 2 As shown, taking the annular grinding wheel as an example, the full convex envelope profile of the tool cross-section curve and the interpolation profile 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 to further plan the free-form surface turning trajectory.

[0070] For ball end mills or grinding wheels, the tool is symmetrical about the tool shaft (y h =0 axis) rotation, so it is necessary to interpolate the 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 moves 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 around x w = Rotation matrix R(α) about axis 0

[0075]

[0076] The point cloud of the three-dimensional circular 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, the envelope machining trajectory of the free-form surface workpiece is planned. Solve the three-dimensional normal vector nor(nx,ny,nz) of the above tool surface point cloud. Let the workpiece free-form surface point cloud matrix be 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 free-form surface surface of the workpiece, 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 tangent point coordinates L(x) of the tool surface point cloud corresponding to the workpiece free-form surface point cloud matrix can be obtained. 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 as an example is as low as 12nm.

[0082] This method extracts all convex envelope points of the actual workpiece cross-sectional curve and, based on the fully convex envelope contour, solves a fully convex function that minimizes the error with it, ensuring a monotonically increasing slope. The newly solved tool cross-sectional curve is then expanded into a three-dimensional point cloud of the tool surface. Based on the three-dimensional point cloud of the tool surface, the envelope machining trajectory of the free-form workpiece is planned, minimizing the error in the tool curve cross-sectional shape.

[0083] Example 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 convex envelope points, discard 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 convex envelope interpolation profile of the tool cross-section curve, and obtain a new tool cross-section curve according to the convex envelope interpolation profile of the new tool cross-section curve;

[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 for each module are as follows:

[0089] Furthermore, the module 1 further includes 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 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 two vectors are cross-producted. When the point (x i ,y i ) is a convex envelope point; otherwise, the point is determined to be a concave envelope point.

[0090] Furthermore, the module 1 further includes a second submodule, which is configured to determine the set of all convex envelope points of the tool cross-section curve, and after all points are sequentially determined to be concave and convex, a new tool cross-section curve discrete point matrix (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, then 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 the 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 ) with the y-axis is θi ,θ i =arctan(x' i / y' i ) then any point of the fully convex envelope can be written as a parametric equation,

[0093]

[0094] Define the parameter variable matrix θ j , the interval is Δθ, the above parametric equation is 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 the 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 as (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 the free-form surface turning trajectory planning of the turning tool, specifically the new tool section curve T(x h ,y h ) is regarded as the rake face profile of the turning tool to further perform free-form surface turning trajectory planning;

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

[0107]

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

[0109]

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

[0111] Solve the above tool surface point cloud 3D normal vector nor(nx,ny,nz). Let the workpiece free surface point cloud matrix be F(X,Y,Z), and solve the workpiece free surface point cloud 3D normal vector NOR(NX,NY,NZ). 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 3D normal vector of the tool surface point cloud is equal to the 3D normal vector of the workpiece free surface point cloud. In this way, the coordinates of the tool surface point cloud tangent point L(x) corresponding to the workpiece free surface point cloud matrix can be obtained. 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] Example 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 envelopment machining trajectory planning method based on an arbitrary curve section tool in embodiment one.

[0115] The memory and processor are connected via a bus, which can include any number of interconnected buses and bridges. The bus connects various circuits within one or more processors and the memory. The bus can also connect various other circuits, such as peripherals, voltage regulators, and power management circuits. These are well known in the art and are not further described in this embodiment. A bus interface provides an interface between the bus and a transceiver. A transceiver can be a single component or multiple components, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over a wireless medium via an antenna. The antenna also receives the data and transmits it to the processor. The processor is responsible for managing the bus and general processing, and can also provide various functions, including timing, peripheral interfacing, 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] Example 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 will understand that all or part of the steps in the method described in the above 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 enabling 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] Specifically, see the free-form surface envelope machining trajectory planning method based on the arbitrary curve section tool provided in Example One, which will not be repeated here.

