Indexing roundness error separation method based on eccentric tilt error coupling

Abstract

The invention relates to an indexing method roundness error separation method, in particular to an indexing method roundness error separation method based on eccentric tilt error coupling. The objective of the invention is to solve the problem that the size of the indexing angle deviation and the indexing accuracy have great influence on the effect of an indexing method roundness error separation method. Aiming at the condition that the size of the indexing angle deviation and the indexing accuracy have great influence on the effect of the indexing method roundness error separation method, an indexing angle error transmission model of the indexing method roundness error separation method based on eccentric and inclined error coupling is provided, and the influence of the eccentric and inclined errors on the indexing angle error is analyzed; and correspondingly adjusting each offset range according to the analysis structure so as to reduce the transposition angle deviation and further reduce the influence of the transposition angle deviation on the error separation precision of the transposition method. The invention belongs to the technical field of ultra-precise geometric measurement.

Description

Technical Field

[0001] The invention relates to a roundness error separation method using a rotation method, and belongs to the technical field of ultra-precision geometric measurement. Background Art

[0002] Since the 1960s, with the development of emerging science and technology such as atomic energy, aerospace, microelectronics, information and bioengineering, higher and higher requirements have been put forward for the measurement accuracy of the rotation error of the precision spindle system and the roundness error of the workpiece. For example, in the process of ultra-precision machining and measurement, the roundness error of the specified circular section of the quartz hemisphere, which is usually used as a circular standard for comparison and calibration, is generally between 10nm and 50nm; the roundness tolerance of any circular section of the curved mirror in the normal direction of the X-ray microscope is 5nm; the fields of aspheric lenses, free-form surfaces and microstructure optics also usually require the shape error of the workpiece to be at the nanometer level.

[0003] To ensure high-precision measurement, the error caused by the measuring instrument can only account for a small part of the allowable error of the workpiece, about (1 / 3 to 1 / 10). But in fact, many workpiece accuracy indicators now reach or exceed the accuracy level of the most accurate roundness measuring instrument currently used to measure roundness. If we want to further improve the measurement accuracy of the instrument, it is difficult to meet the growing requirements by relying solely on a large amount of investment in mechanical processing. Therefore, without further requiring the improvement of the spindle rotation accuracy, the precise measurement of the circular contour of the workpiece is a very valuable research issue.

[0004] Error separation technology is a measurement technology that separates useful signal components from error signals by transforming information sources or estimating model parameters. It can achieve a level of accuracy that is difficult to achieve with "hard technology" at a relatively low cost, so error separation technology has been quickly accepted by scholars and experts from various countries. There are two main types of error separation technology: the indexing method and the multi-probe method. The indexing method mainly relies on a high-precision angle indexing turntable (i.e., the error separation table) to achieve the relative angle between the spindle and the measured circular contour to obtain additional information to achieve error separation, such as the two-step method, the multi-step method, the multi-step method, etc. The indexing angle deviation and indexing accuracy will have a great impact on the separation effect of such methods. At the same time, it is found through analysis that the axis tilt of the error separation table also affects the indexing angle detected by the sensor, thereby further generating an indexing angle deviation. Therefore, considering the eccentricity and tilt of the error separation table, a indexing angle error transmission model of the indexing method roundness error separation method based on the coupling of eccentricity and tilt errors is established. Summary of the invention

[0005] The present invention aims to solve the problem that the indexing angle deviation and indexing accuracy have a great influence on the effect of the indexing method for roundness error separation, and further proposes a indexing method for roundness error separation based on eccentricity and tilt error coupling.

