Analysis method and correction method and correction system for relative spatial pointing error of vertical five-axis rotary table

Abstract

The present application belongs to the technical field of precision servo equipment, and provides a vertical five-axis rotary table relative space pointing error analysis method, correction method and correction system. The outer two frames and the inner three frames of the five-axis rotary table are controlled to move at the same speed and acceleration from the same initial position to the same target position, and the relative pointing error of the outer two frames and the inner three frames is measured multiple times. The outer two frames of the five-axis rotary table are modeled based on the multi-body theory. The potential error terms are analyzed based on the mechanical relationship and motion characteristics of the outer two frames of the five-axis rotary table. The characteristic matrix is derived and obtained, and the space pointing model is further derived. The mathematical model of the angle difference between the actual pointing and the ideal pointing in the X direction and the Y direction is derived. According to the measurement value of the autocollimator, the unknown parameters of the mathematical model of the angle difference between the actual pointing and the ideal pointing in the X direction and the Y direction are identified to obtain the error model. The present application is used to correct the relative space pointing error of the five-axis rotary table.

Description

Technical Field

[0001] This invention belongs to the field of precision servo equipment technology, specifically relating to an analysis method, correction method, and correction system for the relative spatial pointing error of a vertical five-axis rotary table. Background Technology

[0002] The five-axis turntable is a core component of an optical guidance hardware-in-the-loop simulation system. Its main function is to simulate the motion of guided weapons and targets, thereby simulating the relative spatial relationship between them. With the continuous development of precision guidance technology, primarily optical guidance, the five-axis turntable has been widely used in simulation. However, in actual simulation applications, due to installation errors, mechanical errors, and control errors, the position and attitude of the guided weapon mounted on it, as well as the relative position of the target, differ from the ideal state, thus reducing the accuracy of the simulation system and the reliability of the experimental results.

[0003] A five-axis rotary table is composed of a two-axis rotary table and a three-axis rotary table, with the two-axis rotary table forming the outer two frames and the three-axis rotary table forming the inner three frames. The outer two frames and the inner three frames are independent of each other, and their respective spatial orientations can be formed through axis movement. Theoretically, when the same command is applied to the outer two frames and the inner three frames, their spatial orientations should be exactly the same. However, in actual equipment, due to various errors, there will be errors in the relative spatial orientation between them. Therefore, it is necessary to find a suitable method to model the relative spatial orientation of the five-axis rotary table and derive a mathematical expression for the orientation error based on this model, thereby correcting the relative spatial orientation error of the five-axis rotary table. Summary of the Invention

[0004] This invention provides a method for analyzing the relative spatial pointing error of a vertical five-axis turntable. The relative spatial pointing of the vertical five-axis turntable is measured by an optical instrument autocollimator, and the relative spatial pointing of the vertical five-axis turntable is modeled based on many-body theory to obtain an approximate mathematical model. Then, the error parameters in the model are identified to obtain an error model, which serves as the basis for subsequent corrections.

[0005] The present invention also provides a method for correcting the relative spatial pointing error of a vertical five-axis turntable, in order to correct the relative spatial pointing error of the five-axis turntable.

[0006] The present invention also provides a system for correcting the relative spatial pointing error of a vertical five-axis turntable, in order to realize a method for correcting the relative spatial pointing error of a five-axis turntable.

[0007] This invention is achieved through the following technical solution: A method for analyzing the relative spatial pointing error of a vertical five-axis turntable. The method involves measuring the relative spatial pointing of the outer two frames of the vertical five-axis turntable relative to the inner three frames using an optical instrument autocollimator, modeling the relative spatial pointing of the vertical five-axis turntable based on many-body theory to obtain an approximate mathematical model, and then identifying the error parameters in the model to obtain an error model.

[0008] Furthermore, the analytical method specifically includes the following steps: Step 1: Control the outer two frames and inner three frames of the five-axis turntable to move from the same initial position to the same target position with the same speed and acceleration, and measure the relative pointing error of the outer two frames and inner three frames multiple times; Step 2: Based on the measurement results of Step 1, model the two outer frames of the five-axis turntable based on multibody theory; Step 3: Based on the mechanical relationship and motion characteristics of the two outer frames of the five-axis rotary table, analyze the potential error terms; Step 4: Based on the error term in Step 3, derive and obtain the feature matrix, and further derive the spatial pointing model; Step 5: Derive the spatial pointing model from Step 4 X towards and Y A mathematical model of the difference between the actual pointing angle and the ideal pointing angle; Step 6: Based on the measurements from the autocollimator, identify the unknown parameters of the mathematical model for the difference between the actual and ideal pointing angles in the X and Y directions from Step 5 to obtain the error model.

