Geometric Error Decoupling Method and Device for Cradle-Type Five-Axis Turntable

Abstract

This invention provides a geometric error decoupling method and apparatus for a cradle-type five-axis turntable. The method includes: constructing a serial kinematic chain based on the orthogonal geometric relationship between the A-axis and C-axis rotation centerlines, and the physical connection hierarchy between the A-axis and C-axis; planning spatially skewed measurement points based on the normal vector direction of the C-axis rotation plane in the serial kinematic chain and the spatial position change law of the C-axis rotation center under different swing angles of the A-axis; controlling the A-axis to lock at multiple non-zero swing angles based on the spatially skewed measurement points, and controlling the C-axis to complete a full rotation at each non-zero swing angle, obtaining the motion trajectory of the spatially skewed measurement points under multiple postures; and calculating the tilt error and offset error of the A-axis itself based on the motion trajectory of the spatially skewed measurement points under each posture, obtaining the geometric error parameters of the A-axis and C-axis. This invention improves the geometric positioning accuracy of the cradle-type five-axis turntable under multiple postures.

Description

Technical Field

[0001] This invention relates to the field of computer technology, and in particular to a geometric error decoupling method and apparatus for cradle-type five-axis rotary tables. Background Technology

[0002] In five-axis CNC machine tools and precision measuring equipment, cradle-type five-axis rotary tables (A / C axis structure) are widely used due to their compact structure and high rigidity. However, due to manufacturing and assembly errors, the rotation axis of the rotary table often has geometric errors (such as axis tilting, offset, etc.). These errors are directly transmitted to the tool or workpiece end, seriously affecting machining accuracy. In the prior art, a common method is the overall error compensation method based on the measurement of a single cycloidal trajectory. This method typically controls the rotary table to perform continuous rotational motion along a single axis, uses a ballbar or laser tracker to measure the actual motion trajectory of the end effector in space, compares this trajectory with the ideal circular arc trajectory, and uses the least squares method to fit a comprehensive error parameter that includes positional and angular errors, and then establishes an error mapping table for compensation.

[0003] However, existing methods cannot effectively decouple coupling errors in series transmission links, resulting in limited compensation accuracy. Specifically, the C-axis (table rotation axis) of a cradle-type turntable is mounted on the A-axis (oscillating axis), forming a series kinematic chain. When the A-axis is at a non-zero angle, the rotational motion of the C-axis is simultaneously affected by both the geometric errors of the A-axis itself (such as the tilt of the A-axis axis) and the geometric errors of the C-axis itself. Existing monocycloidal trajectory measurement methods combine this "parasitic motion" caused by the transmission of errors from the upstream axis with the "intrinsic errors" of the downstream axis itself into a single overall error for fitting. Due to the lack of in-depth analysis of the topological relationship between the spatial distribution of non-planar measurement points and the direction of the transmission link, it is difficult to separate the independent geometric error components of each axis from the mixed error. This error coupling phenomenon leads to distortion of the compensation model under complex postures, especially in multi-axis linkage machining, reducing the geometric positioning accuracy of the cradle-type five-axis turntable under multiple postures. Summary of the Invention

[0004] This invention provides a geometric error decoupling method and apparatus for cradle-type five-axis turntables, aiming to improve the geometric positioning accuracy of cradle-type five-axis turntables under multiple postures by using the differentiated responses of spatially dissimilar measuring points and the logical constraints of the transmission link flow direction.

[0005] In a first aspect, the present invention provides a geometric error decoupling method for a cradle-type five-axis rotary table, comprising:

[0006] Based on the orthogonal geometric relationship between the rotation center lines of the A-axis and C-axis of the cradle-type five-axis turntable, and the physical connection hierarchy between the A-axis and C-axis, a unidirectional transmission link flow topology structure from the drive end of the A-axis to the load end of the C-axis is constructed to obtain a serial kinematic chain characterizing the error transmission path.

[0007] Based on the normal vector direction of the C-axis rotation plane in the series kinematic chain, and the spatial position change law of the C-axis rotation center under different swing angles of the A-axis, spatially skewed measuring points are planned to be distributed on the C-axis rotation circumference and spatially skewed relative to the C-axis rotation center.

[0008] Based on the spatial non-plane measuring points, the A-axis is locked at multiple non-zero swing angles, and the C-axis is controlled to complete a full rotation at each non-zero swing angle, so as to obtain the motion trajectory of the spatial non-plane measuring points under multiple attitudes.

[0009] Based on the motion trajectory inversion calculation of the spatial non-planar measurement points under each attitude, the tilt error and offset error of the A-axis itself are calculated, and the geometric error parameters of the A-axis and C-axis are obtained.

[0010] In a second aspect, the present invention also provides a geometric error decoupling device for a cradle-type five-axis turntable, used to implement the geometric error decoupling method for a cradle-type five-axis turntable as described in the first aspect; the geometric error decoupling device for a cradle-type five-axis turntable includes:

[0011] The transmission link construction module is used to construct a unidirectional transmission link flow topology structure from the A-axis drive end to the C-axis load end based on the orthogonal geometric relationship between the A-axis rotation center line and the C-axis rotation center line of the cradle-type five-axis turntable, as well as the physical connection hierarchy between the A-axis and the C-axis, and obtain a serial kinematic chain that characterizes the error transmission path.

[0012] The measuring point positioning module is used to plan spatially skewed measuring points distributed on the C-axis rotation circumference and spatially skewed relative to the C-axis rotation center, based on the normal vector direction of the C-axis rotation plane in the series motion chain and the spatial position change law of the C-axis rotation center under different swing angles of the A-axis.

[0013] The motion trajectory analysis module is used to control the A-axis to lock at multiple non-zero swing angles based on the spatial non-plane measuring points, and to control the C-axis to complete a full rotation at each non-zero swing angle, so as to obtain the motion trajectory of the spatial non-plane measuring points under multiple postures.

[0014] The geometric error decoupling module is used to calculate the tilt and offset errors of the A-axis itself based on the motion trajectory inversion of the spatial non-planar measurement points under each attitude, and to obtain the geometric error parameters of the A-axis and the C-axis.

[0015] Thirdly, the present invention also provides an electronic device, comprising: a memory for storing computer software programs; and a processor for reading and executing the computer software programs, thereby realizing the geometric error decoupling method for a cradle-type five-axis turntable as described above.

[0016] Fourthly, the present invention also provides a non-transitory computer-readable storage medium storing a computer software program, which, when executed by a processor, implements the geometric error decoupling method for a cradle-type five-axis rotary table as described above.

[0017] Fifthly, the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the geometric error decoupling method for a cradle-type five-axis rotary table as described above.

[0018] The geometric error decoupling method for a cradle-type five-axis turntable provided in this invention, based on the orthogonal geometric constraints and hierarchical physical connection relationship between the A-axis and C-axis of the cradle-type five-axis turntable, constructs a unidirectional transmission link serial kinematic chain from the drive end of the A-axis to the load end of the C-axis. This results in a complete reproduction of the error transmission logic of the A and C axes, and a clear upstream and downstream transmission topology relationship. It overcomes the limitation of existing technologies that lack a clear error transmission link model, accurately defines the error transmission relationship between the A-axis as the upstream reference axis and the C-axis as the downstream driven axis, clarifies the coupling causes of parasitic motion caused by A-axis error and intrinsic error of the C-axis, and obtains a method to accurately locate the root causes of multiple error aliasing. Based on the error transmission topology characteristics, combined with the spatial displacement variation law of the C-axis rotation plane normal vector and rotation center under different A-axis swing angles, a measurement point array spatially skewed around the rotation circumference of the C-axis and distributed relative to the rotation center is specifically planned, resulting in a spatial measurement point layout that can produce differentiated responses to parasitic errors of the A-axis and intrinsic errors of the C-axis. Based on a differentiated measurement point layout, the A-axis is locked to multiple non-zero working postures, and the C-axis is driven to complete a full rotation. Complete measurement point motion trajectory data containing different error characteristics under multi-posture conditions are collected, realizing feature decomposition and data retention of coupling errors under different spatial postures, resulting in multiple sets of spatial trajectory datasets carrying differentiated error information. Based on the multi-dimensional differentiated trajectory data, a trajectory inversion algorithm is used to specifically isolate the parasitic motion errors caused by A-axis tilt and offset, and the intrinsic errors of the C-axis itself. The independent and non-overlapping geometric error parameters of the A-axis and C-axis are accurately solved, obtaining independent error components that achieve complete decoupling of the series transmission link errors. Therefore, this embodiment of the invention solves the problem of limited compensation accuracy caused by the inability to decouple coupling errors in the series transmission link in existing methods by using the differentiated response of spatially non-planar measurement points and the logical constraints of the transmission link flow direction, thus improving the geometric positioning accuracy of the cradle-type five-axis turntable under multiple postures. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the geometric error decoupling method for a cradle-type five-axis rotary table provided in an embodiment of the present invention.

[0020] Figure 2 This is a schematic diagram of the geometric error decoupling device for a cradle-type five-axis rotary table provided in an embodiment of the present invention;

[0021] Figure 3 An embodiment diagram of the electronic device provided in this invention;

[0022] Figure 4 An embodiment diagram of a computer-readable storage medium provided in accordance with the present invention. Detailed Implementation

[0023] 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.

[0024] In the description of this invention, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0025] In the description of this invention, the term "for example" is used to mean "used as an example, illustration, or description." Any embodiment described as "for example" in this invention is not necessarily to be construed as being more preferred or advantageous than other embodiments. The following description is provided to enable any person skilled in the art to make and use the invention. Details are set forth in the following description for purposes of explanation. It should be understood that those skilled in the art will recognize that the invention can be made without using these specific details. In other instances, well-known structures and processes will not be described in detail to avoid obscuring the description of the invention with unnecessary detail. Therefore, the invention is not intended to be limited to the embodiments shown, but is consistent with the broadest scope of the principles and features disclosed herein.

[0026] See Figure 1 , Figure 1This is a flowchart illustrating the geometric error decoupling method for a cradle-type five-axis turntable provided by the present invention. In this embodiment, the executing entity of the geometric error decoupling method for a cradle-type five-axis turntable is the turntable control device. Therefore, the geometric error decoupling method for a cradle-type five-axis turntable includes:

[0027] Step 10: Based on the orthogonal geometric relationship between the rotation center lines of the A-axis and C-axis of the cradle-type five-axis turntable, and the physical connection hierarchy between the A-axis and C-axis, construct a unidirectional transmission link flow topology structure from the A-axis drive end to the C-axis load end, and obtain a serial kinematic chain characterizing the error transmission path.

