A method and system for compensating spindle eccentricity error of circular grating encoder

Abstract

The present invention discloses a method and system for compensating for spindle eccentricity error of a circular grating encoder. The method utilizes the principle of evenly arranging capacitive displacement sensors to obtain the instantaneous vector of the spindle axis displacement, establishes a three-point error separation model, separates the roundness error of a standard sphere from the radial rotation error of the spindle, and thereby obtains an accurate radial rotation error of the spindle. A high-precision autocollimator is used to calibrate the circular grating encoder, and the average of multiple measurements is used as the system error to perform angle compensation on the circular grating encoder. Through angle compensation, the circular grating encoder achieves an angular measurement accuracy of ±1.62″ after eliminating the system error, which is two arc seconds higher than the nominal accuracy of ±2.79″. The present invention can effectively eliminate the influence of spindle installation eccentricity on the angular measurement accuracy of the circular grating, and is of great significance for improving the angular measurement accuracy of the circular grating encoder.

Description

Technical Field

[0001] The present invention belongs to the field of precision measurement technology, and in particular relates to a method and system for compensating a main shaft eccentricity error of a circular grating encoder. Background Art

[0002] Precision turntables are widely used in aerospace, intelligent robotics, high-end CNC machine tools, high-precision coordinate measuring machines, and other fields. Circular grating encoders, core components of precision turntables, offer advantages such as high resolution, compact size, easy installation, fast response, and simple processing circuitry. Furthermore, the photoelectric pulse signals from circular grating encoders exhibit strong anti-interference capabilities, effectively ensuring the operation and machining accuracy of CNC machine tools. With technological advancements, the requirements for angular measurement accuracy in various instruments and equipment are becoming increasingly stringent, placing increasing demands on the measurement accuracy of circular grating encoders. A research report by Heidenhain, a leading international manufacturer and distributor of high-end circular grating sensors, clearly states that installation eccentricity accounts for over 80% of angular measurement errors. This significant impact on the angular measurement accuracy of circular grating encoders makes it crucial to measure and determine the eccentricity parameter and compensate for the resulting error. During installation, eccentricity primarily involves the eccentricity of the circular grating relative to the shafting system and the installation error of the shafting system itself. Installation eccentricity can cause angular measurement errors in the encoder. Among them, the installation eccentricity error of the shaft system itself is the most basic error. The installation eccentricity of the circular grating is also caused by the eccentricity error of the main shaft. Therefore, in order to ensure the angle measurement accuracy of the circular grating encoder, it is necessary to first accurately measure the installation eccentricity error of the shaft system and compensate for it on this basis to improve the angle measurement accuracy of the circular grating encoder.

[0003] Currently, there is extensive research in China on spindle assembly eccentricity error, and various spindle eccentricity error measurement methods have been proposed. Among them, a method using a standard sphere and a capacitive displacement sensor to collect data on the instantaneous vector of the spindle axis displacement can achieve nanometer-level accuracy, which is sufficient for compensating the spindle rotation error of a circular grating encoder. However, the instantaneous vector measured by the capacitive displacement sensor on the standard sphere at different positions on the circumference includes the roundness error of the standard sphere and the radial rotation error of the spindle. To obtain a more accurate spindle radial rotation error, the roundness error of the standard sphere in the collected data cannot be ignored. To this end, a three-point error separation model is established to perform error separation on the data collected by the capacitive displacement sensor, thereby obtaining a more accurate spindle rotation error. Based on angle compensation and consideration of environmental factors, a spindle rotation eccentricity error compensation model for a circular grating encoder is established based on the spindle radial rotation error separated by the model, achieving precise compensation for the angular measurement error caused by the circular grating encoder's spindle rotation eccentricity. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a circular grating encoder spindle eccentricity error compensation method and system in response to the above-mentioned deficiencies in the prior art, so as to solve the technical problem that the circular grating encoder spindle rotation error factor affects the angular measurement accuracy.

[0005] The present invention adopts the following technical solutions:

[0006] A method for compensating for spindle eccentricity error of a circular grating encoder comprises the following steps:

[0007] S1. Collect the rotation error data of the standard ball in a full circle, and indirectly determine the radial error motion of the spindle by measuring the outer contour of the standard ball;

[0008] S2. Collect the rotation error data of the spindle radial error motion determined in step S1, establish a three-point error separation model, separate the roundness error data of the standard ball and the radial rotation error data of the spindle, and obtain an accurate spindle radial rotation error;

[0009] S3. Calibrate the circular grating encoder, perform angle compensation on the circular grating encoder using the average of multiple measurements, consider the impact of environmental factors on the angle measurement accuracy of the circular grating encoder after angle compensation, and obtain the environmental conditions for the best angle measurement accuracy of the circular grating encoder;

[0010] S4. Under the environmental conditions of the angle compensation in step S3 and the optimal angular measurement accuracy of the circular grating encoder, a circular grating encoder spindle rotation eccentricity error compensation model is established based on the spindle radial rotation error obtained in step S2 to achieve accurate compensation for the angular measurement error caused by the spindle rotation eccentricity of the circular grating encoder.