[0120] Example Five

[0121] In a fourth aspect, the present application also provides a computer program product, comprising computer programs / instructions, which, when executed by a processor, implement the steps of the free-form surface envelope machining trajectory planning method based on the arbitrary curve section tool in Example One; which will not be repeated here.

[0122] Although the specific embodiments of the present disclosure are described above with reference to the accompanying drawings, it is not a limitation on the protection scope of the present disclosure, and those skilled in the art should understand that various modifications or changes made on the basis of the technical solutions of the present disclosure without creative labor are still within the protection scope 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: Calculate the convex envelope interpolation profile of the new tool cross-section curve, and obtain the new tool cross-section curve according to the convex envelope interpolation profile of the new tool cross-section curve; Step 3: Obtain a tool surface point cloud based on the new tool cross-section curve obtained in step 2, and plan the envelope machining trajectory of the free-form surface workpiece based on the tool surface point cloud; The method for determining the set of all convex envelope points of the tool cross-section curve is as follows: after determining the concavity and convexity of all points in order, a new discrete point matrix of the tool cross-section curve is obtained; the second-order derivative of the discrete point matrix is ​​calculated, and if there is a point where the second-order derivative is greater than or equal to zero, the determination and extraction of convex envelope points of the discrete point matrix are repeated until the second-order derivative at each point of the discrete point matrix is ​​always less than zero, thereby obtaining the set of all convex envelope points of the tool cross-section curve; The new tool cross-section curve convex envelope interpolation profile is determined as follows: Assume that any point of the fully convex envelope of the tool section curve ( x’ i , y’ i )and y The angle between the axes is 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 parameter variable matrix θ j , the interval is Δθ , for the above parametric equations based on variables 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: ； The new tool section curve generation method is as follows: Tool cross-section curve convex envelope interpolation profile ( x j , y j )The slope of each point k j , the slope is a step function, extract the midpoint of each step, and set the coordinates of the midpoint to be ( 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 ) 。 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: suppose the discrete points of the tool cross-section curve ( x i , y i ), where any point has a vector with two adjacent points 、 ,vector 、 The angle is φ , perform cross product of two vectors, when When , we can determine the point ( x 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: 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 to further plan the free-form surface turning trajectory.

4. 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 shaft ( y h =0 axis) and rotate the new tool section curve T ( x h , y h ) is extended to three-dimensional space; define y h =0 axis rotation matrix R ( β ),as follows: The three-dimensional ball end mill or grinding wheel surface point cloud is as follows: ; β is the angle of rotation of the arc curve of the grinding wheel or three-dimensional ball end mill around the Y axis.

5. 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, set the origin of the two-dimensional interpolation profile T ( 0, 0 ) in the grinding wheel ring coordinate system W ( x w , y w , z w ) in the coordinates are ( 0, -r ); Grinding wheel around the circular axis ( x w =0) rotation, so the two-dimensional interpolation contour needs to be T ( x h , y h ) is extended to three-dimensional space, defining x w =0 axis rotation matrix R (α) is as follows: The three-dimensional circular grinding wheel surface point cloud is as follows: ； Among them, α is the angle of rotation of the arc curve of the grinding wheel around the X axis.

6. The free-form surface enveloping machining trajectory planning method based on an arbitrary curve section tool according to any one of claims 4 or 5, 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: Solving tool surface point cloud 3D normal vector nor( nx ,ny, nz ); Assume that the workpiece free surface point cloud matrix is F ( X, Y, Z ), solve the three-dimensional normal vector NOR( NX ,NY, NZ ) Obtain the coordinates of the tangent points of the tool surface point cloud corresponding to the workpiece free surface point cloud matrix point by point 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 ) 。 7. A free-form surface enveloping machining trajectory planning system based on an arbitrary curve section tool, adopting the free-form surface enveloping machining trajectory planning method based on an arbitrary curve section tool according to any one of claims 1 to 6, characterized in that: include: Module 1: is configured to determine the convexity of discrete points of the tool cross-sectional curve, retain convex envelope points, discard 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 convex envelope interpolation profile of the tool cross-section curve, and obtain a new tool cross-section curve according to the convex envelope interpolation profile of the new tool cross-section curve; 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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