[0009] Furthermore, step 1 specifically involves real-time acquisition of measurement data from a collimator during the five-axis turntable movement to obtain the spatial relative pointing error at each position of the turntable during its movement, which are respectively... X The angle difference between the actual pointing and the ideal pointing and Y The angle difference between the actual pointing direction and the ideal pointing direction is denoted as . and .

[0010] Furthermore, step 2 specifically involves, according to low-order volume theory, the ideal spatial orientation of the two outer frames can be expressed as follows: (1) Under the influence of error, the actual spatial orientation of the two outer frames can be represented as follows: (2) In the formula, This indicates that the initial space points to a vector, i.e. ; This indicates the ideal spatial orientation of the outer two frames under error-free conditions, which is the actual spatial orientation of the inner three frames. This indicates the actual spatial orientation of the two outer frames under the influence of error; This represents the relative position transformation matrix of the yaw axes of the outer two frames relative to the base; This represents the relative position error transformation matrix of the yaw axes of the outer two frames relative to the base; This represents the relative motion transformation matrix of the outer two frames' yaw axes relative to the base; This represents the transformation matrix of the relative motion error between the yaw axes of the outer two frames and the base. This represents the relative position transformation matrix of the pitch axis of the outer two frames with respect to the yaw axis of the outer two frames; This represents the relative position error transformation matrix of the pitch axis of the two outer frames with respect to the yaw axis of the two outer frames; This represents the relative motion transformation matrix between the pitch axes of the two outer frames and the yaw axes of the two outer frames. This represents the relative motion error transformation matrix between the pitch axes of the two outer frames and the yaw axes of the two outer frames; Based on this, the relative spatial pointing error is defined. for: (3) In subsequent analyses of the compensation effect, this indicator will be the primary evaluation criterion.

[0011] Furthermore, step 3 specifically involves analysis showing that the mechanical error portion of the spatial orientation error of the two outer frames of the five-axis turntable is caused by perpendicularity, intersection, rotation tilt angle error, rotation position error, and angular position error.

[0012] Furthermore, step 4 specifically includes the following: ,

[0013] , , , , , , in, Indicates the yaw axis rotation angle of the outer two frames; b This indicates the rotation angle of the pitch axis of the two outer frames.

[0014] Based on arbitrary error terms If all are small quantities, then , Meanwhile, ignoring the principle of simplifying higher-order minima, the above equation (2) is simplified; the final simplified result is as follows. (4) in, (5) Further simplification, making (6) Substituting equation (6) into equation (5), we obtain the simplified result as follows: (7) This is a vector representation of the actual spatial orientation of the two outer frames of a vertical five-axis turntable under the influence of error.

[0015] Furthermore, step 5 specifically involves determining the relationship between the rotation sequence and the rotation. (8) (9) Substituting the simplified result of equation (7) into equations (8) and (9), we obtain... X towards and Y Mathematical model of the difference in angle between actual and ideal pointing. (10).

[0016] Furthermore, step 6 specifically involves expressing equation (10) in its basic form as follows: (11) Several points should be noted regarding equation (11): This is an estimated value. It is a parameter matrix. , The format is as follows, where n Indicates the amount of data used for identification. ,

[0017] The parameters to be identified This is the error term.

[0018] Therefore, the difference between the measured value and the estimated value of the autocollimator is (12) in, For the actual autocollimator X , Y Two-way measurement values.

[0019] Based on the idea of ​​least squares, the sum of squared residuals is used as the criterion for evaluating the estimation effect, that is... (13) make ,get The estimated value As shown in equation (14) below (14).

[0020] A method for correcting the relative spatial pointing error of a vertical five-axis rotary table, wherein the correction method uses an error model obtained by the analysis method described above to correct the relative spatial pointing error of the vertical five-axis rotary table. The correction method specifically involves calculating the parameters to be identified using the above formula (14). ~ Substituting the actual estimated value into equation (7) above, we obtain the analytical expression for the actual spatial pointing vector of the outer two frames under the influence of error. To ensure that the actual spatial pointing can still approximate the ideal spatial pointing to the greatest extent under the influence of error, the following relationship can be defined: (15) In equation (15), It can be achieved by initially giving the yaw angle With pitch angle It can be obtained directly, and The specific mathematical expression is shown in equation (7) above, which contains two unknown terms. and By solving the nonlinear equation system using numerical methods, we obtain... and The calculated values ​​are the corrected yaw and pitch angles of the outer two frames.

