A method and system for modeling geometric pose error of a gear axial roll forming machine tool

Abstract

The application discloses a kind of gear axial rolling forming machine tool geometric pose error modeling method and system, belong to metal processing and error transmission modeling technical field.The method includes: the topological graph of axial rolling machine tool is constructed;Based on topological graph, obtain geometric pose error;According to the basis of homogeneous coordinate transformation theory, deduce basic change matrix;Based on basic change matrix, obtain the error-free motion change matrix of roll wheel coordinate system and workpiece coordinate system;Based on error-free motion change matrix, obtain the actual pose error matrix of roll wheel coordinate system and workpiece coordinate system under the condition that there is geometric error;Establish the involute tooth surface equation of roll wheel under roll wheel coordinate, and obtain the workpiece tooth surface pose error equation based on tooth surface equation and actual pose error matrix;Based on geometric pose error and workpiece tooth surface pose error equation, the pose error modeling of axial rolling machine tool is established.The application accurately describes the influence of machine tool geometric error on workpiece tooth surface.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of metal processing and error transmission modeling, and particularly relates to a gear axial rolling forming machine tool geometric pose error modeling method and system. BACKGROUND

[0002] High-performance precision gears are indispensable core basic parts of high-end equipment in the fields of aerospace, transportation, energy, etc., and the performance and precision of the gears directly determine the service life of the high-end equipment in China. At present, the coupling mechanism of heterogenous errors of the rolling forming and the dynamic evolution mechanism of the workpiece geometric error are unknown, which leads to low forming precision and seriously restricts the industrial application of the high-efficiency precision axial rolling forming technology of cylindrical gears.

[0003] It is found through the analysis of the relationship between the heterogenous errors of the rolling machine tool and the geometric errors of the workpiece that the geometric pose error of the machine tool is the main factor causing the geometric error of the workpiece, which causes the actual position and movement of the rolling wheel relative to the workpiece to deviate from the theoretical trajectory through the influence of the perpendicularity, parallelism and position error of each movement axis of the machine tool during the rolling forming process, and finally produces the geometric error. Therefore, it is particularly necessary to carry out the error tracing analysis of the geometric pose error of the machine tool, study the transmission law of the geometric pose error of the machine tool on the workpiece tooth surface pose, establish the geometric pose error model of the axial rolling machine tool, and reveal the action mechanism of the geometric pose error of the machine tool on the workpiece tooth surface pose error. SUMMARY

[0004] The application aims at solving the problems of the prior art and provides a gear axial rolling forming machine tool geometric pose error modeling method and system. The topological structure diagram of the machine tool is established by using the movement relationship of each axis of the machine tool, the geometric pose error items contained in each movement axis are studied through the error tracing analysis of the geometric pose error of the movement axis of the machine tool, the geometric pose error matrix of the machine tool is established, the model of the geometric pose error of the machine tool on the workpiece tooth surface pose error is established in combination with the tooth surface equation of the rolling wheel, and finally the influence of the geometric pose error of the machine tool on the workpiece tooth surface pose is analyzed by assigning values to the geometric pose error of the machine tool.

[0005] To achieve the above object, the application provides the following scheme: a gear axial rolling forming machine tool geometric pose error modeling method, comprising the following steps:

[0006] S1, constructing a topological diagram of the axial rolling machine tool based on the spatial structure of the axial rolling machine tool and the movement relationship of the movement axes;

[0007] S2, obtaining the geometric pose error of the movement axes of the axial rolling machine tool based on the topological diagram;

[0008] S3, obtaining a basic change matrix according to the homogeneous coordinate transformation theory;

[0009] S4. Based on the aforementioned basic transformation matrix, obtain the error-free motion transformation matrix between the rolling mill coordinate system and the workpiece coordinate system when the motion axis has no error. ;

[0010] S5. Based on the error-free motion transformation matrix To obtain the actual pose error matrix between the rolling mill coordinate system and the workpiece coordinate system under the condition of geometric error;

[0011] S6. Establish the equation of the involute tooth surface of the rolling mill in the rolling mill coordinate system. And based on the tooth surface equation And from the actual pose error matrix, the workpiece tooth surface pose error equation is obtained. ;

[0012] S7. Based on the geometric pose error and the workpiece tooth surface pose error equation Modeling of the positional error of the axial rolling mill.

