An ultra-precision rotating shaft system rotation error measurement system and a measurement method

Abstract

The application discloses a kind of super-precision rotary shaft system rotation error measurement system and measurement method, the system includes rotary index plate, servo motor, spring, main shaft, marble platform and movable sensor clamping device etc.;The method comprises: the angle of rotation body control sensor on rotary index plate is used, so that radial and axial sensor is all in optimum measurement position;The installation height of rotary index plate is adjusted;When measurement system is stable operation, simultaneously utilize three high-precision displacement sensors arranged in optimum measurement position, real-time synchronous acquisition of the dynamic displacement data of rotary table main shaft is carried out;Wavelet denoising algorithm is used to pretreat original signal, then, Fourier transform analysis is carried out to 20 rotation stable operation data after processing, and frequency domain signal is obtained;Synchronous motion error and asynchronous motion error are extracted from the measurement data after denoising processing, and based on three-point method error separation principle, mathematical model parameters are solved using measurement data.

Description

Technical Field

[0001] This invention belongs to the field of spindle measurement, specifically relating to an ultra-precision rotary shaft system rotation error measurement system and method. Background Technology

[0002] With the development of modern science and technology, the requirements for the shape accuracy of ultra-precision rotating parts in fields such as precision machinery, aerospace, and military science are constantly increasing, posing greater challenges to rotational error measurement technology. How to effectively utilize error separation technology to improve the measurement accuracy of the spindle has become an important issue that urgently needs to be addressed.

[0003] Currently, the most commonly used methods for precision spindle measurement both domestically and internationally fall into two main categories: one is the multi-step method, including the two-step method and the reverse method evolved from it; the other is the three-point method, including its derivatives such as the two-point method and the four-point method. These methods all require two complex Fourier transform operations using the time delay and phase shift characteristics of the discrete Fourier transform when solving the error separation equation. However, whether it's the precise control of the rotation angle in the multi-step method or the optimized selection of the sensor position in the three-point method, the problem of incomplete harmonic suppression is unavoidable. This leads to significant distortion in the separated roundness and shape errors, making it impossible to completely separate the pure rotational motion error of the rotating shaft. Summary of the Invention

[0004] This invention provides an ultra-precision rotary shaft system rotation error measurement system and method. Based on the three-point rotation error separation technology, a simple fixture and vibration-damping platform are designed to provide a good measurement environment. Furthermore, the roundness error separation method based on matrix solution is improved. This method effectively avoids complex Fourier transform processes, better suppresses harmonic interference, significantly improves the measurement accuracy of rotation errors, and achieves precise separation of pure rotation error motion of the rotary shaft.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] An ultra-precision rotary shaft system rotation error measurement system includes a rotary indexing plate, a servo motor, a first flange, a second flange, a third flange, fastening connectors, springs, a spindle, a marble platform, and a movable sensor clamping device.

[0007] The rotary indexing plate is installed on the top of the marble platform. A movable sensor clamping device is set on the rotary indexing plate to clamp and position the sensor, as well as control the angle of the sensor on the rotary indexing plate.

[0008] One end of the spindle is used to install a standard ball, and the other end passes through the marble platform and is connected to one end of the second flange through a set screw; the first flange is connected to the bottom of the marble platform through a support rod, the servo motor is installed at the bottom of the first flange, the output end of the servo motor is connected to one end of the third flange through a shock absorption system, and the other end of the third flange is connected to the other end of the second flange through a nylon rope.

[0009] A further improvement of the present invention is that the movable sensor clamping device includes a rotating body, an axial sensor clamping device, and a radial sensor clamping device, wherein the rotating body is fixed on a rotary indexing plate and is used to control the angle of the sensor on the rotary indexing plate, and the axial sensor clamping device and the radial sensor clamping device are used to clamp and position the sensor.

[0010] A further improvement of the present invention is that multiple radial sensor holders and multiple axial sensor holders are provided.

[0011] A further improvement of the present invention is that the rotary indexing plate uses a rotating structure to divide the circumference into 120 parts, and is used in conjunction with a rotating body, which can significantly improve the measurement step accuracy from 6° to 0.5°.

[0012] A further improvement of the present invention is that the support rod is divided into a first support rod and a second support rod.

[0013] A further improvement of the present invention is that the shock absorption system includes a spring, both ends of which are provided with nuts, and the shock absorption system is mounted on the marble platform via a fourth flange.

[0014] A method for measuring the rotational error of an ultra-precision rotating shaft system, the method being based on the aforementioned ultra-precision rotating shaft system rotational error measurement system, includes the following steps:

[0015] 1) Use the rotating body to control the angle of the sensor on the rotary indexing plate so that both the radial and axial sensors are in the optimal measurement position. Securely fix the rotating body on the rotary indexing plate and use the radial sensor clamp and axial sensor clamp to clamp and position the sensor. At the same time, adjust the installation height of the rotary indexing plate to ensure that the sensor measurement center is at the same height as the center of the standard ball on the spindle.

[0016] 2) Once the measurement system is running smoothly, three high-precision displacement sensors positioned at the optimal measurement locations are used to synchronously collect the dynamic displacement data of the turntable spindle in real time. The three sets of displacement data collected are denoted as S1, S2, and S3, respectively. These three sets of data serve as the original basic data for subsequent analysis.

