Five-axis numerical control machining simulation-oriented tool swept volume entity modeling method

Abstract

The invention discloses a five-axis numerical control machining simulation-oriented tool swept volume entity modeling method, which comprises the following steps of: firstly, describing a tool shaft section contour line by adopting a rotation contour point, and constructing a tool rotation body model through connection of a tool layer and a triangular surface; secondly, a calculation method of a cutter axis point velocity vector is provided by classifying cutter movement tracks in machining; secondly, calculating a normal vector of a point on the cutter layer, and solving a critical contour point and a reserved point of the cutter layer by combining an envelope theory; then, a construction method of a tool swept volume surface contour point set is researched, and a closed triangular mesh surface of the swept volume is constructed by using a contour point sequence number corresponding relation; finally, the effectiveness of the algorithm is verified through a tool swept volume generation result under various motion trails. The method is suitable for various cutter types, and can meet the requirements of numerical control machining simulation.

Description

Technical Field

[0001] The present invention belongs to the technical field of numerical control machining simulation, and in particular relates to a tool-swept body solid modeling method for five-axis numerical control machining simulation. Background Art

[0002] In CNC machining geometry simulation, the workpiece material removal process is simulated through Boolean operations between the tool-swept volume and the blank model. The calculation of the tool-swept volume is a core technology of CNC simulation systems. Because five-axis machining increases the tool's degrees of freedom, the shape of the tool-swept volume is very complex and difficult to express directly using analytical formulas. Currently, extensive research has been conducted both domestically and internationally on algorithms for generating tool-swept volumes, primarily including the swept envelope differential equation (SEDE) method, implicit surface modeling, and envelope theory.

[0003] In the study of tool-swept-volume modeling using the SEDE method, Blackmore et al. used the SEDE equation to express the boundaries of the swept volume and automatically generated boundary points, reducing the complexity of the swept-volume calculation. Lev et al. proposed an enhanced self-intersection algorithm and applied the SEDE equation to modeling swept-volume motions of ball-end tools with self-intersections. Wang et al. combined the SEDE equation with approximate formulas to calculate various swept-volume motions, including five-axis CNC milling.

[0004] In the study of implicit surface modeling of tool-swept volumes, Lee et al., based on the Gaussian mapping concept, mapped the tool model onto a Gaussian sphere, obtaining a closed curve on the sphere and subsequently constructing the tool-swept volume. Li Baichun et al., based on Gaussian mapping theory and using GPUs as the primary hardware platform, proposed a parallel computing-based modeling method for tool-swept volumes.

[0005] Compared with the above two algorithms, the application of envelope theory is more extensive. Wang Qing et al. established a tool swept body based on envelope theory, and performed Boolean operations on the tool swept body model and the workpiece to realize virtual cutting in simulation. Li Xiancai et al. used NUBSS curves to represent the tool, and combined with envelope theory to obtain an analytical expression of the tool swept body surface. Zhu Limin et al. proposed a two-parameter spherical family envelope representation method for the tool rotation body swept surface. On this basis, Ding et al. proposed a method for generating a five-axis milling tool swept body through conformal geometric algebra, and constructed an envelope expression based on point pairs. Zhao Zhenglong improved the calculation model of the instantaneous contour line of the tool swept body on the basis of expressing the tool surface as a spherical model of a rotation body, thereby improving the solution efficiency. Xu Zhiqi et al. solved the tool swept body by intersecting several cutting planes with the scanning element curve. Luo Guibing solved the tool movement speed by the speed of the point on the tool axis, simplifying the solution of the tool instantaneous contour line. Zhu et al. considered the curvature and torsion of the tool path, as well as the changes in tool posture, and proposed a method for calculating the tool motion envelope based on the spiral theory. They also obtained the cutting edge contact area (CWE). Dogrusadik proposed a swept volume generation algorithm for five-axis CNC milling of flat-bottomed milling cutters. Compared with previous algorithms, this algorithm has fewer steps. Summary of the Invention

[0006] In view of the above problems, the present invention provides a tool-swept body solid modeling method for five-axis CNC machining simulation.

[0007] A tool-swept volume solid modeling method for five-axis numerical control machining simulation of the present invention comprises the following steps:

[0008] Step 1: Create a tool rotation model.

[0009] Establish tool coordinate system O T -X T Y T Z T , whose coordinate origin is O T Coincident with the initial tool position, coordinate axis Z T The positive direction is consistent with the direction of the tool axis vector, and the coordinate axis X T Pointing to the tool radius direction; defining the tool axis section as using the tool coordinate system coordinate plane X T O T Z T Cutting tool section; tool rotation contour point d i (x i ,z i ), i = 1,…, n are discrete points on the contour line of the tool axis section; any contour line of the tool axis section can be decomposed into several straight line segments and circular arc segments, where the rotation contour points of the straight line segment are its two end points, and the rotation contour points of the circular arc segment include the two end points and the intermediate interpolation points.

[0010] Draw the tool axis section profile around the coordinate axis Z T Rotate to obtain the rotating surface of the tool; define the tool layer M of a certain tool i (i=1,…,n) is the rotation contour point d i The ring formed by rotation is expressed in the tool coordinate system as:

[0011]

[0012] Where, the subscript T indicates the coordinate system TCS, and θ is the rotation contour point d i Around the coordinate axis Z T Angle of rotation.