[0021] A system for correcting the relative spatial pointing error of a vertical five-axis rotary table, the system employing the correction method described above, and comprising: The measurement module is used to control the outer two frames and inner three frames of the five-axis turntable to move continuously from the same initial position to the same target position at the same speed and acceleration, and to measure the relative pointing error of the outer two frames and inner three frames multiple times. The analysis module is used to model the outer two frames of the five-axis rotary table based on the measurement results from the measurement module and multibody theory. Based on the mechanical relationship and motion characteristics of the two outer frames of the five-axis rotary table, potential error terms are analyzed; Based on the error term, the feature matrix is ​​derived and obtained, and the spatial pointing model is further derived. Derived from the spatial pointing model X towards and Y A mathematical model of the difference between the actual pointing angle and the ideal pointing angle; The error model is obtained by identifying unknown parameters of the difference between the actual and ideal pointing angles in the X and Y directions based on the measurements of the autocollimator. The correction module is used to correct the relative spatial pointing error of the vertical five-axis rotary table based on the error model obtained from the analysis module.

[0022] The beneficial effects of this invention are: This invention analyzes and models the error terms of a vertical five-axis turntable, clarifies the impact of each error term on spatial pointing error, and further guides the design of the turntable.

[0023] This invention further identifies the error model based on the measurement results of spatial pointing error. The identification results can clarify the types and specific values ​​of the error terms currently existing in the turntable, which helps to improve the structural design of the turntable.

[0024] For turntable equipment, due to limitations in manufacturing processes and environmental factors, its precision is finite, and some mechanical errors are inevitable. These errors are difficult to reduce by further improving the manufacturing process or increasing manufacturing precision. Therefore, using algorithms to correct these errors is a more reasonable and efficient method. This invention establishes an error model to accurately describe the errors, and the proposed compensation algorithm can effectively correct these mechanical errors, thereby overcoming the limitations of manufacturing processes and improving the pointing accuracy of the turntable equipment. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the low-order volume array model of the outer two frames of the vertical five-axis turntable of the present invention.

[0026] Figure 2 This is a comparison diagram of the relative spatial pointing error before and after the error correction of the present invention.

[0027] Figure 3 This is a flowchart of the method of the present invention. Detailed Implementation

[0028] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0029] It should be understood that, when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0030] It should also be understood that the terminology used in this application specification is for the purpose of describing particular embodiments only and is not intended to limit the application. As used in this application specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0031] The following is in conjunction with the appendix to this application specification. Figure 1-2 The technical solutions in the embodiments of this application are clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0032] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0033] Example 1 This implementation example Figure 1 As shown, the world system is defined. X The axial direction is the initial spatial orientation of the outer two frames. Y The axis direction is the direction of the pitch axis of the outer two frames. Z The axis direction is the direction of the yaw axis of the outer two frames. According to the mechanical structure, since the yaw axis of the outer two frames of the vertical five-axis turntable is fixed to the base, the rotation sequence of the outer two frames of the vertical five-axis turntable is defined as first rotating around the yaw axis, then rotating around the pitch axis. The base is defined as... The yaw axis of the body and the outer two frames is The pitch axis of the body and the two outer frames is Establish a low-order volume array.

[0034] This embodiment provides a method for analyzing the relative spatial pointing error of a vertical five-axis turntable. The method involves measuring the relative spatial pointing of the outer two frames of the vertical five-axis turntable relative to the inner three frames using an optical instrument autocollimator, modeling the relative spatial pointing of the vertical five-axis turntable based on many-body theory to obtain an approximate mathematical model, and then identifying the error parameters in the model to obtain an error model.

[0035] Furthermore, the analytical method specifically includes the following steps: Step 1: Control the outer two frames and inner three frames of the five-axis turntable to move from the same initial position to the same target position with the same speed and acceleration, and measure the relative pointing error of the outer two frames and inner three frames multiple times; Step 2: Based on the measurement results of Step 1, model the two outer frames of the five-axis turntable based on multibody theory; Step 3: Based on the mechanical relationship and motion characteristics of the two outer frames of the five-axis rotary table, analyze the potential error terms; Step 4: Based on the error term in Step 3, derive and obtain the feature matrix, and further derive the spatial pointing model; Step 5: Derive the spatial pointing model from Step 4 X towards and Y A mathematical model of the difference between the actual pointing angle and the ideal pointing angle; Step 6: Based on the measurements from the autocollimator, identify the unknown parameters of the mathematical model for the difference between the actual and ideal pointing angles in the X and Y directions from Step 5 to obtain the error model.

[0036] Furthermore, step 1 specifically involves the outer two frames and inner three frames of the five-axis turntable moving continuously from the same initial position to the same target position with the same speed and acceleration. During the turntable's movement, measurement data from the collimator is collected in real time to obtain the spatial relative pointing error at each position of the turntable's movement, which is respectively... X The angle difference between the actual pointing and the ideal pointing and Y The angle difference between the actual pointing direction and the ideal pointing direction is denoted as . and .