[0017] 3) Since there is high noise interference in the original displacement signals collected by each displacement sensor, wavelet denoising algorithm is used to preprocess the original signal. Then, Fourier transform analysis is performed on the processed 20-turn stable operation data to obtain the frequency domain signal. Then, the DC component, first harmonic component and high-frequency harmonic components above the 50th order are removed by filtering technology.

[0018] 4) Extract synchronous motion error and asynchronous motion error from the noise-reduced measurement data, and solve the mathematical model parameters using the measurement data based on the three-point error separation principle. First, discretize the mathematical model and effectively separate the synchronous and asynchronous components in the frequency domain through Fourier transform and inverse Fourier transform. The synchronous component is obtained by calculating the average profile of multi-turn measurement data and is represented as integer harmonic components in the frequency domain. The asynchronous component corresponds to the non-integer harmonic components in the Fourier domain. Finally, based on the extracted synchronous motion error, the frequency domain three-point error separation algorithm is used to further separate and calculate the roundness error and spindle rotation error.

[0019] A further improvement of the present invention is that the specific implementation method of step 2) is as follows:

[0020] Once the measurement system is running smoothly, the system simultaneously uses three high-precision displacement sensors positioned at the optimal measurement location to collect dynamic displacement data of the turntable spindle in real time. The three sets of displacement data collected are denoted as S1, S2, and S3, and the data is collected over 20 revolutions.

[0021] A further improvement of this invention is that the specific implementation method of step 3) is as follows:

[0022] Because the original displacement signals acquired by each displacement sensor contain high levels of noise interference, wavelet transform is performed on the original signal x(t) to obtain the wavelet coefficients:

[0023] W j，k =∫x(t)ψ j,k (t)dt

[0024] Where, ψ j,k (t) is the wavelet basis function; wavelet coefficients are processed using either soft or hard thresholding:

[0025]

[0026] Where λ is the threshold, calculated based on the noise standard deviation σ:

[0027]

[0028] Where N is the signal length; the inverse wavelet transform is performed on the processed wavelet coefficients to obtain the denoised signal x.d (t);

[0029] For the denoised signal x d Perform a Fourier transform on (t) to obtain the frequency domain signal:

[0030]

[0031] Then process it accordingly:

[0032] Remove DC component: X(0) = 0;

[0033] Remove the first-order component: X(f1) = 0, X(-f1) = 0, where f1 is the fundamental frequency;

[0034] Remove high-frequency components after the 50th order: X(f) = 0, f > 50f1;

[0035] Finally, the signal is converted back to the time domain using the inverse Fourier transform:

[0036]

[0037] That is, we get S1 f (θ), S2 f (θ), S3 f (θ).

[0038] A further improvement of this invention is that the specific implementation method of step 4) is as follows:

[0039] After wavelet denoising, the discrete measurement signal is defined as:

[0040] x(θ)=x s (θ)+x a (θ)

[0041] in:

[0042] x s (θ) represents the synchronous motion error;

[0043] x a (θ) represents the asynchronous motion error;

[0044] The signal is converted to the frequency domain using Fourier transform:

[0045] X(f)=F[x(θ)]=Xs(f)+Xa(f)

[0046] Two methods for extracting synchronous and asynchronous errors are employed:

[0047] Method 1: Temporal Extraction

[0048] Synchronization component S sync(θ) can be obtained by calculating the average profile from multiple rotations of measurement data, and it is expressed in the time domain as follows:

[0049] S sync (θ)=∑S(θ) / N

[0050] Asynchronous component S asyn (θ) is the difference between the total error and the synchronization error, which is expressed in the time domain as:

[0051] S asyn (θ)=S(θ)-S sync (θ)

[0052] Method 2: Frequency Domain Extraction

[0053] Synchronization component S1 f (θ) can be obtained by calculating the average profile from multi-cycle measurement data, and its Fourier transform is expressed as an integer harmonic:

[0054]

[0055] in:

[0056] f0 is the fundamental frequency;

[0057] fn = nf0 is an integer harmonic frequency;

[0058] δ(f) is the unit impulse function;

[0059] Inverse Fourier transform recovers the time-domain synchronization error signal:

[0060] x s (θ)=F -1 [X s (f)]

[0061] Asynchronous motion errors correspond to non-integer harmonics, which can be obtained by filtering out the synchronization component:

[0062] X a (f)=X(f)-X s (f)

[0063] Inverse Fourier transform recovers the time-domain synchronization error signal:

[0064] x a (θ)=F -1 [X a (f)]

[0065] To reduce the computational conversion between the time and frequency domains, denoising, synchronization error extraction, and asynchronous error extraction are all performed in the frequency domain.

[0066] The principle of the matrix three-point method is as follows:

[0067] By performing a Fourier transform on the measured circular profile, the complex profile curve is decomposed into a periodic waveform composed of harmonics of different orders.

