A self-calibration method and system for positioning error of a rotary table angle measurement system

Abstract

The application discloses a positioning error self-calibration method and system of a rotary table angle measuring system. The method comprises the following steps: collecting a Moire signal output in a whole circumferential rotation process in real time by using a reading head of the rotary table angle measuring system; analyzing a phase error function of the Moire signal and obtaining amplitudes of each order component in a frequency domain; separating a rotary table eccentricity by using a relationship model of the first order amplitude and the rotary table eccentricity; establishing a positioning error model caused by the eccentricity; and realizing the rotary table positioning error self-calibration by using a positioning error compensation model. The system comprises a Moire signal collecting module, an amplitude obtaining module, an eccentricity obtaining module, a positioning error model establishing module and a rotary table positioning error self-calibration module. The positioning error compensation and calibration are realized by using the Moire signal of the rotary table angle measuring system, so that the positioning precision of the rotary table angle measuring system can be improved more quickly and conveniently.

Description

Technical Field

[0001] This invention relates to the field of angle measurement, and specifically to a method and system for self-calibrating positioning errors in a turntable angle measurement system. Background Technology

[0002] Turntable angle measurement systems are widely used in articulated coordinate measuring machines (CMMs), robotics, and other fields due to their high angle measurement accuracy and high resolution. With technological advancements, the requirements for angle measurement accuracy in various applications are increasingly demanding. The most significant source of positioning error in turntable angle measurement systems is eccentricity error, which accounts for approximately 80% of the total positioning error. Therefore, compensating for eccentricity error can effectively improve the positioning accuracy of turntable angle measurement systems. Currently, there are two main methods for calibrating turntable positioning errors: one is to use hardware compensation methods to calibrate the positioning error; the other is to use software methods to fit and calibrate the positioning error.

[0003] Hardware calibration methods for turntable positioning errors mainly involve monitoring and calibrating positioning errors using multiple readheads or specialized grating disks to improve turntable positioning accuracy. For example, the paper "The NIM continuous fullcircle angle standard" (https: / / doi.org / 10.1088 / 1361-6501 / aac6a6) uses an equal-division averaging algorithm, employing four readheads evenly distributed to achieve hardware compensation for positioning errors. The effectiveness of hardware compensation methods is limited only by the number and layout of readheads, and can achieve good compensation results; however, on the other hand, the increased number of readheads and specialized grating disks bring about high costs and high system complexity.

[0004] Software compensation methods utilize high-precision external calibration instruments to calibrate errors and then fit and calibrate the positioning errors using software methods. For example, the paper "Study on the compensation for mounting eccentric errors of circular grating angle sensors" (doi:10.4028 / www.scientific.net / AMR.301-303.1552) proposes a method to compensate for turntable positioning errors by using a nonlinear least squares method to obtain the eccentricity parameter. Although software calibration methods are highly flexible, they require external calibration instruments to obtain the error compensation function.

[0005] The two turntable positioning error compensation methods mentioned above have high equipment requirements and require additional calibration instruments to calibrate the turntable positioning error. They are limited by cumbersome procedures and high costs. Summary of the Invention

[0006] The technical problem to be solved by this invention is to break through the limitations of the prior art and propose a self-calibration method and system for positioning error of a turntable angle measurement system, which improves positioning accuracy through the turntable angle measurement system's own signals without relying on other calibration instruments and complex turntable hardware calibration systems.

[0007] One aspect of the present invention provides a self-calibration method for positioning error of a turntable angle measurement system, comprising the following steps:

[0008] Using the reading head of the turntable angle measuring system, the moiré signal output during the full circular rotation process is collected in real time;

[0009] Analyze the phase error function of the moiré signal and obtain the amplitude of each order component in the frequency domain;

[0010] The turntable eccentricity was separated using a model relating the first-order amplitude to the turntable eccentricity.

[0011] Establish a positioning error model caused by eccentricity;

[0012] A positioning error compensation model is used to achieve self-calibration of the turntable positioning error.

[0013] Another aspect of the present invention provides a self-calibration system for positioning error of a turntable angle measurement system, comprising:

[0014] The moiré signal acquisition module is used to acquire the moiré signal output during the entire circular rotation process in real time using the reading head of the turntable angle measurement system.

[0015] The amplitude acquisition module is used to analyze the phase error function of the moiré signal and obtain the amplitude of each order component in the frequency domain.

[0016] The eccentricity acquisition module is used to separate the turntable eccentricity using the relationship model between the first-order amplitude and the turntable eccentricity.

[0017] The positioning error model building module is used to build a positioning error model caused by eccentricity.