[0037] Furthermore, step 2 specifically involves, as follows: Figure 1 As shown, according to low-order volume theory, the ideal spatial orientation of the two outer frames can be represented as follows: (1) Under the influence of error, the actual spatial orientation of the two outer frames can be represented as follows: (2) In the formula, This indicates that the initial space points to a vector, i.e. ; This indicates the ideal spatial orientation of the outer two frames under error-free conditions, which is the actual spatial orientation of the inner three frames. This indicates the actual spatial orientation of the two outer frames under the influence of error; This represents the relative position transformation matrix of the yaw axes of the outer two frames relative to the base; This represents the relative position error transformation matrix of the yaw axes of the outer two frames relative to the base; This represents the relative motion transformation matrix of the outer two frames' yaw axes relative to the base; This represents the transformation matrix of the relative motion error between the yaw axes of the outer two frames and the base. This represents the relative position transformation matrix of the pitch axis of the outer two frames with respect to the yaw axis of the outer two frames; This represents the relative position error transformation matrix of the pitch axis of the two outer frames with respect to the yaw axis of the two outer frames; This represents the relative motion transformation matrix between the pitch axes of the two outer frames and the yaw axes of the two outer frames. This represents the relative motion error transformation matrix between the pitch axes of the two outer frames and the yaw axes of the two outer frames; Based on this, the relative spatial pointing error is defined. for: (3) In subsequent analyses of the compensation effect, this indicator will be the primary evaluation criterion.

[0038] Furthermore, step 3 specifically involves analysis showing that the mechanical error portion of the spatial pointing error of the two outer frames of the five-axis turntable is mainly caused by perpendicularity, intersection, rotation angle error, rotation position error, angular position error, and mechanical deformation. The first five error terms have clear physical meanings and effects, and their corresponding coefficients are shown in Table 1. However, since the source of mechanical deformation is uncertain and it has a certain degree of randomness, it cannot be precisely modeled. Nevertheless, its effect is the same as the aforementioned five error terms, producing a translational or rotational effect on the actual pointing. Therefore, the error caused by mechanical deformation can be unified within the error terms declared in Table 1, assuming that the effect of the shaft system after passing through these five error terms already includes the effect of mechanical deformation.

[0039] Table 1. Error Items for the Outer Frames of the Five-Axis Rotary Table

[0040] Furthermore, step 4 specifically includes the following: ,

[0041] , , , , , , in, Indicates the yaw axis rotation angle of the outer two frames; b Indicates the pitch axis rotation angle of the outer two frames; This represents the relative position transformation matrix of the yaw axes of the outer two frames relative to the base; This represents the relative position error transformation matrix of the yaw axes of the outer two frames relative to the base; This represents the relative motion transformation matrix of the outer two frames' yaw axes relative to the base; This represents the transformation matrix of the relative motion error between the yaw axes of the outer two frames and the base. This represents the relative position transformation matrix of the pitch axis of the outer two frames with respect to the yaw axis of the outer two frames; This represents the relative position error transformation matrix of the pitch axis of the two outer frames with respect to the yaw axis of the two outer frames; This represents the relative motion transformation matrix between the pitch axes of the two outer frames and the yaw axes of the two outer frames. This represents the relative motion error transformation matrix between the pitch axis and the yaw axis of the outer two frames.

[0042] Based on arbitrary error terms If all are small quantities, then , Meanwhile, ignoring the principle of simplifying higher-order minima, the above equation (2) is simplified; the final simplified result is as follows. (4) in, (5) Further simplification, making (6) Substituting equation (6) into equation (5), we obtain the simplified result as follows: (7) This is a vector representation of the actual spatial orientation of the two outer frames of a vertical five-axis turntable under the influence of error.

[0043] Furthermore, step 5 specifically involves determining the relationship between the rotation sequence and the rotation. (8) (9) Substituting the simplified result of equation (7) into equations (8) and (9), we obtain... X towards and Y Mathematical model of the difference in angle between actual and ideal pointing. (10).

[0044] Furthermore, step 6 specifically involves expressing equation (10) in its basic form as follows: (11) Several points should be noted regarding equation (11): This is an estimated value. It is a parameter matrix. , The format is as follows, where n Indicates the amount of data used for identification. ,

[0045] The parameters to be identified This is the error term.

[0046] Therefore, the difference between the measured value and the estimated value of the autocollimator is (12) in, For the actual autocollimator X , Y Two-way measurement values.

[0047] Based on the idea of ​​least squares, the sum of squared residuals is used as the criterion for evaluating the estimation effect, that is... (13) make ,get The estimated value As shown in equation (14) below (14).