[0068]

[0069] In this context, the angle variable is represented by θ, which describes the position on the measured circular profile; A0 represents the DC component of the measured circular profile, reflecting the average radius of the profile; the upper limit of the order of the harmonic expansion is M, representing the highest order of the harmonic components considered; and A... m B is the cosine of the m-th harmonic component; while B m These coefficients collectively constitute a complete characteristic description of the measured circular profile in the frequency domain, reflecting the magnitude and distribution characteristics of each harmonic component of the profile error. According to the least squares principle, the least squares center coordinates (a, b) of the measured circular profile s(θ) are:

[0070]

[0071] If r1(θ1) represents the roundness error, it can be obtained from the relationship between the coordinates.

[0072] s(θ)cosθ=r1(θ1)cosθ1+A1

[0073] s(θ)sinθ=r1(θ1)sinθ1+B1

[0074] Merging

[0075] s(θ)=r1(θ1)cos(θ1-θ)+A1cosθ+B1sinθ

[0076] If r(θ) represents the sum of all terms in the Fourier series of the circular profile except for the first-order component, then it is expressed as:

[0077]

[0078] Then we obtain the new s(θ):

[0079] s(θ)=r(θ)+A1cosθ+B1sinθ

[0080] If we define the radial rotational error motion of the rotating shaft as:

[0081] δ x (θ)=δ(θ)cosθ

[0082] δ y (θ)=δ(θ)sinθ

[0083] During measurement, three sensors are fixed, and the workpiece is rotated clockwise around the axis of rotation. The output signals of the three sensors are as follows:

[0084]

[0085] The above equation can be written in matrix form:

[0086] V = Ae

[0087] in:

[0088]

[0089] in:

[0090] i represents the position of the sampling point, and its value range is: i = 0, 1, 2, ..., N-1, where N is the number of sampling points in each period;

[0091] p n The number of sampling interval points between the displacement sensor and the x-axis is represented by the following formula:

[0092]

[0093] V is a column vector composed of the output signals of sensors 0, 1, and 2.

[0094] e represents the column vector composed of the contour shape error and rotation error of the measured circle after delays p0, p1, p2;

[0095] A is the output coefficient matrix of the measurement sensor;

[0096] To separate roundness error, it is necessary to ensure that:

[0097]

[0098] Let c0 = 1, then we can solve for the weighting coefficients:

[0099]

[0100] Substitute c0, c1, and c2 into V n (i) = obtained from CV

[0101] V n (i)=c0r(i+p0)+c1r(i+p1)+c2r(i+p2)

[0102] Where r(i+p0), r(i+p1), and r(i+p2) are the discretized forms of the circular contour series;

[0103] V n(i) is the weighted sum of the output signals of the three sensors, and r(i) is an unknown discrete sequence with periodicity, so r(i) is expressed as:

[0104]

[0105] After the time delay, it can be written as:

[0106]

[0107] Then substitute V n (i)=c0r(i+p0)+c1r(i+p1)+c2r(i+p2) can be rewritten as:

[0108] V n (i) N×1 =D N×N r(i) N×1

[0109] In the formula D N×N The error separation weight coefficient matrix for the three-point method is shown below.

[0110]

[0111] When p = q When p≠q l = 0, 1, 2.

[0112] Since rank(D,V) n (i))=rank(D)=N, so V n (i) N×1 =D N×N r(i) N×1 There is a unique solution:

[0113]

[0114] Therefore, the roundness error of the measured circle profile is

[0115] f = [r(i)] max -[r(i)] min ,i=0,1,2,...,N-1.

[0116] Since the sensor signal acquires a circular profile signal, which consists of roundness error and rotation error, in order to separate the pure rotation error motion, the separated r(i) is substituted back into V=Ae and combined with... get:

[0117]

[0118] make

[0119] The above formula can then be written as:

[0120]

[0121] Then the least squares coordinates of the center (A1, B1) of the measured circular profile are obtained as follows:

[0122]

[0123] The rotational error of the measured shaft is expressed as:

[0124]

[0125] Compared with the prior art, the present invention has at least the following beneficial technical effects:

[0126] In this invention, the design of the rotary indexing plate is one of the key technologies. To achieve high-precision rotary positioning, the circumference of the indexing plate is evenly divided into 120 equal parts, and these parts are matched with specific threaded holes on the rotating component in five equal parts. This structural design allows for high-precision indexing with an accuracy of 0.5°. Simultaneously, this indexing method ensures the accurate installation angle of the sensor, avoiding measurement deviations caused by installation errors, thereby improving the stability and reliability of the measurement.

[0127] To further improve measurement accuracy, this invention introduces an improved matrix three-point method algorithm. The core idea of ​​this algorithm is to utilize three sensors to monitor the spindle rotation state in real time and perform multi-level processing and analysis on the sensor data. First, to address potential noise, eccentricity errors, and high-order non-rotational error terms in the original data, this invention employs wavelet filtering. By decomposing and reconstructing the signal through wavelet transform, it effectively removes DC components, eccentricity errors, and non-rotational error terms of order 50 and above. This preprocessing method not only improves signal purity but also significantly enhances the computational efficiency and accuracy of subsequent algorithms. After data preprocessing, the system uses a weighted function to synthesize errors, inputting the three sets of sensor data into the matrix three-point method algorithm for comprehensive calculation. The unique feature of the matrix three-point method algorithm is that it accurately separates roundness errors and rotational errors through matrix operations, thus avoiding the problems of incomplete error separation and signal confusion in traditional algorithms. Simultaneously, through optimized weighted function design, the system can adaptively suppress error terms of different frequencies, especially exhibiting excellent suppression effects on high-order harmonic interference.

