A Roundness Error Separation Method Based on the Coupling of Eccentric Inclination Error by Indexing

Abstract

A roundness error separation method by indexing method based on the coupling of eccentric and tilt errors, which relates to a roundness error separation method by indexing method. The present invention aims to solve the problem that the magnitude of the indexing angle deviation and the indexing accuracy have a great impact on the effect of the roundness error separation method by indexing method. In view of the situation that the magnitude of the indexing angle deviation and the indexing accuracy have a great impact on the effect of the roundness error separation method by indexing method, the present invention proposes a transfer angle error transfer model of the roundness error separation method by indexing method based on the coupling of eccentric and tilt errors, analyzes the influence of eccentric and tilt errors on the indexing angle error, and adjusts the respective offset ranges accordingly according to the analysis results to reduce the indexing angle deviation, thereby reducing the influence of the indexing angle deviation on the roundness error separation accuracy. The present invention belongs to the field of ultra-precision geometric measurement technology.

Description

Technical Field

[0001] The present invention relates to a roundness error separation method by the indexing method, belonging to the technical field of ultra-precision geometric measurement. Background Art

[0002] Since the 1960s, with the development of emerging scientific and technological fields such as atomic energy, aerospace, microelectronics, information, and bioengineering, higher and higher requirements have been put forward for the measurement accuracy of the rotational error of precision spindle systems and the roundness error of workpieces. For example, in the process of ultra-precision machining and measurement, the roundness error of the specified circular cross-section of the quartz hemisphere, which is usually used as a round standard for comparison and calibration, is generally between 10 nm and 50 nm; the roundness tolerance in the normal direction of any circular cross-section of the curved mirror in an X-ray microscope is 5 nm; in the fields of aspherical lenses, free-form surfaces, and micro-structured optics, the shape error of workpieces is usually required to be in the nanometer range.

[0003] 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, the precision indexes of many current workpieces have reached or exceeded the precision level of the roundness measuring instrument with the highest precision currently used for measuring roundness. And if we want to further improve the measurement accuracy of the instrument, it is very difficult to meet the growing requirements only by relying on a large amount of investment in mechanical processing. Therefore, on the basis of not further requiring the improvement of the spindle rotational accuracy, the precise measurement of the circular contour of the workpiece is a very valuable research topic.

[0004] Error separation technology is a measurement technology that separates the useful signal component from the error signal by means of information source transformation or model parameter estimation. It can achieve a precision level that is difficult to reach by "hard technology" at a relatively low cost. Therefore, error separation technology has been quickly accepted by scholars and experts in various countries. Error separation technology is mainly divided into two types: the indexing method and the multi-probe method. Among them, the indexing method mainly relies on a high-precision angular indexing turntable (i.e., the error separation table) to obtain additional information by achieving the relative rotation angle between the spindle and the measured circular contour, so as to achieve error separation, such as the two-step method, the multi-step method, the multiple multi-step method, etc. The size of the indexing angle deviation and the indexing accuracy will have a great impact on the separation effect of such methods. At the same time, through analysis, it is found that the tilt of the axis of the error separation table also affects the size of the indexing angle detected by the sensor, thereby further generating an indexing angle deviation. Therefore, considering the eccentricity and tilt effects of the error separation table comprehensively, a transfer angle error transfer model of the roundness error separation method by the indexing method based on the coupling of eccentricity and tilt errors is established. Summary of the Invention

[0005] In order to solve the problem that the size of the indexing angle deviation and the indexing accuracy have a great impact on the effect of the roundness error separation method by the indexing method, the present invention further provides a roundness error separation method by the indexing method based on the coupling of eccentricity and tilt errors.

