A circle profile error separation method based on discrete sampling point cumulative term and method

Abstract

A circle profile error separation method based on discrete sampling point cumulative term and method, it relates to a kind of circle profile error separation method, to solve the problems such as harmonic suppression and long measurement time, complex calculation in prior art, the present application includes the following steps: first position signal is obtained by sensor acquisition, error separation platform is applied to the workpiece to be measured to carry out indexing, so that the workpiece to be measured and instrument rotation main shaft produce a fixed size indexing angle θ=2π / N, i.e. turn through unit sampling angle size, sensor collects second indexing signal at this time, finally, the first and second indexing signals collected are processed, the main shaft rotation error signal is separated from the circle profile error information, and the circle profile signal after removing error is obtained.The signal obtained by the discrete sampling point cumulative term and method for roundness error separation is consistent with the original given signal, which verifies the feasibility and effectiveness of the method for roundness error separation from principle.The present application belongs to the technical field of ultra-precision geometric measurement.

Description

TECHNICAL FIELD

[0001] The present application relates to a circle profile error separation method, in particular to a circle profile error separation method based on discrete sampling point cumulative term and method, and belongs to the field of ultra-precision geometric measurement. BACKGROUND

[0002] Since the 1960s, with the development of emerging science and technology such as atomic energy, aerospace, microelectronics, information and biological engineering, the measurement accuracy of precision spindle system rotation error and workpiece roundness error has been increasingly required. For example, in the process of ultra-precision machining and measurement, the roundness error of the specified circle section of the quartz hemisphere of the round standard used for comparison and calibration is generally between 10nm and 50nm; the roundness tolerance of the normal direction of any circle section of the curved mirror in the X-ray microscope is 5nm; and the workpiece shape error is usually in the nanometer level in the fields of aspherical lens, free-form surface and microstructure optics.

[0003] In order to ensure high-precision measurement, the error brought by the measuring instrument can only account for a small part of the allowable error of the workpiece, about (1 / 3-1 / 10). However, in fact, many workpiece precision indicators have reached or are higher than the precision level of the highest precision roundness measuring instrument currently used for measuring roundness. If the measuring precision of the instrument is to be further improved, it is difficult to meet the growing requirements by relying only on a large amount of mechanical processing investment. Therefore, on the basis of not further improving the rotation accuracy of the spindle, the precision measurement of the workpiece circle profile is a valuable research problem.

[0004] Error separation technology is a measurement technology that separates useful signal components from error signals through information source transformation or model parameter estimation. It can achieve a precision level that is difficult to achieve by "hard technology" at a relatively small cost, so error separation technology is rapidly accepted by scholars and experts from various countries. Error separation technology is mainly divided into two types: indexing method and multi-probe method. The accuracy of the multi-probe method is mainly limited by the differences in electrical characteristics between the probes, making it difficult to further improve the accuracy. The multi-step method is commonly used in the indexing method, which is complex in calculation and has a principle error. SUMMARY

[0005] The present application is to solve the problems of harmonic suppression, long measurement time, and complex calculation in the prior art, and further proposes a circle profile error separation method based on discrete sampling point cumulative term and method.

[0006] The technical scheme adopted by the present application to solve the above problems is:

[0007] In the super-precision roundness measurement, the rotation error of the main shaft of the roundness gauge will be mixed into the roundness profile signal to be measured due to the structure limitation of the roundness gauge. Therefore, in order to realize the roundness measurement with higher precision, the error separation algorithm is needed to remove the rotation error of the main shaft, so as to obtain the pure roundness signal.

[0008] The present application comprises the following steps:

[0009] Step one, the first rotation position signal is acquired by the sensor,

[0010] Step two, the error separation table is applied to rotate the workpiece to be measured, so that a fixed rotation angle θ=2π / N between the workpiece to be measured and the rotation main shaft of the instrument is generated, that is, the unit sampling angle size is rotated, and the second rotation position signal is acquired by the sensor at this time,

[0011] Step three, the first rotation position signal and the second rotation position signal acquired by the sensor are processed, the rotation error signal of the main shaft is separated from the roundness profile error information, and the roundness profile signal after removing the error is obtained.