[0013] The tool layer ring is sampled, and the sampling point of the tool layer ring is called the vertex of the tool layer. i The j-th vertex is recorded as vertex D i_j ; In the tool coordinate system, D i_j The coordinates are expressed as:

[0014]

[0015] Where m is the number of vertices in the tool layer.

[0016] The adjacent tool layer vertices are connected in sequence to form triangular faces to obtain the tool rotation model.

[0017] Step 2: Calculate the movement speed of the tool axis point.

[0018] The position of the tool in the workpiece coordinate system is represented by cl t (x t ,y t ,z t ,i t ,j t ,k t ), where (x t ,y t ,z t ) represents the position vector of the tool position in the workpiece coordinate system, (i t ,j t ,k t ) represents the unit vector of the tool axis direction in the workpiece coordinate system.

[0019] The tool motion trajectory in machining simulation is divided into four types:

[0020] (1) Axial movement:

[0021] The movement of the tool along the tool axis is called axial movement. Let the unit motion vector of the tool movement direction be e t, the mathematical description of the tool axial motion is as follows:

[0022] (i t ,j t ,k t ) T =(i t+1 ,j t+1 ,k t+1 ) T =±e t (3)

[0023] For axial motion, the tool generates a swept volume envelope by moving the top or bottom surface; the tool moves from the position cl t Move downward to position cl t+1 , the tool-swept volume is constructed as follows:

[0024] When the tool top radius is greater than or equal to the bottom radius, the top tool layer of the two pose tools, namely the tool layer M n-1 The vertices construct the triangle surface of the envelope, and then compare it with the pose cl t The top surface of the tool, the position cl t+1 The bottom and side surfaces of the tool together constitute the swept volume.

[0025] When the tool bottom radius is larger than the top radius, the bottom tool layer of the two pose tools, that is, the vertex of the tool layer M2, is used to construct the triangle surface of the envelope surface, and then the triangle surface of the pose cl is used to construct the triangle surface of the envelope surface. t The top and side surfaces of the tool, the position cl t+1 The bottom surface of the tool at each location together constitutes the swept volume.

[0026] (2) Fixed axis linear motion.

[0027] Fixed-axis linear motion is a motion in which the tool position point trajectory is a straight line and the tool axis vector direction does not change. For fixed-axis linear motion, the velocity vector of any point on the tool axis is the same. The velocity vector calculation formula for any point on the tool axis in fixed-axis linear motion is as follows:

[0028] V=(x t+1 ,y t+1 ,z t+1 ) T -(x t ,y t ,z t ) T (4)

[0029] (3) Fixed axis circular motion.

[0030] Fixed-axis circular motion is a motion in which the tool position point trajectory is an arc in a plane and the direction of the tool axis vector remains unchanged. The characteristics of fixed-axis circular motion are similar to fixed-axis linear motion. The velocity vector of any point on the tool axis at the same position is the same. However, unlike fixed-axis linear motion, the velocity vector of fixed-axis circular motion changes continuously with the tool movement. Therefore, circular interpolation is required for the tool position point trajectory to obtain an approximate value of the velocity vector. The direction of the tool's velocity vector points from the previous interpolation point to the next interpolation point, and every two adjacent interpolation points can generate a tool sweep volume.

[0031] (4) Change axis movement.

[0032] Variable axis motion refers to the change in the tool axis direction during the tool movement. For variable axis motion, it is necessary to perform linear interpolation on the tool position trajectory and the tool axis vector at the same time. The interpolation formula is as follows:

[0033]

[0034] Where k∈[0,1]; since the velocity directions of various points on the tool axis are different for the same position of the variable axis motion, the velocity vector of each tool axis point needs to be solved; the coordinates of the tool axis point at the interpolation point k that is at a distance l from the tool position point are expressed as:

[0035] (x k_l ,y k_l ,z k_l ) T =(x k ,y k ,z k ) T +l·(i k ,j k ,k k ) T (6)

[0036] The velocity vector calculation formula of the tool axis point is as follows:

[0037] V k_l =(x k+1_l ,y k+1_l ,z k+1_l ) T -(x k_l ,y k_l ,z k_l ) T (7)

[0038] Similar to the fixed-axis circular motion, the variable-axis motion also constructs a swept volume model by using the tool between two adjacent interpolation points.

[0039] Step 3: Calculate the normal vector of the tool layer.

[0040] If the tool layer M i-1 With M i They are all formed by the straight line segment rotation contour points of the tool axis section contour line, so the tool layer M i Point D i Normal vector N i_T Expressed as:

[0041]

[0042] If the tool layer M i-1 With M i They are all formed by the arc segment rotation contour point of the tool axis section contour line, so the normal vector N i_T It is represented by the normal vector at that point on the arc surface, as shown below:

[0043]

[0044] Step 4: Calculate the critical contour points and retention points of the tool layer.

[0045] According to the rotary characteristics of the tool, the tool layer M i The reverse extension lines of the normal vectors of all points on the tool intersect with the tool axis at the same point, which is marked as point Q i ; Define point P i Tool layer M i The critical contour point, its position vector P in the workpiece coordinate system i_W (t) is expressed as:

[0046] P i_W (t) = P W (t)+|P W Q i |·I W (t)+|P i Q i |·N P_i_W (t) (10)

[0047] Where, P W is the tool position in the workpiece coordinate system, I W is the tool axis vector in the workpiece coordinate system, N P_i_W (t) is the point P at position t in the workpiece coordinate system i The normal vector of .