[0018] The turntable positioning error self-calibration module is used to achieve turntable positioning error self-calibration using a positioning error compensation model.

[0019] The beneficial effects of this invention are as follows: This invention proposes a more convenient and faster method and system for calibrating the error of a turntable positioning angle measurement system. Based on the moiré signal output by the turntable angle measurement system's own reading head, this invention establishes a positioning error compensation function, effectively improving the positioning accuracy of the turntable angle measurement system. Compared with traditional calibration methods, this method simplifies the positioning error calibration process and reduces costs. Attached Figure Description

[0020] Figure 1a This is a schematic diagram of the formation of the turntable moiré signal;

[0021] Figure 1b yes Figure 1a Top view;

[0022] Figure 2 This is a flowchart of the turntable error function separation process;

[0023] Figure 3 This is a schematic diagram illustrating the angle measurement error caused by the turntable's eccentricity.

[0024] Figure 4 This is a flowchart of the turntable eccentricity error compensation process;

[0025] Figure 5 This is a diagram of the self-calibration system for the positioning error of the turntable angle measurement system. Detailed Implementation

[0026] Figure 1a This is a schematic diagram of the formation of the moiré signal on the turntable. As shown in the diagram, the rotating axis of the turntable drives the grating disk to rotate. The relative position of the scale grating on the grating disk and the indicator grating in the turntable reading head changes, causing the fixed light intensity L emitted from the reading head to output a changing light intensity L'(θ) through the grating transmission system composed of the indicator grating and the transmission grating. The light intensity L'(θ) is received by the photoelectric sensor and converted into a changing moiré signal m(θ).

[0027] In this process, such as Figure 1b As shown in the top view, the eccentricity of the turntable causes the rotation center O and the turntable center R to not coincide, resulting in an additional relative motion Δx(θ) between the scale grating and the indicator grating.

[0028] Δx(θ)=RA-OA≈B'R=|RO|cosθ=e·cosθ(1)

[0029] Where A is the center of the reading head, O is the center of rotation, θ is the circumferential angle position of the turntable, AB and OA have the same length, and B'O is perpendicular to AB. The eccentricity OR is generally on the order of micrometers, so BR can be approximated as B'R.

[0030] Δx(θ) affects the transmission function T1(x-Δx(θ),y) of the scale grating. Therefore, the transmission functions of the indicator grating and the scale grating are respectively:

[0031]

[0032] Where a m and a n α represents the Fourier coefficients, m and n represent the Fourier series, f1 and f0 represent the spatial frequencies of the grating, and α represents the angle between the indicator grating and the scale grating.

[0033] The varying light intensity L'(θ) output by the grating transmission system composed of two gratings is:

[0034]

[0035] The general expression for the moiré fringes composed of the maximum period and its harmonics generated by the beat phenomenon is obtained by extracting m = -n. The constant terms in the combined formula (4) are as follows:

[0036]

[0037] f x f y These are the components of the spatial frequency of the grating sub-transmission system along the x-axis and y-axis, respectively.

[0038] In summary, the expression for the Mohr signal m(θ) output by the turntable is:

[0039]

[0040] Where k is the photoelectric conversion coefficient of the photoelectric sensor.

[0041] Figure 2 This is a schematic diagram illustrating the separation of the turntable phase error function. Figure 1a As can be seen from the principle, the attitude error of the turntable will cause a change in the relative position of the indicator grating and the scale grating, thereby changing the output moiré signal m(θ). Now it is necessary to reduce the phase error function φ in the moiré signal. E (θ) is stripped, and the operation steps are as follows:

[0042] An ideal Mohr signal m0(θ) is constructed based on the turntable rotation speed ω. The phase functions φ(θ) and φ0(θ) corresponding to the turntable output Mohr signal m(θ) and the ideal Mohr signal m0(θ) are calculated. The phase error function φ corresponding to m(θ) is obtained by subtracting the phase functions of the two Mohr signals. E (θ):

[0043] φ E (θ)=φ0(θ)-φ(θ) (7)

[0044] Phase error function φ of the moiré signal E (θ) Perform Fourier analysis to obtain the amplitude information F(i) of each order of phase error in the frequency domain, where F(1) represents the phase error caused by eccentricity. Separate the phase error function φ caused by eccentricity from formula (6). e (θ) is:

[0045] φ e (θ)=2πnf1(ecosθ)cosα,n=1(8)

[0046] The phase error function φ eBy combining (θ) and F(1), we can obtain the magnitude of the turntable eccentricity e:

[0047] F(1)=(φ e (θ)) max =2πf1e(9)

[0048] Since the included angle α of the grating is small, cosα can be approximated as 1.

