Spindle radial rotation error separation method based on multi-point method

Abstract

The invention provides a spindle radial rotation error separation method based on a multi-point method. The spindle radial rotation error separation method comprises the steps that firstly, displacement data of a spindle are collected through a first directional displacement sensor and a second directional displacement sensor; step 2, inputting displacement data into an error separation model, and outputting a forward rotation error and a backward rotation error; wherein the establishment of the error separation model comprises the following steps: (1) based on kinematics analysis of a main shaft, establishing measurement data of a main shaft radial rotation error test model to obtain a direction displacement error measurement model and a direction displacement error measurement model; and (2) eliminating a sensor installation offset error and a test rod roundness error based on an improved multi-point error separation method to obtain a pure spindle radial rotation error. According to the invention, on the basis of eliminating the offset error of sensor installation and the roundness error of the test detection rod in the measurement data, the pure spindle radial rotation error is obtained, and the high-precision measurement of the spindle radial rotation error is realized.

Description

Technical Field

[0001] This invention belongs to the field of CNC machine tool operation technology, specifically relating to a spindle radial rotation error separation method based on a multi-point method. Background Technology

[0002] As a key piece of equipment supporting modern manufacturing, CNC machine tools undertake the machining of various parts in the aerospace field. Their machining accuracy directly affects the performance of critical components in core equipment such as rocket engines and spacecraft, making them a vital guarantee for aerospace manufacturing and listed as the top of the "seven bottlenecks" that my country's manufacturing industry needs to overcome. This crucial equipment achieves multi-axis linkage through embedded computer digital programs, completing composite machining processes such as turning, milling, and drilling. Its positioning accuracy during machining typically reaches the micrometer level, making it irreplaceable in the precision machining of typical aerospace components.

[0003] As a core component of CNC machine tools, the spindle's precision during operation directly affects the machining quality of parts. A spindle system includes high-precision bearings, servo motors, hydraulic systems, and cooling devices. Typically, the spindle's radial accuracy needs to be monitored during high-speed rotation to prevent rotational errors from causing the machined parts to fail to meet design tolerances, reducing the machining accuracy of precision parts, or even resulting in non-compliant parts. Therefore, spindle rotational errors not only lead to unsatisfactory surface quality of machined parts and tool wear, but also reduce machine tool processing efficiency.

[0004] To obtain high-precision spindle radial rotation error, patent publication CN114218981B discloses a method for separating mandrel roundness error from spindle rotation error in CNC machine tools. While this method can separate mandrel roundness error from spindle error motion by extracting and using signal segments and their reverse method from synchronous error motion, it does not address or eliminate the influence of sensor installation offset error on the measured radial rotation error. Patent publication CN117890105A discloses an ultra-precision spindle measurement method based on multi-point error separation technology. Although it can significantly reduce the measurement uncertainty of traditional three-point error separation technology through frequency domain fusion algorithms and eliminate the influence of probe roundness profile on spindle measurement results, it also does not address the influence of sensor installation offset error on the measurement results.

[0005] In traditional spindle error testing equipment, the use of standard parts for spindle error measurement can have an impact. For example, the roundness error of the probe and the installation offset error of the sensor can affect the measurement results. In order to obtain the spindle radial rotation error, other errors in the measurement data need to be eliminated to achieve high-precision measurement of the spindle radial rotation error. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of existing technologies that cannot retain radial rotation error by eliminating other errors based on measurement data. Instead, it provides a spindle radial rotation error separation method based on a multi-point method. This method eliminates the offset error of sensor installation and the roundness error of the test bar from the measurement data by adjusting the distance between the displacement sensor and the surface of the test bar, thereby obtaining a pure spindle radial rotation error and achieving high-precision measurement of spindle radial rotation error.

[0007] To achieve the above objectives, the technical solution provided by this invention is:

[0008] A method for separating spindle radial rotation error based on a multi-point method includes the following steps:

[0009] Step 1, through To displacement sensor and The displacement data of the spindle is collected from the displacement sensor;

[0010] Step 2: Input the displacement data into the error separation model and output... Towards rotation error and The gyration error; wherein: the establishment of the error separation model includes:

[0011] (1) Based on the kinematic analysis of the spindle, the measurement data of the spindle radial rotation error test model were established, and the results were obtained. Displacement error measurement model and The displacement error measurement model is expressed as follows:

[0012] Formula (1)

[0013] In formula (1), express To the displacement sensor Orthogonal intersection of displacement sensors of Towards distance, express Shape error of the test bar in the direction, express The measured value of the displacement sensor, Indicates the radius of the measuring rod. This indicates the radial rotation error of the spindle. express The bias error of the sensor, ,in, express Installation bias error of displacement sensor express Installation offset error of displacement sensor;

[0014] Formula (2)

[0015] In formula (2), express To the displacement sensor Orthogonal intersection of displacement sensors of Towards distance, express The roundness error of the test bar in the direction. express The measured value of the displacement sensor;

[0016] (2) Based on the improved multi-point error separation method, the sensor installation bias error and the test bar roundness error are eliminated to obtain the pure spindle radial rotation error.