[0013] More preferably, in S1, the axial rolling mill includes four motion axes: the axial guide rail Z-axis, the radial pallet Y-axis, the rolling roller A-axis, and the rotary table B-axis;

[0014] Based on the aforementioned topology, the axial rolling mill is divided into two motion chains: the rolling wheel tool motion chain and the gear workpiece motion chain.

[0015] More preferably, S4 includes the following steps:

[0016] S41. Based on the aforementioned basic change matrix, the radial pallet Y-axis movement is obtained respectively. Then, the motion transformation matrix from the bed coordinate system to the radial tray Y-axis coordinate system. Rotation of the A-axis of the rolling mill Subsequently, the motion transformation matrix from the radial pallet Y-axis coordinate system to the rolling mill A-axis coordinate system. The motion transformation matrix from the A-axis coordinate system of the rolling mill to the rolling mill coordinate system Z-axis movement of the axial guide rail Subsequently, the motion transformation matrix from the bed coordinate system to the Z-axis coordinate system of the guide rails. Rotation of the B-axis of the rotary table Then, the motion transformation matrix of the axial guide rail from the Z-axis coordinate system to the B-axis coordinate system. and the motion transformation matrix from the B-axis coordinate system to the workpiece coordinate system ;

[0017] S42. Based on the transmission relationship of the kinematic chain of the axial rolling mill and the motion transformation matrix obtained in S41, the error-free motion transformation matrix is ​​obtained. .

[0018] More preferably, the error-free motion transformation matrix include:

[0019] ;

[0020] In the formula, the superscript -1 indicates the inverse matrix of the corresponding motion change matrix; Indicates the rotation angle of the rolling mill; Indicates the rotation of the rolling mill. The rotation angle of the gear workpiece.

[0021] More preferably, in S6, the involute tooth surface equation include:

[0022] ;

[0023] In the formula, , , These represent the coordinate values ​​of the involute tooth surface equation along the X-axis, Y-axis, and Z-axis, respectively; Indicates the development angle of an involute; , Indicates the radius of the tip circle of the rolling mill teeth; Indicates the base circle radius of the rolling mill; For the helical parameters, , This refers to the width of the rolling gear teeth.

[0024] More preferably, in S6, the workpiece tooth surface pose error equation include:

[0025] ;

[0026] In the formula, This represents the X-axis coordinate value of the workpiece tooth surface pose error equation. This represents the Y-axis coordinate value of the workpiece tooth surface pose error equation. This represents the Z-axis coordinate value of the workpiece tooth surface pose error equation. This represents the actual pose error change matrix.

[0027] More preferably, in S7, the method for modeling the axial rolling mill pose error includes:

[0028] The geometric pose error is assigned a value, and simulation calculation is performed in MATLAB to obtain the relationship between the geometric pose error and the workpiece tooth surface pose error equation.

[0029] The present invention also provides a geometric pose error modeling system for a gear axial rolling forming machine tool, comprising:

[0030] The topology construction module is used to construct the topology of the axial rolling mill based on its spatial structure and the motion relationships of its axes.

[0031] The geometric pose error acquisition module is used to obtain the geometric pose error of the axial rolling mill axis based on the topology graph.

[0032] The basic transformation matrix acquisition module is used to obtain the basic transformation matrix based on the theory of homogeneous coordinate transformation.

[0033] The error-free motion transformation matrix acquisition module is used to obtain the error-free motion transformation matrix of the rolling mill coordinate system and the workpiece coordinate system under the condition that the motion axis is error-free, based on the basic transformation matrix.

[0034] The actual pose error matrix acquisition module is used to obtain the actual pose error matrix between the rolling mill coordinate system and the workpiece coordinate system under the condition of geometric error, based on the error-free motion change matrix.