[0048] Example 2 Based on Embodiment 1, this embodiment also provides a method for correcting the relative spatial pointing error of a vertical five-axis turntable. The correction method uses the error model obtained by the analysis method of relative spatial pointing error of a vertical five-axis turntable as described in claim 8 to correct the relative spatial pointing error of the vertical five-axis turntable. The correction method specifically involves calculating the parameters to be identified using the above formula (14). ~ The actual estimated value is substituted into the above equation (7) to obtain the analytical expression of the actual spatial pointing vector of the outer two frames under the action of error; further, according to equations (1) and (2), for any yaw angle given to the outer two frames of the vertical five-axis turntable With pitch angle Each of these can correspond to an ideal space pointing vector. With respect to the actual space pointing vector Assume there exists another set of yaw angles. With pitch angle Its corresponding actual spatial pointing vector is To ensure that, under the influence of errors, the actual spatial pointing can still approximate the ideal spatial pointing as closely as possible, the following relationship can be defined: (15) In equation (15), It can be achieved by initially giving the yaw angle With pitch angle It can be obtained directly, while The specific mathematical expression is shown in equation (7) above, which contains two unknown terms. and By solving the nonlinear equation system using numerical methods, we can obtain... and The calculated values ​​are the corrected yaw and pitch angles of the outer two frames.

[0049] In the simulation environment, the error term parameters are set as shown in Table 2 below. Table 2. Parameter settings for error terms of the outer two frames of the five-axis rotary table.

[0050] Using the inner three frames as a reference, the error parameters of the outer two frames are identified. The yaw axis and pitch axis of the outer two frames are simultaneously simulated 3000 times from the initial position of -70° with a step size of 0.04°. The spatial pointing vector corresponding to a single motion is obtained according to equation (2), and the outer two frames are obtained by numerical calculation. X, Y The angle difference between the actual and ideal pointing directions is used as the measurement data of the autocollimator, and a certain amount of Gaussian white noise is artificially introduced as measurement noise. Substituting the relevant data into equation (14), the identification results are shown in Table 3 below. Table 3 Parameter Identification Results

[0051] As can be seen from Table 3, the parameter identification effect is very good.

[0052] Rotate the yaw and pitch axes from -80° to 80° in 1° increments and simulate continuously to obtain a total of 25,921 sets of yaw and pitch angle inputs for the outer two frames. Based on the parameters obtained through identification and the error correction method described above, solve for the corrected yaw and pitch angles of the outer two frames. After obtaining the corrected yaw and pitch angles of the outer two frames, solve for the corrected relative spatial pointing error based on equation (3), compare it with the original relative spatial pointing error, and plot the curve as shown below. Figure 2 As shown in the figure, the upper yellow surface represents the pointing error for each set of outer frame yaw and pitch angle inputs before correction, while the lower blue surface represents the pointing error for the same set of outer frame yaw and pitch angle inputs after correction. The figure shows that after correction, the spatial pointing error at all angles is significantly reduced compared to before correction, demonstrating a significant correction effect.

[0053] Example 3 This embodiment, based on Embodiment 2, further provides a system for correcting the relative spatial pointing error of a vertical five-axis rotary table. The correction system uses the method described above for correcting the relative spatial pointing error of a vertical five-axis rotary table. The correction system includes a measurement module, an analysis module, and a correction module. The measurement module is used to control the outer two frames and inner three frames of the five-axis turntable to move continuously from the same initial position to the same target position at the same speed and acceleration, and to measure the relative pointing error of the outer two frames and inner three frames multiple times. The analysis module is used to model the outer two frames of the five-axis rotary table based on the measurement results of the measurement module and the multibody theory. Based on the mechanical relationship and motion characteristics of the two outer frames of the five-axis rotary table, potential error terms are analyzed; Based on the error term, the feature matrix is ​​derived and obtained, and the spatial pointing model is further derived. Derived from the spatial pointing model X towards and Y A mathematical model of the difference between the actual pointing angle and the ideal pointing angle; The error model is obtained by identifying unknown parameters of the difference between the actual and ideal pointing angles in the X and Y directions based on the measurements of the autocollimator. The correction module is used to correct the relative spatial pointing error of the vertical five-axis rotary table based on the error model obtained by the analysis module.

[0054] The analysis module measures the relative spatial orientation of the vertical five-axis turntable using an optical instrument autocollimator, models the relative spatial orientation of the vertical five-axis turntable based on many-body theory and obtains an approximate mathematical model, and then identifies the error parameters in the model to obtain an error model.

[0055] Furthermore, the measurement module is used to control the outer two frames and inner three frames of the five-axis turntable to move continuously from the same initial position to the same target position at the same speed and acceleration, and to measure the relative pointing error of the outer two frames and inner three frames multiple times. Specifically, the outer two frames and inner three frames of the five-axis turntable move continuously from the same initial position to the same target position at the same speed and acceleration. During the turntable movement, measurement data from the collimator is collected in real time to obtain the spatial relative pointing error at each position of the turntable movement, which are respectively... X The angle difference between the actual pointing and the ideal pointing and Y The angle difference between the actual pointing direction and the ideal pointing direction is denoted as . and .