[0017] As a further limitation of the present invention, in step two, the test system in the spindle radial rotation error test model obtains the displacement data input therein through an error separation model. Radial rotation error values ​​and Radial rotation error value; specifically:

[0018] Step (21) is based on Radial rotation error values ​​and The radial rotation error value is used to eliminate the sensor installation offset error through the fully adaptive noise set empirical mode decomposition algorithm in the corresponding improved multi-point error separation method within the error separation model; specifically, Radial rotation error values ​​and After adding Gaussian white noise to the radial rotation error value, EMD and IMF are decomposed again. The average value is calculated first and the residual is updated. The above process is repeated until the decomposition is completed and the decomposed signal is obtained.

[0019] Step (22) Install the two eddy current displacement sensors on the test bar respectively. Xianghe Direction, assuming collection per lap 1 data point, spindle rotates continuously Rotation, two displacement sensors collect 2 sets of data Displacement data; through the analysis of The data is processed to obtain the roundness error data of the test bar; after the second stage measurement of the spindle, the roundness error data of the test bar obtained from the first measurement is substituted into the spindle rotation error to solve the spindle rotation error.

[0020] use The roundness error of the outer circle of the test bar is calculated from the displacement data collected by the displacement sensor, and the test results are output by the spindle radial rotation error test model.

[0021] As a further limitation of the present invention, in step (21), the fully adaptive noise set empirical mode decomposition algorithm for eliminating sensor installation bias error includes the following detailed steps:

[0022] Step (a) Add Gaussian white noise to the signal to be decomposed In the process, new signals were obtained. ,in, This represents Gaussian white noise, where Signal to be decomposed include Radial rotation error values ​​and Radial rotation error value;

[0023] For new signals EMD decomposition was performed to obtain the first-order intrinsic mode components. , is represented as:

[0024] Formula (3)

[0025] In formula (3), Indicates the first One modal component, Indicates the first The residuals after EMD decomposition;

[0026] Step (b) performs an overall average of the generated N modal components to obtain the first intrinsic mode component of the CEEMDAN decomposition. The expression is:

[0027] Formula (4)

[0028] Step (c) Calculate the residual after removing the first modal component. The expression is:

[0029] Formula (5)

[0030] In formula (5), Indicates the signal to be decomposed. Indicates the first intrinsic mode component;

[0031] Step (d) Residual after the first modal component A new signal is obtained by re-introducing paired Gaussian white noise. The new signal is then used as the carrier for EMD decomposition to obtain the first-order modal components. Therefore, the second intrinsic mode component is obtained by performing CEEMDAN decomposition. , is represented as:

[0032] Formula (6)

[0033] In formula (6), Indicates the first One first-order modal component;

[0034] Step (e) Calculate the residual after removing the second intrinsic mode component. , is represented as:

[0035] Formula (7)

[0036] In formula (7), Indicates the signal to be decomposed. Indicates the second intrinsic mode component;

[0037] Step (f) repeats steps (a) to (e) until the acquired residual signal is a monotonic function, at which point the signal to be decomposed is decomposed. This can be represented as:

[0038] Formula (8)

[0039] In formula (8), Indicates the first Each intrinsic mode component Indicates the first Error after each intrinsic mode component.

[0040] As a further limitation of the present invention, in step (22), the error separation model removes the roundness error of the test bar based on error data, and its calculation process includes:

[0041] Step (a') calculates the shape error, with the orthogonal intersection point of the two displacement sensors as the coordinate origin. When the spindle rotates, for the first The geometric relationship between the sampling points is expressed as follows:

[0042] Formula (9)

[0043] In formula (9), Indicates the outer circle contour of the test bar and The distance from the intersection point of the positive axes to the origin of the coordinate system. This represents the distance from the outer contour of the axis trajectory to the origin of the coordinate system. This represents the distance from the axis of motion trajectory to the outer contour of the mandrel. ,in, This indicates the distance from the axis center trajectory to the outer circle contour of the test bar when it is not being tested. Indicates the shape error of the test bar;