[0035] The workpiece tooth surface pose error acquisition module is used to establish the involute tooth surface equation of the rolling wheel in the rolling wheel coordinate, and obtain the workpiece tooth surface pose error equation based on the involute tooth surface equation and the actual pose error matrix.

[0036] The pose error modeling module is used to model the pose error of the axial rolling mill based on the geometric pose error and the workpiece tooth surface pose error equation.

[0037] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0038] The method proposed in this invention establishes a topology diagram of the machine tool by utilizing the motion relationships of each axis of the axial rolling mill. Through source analysis of the geometric pose error of the machine tool's motion axes, the geometric pose error terms contained in each motion axis are studied, and a machine tool pose error matrix is ​​established. Combined with the workpiece tooth surface pose error equation, a model of the influence of machine tool geometric pose error on workpiece tooth surface pose error is established. Finally, by assigning values ​​to the machine tool geometric pose error, the influence of machine tool geometric pose error on workpiece tooth surface pose can be obtained. Attached Figure Description

[0039] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0040] Figure 1 This is a global view of the axial rolling mill in an embodiment of the present invention;

[0041] Figure 2This is a cross-sectional view and structural layout diagram of the axial rolling mill in an embodiment of the present invention;

[0042] Figure 3 This is a topological diagram of the axial rolling mill structure in an embodiment of the present invention;

[0043] Figure 4 This is a geometric position error diagram of the axial rolling mill in an embodiment of the present invention;

[0044] Figure 5 This is a diagram illustrating the basic translational motion of the coordinate system in an embodiment of the present invention.

[0045] Figure 6 This is a diagram showing the basic rotational motion of the coordinate system in an embodiment of the present invention; wherein, (a) represents rotation along the X-axis; (b) represents rotation along the Y-axis; and (c) represents rotation along the X-axis.

[0046] Figure 7 This is a motion diagram of the axial rolling mill in an embodiment of the present invention.

[0047] Explanation of reference numerals in the attached figures:

[0048] 0-Bed, 1-Axial guide rail Z-axis, 2-Rotary table B-axis, 3-Workpiece, 4-Radial pallet Y-axis, 5-Rolling wheel A-axis, 6-Rolling wheel, 7-Linear guide rail. Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0050] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] First, let's explain the coordinate system used:

[0052] Global coordinate system: such as Figure 2 As shown, the lower left corner is the global coordinate system of the axial rolling mill. The global coordinate system does not change with the movement or rotation of the object and is a "static reference" in space. The global coordinate system here is consistent with the bed coordinate system.

[0053] Cartesian coordinate system: following the right-hand screw rule, it is a fixed and unified reference system, that is, a global coordinate system.

[0054] Roller Coordinate System: A local coordinate system with the six components of the rolling wheel as the object. As the components move, the initial pose of the local coordinate system is consistent with the global coordinate system.

[0055] Workpiece coordinate system: A local coordinate system with the three parts of the workpiece as the object. As the parts move, the initial pose of the local coordinate system is consistent with the global coordinate system.

[0056] Bed coordinate system: A global coordinate system with the machine tool bed 0 as the object.

[0057] Radial tray Y-axis coordinate system: A local coordinate system with the four components of the radial tray Y-axis as the object. As the components move, the initial pose of the local coordinate system is consistent with the global coordinate system.

[0058] Roller A-axis coordinate system: A local coordinate system with the roller A-axis 5 component as the object. As the component moves, the initial pose of the local coordinate system is consistent with the global coordinate system.

[0059] The Z-axis coordinate system of the axial guide rail is a local coordinate system with the Z-axis 1 component as the object. As the component moves on the linear guide rail 7, the initial pose of the local coordinate system is consistent with the global coordinate system.

[0060] B-axis coordinate system: A local coordinate system with the B-axis 2 component of the rotary table as the object. As the component moves, the initial pose of the local coordinate system is consistent with the global coordinate system.