[0028] Optionally, the mechanical structure of the cradle-type five-axis rotary table consists of two parts: an A-axis swing mechanism and a C-axis rotary mechanism. The A-axis swing mechanism includes an A-axis drive motor, an A-axis worm gear reducer, an A-axis swing cradle body, and an A-axis support bearing housing. The A-axis rotation center line is the theoretical axis of rotation around which the A-axis swing cradle body performs its swing motion, and this axis extends horizontally in the machine tool coordinate system of the cradle-type five-axis rotary table. The C-axis rotary mechanism includes a C-axis drive motor, a C-axis direct-drive torque motor, a C-axis rotary table, and a C-axis crossed roller bearing. The C-axis rotation center line is the theoretical axis of rotation around which the C-axis rotary table performs its rotary motion. In the theoretical design state of the cradle-type five-axis turntable, when the cradle body is at the zero-degree swing angle position when the A-axis swings, the rotation center line of the C-axis and the rotation center line of the A-axis are perpendicular to each other in space and intersect at a point. This point is defined as the theoretical rotation center point of the cradle-type five-axis turntable. This spatial relationship of being perpendicular to each other and intersecting is the aforementioned orthogonal geometric relationship.

[0029] The physical connection hierarchy between the A-axis and C-axis refers to the load-bearing subordination relationship between the two rotary axes in a cradle-type five-axis rotary table during mechanical assembly. Specifically, the outer ring of the C-axis crossed roller bearing is bolted to the upper surface of the A-axis oscillating cradle body, and the C-axis rotary table is mounted on the inner ring of the C-axis crossed roller bearing, thus forming an assembly structure in which the entire C-axis rotary mechanism is supported by the A-axis oscillating cradle body. The A-axis oscillating cradle body is then mounted on the fixed base of the cradle-type five-axis rotary table via the A-axis support bearing seat. Therefore, from the perspective of power transmission and motion load bearing, the output torque of the A-axis drive motor is transmitted to the A-axis oscillating cradle body via the A-axis worm gear reducer, causing the A-axis oscillating cradle body to oscillate around the A-axis rotation center line; the output torque of the C-axis direct drive torque motor is directly transmitted to the C-axis rotary table, causing the C-axis rotary table to rotate around the C-axis rotation center line. Since the C-axis rotary mechanism is physically attached to the A-axis oscillating cradle body, any spatial pose change of the A-axis oscillating cradle body will directly cause the C-axis rotary mechanism to undergo the same spatial pose change. However, the rotational motion of the C-axis rotary table will not affect the spatial pose of the A-axis oscillating cradle body in the reverse direction. This characteristic of error being transmitted only from the upstream axis to the downstream axis and not in the reverse direction constitutes a unidirectional transmission link.

[0030] Based on the aforementioned orthogonal geometric relationships and physical connection hierarchy, the turntable control device constructs a unidirectional transmission link flow topology. This topology is represented in the form of a directed graph, where nodes include the A-axis drive end node, the A-axis swing cradle body node, the C-axis bearing load end node, and the C-axis rotary table node. Directed edges represent the error propagation direction. Specifically, the first directed edge points from the A-axis drive end node to the A-axis swing cradle body node, representing the transmission of geometric errors from the A-axis drive end to the A-axis swing cradle body; the second directed edge points from the A-axis swing cradle body node to the C-axis bearing load end node, representing the transmission of spatial pose errors from the A-axis swing cradle body to the C-axis bearing load end; and the third directed edge points from the C-axis bearing load end node to the C-axis rotary table node, representing the superposition of geometric errors at the C-axis bearing load end and the C-axis rotary table itself, which together affect the final motion output of the C-axis rotary table. The directed graph consisting of nodes and directed edges described above is the unidirectional transmission link flow topology. The complete error transmission path described by this structure from the A-axis drive end to the C-axis rotary table is the serial kinematic chain that characterizes the error transmission path.

[0031] For example, the rotation center line of the A-axis of a cradle-type five-axis rotary table extends horizontally along the X-axis in the machine tool coordinate system, while the rotation center line of the C-axis extends vertically along the Z-axis when the A-axis is at a zero-degree swing angle. The two rotation center lines are orthogonal at the theoretical rotation center point. The C-axis rotary table is mounted on the upper surface of the A-axis swing cradle body via a C-axis crossed roller bearing. The A-axis swing cradle body is mounted on a fixed base via A-axis support bearing seats on both sides. By reading the mechanical assembly drawing data of this cradle-type five-axis rotary table, the physical connection hierarchy of the A-axis swing cradle body supporting the C-axis rotary mechanism is identified. Based on this, a unidirectional transmission link flow topology is constructed: A-axis drive end → A-axis swing cradle body → C-axis bearing support end → C-axis rotary table. The error transmission direction flows unidirectionally from upstream to downstream along this path, thus obtaining the serial kinematic chain characterizing the error transmission path of this cradle-type five-axis rotary table.

[0032] Step 20: Based on the normal vector direction of the C-axis rotation plane in the series kinematic chain, and the spatial position change law of the C-axis rotation center under different swing angles of the A-axis, plan spatially skewed measurement points distributed on the C-axis rotation circumference and spatially skewed relative to the C-axis rotation center.

[0033] Optionally, the turntable control device, based on the normal vector direction of the C-axis rotation plane in the series motion chain and the spatial position change law of the C-axis rotation center under different swing angles of the A-axis, plans spatially skewed measurement points distributed on the C-axis rotation circumference and spatially skewed relative to the C-axis rotation center, as described in steps 201 to 204. Here, the C-axis rotation plane refers to the plane swept by the C-axis rotary table when it rotates around the C-axis rotation center line under theoretical conditions, and the normal vector direction of this plane is consistent with the theoretical direction of the C-axis rotation center line. Spatially skewed distribution means that the planned measurement points are not in the same plane; that is, the plane determined by any three measurement points is not coplanar with other measurement points. This spatial distribution allows the measurement points to sensitively capture the projection components of the geometric errors of the A-axis and C-axis in different directions.

[0034] Step 30: Based on the spatial non-plane measuring points, control the A-axis to lock at multiple non-zero swing angles, and control the C-axis to complete a full rotation at each non-zero swing angle to obtain the motion trajectory of the spatial non-plane measuring points under multiple attitudes.

[0035] Optionally, the turntable control device controls the A-axis to lock at multiple non-zero swing angles based on spatially skewed measuring points, and controls the C-axis to complete a full rotation at each non-zero swing angle, thus obtaining the motion trajectory of the spatially skewed measuring points under multiple attitudes. A non-zero swing angle refers to the angle by which the A-axis swing cradle body deflects relative to its zero-degree swing angle position; this angle is not equal to zero degrees. The purpose of selecting multiple non-zero swing angles is to place the A-axis swing cradle body in different spatial tilt attitudes, thereby causing the C-axis rotation centerline to exhibit different tilt directions in space, and thus causing the rotational motion of the C-axis rotary table to produce different sensitive directions for the geometric errors of the A-axis and C-axis under different spatial attitudes.

[0036] The turntable control device selects at least three non-zero swing angles from a preset set of angles. These selected angles are distributed within the swing stroke range of the A-axis to ensure sufficient diversity in the tilt direction of the C-axis rotation centerline in space. At each non-zero swing angle, a position control command is sent to the A-axis drive motor to drive the A-axis swing cradle body to swing to the target non-zero swing angle position. Once the A-axis swing cradle body reaches the target position, the A-axis mechanical locking mechanism is activated. This mechanism, via hydraulic or pneumatic means, rigidly fixes the A-axis swing cradle body to the current angle position, eliminating the influence of the meshing clearance of the worm gear pair in the A-axis drive transmission chain on the positional stability of the A-axis, and ensuring that the A-axis swing cradle body does not experience any angular displacement during subsequent C-axis rotation.

[0037] After the A-axis is locked, the turntable control device sends a continuous rotation control command to the C-axis direct drive torque motor, driving the C-axis rotary table to complete a full 360-degree rotation at a constant angular velocity. During the full rotation of the C-axis rotary table, the measurement target mounted on the C-axis rotary table moves synchronously. The external measuring device continuously acquires the three-dimensional spatial coordinates of the measurement target in the machine tool coordinate system at a preset sampling frequency, obtaining a discrete spatial coordinate sequence of the measurement target during the full rotation of the C-axis. This discrete spatial coordinate sequence constitutes the motion trajectory of the spatially skewed measuring point under the current non-zero swing angle posture of the A-axis. The turntable control device repeats the above process of A-axis locking, C-axis full rotation, and motion trajectory acquisition for each selected non-zero swing angle until the motion trajectory acquisition under all non-zero swing angles is completed. The resulting multiple sets of motion trajectory data, each corresponding to a specific non-zero swing angle posture of the A-axis, together constitute a set of motion trajectories of the spatially skewed measuring point under multiple postures.

[0038] For example, three non-zero swing angles are selected from a preset angle set: 30 degrees, 60 degrees, and 90 degrees. A position control command is sent to the A-axis drive motor to drive the A-axis swing cradle body to swing to the 30-degree position. Then, the A-axis hydraulic locking mechanism is activated to rigidly lock the A-axis swing cradle body at the 30-degree position. After the A-axis is locked, a continuous rotation control command is sent to the C-axis direct drive torque motor to drive the C-axis rotary table to complete a full 360-degree rotation at a constant angular velocity of five revolutions per minute. Simultaneously, the laser tracker collects the three-dimensional coordinates of the measurement target mounted on the surface of the C-axis rotary table at a sampling frequency of one hundred times per second, obtaining the first set of motion trajectories at the 30-degree orientation. Subsequently, the A-axis hydraulic locking is released, and the A-axis swing cradle body is driven to swing sequentially to the 60-degree and 90-degree positions. The locking, rotation, and acquisition process is repeated at each position to obtain the second set of motion trajectories at the 60-degree orientation and the third set of motion trajectories at the 90-degree orientation, respectively. The three sets of motion trajectories together constitute the set of motion trajectories of the spatially skewed measurement points under multiple orientations.