[0048] Derivative the position parameter t, and get point P i The velocity vector V at P_i_W (t), the formula is as follows:

[0049]

[0050] Critical contour point Pi The following tangency conditions are met:

[0051]

[0052] The following relationship is learned through rigid body kinematics:

[0053]

[0054] Through the above analysis, we can get the tool layer M i Corresponding tool axis point Q i The velocity vector and the critical contour point P i The normal vector is perpendicular to the point Q. i The local coordinate system O at Q -X Q Y Q Z Q , whose coordinate origin is O Q That is point Q i , coordinate axis X Q The positive direction of the velocity vector V Q_i_W Coincident, coordinate axis Z Q The positive direction of X Q ×I W The direction is consistent.

[0055] In order to transform the normal vector N P_i_W Expressed as a vector N in the local coordinate system P_i_Q , define it with the coordinate axis Z Q The angle between them is γ; since vector N P_i_Q Will be located on the coordinate axis Z Q On both sides of , so this vector has two expressions, namely (0, sinγ, cosγ) and (0, -sinγ, cosγ), where:

[0056]

[0057] Where α is the vector N P_i_Q With the tool axis vector I W The angle between the coordinate axis Y and Q With the tool axis vector I W The angle between P_i_Q The specific expression form to be chosen depends on the calculation results of the subsequent critical contour points.

[0058] Define coordinate system O Q -X Q Y Q Z Q The transformation matrix to the workpiece coordinate system is W R Q , the expression is as follows:

[0059] W R Q =[X Q Y Q Z Q ] (15)

[0060] Where, X Q 、Y Q , Z Q Represents coordinate system O Q -X Q Y Q Z Q The unit column vector of each coordinate axis in the workpiece coordinate system.

[0061] VectorN P_i_Q With the matrix W R Q Multiply to get the normal vector N P_i_W ,Right now:

[0062] N P_i_W = W R Q N P_i_Q (16)

[0063] To determine the vector N P_i_Q The expression form is solved by substitution method: First, assume that the vector N P_i_Q The coordinates are (0, sinγ, cosγ), and then the normal vector N is calculated P_i_W The coordinates of the tool layer M are substituted into formula (10) to calculate i The critical contour point P i Coordinates of point P i Located at tool layer M i If the vector N P_i_Q The coordinates are changed to (0, -sinγ, cosγ), and the critical contour point P is recalculated. i 's coordinates.

[0064] The angles α and β have different values, and the number of critical contour points is also different, which may be 0, 1, and 2. Their relationship is as follows:

[0065]

[0066] The construction of the tool sweep body solid model requires the use of the tool layer vertices of the tool rotation body model, including the tool layer vertices of the front surface of the tool in the starting posture and the tool layer vertices of the back surface of the tool in the ending posture. These two parts of points are uniformly defined as reserved points. In order to determine the tool layer M i The reserved points of the tool layer need to be divided by the critical contour points of the tool layer; since the tool layer Mi The number of critical contour points may be 0, 1, or 2. Therefore, the calculation of tool layer retention points is divided into the following two cases:

[0067] Tool layer M i There are 0 or 1 critical contour points, and the tool layer M is optional. i A vertex D i_j , determine whether it is a reserved point, if so, then the tool layer M i All vertices of are reserved points; otherwise, none of them are.

[0068] Tool layer M i There are two critical contour points, defining the tool layer M i The center of the circle points to the critical contour point P i The vector is C i If V Q_i_W ×C i The vector of the knife axis vector I W The angle between the two is an acute angle, then the vector C i The corresponding critical contour point is denoted as P i_1 ; Otherwise, vector C i The corresponding critical contour point is denoted as P i_2 ; by P i_1 Rotate along the tool rotation direction to P i_2 The tool layer vertices passed through are the reserved points.

[0069] Step 5: Construct the tool swept body solid model.

[0070] (1) Construct the front and back surface triangular meshes of the tool at the initial and final positions.

[0071] Define tool layer M i The surface contour point set of the swept volume is T i , T i The calculation steps are as follows:

[0072] S1: Set the tool layer M i The reserved points are stored in the point set T i .

[0073] S2: Determine tool layer M i The number of critical contour points, if it is 0, go to S7; if it is 1, go to S3; if it is 2, go to S4.

[0074] S3: Find the distance critical contour point P i The two nearest reserved points, if the reserved points are formed by the critical contour point P i If the point is obtained by rotating along the direction of tool rotation, the point is recorded as D i_SI Otherwise, record the point as D i_EI , and go to S5.

[0075] S4: Distance from critical contour point P i_1 The most recent retention point is denoted as D i_SI , the distance from the critical contour point P i_2 The most recent retention point is denoted as D i_EI .

[0076] S5: Move the reserved point from point D according to the tool rotation direction i_SI To point D i_EI Arrange in order.

[0077] S6: If the tool layer M i There is only one critical contour point, so let P i_1 =P i_2 =P i ; Then, in the point set T i , point P i_1 Insert to point D i_SI Before, click P i_2 Insert to point D i_EI Then; at the same time, let D i_SI-1 =P i_1 , D i_EI+1 =P i_2 .

[0078] S7: End.

[0079] (2) Construct a triangular mesh of the middle envelope surface of the swept volume.

[0080] The critical contour points of each tool layer of the tool are connected in sequence to generate the critical contour line; the corresponding points on the critical contour lines of the tools at adjacent positions are connected in sequence and a triangular mesh is constructed to form the intermediate envelope surface of the swept body.