[0056] Furthermore, the analysis module, based on the measurement results from the measurement module, models the outer two frames of the five-axis rotary table using multibody theory, specifically as follows: Figure 1As shown, according to low-order volume theory, the ideal spatial orientation of the two outer frames can be represented as follows: (1) Under the influence of error, the actual spatial orientation of the two outer frames can be represented as follows: (2) In the formula, This indicates that the initial space points to a vector, i.e. ; This indicates the ideal spatial orientation of the outer two frames under error-free conditions, which is the actual spatial orientation of the inner three frames. This indicates the actual spatial orientation of the two outer frames under the influence of error; This represents the relative position transformation matrix of the yaw axes of the outer two frames relative to the base; This represents the relative position error transformation matrix of the yaw axes of the outer two frames relative to the base; This represents the relative motion transformation matrix of the outer two frames' yaw axes relative to the base; This represents the transformation matrix of the relative motion error between the yaw axes of the outer two frames and the base. This represents the relative position transformation matrix of the pitch axis of the outer two frames with respect to the yaw axis of the outer two frames; This represents the relative position error transformation matrix of the pitch axis of the two outer frames with respect to the yaw axis of the two outer frames; This represents the relative motion transformation matrix between the pitch axes of the two outer frames and the yaw axes of the two outer frames. This represents the relative motion error transformation matrix between the pitch axes of the two outer frames and the yaw axes of the two outer frames; Based on this, the relative spatial pointing error is defined as: (3) In subsequent analyses of the compensation effect, this indicator will be the primary evaluation criterion.

[0057] Furthermore, the analysis module, based on the mechanical relationship and motion characteristics of the two outer frames of the five-axis turntable, analyzes potential error terms. Specifically, the mechanical error portion of the spatial pointing error of the two outer frames of the five-axis turntable is mainly caused by perpendicularity, intersection, rotation angle error, rotation position error, angular position error, and mechanical deformation. Among these, the first five error terms have clear physical meanings and effects, and their corresponding error term coefficients are shown in Table 1 below. However, since the source of mechanical deformation cannot be determined and it has a certain degree of randomness, it cannot be accurately modeled. But its effect is the same as the above five error terms; it will produce a translational or rotational effect on the actual pointing. Therefore, the error caused by mechanical deformation can be unified in the error terms declared in Table 1, assuming that the effect of the shaft system after passing through these five error terms already includes the effect of mechanical deformation.

[0058] Table 1. Error Items for the Outer Frames of the Five-Axis Rotary Table

[0059] Furthermore, the analysis module, based on the error term, derives and obtains the feature matrix, and further derives the spatial pointing model as follows: ,

[0060] , , , , , , in, Indicates the yaw axis rotation angle of the outer two frames; b Indicates the pitch axis rotation angle of the outer two frames; This represents the relative position transformation matrix of the yaw axes of the outer two frames relative to the base; This represents the relative position error transformation matrix of the yaw axes of the outer two frames relative to the base; This represents the relative motion transformation matrix of the outer two frames' yaw axes relative to the base; This represents the transformation matrix of the relative motion error between the yaw axes of the outer two frames and the base. This represents the relative position transformation matrix of the pitch axis of the outer two frames with respect to the yaw axis of the outer two frames; This represents the relative position error transformation matrix of the pitch axis of the two outer frames with respect to the yaw axis of the two outer frames; This represents the relative motion transformation matrix between the pitch axes of the two outer frames and the yaw axes of the two outer frames. This represents the relative motion error transformation matrix between the pitch axis and the yaw axis of the outer two frames.

[0061] Based on arbitrary error terms If all are small quantities, then , Meanwhile, ignoring the principle of simplifying higher-order minima, the above equation (2) is simplified; the final simplified result is as follows. (4) in, (5) Further simplification, making (6) Substituting equation (6) into equation (5), we obtain the simplified result as follows: (7) This is a vector representation of the actual spatial orientation of the two outer frames of a vertical five-axis turntable under the influence of error.

[0062] Furthermore, the analysis module derives based on the spatial pointing model. X towards and Y The mathematical model for the difference in angle between the actual pointing direction and the ideal pointing direction is specifically derived from the relationship between the rotation sequence and the rotation. (8) (9) Substituting the simplified result of equation (7) into equations (8) and (9), we obtain... X towards and Y Mathematical model of the difference in angle between actual and ideal pointing. (10).

[0063] Furthermore, the analysis module identifies the unknown parameters of the mathematical model of the difference between the actual and ideal pointing angles in the X and Y directions based on the measurements from the autocollimator, and obtains the error model specifically as follows: Equation (10) is expressed in its basic form as follows. (11) Several points should be noted regarding equation (11): This is an estimated value. It is a parameter matrix. , The format is as follows, where n Indicates the amount of data used for identification. ,

[0064] The parameters to be identified This is the error term.