[0006] The technical solution adopted by the present invention to solve the above problems is as follows: The present invention specifically includes:

[0007] Step 1: The axis of rotation of the turntable spindle is L 1 , the axis of rotation of the error separation table is L 2 , and the central axis of the workpiece to be measured is L 3 . For the convenience of description, the intersections of the three axes with the tabletop of the error separation table are respectively denoted as P, P′, and P 1 , where the center P 1 of the circular contour to be measured on this plane has an eccentricity e with the center P′ of the error separation table, and the corresponding eccentric angle is

[0008] Step 2: The points obtained by projecting each intersection along the axis of rotation of the spindle onto the horizontal plane are respectively denoted as O, O′, and O 1 . On this plane, there is an eccentricity e′ between the corresponding projection O′ of the error separation table and the center P′ of the error separation table, and the corresponding eccentric angle is γ. The center of the cross-section of the circular contour to be measured is Q;

[0009] Step 3: Project the above three-dimensional relationship onto a plane perpendicular to the axis of rotation of the spindle to obtain the projection plan view of the eccentric tilt coupling error model and the geometric relationship between P′P and O′O;

[0010] Step 4: The eccentricities of the centers O 1 , O 2 of the circular contour to be measured before and after indexing relative to the center of rotation O′ of the error separation table are e 1 ″ and e 2 ″, and the corresponding eccentric angles are respectively and to obtain the geometric relationship formula;

[0011] Step 5: The offset of the sensor probe relative to the center of rotation of the spindle along the direction perpendicular to the measurement direction is d. A perpendicular line is drawn from the center of rotation of the spindle to the measurement direction after offset and intersects it at point O″. The indexing angle given by the error separation table is α, and the actual indexing angle detected by the sensor and acting on the signals collected before and after indexing is the angle β between the connections of point O″ with the centers O 1 , O 2 of the circular contour before and after indexing. The indexing angle error is obtained from the indexing angle error transfer model of the roundness error separation method by eccentric tilt error coupling.

[0012] Furthermore, the set relationship formula obtained in Step 4 is:

[0013]

[0014] In formula (1), θ represents the inclination angle of the circular contour to be measured relative to the axis of rotation of the turntable.

[0015] Furthermore, the indexing angle error is expressed as:

[0016]

[0017] The beneficial effects of the present invention are as follows: In view of the situation that the indexing angle deviation and indexing accuracy have a great impact on the effect of the indexing method for roundness error separation, the present invention proposes an indexing angle error transfer model for the indexing method for roundness error separation based on the coupling of eccentricity and tilt errors, analyzes the influence of eccentricity and tilt errors on the indexing angle error, and adjusts the respective offset ranges accordingly according to the analysis results to reduce the indexing angle deviation, thereby reducing the influence of the indexing angle deviation on the separation accuracy of the indexing method for roundness error. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a schematic diagram of the indexing angle error transfer model for the indexing method for roundness error separation based on the coupling of eccentricity and tilt errors;

[0019] Figure 2 is a plan view of the indexing angle error transfer model for the indexing method for roundness error separation based on the coupling of eccentricity and tilt errors;

[0020] Figure 3 is a schematic diagram of the influence of the eccentricity magnitude on the indexing angle error when γ = π / 4;

[0021] Figure 4 is a schematic diagram of the influence of the axis size of the error separation table on the indexing angle error when e = 1μm and e' = 0.1μm. DETAILED DESCRIPTION OF THE INVENTION

[0022] DETAILED DESCRIPTION OF THE INVENTION I: As Figures 1 to 3 shown, a method for separating roundness error by indexing based on the coupling of eccentricity and tilt errors,

[0023] given the eccentricity e of the center of the circular contour of the workpiece to be measured relative to the error separation table and the eccentricity e' of the error separation table relative to the rotational center of the spindle, a simulation analysis is carried out on the influence of the eccentric angle of the center of the circular contour and the eccentric angle γ of the error separation table on the deviation δα between the actual indexing angle and the given indexing angle;

[0024] For different roundness error separation methods, each indexing angle is selected according to the magnitude order of the indexing angle rotation for analysis. When e = 1μm and e' = 1μm, the influence of the two eccentric angles γ on the indexing angle error δα is as Figure 2 shown;