[0061] Example 1:

[0062] This embodiment provides a method for modeling the geometric pose error of a gear axial rolling forming machine tool, including the following steps:

[0063] S1. Based on the spatial structure of the axial rolling mill and the motion relationship of the motion axes, construct the topology diagram of the axial rolling mill.

[0064] like Figure 1 As shown, the axial rolling mill is the research object of this invention. The structure of the axial rolling mill is analyzed. The axial rolling mill includes four motion axes: linear axes (Z-axis 1 for the axial guide rail and Y-axis 4 for the radial tray), and rotary axes (A-axis 5 for the rolling roller and B-axis 2 for the rotary table). Based on the spatial structure of the axial rolling mill and the motion relationships of each motion axis, the following is established: Figure 3 The topology diagram of the axial rolling mill is shown. The topology diagram is divided into two motion chains: the rolling mill tool motion chain (0-4-5-6) and the gear workpiece motion chain (0-1-2-3).

[0065] S2. Based on the topology graph, the geometric position and orientation error of the axial rolling mill axis is obtained.

[0066] The geometric positional error of an axial rolling mill is mainly caused by perpendicularity, parallelism, and positional errors generated during the manufacturing, assembly, and debugging of its components. These errors do not change with the machine tool's movement, are independent of the actual moving position, and are a fixed value. Figure 4 As shown. In this embodiment, the X-axis, Y-axis, and Z-axis are all relative to the local coordinate system. For example, the rolling mill A-axis 5 has a positional error in the X direction. Here, the X direction is the X direction established relative to the initial local coordinate system of the rolling mill A-axis 5. The parallelism error between the rolling mill A-axis 5 and the Z-axis in the ZX plane is also described in the same way. The Z-axis is described in the same way. The global coordinate system is only used when analyzing the perpendicularity error between the radial pallet Y-axis 4, the axial guide rail Z-axis 1, and the X-axis, because the X-axis is not the motion axis of the axial rolling mill. The radial pallet Y-axis 4 and the axial guide rail Z-axis 1 can only produce perpendicularity errors relative to the X-axis in the global coordinate system.

[0067] For the Z-axis guide rail 1, use The perpendicularity error between the axis and the X-axis is described by the geometric pose error matrix of the Z-axis 1 of the axial guide rail. for:

[0068] ;

[0069] In the formula, This indicates that the Z-axis guide rail 1 rotates around the Y-axis. The resulting rotation error matrix; This indicates the perpendicularity error between the Z-axis 1 and the X-axis of the axial guide rail.

[0070] For radial tray Y-axis 4, use To describe its perpendicularity error with the Z-axis of the axial guide rail, using To describe its perpendicularity error with the X-axis, the geometric pose error matrix of the radial tray along the Y-axis is... for:

[0071] ;

[0072] In the formula, This indicates that the radial tray rotates around the X-axis along the Y-axis. The resulting rotation error matrix; Indicates radial tray Y-axis 4-way Z Axis rotation The resulting rotation error matrix; This indicates the perpendicularity error between the Y-axis and the Z-axis; This indicates the perpendicularity error between the Y-axis and the X-axis.

[0073] For the A-axis 5 of the rolling mill, there is a positional error in the X direction. Position error in the Y direction And the parallelism error between the A-axis 5 and the Z-axis of the rolling mill in the ZY plane. Parallelism error between the Z-axis and the ZX-plane The geometric pose error matrix of the rolling mill A-axis 5 can be considered as a synthesis of small motion transformation matrices in four directions. for:

[0074] ;

[0075] In the formula, This represents the translation error matrix of the rolling mill axis A5 along the X direction; This represents the translation error matrix of the rolling mill axis A5 along the Y direction; The matrix representing the rotational error of the rolling mill A-axis 5 about the X-axis. This represents the rotational error matrix of the rolling mill A-axis 5 about the Y-axis; This indicates the positional error of the rolling mill A-axis 5 along the X direction. This indicates the positional error of the rolling mill A-axis 5 along the Y direction. This indicates the parallelism error between the A-axis 5 and the Z-axis of the rolling mill in the ZY plane. This indicates the parallelism error between the A-axis 5 and the Z-axis of the rolling mill in the ZX plane.