[0128] Furthermore, the structural design and algorithm implementation of this invention have significant practical value and potential for widespread application. Because the system employs a combined algorithm processing method based on wavelet filtering and the matrix three-point method, it can adapt to the rotational error measurement requirements under various working conditions. Simultaneously, the device has a simple structure, low manufacturing cost, and easy installation process, which can significantly reduce the manufacturing and usage costs of high-precision measuring equipment. Attached Figure Description

[0129] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0130] Figure 1 This is the original simulation data image.

[0131] Figure 2 The roundness error extracted from the simulated circular contour data, as well as the set roundness error and the roundness error for decentering.

[0132] Figure 3 This is a polar coordinate plot of the rotational error separated from the simulated circular profile data and the set rotational error.

[0133] Figure 4 The difference between the roundness error and the separated roundness error is defined as the algorithm accuracy of the matrix three-point method.

[0134] Figure 5 The difference between the set rotation error and the separated rotation error is used to characterize the algorithm accuracy of the matrix three-point method.

[0135] Figure 6 The influence of roundness error on rotation error in the combined signal is shown in the frequency domain.

[0136] Figure 7 This is a schematic diagram of the structure of an ultra-precision rotary shaft system rotation error measurement system according to the present invention.

[0137] Explanation of reference numerals in the attached figures:

[0138] 1. Rotary indexing plate; 2. Rotating body; 3. Radial sensor holder; 4. Servo motor; 5. First flange; 6. Set screw; 7. Second flange; 8. Third flange; 9. First support rod; 10. Second support rod; 11. Fastening connector; 12. Spring; 13. Axial sensor holder; 14. Fourth flange; 15. Spindle; 16. Marble platform. Detailed Implementation

[0139] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0140] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0141] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0142] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection, an electrical connection, or a communication connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0143] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0144] It should be understood that, when used in this specification and the appended claims, the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0145] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this 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.

[0146] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0147] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0148] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0149] This invention, based on the three-point method for separating rotational errors, designs a simple fixture and a vibration-damping platform to provide a good measurement environment and improves the roundness error separation method based on matrix solution. This method effectively avoids complex Fourier transform processes, better suppresses harmonic interference, significantly improves the measurement accuracy of rotational errors, and achieves precise separation of pure rotational error motion of the rotation axis. The calculation process for an example is as follows:

[0150] Example 1

[0151] like Figure 7As shown, the present invention provides an ultra-precision rotary shaft system rotation error measurement system, including a rotary indexing plate 1, a servo motor 4, a first flange 5, a second flange 7, a third flange 8, a fastening connector 11, a spring 12, a spindle 15, a marble platform 16, and a movable sensor clamping device. The rotary indexing plate 1 is mounted on the top of the marble platform 16, and the movable sensor clamping device is disposed on the rotary indexing plate 1 for clamping and positioning the sensor, as well as controlling the angle of the sensor on the rotary indexing plate 1. One end of the spindle 15 is used to mount a standard ball, and the other end passes through the marble platform 16 and is connected to one end of the second flange 7 through a set screw. The first flange 5 is connected to the bottom of the marble platform 16 through a support rod, the servo motor 4 is mounted on the bottom of the first flange 5, the output end of the servo motor 4 is connected to one end of the third flange 8 through a shock absorption system, and the other end of the third flange 8 is connected to the other end of the second flange 7 through a nylon rope.

[0152] In this embodiment, the first flange 5 is bolted to the set screw 6 and then connected to the marble platform 16 by the first support rod 9 and the second support rod 10. The shock absorption system is formed by the compression of the spring 12 with a nut and then connected to the servo motor 4 through the fastening connector 11. The fastening connector 11 is then connected to the flange 8 and the third flange 8 is connected to the second flange 7 by a nylon rope to form a transmission mechanism. The main shaft 15 is connected to the second flange 7 by a set screw. The measuring part is fixed to the marble platform 16 by the rotary indexing plate 1. The rotating body 2, the axial sensor holder 13 and the radial sensor holder 3 form a movable sensor holding device placed on the rotary indexing plate 1.

[0153] In this embodiment, the movable sensor clamping device includes a rotating body 2, an axial sensor clamping device 13, and a radial sensor clamping device 3. The rotating body 2 is fixed on the rotary indexing plate 1 and is used to control the angle of the sensor on the rotary indexing plate 1. The axial sensor clamping device 13 and the radial sensor clamping device 3 are used to clamp and position the sensor.

[0154] In this embodiment, the support rod is divided into a first support rod 9 and a second support rod 10.

[0155] In this embodiment, the shock absorption system includes a spring 12, with nuts at both ends of the spring 12, and the shock absorption system is mounted on the marble platform 16 via a fourth flange 14.