[0011] Specifically, in step S1, three capacitive displacement sensors are evenly arranged in the circumferential direction to collect the rotation error data of the standard ball throughout the entire circle. When there is an eccentricity error of the main shaft, the capacitive displacement sensors at different circumferential positions measure the roundness error of the standard ball and the radial rotation error of the main shaft.

[0012] Specifically, in step S2, the roundness error data h(n) of the standard ball is:

[0013] h(n)=F -1 [S(k) / G(k)]

[0014] Among them, S(k) and G(k) are the weight functions of the system.

[0015] Furthermore, in step S2, the radial rotation error data d of the spindle x (n), d y (n) is:

[0016]

[0017] Where s1(n) and s3(n) are the sampling data of the first and third sensors, h(n) is the roundness error data of the standard sphere, n is the sampling point position, n = 1, 2, 3...N-1, N is the number of sampling points of the sensor after the test piece rotates one circle, and p3 is the angular position number of the third sensor.

[0018] Specifically, in step S2, the three-point error separation model is:

[0019]

[0020] s(n)=h(n)+c2h(n+p2)+c3h(n+p3)

[0021] Among them, s1(n), s2(n), s3(n) are the sampling data of the first, second and third sensors, h(n) is the roundness error value of the standard ball at the first probe position, h(n+p2) is the roundness error value of the standard ball at the second probe position, h(n+p3) is the roundness error value of the standard ball at the third probe position, c1, c2, c3 are vectors, φ2 and φ3 are the angles between the installation positions of the second and third sensors and the x-axis, d x (n), d y (n) is the radial rotation error data of the main shaft.

[0022] Specifically, in step S3, the circular grating encoder is calibrated as follows:

[0023] The circular grating encoder is calibrated using an autocollimator and a twenty-tetrahedron. Every time the polyhedron rotates one face, the main axis and the circular grating rotate 15°. Starting from the first face of the twenty-tetrahedron, an error data is recorded every 15° rotation, and finally multiple data are recorded when the error data returns to the initial first face. The above steps are repeated, and the error data obtained from multiple measurements are averaged. The obtained error curve is used as the systematic error of the circular grating encoder. The averaged data points are compensated to the circular grating encoder by linear interpolation, thereby realizing systematic error compensation at any angular position of the circular grating encoder.

[0024] Specifically, in step S3, the environmental factors take into account the influence of temperature and preheating time.

[0025] Furthermore, considering the influence of temperature and preheating time on the angle measurement accuracy of the angle-compensated circular grating encoder, the following are the specific effects:

[0026] By controlling a single variable experimental method, the angle measurement accuracy of the circular grating encoder at different temperatures and different preheating times was analyzed, and then the experimental environment parameters that can enable the circular grating encoder to achieve the best angle measurement accuracy were obtained, and the optimal temperature and preheating time were determined.

[0027] Specifically, in step S4, the shaft shaking is analyzed and compensated as an eccentricity error, and the mean method is used to correct the error. The model of the mean method error correction is:

[0028]

[0029] in, is the error correction result of the mean value method, ε(θ+τ1) and ε(θ+τ2) are the graduation errors of the circular grating encoder, ψ(θ1) and ψ(θ2) are the inconsistency errors of the first reading head and the second reading head, δ(θ1) and δ(θ2) are random errors caused by other uncertain factors, and θ is the initial angle value.

[0030] In a second aspect, an embodiment of the present invention provides a circular grating encoder spindle eccentricity error compensation system, comprising:

[0031] The acquisition module is used to collect the rotation error data of the standard ball in a full circle and indirectly determine the radial error motion of the spindle by measuring the outer contour of the standard ball;

[0032] A separation module is used to collect the rotation error data of the spindle radial error motion determined by the acquisition module, establish a three-point error separation model, separate the roundness error data of the standard ball and the radial rotation error data of the spindle, and obtain the accurate spindle radial rotation error;

[0033] The calibration module is used to calibrate the circular grating encoder, perform angle compensation on the circular grating encoder using the average value of multiple measurements, consider the impact of environmental factors on the angle measurement accuracy of the circular grating encoder after angle compensation, and obtain the environmental conditions for the best angle measurement accuracy of the circular grating encoder;

[0034] The compensation module is used to establish a circular grating encoder spindle rotation eccentricity error compensation model based on the spindle radial rotation error obtained by the separation module under the environmental conditions of calibration module angle compensation and optimal circular grating encoder angle measurement accuracy, so as to achieve accurate compensation for the angle measurement error caused by the circular grating encoder spindle rotation eccentricity.

