Forward design method for double-swing-head configuration of five-axis machine tool

Abstract

The invention discloses a forward design method of a five-axis machine tool double-swing-head configuration. Generating a tool path according to the machined workpiece, and extracting a tool path posture set; gaussian mapping is carried out on the tool path attitude set in a Gaussian ball to be expressed by discrete points; identifying boundary points in the discrete points and connecting the boundary points to form a posture continuous area; judging whether the vertex of the Gaussian ball belongs to a posture continuous region or not, taking the included angle between the first rotating shaft piece and the second rotating shaft piece and the included angle between the second rotating shaft piece and the cutter shaft as interaxial angles, and calculating a feasible region of the interaxial angles through the posture continuous region; and then the relationship between the interaxial angle and the two translation vectors is set, so that the design of the zero rotation radius of the double swing heads of the machine tool and the elimination of nonlinear errors are realized. According to the method, forward design is conducted on the inter-axis angle feasible region and the translation vector relation of the five-axis machine tool double-swing-head configuration from the machining requirement of the complex curved surface workpiece, and the method has the advantages that the curved surface machining tool path posture is accurate and reachable, nonlinear errors can be eliminated, and translation axis compensation is avoided.

Description

Technical Field

[0001] The invention relates to a double-swing head design method, in particular to a forward design method for a double-swing head configuration of a five-axis machine tool. Background Art

[0002] As the mother machine of industry, high-precision and high-end five-axis machine tools are the foundation of the equipment manufacturing industry. Many high-precision workpieces are processed by double-swing head five-axis machine tools, among which the design of the double-swing head is the top priority in machine tool design. In the traditional swing head design, due to the existence of the rotation radius, the nonlinear error cannot be eliminated and becomes the main factor affecting the processing accuracy. In the double-swing head machine tool, the rotation radius of the second rotating shaft will change dynamically with the change of the second rotating shaft, resulting in poor surface accuracy and uneven distribution. The highest accuracy of curved surface processing is affected by the structure, and there is an irremovable bottleneck.

[0003] At present, the precision requirements for surface machining are getting higher and higher. However, traditional double-swing head surface machining requires complex post-processing procedures to reduce nonlinear errors due to the nonlinear displacement caused by the rotation radius, and the nonlinear errors cannot be completely eliminated. The machining accuracy is difficult to be further improved, and a lot of costs need to be spent on trajectory planning and interpolation.

[0004] The traditional swing head machine tool design has various shortcomings including:

[0005] (1) There is a rotation radius, and from the perspective of mechanical structure, nonlinear errors cannot be eliminated.

[0006] (2) In order to compensate for the nonlinear error caused by the rotation radius, a lot of cost is required in the post-processing procedure, and the steps are complicated.

[0007] (3) The rotation radius of the first axis will change with the rotation of the second rotating axis, and the nonlinear error will also change nonlinearly, resulting in uneven and uncontrollable accuracy distribution.

[0008] (4) Previous machine tool designs were unable to be personalized for the required working conditions, and were often designed in a universal manner based on intuition, resulting in insufficient performance or redundancy. Summary of the invention

[0009] The purpose of the present invention is to overcome the shortcomings of the prior art and to propose a double-swing head forward design and development scheme that takes the positive correlation between nonlinear error and rotation radius as the theoretical basis and can achieve zero nonlinear error and personalized design.

[0010] In order to achieve the above object, the technical solution adopted by the present invention is:

[0011] The forward design method of the double-swing head configuration of a five-axis machine tool of the present invention comprises:

[0012] Step (1): Generate a tool path according to the workpiece to be processed, extract the posture part of the tool path, and form a tool path posture set;

[0013] Step (2): Gaussian mapping is performed on the tool path posture set, so that the tool path posture is represented by discrete points in the Gaussian sphere after Gaussian mapping;

[0014] Step (3): Identify boundary points among all discrete points in the Gaussian sphere, connect the boundary points to form a posture continuous region, and extract the boundary curve of the posture continuous region;