[0156] Example 2

[0157] This invention provides a method for measuring the rotational error of an ultra-precision rotating shaft system, comprising the following steps:

[0158] 1) A standard ball is fixedly installed on the spindle 15, with its center positioned on the spindle axis. The spindle is rigidly connected via a second flange 7 using set screws. A nylon rope flexibly connects the second flange 7 to the third flange 8. A spring 12 further reduces the impact of servo motor 4 vibration on the spindle rotation error measurement accuracy, forming a highly efficient vibration damping system. The entire damping system is then securely mounted on a highly stable marble platform 16 via a fourth flange 14, thus forming a stable spindle testing platform. The measuring device mainly consists of a self-developed rotary indexing plate 1, a rotating body 2, a radial sensor holder 3, and an axial sensor holder 13. Multiple radial sensor holders 3 and multiple axial sensor holders 13 are provided, reliably connected to the rotary indexing plate 1 via the rotating body 2. The rotary indexing plate 1 divides the circumference into 120 parts through a special rotating structure. Combined with the rotating body 2, this significantly improves the measurement step accuracy from 6° to 0.5°, effectively reducing the number of holes in the indexing plate and manufacturing costs. Meanwhile, the aforementioned testing mechanism is firmly connected to the marble platform 16 by bolts, forming a stable and high-precision ultra-precision rotary shaft system rotation error measurement system;

[0159] 2) The rotating body 2 is used to precisely control the angle of the sensor on the rotary indexing plate 1, ensuring that both the radial and axial sensors are in the optimal measurement position. The rotating body 2 is securely fixed to the rotary indexing plate 1 using screws, and the radial sensor holder 3 and the axial sensor holder 13 are used to reliably clamp and position the sensor. Simultaneously, the installation height of the rotary indexing plate 1 is adjusted to precisely ensure that the sensor measurement center is at the same height as the center of the standard ball on the spindle, thereby effectively improving measurement accuracy and ensuring the reliability and stability of the measurement results.

[0160] 3) Once the measurement system is running smoothly, it simultaneously collects dynamic displacement data of the turntable spindle in real time using three high-precision displacement sensors positioned at the optimal measurement locations. The three sets of displacement data are denoted as S1, S2, and S3, typically collected over 20 revolutions. These three sets of data serve as the raw foundation for subsequent analysis, accurately reflecting the real-time error characteristics of the spindle during rotation and providing reliable data for further error separation, evaluation, and accuracy optimization.

[0161] 4) Due to the high noise interference in the raw displacement signals acquired by each displacement sensor, a wavelet denoising algorithm is used to preprocess the raw signals to effectively suppress random noise components and improve the signal-to-noise ratio and reliability of the measurement signals. Subsequently, the processed 20-revolution stable operation data is subjected to Fourier transform analysis to obtain the frequency domain signal. Then, filtering techniques are used to remove the DC component, first-order harmonic component, and high-frequency harmonic components above the 50th order, eliminating the influence of these interference factors on the measurement results.

[0162] 5) Synchronous motion error and asynchronous motion error are extracted from the noise-reduced measurement data, and the mathematical model parameters are solved using the measurement data based on the three-point error separation principle. First, the mathematical model is discretized, and the synchronous and asynchronous components are effectively separated in the frequency domain through Fourier transform and inverse Fourier transform. The synchronous component is obtained by calculating the average profile of multi-turn measurement data and is represented as integer harmonic components in the frequency domain; while the asynchronous component corresponds to non-integer harmonic components in the Fourier domain. Finally, based on the extracted synchronous motion error, the frequency domain three-point error separation algorithm is used to further accurately separate and calculate the roundness error and spindle rotation error.

[0163] In this embodiment, the specific implementation method of step 3) is as follows:

[0164] Once the measurement system is running smoothly, it simultaneously collects dynamic displacement data of the turntable spindle in real time using three high-precision displacement sensors positioned at optimal measurement locations. The three sets of displacement data are denoted as S1, S2, and S3, typically collected over 20 revolutions. These three sets of data serve as the raw foundation for subsequent analysis, accurately reflecting the real-time error characteristics of the spindle during rotation and providing reliable data for further error separation, evaluation, and accuracy optimization.

[0165] In this embodiment, the specific implementation method of step 4) is as follows:

[0166] Because the original displacement signals acquired by each displacement sensor contain high levels of noise interference, wavelet transform is performed on the original signal x(t) to obtain the wavelet coefficients:

[0167] W j，k =∫x(t)ψ j,k (t)dt

[0168] Where, ψ j,k (t) is the wavelet basis function. Wavelet coefficients are processed using either soft or hard thresholding:

[0169]

[0170] Where λ is the threshold, calculated based on the noise standard deviation σ:

[0171]

[0172] Where N is the signal length. Performing an inverse wavelet transform on the processed wavelet coefficients yields the denoised signal x. d (t). For the denoised signal x d Perform a Fourier transform on (t) to obtain the frequency domain signal:

[0173]

[0174] Then process it accordingly:

[0175] Remove the DC component: X(0) = 0.

[0176] Remove the first-order component: X(f1) = 0, X(-f1) = 0, where f1 is the fundamental frequency.

[0177] Remove high-frequency components after the 50th order: X(f)=0, f>50f1.

[0178] Finally, the signal is converted back to the time domain using the inverse Fourier transform:

[0179]

[0180] That is, we get S1 f (θ), S2 f (θ), S3 f (θ)

[0181] In this embodiment, the specific implementation method of step 5) is as follows:

[0182] After wavelet denoising, the discrete measurement signal is defined as:

[0183] x(θ)=x s (θ)+x a (θ)

[0184] in:

[0185] x s (θ) represents the synchronous motion error.