[0076] For the rotary table B-axis 2, there is a positional error in the X direction. Position error in the Y direction And the parallelism error between the B-axis and Z-axis of the rotary table in the ZY plane. Parallelism error between the Z-axis and the ZX-plane The geometric pose error matrix of the rotary table along axis B2 can be considered as a synthesis of tiny motion transformation matrices in four directions. for:

[0077] ;

[0078] In the formula, This represents the translation error matrix of the rotary table along the X direction of axis B2; This represents the translation error matrix along the Y direction of axis B of the rotary table; This represents the rotation error matrix of the rotary table B-axis 2 about the X-axis; This represents the rotation error matrix of the rotary table B-axis 2 about the Y-axis; This indicates the positional error of the rotary table along axis B2 in the X direction. This indicates the positional error of the rotary table along axis B2 in the Y direction. This indicates the parallelism error between the B-axis and Z-axis of the rotary table in the ZY plane. This indicates the parallelism error between the B-axis and Z-axis of the rotary table in the ZX plane.

[0079] The above analysis shows that there are 11 position-independent geometric errors in the axial rolling mill, as detailed in Table 1.

[0080] Table 1

[0081]

[0082] S3. Based on the fundamental theory of homogeneous coordinate transformation matrix, the basic transformation matrix is ​​obtained. The basic transformation matrix includes: the translation transformation matrix of the axial rolling mill along the X-axis, Y-axis, and Z-axis and the rotation transformation matrix of the axial rolling mill along the X-axis, Y-axis, and Z-axis.

[0083] An axial rolling mill is abstracted as a multibody system, where a Cartesian coordinate system can be established on each feature body. The position and orientation changes between adjacent feature bodies are described using homogeneous coordinate matrices, and the position and orientation changes between multiple levels of feature bodies are described using ordered products of homogeneous coordinate matrices. The basic motions between adjacent feature bodies in a multibody system include translational and rotational motions.

[0084] For translational motion, the translational motion of a multibody system in any direction can be decomposed into three basic translational motions along the X-axis, Y-axis, and Z-axis, as follows: Figure 5 As shown. Figure 5 In the coordinate system Let's define the initial coordinate system. relative to the initial coordinate system The relative coordinate system for basic translational motion.

[0085] For translational motion along the X-axis:

[0086] ;

[0087] In the formula, Represents the translation matrix along the X-axis; This indicates the amount of translation along the X-axis.

[0088] For translational motion along the Y-axis:

[0089] ;

[0090] In the formula, This represents the translation matrix along the Y-axis; This indicates the amount of translation along the Y-axis.

[0091] For translational motion along the Z-axis:

[0092] ;

[0093] In the formula, This represents the translation matrix along the Z-axis; This indicates the amount of translation along the Z-axis.

[0094] For rotational motion, any complex rotational motion of a multibody system is composed of a combination of three basic rotational motions about the X, Y, and Z axes, such as... Figure 6 As shown. Figure 6 In the coordinate system Let's define the initial coordinate system. relative to the initial coordinate system A relative coordinate system for performing basic rotational motion, where and coincide.

[0095] For rotational motion about the X-axis:

[0096] ;

[0097] In the formula, Represents the rotation transformation matrix about the X-axis; This indicates the amount of rotation about the X-axis.

[0098] For rotational motion about the Y-axis:

[0099] ;

[0100] In the formula, Represents the rotation transformation matrix about the Y-axis; This indicates the amount of rotation about the Y-axis.

[0101] For rotational motion about the Z-axis:

[0102] ;

[0103] In the formula, Represents the rotation transformation matrix about the Y-axis; This indicates the amount of rotation about the Y-axis.

[0104] S4. Based on the basic transformation matrix, obtain the error-free motion transformation matrix of the rolling mill coordinate system and the workpiece coordinate system under the condition of no error in the motion axis.