[0039] Step 40: Based on the motion trajectory inversion of the spatial non-planar measurement points under each attitude, calculate the tilt error and offset error of the A-axis itself, and obtain the geometric error parameters of the A-axis and the C-axis.

[0040] Optionally, the turntable control device performs inversion calculations on the tilt and offset errors of the A-axis itself based on the motion trajectory of the spatially skewed measuring points under each attitude, obtaining the geometric error parameters of the A-axis and the C-axis, as detailed in steps 401 to 404. The inversion calculation refers to using the observed actual motion trajectory of the spatially skewed measuring points as known input, establishing a forward model of error propagation in a series of motion chains, and solving it in reverse. This allows for the separation of independent geometric error components for each axis from the combined motion trajectory deviation, which includes the A-axis error propagation component and the C-axis's own error component.

[0041] Because the direction and magnitude of the influence of the A-axis geometric error on the C-axis rotary table motion trajectory vary with the change of the A-axis attitude under different non-zero A-axis oscillation angles, while the influence of the C-axis geometric error on the motion trajectory does not change with the change of the A-axis attitude and remains unchanged in its own coordinate system, the rotary table control device utilizes this difference with attitude change to achieve the decoupling and separation of the A-axis geometric error parameters and the C-axis geometric error parameters through the joint solution of multi-attitude trajectory data.

[0042] The embodiments of the present invention solve the problem that the existing methods are limited in compensation accuracy due to the inability to decouple coupling errors in the series transmission link by using the differential response of spatial non-planar measuring points and the logical constraint of the transmission link flow direction, thereby improving the geometric positioning accuracy of the cradle-type five-axis turntable under multiple postures.

[0043] Optionally, the processes of steps 201 to 204 include:

[0044] Step 201: Based on the direction of the normal vector of the C-axis rotation plane in the series kinematic chain, determine the theoretical rotation axis of the C-axis, and based on the spatial position change law of the C-axis rotation center under different swing angles of the A-axis, determine the actual rotation center of the C-axis under the current locked angle of the A-axis.

[0045] Optionally, the normal vector direction of the C-axis rotation plane refers to the direction vector perpendicular to the theoretical rotation plane of the C-axis rotary table. When the A-axis oscillating cradle body is at a zero-degree oscillation angle, this normal vector direction is parallel to the direction of the third linear axis of the machine tool coordinate system. The theoretical rotation axis of the C-axis refers to the straight line passing through the theoretical rotation center point of the cradle-type five-axis rotary table and having the same direction as the aforementioned normal vector. The spatial position change law of the C-axis rotation center under different A-axis oscillation angles refers to the geometric mapping relationship of its spatial coordinates as the C-axis rotation center moves in an arc around the rotation center line of the A-axis with the change of the A-axis oscillation angle. The current locking angle of the A-axis refers to the target non-zero oscillation angle that will be rigidly fixed by the A-axis mechanical locking mechanism in step 30.

[0046] The rotary table control device acquires the initial vertical distance from the A-axis rotation center line to the C-axis rotation center when the A-axis is at zero degrees. Since the A-axis rotation center line extends along the first linear axis of the machine tool coordinate system, the first coordinate component of the C-axis rotation center in the direction of the first linear axis of the machine tool coordinate system remains 0.

[0047] The rotary table control device multiplies the initial vertical distance by the sine of the current locking angle of the A-axis to obtain the second coordinate component of the actual rotation center of the C-axis in the direction of the second linear axis of the machine coordinate system; it multiplies the initial vertical distance by the cosine of the current locking angle of the A-axis to obtain the third coordinate component of the actual rotation center of the C-axis in the direction of the third linear axis of the machine coordinate system. The three-dimensional coordinate system composed of the first, second, and third coordinate components is the actual rotation center of the C-axis under the current locking angle of the A-axis.

[0048] For example, the rotation center line of the A-axis extends horizontally along the first linear axis of the machine tool coordinate system, and the rotation center line of the C-axis extends vertically along the third linear axis of the machine tool coordinate system when the A-axis is at zero degrees, with an initial vertical distance of 500 mm. When the current locking angle of the A-axis is 30 degrees, the rotary table control device determines the first coordinate component to be 0 mm; multiplying 500 mm by the sine of 30 degrees (0.5) yields the second coordinate component to be 250 mm; multiplying 500 mm by the cosine of 30 degrees (0.866) yields the third coordinate component to be 433 mm. Therefore, the actual rotation center coordinates of the C-axis at 30 degrees are determined to be (0, 250, 433).

[0049] Step 202: Construct a spatial reference frame based on the theoretical rotation axis of the C-axis and the actual rotation center of the C-axis.

[0050] Optionally, the spatial reference system is a local three-dimensional Cartesian coordinate system established with the actual rotation center of the C-axis as its origin. The turntable control device sets the actual rotation center of the C-axis as the origin of the spatial reference system and sets the extension direction of the theoretical rotation axis of the C-axis as the direction of the third coordinate axis of the spatial reference system. A first linear axis direction perpendicular to the theoretical rotation axis of the C-axis is selected in the machine coordinate system and projected onto a plane perpendicular to the third coordinate axis of the spatial reference system, thus obtaining the direction of the first coordinate axis of the spatial reference system. According to the right-hand rule of Cartesian coordinates, the direction of the second coordinate axis of the spatial reference system is calculated by the cross product of the first and third coordinate axis directions. Therefore, the origin, the first coordinate axis direction, the second coordinate axis direction, and the third coordinate axis direction together constitute the spatial reference system.

[0051] For example, the actual rotation center of the C-axis at coordinates (0, 250, 433) is set as the origin of the spatial reference system. Since the A-axis oscillates around the first linear axis, the theoretical rotation axis of the C-axis lies in the plane formed by the second and third linear axes at a 30-degree angle, and forms a 30-degree angle with the third linear axis. This tilt direction is set as the direction of the third coordinate axis of the spatial reference system. The direction of the first linear axis of the machine tool coordinate system is directly set as the direction of the first coordinate axis of the spatial reference system. The direction perpendicular to the first and third coordinate axes is calculated using the right-hand rule cross product and set as the direction of the second coordinate axis of the spatial reference system.

[0052] Step 203: Based on the extension direction of the theoretical rotation axis of the C-axis in the spatial reference system and the spatial coordinates of the actual rotation center of the C-axis under the current locking angle of the A-axis, generate an auxiliary axis that passes through the actual rotation center of the C-axis and is parallel to the theoretical rotation axis of the C-axis, thus obtaining the spatial positioning auxiliary line.

[0053] Optionally, the extension direction of the theoretical rotation axis of the C-axis is the direction vector of the third coordinate axis in the spatial reference system. The spatial coordinates of the actual rotation center of the C-axis under the current locked angle of the A-axis are the absolute three-dimensional coordinates of the origin of the spatial reference system in the machine tool coordinate system.

[0054] The turntable control device uses the spatial coordinates of the actual rotation center of the C-axis as its starting point and the extension direction of the theoretical rotation axis of the C-axis as its direction vector to construct a straight line extending in both directions. This straight line passes through the actual rotation center of the C-axis and remains absolutely parallel to the theoretical rotation axis of the C-axis in space. This constructed straight line is the spatial positioning auxiliary line, which serves as the central reference axis for the distribution of spatially skewed measurement points in subsequent steps, ensuring that the measurement points are distributed in a circle around this auxiliary line.

[0055] For example, taking the actual rotation center of the C-axis with coordinates (0, 250, 433) as the starting point, and the tilt direction of the theoretical rotation axis of the C-axis in a 30-degree attitude (i.e., the direction of the third coordinate axis of the spatial reference system) as the direction vector, a straight line passing through the starting point and parallel to the theoretical rotation axis of the C-axis is generated. This straight line is used as a spatial positioning auxiliary line for the reference positioning of the measurement point in the subsequent 30-degree attitude.

[0056] Step 204: Based on the spatial distance between the spatial positioning auxiliary line and the theoretical rotation axis of the C-axis, and the preset rotation radius of the C-axis, determine the spatial non-planar measuring points.

[0057] Optionally, the turntable control device determines the spatially skewed measurement points based on the spatial distance between the spatial positioning auxiliary line and the theoretical rotation axis of the C-axis, as well as the preset C-axis rotation radius, as described in steps 2041 to 2044. Here, the spatially skewed measurement points refer to measurement points distributed on the circumference of the C-axis rotation and spatially skewed relative to the C-axis rotation center. The preset C-axis rotation radius refers to the set radial distance between the spatially skewed measurement points and the actual rotation center of the C-axis.

[0058] This invention accurately calculates the actual rotation center of the C-axis based on the normal vector of the C-axis rotation plane and the variation law of the A-axis swing angle, and constructs a spatial reference system. This generates a spatial positioning auxiliary line parallel to the theoretical axis, precisely reconstructing the true theoretical rotation reference of the C-axis after the A-axis swings in space. Combining the eccentricity distance between the spatial positioning auxiliary line and the theoretical axis, and the preset rotation radius, spatially skewed measurement points are planned. This allows the planned measurement point array to conform to the actual motion envelope of the C-axis under multiple postures, thus ensuring that the measurement points have maximized orthogonal decoupling characteristics from the parasitic error of the A-axis to the intrinsic error of the C-axis at the data acquisition source. This fundamentally guarantees the solution accuracy of complete decoupling of the coupling error of the serial transmission link and improves the multi-posture geometric positioning accuracy of the cradle-type five-axis turntable.

[0059] Optionally, the process of steps 2041 to 2044 includes:

[0060] Step 2041: Based on the spatial distance and the preset C-axis rotation radius, generate a reference circular trajectory on a plane perpendicular to the theoretical C-axis rotation axis to obtain the initial circular path.

[0061] Optionally, the spatial distance refers to the shortest vertical distance between the spatial positioning auxiliary line and the theoretical C-axis rotation axis. The preset C-axis rotation radius refers to the set radial distance between the spatially skewed measuring point and the actual C-axis rotation center. The plane perpendicular to the theoretical C-axis rotation axis refers to the plane passing through the actual C-axis rotation center and whose normal vector is parallel to the direction vector of the theoretical C-axis rotation axis. On this plane perpendicular to the theoretical C-axis rotation axis, the turntable control device generates a closed circular trajectory with the actual C-axis rotation center as the center and the preset C-axis rotation radius as the radius. This circular trajectory is the reference circular trajectory, which is also the initial circular path.