[0044] Continuous sampling Given a set of displacement data points, with each lap's data points forming a dataset, sum the data points from each dataset and solve for the result. The average of the datasets is expressed as:

[0045] Formula (10)

[0046] In formula (10), This represents the distance from the origin of the coordinate system to the point where the outer contour of the test bar intersects the positive axis. This represents the distance from the outer contour of the axis trajectory to the origin of the coordinate system. This represents the distance from the axis of motion trajectory to the outer circle contour of the mandrel;

[0047] For the collected For each sampled data point, the roundness error remains constant, let Collect a sufficient number of displacement data samples, spindle rotation error tending to constant Rewriting formula (10) yields formula (11), whose expression is:

[0048] Formula (11)

[0049] In formula (11), This represents the distance from the axis of motion trajectory to the outer contour of the mandrel. This means that data collected by non-sensors needs to be derived through geometric relationships to form a functional relationship that includes the actual measurement data.

[0050] According to formula (11), the spindle rotation error is constant. from Data separated from the sampled data; data not collected by sensors. A functional relationship incorporating actual measurement data was derived through geometric relationships;

[0051] Considering that the roundness error of the spindle is included in the distance from the axis of motion trajectory to the outer circle profile of the mandrel. In, it is represented as:

[0052] Formula (12)

[0053] In formula (12), Indicates the distance from the displacement sensor to the coordinate origin. The distance, which is constant; This represents the displacement data collected by the displacement sensor;

[0054] Because the roundness error of the spindle is included In Chinese, the simplified roundness error is expressed as:

[0055] Formula (13)

[0056] In formula (13), This represents the distance from the axis of motion trajectory to the outer contour of the mandrel. This indicates the distance from the axis center trajectory to the outer circle contour of the test bar when it is not being tested. This represents the roundness error of the test bar, where, , This represents the average value of the actual rotation radius of the spindle. Indicates a constant. Indicates the distance from the displacement sensor to the coordinate origin. distance, ,in, This represents the average value of the displacement data actually collected by the displacement sensor for each revolution. This indicates that the displacement sensor actually collected the data at the first revolution of each rotation. The average value of the point displacement dataset;

[0057] The mathematical model for roundness error is expressed as follows:

[0058] Formula (14)

[0059] In formula (14), This represents the average value of the data collected by the displacement sensor. This represents the average value of the data collected by the displacement sensor. This represents the average value of the displacement dataset at the i-th point during each revolution, actually collected by the displacement sensor.

[0060] Step (b') calculates the rotation error. After the measurement and calculation in step (a'), the roundness error of the tested bar profile is obtained. The operation is repeated to perform the second stage measurement to obtain the rotation error of the spindle, which is expressed as:

[0061] Formula (15)

[0062] In formula (15), This represents the distance from the outer contour of the axis trajectory to the origin of the coordinate system. Indicates the outer circle contour of the test bar and The distance from the intersection point of the positive axes to the origin of the coordinate system. This represents the distance from the axis of motion trajectory to the outer circle contour of the mandrel;

[0063] Considering that the rotational error is included in the spindle's center trajectory, the spindle's rotational error is expressed as:

[0064] Formula (16)

[0065] In formula (16), This represents the radius of the circle theoretically formed by the axis. express Spindle rotation error;

[0066] Based on geometric relationships, we obtain:

[0067] Formula (17)

[0068] In formula (17), Indicates the outer circle contour of the test bar and The distance from the intersection point of the positive axes to the origin of the coordinate system. Indicates the roundness error of the mandrel. This indicates the distance from the axis center trajectory to the outer circle contour of the test bar when it is not being tested. Indicates the distance from the displacement sensor to the coordinate origin. distance, This represents the displacement data collected by the displacement sensor;

[0069] The simplified spindle rotation error is expressed as:

[0070] Formula (18)

[0071] In formula (18), express spindle rotation error express spindle rotation error This indicates that the displacement sensor actually collected the data at the first revolution of each rotation. The average value of the point dataset. Indicates the roundness error of the test bar;

[0072] Based on the above measurement steps, the spindle rotation error is measured in the Y direction. This leads to the spindle rotation error.

[0073] As a further limitation of the present invention, the testing process of the error separation model in step two includes:

[0074] Based on the spindle radial rotation accuracy test model To displacement sensor and The error data collected by the displacement sensor includes sensor installation offset error and roundness error, among which:

[0075] The sensor installation bias error is eliminated by a fully adaptive noise set empirical mode decomposition algorithm;

[0076] The roundness error is removed by the bar roundness error separation algorithm.