[0105] Further implementation involves S4 including the following steps:

[0106] S41. Based on the basic transformation matrix, the radial pallet Y-axis 4-axis movement is obtained respectively. Then, the motion transformation matrix from the bed coordinate system to the radial tray Y-axis coordinate system. Rotation of roller A axis 5 Subsequently, the motion transformation matrix from the radial pallet Y-axis coordinate system to the rolling mill A-axis coordinate system. The motion transformation matrix from the A-axis coordinate system of the rolling mill to the rolling mill coordinate system , Axis guide rail Z-axis 1 movement Subsequently, the motion transformation matrix from the bed coordinate system to the Z-axis coordinate system of the guide rails. Rotating table B-axis 2 rotation Subsequently, the motion transformation matrix of the Z-axis coordinate system and the B-axis coordinate system of the axial guide rail. and the motion transformation matrix from the B-axis coordinate system to the workpiece coordinate system .

[0107] The motion transmission relationship between adjacent typical bodies is as follows: Figure 7 As shown. When the axial rolling mill has no geometric errors, the motion transformation matrix between adjacent typical bodies is as follows:

[0108] Radial tray Y-axis 4 movement Then, the motion transformation matrix from the bed coordinate system to the radial tray Y-axis coordinate system. for:

[0109] .

[0110] Roller A-axis 5 rotation Subsequently, the motion transformation matrix from the radial pallet Y-axis coordinate system to the rolling mill A-axis coordinate system. for:

[0111] ;

[0112] In the formula, Indicates the rotation of the A-axis 5 of the rolling mill. Motion matrix at time; This indicates the rotation angle of the rolling mill.

[0113] Since the rolling mill is fixed to the A-axis 5 of the rolling mill and has no movement relative to the A-axis 5, the motion transformation matrix from the A-axis coordinate system to the rolling mill coordinate system is... for:

[0114] ;

[0115] In the formula, This represents the motion matrix from the A-axis coordinate system of the rolling mill to the rolling mill coordinate system.

[0116] The Z-axis moves on the linear guide rail 7. Subsequently, the motion transformation matrix from the bed coordinate system to the Z-axis coordinate system of the guide rails. for:

[0117] .

[0118] Rotating table B-axis 2 rotation Subsequently, the motion transformation matrix of the Z-axis coordinate system and the B-axis coordinate system of the axial guide rail. for:

[0119] ;

[0120] In the formula, This indicates that the rotary table rotates along axis B2. Motion matrix at time; The following indicates the rotation of the rolling mill. The rotation angle of gear workpiece 3.

[0121] Since the gear workpiece 3 is fixed to the B-axis 2 of the rotary table via a tooling fixture, and does not move relative to the B-axis 2, the motion transformation matrix from the B-axis coordinate system to the workpiece coordinate system is... for:

[0122] .

[0123] S42. Based on the transmission relationship of the kinematic chain (6-5-4-0-1-2-3) of the axial rolling mill and the motion transformation matrix obtained in S41, the error-free motion transformation matrix between the rolling mill coordinate system and the workpiece coordinate system is obtained. :

[0124] ;

[0125] In the formula, the superscript -1 represents the inverse of the corresponding motion transformation matrix.

[0126] S5. Based on the error-free motion transformation matrix, obtain the actual pose error matrix between the rolling mill coordinate system and the workpiece coordinate system under the condition of geometric error.

[0127] Based on the influence of geometric pose error on the motion of the axial rolling mill, since the geometric pose error already exists after the axial rolling mill is assembled, deviations have already occurred before the motion axis of the axial rolling mill begins to move; therefore, the actual geometric error model of a single motion axis of the axial rolling mill is as follows. (in, , Indicates the sequence number of two adjacent feature bodies; superscript The expression for geometric pose error is:

[0128] ;

[0129] In the formula, For the ideal motion transformation matrix, Let be the geometric pose error matrix of the motion axis.

[0130] Therefore, considering the presence of geometric errors, based on the kinematic chain (6-5-4-0-1-2-3) transmission relationship of the rolling mill, the actual pose error matrix between the rolling mill coordinate system and the workpiece coordinate system is... for:

[0131] .