[0062] For example, the spatial distance between the spatial positioning auxiliary line and the theoretical rotation axis of the C-axis is 2 mm, and the preset rotation radius of the C-axis is set to 200 mm. On a plane passing through the actual rotation center of the C-axis at coordinates (0, 250, 433) and perpendicular to the theoretical rotation axis of the C-axis, a closed circular trajectory is generated with the actual rotation center of the C-axis as the center and a radius of 200 mm. This circular trajectory is used as the initial circumferential path.

[0063] Step 2042: Based on any starting point on the initial circular path and the tilt angle of the C-axis rotation plane relative to the horizontal plane under the current locking angle of the A-axis, offset the C-axis along the theoretical rotation axis direction by a preset axial step to generate an offset circular trajectory and obtain a set of layered circular paths.

[0064] Optionally, any starting point is a defined position on the initial circular path. The tilt angle of the C-axis rotation plane relative to the horizontal plane at the current A-axis locking angle is the current A-axis locking angle. The preset axial step refers to the set straight-line distance. Offsetting the preset axial step along the theoretical C-axis rotation axis means translating the initial circular path from the plane containing the initial circular path along the positive or negative direction of the theoretical C-axis rotation axis by a preset axial step. The turntable control device translates the initial circular path along the theoretical C-axis rotation axis by the preset axial step, generating a new circular trajectory, which is the offset circular trajectory. This translation process is repeated to generate multiple offset circular trajectories located at different axial positions. The initial circular path and all offset circular trajectories together constitute a layered circular path set.

[0065] For example, the point furthest along the positive direction of the second coordinate axis of the spatial reference system on the initial circular path is selected as an arbitrary starting point. The current locked angle of the A-axis is 30 degrees, i.e., the tilt angle is 30 degrees. The preset axial step size is set to 50 millimeters. The turntable control device translates the initial circular path along the theoretical rotation axis of the C-axis by 50 millimeters and 100 millimeters in the positive direction, and by 50 millimeters and 100 millimeters in the negative direction, generating four offset circular trajectories. This initial circular path and the four offset circular trajectories together form a layered circular path set containing five layers of circular trajectories.

[0066] Step 2043: Based on the circumference of each layer of the circular path set, divide each layer of the circular path into multiple arc segments, and determine the endpoint of each arc segment as the potential measurement point location.

[0067] Optionally, the circumference of each layer of the circular trajectory is calculated based on the preset C-axis rotation radius, using the circumference formula. The number of equal divisions refers to the number of parts into which the circular trajectory is divided. The turntable control device divides the circumference of each layer of the circular trajectory by the number of equal divisions to obtain the arc length of each arc segment. Starting from the corresponding starting point of each layer of the circular trajectory, line segments equal to this arc length are sequentially intercepted along the circular trajectory in a preset rotation direction, dividing each layer of the circular trajectory into multiple arc segments. The start and end points of each arc segment are the endpoints, and the turntable control device determines the three-dimensional coordinates of these endpoints in the machine tool coordinate system as potential measuring point positions.

[0068] For example, assuming a preset C-axis rotation radius of 200 mm, multiplying 200 by 2 and then by 3.14 yields a circumference of 1256 mm for each layer of the circular trajectory. Setting the number of equal divisions to 8, each layer of the circular trajectory is divided into 8 arc segments, each with an arc length of 157 mm. For each layer of the circular trajectory in the set of layered circular paths, starting from the corresponding starting point, an endpoint is determined every 157 mm counterclockwise, resulting in 8 endpoints per layer. A total of 40 endpoints are determined across the five layers of circular trajectories, and the three-dimensional coordinates of these 40 endpoints are used to identify 40 potential measurement point locations.

[0069] Step 2044: Based on the line vector connecting the potential measurement point position of each potential measurement point to the spatial positioning auxiliary line, and the direction vector of the C-axis theoretical rotation axis, determine the spatial non-planar measurement points.

[0070] Optionally, the turntable control device calculates the line vector connecting the potential measuring point position of each potential measuring point to the corresponding perpendicular foot on the spatial positioning auxiliary line, and obtains the direction vector of the theoretical rotation axis of the C-axis.

[0071] The turntable control device determines the spatially skewed measurement points based on the line vector connecting the potential measurement point position of each potential measurement point and the spatial positioning auxiliary line, as well as the direction vector of the theoretical rotation axis of the C-axis, as described in steps 20441 to 20443.

[0072] This invention generates an initial circular path based on spatial distance and a preset C-axis rotation radius, and constructs a layered circular path set by translating along the theoretical C-axis rotation axis with a preset axial step size. Then, it determines the positions of potential measurement points by dividing the circumference equally. Finally, it screens and confirms spatially skewed measurement points based on the spatial geometric relationship between the connecting vector and the direction vector, ensuring that the final spatially skewed measurement points meet the skewed distribution constraint in terms of geometric topology. This ensures the effective separation and high-precision inversion solution of the parasitic error of the A-axis and the intrinsic error of the C-axis, thereby improving the geometric positioning accuracy of the cradle-type five-axis turntable under multiple postures.

[0073] Optionally, the processes of steps 20441 to 20443 include:

[0074] Step 20441: Based on the line vector connecting the potential measuring point position of each potential measuring point to the spatial positioning auxiliary line, and the direction vector of the C-axis theoretical rotation axis, select potential measuring points whose angle between the line vector and the direction vector is not zero and is not 90 degrees, and determine them as initial measuring points.

[0075] Optionally, the connecting vector refers to the directed line segment from the actual rotation center of the C-axis on the spatial positioning auxiliary line to the potential measurement point position. The direction vector of the theoretical rotation axis of the C-axis refers to the direction vector of the third coordinate axis in the spatial reference system. For each potential measurement point in the layered circular path set, the turntable control device calculates the connecting vector from the actual rotation center of the C-axis to the potential measurement point position, and calculates the spatial angle between the connecting vector and the direction vector of the theoretical rotation axis of the C-axis.

[0076] When the spatial angle is equal to 90 degrees, it indicates that the potential measuring point is located on the initial circumferential path that passes through the actual rotation center of the C-axis and is perpendicular to the theoretical rotation axis of the C-axis. These measuring points are in the same plane and cannot provide error constraints in the axial dimension.

[0077] When the spatial angle is 0 degrees, it indicates that the potential measuring point is located on the spatial positioning auxiliary line, which contradicts the physical fact that the preset C-axis rotation radius is greater than zero. Therefore, the turntable control device eliminates potential measuring points with spatial angles of 90 degrees and 0 degrees, and only retains potential measuring points with spatial angles that are neither zero nor 90 degrees, and determines these retained potential measuring points as the initial measuring points.

[0078] For example, the layered circular path set contains one initial circular path and four offset circular trajectories, totaling 40 potential measurement points. Calculate the line vector connecting the actual rotation center of the C-axis at coordinates (0, 250, 433) to the position of each potential measurement point, and calculate the spatial angle between this line vector and the direction vector of the theoretical rotation axis of the C-axis at a 30-degree attitude.

[0079] For the 8 potential measuring points located on the initial circular path, the connecting vector is perpendicular to the direction vector, and the spatial angle is 90 degrees. These 8 potential measuring points are eliminated. For the 32 potential measuring points located on the 4 offset circular trajectories, the connecting vector has a component in the direction of the C-axis theoretical rotation axis, and the spatial angle is neither 0 degrees nor 90 degrees. These 32 potential measuring points are determined as the initial measuring points.

[0080] Step 20442: Based on the phase difference between two adjacent potential measuring points on the C-axis rotation circle and the spatial projection deformation caused by the A-axis swing, potential measuring points located on different layers of circular trajectories are alternately selected to construct a spatial distribution sequence that spirals upward or downward, thus obtaining candidate measuring points.

[0081] Optionally, the phase difference refers to the angular difference between two adjacent selected potential measuring points on their respective circular trajectories relative to their respective center. Spatial projection deformation refers to the degree of deformation caused by the A-axis oscillation leading to the tilt of the C-axis rotation plane, resulting in the orthogonal projection of the measuring point on the machine tool coordinate system's horizontal plane changing from a circle to an ellipse. The turntable control device sorts the initial measuring points according to their axial coordinates on their offset circular trajectories from smallest to largest, forming multiple axial levels. The spatial projection deformation is calculated based on the current A-axis locking angle; the larger the current A-axis locking angle, the greater the spatial projection deformation. The phase difference is dynamically adjusted based on the spatial projection deformation; the larger the spatial projection deformation, the smaller the set phase difference, to compensate for the uneven distribution of measuring points caused by projection deformation. Starting from the level with the smallest axial coordinate, an initial measuring point is selected as the starting point. Then, in the adjacent axial levels, the next initial measuring point is selected according to the adjusted phase difference. This process is repeated alternately between different levels, so that the selected initial measuring points continuously increase or decrease in the circumferential angle and monotonically increase or decrease in the axial coordinate, thereby constructing a spatial distribution sequence that spirals upward or downward. The initial measuring points in this spatial distribution sequence are then determined as candidate measuring points.

[0082] For example, 32 initial measuring points are distributed along four offset circular trajectories with axial coordinates of -100, -50, 50, and 100 mm. The current locking angle of the A-axis is 30 degrees. The corresponding spatial projection deformation is calculated, and the phase difference is set to 45 degrees accordingly. The first initial measuring point is selected from the layer with axial coordinates of -100 mm. The second initial measuring point with a phase difference of 45 degrees relative to the previous measuring point is selected from the layer with axial coordinates of -50 mm. The third initial measuring point with a phase difference increasing by 45 degrees is selected from the layer with axial coordinates of 50 mm. The fourth initial measuring point with a phase difference increasing by 45 degrees is selected from the layer with axial coordinates of 100 mm. These four initial measuring points are spaced 45 degrees apart circumferentially and increase sequentially axially, constructing a spiral-shaped spatial distribution sequence. These four initial measuring points are then identified as candidate measuring points.

[0083] Step 20443: Based on the spatial connectivity of the first and last measurement points in the candidate measurement points and the motion continuity of the C-axis rotation, close the candidate measurement points to form a closed spatial polygonal loop, and obtain spatial non-planar measurement points.