[0049] Figure 3 This is a schematic diagram illustrating the positioning error caused by turntable eccentricity. Based on the previously calculated turntable eccentricity *e*, a model can be built to calculate the positioning error. In the diagram, R is the center of the grating disk, O is the rotation center, θ is the circumferential angle position of the turntable, θ' is the measured circumferential angle position of the reading head, and Δθ... P Let r be the grating radius and r be the positioning error of the turntable. Then, through the geometric model, we can know that:

[0050]

[0051]

[0052] Based on the model of turntable positioning error, this invention can calculate the eccentricity e using the signal output from the turntable's own reading head, and achieve self-calibration of the positioning error:

[0053]

[0054] Figure 4 This is a flowchart of a turntable positioning error self-calibration method. Based on the principle described above, the turntable positioning error is self-calibrated.

[0055] a. Use the turntable's own reading head to collect the Mohr signal m(θ) output during the full circular rotation process, where θ is the angular position of the turntable;

[0056] b. Analyze the phase error function E(θ) of the Mohr signal m(θ), and perform discrete Fourier analysis on the phase error function E(θ) to obtain the frequency amplitude F(i) corresponding to each order of the error function;

[0057] c. The turntable eccentricity e is separated using the relationship model between the first-order amplitude F(1) and the turntable eccentricity;

[0058] d. Establish a positioning error model caused by eccentricity: Δθ P =esinθ' / r, where θ' is the circumferential angle position of the turntable and r is the radius of the grating;

[0059] e. Achieving turntable positioning error self-calibration using a positioning error compensation model: θ=θ'-Δθ P .

[0060] like Figure 5As shown, a self-calibration system for positioning error of a turntable angle measuring system includes a moiré signal acquisition module, which is used to acquire the moiré signal output during the full circumferential rotation process in real time using the turntable angle measuring system's own reading head.

[0061] The amplitude acquisition module is used to analyze the phase error function of the moiré signal and obtain the amplitude of each order component in the frequency domain.

[0062] The eccentricity acquisition module is used to separate the turntable eccentricity using the relationship model between the first-order amplitude and the turntable eccentricity.

[0063] The positioning error model building module is used to build a positioning error model caused by eccentricity.

[0064] The turntable positioning error self-calibration module is used to achieve turntable positioning error self-calibration using a positioning error compensation model.

[0065] It is worth noting that positioning error compensation is a crucial step in improving the angular measurement accuracy of the turntable angle measurement 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.

[0066] 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.

[0067] 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 self-calibration method for positioning error of a turntable angle measurement system, characterized in that... The method includes the following steps: Using the reading head of the turntable angle measuring system, the moiré signal output during the full circular rotation process is collected in real time; Analyze the phase error function of the moiré signal and obtain the amplitude of each order component in the frequency domain; The turntable eccentricity was separated using a model relating the first-order amplitude to the turntable eccentricity. Establish a positioning error model caused by eccentricity; The positioning error of the turntable is self-calibrated using a positioning error compensation model. The phase error function is obtained by subtracting the moiré signal output from the turntable from the ideal moiré signal; The specific method for separating the turntable eccentricity using the relationship model between the first-order amplitude and turntable eccentricity is as follows: Where e is the turntable eccentricity, and F(1) is the first-order amplitude. f1 is the phase error function, and f1 is the spatial frequency of the scale grating; The positioning error model is as follows: ； Where r is the grating radius and θ' is the measured value of the circumferential angular position of the reading head.

2. The self-calibration method for positioning error of a turntable angle measurement system according to claim 1, characterized in that: Discrete Fourier analysis is performed on the phase error function to obtain the amplitude of each order component in the frequency domain.

3. The self-calibration method for positioning error of a turntable angle measurement system according to claim 1, characterized in that: The self-calibration is expressed as: Where θ is the calibrated turntable circumference angle.

4. A self-calibration system for positioning error of a turntable angle measurement system, used to implement the method according to any one of claims 1-3, characterized in that, include: The moiré signal acquisition module is used to acquire the moiré signal output during the entire circular rotation process in real time using the reading head of the turntable angle measurement system. The amplitude acquisition module is used to analyze the phase error function of the moiré signal and obtain the amplitude of each order component in the frequency domain. The eccentricity acquisition module is used to separate the turntable eccentricity using the relationship model between the first-order amplitude and the turntable eccentricity. The positioning error model building module is used to build a positioning error model caused by eccentricity. The turntable positioning error self-calibration module is used to achieve turntable positioning error self-calibration using a positioning error compensation model.

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