[0015] Step (4): determine whether the vertex of the Gaussian sphere belongs to the posture continuous area, take the angle α1 between the first rotating shaft and the second rotating shaft of the double swing head and the angle α2 between the second rotating shaft and the tool axis as the axis angle, and calculate the feasible domain of the two axis angles through the boundary curve;

[0016] Step (5): Set the axis angle α1 and the translation vector v1 from the center of the first rotating shaft O1 to the center of the second rotating shaft O2, and from the center of the second rotating shaft O2 to the tool end P T The relationship between the translation vector v2, and the relationship between the axis angle α1 and the two translation vectors, and the feasible domain of the two axis angles are forward constructed to construct the machine tool double swing head and manufacture it.

[0017] The machine tool double swing head comprises a first rotating shaft, a second rotating shaft and a tool shaft, wherein the second rotating shaft and the tool shaft are integrally arranged rotatably around the first rotating shaft, the tool shaft is rotatably arranged around the second rotating shaft, and a tool for processing a product is mounted on the tool shaft;

[0018] The tool shaft is connected to the rotating part of the second rotating shaft through a connecting rod or a bracket, the fixed part of the second rotating shaft is connected to the rotating part of the first rotating shaft through a connecting rod or a bracket, and the fixed part of the first rotating shaft remains fixed.

[0019] The tool path posture set is a set of all posture vectors on the machining path, and the posture vector is a unit direction vector representing the direction of the tool axis in the machine tool coordinate system during the machining process.

[0020] In the step (1), after Gaussian mapping, each tool path posture is represented by a discrete point in the Gaussian sphere, so that each tool path posture is represented by a plurality of discrete points in the Gaussian sphere.

[0021] When the posture continuous region contains Gaussian sphere vertices, step (4) is specifically as follows:

[0022] (4.1A) The angle α1 between the first rotating shaft and the second rotating shaft of the double swing head and the angle α2 between the second rotating shaft and the tool axis are both used as the axis angle, and the two axis angles are set to be equal;

[0023] (4.2A) The polar angle of the point with the largest polar angle in the boundary curve of step (3) is extracted as the maximum polar angle θ of the posture continuous area. S ;

[0024] (4.3A) According to the maximum polar angle θ of the attitude continuous area S , the feasible region of the two axis angles is set according to the following formula:

[0025]

[0026] Among them, θ S Indicates the maximum polar angle of the attitude continuous area when the attitude continuous area contains the vertex of the Gaussian sphere;

[0027] When the posture continuous area does not contain the Gaussian sphere vertex, the step (4) is specifically as follows:

[0028] (4.1B) The polar angle of the point with the largest polar angle in the boundary curve of step (3) is extracted as the maximum polar angle θ of the posture continuous area. max , extract the polar angle of the point with the smallest polar angle in the boundary curve of step (3) as the minimum polar angle θ of the posture continuous area min ;

[0029] (4.2B) According to the maximum polar angle θ of the attitude continuous area max , minimum polar angle θ min , the feasible region of the two axis angles is set according to the following formula:

[0030] When α1≥α2:

[0031]

[0032] θ max -α2≤α1≤θ min +α2

[0033] When α2 ≥ α1:

[0034]

[0035] θ max -α1≤α2≤θ min +α1

[0036] Among them, θ max ,θ min They respectively represent the maximum polar angle and the minimum polar angle of the attitude continuous area when the attitude continuous area does not contain the vertex of the Gaussian sphere.

[0037] The step (5) is specifically as follows:

[0038] First, a first coordinate system is established with the center O1 of the first rotating shaft as the origin and the direction of the axis of the first rotating shaft toward the tool as the z-axis. A translation vector v1 is established in the first coordinate system from the center O1 of the first rotating shaft to the center O2 of the second rotating shaft, where v1 = (x1, y1, z1), and x1, y1, and z1 represent the components of the translation vector v1 in the x, y, and z-axis directions in the first coordinate system, respectively;