[0186] x a (θ) represents the asynchronous motion error.

[0187] The signal is converted to the frequency domain using Fourier transform:

[0188] X(f)=F[x(θ)]=Xs(f)+Xa(f)

[0189] The following introduces two methods for extracting synchronous and asynchronous errors:

[0190] Method 1: Temporal Extraction

[0191] Synchronization component S sync (θ) can be obtained by calculating the average profile from multiple rotations of measurement data, and it is expressed in the time domain as follows:

[0192] S sync (θ)=∑S(θ) / N

[0193] Asynchronous component S asyn(θ) is the difference between the total error and the synchronization error, which is expressed in the time domain as:

[0194] S asyn (θ)=S(θ)-S sync (θ)

[0195] Method 2: Frequency Domain Extraction

[0196] Synchronization component S1 f (θ) can be obtained by calculating the average profile from multi-cycle measurement data, and its Fourier transform is expressed as an integer harmonic:

[0197]

[0198] in:

[0199] f0 is the fundamental frequency

[0200] fn = nf0 is an integer harmonic frequency.

[0201] δ(f) is the unit impulse function

[0202] Inverse Fourier transform recovers the time-domain synchronization error signal:

[0203] x s (θ)=F -1 [X s (f)]

[0204] Asynchronous motion errors correspond to non-integer harmonics, which can be obtained by filtering out the synchronization component:

[0205] X a (f)=X(f)-X s (f)

[0206] Inverse Fourier transform recovers the time-domain synchronization error signal:

[0207] x a (θ)=F -1 [X a (f)]

[0208] To reduce the computational conversion between the time and frequency domains, denoising, synchronization error extraction, and asynchronous error extraction are all performed in the frequency domain.

[0209] The principle of the matrix three-point method is as follows:

[0210] The actual shape of the measured circular profile is essentially a closed and periodic complex curve, therefore it can be effectively described and analyzed using Fourier series. By performing a Fourier transform on the measured circular profile, the complex profile curve is decomposed into a periodic waveform composed of harmonics of different orders, i.e.

[0211]

[0212] In this context, the angle variable is represented by θ, which describes the position on the measured circular profile; A0 represents the DC component of the measured circular profile, reflecting the average radius of the profile; the upper limit of the order of the harmonic expansion is M, representing the highest order of the harmonic components considered; and A... m B is the cosine of the m-th harmonic component; while B m Let be the sinusoidal quantity of the m-th harmonic component. These coefficients together constitute a complete characteristic description of the measured circular profile in the frequency domain, accurately reflecting the magnitude and distribution characteristics of each harmonic component of the profile error. According to the least squares principle, the least squares center coordinates (a, b) of the measured circular profile s(θ) are:

[0213]

[0214] It can be seen that in actual measurement, the first harmonic component of the measured circular profile corresponds to the DC offset caused by the workpiece installation eccentricity. If r1(θ1) represents the roundness error, it can be obtained from the relationship between the coordinates.

[0215] s(θ)cosθ=r1(θ1)cosθ1+A1

[0216] s(θ)sinθ=r1(θ1)sinθ1+B1

[0217] Merging can yield

[0218] s(θ)=r1(θ1)cos(θ1-θ)+A1cosθ+B1sinθ

[0219] If r(θ) represents the sum of all terms in the Fourier series of the circular profile except for the first-order component, it can be expressed as:

[0220]

[0221] Then we can obtain the new s(θ):

[0222] s(θ)=r(θ)+A1cosθ+B1sinθ

[0223] If we define the radial rotational error motion of the rotating shaft as:

[0224] δ x (θ)=δ(θ)cosθ

[0225] δ y (θ)=δ(θ)sinθ

[0226] During measurement, three sensors are fixed, and the workpiece is rotated clockwise around the axis of rotation. The output signals of the three sensors are as follows:

[0227]

[0228] The above equation can be written in matrix form:

[0229] V = Ae

[0230] in:

[0231]

[0232] in:

[0233] i represents the position of the sampling point, and its value range is: i = 0, 1, 2, ..., N-1, where N is the number of sampling points in each period;

[0234] p n The number of sampling interval points between the displacement sensor and the x-axis is represented by the following formula:

[0235]

[0236] V is a column vector composed of the output signals of sensors 0, 1, and 2.

[0237] e represents the column vector composed of the contour shape error and rotation error of the measured circle after delays p0, p1, p2;

[0238] A is the output coefficient matrix of the measurement sensor.

[0239] To separate roundness error, it is necessary to ensure that:

[0240]

[0241] Let c0 = 1, then we can solve for the weighting coefficients:

[0242]

[0243] Substitute c0, c1, and c2 into V n (i) = obtained from CV

[0244] V n (i)=c0r(i+p0)+c1r(i+p1)+c2r(i+p2)

[0245] Where r(i+p0), r(i+p1), and r(i+p2) are the discretized forms of the circular contour series.

[0246] V n (i) is the weighted sum of the output signals of the three sensors, and r(i) is an unknown discrete sequence with periodicity, so r(i) can be expressed as:

[0247]

[0248] After the time delay, it can be written as:

[0249]

[0250] Then substitute V n (i)=c0r(i+p0)+c1r(i+p1)+c2r(i+p2) can be rewritten as:

[0251] V n (i) N×1 =D N×N r(i) N×1

[0252] In the formula D N×N The error separation weight coefficient matrix for the three-point method is shown below.

