A Method and System for Separating Eccentricity Errors in Turntable Angle Measurement Systems Based on Single Reader Signals

Abstract

This invention discloses a method and system for separating eccentricity errors in a turntable angle measurement system based on a single reading head signal. The method includes uniformly rotating the turntable and acquiring the actual moiré signal output from a single reading head, calculating the phase function of the actual moiré signal; establishing an ideal moiré signal based on the turntable rotation speed, and calculating the phase function of the ideal moiré signal; obtaining the phase error function of the moiré signal based on the two phase functions; acquiring the amplitude of each order of phase error components in the frequency domain; establishing a phase error model caused by turntable eccentricity; and completing eccentricity error separation based on the amplitude of the first-order phase error harmonic and the phase error model. The system includes an actual moiré signal phase function acquisition unit, an ideal moiré signal phase function acquisition unit, a moiré signal phase error function acquisition unit, an amplitude acquisition unit, a phase error model establishment unit, and an eccentricity error separation unit. This invention enables more convenient and rapid monitoring and separation of eccentricity errors in a turntable angle measurement system.

Description

Technical Field

[0001] This invention relates to the field of angle measurement, and specifically to a method and system for separating eccentricity errors in a turntable angle measurement system based on a single reading head signal. Background Technology

[0002] Turntable angle measurement systems are widely used in aerospace, articulated coordinate measuring machines, robotics, and other fields due to their high accuracy and resolution. With technological advancements, the accuracy requirements for turntable angle measurement systems are increasingly demanding in various applications. However, the accuracy of turntable angle measurement systems is significantly affected by installation errors, with eccentricity error being a major contributing factor. Designing a method for separating turntable eccentricity error is of great significance for monitoring the real-time status of the turntable and improving its angle measurement accuracy.

[0003] Currently, scholars both domestically and internationally typically employ two methods to separate the eccentricity of a turntable angle measurement system: one method utilizes the circumferential closure characteristic, based on external reference standards such as polyhedrons and autocollimators, to obtain discrete calibration data using a cross-calibration method, and then performs fitting analysis on the error array to separate the turntable eccentricity error. For example, the paper "The Influence of Circular Grating Eccentricity on the Angular Position Accuracy of Simulated Turntables" (doi:10.3969 / j.issn.1672-9870.2014.03.003) analyzes the relationship between the angle measurement error caused by installation eccentricity and the rotation angle, calibrates the discrete angle measurement error using polyhedrons and autocollimators, and separates the turntable eccentricity error using the least squares fitting method.

[0004] Another method is to monitor and separate the turntable eccentricity error through external sensors. For example, the paper "A New Self-calibration Method for Circular Grating Eccentricity Parameters" (doi:10.3969 / j.issn.0254-3087.2016.11.007.) established a dual-reading-head eccentricity error model, derived the self-calibration formula for the circular grating eccentricity parameter, and used two reading heads mounted diametrically to calibrate the eccentricity parameter of the circular grating, thus separating the turntable eccentricity error.

[0005] The two methods for separating turntable eccentricity errors mentioned above have high requirements for the experimental environment and equipment, and both require additional calibration instruments or sensors to achieve the separation of eccentricity errors. The steps are cumbersome and have significant limitations. Summary of the Invention

[0006] In order to solve the problems existing in the technical background, the present invention aims to provide a method and system for separating eccentricity error of a turntable angle measurement system based on a single reading head signal, which solves the limitations of traditional eccentricity separation methods that are cumbersome and require external equipment.

[0007] One aspect of the present invention provides a method for separating eccentricity errors in a turntable angle measurement system based on a single reading head signal, the method comprising the following steps:

[0008] The turntable is rotated at a constant speed and the actual moiré signal output by a single reading head is collected. The phase function of the actual moiré signal is then calculated.

[0009] An ideal moiré signal is established based on the turntable rotation speed, and the phase function of the ideal moiré signal is calculated.

[0010] Based on the two phase functions mentioned above, the phase error function of the single-readhead moiré signal is obtained;

[0011] The phase error function is analyzed to obtain the amplitude of each phase error component in the frequency domain;

[0012] Establish a phase error model caused by turntable eccentricity;

[0013] The eccentricity error separation is completed based on the amplitude of the first-order phase error harmonic and the phase error model.

[0014] Another aspect of the present invention provides an eccentricity error separation system for a turntable angle measurement system based on a single reading head signal, comprising:

[0015] The actual moiré signal phase function acquisition unit is used to rotate the turntable at a constant speed and acquire the actual moiré signal output by a single reading head, and calculate the phase function of the actual moiré signal;

[0016] An ideal moiré signal phase function acquisition unit is used to establish an ideal moiré signal based on the turntable rotation speed and calculate the phase function of the ideal moiré signal.

[0017] The moiré signal phase error function acquisition unit is used to obtain the single reading head moiré signal phase error function based on the above two phase functions;

[0018] An amplitude acquisition unit is used to analyze the phase error function and obtain the amplitude of each order of phase error components in the frequency domain.

[0019] The phase error model establishment unit is used to establish a phase error model caused by turntable eccentricity.