[0065] Therefore, the difference between the measured value and the estimated value of the autocollimator is (12) in, For the actual autocollimator X , Y Two-way measurement values.

[0066] Based on the idea of ​​least squares, the sum of squared residuals is used as the criterion for evaluating the estimation effect, that is... (13) make ,get The estimated value As shown in equation (14) below (14).

[0067] The correction module is used to correct the relative spatial pointing error of the vertical five-axis turntable based on the error model obtained by the analysis module. Specifically, it calculates the parameters to be identified using the above formula (14). ~ The actual estimated value is substituted into the above equation (7) to obtain the analytical expression of the actual spatial pointing vector of the outer two frames under the action of error; further, according to equations (1) and (2), for any yaw angle given to the outer two frames of the vertical five-axis turntable With pitch angle Each of these can correspond to an ideal space pointing vector. With respect to the actual space pointing vector Assume there exists another set of yaw angles. With pitch angle Its corresponding actual spatial pointing vector is To ensure that, under the influence of errors, the actual spatial pointing can still approximate the ideal spatial pointing as closely as possible, the following relationship can be defined: (15) In equation (15), It can be achieved by initially giving the yaw angle With pitch angle It can be obtained directly, while The specific mathematical expression is shown in equation (7) above, which contains two unknown terms. and By solving the nonlinear equation system using numerical methods, we can obtain... and The calculated values ​​are the corrected yaw and pitch angles of the outer two frames.

Claims

1. A method for analyzing the relative spatial pointing error of a vertical five-axis rotary table, characterized in that, The analysis method involves measuring the relative spatial orientation of the outer two frames of the vertical five-axis turntable relative to the inner three frames using an optical instrument autocollimator, modeling the relative spatial orientation of the vertical five-axis turntable based on multibody theory to obtain an approximate mathematical model, and then identifying the error parameters in the model to obtain an error model. The obtained error model is specifically expressed as a linear parameter estimation model, which represents the mathematical model of the difference between the actual and ideal pointing angles in the X and Y directions. The estimated value vector is composed of the parameter matrix multiplied by the parameter vector to be identified and the error vector superimposed. The measured value vector is determined based on the measurements from the autocollimator, and the residual between the measured value vector and the estimated value vector is calculated. Based on the least squares method, an objective function is constructed with the goal of minimizing the sum of squared residuals. By solving the equation of the objective function with a partial derivative of zero with respect to the parameter vector to be identified, the estimated value of the parameter vector to be identified can be obtained.

2. The analytical method according to claim 1, characterized in that, The analytical method specifically includes the following steps: Step 1: Control the outer two frames and inner three frames of the five-axis turntable to move from the same initial position to the same target position with the same speed and acceleration, and measure the relative pointing error of the outer two frames and inner three frames multiple times; Step 2: Based on the measurement results of Step 1, model the two outer frames of the five-axis turntable based on multibody theory; Step 3: Based on the mechanical relationship and motion characteristics of the two outer frames of the five-axis rotary table, analyze the potential error terms; Step 4: Based on the error term in Step 3, derive and obtain the feature matrix, and further derive the spatial pointing model; Step 5: Derive the spatial pointing model from Step 4 X towards and Y A mathematical model of the difference between the actual pointing angle and the ideal pointing angle; formula Step 6: Adjust the values ​​from Step 5 based on the autocollimator measurements. X towards and Y An error model is obtained by identifying unknown parameters in a mathematical model of the difference between the actual and ideal pointing angles.

3. The analytical method according to claim 2, characterized in that, Step 1 specifically involves acquiring measurement data from a collimator in real time during the five-axis turntable's movement to obtain the spatial relative pointing error at each position of the turntable during its movement. X The angle difference between the actual pointing and the ideal pointing and Y The angle difference between the actual pointing direction and the ideal pointing direction is denoted as . and .

4. The analytical method according to claim 2, characterized in that, Step 2 specifically involves, according to low-order volume theory, the ideal spatial orientation of the two outer frames can be represented as follows: (1) Under the influence of error, the actual spatial orientation of the two outer frames can be represented as follows: (2) In the formula, This indicates that the initial space points to a vector, i.e. ; This indicates the ideal spatial orientation of the outer two frames under error-free conditions, which is the actual spatial orientation of the inner three frames. This indicates the actual spatial orientation of the two outer frames under the influence of error; This represents the relative position transformation matrix of the yaw axes of the outer two frames relative to the base; This represents the relative position error transformation matrix of the yaw axes of the outer two frames relative to the base; This represents the relative motion transformation matrix of the outer two frames' yaw axes relative to the base; This represents the transformation matrix of the relative motion error between the yaw axes of the outer two frames and the base. This represents the relative position transformation matrix of the pitch axis of the outer two frames with respect to the yaw axis of the outer two frames; This represents the relative position error transformation matrix of the pitch axis of the two outer frames with respect to the yaw axis of the two outer frames; This represents the relative motion transformation matrix between the pitch axes of the two outer frames and the yaw axes of the two outer frames. This represents the relative motion error transformation matrix between the pitch axes of the two outer frames and the yaw axes of the two outer frames; Based on this, the relative spatial pointing error is defined. for: (3) In subsequent analyses of the compensation effect, this indicator will be the primary evaluation criterion.