[0035] Compared with the prior art, the present invention has at least the following beneficial effects:

[0036] A method for compensating spindle eccentricity errors in circular grating encoders uses the outer contour of a standard sphere to indirectly measure the spindle's radial error motion. This overcomes the inability to directly measure the ideal axis center and enables measurement of the spindle's complex two-dimensional radial rotational motion. The rotational profiles of the standard sphere, measured using three capacitive displacement sensors, are synthesized to improve measurement accuracy. A three-point error separation model is employed to separate the roundness error of the standard sphere from the spindle's radial rotational error, further enhancing measurement accuracy and providing a more accurate estimate of the spindle's radial rotational error. The problem of roundness error introduced by using a standard sphere for spindle rotation error measurement is solved; a method for angular compensation of a circular grating encoder is provided by using an autocollimator, and the high precision of the autocollimator is utilized to calibrate the circular grating encoder, and the mean of multiple sets of calibration data is used as the system error to perform angular compensation on the circular grating encoder, thereby eliminating the influence of the measurement errors existing in the mechanical structure of the turntable, the grating, and the reading head itself on the angular measurement accuracy of the circular grating encoder; the optimization of the provided experimental environment is provided, and the angular measurement accuracy of the circular grating encoder at different temperatures and different preheating times is analyzed by an experimental method of controlling a single variable, and then the experimental environment parameters that can enable the circular grating encoder to achieve the best angular measurement accuracy are obtained, and the optimal temperature and preheating time are set in subsequent experiments, thereby reducing the influence of environmental factors on the angular measurement accuracy; the provided circular grating encoder spindle rotation eccentricity error compensation model regards the axis shake error as a type of eccentricity error, the only difference is that the direction of the eccentricity is random. Therefore, the shaft shaking can be analyzed and compensated as an eccentricity error; on the basis of angle compensation and consideration of the influence of environmental factors, a circular grating encoder spindle rotation eccentricity error compensation model is established based on the spindle radial rotation error separated by the model, so as to realize accurate compensation of the angular measurement error caused by the spindle rotation eccentricity of the circular grating encoder.

[0037] Furthermore, by arranging sensors at different positions on the circumference for data collection, the rotation error data at different positions at the same time can be obtained. Fitting the above rotation error data can obtain more accurate measurement values, and then separate more accurate radial rotation errors, providing a basis for spindle rotation error compensation.

[0038] Furthermore, the roundness error data h(n) of the standard ball is an inevitable error data in the spindle rotation error measured by the capacitive displacement sensor and cannot be ignored. Therefore, the roundness error needs to be considered.

[0039] Furthermore, the spindle radial rotation error data d x (n), d y (n) is the main part of the spindle rotation error and is also the result to be finally separated. The radial rotation error is further separated to obtain its rotation errors along the X and Y directions, which is more accurate and specific.

[0040] Furthermore, using the three-point error separation model, the key to spindle rotation error measurement lies in separating the spindle rotation error from the roundness error of the test piece. The three-point method is suitable for on-machine measurement because it does not require repeatability of the spindle rotation error. Due to the three-point method's ability to measure on-machine, the spindle rotation error can be measured while the bead turntable is operating.

[0041] Furthermore, the circular grating encoder is calibrated. Measurement errors in the spindle eccentricity, the mechanical structure of the turntable, the grating, and the readhead itself have a certain impact on the angular measurement accuracy of the circular grating encoder. Therefore, systematic errors should be eliminated as much as possible.

[0042] Furthermore, environmental factors, such as temperature and warm-up time, influence the angle measurement accuracy. Experiments were conducted on each of these factors separately. By controlling the variables and setting different values for each influencing factor, experiments were then conducted using a dynamic test system to analyze the influence of various factors on the angle measurement accuracy of the circular grating encoder under different experimental environments.

[0043] Furthermore, considering the effects of temperature and warm-up time on the angle-compensated circular grating encoder's angular measurement accuracy, and understanding their influence on angular measurement accuracy, we found that under normal ambient temperature fluctuations, the angular measurement accuracy of the circular grating is largely unaffected by ambient temperature. Therefore, when performing dynamic testing of the circular grating at ambient temperature, the effect of ambient temperature on its angular measurement accuracy does not need to be considered. Initially, the angular measurement accuracy of the circular grating improves with increasing warm-up time. When the warm-up time reaches 10 minutes, the angular measurement error of the circular grating stabilizes, indicating that the entire system has reached dynamic equilibrium. Therefore, when performing dynamic testing of the circular grating, a warm-up time of at least 10 minutes is required, at which point the circular grating dynamic system reaches dynamic equilibrium and the circular grating's angular measurement performance reaches its optimal state.