[0084] Optionally, the spatial connectivity of the first and last measuring points refers to the spatial straight-line distance and transition smoothness between the first and last candidate measuring points in the spatial distribution sequence. Motion continuity refers to the requirement that the measuring equipment continuously and uninterruptedly collects data when the C-axis rotary table rotates a full 360 degrees, requiring the measuring point sequence to form a closed-loop trajectory without breaks in space. The rotary table control device calculates the spatial straight-line distance from the last candidate measuring point to the first candidate measuring point in the spatial distribution sequence.

[0085] If the spatial straight-line distance is greater than a preset connectivity threshold, a transitional measurement point is inserted between the last candidate measurement point and the first candidate measurement point using an equidistant interpolation algorithm, ensuring that the distance between adjacent measurement points is less than or equal to the connectivity threshold. If the spatial straight-line distance is less than or equal to the preset connectivity threshold, the last candidate measurement point is directly connected to the first candidate measurement point. The candidate measurement points and any inserted transitional measurement points are then connected sequentially with straight-line segments according to their spatial distribution sequence, closing the loop at both ends to form a closed spatial polygonal loop. All nodes on this closed spatial polygonal loop are the finally determined spatial non-planar measurement points.

[0086] For example, the candidate measurement points include four initial measurement points. The spatial distribution sequence starts at the first initial measurement point at the -100 mm level along the axial coordinate and ends at the fourth initial measurement point at the 100 mm level along the axial coordinate. The spatial straight-line distance from the fourth initial measurement point to the first initial measurement point is calculated and found to be greater than the preset connectivity threshold of 50 mm. Two transition measurement points are inserted between the fourth and first initial measurement points using an equidistant interpolation algorithm, ensuring that the spatial distance between adjacent measurement points is less than 50 mm. These four candidate measurement points and two transition measurement points are then connected sequentially with straight-line segments, closing the loop at both ends to form a closed spatial polygonal loop containing six nodes. These six nodes are then identified as the final spatial non-planar measurement points.

[0087] This invention establishes initial measurement points by accurately eliminating coplanar measurement points based on the angle between the connecting vector and the direction vector. It dynamically adjusts the phase difference by combining spatial projection deformation and alternately selects and constructs a spiral candidate measurement point sequence at different axial levels. Finally, it forms a closed spatial polygonal loop based on the spatial connectivity and motion continuity of the beginning and end. This breaks the limitations of single-plane or regular array measurement point distribution in three-dimensional space, and constructs a heteroplanar spiral measurement point topology with high axial span, continuous circumferential phase shift, and smooth closure at the beginning and end. This allows the spatial heteroplanar measurement points to capture the coupling response characteristics of parasitic errors on the A-axis and intrinsic errors on the C-axis in multiple dimensions during the full rotation of the C-axis. This fundamentally eliminates the error observation singularity and ill-conditioned decoupling model problems caused by coplanar measurement points, thereby improving the solution accuracy of complete decoupling of coupling errors in the series drive link and the multi-pose geometric positioning accuracy of the cradle-type five-axis turntable.

[0088] Optionally, the processes of steps 401 to 404 include:

[0089] Step 401: Based on the motion trajectory of the spatial skew measurement points under each attitude and the theoretical position of the C-axis rotation center under each non-zero swing angle, calculate the radial deviation component and axial deviation component of each spatial skew measurement point relative to its corresponding theoretical rotation center to obtain C-axis composite deviation data containing A-axis attitude information.

[0090] Optionally, the theoretical center of rotation refers to the center point around which the C-axis rotary table rotates under ideal, error-free conditions; its spatial coordinates are the actual C-axis rotation center determined in the aforementioned steps. The motion trajectory of the spatially skewed measuring points includes multiple discrete spatial coordinates continuously acquired by external measuring equipment during the full rotation of the C-axis rotary table. The radial deviation component refers to the difference between the actual vertical distance from the discrete spatial coordinates to the spatial positioning auxiliary line and the preset C-axis rotation radius. The axial deviation component refers to the difference between the actual projected length of the discrete spatial coordinates along the theoretical rotation axis of the C-axis and the theoretical axial coordinate of the discrete spatial coordinates in the layered circular path set.

[0091] For each discrete spatial coordinate in the motion trajectory, the turntable control device calculates the vertical distance from that coordinate to the spatial positioning auxiliary line. Subtracting the preset C-axis rotation radius from this vertical distance yields the radial deviation component of that discrete spatial coordinate. Simultaneously, the turntable control device calculates the projected length of that discrete spatial coordinate along the theoretical C-axis rotation axis. Subtracting this projected length from the corresponding theoretical axial coordinate yields the axial deviation component of that discrete spatial coordinate. The turntable control device combines all radial and axial deviation components of each spatially skewed measuring point during a full rotation to form C-axis composite deviation data that includes attitude information at the current A-axis locking angle.

[0092] For example, in a 30-degree orientation, the spatial non-planar measurement point contains 6 nodes. During the full rotation of the C-axis rotary table, the laser tracker collects 600 discrete spatial coordinates, with the theoretical rotation center coordinates being (0, 250, 433). For one of the discrete spatial coordinates, its vertical distance to the spatial positioning auxiliary line is calculated to be 200.05 mm. Subtracting this from the preset C-axis rotation radius of 200 mm yields a radial deviation component of 0.05 mm. The projection length of this discrete spatial coordinate onto the theoretical C-axis rotation axis is calculated to be 50.02 mm. Subtracting this from the theoretical axial coordinate of the level where the measurement point is located (50 mm) yields an axial deviation component of 0.02 mm. By traversing all 600 discrete spatial coordinates, the C-axis composite deviation data for the 30-degree orientation is obtained. The calculation process for the 60-degree and 90-degree orientations is exactly the same.

[0093] Step 402: Based on the projection relationship of the A-axis error to the C-axis in the serial kinematic chain, and the variation law of the axial deviation component in the C-axis composite deviation data with the swing angle of the A-axis, the projection error component caused by the geometric error of the A-axis is separated to obtain the C-axis geometric error parameter after removing the A-axis transmission error.

[0094] Optionally, the projection relationship refers to the mathematical relationship whereby the projection of the geometric error of the A-axis oscillating cradle body onto the C-axis rotary table, when transmitted to the C-axis rotary table, is proportional to the trigonometric function value of the A-axis oscillation angle. The variation law refers to the fact that since the geometric error of the C-axis rotary table itself does not change with the A-axis oscillation angle, while the projection error component transmitted from the A-axis to the C-axis changes according to a trigonometric function with the A-axis oscillation angle, the axial deviation component includes both a constant component and a variable component that varies with the angle. The rotary table control device extracts the axial deviation components at the same phase position under different non-zero oscillation angles and constructs an overdetermined system of equations with the A-axis and C-axis geometric error parameters as unknowns. The turntable control device solves the overdetermined equations using the least squares method, attributing the axial deviation component that varies with the A-axis swing angle to the projection error component caused by the A-axis geometric error, and attributing the constant axial deviation component that does not vary with the A-axis swing angle to the geometric error of the C-axis rotary table itself, thereby separating and obtaining the C-axis geometric error parameters after eliminating the A-axis transmission error.

[0095] For example, suppose we extract the axial deviation components at the 0-degree phase position on the C-axis rotation circumference at 30°, 60°, and 90° attitudes, which are 0.02, 0.03, and 0.04 mm, respectively. We construct a system of equations, where the unknowns include the projection coefficient of the A-axis tilt error along the third linear axis and the axial geometric error of the C-axis rotary table itself. Solving this system of equations using the least squares method, we calculate the axial geometric error of the C-axis rotary table itself to be 0.01 mm. This 0.01 mm is one component of the C-axis geometric error parameter after eliminating the A-axis transmitted error. By iterating through all phase positions, we obtain the complete C-axis geometric error parameters.

[0096] Step 403: Separate the C-axis geometric error component from the motion trajectory of the spatially skewed measurement points in each attitude to obtain the radial residual deviation.

[0097] Optionally, removing the C-axis geometric error component means substituting the C-axis geometric error parameters obtained in step 402 into the error propagation positive model of the serial motion chain to calculate the theoretical trajectory deviation caused only by the geometric error of the C-axis rotary table itself. This theoretical trajectory deviation is the C-axis geometric error component. The radial residual deviation refers to the radial deviation caused by the propagation of the A-axis geometric error after subtracting the radial deviation portion of the C-axis geometric error component from the radial deviation component of the actual motion trajectory. For each discrete spatial coordinate in each posture, the turntable control device subtracts the radial deviation portion of the C-axis geometric error component at the corresponding position from the radial deviation component of the actual motion trajectory to obtain the radial residual deviation at that position. By traversing all discrete spatial coordinates in all postures, multiple sets of radial residual deviations reflecting the characteristics of the A-axis geometric error propagation are obtained.

[0098] For example, at a 30-degree attitude, for a spatially skewed measuring point at a phase of 0 degrees, the radial deviation component of its actual motion trajectory is 0.05 mm.

[0099] Assuming that the C-axis geometric error parameters obtained in step 402 are substituted into the error propagation positive model, the radial deviation at this position caused solely by the geometric error of the C-axis rotary table is calculated to be 0.02 mm. Subtracting 0.02 mm from 0.05 mm yields 0.03 mm, which is the radial residual deviation at the 0-degree phase position under a 30-degree attitude. By traversing all measuring points and all attitudes, multiple sets of radial residual deviations are obtained.

[0100] Step 404: Based on the geometric mapping relationship between the radial residual deviation and the A-axis swing angle, the tilt error and offset error of the A-axis itself are calculated to obtain the geometric error parameters of the A-axis.

[0101] Optionally, the turntable control device inverts and calculates the tilt and offset errors of the A-axis itself based on the geometric mapping relationship between the radial residual deviation and the A-axis swing angle, thus obtaining the A-axis geometric error parameters. The geometric mapping relationship refers to the influence of the tilt and offset errors of the A-axis swing cradle itself on the radial motion trajectory of the C-axis rotary table at different A-axis swing angles. This relationship is expressed as a trigonometric function mapping of the radial residual deviation with the A-axis swing angle. In one embodiment, for example, the turntable control device uses radial residual deviation data at multiple non-zero swing angles to establish an inversion solution model containing unknown parameters of the A-axis tilt and offset errors. This model is then solved using a numerical optimization algorithm, ultimately separating and calculating the independent A-axis geometric error parameters, as described in steps 4041 to 4044.