[0253]

[0254] When p = q When p≠q l = 0, 1, 2.

[0255] Since rank(D,V) n (i))=rank(D)=N, so V n (i) N×1 =D N×N r(i) N×1 There is a unique solution:

[0256]

[0257] Therefore, the roundness error of the measured circle profile is

[0258] f = [r(i)] max -[r(i)] min ,i=0,1,2,...,N-1.

[0259] Since the sensor signal acquires a circular profile signal, which consists of roundness error and rotation error, in order to separate the pure rotation error motion, the separated r(i) is substituted back into V=Ae and combined with... get:

[0260]

[0261] make

[0262] The above formula can then be written as:

[0263]

[0264] Then the least squares coordinates of the center (A1, B1) of the measured circular profile are obtained as follows:

[0265]

[0266] The rotational error of the measured shaft can be expressed as:

[0267]

[0268] In summary, using the method of this invention, point cloud data of an arc surface in an arc groove, which has been measured by a non-contact measurement method, is calculated. A good initial axis is obtained using the normal vector cross product method, and the optimal axis direction is calculated using a multi-directional iterative step-size search method. The axis position and radius of the arc surface are also calculated. (Refer to...) Figure 6 and Figure 7 As shown. Figure 6 The initial arc surface axis direction obtained using the method of this invention, Figure 7 The optimal axis direction is obtained by using a multi-directional iterative step-size search method.

[0269] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the scope of the invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0270] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can be appropriately combined to form other embodiments that can be understood by those skilled in the art. The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for measuring the rotational error of an ultra-precision rotating shaft system, characterized in that, The method is based on an ultra-precision rotary shaft system rotation error measurement system, which includes a rotary indexing plate (1), a servo motor (4), a first flange (5), a second flange (7), a third flange (8), a fastening connector (11), a spring (12), a spindle (15), a marble platform (16), and a movable sensor clamping device. The rotary indexing plate (1) is installed on the top of the marble platform (16). The movable sensor clamping device is set on the rotary indexing plate (1) for clamping and positioning the sensor, as well as controlling the angle of the sensor on the rotary indexing plate (1). One end of the spindle (15) is used to install a standard ball, and the other end passes through the marble platform (16) and is connected to one end of the second flange (7) by a set screw; the first flange (5) is connected to the bottom of the marble platform (16) by a support rod, the servo motor (4) is installed at the bottom of the first flange (5), the output end of the servo motor (4) is connected to one end of the third flange (8) through a shock absorption system, and the other end of the third flange (8) is connected to the other end of the second flange (7) by a nylon rope; The movable sensor clamping device includes a rotating body (2), an axial sensor clamp (13), and a radial sensor clamp (3). The rotating body (2) is fixed on the rotary indexing plate (1) and is used to control the angle of the sensor on the rotary indexing plate (1). The axial sensor clamp (13) and the radial sensor clamp (3) are used to clamp and position the sensor. The method includes the following steps: 1) Use the rotating body (2) to control the angle of the sensor on the rotary indexing plate (1) so that both the radial and axial sensors are in the best measurement position. Fix the rotating body (2) firmly on the rotary indexing plate (1) and use the radial sensor clamp (3) and the axial sensor clamp (13) to clamp and position the sensor. At the same time, adjust the installation height of the rotary indexing plate (1) to ensure that the sensor measurement center is at the same height as the center of the standard ball on the spindle. 2) Once the measurement system is running smoothly, three high-precision displacement sensors positioned at the optimal measurement locations are used to synchronously collect the dynamic displacement data of the turntable spindle in real time. The three sets of displacement data collected are denoted as S1, S2, and S3, respectively. These three sets of data serve as the original basic data for subsequent analysis. 3) Due to the high noise interference in the raw displacement signals collected by each displacement sensor, a wavelet denoising algorithm is used to preprocess the raw signals. Then, the processed 20-revolution stable operation data is subjected to Fourier transform analysis to obtain the frequency domain signal. Finally, filtering techniques are used to remove the DC component, first-order harmonic component, and high-frequency harmonic components above the 50th order. The specific implementation method is as follows: Because the raw displacement signals collected by each displacement sensor contain high levels of noise interference, the raw signals... Perform wavelet transform to obtain wavelet coefficients: in, These are wavelet basis functions; wavelet coefficients are processed using either soft or hard thresholding. in, It is a threshold, based on the noise standard deviation. calculate: in, It is the signal length; perform inverse wavelet transform on the processed wavelet coefficients to obtain the denoised signal. ; For denoised signals Perform a Fourier transform to obtain the frequency domain signal: Then process it accordingly: Remove DC component: ; Remove first-order components: ,in The fundamental frequency; Remove high-frequency components after the 50th order: ; Finally, the signal is converted back to the time domain using the inverse Fourier transform: That is, get , , ; 4) Extract synchronous motion error and asynchronous motion error from the noise-reduced measurement data, and solve the mathematical model parameters using the measurement data based on the three-point error separation principle. First, the mathematical model is discretized, and the synchronous and asynchronous components are effectively separated in the frequency domain through Fourier transform and inverse Fourier transform. The synchronous component is obtained by calculating the average profile of multi-turn measurement data and is represented as integer harmonic components in the frequency domain. The asynchronous component corresponds to the non-integer harmonic components in the Fourier domain. Finally, based on the extracted synchronous motion error, the frequency domain three-point error separation algorithm is used to further separate and calculate the roundness error and spindle rotation error.