[0044] Furthermore, the circular grating encoder spindle rotation eccentricity error compensation model has an angular measurement accuracy of ±1.79″ before compensation and ±1.02″ after compensation. Through the comprehensive eccentricity error compensation model, the angular measurement accuracy of the circular grating dynamic test system is improved by 1.54″. The accurate spindle rotation error is calculated by the three-point error separation model, and the rotation error is substituted into the eccentricity error compensation model for further compensation, which ultimately has a significant effect on improving the angular measurement accuracy of the circular grating encoder.

[0045] Furthermore, the principle of error correction using the mean value method is simple. The two readheads use the same model and are adjusted and installed strictly according to assembly specifications. Furthermore, readhead inconsistency is a high-frequency error and can generally be ignored when measuring angles over a wide range of full circles or when the angle measurement interval is an integer multiple of the signal period. While graduation errors and random errors are unavoidable in practical applications, their magnitude is smaller than the angle measurement error caused by eccentric mounting of the circular grating. Therefore, they can be ignored in the eccentricity error compensation model. After compensating for eccentricity, error correction using the mean value method can correct the spindle rotation error as the primary influencing factor.

[0046] In summary, the present invention realizes the measurement of complex two-dimensional radial rotational motion of the spindle, improves the accuracy of the measurement results, further improves the precision of the measurement results, obtains more accurate spindle radial rotation error, reduces the influence of environmental factors on angular measurement accuracy, and realizes precise compensation for the angular measurement error caused by the eccentricity of the spindle rotation of the circular grating encoder.

[0047] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is a schematic diagram of the spindle rotation error;

[0049] Figure 2 This is a schematic diagram of the spindle rotation error separation;

[0050] Figure 3 This is the principle diagram of error separation using the three-point method;

[0051] Figure 4 This is the data collection result of the capacitive displacement sensor;

[0052] Figure 5 are the roundness error and radial rotation error obtained based on model separation;

[0053] Figure 6 This is the angle measurement accuracy curve of the circular grating encoder after compensation;

[0054] Figure 7 This is a curve diagram showing the effect of temperature and warm-up time on angle measurement accuracy;

[0055] Figure 8 This is the principle diagram of spindle rotation error compensation;

[0056] Figure 9 This is the angle measurement accuracy curve after spindle rotation error compensation. DETAILED DESCRIPTION

[0057] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0058] In the description of the present invention, it is to be understood that the terms “include” and “comprise” indicate the presence of the described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0059] It should also be understood that the terms used in the present specification are only for the purpose of describing particular embodiments and are not intended to limit the present invention. As used in the present 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.

[0060] It should be further understood that the term "and / or" as used in the present specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items. For example, A and / or B may represent: A alone, A and B simultaneously, or B alone. In addition, the character " / " herein generally indicates that the associated items are in an "or" relationship.

[0061] It should be understood that although the terms "first," "second," and "third" may be used to describe preset ranges in embodiments of the present invention, these preset ranges should not be limited to these terms. These terms are merely used to distinguish one preset range from another. For example, without departing from the scope of embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0062] The word "if," as used herein, may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting," depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to the determination" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)," depending on the context.

[0063] The accompanying drawings illustrate various schematic diagrams of structures according to embodiments disclosed herein. These figures are not drawn to scale; for clarity, some details are exaggerated and some details may be omitted. The shapes of the various regions and layers shown in the figures, as well as their relative sizes and positional relationships, are merely exemplary and may deviate in practice due to manufacturing tolerances or technical limitations. Those skilled in the art may design regions / layers with different shapes, sizes, and relative positions as needed.

[0064] The present invention provides a method for compensating for spindle eccentricity errors in circular grating encoders. This method utilizes the principle of evenly arranged capacitive displacement sensors to obtain the instantaneous vector of spindle axis displacement. A three-point error separation model is established to separate the roundness error of a standard sphere from the radial rotation error of the spindle, thereby accurately determining the radial rotation error of the spindle. A high-precision autocollimator is used to calibrate the circular grating encoder, and the mean of multiple measurements is used as the system error to perform angular compensation for the circular grating encoder. The influence of environmental factors such as temperature and warm-up time is also considered, and a circular grating encoder spindle rotation eccentricity error compensation model is established based on this model, achieving precise compensation for the angular measurement error caused by the spindle rotation eccentricity of the circular grating encoder.

[0065] See also Figure 1 The present invention provides a method for compensating the spindle eccentricity error of a circular grating encoder, comprising the following steps:

[0066] S1. Arrange three capacitive displacement sensors evenly in the circumferential direction and indirectly measure the radial error motion of the spindle by measuring the outer contour of the standard sphere.