[0102] This invention calculates the radial and axial deviation components of spatial skew measuring points relative to the theoretical center of rotation to obtain composite deviation data containing attitude information. It precisely extracts the C-axis geometric error parameters by utilizing the projection relationship of A-axis error transmission and the variation law of axial deviation with the swing angle. Then, it removes the C-axis error component from the actual motion trajectory to obtain the radial residual deviation affected only by the A-axis error. Finally, it solves the problem by inversion based on the geometric mapping relationship between the radial residual deviation and the swing angle. This breaks the barrier of deep coupling between upstream and downstream errors in a series transmission link, achieving decoupling of parasitic motion error of the A-axis and intrinsic error of the C-axis from the mixed trajectory deviation. This yields high-precision A-axis and C-axis geometric error parameters, fundamentally eliminating the model distortion problem caused by error aliasing in the overall compensation method, and improving the spatial geometric positioning accuracy of the cradle-type five-axis turntable under complex multi-attitude linkage machining.

[0103] Optionally, the processes of steps 4041 to 4044 include:

[0104] Step 4041: Based on the radial residual deviation under each attitude and the axial coordinates of the spatially different measuring points in the local coordinate system of the C-axis, group each spatially different measuring point under the same A-axis locking angle according to the magnitude of the axial coordinates to obtain the axially layered measuring point group corresponding to the current A-axis attitude.

[0105] Optionally, the turntable control device acquires the radial residual deviation for each attitude, as well as the axial coordinates of the spatially dissimilar measuring points in the C-axis local coordinate system. The C-axis local coordinate system refers to the spatial reference system constructed in the preceding steps with the actual rotation center of the C-axis as its origin. The axial coordinates refer to the coordinate values ​​of the spatially dissimilar measuring points in the direction of the third coordinate axis of the spatial reference system.

[0106] For the same A-axis locking angle (i.e., the current A-axis attitude), the axial coordinates of all spatially dissimilar measurement points are extracted and sorted and grouped according to the magnitude of the axial coordinate values. Specifically, spatially dissimilar measurement points with the same axial coordinate values ​​or whose axial coordinate values ​​are within the same preset axial interval are grouped into the same set. Thus, each spatially dissimilar measurement point under the same A-axis locking angle is grouped according to the magnitude of its axial coordinates, resulting in an axially layered measurement point group corresponding to the current A-axis attitude.

[0107] For example, at a 30-degree attitude, a closed spatial polygonal loop contains six spatially skewed measurement points with axial coordinates of -100 mm, -50 mm, -25 mm, 25 mm, 50 mm, and 100 mm in the spatial reference frame. Based on the magnitude of their axial coordinates, these six spatially skewed measurement points are divided into six independent sets, each set corresponding to a specific axial level. This results in six axially layered measurement point groups corresponding to the 30-degree attitude. Each axially layered measurement point group contains the three-dimensional coordinates of the measurement points at that level and their corresponding radial residual deviations.

[0108] Step 4042: Based on the first measuring point located at the highest axial position and the second measuring point located at the lowest axial position in the axial layered measuring point group, calculate the vector difference between the mean radial residual deviation of the first measuring point and the mean radial residual deviation of the second measuring point to obtain the extreme difference vector of radial deviation under the current A-axis attitude.

[0109] Optionally, the turntable control device identifies the set of measuring points with the largest axial coordinate values ​​as the first measuring point located at the highest axial position in the axial layered measuring point group, and identifies the set of measuring points with the smallest axial coordinate values ​​as the second measuring point located at the lowest axial position.

[0110] The turntable control device extracts the radial residual deviations of all measuring points in the first measuring point set, calculates the arithmetic mean of these radial residual deviations, and obtains the mean radial residual deviation of the first measuring point. Similarly, it extracts the radial residual deviations of all measuring points in the second measuring point set, calculates the arithmetic mean of these radial residual deviations, and obtains the mean radial residual deviation of the second measuring point.

[0111] The turntable control device subtracts the mean radial residual deviation of the second measuring point from the mean radial residual deviation of the first measuring point, calculates the vector difference between the two, and obtains the extreme difference vector of radial deviation under the current A-axis attitude.

[0112] For example, in a group of six axially layered measuring points at a 30-degree attitude, the first measuring point at the highest axial position is located at an axial coordinate of 100 mm, and the calculated average radial residual deviation of this measuring point is 0.04 mm; the second measuring point at the lowest axial position is located at an axial coordinate of -100 mm, and the calculated average radial residual deviation of this measuring point is 0.01 mm. Subtracting 0.01 from 0.04 yields a vector difference of 0.03 mm, which is the extreme difference vector of radial deviation at a 30-degree attitude.

[0113] Step 4043: Based on the radial deviation extreme difference vector and the axial distance between the first and second measuring points, construct a unit vector pointing in the direction of increasing radial deviation to obtain the A-axis tilt direction vector under the current A-axis attitude.

[0114] Optionally, the turntable control device calculates the axial distance between the first and second measuring points. The algorithm for calculating this axial distance is as follows: subtract the axial coordinate value of the lowest axial position from the axial coordinate value of the highest axial position. Divide the radial deviation extreme value difference vector by this axial distance to obtain the gradient value of the radial deviation as a function of axial position. The direction of radial deviation increase is determined based on the sign of the gradient value.

[0115] When the gradient value is positive, the direction of radial deviation increase is the spatial direction from the second measuring point to the first measuring point; when the gradient value is negative, the direction of radial deviation increase is the spatial direction from the first measuring point to the second measuring point. The turntable control device extracts the spatial vector of the radial deviation increase direction and normalizes the spatial vector. Normalization means dividing the spatial vector by its own magnitude so that the length of the processed vector is 1. This yields a unit vector pointing in the radial deviation increase direction, which is the A-axis tilt direction vector under the current A-axis attitude.

[0116] For example, if the axial coordinate of the first measuring point is 100 mm and the axial coordinate of the second measuring point is -100 mm, subtracting -100 mm from 100 mm yields an axial distance of 200 mm between the first and second measuring points. The radial deviation extreme difference vector is 0.03 mm. Dividing 0.03 mm by 200 mm gives a gradient value of 0.00015. Since the gradient value is positive, the turntable control device determines that the direction of radial deviation increase is from the second measuring point with an axial coordinate of -100 mm to the first measuring point with an axial coordinate of 100 mm, i.e., along the positive direction of the third coordinate axis of the spatial reference system. Extracting the spatial vector in this positive direction and normalizing it yields an A-axis tilt direction vector of length 1.

[0117] Step 4044: Determine the A-axis geometric error parameters based on the A-axis tilt direction vector under each A-axis attitude and the radial residual deviation of each spatially non-planar measuring point in the axial layered measuring point group.

[0118] Optionally, the turntable control device determines the geometric error parameters of the A-axis based on the A-axis tilt direction vector under each A-axis attitude and the radial residual deviation of each spatially different measuring point in the axial layered measuring point group, as in steps 40441 to 40444.

[0119] This invention constructs an axially layered measurement point group by grouping spatially skewed measurement points according to their axial coordinate magnitude. It accurately extracts the mean radial residual deviation of the highest and lowest axially positioned measurement points to calculate the radial deviation extreme difference vector. Then, it combines the axial distance to construct an A-axis tilt direction vector pointing in the direction of increasing radial deviation. Finally, based on the tilt direction vector and radial residual deviation under multiple orientations, it obtains the A-axis geometric error parameters. It utilizes the amplification effect of the axial height difference between spatially skewed measurement points on the A-axis tilt error, reducing the complexity of the three-dimensional spatial trajectory deviation to axial gradient features. This overcomes the deficiency of single-plane measurement points being unable to sensitively capture the A-axis tilt error, achieving high-precision decoupling of the A-axis tilt error and offset error. This fundamentally ensures the convergence speed and solution accuracy of the A-axis geometric error parameter inversion calculation, thereby improving the geometric positioning accuracy of the cradle-type five-axis turntable under multiple orientations.

[0120] Optionally, the processes of steps 40441 to 40444 include:

[0121] Step 40441: Based on the radial residual deviation of each spatially skewed measuring point in the axial layered measuring point group and the phase angle position of each measuring point on the C-axis rotation circumference, the actual geometric center coordinates of the C-axis rotation trajectory under the current A-axis attitude are fitted and generated to obtain the trajectory center point under the current A-axis attitude.

[0122] Optionally, the turntable control device acquires the radial residual deviation of each spatially skewed measuring point in the axially layered measuring point group, as well as the phase angle position of each measuring point on the C-axis rotation circumference. The phase angle position refers to the rotation angle of the spatially skewed measuring point relative to the preset starting point on the C-axis rotation circumference. The turntable control device adds the radial residual deviation of each spatially skewed measuring point to the preset C-axis rotation radius to obtain the actual rotation radius of each spatially skewed measuring point. Using the actual rotation radius and phase angle position, the turntable control device calculates the actual geometric center coordinates of the C-axis rotation trajectory under the current A-axis attitude using a least squares circle fitting algorithm. The calculation process of the least squares circle fitting algorithm is as follows: construct an objective function with the abscissa and ordinate of the actual geometric center coordinates as unknowns. This objective function is the sum of squares of the difference between the actual rotation radius of all spatially skewed measuring points and the distance from the measuring point to the actual geometric center coordinates. By taking the derivative and setting the derivative to zero, the abscissa and ordinate that minimize this sum of squares are calculated. Combined with the known axial coordinates, the three-dimensional actual geometric center coordinates are obtained. The actual geometric center coordinates are the trajectory center point under the current A-axis attitude.

[0123] For example, in a 30-degree attitude, the axial layered measurement point group contains 600 spatially skewed measurement points corresponding to discrete spatial coordinates, with their phase angle positions uniformly distributed from 0 degrees to 360 degrees. The actual rotation radius is obtained by adding the radial residual deviation of each measurement point to a preset C-axis rotation radius of 200 mm. The least squares circle fitting algorithm is used to calculate the x and y coordinates that minimize the sum of squares. Combined with the axial coordinates, the actual geometric center coordinates of the C-axis rotation trajectory in a 30-degree attitude are fitted and generated as (0.02, 250.03, 433.01). These coordinates are taken as the trajectory center point in a 30-degree attitude.