2. The method for measuring the rotational error of an ultra-precision rotating shaft system according to claim 1, characterized in that, The specific implementation method for step 2) is as follows: Once the measurement system is running smoothly, it simultaneously collects dynamic displacement data of the turntable spindle in real time using three high-precision displacement sensors positioned at optimal measurement locations. The three sets of displacement data collected are denoted as follows: , , Collect 20 revolutions of data.

3. The method for measuring the rotational error of an ultra-precision rotating shaft system according to claim 1, characterized in that, The specific implementation method for step 4) is as follows: After wavelet denoising, the discrete measurement signal is defined as: in: This refers to the error in synchronous motion. This refers to asynchronous motion error; The signal is converted to the frequency domain using Fourier transform: Two methods for extracting synchronous and asynchronous errors are employed: Method 1: Temporal Extraction Synchronization components The profile can be obtained by calculating the average profile from multiple measurement data, and it is represented in the time domain as follows. Asynchronous components The difference between the total error and the synchronization error is expressed in the time domain as: Method 2: Frequency Domain Extraction Synchronization components The average profile can be obtained by calculating the data from multiple measurements, and its Fourier transform is expressed as integer harmonics. in: For the fundamental frequency; Integer harmonic frequency; The unit impulse function; Inverse Fourier transform recovers the time-domain synchronization error signal: Asynchronous motion errors correspond to non-integer harmonics, which can be obtained by filtering out the synchronization component: Inverse Fourier transform recovers the time-domain synchronization error signal: To reduce the computational conversion between the time and frequency domains, denoising, synchronization error extraction, and asynchronous error extraction are all performed in the frequency domain. The principle of the matrix three-point method is as follows: By performing a Fourier transform on the measured circular profile, the complex profile curve is decomposed into a periodic waveform composed of harmonics of different orders. Among them, the angle variable is used Indicates the position on the measured circle profile; The DC component representing the measured circular profile reflects the average radius of the profile; the upper limit of the harmonic expansion order is M, indicating the highest order of the harmonic components considered; and It is the cosine of the m-th harmonic component; and These coefficients collectively constitute a complete characteristic description of the measured circular profile in the frequency domain, reflecting the magnitude and distribution characteristics of each harmonic component of the profile error; according to the least squares principle, the measured circular profile... The least-squares center coordinates (a, b) are: If used The roundness error is represented by the relationship between the coordinates. Merging If using The sum of all terms in the Fourier series of a circular profile, excluding the first-order component, is expressed as: Then we get new : If we define the radial rotational error motion of the rotating shaft as: During measurement, three sensors are fixed, and the workpiece is rotated clockwise around the axis of rotation. The output signals of the three sensors are as follows: The above equation can be written in matrix form: in: in: This represents the location of the sampling point, and its value range is: , The number of sampling points in each period; Indicates displacement sensor and The number of sampling interval points between axes is calculated using the following formula: ； This is a column vector consisting of the output signals of sensors 0, 1, and 2. Indicates after a delay , , Then, a column vector is formed by the combined motion of the measured circle's contour shape error and rotational error; The output coefficient matrix of the measurement sensor; To separate roundness error, it is necessary to ensure that: make =1, thus the weight coefficient is obtained: Will , , Substitute Zhongde in This is a discretized form of the series of circular contours; In actual measurement process It is a weighted sum of the output signals from the three sensors. It is an unknown discrete sequence that has periodicity, therefore Represented as: After the time delay, it can be written as: Then substitute Rewritten as: In the formula The error separation weight coefficient matrix for the three-point method is shown below. because so There is a unique solution: Therefore, the roundness error of the measured circle profile is Since the sensor signal acquires a circular profile signal, which consists of roundness error and rotation error, in order to separate the pure rotation error motion, the separated... Substitute back and combined get: make = = The above formula can then be written as: Then the least squares coordinates of the center of the measured circular profile are obtained. )for: The rotational error of the measured shaft is expressed as: 。 4. The method for measuring the rotational error of an ultra-precision rotating shaft system according to claim 1, characterized in that, Multiple radial sensor holders (3) and multiple axial sensor holders (13) are provided.

5. The method for measuring the rotational error of an ultra-precision rotating shaft system according to claim 1, characterized in that, The rotary indexing plate (1) uses a rotating structure to divide the circumference into 120 parts, and is used in conjunction with the rotating body (2), which can significantly improve the measurement step accuracy from 6° to 0.5°.

6. The method for measuring the rotational error of an ultra-precision rotating shaft system according to claim 1, characterized in that, The support rod is divided into a first support rod (9) and a second support rod (10).

7. The method for measuring the rotational error of an ultra-precision rotating shaft system according to claim 1, characterized in that, The damping system includes a spring (12) with nuts at both ends, and the damping system is mounted on the marble platform (16) via a fourth flange (14).

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