[0132] S6. Establish the involute tooth surface equation of the rolling wheel in the rolling wheel coordinate system, and obtain the workpiece tooth surface pose error equation based on the involute tooth surface equation and the actual pose error matrix.

[0133] Involute tooth surface equation include:

[0134] ;

[0135] In the formula, , , The equations of the involute tooth surface along the X-axis are respectively represented. 、 Y-axis 、 Z-axis coordinate value; Indicates the development angle of an involute; , Indicates the radius of the tip circle of the rolling mill teeth; Indicates the base circle radius of the rolling mill; For the helical parameters, , This refers to the width of the rolling gear teeth.

[0136] Tooth surface pose equation under ideal error-free conditions for:

[0137] ;

[0138] In the formula, , , These represent the tooth surface pose equations along the X-axis under ideal, error-free conditions. 、 Y-axis 、 Z-axis coordinate value.

[0139] Then, the equation for the workpiece tooth surface pose error under the condition of geometric pose error is... include:

[0140] ;

[0141] In the formula, This represents the X-axis coordinate value of the workpiece tooth surface pose error equation. This represents the Y-axis coordinate value of the workpiece tooth surface pose error equation. This represents the Z-axis coordinate value of the workpiece tooth surface pose error equation. This represents the actual pose error change matrix.

[0142] S7. Based on the geometric pose error and the workpiece tooth surface pose error equation, model the pose error of the axial rolling mill.

[0143] A further implementation involves, in S7, the method for modeling the axial rolling mill pose error includes:

[0144] By assigning values ​​to the geometric pose error, setting gear parameters and specific geometric pose error terms, and performing simulation calculations in MATLAB, the relationship between the geometric pose error and the workpiece tooth surface pose error equation is obtained. This completes the modeling of the geometric pose error of the gear axial rolling mill, which can vividly describe the influence of the geometric pose error on the workpiece tooth surface pose.

[0145] Example 2:

[0146] This embodiment provides a geometric pose error modeling system for a gear axial rolling forming machine tool, including: a topology graph construction module for constructing a topology graph of the axial rolling machine tool based on its spatial structure and the motion relationships of its motion axes; a geometric pose error acquisition module for obtaining the geometric pose error of the motion axes of the axial rolling machine tool based on the topology graph; a basic transformation matrix acquisition module for obtaining the basic transformation matrix based on the theory of homogeneous coordinate transformation; and an error-free motion transformation matrix acquisition module for obtaining the gear position error when the motion axes are error-free, based on the basic transformation matrix. The system includes: an error-free motion transformation matrix for the coordinate system and the workpiece coordinate system; an actual pose error matrix acquisition module, used to obtain the actual pose error matrix of the rolling mill coordinate system and the workpiece coordinate system under the condition of geometric error based on the error-free motion transformation matrix; a workpiece tooth surface pose error acquisition module, used to establish the involute tooth surface equation of the rolling mill in the rolling mill coordinate system, and obtain the workpiece tooth surface pose error equation based on the involute tooth surface equation and the actual pose error matrix; and a pose error modeling module, used to model the axial rolling mill pose error based on the geometric pose error and the workpiece tooth surface pose error equation.