[0077] The advantages of this invention are:

[0078] 1. This invention is based on the change in distance between the displacement sensor and the surface of the test bar, eliminating the offset error of sensor installation and the roundness error of the test bar in the measurement data, and obtaining the pure spindle radial rotation error, thus achieving high-precision measurement of spindle radial rotation error.

[0079] 2. Based on the established spindle radial rotation accuracy test model, the data collected by the displacement sensor contains bias errors caused by sensor bias, which cannot be eliminated by Fourier transform. Therefore, this invention eliminates bias errors by using fully adaptive noise set empirical mode decomposition.

[0080] 3. To verify the effectiveness and correctness of the improved multi-point error separation algorithm, this invention simulates and generates radial motion error data. Based on the characteristics of the actual data, the simulated signal consists of random values ​​and a sine function, specifically composed of rotation error, offset error, and roundness error. After separation by the improved multi-point error separation algorithm, the rotation error and roundness error of the spindle are obtained. The separation results from the simulation experiment show that the algorithm of this invention has a very good separation effect.

[0081] 4. This invention uses an X-axis sensor to collect displacement data, which can be used to calculate the shape error of the outer circle of the test bar, laying the foundation for the calculation of the spindle rotation error.

[0082] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0083] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0084] Figure 1 The present invention provides a flowchart of a spindle radial rotation error separation method based on a multi-point method;

[0085] Figure 2 : A schematic diagram of the spindle radial error test provided by this invention;

[0086] Figure 3 : A schematic diagram of the error separation model provided by this invention;

[0087] Figure 4 The CEEMDAN algorithm flowchart provided by this invention;

[0088] Figure 5 : Schematic diagram of the error separation measurement method provided by this invention;

[0089] Figure 6 Illustration of the radial error data generated in the spindle radial rotation error separation method provided by this invention;

[0090] Figure 7 The following is a comparison diagram of the separation results of radial rotation error provided by the present invention, wherein (a) is the roundness error diagram after separation and (b) is the rotation error diagram after separation. Detailed Implementation

[0091] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0092] like Figure 1 As shown in the figure, this invention discloses a method for separating the radial rotation error of a spindle based on a multi-point method, including the following steps:

[0093] Step 1, through To displacement sensor and The displacement data of the spindle is collected from the displacement sensor;

[0094] Step 2: Input the displacement data into the error separation model and output... Towards rotation error and The gyration error; where: the establishment of the error separation model includes:

[0095] (1) Due to the influence of the spindle radial rotation error, therefore, , and They are not at the same point. During spindle rotation, the roundness error of the probe, the sensor's installation offset error, and the spindle's rotation error will all cause changes in the distance between the displacement sensor and the surface of the probe being measured. However, the distance from the X-axis displacement sensor to... distance Since it is fixed and unchanging, this embodiment of the invention establishes the measurement data of the spindle radial rotation error test model based on the kinematic analysis of the spindle, and obtains... Displacement error measurement model and The displacement error measurement model is expressed as follows:

[0096] Formula (1)

[0097] In formula (1), express To the displacement sensor Orthogonal intersection of displacement sensors of Towards distance, express Shape error of the test bar in the direction, express The measured value of the displacement sensor, Indicates the radius of the measuring rod. This indicates the radial rotation error of the spindle. express The bias error of the sensor, ,in, express Installation bias error of displacement sensor express Installation offset error of displacement sensor;

[0098] Formula (2)

[0099] In formula (2), express To the displacement sensor Orthogonal intersection of displacement sensors of Towards distance, express The roundness error of the test bar in the direction. express The measured value of the displacement sensor.

[0100] (2) Based on the improved multi-point error separation method, the sensor installation bias error and the test bar roundness error are eliminated to obtain the pure spindle radial rotation error.

[0101] Among them, such as Figure 3 As shown, the testing process of the above error separation model includes: based on the spindle radial rotation accuracy test model, To displacement sensor and The error data collected by the displacement sensor contains sensor installation offset error and roundness error. Specifically, the sensor installation offset error is removed by a fully adaptive noise set empirical mode decomposition algorithm, and the roundness error is removed by a bar roundness error separation algorithm.

[0102] In step (1) of the above embodiment of the present invention, the radial error data of the tested spindle includes the roundness error of the test bar, the offset error of the displacement sensor installation, etc. In order to accurately calculate the radial rotation error of the spindle, the offset error of the sensor installation and the roundness error of the test bar need to be eliminated. Figure 2 The diagram shown illustrates the test for the spindle radial error. Figure 2 middle For the ideal center of rotation, This represents the actual average rotation center trajectory of the spindle.