[0124] Step 40442: Based on the coordinates of the trajectory center point and the theoretical rotation center of the C-axis in the series motion chain, calculate the spatial displacement vector between the two points to obtain the A-axis offset projection vector under the current A-axis attitude.

[0125] Optionally, the turntable control device acquires the trajectory center point and the theoretical rotation center coordinates of the C-axis in the series motion chain. The theoretical rotation center coordinates of the C-axis are the three-dimensional coordinates of the actual rotation center (i.e., the theoretical rotation center) of the C-axis under the current locked angle of the A-axis determined in the aforementioned steps.

[0126] The turntable control device calculates the spatial displacement vector between the trajectory center point and the theoretical rotation center coordinates of the C-axis. The algorithm for calculating the spatial displacement vector is as follows: subtract the three coordinate components corresponding to the theoretical rotation center coordinates of the C-axis from the three coordinate components of the trajectory center point, obtaining three coordinate differences. The three-dimensional vector formed by these three coordinate differences is the spatial displacement vector. This spatial displacement vector reflects the degree and direction of the deviation of the C-axis rotation trajectory center from its theoretical position due to A-axis geometric errors. This spatial displacement vector is determined as the A-axis offset projection vector under the current A-axis attitude.

[0127] For example, the trajectory center point at a 30-degree attitude is (0.02, 250.03, 433.01), and the theoretical rotation center coordinates of the C-axis are (0, 250, 433). Subtracting the x-coordinate (0) of the theoretical rotation center coordinates of the C-axis from the x-coordinate (0.02) of the trajectory center point gives a difference of 0.02; subtracting 250 from the y-coordinate (250.03) gives a difference of 0.03; and subtracting 433 from the axial coordinate (433.01) gives a difference of 0.01. The three-dimensional vector (0.02, 0.03, 0.01) is the A-axis offset projection vector at a 30-degree attitude.

[0128] Step 40443: Based on the A-axis tilt direction vector under different A-axis attitudes, construct a family of straight lines passing through the C-axis rotation center under each attitude in space. Select the two straight lines with the smallest spatial divergence in the family of straight lines as the boundary constraints of the actual A-axis rotation axis to obtain the spatial position of the actual A-axis rotation axis.

[0129] Optionally, the turntable control device acquires the A-axis tilt direction vector under different A-axis postures and the C-axis rotation center (i.e., the coordinates of the theoretical C-axis rotation center) under each posture.

[0130] The turntable control device uses the C-axis rotation center in various postures as the spatial starting point and the corresponding A-axis tilt direction vector as the direction vector, constructing multiple infinitely extending straight lines in three-dimensional space. These lines together form a family of straight lines. Spatial divergence refers to the degree of intersection or parallelism of the straight lines in the family of lines in space. The length of the common perpendicular and the spatial angle between any two straight lines in the family of lines are calculated. The two lines with the shortest common perpendicular length and the smallest spatial angle are selected; these two lines are the two lines with the smallest spatial divergence. The coordinates of the midpoint of the common perpendicular of these two lines are calculated, and the direction vectors of these two lines are arithmetically averaged to obtain the average direction vector. A straight line passing through the midpoint coordinates and oriented with the average direction vector is constructed; this straight line is the actual spatial position of the A-axis rotation axis.

[0131] For example, the turntable control device acquires the A-axis tilt direction vector and the corresponding theoretical rotation center coordinates of the C-axis at three orientations: 30 degrees, 60 degrees, and 90 degrees. This data is used to construct a family of three spatial straight lines. The lengths of the common perpendiculars between each pair of these three lines are calculated. It is found that the two lines corresponding to 30 degrees and 90 degrees have the shortest common perpendicular length (0.005 mm) and the smallest spatial angle. These two lines are selected, and the midpoint coordinates of their common perpendicular are calculated as (0.01, 0, 0). The arithmetic mean of the direction vectors of the two lines is then used to obtain the average direction vector along the first linear axis of the machine coordinate system. A straight line passing through (0.01, 0, 0) and along the first linear axis is constructed to obtain the actual spatial position of the A-axis rotation axis.

[0132] Step 40444: Based on the actual spatial position of the A-axis rotation axis and the A-axis offset projection vector under various attitudes, calculate the spatial perpendicular distance and spatial angle between the actual A-axis rotation axis and the theoretical C-axis rotation axis to obtain the A-axis geometric error parameters.

[0133] Optionally, the turntable control device acquires the actual spatial position of the A-axis rotation axis and the theoretical C-axis rotation axis. The theoretical C-axis rotation axis refers to a straight line passing through the theoretical rotation center point of the cradle-type five-axis turntable and whose direction is consistent with the direction of the normal vector of the C-axis rotation plane.

[0134] The turntable control device calculates the spatial perpendicular distance and spatial angle between the actual rotation axis of axis A and the theoretical rotation axis of axis C. The algorithm for calculating the spatial perpendicular distance is as follows: extract the direction vectors of the actual rotation axis of axis A and the theoretical rotation axis of axis C, perform a cross product to obtain the common perpendicular direction vector; arbitrarily select a point on each axis to construct a connecting vector, project this connecting vector onto the common perpendicular direction vector, and take the absolute value of the projected length as the spatial perpendicular distance. The algorithm for calculating the spatial angle is as follows: calculate the dot product of the two direction vectors, divide by the product of the magnitudes of the two direction vectors, and then calculate the inverse cosine value to obtain the spatial angle.

[0135] The turntable control device calculates the vertical distance and spatial angle in space, and then performs weighted correction by combining the A-axis offset projection vector under various postures, finally obtaining the A-axis geometric error parameters that include A-axis tilt error and A-axis offset error.

[0136] For example, the actual rotation axis of the A-axis passes through (0.01, 0, 0) and is along the direction of the first linear axis, while the theoretical rotation axis of the C-axis passes through (0, 0, 0) and is along the direction of the third linear axis. Extracting the direction vectors of both axes and performing cross product and projection calculations yields a spatial vertical distance of 0.01 mm; calculating the spatial angle using dot product and inverse cosine yields 0.002 degrees. Combining the 0.01 mm and 0.002 degrees with the A-axis offset projection vectors at 30 degrees, 60 degrees, and 90 degrees for weighted correction, the precise geometric error parameters of the A-axis are finally obtained.

[0137] This invention quantifies the trajectory offset caused by A-axis error by generating a trajectory center point based on radial residual deviation and phase angle position fitting. It calculates the spatial displacement vector between the trajectory center point and the theoretical rotation center to extract the A-axis offset projection vector. Then, it constructs a family of straight lines using the A-axis tilt direction vector under multiple orientations and selects the line with the smallest divergence to accurately reconstruct the spatial position of the actual A-axis rotation axis. Finally, it calculates the spatial perpendicular distance and angle between the actual rotation axis and the theoretical rotation axis and corrects it using the offset projection vector. Therefore, at the geometric analytical level, it achieves dimensionality reduction reconstruction from discrete trajectory deviations to continuous axis spatial pose, accurately quantifies the spatial tilt and offset of the actual A-axis rotation axis relative to the ideal state, eliminates random noise interference and model singularity in the multi-orientation data fusion process, and obtains high-precision A-axis geometric error parameters. This provides support for the complete decoupling of the serial transmission link error of the cradle-type five-axis turntable and the multi-orientation geometric positioning accuracy, thereby improving the geometric positioning accuracy of the cradle-type five-axis turntable under multiple orientations.

[0138] Furthermore, the geometric error decoupling device for a cradle-type five-axis turntable provided by the present invention will be described below. The geometric error decoupling device for a cradle-type five-axis turntable described below can be referred to in correspondence with the geometric error decoupling method for a cradle-type five-axis turntable described above.

[0139] Optionally, refer to Figure 2 , Figure 2 This is a schematic diagram of the geometric error decoupling device for a cradle-type five-axis turntable provided by the present invention. The geometric error decoupling device for a cradle-type five-axis turntable includes:

[0140] The transmission link construction module 210 is used to construct a unidirectional transmission link flow topology structure from the A-axis drive end to the C-axis load end based on the orthogonal geometric relationship between the A-axis rotation center line and the C-axis rotation center line of the cradle-type five-axis turntable, as well as the physical connection hierarchy between the A-axis and the C-axis, so as to obtain a serial kinematic chain that characterizes the error transmission path.

[0141] The measuring point positioning module 220 is used to plan spatially skewed measuring points distributed on the circumference of the C-axis rotation and spatially skewed relative to the C-axis rotation center, based on the normal vector direction of the C-axis rotation plane in the series motion chain and the spatial position change law of the C-axis rotation center under different swing angles of the A-axis.

[0142] The motion trajectory analysis module 230 is used to control the A-axis to lock at multiple non-zero swing angles based on the spatial non-plane measuring points, and to control the C-axis to complete a full rotation at each non-zero swing angle, so as to obtain the motion trajectory of the spatial non-plane measuring points under multiple attitudes.

[0143] The geometric error decoupling module 240 is used to calculate the tilt error and offset error of the A-axis itself based on the motion trajectory inversion of the spatial non-planar measurement points under each attitude, and to obtain the geometric error parameters of the A-axis and the geometric error parameters of the C-axis.

[0144] The embodiments of the present invention solve the problem that the existing methods are limited in compensation accuracy due to the inability to decouple coupling errors in the series transmission link by using the differential response of spatial non-planar measuring points and the logical constraint of the transmission link flow direction, thereby improving the geometric positioning accuracy of the cradle-type five-axis turntable under multiple postures.

[0145] Please see Figure 3 , Figure 3 An embodiment diagram of an electronic device provided in accordance with the present invention. For example... Figure 3 As shown, an embodiment of the present invention provides an electronic device 300, including a memory 310, a processor 320, and a computer program 311 stored in the memory 310 and executable on the processor 320. When the processor 320 executes the computer program 311, it implements the processes of steps 10 to 40.

[0146] Please see Figure 4 , Figure 4 An embodiment diagram of a computer-readable storage medium provided in accordance with an embodiment of the present invention is shown. Figure 4As shown, this embodiment provides a computer-readable storage medium 400 on which a computer program 311 is stored. When the computer program 311 is executed by a processor, it implements the processes of steps 10 to 40.

[0147] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer is able to execute the geometric error decoupling method for a cradle-type five-axis turntable provided by the above methods, which includes steps 10 to 40.