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

[0007] Step 1: The rotary axis of the turntable spindle is L 1 , the rotation axis of the error separation table is L 2 , the center axis of the workpiece to be measured is L 3 For the convenience of expression, the intersection points of the three axes and the error separation table are recorded as P, P′, P 1 , where the center P of the measured circle contour on the plane 1 There is an eccentricity between the error separation platform center P', the magnitude of which is e, and the corresponding eccentricity angle is

[0008] Step 2: Project each intersection point along the main shaft rotation axis onto the horizontal plane and record the points obtained as O, O′, O 1 There is an eccentricity between the corresponding projection O′ of the error separation platform and the center P′ of the error separation platform on the plane, and its magnitude is e′, the corresponding eccentricity angle is γ, and the center of the measured circular profile section is Q;

[0009] Step 3, project the above three-dimensional relationship onto a plane perpendicular to the main shaft rotation axis to obtain the projection plane diagram of the eccentricity and tilt coupling error model and the geometric relationship between P′P and O′O;

[0010] Step 4: The center O of the measured circle contour before and after the rotation in the projection view 1 , O 2 The eccentricity relative to the rotation center O' of the error separation table is e 1 ″ and e 2 ″, and the corresponding eccentric angles are and Obtain geometric relationship;

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

[0012] Furthermore, the set relation obtained in step 4 is:

[0013]

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

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

[0016]

[0017] The beneficial effects of the present invention are as follows: in view of the fact that the size of the index angle deviation and the indexing accuracy have a great influence on the effect of the index method roundness error separation method, the present invention proposes a index angle error transmission model of the index method roundness error separation method based on the coupling of eccentricity and tilt errors, analyzes the influence of eccentricity and tilt errors on the index angle error, and adjusts each bias range accordingly according to the analysis structure to reduce the index angle deviation and thus reduce the influence of the index angle deviation on the error separation accuracy of the index method. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0019] Figure 2 It is a plane diagram of the roundness error separation method based on the transposition method of eccentricity and tilt error coupling and the transposition angle error transfer model;

[0020] Figure 3 yes Schematic diagram of the effect of eccentricity on indexing angle error when γ = π / 4;

[0021] Figure 4 This is a schematic diagram of the effect of the error separation table axis size on the index angle error when e=1μm and e′=0.1μm. DETAILED DESCRIPTION

[0022] Specific implementation method 1: Figures 1 to 3 As shown in the figure, a method for separating roundness errors by using the indexing method based on the coupling of eccentricity and tilt errors is proposed.

[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 spindle rotation center, the eccentricity angle of the circular contour center is calculated. And the simulation analysis of the influence of the eccentric angle γ of the error separation table on the deviation δα between the actual indexing angle and the given indexing angle;

[0024] According to the magnitude of the rotation angle of different roundness error separation methods, each rotation angle is selected for analysis. When e = 1 μm and e′ = 1 μm, the two eccentric angles The influence of γ on the index angle error δα is as follows Figure 2 As shown;

[0025] The influence of each eccentricity on the index angle in the eccentricity tilt error coupled index angle error transmission model is analyzed. γ=π / 4When the index angle is taken according to the index angle magnitude of different index method roundness error separation methods, the influence of the two offsets e and e′ on the index angle deviation is plotted separately, and the obtained curve is as follows Figure 3 As shown;

[0026] The influence of the inclination angle θ of the rotation axis of the error separation table on the index angle error δα in the eccentricity and inclination error coupled index angle error transmission model is analyzed. When the circular contour eccentricity error e = 1 μm and the eccentricity of the error separation table e′ = 0.1 μm, the range of the inclination angle θ of the rotation axis of the error separation table is [0, π / 2]. The results are as follows: Figure 4 As shown;

[0027] From the above simulation results, it can be obtained that the influence of eccentricity and inclination angle on the indexing angle deviation can be represented by the above curves respectively. Therefore, in the actual process of roundness error separation by indexing method, the eccentricity and inclination biases should be adjusted as much as possible according to the above results to minimize the influence of indexing angle.

[0028] The above is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with this profession can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement made to the above embodiments without departing from the content of the technical solution of the present invention, based on the technical essence of the present invention, within the spirit and principles of the present invention, 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 main shaft rotation axis onto the horizontal plane 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 plane and the center P′ of the error separation platform, and the size of the eccentricity is e′, the corresponding eccentricity angle is γ, and the center of the measured circular profile section is Q; Step 3, project the above three-dimensional relationship onto a plane perpendicular to the main shaft rotation axis to obtain the projection plane diagram of the eccentric tilt coupling error model and the 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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