[0025] Analyze the influence of each eccentricity in the indexing angle error transfer model of the eccentricity-tilt error coupling on the indexing angle, and take When γ = π / 4 and the indexing angles are taken for different indexing roundness error separation methods according to the order of magnitude of the indexing angle, the curves showing the influence of the two offsets e and e′ on the indexing angle deviation are plotted as follows Figure 3 shown;

[0026] Analyze the influence of the inclination angle θ of the rotation axis of the error separation table on the indexing angle error δα in the error transfer model of the eccentric tilt error coupling indexing angle. When the eccentricity error of the circular contour e = 1 μm and the eccentricity of the error separation table e′ = 0.1 μm, and the range of the inclination angle θ of the rotation axis of the error separation table is [0, π / 2], the obtained results are as follows Figure 4 shown;

[0027] Then, from the above simulation results, the influence of the eccentricity and the inclination angle on the indexing angle deviation can be represented by the above curves respectively. Therefore, during the actual indexing roundness error separation process, the two offsets of eccentricity and inclination should be adjusted as much as possible according to the above results to minimize the influence of the indexing angle.

[0028] The above is only a preferred embodiment of the present invention, and it does not impose any form of limitation on the present invention. Although the present invention has been disclosed above with a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or decorations to equivalent changes within the scope of the technical solution of the present invention by using the disclosed technical content above. However, as long as it does not depart from the technical solution content of the present invention and is based on the technical essence of the present invention, any simple modification, equivalent replacement, and improvement of the above embodiments still fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for separating roundness errors by indexing method based on coupling of eccentricity and tilt errors, characterized in that: Specifically include: Step 1. The rotation axis of the turntable spindle is L1, the rotation axis of the error separation table is L2, and the center axis of the workpiece to be measured is L3. For the convenience of expression, the intersection points of the three axes and the surface of the error separation table are recorded as P, P', and P1 respectively. There is an eccentricity between the center of the measured circular contour P1 and the center of the error separation table P' on the plane, and its magnitude is e. The corresponding eccentricity angle is Step 2: Project each intersection point along the horizontal plane in the direction of the main shaft rotation axis and record the points obtained as O, O′, and O1 respectively. There is an eccentricity between the corresponding projection O′ of the error separation platform on the horizontal plane in the direction of the main shaft rotation axis of each intersection point and the center P′ of the error separation platform, and the size is e′. The corresponding eccentricity angle is γ, and the center of the measured circular profile section is Q; Step 3, project the three-dimensional relationship obtained in step 2 onto a plane perpendicular to the main shaft rotation axis to obtain a projection plane diagram of the eccentric tilt coupling error model and a geometric relationship between P′P and O′O; Step 4: Under the projection view, the eccentricity of the measured circle contour center O1 and O2 relative to the rotation center O' of the error separation table before and after the indexing is e1" and e2", and the corresponding eccentricity angles are and Obtain geometric relationship; Step 5. The offset of the sensor probe relative to the spindle rotation center along the measuring direction perpendicular to the measuring direction is d. A perpendicular line is drawn from the spindle rotation center to the sensor measuring direction after the offset and intersects it at point O". The indexing angle given by the error separation table is α. The indexing angle actually detected by the sensor and acting on the collected signals before and after the indexing is the angle β between the line connecting the point O" and the center of the circular contour O1 and O2 before and after the indexing. The indexing angle error is obtained by the indexing angle error transmission model of the indexing method roundness error separation method coupled with eccentricity and tilt errors.

2. The method for separating roundness errors by indexing method based on coupling of eccentricity and tilt errors according to claim 1, characterized in that: The set relation obtained in step 4 is: In formula (1), θ represents the inclination angle of the measured circular profile relative to the rotation axis of the turntable.

3. The method for separating roundness errors by indexing method based on eccentricity and tilt error coupling according to claim 1, characterized in that: The index angle error is expressed as:

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