[0081] The beneficial technical effects of the present invention are:

[0082] This paper studies tool-swept volume modeling for CNC machining simulation. It proposes a method for calculating critical tool contour points and retained points based on envelope theory and discrete tool layers. By constructing a closed triangular mesh through point number correspondence, it achieves the generation of a solid model of the tool-swept volume. The correctness of the modeling method is verified through case studies of tool-swept volumes with different motion trajectories. This method is applicable to a variety of tool types and can meet the needs of CNC machining simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 Schematic diagram of the tool axis cross-section contour line.

[0084] Figure 2 Schematic diagram of the triangular surface structure of the tool rotation body.

[0085] Figure 3Schematic diagram of tool motion trajectory classification.

[0086] Figure 4 Schematic diagram for the volume swept by the tool's axial motion.

[0087] Figure 5 Schematic diagram of circular interpolation of tool position point trajectory.

[0088] Figure 6 Schematic diagram of the local coordinate system.

[0089] Figure 7 Schematic diagram of the normal vector in the local coordinate system.

[0090] Figure 8 Reserve point calculation diagram for tool layer.

[0091] Figure 9 Schematic diagram of the triangular mesh structure of the front and rear surfaces of the tool in the initial and final positions.

[0092] Figure 10 Generate result plots for the tool revolution model.

[0093] Figure 11 Generate a plot of the results for a flat-bottomed cylindrical milling cutter swept volume.

[0094] Figure 12 Generate a plot of the results for a tapered ball end mill swept volume. DETAILED DESCRIPTION

[0095] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0096] A tool-swept volume solid modeling method for five-axis numerical control machining simulation of the present invention comprises the following steps:

[0097] Step 1: Create a tool rotation model.

[0098] Establish tool coordinate system O T -X T Y T Z T , whose coordinate origin is O T Coincident with the initial tool position, coordinate axis Z T The positive direction is consistent with the direction of the tool axis vector, and the coordinate axis X T Pointing to the tool radius direction; defining the tool axis section as using the tool coordinate system coordinate plane X T O T Z T Cutting tool section. Tool rotation contour point d i (x i ,z i), i = 1, ..., n are discrete points on the contour line of the tool axis section; any contour line of the tool axis section can be decomposed into several straight line segments and circular arc segments, where the rotation contour points of the straight line segment are its two end points, and the rotation contour points of the circular arc segment include the two end points and the intermediate interpolation points, such as Figure 1 shown.

[0099] Draw the tool axis section profile around the coordinate axis Z T Rotate to obtain the rotating surface of the tool; define the tool layer M of a certain tool i (i=1,…,n) is the rotation contour point d i The ring formed by rotation is expressed in the tool coordinate system as:

[0100]

[0101] Where, the subscript T indicates the coordinate system TCS, and θ is the rotation contour point d i Around the coordinate axis Z T Angle of rotation.

[0102] The tool layer ring is sampled, and the sampling point of the tool layer ring is called the vertex of the tool layer. i The j-th vertex is recorded as vertex D i_j ; In the tool coordinate system, D i_j The coordinates are expressed as:

[0103]

[0104] Where m is the number of vertices in the tool layer.

[0105] Connect the adjacent tool layer vertices into triangular faces in sequence to obtain the tool rotation model, such as Figure 2 shown.

[0106] Step 2: Calculate the movement speed of the tool axis point.

[0107] The position of the tool in the workpiece coordinate system is represented by cl t (x t ,y t ,z t ,i t ,j t ,k t ), where (x t ,y t ,z t ) represents the position vector of the tool position in the workpiece coordinate system, (i t ,j t ,k t ) represents the unit vector of the tool axis direction in the workpiece coordinate system.

[0108] The tool motion trajectory in machining simulation is divided into four types, such as Figure 3 As shown:

[0109] (1) Axial movement (such as Figure 3 (as shown in (a)).

[0110] The movement of the tool along the tool axis is called axial movement. Let the unit motion vector of the tool movement direction be e t , the mathematical description of the tool axial motion is as follows:

[0111] (i t ,j t ,k t ) T =(i t+1 ,j t+1 ,k t+1 ) T =±e t (3)

[0112] For axial motion, the tool generates a swept volume envelope by moving the top or bottom surface; the tool moves from the position cl t Move downward to position cl t+1 , the tool-swept volume is constructed as follows:

[0113] When the tool top radius is greater than or equal to the bottom radius, the top tool layer of the two pose tools, namely the tool layer M n-1 The vertices construct the triangle surface of the envelope, and then compare it with the pose cl t The top surface of the tool, the position cl t+1 The bottom and side surfaces of the tool together constitute the swept volume, such as Figure 4 As shown in (a).

[0114] When the tool bottom radius is larger than the top radius, the bottom tool layer of the two pose tools, that is, the vertex of the tool layer M2, is used to construct the triangle surface of the envelope surface, and then the triangle surface of the pose cl is used to construct the triangle surface of the envelope surface. t The top and side surfaces of the tool, the position cl t+1 The bottom surface of the tool at composes the swept volume, such as Figure 4 (b) shown.

[0115] (2) Fixed axis linear motion (such as Figure 3 (as shown in (b)).