[0067] Three capacitive displacement sensors are evenly arranged to collect the rotation error data of the standard ball throughout the entire circle. Based on the principle that the capacitive displacement sensor obtains the instantaneous vector of the spindle axis displacement, when the spindle has an eccentricity error, the instantaneous vector measured by the capacitive displacement sensors at different positions on the circumference of the standard ball includes the roundness error of the standard ball and the radial rotation error of the spindle.

[0068] The instantaneous position of the spindle's rotational axis in space is constantly changing. The displacement of the spindle's rotational axis relative to the mean axis at its average position is defined as the spindle's rotational error motion. In addition to rotation about the z-axis, the spindle's rotational axis movement in the x and y directions is known as radial error motion, rotation about the x and y axes is known as inclination error motion, and movement along the z-axis is known as axial error motion. These error motions are collectively referred to as the spindle's rotational error motion. Radial error motion is a two-dimensional planar motion, making its measurement more complex. Because it is impossible to directly measure the ideal axis center, the spindle's radial error motion must be indirectly measured using a standard sphere, a standard shaft, or the spindle's outer contour.

[0069] S2. Collecting the rotation error data of the spindle radial error motion determined in step S1, establishing a three-point error separation model, separating the roundness error of the standard ball and the radial rotation error of the spindle, and obtaining an accurate spindle radial rotation error;

[0070] In order to obtain accurate spindle radial rotation error data, a three-point error separation model is established to separate the roundness error of the standard ball and the radial rotation error of the spindle, thereby obtaining the accurate spindle radial rotation error.

[0071] See also Figure 2 The three-point method uses three linear displacement sensors to measure the spindle, separating the spindle's 2-D rotation error (radial rotation error) from its roundness error. Ideally, the measurement data would include both the spindle's rotational motion error and the measured cross-section's form error. The three-point error separation technique effectively separates these two errors.

[0072] See also Figure 3 Ideally, the measurement data includes the rotational motion error of the spindle and the shape error of the measured section. The three-point error separation technology is to effectively separate the above two errors.

[0073] The basic equation of the three-point method, that is, the readings of the three sensors are:

[0074]

[0075] Among them, S i (θ) is the sensor reading, i=1, 2, 3; is the angle between the installation position of each sensor and the x-axis, i = 1, 2, 3; h(θ) is the roundness error of the test piece; d x (θ), d y (θ) is the component of the spindle rotation error in the x and y directions.

[0076] Pick Discretize θ and express it in a matrix as:

[0077]

[0078] Where n is the sampling point position, n = 1, 2, 3...N-1; N is the number of sampling points of the sensor when the test piece rotates one circle; p i is the sensor angular position number, where i=1, 2, 3.

[0079] Multiply both sides of Equation (2) by the row vector [c1 c2 c3] on the left, and take z(n) = c1s1(n) + c2s2(n) + c3s3(n), then:

[0080]

[0081] make

[0082]

[0083] Take c1 = 1 and solve the equation to get:

[0084]

[0085] Among them, Δθ is the sampling angle of the sensor, Δθ = 2л / N.

[0086] Substitute c1, c2, c3 into formula (3), and record

[0087] s(n)=c1s1(n)+c2s2(n)+c3s3(n) (4)

[0088] but

[0089] s(n)=h(n)+c2h(n+p2)+c3h(n+p3) (5)

[0090] Performing Fourier transform on both sides of equation (5) yields:

[0091]

[0092] Then the system weight function G(k) is:

[0093]

[0094] The roundness error of the workpiece is:

[0095] h(n)=F -1 [S(k) / G(k)] (8)

[0096] The radial motion error is

[0097]

[0098] At this point, the roundness error and radial motion error can be separated from the discrete readings of the sensor through equations (8) and (9).

[0099] See also Figure 4 and Figure 5 According to the model calculation results, the roundness error is 0.2106μm and the spindle radial rotation error is 0.6415μm. This provides a more accurate spindle radial rotation error after eliminating the standard ball roundness error, providing the prerequisite for subsequent spindle radial rotation error compensation.

[0100] S3. Use a high-precision autocollimator to calibrate the circular grating encoder, and use the average of multiple measurements as the system error to perform angle compensation on the circular grating encoder. To further improve the angle measurement accuracy of the circular grating encoder after angle compensation, analyze the influence of environmental factors on the angle measurement accuracy, and then take measures to reduce their influence on the angle measurement accuracy.

[0101] In addition to the influence of spindle eccentricity on the angle measurement accuracy of circular grating encoders, measurement errors in the mechanical structure of the turntable, the grating, and the readhead itself also have a certain impact on the angle measurement accuracy of circular grating encoders. Therefore, before performing spindle radial rotation error compensation, systematic errors should be eliminated as much as possible. A high-precision autocollimator is used to calibrate the circular grating encoder, and the average of multiple measurements is used as the systematic error to perform angle compensation on the circular grating encoder.