[0103] In step two of the embodiments of the present invention, the test system in the spindle radial rotation error test model obtains the displacement data input into it through the error separation model. Radial rotation error values ​​and Radial rotation error value; specifically:

[0104] Step (21) is based on Radial rotation error values ​​and The radial rotation error is eliminated by using a fully adaptive noise set empirical mode decomposition algorithm in the correspondingly improved multi-point error separation method within the error separation model to remove the sensor installation offset error; specifically, Radial rotation error values ​​and After adding Gaussian white noise to the radial rotation error value, EMD (Empirical Mode Decomposition) and IMF (Intrinsic Modal Function) are performed again. The average value is calculated first, and then the residual is updated. The above process is repeated until the decomposition is completed, and the decomposed signal is obtained.

[0105] like Figure 4 As shown, in step (21) of this embodiment of the invention, the sensor installation bias error is eliminated by the fully adaptive noise set empirical mode decomposition algorithm. The detailed steps include:

[0106] Step (a) Add Gaussian white noise to the signal to be decomposed In the process, new signals were obtained. ,in, This represents Gaussian white noise, where Signal to be decomposed include Radial rotation error values ​​and Radial rotation error value;

[0107] For new signals EMD decomposition was performed to obtain the first-order intrinsic mode components. , is represented as:

[0108] Formula (3)

[0109] In formula (3), Indicates the first One modal component, Indicates the first The residuals after EMD decomposition;

[0110] like Figure 4 As shown, step (b) performs an overall average of the generated N modal components to obtain the first intrinsic mode component of the CEEMDAN decomposition. The expression is:

[0111] Formula (4)

[0112] Step (c) Calculate the residual after removing the first modal component. The expression is:

[0113] Formula (5)

[0114] In formula (5), Indicates the signal to be decomposed. Indicates the first intrinsic mode component;

[0115] Step (d) Residual after the first modal component A new signal is obtained by re-introducing paired Gaussian white noise. The new signal is then used as the carrier for EMD decomposition to obtain the first-order modal components. Therefore, the second intrinsic mode component is obtained by performing CEEMDAN decomposition. It is represented as:

[0116] Formula (6)

[0117] In formula (6), Indicates the first One first-order modal component;

[0118] Step (e) calculates the error after removing the second intrinsic mode component, which is expressed as:

[0119] Formula (7)

[0120] In formula (7), Indicates the signal to be decomposed. Indicates the second intrinsic mode component;

[0121] Step (f) repeats steps (a) to (e) until the acquired residual signal is a monotonic function, at which point the signal to be decomposed is decomposed. This can be represented as:

[0122] Formula (8)

[0123] In formula (8), Indicates the first Each intrinsic mode component Indicates the first Error after each intrinsic mode component.

[0124] Step (22) During the shape error separation process of the measuring bar, two eddy current displacement sensors are respectively installed on the measuring bar. Xianghe Assuming data is collected every lap... 1 data point, spindle rotates continuously Rotation, two displacement sensors can collect two sets of data. Displacement data; through the analysis of The data is processed to obtain the roundness error data of the test bar. After the second stage measurement of the spindle, the shape error of the first measurement is substituted into the solution of the spindle rotation error; The roundness error of the outer circle of the test bar is calculated from the displacement data collected by the displacement sensor, and the test results are output by the spindle radial rotation error test model.

[0125] like Figure 5 As shown, in step (22) of this embodiment of the invention, the error separation model removes the roundness error of the test bar based on the error data, and its calculation process includes:

[0126] Step (a') calculates the shape error, with the orthogonal intersection point of the two displacement sensors as the coordinate origin. When the spindle rotates, for the first The geometric relationship between the sampling points is expressed as follows:

[0127] Formula (9)

[0128] In formula (9), Indicates the outer circle contour of the test bar and The distance from the intersection point of the positive axes to the origin of the coordinate system. This represents the distance from the outer contour of the axis trajectory to the origin of the coordinate system. This represents the distance from the axis of motion trajectory to the outer contour of the mandrel. ,in, This indicates the distance from the axis center trajectory to the outer circle contour of the test bar when it is not being tested. Indicates the shape error of the test bar;

[0129] Continuous sampling Given a set of displacement data points, with each lap's data points forming a dataset, sum the data points from each dataset and solve for the result. The average of the datasets is expressed as:

[0130] Formula (10)

[0131] In formula (10), This represents the distance from the origin of the coordinate system to the point where the outer contour of the test bar intersects the positive axis. This represents the distance from the outer contour of the axis trajectory to the origin of the coordinate system. This represents the distance from the axis of motion trajectory to the outer circle contour of the mandrel;

[0132] For the collected For each sampled data point, the roundness error remains constant, let As long as enough displacement data samples are collected, the spindle rotation error will be reduced. It will tend to a constant. Rewriting formula (10) yields formula (11), whose expression is:

[0133] Formula (11)

[0134] In formula (11), This represents the distance from the axis of motion trajectory to the outer contour of the mandrel. This means that data collected by non-sensors needs to be derived through geometric relationships to form a functional relationship that includes the actual measurement data.