[0039] Then, a second coordinate system is established with the center O2 of the second rotating shaft as the origin and the direction of the axis of the second rotating shaft toward the tool as the z-axis. In the second coordinate system, a coordinate system is established from the center O2 of the second rotating shaft to the end P of the tool. T The translation vector v2, v2 = (x2, y2, z2), x2, y2, z2 represent the components of the translation vector v2 in the x, y, z axis directions in the second coordinate system respectively;

[0040] Then, the relationship between the two translation vectors and the axis angle α1 is established, as shown in the following formula:

[0041] x1=0

[0042] z2 sinα1=-y1

[0043] Finally, combining the relationship between the axis angle α1 and the two translation vectors and the feasible domain of the two axis angles, the double swing head of the machine tool is forward constructed and manufactured.

[0044] The beneficial effects of the present invention are:

[0045] By using the present invention, the feasible domain of two inter-axis angles can be quickly and effectively calculated from the tool path of a specific workpiece, providing a basis for forward design and avoiding blind attempts, as well as insufficient performance or excessive redundancy caused by mismatched workspaces.

[0046] Compared with the traditional machine tool swing head design, the forward design method of the double swing head configuration based on the zero rotation radius theory can eliminate nonlinear errors, and especially includes the inverse solution of the feasible domain. Since the nonlinear error can be eliminated, the complex post-processing procedures for compensating for the nonlinear error are further avoided, thereby greatly improving production efficiency.

[0047] The invention can completely eliminate nonlinear errors through the design of zero rotation radius, greatly improve the surface processing accuracy and surface quality. It is suitable for ultra-high precision surface processing, can eliminate nonlinear errors in the trajectory interpolation process, and avoid complex post-processing procedures. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The present invention is further described below in conjunction with the accompanying drawings and embodiments;

[0049] Figure 1 is a general flow chart of the method of the present invention;

[0050] Figure 2 It is a schematic diagram of the double swing head configuration of the method of the present invention;

[0051] Figure 3 It is a topological relationship diagram of the double swing head configuration of the method of the present invention;

[0052] Figure 4 A schematic diagram of triangulation of a tool path region not including vertices in the method of the present invention;

[0053] Figure 5 A schematic diagram of triangulation of the tool path region including vertices in the method of the present invention;

[0054] Figure 6 It is a two-dimensional schematic diagram of the inter-axis angle configuration and the posture accessible space of the present invention;

[0055] Figure 7 A three-dimensional schematic diagram of the shaft angle configuration and the accessible space of the posture of the present invention;

[0056] Figure 8 It is a schematic diagram of the feasible domain of the inter-axis angle under the specific structure of the present invention. DETAILED DESCRIPTION

[0057] The present invention is further described in detail below with reference to the accompanying drawings and examples.

[0058] According to Figure 1 The steps shown in the figure can finally design Figure 2 and Figure 3 The feasible domain of key parameters such as the two axis angles and the translation vector in the double swing head structure shown in the figure, the specific process of the present invention is as follows:

[0059] The overall flow chart of the method of the present invention is as follows Figure 1 As shown, the method comprises the following steps:

[0060] Step (1): Generate the tool path of the workpiece to be processed by computer-aided manufacturing software. The tool path consists of multiple tool position points. Each tool position point is represented by (x, y, z, i, j, k), which includes two parts of information: the spatial position coordinates of the tool end in the machine tool coordinate system (x, y, z) and the tool posture vector (i, j, k). The posture vector represents the direction of the tool axis and is a unit vector that satisfies i. 2 +j 2 +k 2 = 1, extract the posture part of each tool position in the tool path to form a tool path posture set N is the number of tool position points; each tool path posture is expressed in vector form;

[0061] Step (2): Gaussian mapping is performed on the tool path posture set, that is, the posture vector of each tool position point is moved to the coordinate origin so that it is mapped to a Gaussian sphere. This coordinate system is the machine tool coordinate system used for the tool path. After Gaussian mapping, the tool path posture is represented by discrete points in the Gaussian sphere.