[0116] Fixed-axis linear motion is a motion in which the tool position point trajectory is a straight line and the tool axis vector direction does not change. For fixed-axis linear motion, the velocity vector of any point on the tool axis is the same. The velocity vector calculation formula for any point on the tool axis in fixed-axis linear motion is as follows:

[0117] V=(x t+1 ,yt+1 ,z t+1 ) T -(x t ,y t ,z t ) T (4)

[0118] (3) Fixed axis circular motion (such as Figure 3 (c)).

[0119] The motion trajectory of the tool position point is an arc in the plane and the direction of the tool axis vector remains unchanged, which is called fixed-axis circular motion. The characteristics of fixed-axis circular motion are similar to fixed-axis linear motion. The velocity vector of any point on the tool axis at the same position is the same. However, unlike fixed-axis linear motion, the velocity vector of fixed-axis circular motion will change continuously with the movement of the tool. Therefore, it is necessary to perform circular interpolation on the tool position point trajectory to obtain an approximate value of the velocity vector. The direction of the tool velocity vector points from the previous interpolation point to the next interpolation point. Every two adjacent interpolation points can generate a tool sweep volume, such as Figure 5 shown.

[0120] (4) Change axis motion (such as Figure 3 (d)).

[0121] Variable axis motion refers to the change in the tool axis direction during the tool movement. For variable axis motion, it is necessary to perform linear interpolation on the tool position trajectory and the tool axis vector at the same time. The interpolation formula is as follows:

[0122]

[0123] Where k∈[0,1]; since the velocity directions of various points on the tool axis are different for the same position of the variable axis motion, the velocity vector of each tool axis point needs to be solved; the coordinates of the tool axis point at the interpolation point k that is at a distance l from the tool position point are expressed as:

[0124] (x k_l ,y k_l ,z k_l ) T =(x k ,y k ,z k ) T +l·(i k ,j k ,k k ) T (6)

[0125] The velocity vector calculation formula of the tool axis point is as follows:

[0126] V k_l =(xk+1_l ,y k+1_l ,z k+1_l ) T -(x k_l ,y k_l ,z k_l ) T (7)

[0127] Similar to the fixed-axis circular motion, the variable-axis motion also constructs a swept volume model by using the tool between two adjacent interpolation points.

[0128] Step 3: Calculate the normal vector of the tool layer.

[0129] If the tool layer M i-1 With M i They are all formed by the straight line segment rotation contour points of the tool axis section contour line, so the tool layer M i Point D i Normal vector N i_T Expressed as:

[0130]

[0131] If the tool layer M i-1 With M i They are all formed by the arc segment rotation contour point of the tool axis section contour line, so the normal vector N i_T It is represented by the normal vector at that point on the arc surface, as shown below:

[0132]

[0133] Step 4: Calculate the critical contour points and retention points of the tool layer.

[0134] According to the rotary characteristics of the tool, the tool layer M i The reverse extension lines of the normal vectors of all points on the tool intersect with the tool axis at the same point, which is marked as point Q i ; Define point P i Tool layer M i The critical contour point, its position vector P in the workpiece coordinate system i_W (t) is expressed as:

[0135] P i_W (t) = P W (t)+|P W Q i |·I W (t)+|P i Q i |·N P_i_W (t)(10)

[0136] Where, P W is the tool position in the workpiece coordinate system, IW is the tool axis vector in the workpiece coordinate system, N P_i_W (t) is the point P at position t in the workpiece coordinate system i The normal vector of .

[0137] Derivative the position parameter t, and get point P i The velocity vector V at P_i_W (t), the formula is as follows:

[0138]

[0139] Critical contour point P i The following tangency conditions are met:

[0140]

[0141] The following relationship is learned through rigid body kinematics:

[0142]

[0143] Through the above analysis, we can get the tool layer M i Corresponding tool axis point Q i The velocity vector and the critical contour point P i The normal vector is perpendicular to the point Q. i The local coordinate system O at Q -X Q Y Q Z Q , whose coordinate origin is O Q That is point Q i , coordinate axis X Q The positive direction of the velocity vector V Q_i_W Coincident, coordinate axis Z Q The positive direction of X Q ×I W The direction is consistent, such as Figure 6 shown.

[0144] In order to transform the normal vector N P_i_W Expressed as a vector N in the local coordinate system P_i_Q , define it with the coordinate axis Z Q The angle between them is γ; since vector N P_i_Q Will be located on the coordinate axis Z Q On both sides of , so this vector has two expressions, namely (0, sinγ, cosγ) and (0, -sinγ, cosγ), as shown Figure 7 As shown, where:

[0145]

[0146] Where α is the vector N P_i_QWith the tool axis vector I W The angle between the coordinate axis Y and Q With the tool axis vector I W The angle between P_i_Q The specific expression form to be chosen depends on the calculation results of the subsequent critical contour points.

[0147] Define coordinate system O Q -X Q Y Q Z Q The transformation matrix to the workpiece coordinate system is W R Q , the expression is as follows:

[0148] W R Q =[X Q Y Q Z Q ] (15)

[0149] Where, X Q 、Y Q , Z Q Represents coordinate system O Q -X Q Y Q Z Q The unit column vector of each coordinate axis in the workpiece coordinate system.

[0150] VectorN P_i_Q With the matrix W R Q Multiply to get the normal vector N P_i_W ,Right now:

[0151] N P_i_W = W R Q N P_i_Q (16)

[0152] To determine the vector N P_i_Q The expression form is solved by substitution method: First, assume that the vector N P_i_Q The coordinates are (0, sinγ, cosγ), and then the normal vector N is calculated P_i_W The coordinates of the tool layer M are substituted into formula (10) to calculate i The critical contour point P i Coordinates of point P i Located at tool layer M i If the vector N P_i_Q The coordinates are changed to (0, -sinγ, cosγ), and the critical contour point P is recalculated. i 's coordinates.