[0135] According to formula (11), the spindle rotation error is constant. from Data separated from the sampled data; data not collected by sensors. The data is not collected by sensors; a functional relationship containing actual measurement data is derived through geometric relationships. This considers that the roundness error of the spindle is included in the distance from the axis's motion trajectory to the outer circle profile of the spindle. In, it is represented as:

[0136] Formula (12)

[0137] In formula (12), Indicates the distance from the displacement sensor to the coordinate origin. The distance, which is constant; This represents the displacement data acquired by the displacement sensor; since the roundness error of the spindle is included... In Chinese, the simplified roundness error is expressed as:

[0138] Formula (13)

[0139] In formula (13), This represents the distance from the axis of motion trajectory to the outer contour of the mandrel. This indicates the distance from the axis center trajectory to the outer circle contour of the test bar when it is not being tested. This represents the roundness error of the test bar, where, , This represents the average value of the actual rotation radius of the spindle. Indicates a constant. Indicates the distance from the displacement sensor to the coordinate origin. distance, ,in, This represents the average value of the displacement data actually collected by the displacement sensor for each revolution. This indicates that the displacement sensor actually collected the data at the first revolution of each rotation. The average value of the point displacement dataset.

[0140] The mathematical model for roundness error is expressed as follows:

[0141] Formula (14)

[0142] In formula (14), This represents the average value of the data collected by the displacement sensor. This represents the average value of the data collected by the displacement sensor. This represents the average value of the displacement data set at the first point in each revolution actually collected by the displacement sensor. In this embodiment of the invention, the shape error of the outer circle of the test bar can be calculated by using a single X-axis sensor to collect displacement data, thus laying the foundation for the calculation of the spindle rotation error.

[0143] Step (b') calculates the rotation error. After the first stage of measurement is completed, the shape error of the tested bar profile is obtained. After the measurement and calculation in step (a'), the roundness error of the tested bar profile is obtained. The second stage of measurement is performed by repeating the previous operation to obtain the rotation error of the spindle, expressed as:

[0144] Formula (15)

[0145] In formula (15), This represents the distance from the outer contour of the axis trajectory to the origin of the coordinate system. Indicates the outer circle contour of the test bar and The distance from the intersection point of the positive axes to the origin of the coordinate system. This indicates the distance from the axis of motion trajectory to the outer circle contour of the mandrel.

[0146] Considering that the rotational error is included in the spindle's axis trajectory, the spindle's rotational error can be obtained and expressed as:

[0147] Formula (16)

[0148] In formula (16), This represents the radius of the circle theoretically formed by the axis. express Spindle rotation error.

[0149] Based on geometric relationships, we obtain:

[0150] Formula (17)

[0151] In formula (17), Indicates the outer circle contour of the test bar and The distance from the intersection point of the positive axes to the origin of the coordinate system. Indicates the roundness error of the mandrel. This indicates the distance from the axis center trajectory to the outer circle contour of the test bar when it is not being tested. Indicates the distance from the displacement sensor to the coordinate origin. distance, This represents the displacement data collected by the displacement sensor.

[0152] After simplification, the spindle rotation error is obtained, expressed as:

[0153] Formula (18)

[0154] In formula (18), express spindle rotation error express The average value of the data collected by the displacement sensor This indicates that the displacement sensor actually collected the data at the first revolution of each rotation. The average value of the point dataset. This indicates the roundness error of the test bar.

[0155] According to the above measurement steps, this embodiment of the invention measures the spindle rotation error in the Y direction. This leads to the spindle rotation error.

[0156] To verify the effectiveness and correctness of the improved multi-point error separation algorithm, radial motion error data was simulated. Based on the characteristics of the actual data, the simulated signal consisted of random values ​​and a sine function, such as... Figure 6 As shown, the data consists of rotational error, offset error, and roundness error. After separation using the algorithm described above, the spindle's rotational error and roundness error can be obtained, as shown below. Figure 7 As shown, Figure 7 (a) represents the roundness error after separation. Figure 7 (b) represents the rotational error after separation. By comparing the separation results, from... Figure 7 As shown in the figure, the spindle error separation algorithm has a very good separation effect.