[0012] The present application has the following beneficial effects:

[0013] 1. The present application proposes a roundness profile error separation method based on the discrete sampling point cumulative term and method without harmonic suppression, aiming at the problems of harmonic suppression and long measurement time, complex calculation and the like in the rotation method, so as to reduce the influence of harmonic suppression in the roundness error separation process, and improve the roundness profile measurement precision.

[0014] 2. In the super-precision roundness measurement, the rotation error of the main shaft of the roundness gauge will be mixed into the roundness profile signal to be measured due to the structure limitation of the roundness gauge. Therefore, in order to realize the roundness measurement with higher precision, the error separation algorithm is needed to remove the rotation error of the main shaft, so as to obtain the pure roundness signal.

[0015] 3. The present application can realize the nanometer-level super-precision roundness measurement. The rotation error of the main shaft in the measurement signal is removed through the additional information source conversion between the two rotation positions, the pure roundness profile measurement error is obtained, and the roundness of the workpiece is measured more accurately and precisely.

[0016] 4. The signal obtained by the roundness error separation through the discrete sampling point cumulative term and method is consistent with the original given signal, which verifies the feasibility and effectiveness of the roundness error separation method in principle. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 is the principle diagram of the discrete sampling point cumulative term and method of the present application;

[0018] Figure 2 is the signal diagram collected at the two rotation positions of the present application;

[0019] Figure 3 is a comparison between the signal obtained by roundness error separation and the original signal;

[0020] wherein a is the roundness error signal of the workpiece compared to the contour;

[0021] b is the spindle rotation error signal compared. DETAILED DESCRIPTION

[0022] Specific implementation one: combined Figure 1 To Figure 3 illustrates the present embodiment, the present embodiment describes a roundness error separation method based on discrete sampling point cumulative sum method, the present embodiment is to verify the effect of discrete sampling point cumulative sum method roundness error separation, generate spindle rotation error signal and roundness error signal, and from which can be obtained the first shift and the second shift sensor acquisition signal, two shift acquisition signal as shown below Figure 2 .

[0023] Subsequently, the discrete sampling point cumulative sum roundness error separation method is applied to process the acquisition signal at the two shifts, and the roundness error signal and the spindle rotation error signal separated by the method can be calculated and compared with the two original signals generated as shown in Figure 3.

[0024] The signal obtained by the discrete sampling point cumulative sum method for roundness error separation is consistent with the original given signal, which verifies the feasibility and effectiveness of the method for roundness error separation in principle.

[0025] Specific implementation two: the first shift sensor acquisition signal described in the present embodiment specifically includes:

[0026] In the case of N sampling points, let a i be the roundness error of each point of the measured roundness, b i be the signal at each sampling point of the spindle rotation error, wherein i = 1, 2, …, N, the sensor measurement signal obtained at the first shift N sampling points is the integrated error of the measured roundness error and the spindle rotation error V i , wherein i = 1, 2, …, N, the measurement signal at the first shift is represented as:

[0027]

[0028] In formula (1), V1 represents the signal measured by the sensor at the first sampling point when the measured workpiece and the spindle are at the first shift; V2 represents the signal measured by the sensor at the second sampling point when the measured workpiece and the spindle are at the first shift; Vi represents the signal measured by the sensor at the i sampling point when the measured workpiece and the spindle are at the first shift; V N represents the signal measured by the sensor at the N sampling point when the measured workpiece and the spindle are at the first shift.

[0029] Specific implementation three: the second displacement of the sensor acquisition signal specific to include:

[0030] The error separation table is turned through a small angle, the rotation angle θ = 2π / N, that is, the unit sampling angle size, at this time the a i point on the measured circle profile and the b i-1 point on the main shaft correspond, the measurement result at this time is recorded as V i ', wherein i = 1, 2, …, N, the signal obtained by measuring at the second displacement is represented as:

[0031]

[0032] The dislocation subtraction processing of each formula in formula (1) and (2) has:

[0033]