[0062] Step (3): Use the triangulation method to identify the boundary points of all discrete points in the Gaussian sphere, connect the boundary points to form a posture continuous region D{Q} and extract the boundary curve B of the posture continuous region a , that is, find the boundary B in the node-edge-face-topology a ,B a is a polymorph in the Gaussian sphere, defined as B a ={p1,p2…p m}(m is the number of polygon nodes, where p i =(x i ,y i ,z i ) is a three-dimensional Cartesian coordinate). The triangulation method is Delaunay triangulation.

[0063] B a Convert to spherical coordinates. Select spherical coordinate system The spherical coordinate system is consistent with the machine tool coordinate system, where r is the radius of the sphere (the distance from the origin to the point), θ is the polar angle (the angle between the point and the positive direction of the z-axis, ranging from [0,π]), is the azimuth (the rotation angle of a point on the xy plane relative to the positive direction of the x-axis, ranging from [0,2π)), the Gaussian sphere is the unit sphere, r = 1. For each point p_i, the corresponding spherical coordinates (θ i ,φ i ):

[0064] θ i =arccos(z i ),φ i =arctan 2(y i ,x i )

[0065] Thus, polygon B can be represented as:

[0066] B a ={(θ1,φ1),(θ2,φ2),…,(θ m ,φ m )};

[0067] Step (4): Determine whether the vertex (0,0,1) of the Gaussian sphere belongs to the posture continuous region D{Q}, that is, determine the condition (0,0,1)∈D{Q}, and take the angle α1 between the first rotating shaft and the second rotating shaft of the double swing head and the angle α2 between the second rotating shaft and the tool axis as the axis angle, and pass the boundary curve B a , combined with the relationship between the axis angle and the posture reachable space and the relationship between the posture reachable space and the tool path posture set, the feasible domain of the two axis angles is calculated. The posture reachable space refers to the set of all postures that the tool can reach in the machine tool coordinate system, such as Figure 7 As shown in the figure, the accessible space of the posture can be clearly represented as a distribution area of ​​Gaussian sum after Gaussian mapping;

[0068] Step (5): Set the axis angle α1 and the translation vector v1 from the center of the first rotating shaft O1 to the center of the second rotating shaft O2, and from the center of the second rotating shaft O2 to the tool end P T The relationship between the translation vector v2, and the relationship between the axis angle α1 and the two translation vectors, and the feasible domain of the two axis angles are forward constructed to construct the machine tool double swing head and manufacture it.

[0069] The forward design method refers to forward designing the feasible design range of the inter-axis angles α1 and α2 and the relationship between the translation vectors v1 and v2 based on the requirements of satisfying the kinematic posture accessibility of the double-swing head configuration and eliminating nonlinear errors.

[0070] The key design parameters and contents of the double-swing head configuration are: the feasible design range of the axis angle α1 between the first rotating axis and the second rotating axis, the axis angle α2 between the second rotating axis and the tool axis, and the relationship between the axis angle α1 and the translation vectors v1 and v2.

[0071] The kinematic posture accessibility of the double-swing head configuration refers to the coverage of the tool path posture set of the workpiece to be processed by the posture accessibility space. The feasible design range determined by the forward design method can ensure the kinematic posture accessibility of the double-swing head configuration.

[0072] like Figure 2 As shown, the double swing head of the machine tool includes a first rotating shaft, a second rotating shaft and a tool shaft, the second rotating shaft and the tool shaft are integrally arranged rotatably around the first rotating shaft, the tool shaft is rotatably arranged around the second rotating shaft, and a tool for processing a product is installed on the tool shaft;

[0073] The tool shaft is connected to the rotating part of the second rotating shaft member through a connecting rod or a bracket, the fixed part of the second rotating shaft member is connected to the rotating part of the first rotating shaft member through a connecting rod or a bracket, and the fixed part of the first rotating shaft member remains fixed.

[0074] The tool path posture set is the set of all posture vectors on the machining path. The posture vector is the three-dimensional rotation angle of the tool expressed in the machine tool coordinate system during the machining process.