[0020] The eccentricity error separation unit is used to complete the eccentricity error separation based on the amplitude of the first-order phase error harmonic and the phase error model.

[0021] The beneficial effects of this invention are as follows: This invention uses the turntable's own single reading head signal for eccentricity error separation. Compared with traditional methods based on external reference instruments such as polyhedrons and autocollimators, or using multiple sensors and multiple reading heads for turntable angle measurement system eccentricity error separation, this invention can more conveniently and quickly monitor and separate the eccentricity error of the turntable angle measurement system. It provides a method for monitoring and separating turntable eccentricity error, enabling faster and more convenient separation of turntable eccentricity errors. Attached Figure Description

[0022] Figure 1 This is a schematic diagram showing the operation of the turntable when it is eccentric.

[0023] Figure 2 This is a schematic diagram of the displacement error caused by the grating's eccentricity;

[0024] Figure 3 This is a schematic diagram of grating transmission under eccentric conditions;

[0025] Figure 4 This is a schematic diagram of the phase deviation of the moiré signal;

[0026] Figure 5 This is a flowchart of the eccentricity error separation process for the turntable angle measurement system;

[0027] Figure 6 This is a structural diagram of the eccentricity error separation system of the turntable angle measurement system. Detailed Implementation

[0028] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings:

[0029] Figure 1 This is a schematic diagram of the turntable operating with eccentricity. The turntable rotates at a speed ω. Due to its eccentricity, the rotation center R of the grating disk and the geometric center O do not coincide. The length of RO is the turntable eccentricity e. This error causes the moiré signal u(θ) output by the turntable angle measurement system to be inconsistent with the ideal moiré signal u0(θ) at this speed. u(θ) contains a phase error function.

[0030] Figure 2 This is a schematic diagram of grating displacement error. The eccentricity of the turntable causes a displacement error L when the grating rotates. e (θ). Establish the x-axis with the direction from the grating disk rotation center R to the reading head as the positive direction. Let P be the intersection of the outer edge of the grating disk's engraving and the positive x-axis, where OP is the radius of the circular grating, and RP is the change in RP with the position of the rotary table's circumferential angle θ, which is L. e (θ). Assuming OD⊥RP, under actual operating conditions RO and RD are at the micrometer level, therefore:

[0031]

[0032] Displacement error L e The expression for (θ) is shown in formula (2):

[0033] L e (θ)=RP-OP≈RD=|RO|cosθ=e·cosθ (2)

[0034] Figure 3 This is a schematic diagram of grating transmission under eccentric conditions. Eccentricity of the turntable causes a displacement error L in the grating disk during rotation. e This displacement error will cause the moiré signal u(θ) output by the turntable angle measurement system to contain a phase error caused by eccentricity.

[0035] The transmission grating system, consisting of an indicator grating and a scale grating, generates varying light intensity as the turntable rotates. This light intensity is then converted into a moiré signal u(θ) by a photoelectric sensor in the grating reading head.

[0036] Establish as Figure 3 The xy-axis coordinate system shown indicates the grating transmission function L1(x) and the scale grating transmission function L2(xL). e (θ), y) represent (the indicator grating is stationary, and the scale grating is subject to displacement error L) respectively. e (θ) will have a corresponding offset:

[0037]

[0038] Where n and m are Fourier series, A n B m γ represents the Fourier coefficients, f1 and f2 are the spatial frequencies of the two gratings, and γ is the angle between the two gratings.

[0039] The relationship between the transmission function of the transmission grating system composed of two gratings and the circumferential angle θ of the turntable is as follows:

[0040]

[0041] The expression for the moiré fringes composed of the maximum period and its harmonics generated by the beat phenomenon is obtained by extracting the m = -n term from equation (4). The constant terms in the combined equation (4) are as follows:

[0042]

[0043] F x F y These are the components of the spatial frequency of the transmission function along the x-axis and y-axis, respectively.

[0044] Assume the parallel light intensity emitted by the reading head is I. rIf the conversion coefficient of the photoelectric sensor is K, then the moiré signal u(θ) output by the turntable is:

[0045]

[0046] According to formula (6), the displacement error L caused by eccentricity is e (θ) introduces a phase error function into the output Moiré signal u(θ).

[0047]

[0048] Since the two gratings are nearly parallel, γ approaches zero, and cosγ≈1.

[0049] Figure 4 This is a schematic diagram of the phase deviation of the moiré signal. Due to various factors affecting the rotation of the turntable, the actual moiré signal u(θ) introduces a phase error function compared to the ideal moiré signal u0(θ).

[0050]

[0051] in and This represents the phase function of the moiré signal and the ideal moiré signal output by a single reading head.

[0052] Through the Discrete Fourier analysis is performed to transform the time-domain information into frequency-domain information. The amplitude values ​​of each order in the frequency domain are A(i), where A(1) is the amplitude of the first-order phase error caused by eccentricity. The A(1) obtained from the discrete Fourier analysis is combined with formula (7), where when cosθ=1... Take the maximum value, at this point:

[0053] A(1)=(2πf2(ecosθ)cosγ) max =2πf2e (9)

[0054] Since f2 is a constant value determined by the number of grating circumference lines, the eccentricity error e of the turntable can be separated from it.