[0034] In formula (2) to (4): V1' represents the signal measured by the sensor at the first sampling point when the measured workpiece and the main shaft are located at the second displacement; V2' represents the signal measured by the sensor at the second sampling point when the measured workpiece and the main shaft are located at the second displacement; Vi' represents the signal measured by the sensor at the i-th sampling point when the measured workpiece and the main shaft are located at the second displacement; V N ' represents the signal measured by the sensor at the Nth sampling point when the measured workpiece and the main shaft are located at the second displacement;

[0035] The cumulative terms of the first i formulas in formula (3) and (4) are added respectively, and the following formula is obtained:

[0036]

[0037] Specific implementation four: the error of each sampling point of the measured circle profile in this embodiment is:

[0038]

[0039] The main shaft rotation error at each sampling point is:

[0040]

[0041] The above merely describes preferred embodiments of the present application, and is not intended to limit the present application in any form. Although the present application has been disclosed with preferred embodiments as above, it is not intended to limit the present application. Any person skilled in the art, without departing from the technical solution of the present application, can make some changes or modifications to the above disclosed technical content to obtain equivalent embodiments with equivalent changes. However, as long as it does not deviate from the technical solution of the present application, and is within the spirit and principles of the present application, any simple modification, equivalent replacement and improvement of the above embodiments are still within the protection scope of the technical solution of the present application.

Claims

1. A circular profile error separation method based on discrete sampling point cumulants and method, characterized by, The method comprises the following steps: Step one, obtaining a first sensor acquisition signal at a first indexing position by a sensor, Step two, the workpiece is indexed by the error separation station, so that a fixed indexing angle is generated between the workpiece and the instrument rotary spindle θ = 2π / N N That is, the sensor collects the sensor signal at the second indexing position when the unit sampling angle size is rotated. Step three, processing the first sensor acquisition signal at the first indexing position and the second sensor acquisition signal at the second indexing position collected by the sensor, separating the spindle rotation error signal from the circular contour error information, and obtaining the circular contour signal after removing the error; The first sensor acquisition signal at the first indexing position specifically comprises: In the case of the sampling point number N , let a i be the roundness error of each point on the measured circle profile, b i be the signal of each collection point of the spindle rotation error, where i =1, 2, …, N , the signals measured by the sensor at the first rotation position N are the integrated errors of the measured circle profile error and the spindle rotation error V i , where i =1, 2, …, N , the measured signals at the first rotation position are represented as: (1) In formula (1), V1 represents a signal measured by the sensor at a first sampling point when the workpiece under test and the main shaft are located at the first indexing position; V2 represents a signal measured by the sensor at a second sampling point when the workpiece under test and the main shaft are located at the first indexing position; Vi represents a signal measured by the sensor at an i-th sampling point when the workpiece under test and the main shaft are located at the first indexing position; and V N represents a signal measured by the sensor at an N-th sampling point when the workpiece under test and the main shaft are located at the first indexing position. The second sensor acquisition signal at the second indexing position specifically comprises: The error separation stage is turned through a small angle, the rotation angle θ = 2π / N , i.e. through a unit sampling angle size, at this time the point on the measured circle contour a i corresponds to the point on the main shaft b i-1 , and the measurement result at this time is recorded as V i , wherein i = 1, 2, …, N , and the signal obtained by measurement at the second rotation position is represented as: (2) The misaligned subtraction processing of each formula in formulas (1) and (2) has: (3) (4) In formulas (2) to (4): V1 ' V1 represents the signal measured by the sensor at the first sampling point when the workpiece under test is in the second rotational position of the spindle; V2 ' V2 represents the signal measured by the sensor at the second sampling point when the workpiece under test is in the second rotational position of the spindle; Vi ' Vi represents the signal measured by the sensor at the i-th sampling point when the workpiece under test is in the second rotational position of the spindle; V N ' VN represents the signal measured by the sensor at the N-th sampling point when the workpiece under test is in the second rotational position of the spindle; The former i-1 formulas and the latter N-i+1 formulas of formula (3) are added respectively, and formula (5) is obtained: (5) The error of each sampling point of the measured circular contour is: （6） Then, the former i-1 formulas and the latter N-i+1 formulas of formula (4) are added, and according to the above derivation, the spindle rotation error of each sampling point is: (7)。

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