[0075] In step (1), after Gaussian mapping, each tool path posture vector is represented by a discrete point in the Gaussian sphere, and thus each tool path posture is represented by a number of discrete points in the Gaussian sphere.

[0076] When the posture continuous region contains Gaussian sphere vertices, such as Figure 5 As shown, step (4) is specifically as follows:

[0077] (4.1A) The angle α1 between the first rotating shaft and the second rotating shaft of the double swing head and the angle α2 between the second rotating shaft and the tool axis are both used as the axis angle, and the two axis angles are set to be equal;

[0078] (4.2A) The polar angle of the point with the largest polar angle in the boundary curve of step (3) is taken as the maximum polar angle θ of the posture continuous region when the posture continuous region contains the vertex of the Gaussian sphere. S ; The spherical coordinate system where the polar angle is located and the machine tool coordinate system where the attitude vector is located have the same axis direction and origin.

[0079] (4.3A) According to the maximum polar angle θ of the attitude continuous area S , combined with the relationship between the axis angle and the posture reachable space and the relationship between the posture reachable space and the tool path posture set, the feasible domain of the two axis angles is set according to the following formula:

[0080]

[0081] Among them, θ S is the maximum polar angle of the attitude continuous region when the attitude continuous region contains the vertex of the Gaussian sphere;

[0082] In the above formula is the space Ω that can be reached according to the posture T The relationship between the attitude continuous area D{Q} and the maximum polar angle θ of the attitude continuous area is obtained S Relationship; specifically:

[0083] The posture reachable space is expressed as:

[0084]

[0085] The relationship between the posture reachable space and the posture continuous area is:

[0086] When the posture continuous region does not contain the Gaussian sphere vertex, Figure 4 As shown, step (4) is specifically as follows:

[0087] (4.1B) In step (3), the boundary curve B a The polar angle of the point with the largest polar angle is extracted as the maximum polar angle θ of the posture continuous region when the posture continuous region does not contain the Gaussian sphere vertex max , extract the polar angle of the point with the smallest polar angle in the boundary curve of step (3) as the minimum polar angle θ of the posture continuous area min ;

[0088] Extract the maximum polar angle, defined as θ max ; Extract the minimum polar angle, defined as θ min ;

[0089] Extract the maximum azimuth, defined as φ max ; Extract the minimum azimuth, defined as φ min ;

[0090] Then the final posture continuous area range is:

[0091]

[0092] (4.2B) According to the maximum polar angle θ of the attitude continuous area max , minimum polar angle θ min , combined with the relationship between the axis angle and the posture reachable space and the relationship between the posture reachable space and the tool path posture set, the feasible domain of the two axis angles is set according to the following formula:

[0093] When α1≥α2:

[0094]

[0095] θ max -α2≤α1≤θ min +α2

[0096] Among them, when hour, The two ends of are equal, that is

[0098] The schematic diagram of the feasible domain of the axis angle is as follows Figure 8 As shown,

[0099]

[0100] When α2 ≥ α1:

[0101]

[0102] θ max -α1≤α2≤θ min +α1

[0103] when When α2 is feasible, The two ends of are equal, that is

[0104] Among them, θ max ,θ min They respectively represent the maximum polar angle and the minimum polar angle of the attitude continuous area when the attitude continuous area does not contain the vertex of the Gaussian sphere.

[0105] like Figure 6 and Figure 7 As shown in the figure, the relationship between the reachable space of the tool axis posture and the inter-axis angle configuration is as follows: At this time, the polar angle range of the reachable space of the posture is:

[0106] Ω T Polar angle range: (|α1-α2|, (α1+α2))

[0107] According to the conditions The feasible domain of the two axis angles can be obtained.

[0108] Step (5) is specifically as follows: Figure 3 As shown,

[0109] First, a first coordinate system is established with the center O1 of the first rotating axis as the origin and the direction of the first rotating axis axis toward the tool as the z-axis. In the first coordinate system, a translation vector v1 is established from the center O1 of the first rotating axis to the center O2 of the second rotating axis, v1 = (x1, y1, z1), x1, y1, z1 respectively represent the components of the translation vector v1 in the x, y, z-axis directions in the first coordinate system; the first coordinate system and the second coordinate system are both rectangular coordinate systems.