[0055]

[0056] Figure 5 This is a flowchart illustrating the eccentricity error separation process for a turntable angle measurement system based on a single reading head signal. The eccentricity error of the turntable is separated according to the principles described above.

[0057] a. Rotate the turntable at a constant speed ω and collect the Mohr signal u(θ) output by a single reading head of the turntable during the full circumference rotation. θ is the circumferential angle position of the turntable.

[0058] b. Obtain the ideal Mohr signal u0(θ) at rotational speed ω through simulation;

[0059] c. Calculate the phase functions of the ideal moiré signal u0(θ) and the acquired single-readhead moiré signal u(θ). and

[0060] d. To and By performing interpolation, the phase error function of the single-readhead moiré signal u(θ) is obtained.

[0061] e. Regarding the phase error function Perform discrete Fourier analysis to obtain the amplitude A(i) of each phase error component in the frequency domain, where i is the harmonic order;

[0062] f. Establish a phase error function model caused by turntable eccentricity. e is the turntable eccentricity, f2 is the spatial frequency of the grating, and γ is the angle between the indicator grating and the scale grating;

[0063] g. Extract the first-order phase error harmonic amplitude A(1) from step e, and complete the separation of turntable eccentricity error according to A(1)=2πf2(ecosθ)cosγ.

[0064] like Figure 6 As shown, the eccentricity error separation system of the turntable angle measurement system based on a single reading head signal includes an actual moiré signal phase function acquisition unit, which is used to rotate the turntable at a constant speed and acquire the actual moiré signal output by the single reading head, and calculate the phase function of the actual moiré signal.

[0065] The ideal moiré signal phase function acquisition unit is used to establish an ideal moiré signal based on the turntable rotation speed and calculate the phase function of the ideal moiré signal.

[0066] The moiré signal phase error function acquisition unit is used to obtain the single-readhead moiré signal phase error function based on the above two phase functions.

[0067] An amplitude acquisition unit is used to analyze the phase error function and obtain the amplitude of each order of phase error components in the frequency domain.

[0068] The phase error model establishment unit is used to establish a phase error model caused by turntable eccentricity.

[0069] The eccentricity error separation unit is used to complete the eccentricity error separation based on the amplitude of the first-order phase error harmonic and the phase error model.

[0070] It is worth noting that eccentricity error has a significant impact on angular measurement accuracy; therefore, monitoring and separation of turntable eccentricity measurement are essential components of a turntable testing system. Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0071] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0072] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for separating the eccentricity error of a turntable angle measuring system based on single readhead signals, characterized in that The method includes the following steps: The turntable is rotated at a constant speed and the actual moiré signal output by a single reading head is collected. The phase function of the actual moiré signal is then calculated. An ideal moiré signal is established based on the turntable rotation speed, and the phase function of the ideal moiré signal is calculated. Based on the two phase functions mentioned above, the phase error function of the single-readhead moiré signal is obtained; The phase error function is analyzed to obtain the amplitude of each phase error component in the frequency domain; Establish a phase error model caused by turntable eccentricity; Eccentricity error separation is achieved based on the amplitude of the first-order phase error harmonic and the phase error model. The phase error model is as follows: Where e is the turntable eccentricity error, f2 is the spatial frequency of the grating, γ is the angle between the indicator grating and the scale grating, and θ is the circumferential position of the turntable.

2. The single readhead signal based goniometer system eccentricity error separation method of claim 1, wherein: The actual Mohr signal is obtained by rotating the turntable one revolution.

3. The single readhead signal based goniometer system eccentricity error separation method of claim 1, wherein: The moiré signal phase error function is obtained by processing the difference between two phase functions.

4. The single readhead signal based goniometer system eccentricity error separation method of claim 1, wherein: The phase error function is analyzed specifically using Discrete Fourier Analysis.

5. The single readhead signal based goniometer system eccentricity error separation method of claim 1, wherein: Let the first order phase error harmonic amplitude be A(l), then 6. A turntable angle measuring system eccentricity error separation system based on single readhead signal, characterized in that, include: The actual moiré signal phase function acquisition unit is used to rotate the turntable at a constant speed and acquire the actual moiré signal output by a single reading head, and calculate the phase function of the actual moiré signal; An ideal moiré signal phase function acquisition unit is used to establish an ideal moiré signal based on the turntable rotation speed and calculate the phase function of the ideal moiré signal. The moiré signal phase error function acquisition unit is used to obtain the single reading head moiré signal phase error function based on the above two phase functions; An amplitude acquisition unit is used to analyze the phase error function and obtain the amplitude of each order of phase error components in the frequency domain. Phase error model unit, used to establish a phase error model caused by turntable eccentricity; An eccentricity error separation unit is used to complete eccentricity error separation based on the amplitude of the first-order phase error harmonic and the phase error model. The phase error model is as follows: Where e is the turntable eccentricity error, f2 is the spatial frequency of the grating, γ is the angle between the indicator grating and the scale grating, and θ is the circumferential position of the turntable.

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