[0148] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0149] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0150] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. These modifications or substitutions do not cause the essence of the corresponding technical solutions to depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A geometric error decoupling method for a cradle-type five-axis rotary table, characterized in that, include: Based on the orthogonal geometric relationship between the rotation center lines of the A-axis and C-axis of the cradle-type five-axis turntable, and the physical connection hierarchy between the A-axis and C-axis, a unidirectional transmission link flow topology structure from the drive end of the A-axis to the load end of the C-axis is constructed to obtain a serial kinematic chain characterizing the error transmission path. Based on the normal vector direction of the C-axis rotation plane in the series kinematic chain, and the spatial position change law of the C-axis rotation center under different swing angles of the A-axis, spatially skewed measuring points are planned to be distributed on the C-axis rotation circumference and spatially skewed relative to the C-axis rotation center. Based on the spatial non-plane measuring points, the A-axis is locked at multiple non-zero swing angles, and the C-axis is controlled to complete a full rotation at each non-zero swing angle, so as to obtain the motion trajectory of the spatial non-plane measuring points under multiple attitudes. Based on the motion trajectory inversion calculation of the spatial non-planar measurement points under each attitude, the tilt error and offset error of the A-axis itself are calculated, and the geometric error parameters of the A-axis and C-axis are obtained.

2. The geometric error decoupling method for a cradle-type five-axis rotary table according to claim 1, characterized in that, The motion trajectory inversion calculation based on spatial non-planar measurement points under each attitude calculates the tilt error and offset error of the A-axis itself, obtaining the geometric error parameters of the A-axis and the C-axis, including: Based on the motion trajectory of the spatial skew measurement points under each attitude and the theoretical position of the C-axis rotation center under each non-zero swing angle, the radial deviation component and axial deviation component of each spatial skew measurement point relative to its corresponding theoretical rotation center are calculated to obtain the C-axis composite deviation data containing A-axis attitude information. Based on the projection relationship of the A-axis error to the C-axis in the series kinematic chain, and the variation law of the axial deviation component in the C-axis composite deviation data with the swing angle of the A-axis, the projection error component caused by the geometric error of the A-axis is separated, and the geometric error parameters of the C-axis after removing the A-axis transmission error are obtained. The radial residual deviation is obtained by separating the C-axis geometric error component from the motion trajectory of the spatial non-planar measurement points under each attitude; Based on the geometric mapping relationship between the radial residual deviation and the A-axis swing angle, the tilt error and offset error of the A-axis itself are calculated to obtain the geometric error parameters of the A-axis.

3. The geometric error decoupling method for a cradle-type five-axis rotary table according to claim 2, characterized in that, The tilt error and offset error of the A-axis itself are calculated by inverting the geometric mapping relationship between the radial residual deviation and the A-axis swing angle to obtain the geometric error parameters of the A-axis, including: Based on the radial residual deviation under each attitude and the axial coordinates of the spatial non-planar measurement points in the local coordinate system of the C-axis, each spatial non-planar measurement point under the same A-axis locking angle is grouped according to the magnitude of the axial coordinates to obtain the axial layered measurement point group corresponding to the current A-axis attitude. Based on the first measuring point located at the highest axial position and the second measuring point located at the lowest axial position in the axial layered measuring point group, the vector difference between the mean radial residual deviation of the first measuring point and the mean radial residual deviation of the second measuring point is calculated to obtain the extreme difference vector of radial deviation under the current A-axis attitude. Based on the radial deviation extreme difference vector and the axial distance between the first and second measuring points, a unit vector pointing in the direction of increasing radial deviation is constructed to obtain the A-axis tilt direction vector under the current A-axis attitude; The geometric error parameters of the A-axis are determined based on the A-axis tilt direction vector under each A-axis attitude and the radial residual deviation of each spatially non-planar measuring point in the axial layered measuring point group.

4. The geometric error decoupling method for a cradle-type five-axis rotary table according to claim 3, characterized in that, The A-axis geometric error parameters are determined based on the A-axis tilt direction vector under each A-axis attitude and the radial residual deviation of each spatially non-planar measuring point in the axial layered measuring point group, including: Based on the radial residual deviation of each spatial non-plane measuring point in the axial layered measuring point group, and the phase angle position of each measuring point on the C-axis rotation circumference, the actual geometric center coordinates of the C-axis rotation trajectory under the current A-axis attitude are fitted and generated to obtain the trajectory center point under the current A-axis attitude. Based on the coordinates of the trajectory center point and the theoretical rotation center of the C-axis in the series motion chain, the spatial displacement vector between the two points is calculated to obtain the A-axis offset projection vector under the current A-axis attitude. Based on the A-axis tilt direction vector under different A-axis attitudes, a family of straight lines passing through the C-axis rotation center under each attitude is constructed in space. The two straight lines with the smallest spatial divergence in the family of straight lines are selected as the boundary constraints of the actual A-axis rotation axis, and the spatial position of the actual A-axis rotation axis is obtained. Based on the actual spatial position of the A-axis rotation axis and the A-axis offset projection vector under various postures, the spatial perpendicular distance and spatial angle between the actual A-axis rotation axis and the theoretical C-axis rotation axis are calculated to obtain the geometric error parameters of the A-axis.

5. The geometric error decoupling method for a cradle-type five-axis rotary table according to claim 1, characterized in that, The planned spatially skewed measurement points, distributed along the circumference of the C-axis and spatially skewed relative to the center of rotation of the C-axis, include: Based on the direction of the normal vector of the C-axis rotation plane in the series kinematic chain, the theoretical rotation axis of the C-axis is determined, and based on the spatial position change law of the C-axis rotation center under different swing angles of the A-axis, the actual rotation center of the C-axis under the current locked angle of the A-axis is determined. A spatial reference system is constructed based on the theoretical rotation axis of the C-axis and the actual rotation center of the C-axis. Based on the extension direction of the theoretical rotation axis of the C-axis in the spatial reference system, and the spatial coordinates of the actual rotation center of the C-axis under the current locking angle of the A-axis, an auxiliary axis is generated that passes through the actual rotation center of the C-axis and is parallel to the theoretical rotation axis of the C-axis, thus obtaining a spatial positioning auxiliary line; Based on the spatial distance between the spatial positioning auxiliary line and the theoretical rotation axis of the C-axis, and the preset rotation radius of the C-axis, the spatial non-planar measuring points are determined.

6. The geometric error decoupling method for a cradle-type five-axis rotary table according to claim 5, characterized in that, The determination of the spatially skewed measurement points based on the spatial positioning auxiliary line and the theoretical C-axis rotation axis, and the preset C-axis rotation radius, includes: Based on the spatial distance and the preset C-axis rotation radius, a reference circular trajectory is generated on a plane perpendicular to the theoretical C-axis rotation axis to obtain the initial circular path; Based on any starting point on the initial circular path and the tilt angle of the C-axis rotation plane relative to the horizontal plane under the current locking angle of the A-axis, a preset axial step is offset along the theoretical rotation axis of the C-axis to generate an offset circular trajectory, thus obtaining a set of layered circular paths. Based on the circumference of each layer of the circular path set, each layer of the circular path is divided into multiple arc segments, and the endpoint of each arc segment is determined as the potential measurement point location. Based on the line vector connecting the potential measurement point position of each potential measurement point to the spatial positioning auxiliary line, and the direction vector of the C-axis theoretical rotation axis, the spatial non-plane measurement points are determined.

7. The geometric error decoupling method for a cradle-type five-axis rotary table according to claim 6, characterized in that, The determination of the spatially skewed measurement points based on the line vector connecting the potential measurement point position of each potential measurement point to the spatial positioning auxiliary line, and the direction vector of the C-axis theoretical rotation axis, includes: Based on the line vector connecting the potential measuring point position of each potential measuring point to the spatial positioning auxiliary line, and the direction vector of the C-axis theoretical rotation axis, potential measuring points whose angle between the line vector and the direction vector is not zero and not 90 degrees are selected and determined as initial measuring points; Based on the phase difference between two adjacent potential measuring points in the initial measuring points on the C-axis rotation circle, and the spatial projection deformation caused by the A-axis swing, potential measuring points located on different layers of circular trajectories are alternately selected to construct a spatial distribution sequence that spirals upward or downward, thus obtaining candidate measuring points. Based on the spatial connectivity of the first and last measuring points in the candidate measuring points and the motion continuity of the C-axis rotation, the candidate measuring points are closed to form a closed spatial polygonal loop, thus obtaining the spatial non-planar measuring points.

8. A geometric error decoupling device for a cradle-type five-axis rotary table, characterized in that, Used to implement the geometric error decoupling method for a cradle-type five-axis rotary table as described in any one of claims 1 to 7; The geometric error decoupling device for the cradle-type five-axis rotary table includes: The transmission link construction module is used to construct a unidirectional transmission link flow topology structure from the A-axis drive end to the C-axis load end based on the orthogonal geometric relationship between the A-axis rotation center line and the C-axis rotation center line of the cradle-type five-axis turntable, as well as the physical connection hierarchy between the A-axis and the C-axis, and obtain a serial kinematic chain that characterizes the error transmission path. The measuring point positioning module is used to plan spatially skewed measuring points distributed on the C-axis rotation circumference and spatially skewed relative to the C-axis rotation center, based on the normal vector direction of the C-axis rotation plane in the series motion chain and the spatial position change law of the C-axis rotation center under different swing angles of the A-axis. The motion trajectory analysis module is used to control the A-axis to lock at multiple non-zero swing angles based on the spatial non-plane measuring points, and to control the C-axis to complete a full rotation at each non-zero swing angle, so as to obtain the motion trajectory of the spatial non-plane measuring points under multiple postures. The geometric error decoupling module is used to calculate the tilt and offset errors of the A-axis itself based on the motion trajectory inversion of the spatial non-planar measurement points under each attitude, and to obtain the geometric error parameters of the A-axis and the C-axis.

9. An electronic device, comprising: Memory, used to store computer software programs; A processor for reading and executing computer software programs, characterized in that, when the processor executes the computer software programs, it implements the geometric error decoupling method for a cradle-type five-axis rotary table as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium, wherein a computer software program is stored therein, characterized in that, When the computer software program is executed by the processor, it implements the geometric error decoupling method for a cradle-type five-axis turntable as described in any one of claims 1 to 7.

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