[0153] The angles α and β have different values, and the number of critical contour points is also different, which may be 0, 1, and 2. Their relationship is as follows:

[0154]

[0155] The construction of the tool sweep body solid model requires the use of the tool layer vertices of the tool rotation body model, including the tool layer vertices of the front surface of the tool in the starting posture and the tool layer vertices of the back surface of the tool in the ending posture. These two parts of points are uniformly defined as reserved points. In order to determine the tool layer M i The reserved points of the tool layer need to be divided by the critical contour points of the tool layer; since the tool layer M i The number of critical contour points may be 0, 1, or 2. Therefore, the calculation of tool layer retention points is divided into the following two cases:

[0156] Tool layer M i There are 0 or 1 critical contour points, and the tool layer M is optional. i A vertex D i_j , determine whether it is a reserved point, if so, then the tool layer M i All vertices of are reserved points; otherwise, none of them are.

[0157] Tool layer M i There are two critical contour points, defining the tool layer M i The center of the circle points to the critical contour point P i The vector is C i If V Q_i_W ×C i The vector of the knife axis vector I W The angle between the two is an acute angle, then the vector C i The corresponding critical contour point is denoted as P i_1 ; Otherwise, vector C i The corresponding critical contour point is denoted as P i_2 ; by P i_1 Rotate along the tool rotation direction to P i_2 The vertices of the tool layer passed through are the reserved points, such as Figure 8 shown.

[0158] Step 5: Construct the tool swept body solid model.

[0159] (1) Construct the front and back surface triangular meshes of the tool at the initial and final positions.

[0160] Define tool layer M i The surface contour point set of the swept volume is T i , T i The calculation steps are as follows:

[0161] S1: Set the tool layer Mi The reserved points are stored in the point set T i .

[0162] S2: Determine tool layer M i The number of critical contour points, if it is 0, go to S7; if it is 1, go to S3; if it is 2, go to S4.

[0163] S3: Find the distance critical contour point P i The two nearest reserved points, if the reserved points are formed by the critical contour point P i If the point is obtained by rotating along the direction of tool rotation, the point is recorded as D i_SI Otherwise, record the point as D i_EI , and go to S5.

[0164] S4: Distance from critical contour point P i_1 The most recent retention point is denoted as D i_SI , the distance from the critical contour point P i_2 The most recent retention point is denoted as D i_EI .

[0165] S5: Move the reserved point from point D according to the tool rotation direction i_SI To point D i_EI Arrange in order.

[0166] S6: If the tool layer M i There is only one critical contour point, so let P i_1 =P i_2 =P i ; Then, in the point set T i , point P i_1 Insert to point D i_SI Before, click P i_2 Insert to point D i_EI Then; at the same time, let D i_SI-1 =P i_1 , D i_EI+1 =P i_2 .

[0167] S7: End.

[0168] The present invention is based on the adjacent tool layer point set T i The point number correspondence relationship is constructed to construct the triangular mesh of the front surface of the tool at the starting position and the back surface of the tool at the ending position, such as Figure 9 shown.

[0169] (2) Construct a triangular mesh of the middle envelope surface of the swept volume.

[0170] The critical contour points of each tool layer of the tool are connected in sequence to generate the critical contour line; the corresponding points on the critical contour lines of the tools at adjacent positions are connected in sequence and a triangular mesh is constructed to form the intermediate envelope surface of the swept body.

[0171] Algorithm verification:

[0172] The present invention uses a flat-bottomed cylindrical milling cutter and a tapered ball-end milling cutter as examples to verify the correctness of the tool sweep volume modeling algorithm. The number of sampling points m in the tool layer is set to 36, and the coordinates of its rotation contour points are shown in Tables 1 and 2 respectively. c and f represent the tool arc radius and the number of intermediate interpolation points, respectively. The algorithm development was completed in Win11 environment based on VC++ and OSG environment. The generated results of the rotary body model of the flat-bottomed cylindrical milling cutter and the tapered ball-end milling cutter are shown in the figure. Figure 10 As shown:

[0173] Table 1 Coordinates of contour points of flat-bottomed cylindrical milling cutter

[0174]

[0175] Table 2 Coordinates of contour points of tapered ball-end milling cutter

[0176]

[0177] Four trajectories, G1, G2, G3, and G4, are planned for the flat-bottomed cylindrical milling cutter and tapered ball-end milling cutter constructed above, as shown in Table 3.

[0178] Table 3 Posture parameters of motion trajectory

[0179]

[0180] According to the motion trajectory in Table 3, the tool swept body solid models of the flat-bottomed cylindrical milling cutter and the tapered ball-end milling cutter are constructed as follows: Figure 11 and Figure 12 shown.

[0181] The example verification results show that the algorithm can well generate the tool swept volume according to the given tool parameters and motion path, and no non-manifold triangles appear in the construction of the solid model.