[0102] The high-precision autocollimator is utilized to calibrate the circular encoder. The average of multiple sets of calibration data is used as the system error to compensate for the circular encoder's angle measurement accuracy. This eliminates the effects of measurement errors inherent in the turntable's mechanical structure, the grating, and the readhead itself on the circular encoder's angular measurement accuracy. The nominal accuracy of the Automel autocollimator used for calibration is ±0.1", while the nominal accuracy of the Renishaw circular encoder being calibrated is ±2.79". Therefore, the autocollimator is capable of achieving precise calibration of the circular encoder.

[0103] The circular grating encoder is calibrated using an autocollimator and a twenty-tetrahedron. Every time the polyhedron rotates one face, the spindle and the circular grating rotate 15°. Starting from the first face of the twenty-tetrahedron, an error data is recorded every 15° rotation until it returns to the initial first face, with a total of 25 data recorded.

[0104] Repeat the above steps and average the error data obtained from multiple measurements. The resulting error curve can be considered as the systematic error of the circular grating encoder. The 25 averaged data points are compensated to the circular grating encoder using the linear interpolation method, thus realizing the systematic error compensation at any angular position of the circular grating encoder.

[0105] See also Figure 6 By means of angle compensation, the angle measurement accuracy of the circular grating encoder reaches ±1.62″ after eliminating the system error, which is 2.34 arc seconds higher than the nominal accuracy of ±2.79″. Therefore, it is feasible and effective to use mean value to compensate for the system error.

[0106] In order to further improve the angle measurement accuracy of the circular grating encoder system, it is necessary to analyze the impact of environmental factors on the angle measurement accuracy through experiments, so as to obtain the optimal setting parameters for various environmental factors.

[0107] By controlling a single variable in the experiment, the angle measurement accuracy of the circular grating encoder at different temperatures and different preheating times was analyzed, and then the experimental environment parameters that can enable the circular grating encoder to achieve the best angle measurement accuracy were obtained. In subsequent experiments, the optimal temperature and preheating time were set to reduce the impact of environmental factors on the angle measurement accuracy.

[0108] Environmental factors primarily include temperature, vibration, electromagnetic fields, and warm-up time. The impact of vibration and electromagnetic fields primarily affects the performance of precision components such as readheads and circular encoders in strong magnetic fields and high vibration environments, specifically their shock resistance and interference immunity. However, the vibration and magnetic fields in the experimental environment are very weak and therefore not considered. Therefore, the main environmental factors considered are the impact of temperature and warm-up time.

[0109] See also Figure 7 Temperature changes in the experimental environment will not significantly affect the angle measurement accuracy of the circular grating encoder, so the influence of temperature factors does not need to be considered in normal experimental environments. However, the warm-up time has a significant impact on angle measurement accuracy. If the warm-up time is too short, the entire system will not reach a state of dynamic balance, and the internal vibration will have a significant impact on the angle measurement accuracy. Therefore, the warm-up time cannot be ignored. According to experimental results, after the entire system is powered on and preheated for 12 minutes, the entire shaft system reaches a state of dynamic balance, at which point the optimal angle measurement accuracy can be guaranteed.

[0110] S4. On the basis of the angle compensation in step S3 and the influence of environmental factors, a circular grating encoder spindle rotation eccentricity error compensation model is established based on the spindle radial rotation error separated by the three-point error separation model in step S2, so as to achieve accurate compensation for the angular measurement error caused by the spindle rotation eccentricity of the circular grating encoder.

[0111] During the installation process, the eccentricity error mainly includes the eccentricity of the circular grating relative to the shaft system and the installation error of the shaft system itself. The installation eccentricity will cause the encoder to produce angular measurement error.

[0112] Among these, the most fundamental error is the installation eccentricity of the shaft system itself. The installation eccentricity of the rotary encoder is also caused by the eccentricity of the spindle. Therefore, the spindle installation error must be compensated first. Shaft wobble can be considered a type of eccentricity error, differing only in the random direction of eccentricity. Therefore, shaft wobble can be analyzed and compensated as an eccentricity error.

[0113] According to the error separation model results, the spindle radial rotation error is 0.6415 μm, and the spindle is preheated for more than twelve minutes before the experiment begins.

[0114] See also Figure 8 and Figure 9 For the double-reading head circular grating angle measurement system, the average method is the conventional error correction method.

[0115] The theoretical model of mean error correction is:

[0116]

[0117] The mean value method is simple to calculate, but it requires high installation accuracy of the two reading heads. When there is no installation error of the reading heads, τ1 = 0° and τ2 = 180°.

[0118] At this time, formula (10) becomes:

[0119]

[0120] Among them, the angular measurement errors caused by the eccentricity of the circular grating installation and the radial runout of the shaft system are eliminated.