[0157] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A method for separating spindle radial rotation error based on a multi-point method, characterized in that, Includes the following steps: Step 1, through To displacement sensor and The displacement data of the spindle is collected from the displacement sensor; Step 2: Input the displacement data into the error separation model and output... Towards rotation error and The gyration error; wherein: the establishment of the error separation model includes: (1) Based on the kinematic analysis of the spindle, the measurement data of the spindle radial rotation error test model were established, and the results were obtained. Displacement error measurement model and The displacement error measurement model is expressed as follows: Formula (1) In formula (1), express To the displacement sensor Orthogonal intersection of displacement sensors of Towards distance, express Shape error of the test bar in the direction, express The measured value of the displacement sensor, Indicates the radius of the measuring rod. This indicates the radial rotation error of the spindle. express The bias error of the sensor, ,in, express Installation bias error of displacement sensor express Installation offset error of displacement sensor; Formula (2) In formula (2), express To the displacement sensor Orthogonal intersection of displacement sensors of Towards distance, express The roundness error of the test bar in the direction. express The measured value of the displacement sensor; (2) Based on the improved multi-point error separation method, the sensor installation bias error and the test bar roundness error are eliminated to obtain the pure spindle radial rotation error.

2. The spindle radial rotation error separation method based on a multi-point method according to claim 1, characterized in that, In step two, the test system in the spindle radial rotation error test model takes the input displacement data and obtains it through the error separation model. Radial rotation error values ​​and Radial rotation error value; specifically: Step (21) is based on Radial rotation error values ​​and The radial rotation error value is used to eliminate the sensor installation offset error through the fully adaptive noise set empirical mode decomposition algorithm in the corresponding improved multi-point error separation method within the error separation model; specifically, Radial rotation error values ​​and After adding Gaussian white noise to the radial rotation error value, EMD and IMF are decomposed again. The average value is calculated first and the residual is updated. The above process is repeated until the decomposition is completed and the decomposed signal is obtained. Step (22) Install the two eddy current displacement sensors on the test bar respectively. Xianghe Direction, assuming collection per lap 1 data point, spindle rotates continuously Rotation, two displacement sensors collect 2 sets of data Displacement data; through the analysis of The data is processed to obtain the roundness error data of the test bar; After the second stage of spindle measurement, the roundness error data of the test bar obtained from the first measurement is used to solve for the spindle rotation error; use The roundness error of the outer circle of the test bar is calculated from the displacement data collected by the displacement sensor, and the test results are output by the spindle radial rotation error test model.

3. The spindle radial rotation error separation method based on a multi-point method according to claim 2, characterized in that, In step (21), the fully adaptive noise set empirical mode decomposition algorithm eliminates sensor installation bias errors, and its detailed steps include: Step (a) Add Gaussian white noise to the signal to be decomposed In the process, new signals were obtained. ,in, This represents Gaussian white noise, where Signal to be decomposed include Radial rotation error values ​​and Radial rotation error value; For new signals EMD decomposition was performed to obtain the first-order intrinsic mode components. , is represented as: Formula (3) In formula (3), Indicates the first One modal component, Indicates the first The residuals after EMD decomposition; Step (b) performs an overall average of the generated N modal components to obtain the first intrinsic mode component of the CEEMDAN decomposition. The expression is: Formula (4) Step (c) Calculate the residual after removing the first modal component. The expression is: Formula (5) In formula (5), Indicates the signal to be decomposed. Indicates the first intrinsic mode component; Step (d) Residual after the first modal component A new signal is obtained by re-introducing paired Gaussian white noise. The new signal is then used as the carrier for EMD decomposition to obtain the first-order modal components. Therefore, the second intrinsic mode component is obtained by performing CEEMDAN decomposition. , is represented as: Formula (6) In formula (6), Indicates the first One first-order modal component; Step (e) Calculate the residual after removing the second intrinsic mode component. , is represented as: Formula (7) In formula (7), Indicates the signal to be decomposed. Indicates the second intrinsic mode component; Step (f) repeats steps (a) to (e) until the acquired residual signal is a monotonic function, at which point the signal to be decomposed is decomposed. This can be represented as: Formula (8) In formula (8), Indicates the first Each intrinsic mode component Indicates the first Error after each intrinsic mode component.