[0110] Then, a second coordinate system is established with the center O2 of the second rotating shaft as the origin and the direction of the axis of the second rotating shaft toward the tool as the z-axis. In the second coordinate system, a coordinate system is established from the center O2 of the second rotating shaft to the end P of the tool. T The translation vector v2, v2 = (x2, y2, z2), x2, y2, z2 represent the components of the translation vector v2 in the x, y, z axis directions in the second coordinate system respectively;

[0111] The first coordinate system is consistent with the machine tool coordinate system in the direction of the coordinate axis. The x-axis directions of the first coordinate system and the second coordinate system are both perpendicular to the plane where v1 and v2 are located and outward, and the y-axis direction is determined according to the right-hand rule;

[0112] According to the zero rotation radius theory, the intersection of the axes of the two rotating shafts and the end of the tool P T For the same point, we can get

[0113]

[0114] This is a necessary and sufficient condition for the tool end point to be on the axis of the second rotation axis. Then the origin O2 of the second rotation axis coordinate system points to the tool end P T The translation vector v2 is expressed as v2 = (0, z2 sinα1, z2 cosα1) in the first coordinate system, pointing from O1 to P T The translation vector In the first coordinate system, it is expressed as

[0116] Then, the relationship between the two translation vectors and the axis angle α1 is established, as shown in the following formula:

[0117]

[0118] Finally, combining the relationship between the axis angle α1 and the two translation vectors and the feasible domain of the two axis angles, the double swing head of the machine tool is forward constructed and manufactured.

[0119] Finally, the actual setting of the axis angle α1 satisfies the following relationship as the relationship between the axis angle α1 and the two translation vectors:

[0120] z2 sinα1=-y1

[0121] It can realize the zero rotation radius of the double swing head of the machine tool, that is, the intersection point of the axes of the two rotating shafts and the end point of the tool P T Where y1 represents the component of the translation vector v1 in the y-axis direction from the center O1 of the first rotating shaft to the center O2 of the second rotating shaft in the first coordinate system, and z2 represents the component of the translation vector v1 in the y-axis direction from the center O2 of the second rotating shaft to the end P of the tool in the second coordinate system. T The component of the translation vector v2 in the z-axis direction. The requirement for eliminating nonlinear errors is achieved by designing a zero rotation radius, which means that the first rotating shaft axis and the second rotating shaft axis form an intersection and coincide with the end of the tool.

Claims

1. A forward design method for a double swing head configuration of a five-axis machine tool, characterized in that: The method comprises the following steps: Step (1): Generate a tool path according to the workpiece to be processed, extract the posture part of the tool path, and form a tool path posture set; Step (2): Gaussian mapping is performed on the tool path posture set, so that the tool path posture is represented by discrete points in the Gaussian sphere after Gaussian mapping; Step (3): Identify boundary points among all discrete points in the Gaussian sphere, connect the boundary points to form a posture continuous region, and extract the boundary curve of the posture continuous region; Step (4): determine whether the vertex of the Gaussian sphere belongs to the posture continuous area, take the angle α1 between the first rotating shaft and the second rotating shaft of the double swing head and the angle α2 between the second rotating shaft and the tool axis as the axis angle, and calculate the feasible domain of the two axis angles through the boundary curve; Step (5): Set the axis angle α1 and the translation vector v1 from the center of the first rotating shaft O1 to the center of the second rotating shaft O2, and from the center of the second rotating shaft O2 to the tool end P T The relationship between the translation vector v2, and the relationship between the axis angle α1 and the two translation vectors, and the feasible domain of the two axis angles are forward constructed to construct the machine tool double swing head and manufacture it.