[0121] In another embodiment of the present invention, a circular grating encoder spindle eccentricity error compensation system is provided, which can be used to implement the above-mentioned circular grating encoder spindle eccentricity error compensation method. Specifically, the circular grating encoder spindle eccentricity error compensation system includes an acquisition module, a separation module, a calibration module and a compensation module.

[0122] The acquisition module is used to collect the rotation error data of the standard ball in a full circle, and indirectly determine the radial error motion of the spindle by measuring the outer contour of the standard ball;

[0123] A separation module is used to collect the rotation error data of the spindle radial error motion determined by the acquisition module, establish a three-point error separation model, separate the roundness error data of the standard ball and the radial rotation error data of the spindle, and obtain the accurate spindle radial rotation error;

[0124] The calibration module is used to calibrate the circular grating encoder, perform angle compensation on the circular grating encoder using the average value of multiple measurements, consider the impact of environmental factors on the angle measurement accuracy of the circular grating encoder after angle compensation, and obtain the environmental conditions for the best angle measurement accuracy of the circular grating encoder;

[0125] The compensation module is used to establish a circular grating encoder spindle rotation eccentricity error compensation model based on the spindle radial rotation error obtained by the separation module under the environmental conditions of calibration module angle compensation and optimal circular grating encoder angle measurement accuracy, so as to achieve accurate compensation for the angle measurement error caused by the circular grating encoder spindle rotation eccentricity.

[0126] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0127] A high-precision autocollimator was used to calibrate the circular grating encoder, and the average of multiple measurements was used as the system error to compensate for the circular grating encoder's angle. Through angle compensation, the circular grating encoder achieved an angular measurement accuracy of ±1.62″ after eliminating the systematic error, which is approximately two arc seconds higher than the nominal accuracy of ±2.79″. Therefore, using the mean value to compensate for the systematic error is feasible and effective. At the same time, the influence of environmental factors such as temperature and warm-up time was taken into consideration. According to experimental results, after the entire system was powered on and preheated for 12 minutes, the entire shaft system reached a state of dynamic balance, at which point the optimal angular measurement accuracy could be guaranteed. Compared with direct measurement without preheating, the angular measurement accuracy was improved by 0.3″. Based on this, a circular grating encoder spindle rotation eccentricity error compensation model was established to achieve precise compensation for the angular measurement error caused by the circular grating encoder spindle rotation eccentricity.

[0128] Combined with the experimental results, the average angle measurement error of the circular grating encoder before compensation is ±1.62". After the error separation model is used to obtain the accurate spindle rotation eccentricity, error compensation is performed. The average angle measurement error of the circular grating encoder is ±1.32". By adopting the circular grating encoder spindle rotation eccentricity error compensation model, the angle measurement error caused by the spindle eccentricity can be effectively compensated, and the encoder angle measurement accuracy is improved by about 0.6".

[0129] Therefore, the present invention adopts a circular grating spindle rotation error compensation model based on the error separation principle, which can effectively eliminate the influence of spindle installation eccentricity on the circular grating angle measurement accuracy, and is of great significance for improving the angle measurement accuracy of the circular grating encoder.

[0130] In summary, the present invention provides a method and system for compensating for spindle eccentricity in a circular grating encoder. Based on the three-point error separation principle, this method performs error separation on data collected by a capacitive displacement sensor, thereby obtaining a more accurate spindle rotation error. Furthermore, while angular compensation is applied and environmental factors are considered, a spindle rotation eccentricity compensation model for a circular grating encoder is established based on the spindle radial rotation error separated by the model. This allows for precise compensation of the angular measurement error caused by the spindle rotation eccentricity of the circular grating encoder.

[0131] The above content is only for explaining the technical idea of the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A method for compensating the spindle eccentricity error of a circular grating encoder, characterized in that: The following steps are involved: S1. Collect the rotation error data of the standard ball over the entire circumference. The radial error motion of the spindle is indirectly determined by measuring the outer contour of the standard ball. Three capacitive displacement sensors are evenly arranged in the circumferential direction to collect the rotation error data of the standard ball over the entire circumference. When the spindle has an eccentric error, the capacitive displacement sensors at different circumferential positions measure the roundness error of the standard ball and the radial rotation error of the spindle. S2. Collect the rotation error data of the spindle radial error motion determined in step S1, establish a three-point error separation model, separate the roundness error data of the standard ball and the radial rotation error data of the spindle, and obtain the accurate spindle radial rotation error. The three-point error separation model is specifically as follows: in, 、 、 is the sampling data of the first, second and third sensors, is the roundness error value of the standard ball at the first probe position, is the roundness error value of the standard ball at the second probe position, is the roundness error value of the standard ball at the third probe position, c 1. c 2. c 3 is a vector, and The installation position of the second and third sensors is x The angle of the axis, , The radial rotation error data of the main shaft; S3. Calibrate the circular grating encoder, perform angle compensation on the circular grating encoder using the average of multiple measurements, consider the impact of environmental factors on the angle measurement accuracy of the circular grating encoder after angle compensation, and obtain the environmental conditions for the best angle measurement accuracy of the circular grating encoder; S4. Under the environmental conditions of the angle compensation in step S3 and the optimal angular measurement accuracy of the circular grating encoder, a circular grating encoder spindle rotation eccentricity error compensation model is established based on the spindle radial rotation error obtained in step S2 to achieve accurate compensation for the angular measurement error caused by the spindle rotation eccentricity of the circular grating encoder.