[0147] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for modeling geometric pose errors of a gear axial roll forming machine tool, the method comprising: determining a plurality of geometric pose errors of the gear axial roll forming machine tool; and determining a plurality of geometric pose error correlations of the gear axial roll forming machine tool. The method comprises the following steps: S1, constructing a topological graph of the axial rolling machine based on the spatial structure of the axial rolling machine and the motion relationship of the motion axes; S2, obtaining geometric pose errors of the motion axes of the axial rolling machine based on the topological graph; S3, obtaining a basic change matrix according to the homogeneous coordinate transformation theory; S4, obtaining, based on the basic change matrix, an error-free motion change matrix of the roll coordinate system and the workpiece coordinate system under the condition that the motion axis is error-free ; S5、based on the error-free motion change matrix obtain the actual pose error matrix of the roll coordinate system and the workpiece coordinate system in the presence of geometric errors; S6、establishing the involute tooth surface equation of the roll under the roll coordinate , and obtaining the workpiece tooth surface pose error equation based on the tooth surface equation and the actual pose error matrix ; S7、based on the geometric pose error and the workpiece tooth surface pose error equation Modeling the pose error of the axial rolling machine S4 comprises the following steps: S41, based on the basic change matrix, respectively, get radial tray Y axis movement After, the motion transformation matrix of the bed body coordinate system to the radial tray Y axis coordinate system , roll A axis rotation After, the motion transformation matrix of the radial tray Y axis coordinate system to the roll A axis coordinate system , the motion change matrix of the roll A axis coordinate system to the roll coordinate system , axial guide rail Z axis movement After, the motion change matrix of the bed body coordinate system to the axial guide rail Z axis coordinate system , rotary table B axis rotation After, the motion change matrix of the axial guide rail Z axis coordinate system to the B axis coordinate system And the motion change matrix of the B axis coordinate system to the workpiece coordinate system ; S42, obtaining the error-free motion change matrix based on the transmission relationship of the kinematic chain of the axial rolling machine tool and the motion change matrix obtained in S41 ; The error-free motion change matrix comprises: ； wherein the superscript -1 indicates the inverse of the corresponding motion change matrix; denotes the rotation angle of the roll; denotes the rotation of the roll denotes the rotation angle of the gear workpiece.

2. The method of claim 1, wherein, In S1, the axial rolling machine comprises four motion axes: an axial guide rail Z axis, a radial tray Y axis, a rolling wheel A axis, and a rotary table B axis; And based on the topological graph, the axial rolling machine is divided into two motion chains: a rolling wheel cutter motion chain and a gear workpiece motion chain.

3. The method of claim 1, wherein, In S6, the involute tooth surface equation comprises: ； wherein, , , respectively represent the coordinate values of the involute tooth surface equation along the X axis 、 Y axis 、 Z axis; represents the involute development angle; , represents the roll wheel addendum circle radius; represents the roll wheel base circle radius; is a helix parameter, , is the roll wheel tooth width.

4. The method of claim 1, wherein, In S6, the workpiece tooth surface pose error equation comprises: ； In the formula, represents the coordinate value of the workpiece tooth surface pose error equation along the X axis, represents the coordinate value of the workpiece tooth surface pose error equation along the Y axis, represents the coordinate value of the workpiece tooth surface pose error equation along the Z axis; represents the actual pose error change matrix.

5. The method of claim 1, wherein, In S7, the method for modeling the pose error of the axial rolling machine comprises: The geometric pose error is valued and simulated and calculated in MATLAB to obtain the relationship of the geometric pose error to the workpiece tooth surface pose error equation.

6. A system for modeling geometric pose errors of a gear axial roll forming machine, the system for implementing the method of any one of claims 1-5, characterized in that, It comprises: A topological graph construction module for constructing a topological graph of the axial rolling machine based on the spatial structure of the axial rolling machine and the motion relationship of the motion axes; A geometric pose error acquisition module for obtaining geometric pose errors of the motion axes of the axial rolling machine based on the topological graph; A basic change matrix acquisition module for obtaining a basic change matrix according to the homogeneous coordinate transformation theory; An error-free motion transformation matrix acquisition module for obtaining an error-free motion transformation matrix of the rolling wheel coordinate system and the workpiece coordinate system under the condition that the motion axes are error-free based on the basic change matrix; An actual pose error matrix acquisition module for obtaining an actual pose error matrix of the rolling wheel coordinate system and the workpiece coordinate system under the condition that there are geometric errors based on the error-free motion transformation matrix; A workpiece tooth surface pose error acquisition module for establishing an involute tooth surface equation of the rolling wheel in the rolling wheel coordinate system, and obtaining a workpiece tooth surface pose error equation based on the involute tooth surface equation and the actual pose error matrix; A pose error modeling module for modeling the pose error of the axial rolling machine based on the geometric pose error and the workpiece tooth surface pose error equation.

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