4. The spindle radial rotation error separation method based on a multi-point method according to claim 2, characterized in that, In step (22), the error separation model removes the roundness error of the test bar based on the error data, and its calculation process includes: Step (a') calculates the shape error, with the orthogonal intersection point of the two displacement sensors as the coordinate origin. When the spindle rotates, for the first The geometric relationship between the sampling points is expressed as follows: Official(9) In formula (9), Indicates the outer circle contour of the test bar and The distance from the intersection point of the positive axes to the origin of the coordinate system. This represents the distance from the outer contour of the axis trajectory to the origin of the coordinate system. This represents the distance from the axis of motion trajectory to the outer contour of the mandrel. ,in, This indicates the distance from the axis center trajectory to the outer circle contour of the test bar when it is not being tested. Indicates the shape error of the test bar; Continuous sampling Given a set of displacement data points, with each lap's data points forming a dataset, sum the data points from each dataset and solve for the result. The average of the datasets is expressed as: Official(10) In formula (10), This represents the distance from the origin of the coordinate system to the point where the outer contour of the test bar intersects the positive axis. This represents the distance from the outer contour of the axis trajectory to the origin of the coordinate system. This represents the distance from the axis of motion trajectory to the outer circle contour of the mandrel; For the collected For each sampled data point, the roundness error remains constant, let Collect a sufficient number of displacement data samples, spindle rotation error tending to constant Rewriting formula (10) yields formula (11), whose expression is: Official(11) In formula (11), This represents the distance from the axis of motion trajectory to the outer contour of the mandrel. This means that data collected by non-sensors needs to be derived through geometric relationships to form a functional relationship that includes the actual measurement data. According to formula (11), the spindle rotation error is constant. from Data separated from the sampled data; data not collected by sensors. A functional relationship incorporating actual measurement data was derived through geometric relationships; Considering that the roundness error of the spindle is included in the distance from the axis of motion trajectory to the outer circle profile of the mandrel. In, it is represented as: Formula(12) In formula (12), Indicates the distance from the displacement sensor to the coordinate origin. The distance, which is constant; This represents the displacement data collected by the displacement sensor; Because the roundness error of the spindle is included In Chinese, the simplified roundness error is expressed as: Official(13) In formula (13), This represents the distance from the axis of motion trajectory to the outer contour of the mandrel. This indicates the distance from the axis center trajectory to the outer circle contour of the test bar when it is not being tested. This represents the roundness error of the test bar, where, , This represents the average value of the actual rotation radius of the spindle. Indicates a constant. Indicates the distance from the displacement sensor to the coordinate origin. distance, ,in, This represents the average value of the displacement data actually collected by the displacement sensor for each revolution. This indicates that the displacement sensor actually collected the data at the first revolution of each rotation. The average value of the point displacement dataset; The mathematical model for roundness error is expressed as follows: Official(14) In formula (14), This represents the average value of the data collected by the displacement sensor. This represents the average value of the data collected by the displacement sensor. This represents the average value of the displacement dataset at the i-th point during each revolution, actually collected by the displacement sensor. Step (b') calculates the rotation error. After the measurement and calculation in step (a'), the roundness error of the tested bar profile is obtained. The operation is repeated to perform the second stage measurement to obtain the rotation error of the spindle, which is expressed as: Official(15) In formula (15), This represents the distance from the outer contour of the axis trajectory to the origin of the coordinate system. Indicates the outer circle contour of the test bar and The distance from the intersection point of the positive axes to the origin of the coordinate system. This represents the distance from the axis of motion trajectory to the outer circle contour of the mandrel; Considering that the rotational error is included in the spindle's center trajectory, the spindle's rotational error is expressed as: Official(16) In formula (16), This represents the radius of the circle theoretically formed by the axes. express Spindle rotation error; Based on geometric relationships, we obtain: Official(17) In formula (17), Indicates the outer circle contour of the test bar and The distance from the intersection point of the positive axes to the origin of the coordinate system. Indicates the roundness error of the mandrel. This indicates the distance from the axis center trajectory to the outer circle contour of the test bar when it is not being tested. Indicates the distance from the displacement sensor to the coordinate origin. distance, This represents the displacement data collected by the displacement sensor; The simplified spindle rotation error is expressed as: Official(18) In formula (18), express spindle rotation error express The average value of the data collected by the displacement sensor This indicates that the displacement sensor actually collected the data at the first revolution of each rotation. The average value of the point dataset. Indicates the roundness error of the test bar; Based on the above measurement steps, the spindle rotation error is measured in the Y direction. This leads to the spindle rotation error.

5. The spindle radial rotation error separation method based on a multi-point method according to claim 1, characterized in that, The testing process for the error separation model in step two includes: Based on the spindle radial rotation accuracy test model To displacement sensor and The error data collected by the displacement sensor includes sensor installation offset error and roundness error, among which: The sensor installation bias error is eliminated by a fully adaptive noise set empirical mode decomposition algorithm; The roundness error is removed by the bar roundness error separation algorithm.

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