2. The forward design method for a double swing head configuration of a five-axis machine tool according to claim 1, characterized in that: The machine tool double swing head comprises a first rotating shaft, a second rotating shaft and a tool shaft, wherein the second rotating shaft and the tool shaft are integrally arranged rotatably around the first rotating shaft, the tool shaft is rotatably arranged around the second rotating shaft, and a tool for processing a product is mounted on the tool shaft; The tool shaft is connected to the rotating part of the second rotating shaft through a connecting rod or a bracket, the fixed part of the second rotating shaft is connected to the rotating part of the first rotating shaft through a connecting rod or a bracket, and the fixed part of the first rotating shaft remains fixed.

3. The forward design method for a double swing head configuration of a five-axis machine tool according to claim 1, characterized in that: The tool path posture set is a set of all posture vectors on the machining path, and the posture vector is a unit direction vector representing the direction of the tool axis in the machine tool coordinate system during the machining process.

4. The forward design method for a double swing head configuration of a five-axis machine tool according to claim 1, characterized in that: In the step (1), after Gaussian mapping, each tool path posture is represented by a discrete point in the Gaussian sphere, so that each tool path posture is represented by a plurality of discrete points in the Gaussian sphere.

5. The forward design method for a double swing head configuration of a five-axis machine tool according to claim 1, characterized in that: When the posture continuous region contains Gaussian sphere vertices, step (4) is specifically as follows: (4.1A) The angle α1 between the first rotating shaft and the second rotating shaft of the double swing head and the angle α2 between the second rotating shaft and the tool axis are both used as the axis angle, and the two axis angles are set to be equal; (4.2A) The polar angle of the point with the largest polar angle in the boundary curve of step (3) is extracted as the maximum polar angle θ of the posture continuous area. S ; (4.3A) According to the maximum polar angle θ of the attitude continuous area S , the feasible region of the two axis angles is set according to the following formula: Among them, θ S Indicates the maximum polar angle of the attitude continuous area when the attitude continuous area contains the vertex of the Gaussian sphere.

6. The forward design method for a double swing head configuration of a five-axis machine tool according to claim 1, characterized in that: When the posture continuous area does not contain the Gaussian sphere vertex, the step (4) is specifically as follows: (4.1B) The polar angle of the point with the largest polar angle in the boundary curve of step (3) is extracted as the maximum polar angle θ of the posture continuous area. max , extract the polar angle of the point with the smallest polar angle in the boundary curve of step (3) as the minimum polar angle θ of the posture continuous area min ; (4.2B) According to the maximum polar angle θ of the attitude continuous area max , minimum polar angle θ min , the feasible region of the two axis angles is set according to the following formula: When α1≥α2: i max -α2≤α1≤θ min +a2 When α2 ≥ α1: i max -α1≤α2≤θ min +a1 Among them, θ max ,θ min They respectively represent the maximum polar angle and the minimum polar angle of the attitude continuous area when the attitude continuous area does not contain the vertex of the Gaussian sphere.

7. The forward design method for a double swing head configuration of a five-axis machine tool according to claim 1, characterized in that: The step (5) is specifically as follows: First, a first coordinate system is established with the center O1 of the first rotating shaft as the origin and the direction of the axis of the first rotating shaft toward the tool as the z-axis. A translation vector v1 is established in the first coordinate system from the center O1 of the first rotating shaft to the center O2 of the second rotating shaft, where v1 = (x1, y1, z1), and x1, y1, and z1 represent the components of the translation vector v1 in the x, y, and z-axis directions in the first coordinate system, respectively; Then, a second coordinate system is established with the center O2 of the second rotating shaft as the origin and the direction of the axis of the second rotating shaft toward the tool as the z-axis. In the second coordinate system, a coordinate system is established from the center O2 of the second rotating shaft to the end P of the tool. T The translation vector v2, v2 = (x2, y2, z2), x2, y2, z2 represent the components of the translation vector v2 in the x, y, z axis directions in the second coordinate system respectively; Then, the relationship between the two translation vectors and the axis angle α1 is established, as shown in the following formula: x1＝0 z2 sinα1=-y1 Finally, combining the relationship between the axis angle α1 and the two translation vectors and the feasible domain of the two axis angles, the double swing head of the machine tool is forward constructed and manufactured.

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