2. The method for compensating the spindle eccentricity error of a circular grating encoder according to claim 1, characterized in that: In step S2, the roundness error data of the standard ball for: in, 、 is the weight function of the system.

3. The method for compensating the spindle eccentricity error of a circular grating encoder according to claim 2, characterized in that: In step S2, the spindle radial rotation error data , for: in, 、 is the sampling data of the first sensor and the third sensor, is the roundness error data of the standard ball, n is the sampling point location, n =1, 2, 3... N -1, is the number of sampling points of the sensor after the test piece rotates one circle, Number the angular position of the third sensor.

4. The method for compensating the spindle eccentricity error of a circular grating encoder according to claim 1, characterized in that: In step S3, the circular grating encoder is calibrated as follows: The circular grating encoder is calibrated using an autocollimator and a 24-sided prism. Each time the polyhedron rotates one face, the spindle and the circular grating rotate 15°. Starting from the first face of the 24-sided prism, an error data is recorded each time it rotates 15°. This is repeated until the first face is returned to the initial state, and multiple data are recorded. Repeat the above steps, average the error data obtained from multiple measurements, use the obtained error curve as the system error of the circular grating encoder, and compensate the averaged data points into the circular grating encoder using the linear interpolation method to achieve system error compensation at any angular position of the circular grating encoder.

5. The method for compensating the spindle eccentricity error of a circular grating encoder according to claim 1, characterized in that: In step S3, the environmental factors take into account the influence of temperature and preheating time.

6. The method for compensating the spindle eccentricity error of a circular grating encoder according to claim 5, characterized in that: Considering the influence of temperature and preheating time on the angle measurement accuracy of the angle-compensated circular grating encoder, the following are the specific effects: By controlling a single variable experimental method, the angle measurement accuracy of the circular grating encoder at different temperatures and different preheating times was analyzed, and then the experimental environment parameters that can enable the circular grating encoder to achieve the best angle measurement accuracy were obtained, and the optimal temperature and preheating time were determined.

7. The method for compensating the spindle eccentricity error of a circular grating encoder according to claim 1, characterized in that: In step S4, the shaft shaking is analyzed and compensated as an eccentricity error, and the mean method is used to correct the error. The model of the mean method error correction is: in, is the error correction result of the mean method, and is the graduation error of the circular grating encoder, and is the inconsistency error between the first and second reading heads, and is the random error caused by other uncertain factors. is the initial angle value.

8. A circular grating encoder spindle eccentricity error compensation system, characterized in that: include: The acquisition module is used to collect the rotation error data of the standard ball throughout the entire circumference. The radial error motion of the spindle is indirectly determined by measuring the outer contour of the standard ball. Three capacitive displacement sensors are evenly arranged in the circumferential direction to collect the rotation error data of the standard ball throughout the entire circumference. When there is an eccentric error in the spindle, the capacitive displacement sensors at different circumferential positions measure the roundness error of the standard ball and the radial rotation error of the spindle. The separation module is used to collect the rotation error data of the spindle radial error motion determined by the acquisition module, establish a three-point error separation model, separate the roundness error data of the standard ball and the radial rotation error data of the spindle, and obtain the accurate spindle radial rotation error. The three-point error separation model is specifically as follows: in, 、 、 is the sampling data of the first, second and third sensors, is the roundness error value of the standard ball at the first probe position, is the roundness error value of the standard ball at the second probe position, is the roundness error value of the standard ball at the third probe position, c 1. c 2. c 3 is a vector, and The installation position of the second and third sensors is x The angle of the axis, , The radial rotation error data of the main shaft; The calibration module is used to calibrate the circular grating encoder, perform angle compensation on the circular grating encoder using the average value of multiple measurements, consider the impact of environmental factors on the angle measurement accuracy of the circular grating encoder after angle compensation, and obtain the environmental conditions for the best angle measurement accuracy of the circular grating encoder; The compensation module is used to establish a circular grating encoder spindle rotation eccentricity error compensation model based on the spindle radial rotation error obtained by the separation module under the environmental conditions of calibration module angle compensation and optimal circular grating encoder angle measurement accuracy, so as to achieve accurate compensation for the angle measurement error caused by the circular grating encoder spindle rotation eccentricity.

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