Claims

1. A tool-swept volume solid modeling method for five-axis CNC machining simulation, characterized in that: The following steps are involved: Step 1: Establish the tool rotation model; Establish tool coordinate system O T -X T Y T Z T , whose coordinate origin is O T Coincident with the initial tool position, coordinate axis Z T The positive direction is consistent with the direction of the tool axis vector, and the coordinate axis X T Pointing to the tool radius direction; defining the tool axis section as using the tool coordinate system coordinate plane X T O T Z T Cutting tool section; tool rotation contour point d i (x i ,z i ), i = 1, ..., n are discrete points on the contour line of the tool axis section; any contour line of the tool axis section can be decomposed into several straight line segments and circular arc segments, where the rotation contour points of a straight line segment are its two end points, and the rotation contour points of an arc segment include the two end points and the intermediate interpolation points; Draw the tool axis section profile around the coordinate axis Z T Rotate to obtain the rotating surface of the tool; define the tool layer M of a certain tool i (i=1,…,n) is the rotation contour point d i The ring formed by rotation is expressed in the tool coordinate system as: Where, the subscript T indicates the coordinate system TCS, and θ is the rotation contour point d i Around the coordinate axis Z T Angle of rotation; The tool layer ring is sampled, and the sampling point of the tool layer ring is called the vertex of the tool layer. i The j-th vertex is recorded as vertex D i_j ; In the tool coordinate system, D i_j The coordinates are expressed as: Where m is the number of vertices in the tool layer; Connect adjacent tool layer vertices into triangular faces in sequence to obtain a tool rotation model; Step 2: Calculate the movement speed of the tool axis point; The position of the tool in the workpiece coordinate system is represented by cl t (x t ,y t ,z t ,i t ,j t ,k t ), where (x t ,y t ,z t ) represents the position vector of the tool position in the workpiece coordinate system, (i t ,j t ,k t ) represents the unit vector of the tool axis direction in the workpiece coordinate system; The tool motion trajectory in machining simulation is divided into four types: (1) Axial movement: The movement of the tool along the tool axis is called axial movement. Let the unit motion vector of the tool movement direction be e t , the mathematical description of the tool axial motion is as follows: (i t ,j t ,k t ) T =(i t+1 ,j t+1 ,k t+1 ) T =±e t (3) For axial motion, the tool generates a swept volume envelope by moving the top or bottom surface; the tool moves from the position cl t Move downward to position cl t+1 , the tool-swept volume is constructed as follows: When the tool top radius is greater than or equal to the bottom radius, the top tool layer of the two pose tools, namely the tool layer M n-1 The vertices construct the triangle surface of the envelope, and then compare it with the pose cl t The top surface of the tool, the position cl t+1 The bottom surface and side surface of the tool together constitute the swept volume; When the tool bottom radius is larger than the top radius, the bottom tool layer of the two pose tools, that is, the vertex of the tool layer M2, is used to construct the triangle surface of the envelope surface, and then the triangle surface of the pose cl is used to construct the triangle surface of the envelope surface. t The top and side surfaces of the tool, the position cl t+1 The bottom surface of the tool at each location together constitutes a swept volume; (2) Fixed axis linear motion; Fixed-axis linear motion is a motion in which the tool position point trajectory is a straight line and the tool axis vector direction does not change. For fixed-axis linear motion, the velocity vector of any point on the tool axis is the same. The velocity vector calculation formula for any point on the tool axis in fixed-axis linear motion is as follows: V=(x t+1 ,y t+1 ,z t+1 ) T -(x t ,y t ,z t ) T (4) (3) Fixed axis circular motion; Fixed-axis circular motion is a motion in which the tool position trajectory is an arc in a plane and the tool axis vector direction remains unchanged. Fixed-axis circular motion has similar characteristics to fixed-axis linear motion: the velocity vector for any point on the tool axis at the same location is the same. However, unlike fixed-axis linear motion, the velocity vector for fixed-axis circular motion changes continuously with tool movement. Therefore, circular interpolation is required on the tool position trajectory to approximate the velocity vector. The tool velocity vector direction points from the previous interpolation point to the next interpolation point, and each two adjacent interpolation points form a tool sweep volume. (4) variable axis motion; Variable axis motion refers to the change in the tool axis direction during the tool movement. For variable axis motion, it is necessary to perform linear interpolation on the tool position trajectory and the tool axis vector at the same time. The interpolation formula is as follows: Where k∈[0,1]; since the velocity directions of various points on the tool axis are different for the same position of the variable axis motion, the velocity vector of each tool axis point needs to be solved; the coordinates of the tool axis point at the interpolation point k that is at a distance l from the tool position point are expressed as: The velocity vector calculation formula of the tool axis point is as follows: V k_l =(x k+1_l ,y k+1_l ,z k+1_l ) T -(x k_l ,y k_l ,z k_l ) T (7) Similar to the fixed axis circular motion, the variable axis motion also constructs the swept volume model by the tool at two adjacent interpolation points; Step 3: Calculate the normal vector of the tool layer; If the tool layer M i-1 With M i They are all formed by the straight line segment rotation contour points of the tool axis section contour line, so the tool layer M i Point D i Normal vector N i_T Expressed as: If the tool layer M i-1 With M i They are all formed by the arc segment rotation contour point of the tool axis section contour line, so the normal vector N i_T It is represented by the normal vector at that point on the arc surface, as shown below: Step 4: Calculate the critical contour points and reserved points of the tool layer; According