5. The analytical method according to claim 4, characterized in that, Step 3 specifically involves analyzing the mechanical error portion of the spatial orientation error of the two outer frames of the five-axis turntable, which is caused by perpendicularity, intersection, rotation tilt angle error, rotation position error, and angular position error.

6. The analytical method according to claim 5, characterized in that, Step 4 is specifically as follows: ， ， ， ， ， ， ， in, Indicates the yaw axis rotation angle of the outer two frames; b Indicates the pitch axis rotation angle of the outer two frames. Indicates the error term. This represents the component of the error in the X direction. This represents the component of the error in the Y direction. This represents the component of the error in the Z direction; Based on arbitrary error terms If all are small quantities, then , Meanwhile, ignoring the principle of simplifying higher-order minima, the above equation (2) is simplified; the final simplified result is as follows. (4) in, (5) Further simplification, making (6) Substituting equation (6) into equation (5), we obtain the simplified result as follows: (7) This is a vector representation of the actual spatial orientation of the two outer frames of a vertical five-axis turntable under the influence of error.

7. The analytical method according to claim 6, characterized in that, Step 5 specifically involves understanding the relationship between the sequence of rotations and the rotation. (8) (9) in, This represents the angular difference between the actual and ideal direction of the X-axis. This represents the angular difference between the actual and ideal pointing direction of the Y axis; Substituting the simplified result of equation (7) into equations (8) and (9), we obtain... X towards and Y Mathematical model of the difference in angle between actual and ideal pointing. (10)。 8. The analytical method according to claim 7, characterized in that, Specifically, step 6 involves expressing equation (10) in its basic form as follows: (11) Several points should be noted regarding equation (11): This is an estimated value. For the parameter matrix, , The format is as follows, where n Indicates the amount of data used for identification. ， The parameters to be identified For the error term, Therefore, the difference between the measured value and the estimated value of the autocollimator is (12) in, For the actual autocollimator X , Y Two-way measurement values, Based on the idea of ​​least squares, the sum of squared residuals is used as the criterion for evaluating the estimation effect, that is... (13) make ,get The estimated value As shown in equation (14) below (14)。 9. A method for correcting the relative spatial pointing error of a vertical five-axis rotary table, characterized in that, The correction method uses the error model obtained by the analysis method as described in claim 8 to correct the relative spatial pointing error of the vertical five-axis turntable; The correction method specifically involves calculating the parameters to be identified using the above formula (14). ~ Substituting the actual estimated value into equation (7) above, we obtain the analytical expression for the actual spatial pointing vector of the outer two frames under the influence of error. To ensure that the actual spatial pointing can still approximate the ideal spatial pointing to the greatest extent under the influence of error, the following relationship can be defined: (15) In equation (15), It can be achieved by initially giving the yaw angle With pitch angle It can be obtained directly, while The specific mathematical expression is shown in equation (7) above, which contains two unknown terms. and ; By solving the nonlinear equation system using numerical methods, we obtain... and The calculated values ​​are the corrected yaw and pitch angles of the outer two frames.

10. A system for correcting the relative spatial pointing error of a vertical five-axis rotary table, characterized in that, The correction system uses the correction method as described in claim 9, the correction system comprising, The measurement module is used to measure the relative pointing error between the outer two frames and the inner three frames when the outer two frames and the inner three frames of the five-axis turntable move synchronously. The analysis module is used to model the outer two frames of the five-axis rotary table based on the measurement results from the measurement module and multibody theory. Based on the mechanical relationship and motion characteristics of the two outer frames of the five-axis rotary table, potential error terms are analyzed; Based on the error term, the feature matrix is ​​derived and obtained, and the spatial pointing model is further derived. Derived from the spatial pointing model X towards and Y A mathematical model of the difference between the actual pointing angle and the ideal pointing angle; Based on the measurements of the autocollimator X towards and Y An error model is obtained by identifying unknown parameters in a mathematical model of the difference between the actual and ideal pointing angles. The correction module is used to correct the relative spatial pointing error of the vertical five-axis rotary table based on the error model obtained from the analysis module.

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