to the rotary characteristics of the tool, the tool layer M i The reverse extension lines of the normal vectors of all points on the tool intersect with the tool axis at the same point, which is marked as point Q i ; Define point P i Tool layer M i The critical contour point, its position vector P in the workpiece coordinate system i_W (t) is expressed as: P i_W (t)=P W (t)+|P W Q i |·I W (t)+|P i Q i |·N P_i_W (t) (10) Where, P W is the tool position in the workpiece coordinate system, I W is the tool axis vector in the workpiece coordinate system, N P_i_W (t) is the point P at position t in the workpiece coordinate system i The normal vector of Derivative the position parameter t, and get point P i The velocity vector V at P_i_W (t), the formula is as follows: Critical contour point P i The following tangency conditions are met: The following relationship is learned through rigid body kinematics: Through the above analysis, we can get the tool layer M i Corresponding tool axis point Q i The velocity vector and the critical contour point P i The normal vector is perpendicular to the point Q. i The local coordinate system O at Q -X Q Y Q Z Q , whose coordinate origin is O Q That is point Q i , coordinate axis X Q The positive direction of the velocity vector V Q_i_W Coincident, coordinate axis Z Q The positive direction of X Q ×I W The direction is consistent; In order to transform the normal vector N P_i_W Expressed as a vector N in the local coordinate system P_i_Q , define it with the coordinate axis Z Q The angle between them is γ; since vector N P_i_Q Will be located on the coordinate axis Z Q On both sides of , so this vector has two expressions, namely (0, sinγ, cosγ) and (0, -sinγ, cosγ), where: Where α is the vector N P_i_Q With the tool axis vector I W The angle between the coordinate axis Y and Q With the tool axis vector I W The angle between P_i_Q The specific expression form to be chosen depends on the calculation results of the subsequent critical contour points; Define coordinate system O Q -X Q Y Q Z Q The transformation matrix to the workpiece coordinate system is W R Q , the expression is as follows: Where, X Q 、Y Q , Z Q Represents coordinate system O Q -X Q Y Q Z Q The unit column vector of each coordinate axis in the workpiece coordinate system; VectorN P_i_Q With the matrix W R Q Multiply to get the normal vector N P_i_W ,Right now: N P_i_W = W R Q N P_i_Q (16) To determine the vector N P_i_Q The expression form is solved by substitution method: First, assume that the vector N P_i_Q The coordinates are (0, sinγ, cosγ), and then the normal vector N is calculated P_i_W The coordinates of the tool layer M are substituted into formula (10) to calculate i The critical contour point P i Coordinates of point P i Located at tool layer M i If the vector N P_i_Q The coordinates are changed to (0, -sinγ, cosγ), and the critical contour point P is recalculated. i coordinates of The angles α and β have different values, and the number of critical contour points is also different, which may be 0, 1, and 2. Their relationship is as follows: The construction of the tool sweep body solid model requires the use of the tool layer vertices of the tool rotation body model, including the tool layer vertices of the front surface of the tool in the starting posture and the tool layer vertices of the back surface of the tool in the ending posture. These two parts of points are uniformly defined as reserved points. In order to determine the tool layer M i The reserved points of the tool layer need to be divided by the critical contour points of the tool layer; since the tool layer M i The number of critical contour points may be 0, 1, or 2. Therefore, the calculation of tool layer retention points is divided into the following two cases: Tool layer M i There are 0 or 1 critical contour points, and the tool layer M is optional. i A vertex D i_j , determine whether it is a reserved point, if so, then the tool layer M i All vertices of are reserved points; otherwise, none of them are; Tool layer M i There are two critical contour points, defining the tool layer M i The center of the circle points to the critical contour point P i The vector is C i If V Q_i_W ×C i The vector of the knife axis vector I W The angle between the two is an acute angle, then the vector C i The corresponding critical contour point is denoted as P i_1 ;otherwise , vector C i The corresponding critical contour point is denoted as P i_2 ; by P i_1 Rotate along the tool rotation direction to P i_2 The vertices of the tool layer passed through are the reserved points; Step 5: Construct the tool swept body solid model; (1) Construct the front and back surface triangular meshes of the tool at the initial and final positions; Define tool layer M i The surface contour point set of the swept volume is T i , T i The calculation steps are as follows: S1: Set the tool layer M i The reserved points are stored in the point set T i ; S2: Determine tool layer M i If the number of critical contour points is 0, go to S7; if it is 1, go to S3; if it is 2, go to S4; S3: Find the distance critical contour point P i The two nearest reserved points, if the reserved points are formed by the critical contour point P i If the point is obtained by rotating along the direction of tool rotation, the point is recorded as D i_SI Otherwise, record the point as D i_EI , and go to S5; S4: Distance from critical contour point P i_1 The most recent retention point is denoted as D i_SI , the distance from the critical contour point P i_2 The most recent retention point is denoted as D i_EI ; S5: Move the reserved point from point D according to the tool rotation direction i_SI To point D i_EI Arrange in order; S6: If the tool layer M i There is only one critical contour point, so let P i_1 =P i_2 =P i ; Then, in the point set T i , point P i_1 Insert to point D i_SI Before, click P i_2 Insert to point D i_EI Then; at the same time, let D i_SI-1 =P i_1 , D i_EI+1 =P i_2 ; S7: End; (2) Constructing a triangular mesh of the middle envelope of the swept volume; The critical contour points of each tool layer of the tool are connected in sequence to generate the critical contour line; the corresponding points on the critical contour lines of the tools at adjacent positions are connected in sequence and a triangular mesh is constructed to form the intermediate envelope surface of the swept body.

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